From e0967625e99afe6824f2e41c94b7c93cf652e84c Mon Sep 17 00:00:00 2001 From: Vasily Ilin Date: Sun, 15 Nov 2026 05:01:09 +0000 Subject: [PATCH] perf(Zeta5Irrational): share rational certificate arithmetic --- .../Zeta5Irrational/Table/RationalSeries.lean | 24 + LeanPool/Zeta5Irrational/Table/U00.lean | 4984 ++++++------- LeanPool/Zeta5Irrational/Table/U01.lean | 1765 ++--- LeanPool/Zeta5Irrational/Table/U02.lean | 526 +- LeanPool/Zeta5Irrational/Table/U03.lean | 770 +- LeanPool/Zeta5Irrational/Table/U04.lean | 1070 ++- LeanPool/Zeta5Irrational/Table/U05.lean | 1212 ++- LeanPool/Zeta5Irrational/Table/U06.lean | 1523 ++-- LeanPool/Zeta5Irrational/Table/U07.lean | 1622 ++-- LeanPool/Zeta5Irrational/Table/U08.lean | 1795 ++--- LeanPool/Zeta5Irrational/Table/U09.lean | 2038 +++-- LeanPool/Zeta5Irrational/Table/U10.lean | 2035 +++-- LeanPool/Zeta5Irrational/Table/U11.lean | 2098 +++--- LeanPool/Zeta5Irrational/Table/U12.lean | 2448 +++--- LeanPool/Zeta5Irrational/Table/U13.lean | 2447 +++--- LeanPool/Zeta5Irrational/Table/U14.lean | 2448 +++--- LeanPool/Zeta5Irrational/Table/U15.lean | 2578 +++---- LeanPool/Zeta5Irrational/Table/U16.lean | 2855 ++++--- LeanPool/Zeta5Irrational/Table/U17.lean | 2856 ++++--- LeanPool/Zeta5Irrational/Table/U18.lean | 2853 ++++--- LeanPool/Zeta5Irrational/Table/U19.lean | 2921 ++++---- LeanPool/Zeta5Irrational/Table/U20.lean | 3259 ++++---- LeanPool/Zeta5Irrational/Table/U21.lean | 3262 ++++---- LeanPool/Zeta5Irrational/Table/U22.lean | 3258 ++++---- LeanPool/Zeta5Irrational/Table/U23.lean | 3257 ++++---- LeanPool/Zeta5Irrational/Table/U24.lean | 3563 ++++----- LeanPool/Zeta5Irrational/Table/U25.lean | 3671 ++++----- LeanPool/Zeta5Irrational/Table/U26.lean | 3669 ++++----- LeanPool/Zeta5Irrational/Table/U27.lean | 3671 ++++----- LeanPool/Zeta5Irrational/Table/U28.lean | 3736 ++++------ LeanPool/Zeta5Irrational/Table/U29.lean | 4085 +++++----- LeanPool/Zeta5Irrational/Table/U30.lean | 4087 +++++----- LeanPool/Zeta5Irrational/Table/U31.lean | 4092 +++++----- LeanPool/Zeta5Irrational/Table/U32.lean | 4086 +++++----- LeanPool/Zeta5Irrational/Table/U33.lean | 4219 +++++------ LeanPool/Zeta5Irrational/Table/U34.lean | 4498 +++++------ LeanPool/Zeta5Irrational/Table/U35.lean | 4501 +++++------ LeanPool/Zeta5Irrational/Table/U36.lean | 4497 +++++------ LeanPool/Zeta5Irrational/Table/U37.lean | 4495 +++++------ LeanPool/Zeta5Irrational/Table/U38.lean | 4679 +++++------- LeanPool/Zeta5Irrational/Table/U39.lean | 4929 ++++++------ LeanPool/Zeta5Irrational/Table/U40.lean | 4929 ++++++------ LeanPool/Zeta5Irrational/Table/U41.lean | 4925 ++++++------ LeanPool/Zeta5Irrational/Table/U42.lean | 4929 ++++++------ LeanPool/Zeta5Irrational/Table/U43.lean | 5204 ++++++------- LeanPool/Zeta5Irrational/Table/U44.lean | 5342 ++++++------- LeanPool/Zeta5Irrational/Table/U45.lean | 5347 ++++++------- LeanPool/Zeta5Irrational/Table/U46.lean | 5344 ++++++------- LeanPool/Zeta5Irrational/Table/U47.lean | 5656 ++++++-------- LeanPool/Zeta5Irrational/Table/U48.lean | 5767 +++++++------- LeanPool/Zeta5Irrational/Table/U49.lean | 5768 +++++++------- LeanPool/Zeta5Irrational/Table/U50.lean | 5760 +++++++------- LeanPool/Zeta5Irrational/Table/U51.lean | 6186 +++++++-------- LeanPool/Zeta5Irrational/Table/U52.lean | 6184 +++++++-------- LeanPool/Zeta5Irrational/Table/U53.lean | 6396 +++++++--------- LeanPool/Zeta5Irrational/Table/U54.lean | 6612 +++++++---------- LeanPool/Zeta5Irrational/Table/U55.lean | 6606 +++++++--------- LeanPool/Zeta5Irrational/Table/U56.lean | 3414 +++++---- .../Table/UpperCertificate.lean | 56 +- 59 files changed, 95529 insertions(+), 121278 deletions(-) diff --git a/LeanPool/Zeta5Irrational/Table/RationalSeries.lean b/LeanPool/Zeta5Irrational/Table/RationalSeries.lean index 1b20126174..8c0723027c 100644 --- a/LeanPool/Zeta5Irrational/Table/RationalSeries.lean +++ b/LeanPool/Zeta5Irrational/Table/RationalSeries.lean @@ -6,12 +6,16 @@ Authors: Lean Pool contributors module public import LeanPool.Zeta5Irrational.TableCheck +import Mathlib.Analysis.Complex.ExponentialBounds +import Mathlib.Tactic.Linarith /-! # Rational certificates for finite analytic series The table bounds use only rational inputs. Check their finite sums in `ℚ`, then transport one inequality to `ℝ`, avoiding a separate normalization proof for every real operation. +Binary range reduction also checks its rational rounding bound before using the shared +lower bound on `Real.log 2`. -/ public section @@ -62,4 +66,24 @@ lemma arctan_le_of_series_rat {z U : ℚ} (k : ℕ) simpa only [Rat.cast_add, Rat.cast_mul, Rat.cast_sum, Rat.cast_div, Rat.cast_pow, Rat.cast_sub, Rat.cast_one, Rat.cast_ofNat, Rat.cast_natCast, Rat.cast_neg] using h +/-- Check binary range reduction and its final logarithm bound in the rationals. -/ +lemma log_le_of_split_neg_rational {r r' U U' : ℚ} (power m : ℕ) + (certificate : 1 ≤ r' ∧ + 2 * ∑ k ∈ range m, (1 / (2 * (k : ℚ) + 1)) * ((r' - 1) / (r' + 1)) ^ (2 * k + 1) + + 2 * ((r' - 1) / (r' + 1)) ^ (2 * m + 1) / + ((2 * m + 1) * (1 - ((r' - 1) / (r' + 1)) ^ 2)) ≤ U') + (reduction : r = r' / 2 ^ power ∧ U' - power * (6931471803 / 10000000000) ≤ U) : + Real.log (r : ℝ) ≤ (U : ℝ) := by + have hr : (r : ℝ) = (r' : ℝ) / 2 ^ power := by exact_mod_cast reduction.1 + have hr' : (0 : ℝ) < r' := by + exact_mod_cast (lt_of_lt_of_le (by decide : (0 : ℚ) < 1) certificate.1) + have h := log_le_of_split_neg power hr hr' (log_le_of_ge_one_rat m certificate) + have hround : (U' : ℝ) - power * (6931471803 / 10000000000) ≤ U := by + simpa only [Rat.cast_sub, Rat.cast_mul, Rat.cast_natCast, Rat.cast_div, + Rat.cast_ofNat] using (Rat.cast_le (K := ℝ)).2 reduction.2 + have hlog : (6931471803 / 10000000000 : ℝ) ≤ Real.log 2 := by + linarith only [Real.log_two_gt_d9] + have hmul := mul_le_mul_of_nonneg_left hlog (Nat.cast_nonneg (α := ℝ) power) + exact h.trans ((sub_le_sub_left hmul _).trans hround) + end Zeta5Irrational diff --git a/LeanPool/Zeta5Irrational/Table/U00.lean b/LeanPool/Zeta5Irrational/Table/U00.lean index 6ba43ca97b..1d4a3bf6c7 100644 --- a/LeanPool/Zeta5Irrational/Table/U00.lean +++ b/LeanPool/Zeta5Irrational/Table/U00.lean @@ -23,405 +23,336 @@ lemma U_0_1 : have hlg : Real.log (123769636673849 / 20000000000000000 : ℝ) ≤ (-(12712663703508542025099 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (123769636673849 / 20000000000000000 : ℝ) = - (123769636673849 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123769636673849 / 78125000000000 : ℚ)) - (U := (1150279902491457974901 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (123769636673849 / 78125000000000 : ℝ) ≤ - (1150279902491457974901 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (59272418588849 / 10000000000000000 : ℝ)) (q := - (123769636673849 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123769636673849 / 20000000000000000 : ℚ)) + (r' := (123769636673849 / 78125000000000 : ℚ)) + (U := (-(12712663703508542025099 / 2500000000000000000000 : ℚ))) + (U' := (1150279902491457974901 / 2500000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (0 : ℚ)) + (s := (59272418588849 / 10000000000000000 : ℚ)) + (q := (123769636673849 / 20000000000000000 : ℚ)) + (U := (-(12712663703508542025099 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_2 : Uω (aρ 2) (bρ 2) (0 : ℝ) ≤ (-(1962983986998948336949 / 400000000000000000000 : ℝ)) := by have hlg : Real.log (147824769578301 / 20000000000000000 : ℝ) ≤ (-(1962983986998948336949 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (147824769578301 / 20000000000000000 : ℝ) = - (147824769578301 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (147824769578301 / 78125000000000 : ℚ)) - (U := (255086989961051663051 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (147824769578301 / 78125000000000 : ℝ) ≤ - (255086989961051663051 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (59558538983301 / 10000000000000000 : ℝ)) (q := - (147824769578301 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (147824769578301 / 20000000000000000 : ℚ)) + (r' := (147824769578301 / 78125000000000 : ℚ)) + (U := (-(1962983986998948336949 / 400000000000000000000 : ℚ))) + (U' := (255086989961051663051 / 400000000000000000000 : ℚ)) + 8 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (0 : ℚ)) + (s := (59558538983301 / 10000000000000000 : ℚ)) + (q := (147824769578301 / 20000000000000000 : ℚ)) + (U := (-(1962983986998948336949 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_3 : Uω (aρ 3) (bρ 3) (0 : ℝ) ≤ (-(46267520391835680481277 / 10000000000000000000000 : ℝ)) := by have hlg : Real.log (97864936683177 / 10000000000000000 : ℝ) ≤ (-(46267520391835680481277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (97864936683177 / 10000000000000000 : ℝ) = (97864936683177 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (97864936683177 / 78125000000000 : ℚ)) - (U := (2252782229164319518723 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (97864936683177 / 78125000000000 : ℝ) ≤ - (2252782229164319518723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (30033768210677 / 5000000000000000 : ℝ)) (q := - (97864936683177 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (97864936683177 / 10000000000000000 : ℚ)) + (r' := (97864936683177 / 78125000000000 : ℚ)) + (U := (-(46267520391835680481277 / 10000000000000000000000 : ℚ))) + (U' := (2252782229164319518723 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (0 : ℚ)) + (s := (30033768210677 / 5000000000000000 : ℚ)) + (q := (97864936683177 / 10000000000000000 : ℚ)) + (U := (-(46267520391835680481277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_4 : Uω (aρ 4) (bρ 4) (0 : ℝ) ≤ (-(5359553913723040081263 / 1250000000000000000000 : ℝ)) := by have hlg : Real.log (17171580100553 / 1250000000000000 : ℝ) ≤ (-(5359553913723040081263 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (17171580100553 / 1250000000000000 : ℝ) = (17171580100553 / 9765625000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17171580100553 / 9765625000000 : ℚ)) - (U := (705483913901959918737 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17171580100553 / 9765625000000 : ℝ) ≤ - (705483913901959918737 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7420503369 / 1220703125000 : ℝ)) (q := - (17171580100553 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17171580100553 / 1250000000000000 : ℚ)) + (r' := (17171580100553 / 9765625000000 : ℚ)) + (U := (-(5359553913723040081263 / 1250000000000000000000 : ℚ))) + (U' := (705483913901959918737 / 1250000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (0 : ℚ)) + (s := (7420503369 / 1220703125000 : ℚ)) + (q := (17171580100553 / 1250000000000000 : ℚ)) + (U := (-(5359553913723040081263 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_5 : Uω (aρ 5) (bρ 5) (0 : ℝ) ≤ (-(39275139978819449528723 / 10000000000000000000000 : ℝ)) := by have hlg : Real.log (393851349704671 / 20000000000000000 : ℝ) ≤ (-(39275139978819449528723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (393851349704671 / 20000000000000000 : ℝ) = - (393851349704671 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (393851349704671 / 312500000000000 : ℚ)) - (U := (2313690839180550471277 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (393851349704671 / 312500000000000 : ℝ) ≤ - (2313690839180550471277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (61704912359671 / 10000000000000000 : ℝ)) (q := - (393851349704671 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (393851349704671 / 20000000000000000 : ℚ)) + (r' := (393851349704671 / 312500000000000 : ℚ)) + (U := (-(39275139978819449528723 / 10000000000000000000000 : ℚ))) + (U' := (2313690839180550471277 / 10000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (0 : ℚ)) + (s := (61704912359671 / 10000000000000000 : ℚ)) + (q := (393851349704671 / 20000000000000000 : ℚ)) + (U := (-(39275139978819449528723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_6 : Uω (aρ 6) (bρ 6) (0 : ℝ) ≤ (-(7143339604213661208809 / 2000000000000000000000 : ℝ)) := by have hlg : Real.log (281088781634513 / 10000000000000000 : ℝ) ≤ (-(7143339604213661208809 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (281088781634513 / 10000000000000000 : ℝ) = - (281088781634513 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (281088781634513 / 156250000000000 : ℚ)) - (U := (1174426559386338791191 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (281088781634513 / 156250000000000 : ℝ) ≤ - (1174426559386338791191 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (31395375392013 / 5000000000000000 : ℝ)) (q := - (281088781634513 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (281088781634513 / 10000000000000000 : ℚ)) + (r' := (281088781634513 / 156250000000000 : ℚ)) + (U := (-(7143339604213661208809 / 2000000000000000000000 : ℚ))) + (U' := (1174426559386338791191 / 2000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (0 : ℚ)) + (s := (31395375392013 / 5000000000000000 : ℚ)) + (q := (281088781634513 / 10000000000000000 : ℚ)) + (U := (-(7143339604213661208809 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_7 : Uω (aρ 7) (bρ 7) (0 : ℝ) ≤ (-(32351824960621028314427 / 10000000000000000000000 : ℝ)) := by have hlg : Real.log (393530224619551 / 10000000000000000 : ℝ) ≤ (-(32351824960621028314427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (393530224619551 / 10000000000000000 : ℝ) = - (393530224619551 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (393530224619551 / 312500000000000 : ℚ)) - (U := (2305534054378971685573 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (393530224619551 / 312500000000000 : ℝ) ≤ - (2305534054378971685573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (32006127997051 / 5000000000000000 : ℝ)) (q := - (393530224619551 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (393530224619551 / 10000000000000000 : ℚ)) + (r' := (393530224619551 / 312500000000000 : ℚ)) + (U := (-(32351824960621028314427 / 10000000000000000000000 : ℚ))) + (U' := (2305534054378971685573 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (0 : ℚ)) + (s := (32006127997051 / 5000000000000000 : ℚ)) + (q := (393530224619551 / 10000000000000000 : ℚ)) + (U := (-(32351824960621028314427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_8 : Uω (aρ 8) (bρ 8) (0 : ℝ) ≤ (-(7315709960795885799737 / 2500000000000000000000 : ℝ)) := by have hlg : Real.log (214383325750023 / 4000000000000000 : ℝ) ≤ (-(7315709960795885799737 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (214383325750023 / 4000000000000000 : ℝ) = - (214383325750023 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (214383325750023 / 125000000000000 : ℚ)) - (U := (1348629792954114200263 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (214383325750023 / 125000000000000 : ℝ) ≤ - (1348629792954114200263 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13065356833023 / 2000000000000000 : ℝ)) (q := - (214383325750023 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (214383325750023 / 4000000000000000 : ℚ)) + (r' := (214383325750023 / 125000000000000 : ℚ)) + (U := (-(7315709960795885799737 / 2500000000000000000000 : ℚ))) + (U' := (1348629792954114200263 / 2500000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (0 : ℚ)) + (s := (13065356833023 / 2000000000000000 : ℚ)) + (q := (214383325750023 / 4000000000000000 : ℚ)) + (U := (-(7315709960795885799737 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_9 : Uω (aρ 9) (bρ 9) (0 : ℝ) ≤ (-(13245699571552860366621 / 5000000000000000000000 : ℝ)) := by have hlg : Real.log (1414240104474349 / 20000000000000000 : ℝ) ≤ (-(13245699571552860366621 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1414240104474349 / 20000000000000000 : ℝ) = - (1414240104474349 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1414240104474349 / 1250000000000000 : ℚ)) - (U := (617244034447139633379 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1414240104474349 / 1250000000000000 : ℝ) ≤ - (617244034447139633379 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (66684631529349 / 10000000000000000 : ℝ)) (q := - (1414240104474349 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1414240104474349 / 20000000000000000 : ℚ)) + (r' := (1414240104474349 / 1250000000000000 : ℚ)) + (U := (-(13245699571552860366621 / 5000000000000000000000 : ℚ))) + (U' := (617244034447139633379 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (0 : ℚ)) + (s := (66684631529349 / 10000000000000000 : ℚ)) + (q := (1414240104474349 / 20000000000000000 : ℚ)) + (U := (-(13245699571552860366621 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_10 : Uω (aρ 10) (bρ 10) (0 : ℝ) ≤ (-(4811289393237367803367 / 2000000000000000000000 : ℝ)) := by have hlg : Real.log (902073204108467 / 10000000000000000 : ℝ) ≤ (-(4811289393237367803367 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (902073204108467 / 10000000000000000 : ℝ) = - (902073204108467 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (902073204108467 / 625000000000000 : ℚ)) - (U := (733888049162632196633 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (902073204108467 / 625000000000000 : ℝ) ≤ - (733888049162632196633 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (34015950888467 / 5000000000000000 : ℝ)) (q := - (902073204108467 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (902073204108467 / 10000000000000000 : ℚ)) + (r' := (902073204108467 / 625000000000000 : ℚ)) + (U := (-(4811289393237367803367 / 2000000000000000000000 : ℚ))) + (U' := (733888049162632196633 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (0 : ℚ)) + (s := (34015950888467 / 5000000000000000 : ℚ)) + (q := (902073204108467 / 10000000000000000 : ℚ)) + (U := (-(4811289393237367803367 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_11 : Uω (aρ 11) (bρ 11) (0 : ℝ) ≤ (-(21964674985840736154593 / 10000000000000000000000 : ℝ)) := by have hlg : Real.log (2223905254151181 / 20000000000000000 : ℝ) ≤ (-(21964674985840736154593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2223905254151181 / 20000000000000000 : ℝ) = - (2223905254151181 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2223905254151181 / 1250000000000000 : ℚ)) - (U := (5761212226159263845407 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2223905254151181 / 1250000000000000 : ℝ) ≤ - (5761212226159263845407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (69314121506181 / 10000000000000000 : ℝ)) (q := - (2223905254151181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2223905254151181 / 20000000000000000 : ℚ)) + (r' := (2223905254151181 / 1250000000000000 : ℚ)) + (U := (-(21964674985840736154593 / 10000000000000000000000 : ℚ))) + (U' := (5761212226159263845407 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (0 : ℚ)) + (s := (69314121506181 / 10000000000000000 : ℚ)) + (q := (2223905254151181 / 20000000000000000 : ℚ)) + (U := (-(21964674985840736154593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_12 : Uω (aρ 12) (bρ 12) (0 : ℝ) ≤ (-(4043272987456227879851 / 2000000000000000000000 : ℝ)) := by have hlg : Real.log (1324385526764569 / 10000000000000000 : ℝ) ≤ (-(4043272987456227879851 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1324385526764569 / 10000000000000000 : ℝ) = - (1324385526764569 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1324385526764569 / 1250000000000000 : ℚ)) - (U := (115610094343772120149 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1324385526764569 / 1250000000000000 : ℝ) ≤ - (115610094343772120149 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (35239912099569 / 5000000000000000 : ℝ)) (q := - (1324385526764569 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [aρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1324385526764569 / 10000000000000000 : ℚ)) + (r' := (1324385526764569 / 1250000000000000 : ℚ)) + (U := (-(4043272987456227879851 / 2000000000000000000000 : ℚ))) + (U' := (115610094343772120149 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (0 : ℚ)) + (s := (35239912099569 / 5000000000000000 : ℚ)) + (q := (1324385526764569 / 10000000000000000 : ℚ)) + (U := (-(4043272987456227879851 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_13 : Uω (aρ 13) (bρ 13) (0 : ℝ) ≤ (-(4702168270076774782451 / 2500000000000000000000 : ℝ)) := by have hlg : Real.log (3049156407763681 / 20000000000000000 : ℝ) ≤ (-(4702168270076774782451 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3049156407763681 / 20000000000000000 : ℝ) = - (3049156407763681 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3049156407763681 / 2500000000000000 : ℚ)) - (U := (496435582173225217549 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3049156407763681 / 2500000000000000 : ℝ) ≤ - (496435582173225217549 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (71483436838681 / 10000000000000000 : ℝ)) (q := - (3049156407763681 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [aρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3049156407763681 / 20000000000000000 : ℚ)) + (r' := (3049156407763681 / 2500000000000000 : ℚ)) + (U := (-(4702168270076774782451 / 2500000000000000000000 : ℚ))) + (U' := (496435582173225217549 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (0 : ℚ)) + (s := (71483436838681 / 10000000000000000 : ℚ)) + (q := (3049156407763681 / 20000000000000000 : ℚ)) + (U := (-(4702168270076774782451 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_14 : Uω (aρ 14) (bρ 14) (0 : ℝ) ≤ (-(2217195343887504332233 / 1250000000000000000000 : ℝ)) := by have hlg : Real.log (3393887425779091 / 20000000000000000 : ℝ) ≤ (-(2217195343887504332233 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3393887425779091 / 20000000000000000 : ℝ) = - (3393887425779091 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3393887425779091 / 2500000000000000 : ℚ)) - (U := (382106582237495667767 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3393887425779091 / 2500000000000000 : ℝ) ≤ - (382106582237495667767 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (72287169809091 / 10000000000000000 : ℝ)) (q := - (3393887425779091 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [aρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3393887425779091 / 20000000000000000 : ℚ)) + (r' := (3393887425779091 / 2500000000000000 : ℚ)) + (U := (-(2217195343887504332233 / 1250000000000000000000 : ℚ))) + (U' := (382106582237495667767 / 1250000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 14) (t := (0 : ℚ)) + (s := (72287169809091 / 10000000000000000 : ℚ)) + (q := (3393887425779091 / 20000000000000000 : ℚ)) + (U := (-(2217195343887504332233 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_15 : Uω (aρ 15) (bρ 15) (0 : ℝ) ≤ (-(16999000975580328413317 / 10000000000000000000000 : ℝ)) := by have hlg : Real.log (1827017753520839 / 10000000000000000 : ℝ) ≤ (-(16999000975580328413317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1827017753520839 / 10000000000000000 : ℝ) = - (1827017753520839 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1827017753520839 / 1250000000000000 : ℚ)) - (U := (3795414433419671586683 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1827017753520839 / 1250000000000000 : ℝ) ≤ - (3795414433419671586683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (36430986828339 / 5000000000000000 : ℝ)) (q := - (1827017753520839 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [aρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1827017753520839 / 10000000000000000 : ℚ)) + (r' := (1827017753520839 / 1250000000000000 : ℚ)) + (U := (-(16999000975580328413317 / 10000000000000000000000 : ℚ))) + (U' := (3795414433419671586683 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 15) (t := (0 : ℚ)) + (s := (36430986828339 / 5000000000000000 : ℚ)) + (q := (1827017753520839 / 10000000000000000 : ℚ)) + (U := (-(16999000975580328413317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0_16 : Uω (aρ 16) (bρ 16) (0 : ℝ) ≤ (-(1036850562756824007821 / 625000000000000000000 : ℝ)) := by have hlg : Real.log (1903366559739307 / 10000000000000000 : ℝ) ≤ (-(1036850562756824007821 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1903366559739307 / 10000000000000000 : ℝ) = - (1903366559739307 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1903366559739307 / 1250000000000000 : ℚ)) - (U := (262800400305675992179 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1903366559739307 / 1250000000000000 : ℝ) ≤ - (262800400305675992179 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (36593967291807 / 5000000000000000 : ℝ)) (q := - (1903366559739307 / 10000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [aρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1903366559739307 / 10000000000000000 : ℚ)) + (r' := (1903366559739307 / 1250000000000000 : ℚ)) + (U := (-(1036850562756824007821 / 625000000000000000000 : ℚ))) + (U' := (262800400305675992179 / 625000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 16) (t := (0 : ℚ)) + (s := (36593967291807 / 5000000000000000 : ℚ)) + (q := (1903366559739307 / 10000000000000000 : ℚ)) + (U := (-(1036850562756824007821 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_0 : Uρ (0 : ℝ) ≤ (-(27385656762631359502577 / 10000000000000000000000 : ℝ)) := by rw [Uρ_expand, cρ_1, cρ_2, cρ_3, cρ_4, cρ_5, cρ_6, cρ_7, cρ_8, cρ_9, cρ_10, cρ_11, cρ_12, cρ_13, @@ -513,24 +444,21 @@ lemma U_1_1 : have hlg : Real.log (61510201432479 / 10000000000000000 : ℝ) ≤ (-(50911373318893302541507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (61510201432479 / 10000000000000000 : ℝ) = (61510201432479 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (61510201432479 / 39062500000000 : ℚ)) - (U := (4540401105106697458493 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (61510201432479 / 39062500000000 : ℝ) ≤ - (4540401105106697458493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (29440945664979 / 5000000000000000 : ℝ)) (q := - (61510201432479 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (61510201432479 / 10000000000000000 : ℚ)) + (r' := (61510201432479 / 39062500000000 : ℚ)) + (U := (-(50911373318893302541507 / 10000000000000000000000 : ℚ))) + (U' := (4540401105106697458493 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (7174131 / 200000000000 : ℚ)) + (s := (29440945664979 / 5000000000000000 : ℚ)) + (q := (61510201432479 / 10000000000000000 : ℚ)) + (U := (-(50911373318893302541507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_2 : Uω (aρ 2) (bρ 2) (7174131 / 200000000000 : ℝ) ≤ @@ -538,25 +466,21 @@ lemma U_1_2 : have hlg : Real.log (146933153106433 / 20000000000000000 : ℝ) ≤ (-(49135098078763348601453 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (146933153106433 / 20000000000000000 : ℝ) = - (146933153106433 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (146933153106433 / 78125000000000 : ℚ)) - (U := (6316676345236651398547 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (146933153106433 / 78125000000000 : ℝ) ≤ - (6316676345236651398547 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (59025629061433 / 10000000000000000 : ℝ)) (q := - (146933153106433 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (146933153106433 / 20000000000000000 : ℚ)) + (r' := (146933153106433 / 78125000000000 : ℚ)) + (U := (-(49135098078763348601453 / 10000000000000000000000 : ℚ))) + (U' := (6316676345236651398547 / 10000000000000000000000 : ℚ)) + 8 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (7174131 / 200000000000 : ℚ)) + (s := (59025629061433 / 10000000000000000 : ℚ)) + (q := (146933153106433 / 20000000000000000 : ℚ)) + (U := (-(49135098078763348601453 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_3 : Uω (aρ 3) (bρ 3) (7174131 / 200000000000 : ℝ) ≤ @@ -564,25 +488,21 @@ lemma U_1_3 : have hlg : Real.log (194556576856917 / 20000000000000000 : ℝ) ≤ (-(46327645463733161241931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (194556576856917 / 20000000000000000 : ℝ) = - (194556576856917 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194556576856917 / 156250000000000 : ℚ)) - (U := (2192657157266838758069 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194556576856917 / 156250000000000 : ℝ) ≤ - (2192657157266838758069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (59252946461917 / 10000000000000000 : ℝ)) (q := - (194556576856917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194556576856917 / 20000000000000000 : ℚ)) + (r' := (194556576856917 / 156250000000000 : ℚ)) + (U := (-(46327645463733161241931 / 10000000000000000000000 : ℚ))) + (U' := (2192657157266838758069 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (7174131 / 200000000000 : ℚ)) + (s := (59252946461917 / 10000000000000000 : ℚ)) + (q := (194556576856917 / 20000000000000000 : ℚ)) + (U := (-(46327645463733161241931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_4 : Uω (aρ 4) (bρ 4) (7174131 / 200000000000 : ℝ) ≤ @@ -590,25 +510,21 @@ lemma U_1_4 : have hlg : Real.log (273111736229039 / 20000000000000000 : ℝ) ≤ (-(42936065490516840879561 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (273111736229039 / 20000000000000000 : ℝ) = - (273111736229039 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (273111736229039 / 156250000000000 : ℚ)) - (U := (5584237130483159120439 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (273111736229039 / 156250000000000 : ℝ) ≤ - (5584237130483159120439 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (59513924769039 / 10000000000000000 : ℝ)) (q := - (273111736229039 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (273111736229039 / 20000000000000000 : ℚ)) + (r' := (273111736229039 / 156250000000000 : ℚ)) + (U := (-(42936065490516840879561 / 10000000000000000000000 : ℚ))) + (U' := (5584237130483159120439 / 10000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (7174131 / 200000000000 : ℚ)) + (s := (59513924769039 / 10000000000000000 : ℚ)) + (q := (273111736229039 / 20000000000000000 : ℚ)) + (U := (-(42936065490516840879561 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_5 : Uω (aρ 5) (bρ 5) (7174131 / 200000000000 : ℝ) ≤ @@ -616,24 +532,21 @@ lemma U_1_5 : have hlg : Real.log (97882918342561 / 5000000000000000 : ℝ) ≤ (-(7866842272424100993973 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (97882918342561 / 5000000000000000 : ℝ) = (97882918342561 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (97882918342561 / 78125000000000 : ℚ)) - (U := (450923891175899006027 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (97882918342561 / 78125000000000 : ℝ) ≤ - (450923891175899006027 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14935985643811 / 2500000000000000 : ℝ)) (q := - (97882918342561 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (97882918342561 / 5000000000000000 : ℚ)) + (r' := (97882918342561 / 78125000000000 : ℚ)) + (U := (-(7866842272424100993973 / 2000000000000000000000 : ℚ))) + (U' := (450923891175899006027 / 2000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (7174131 / 200000000000 : ℚ)) + (s := (14935985643811 / 2500000000000000 : ℚ)) + (q := (97882918342561 / 5000000000000000 : ℚ)) + (U := (-(7866842272424100993973 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_6 : Uω (aρ 6) (bρ 6) (7174131 / 200000000000 : ℝ) ≤ @@ -641,25 +554,21 @@ lemma U_1_6 : have hlg : Real.log (139724784359361 / 5000000000000000 : ℝ) ≤ (-(1431007411209519275791 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (139724784359361 / 5000000000000000 : ℝ) = - (139724784359361 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (139724784359361 / 78125000000000 : ℚ)) - (U := (232545821510480724209 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (139724784359361 / 78125000000000 : ℝ) ≤ - (232545821510480724209 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14967757875611 / 2500000000000000 : ℝ)) (q := - (139724784359361 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (139724784359361 / 5000000000000000 : ℚ)) + (r' := (139724784359361 / 78125000000000 : ℚ)) + (U := (-(1431007411209519275791 / 400000000000000000000 : ℚ))) + (U' := (232545821510480724209 / 400000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (7174131 / 200000000000 : ℚ)) + (s := (14967757875611 / 2500000000000000 : ℚ)) + (q := (139724784359361 / 5000000000000000 : ℚ)) + (U := (-(1431007411209519275791 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_7 : Uω (aρ 7) (bρ 7) (7174131 / 200000000000 : ℝ) ≤ @@ -667,25 +576,21 @@ lemma U_1_7 : have hlg : Real.log (195628501984759 / 5000000000000000 : ℝ) ≤ (-(40512196593284858497 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (195628501984759 / 5000000000000000 : ℝ) = - (195628501984759 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (195628501984759 / 156250000000000 : ℚ)) - (U := (2809502175465141503 / 12500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (195628501984759 / 156250000000000 : ℝ) ≤ - (2809502175465141503 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14956130311009 / 2500000000000000 : ℝ)) (q := - (195628501984759 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (195628501984759 / 5000000000000000 : ℚ)) + (r' := (195628501984759 / 156250000000000 : ℚ)) + (U := (-(40512196593284858497 / 12500000000000000000 : ℚ))) + (U' := (2809502175465141503 / 12500000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (7174131 / 200000000000 : ℚ)) + (s := (14956130311009 / 2500000000000000 : ℚ)) + (q := (195628501984759 / 5000000000000000 : ℚ)) + (U := (-(40512196593284858497 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_8 : Uω (aρ 8) (bρ 8) (7174131 / 200000000000 : ℝ) ≤ @@ -693,25 +598,21 @@ lemma U_1_8 : have hlg : Real.log (266443970762523 / 5000000000000000 : ℝ) ≤ (-(14660146048277734861007 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (266443970762523 / 5000000000000000 : ℝ) = - (266443970762523 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (266443970762523 / 156250000000000 : ℚ)) - (U := (2668533459222265138993 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (266443970762523 / 156250000000000 : ℝ) ≤ - (2668533459222265138993 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14886186253773 / 2500000000000000 : ℝ)) (q := - (266443970762523 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (266443970762523 / 5000000000000000 : ℚ)) + (r' := (266443970762523 / 156250000000000 : ℚ)) + (U := (-(14660146048277734861007 / 5000000000000000000000 : ℚ))) + (U' := (2668533459222265138993 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (7174131 / 200000000000 : ℚ)) + (s := (14886186253773 / 2500000000000000 : ℚ)) + (q := (266443970762523 / 5000000000000000 : ℚ)) + (U := (-(14660146048277734861007 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_9 : Uω (aρ 9) (bρ 9) (7174131 / 200000000000 : ℝ) ≤ @@ -719,24 +620,21 @@ lemma U_1_9 : have hlg : Real.log (70309505590531 / 1000000000000000 : ℝ) ≤ (-(5309696547214735406207 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (70309505590531 / 1000000000000000 : ℝ) = (70309505590531 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70309505590531 / 62500000000000 : ℚ)) - (U := (235480895185264593793 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (70309505590531 / 62500000000000 : ℝ) ≤ - (235480895185264593793 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2949667270781 / 500000000000000 : ℝ)) (q := - (70309505590531 / 1000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70309505590531 / 1000000000000000 : ℚ)) + (r' := (70309505590531 / 62500000000000 : ℚ)) + (U := (-(5309696547214735406207 / 2000000000000000000000 : ℚ))) + (U' := (235480895185264593793 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (7174131 / 200000000000 : ℚ)) + (s := (2949667270781 / 500000000000000 : ℚ)) + (q := (70309505590531 / 1000000000000000 : ℚ)) + (U := (-(5309696547214735406207 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_10 : Uω (aρ 10) (bρ 10) (7174131 / 200000000000 : ℝ) ≤ @@ -744,26 +642,21 @@ lemma U_1_10 : have hlg : Real.log (1793918993060211 / 20000000000000000 : ℝ) ≤ (-(24113296642670996497633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1793918993060211 / 20000000000000000 : ℝ) = - (1793918993060211 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1793918993060211 / 1250000000000000 : ℚ)) - (U := (3612590569329003502367 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1793918993060211 / 1250000000000000 : ℝ) ≤ - (3612590569329003502367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58163193170211 / 10000000000000000 : ℝ)) (q := - (1793918993060211 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1793918993060211 / 20000000000000000 : ℚ)) + (r' := (1793918993060211 / 1250000000000000 : ℚ)) + (U := (-(24113296642670996497633 / 10000000000000000000000 : ℚ))) + (U' := (3612590569329003502367 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (7174131 / 200000000000 : ℚ)) + (s := (58163193170211 / 10000000000000000 : ℚ)) + (q := (1793918993060211 / 20000000000000000 : ℚ)) + (U := (-(24113296642670996497633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_11 : Uω (aρ 11) (bρ 11) (7174131 / 200000000000 : ℝ) ≤ @@ -771,26 +664,21 @@ lemma U_1_11 : have hlg : Real.log (2211318713475239 / 20000000000000000 : ℝ) ≤ (-(5505358080027453352527 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2211318713475239 / 20000000000000000 : ℝ) = - (2211318713475239 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2211318713475239 / 1250000000000000 : ℚ)) - (U := (1426113722972546647473 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2211318713475239 / 1250000000000000 : ℝ) ≤ - (1426113722972546647473 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (57086287380239 / 10000000000000000 : ℝ)) (q := - (2211318713475239 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2211318713475239 / 20000000000000000 : ℚ)) + (r' := (2211318713475239 / 1250000000000000 : ℚ)) + (U := (-(5505358080027453352527 / 2500000000000000000000 : ℚ))) + (U' := (1426113722972546647473 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (7174131 / 200000000000 : ℚ)) + (s := (57086287380239 / 10000000000000000 : ℚ)) + (q := (2211318713475239 / 20000000000000000 : ℚ)) + (U := (-(5505358080027453352527 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_12 : Uω (aρ 12) (bρ 12) (7174131 / 200000000000 : ℝ) ≤ @@ -798,25 +686,21 @@ lemma U_1_12 : have hlg : Real.log (526754018847003 / 4000000000000000 : ℝ) ≤ (-(10136579785760210337841 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (526754018847003 / 4000000000000000 : ℝ) = - (526754018847003 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (526754018847003 / 500000000000000 : ℚ)) - (U := (260627918739789662159 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (526754018847003 / 500000000000000 : ℝ) ≤ - (260627918739789662159 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11167514291003 / 2000000000000000 : ℝ)) (q := - (526754018847003 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [aρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (526754018847003 / 4000000000000000 : ℚ)) + (r' := (526754018847003 / 500000000000000 : ℚ)) + (U := (-(10136579785760210337841 / 5000000000000000000000 : ℚ))) + (U' := (260627918739789662159 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (7174131 / 200000000000 : ℚ)) + (s := (11167514291003 / 2000000000000000 : ℚ)) + (q := (526754018847003 / 4000000000000000 : ℚ)) + (U := (-(10136579785760210337841 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_13 : Uω (aρ 13) (bρ 13) (7174131 / 200000000000 : ℝ) ≤ @@ -824,25 +708,21 @@ lemma U_1_13 : have hlg : Real.log (606369344182109 / 4000000000000000 : ℝ) ≤ (-(75462414402452552303 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (606369344182109 / 4000000000000000 : ℝ) = - (606369344182109 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (606369344182109 / 500000000000000 : ℚ)) - (U := (7715247233547447697 / 40000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (606369344182109 / 500000000000000 : ℝ) ≤ - (7715247233547447697 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10906491307109 / 2000000000000000 : ℝ)) (q := - (606369344182109 / 4000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [aρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (606369344182109 / 4000000000000000 : ℚ)) + (r' := (606369344182109 / 500000000000000 : ℚ)) + (U := (-(75462414402452552303 / 40000000000000000000 : ℚ))) + (U' := (7715247233547447697 / 40000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (7174131 / 200000000000 : ℚ)) + (s := (10906491307109 / 2000000000000000 : ℚ)) + (q := (606369344182109 / 4000000000000000 : ℚ)) + (U := (-(75462414402452552303 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_14 : Uω (aρ 14) (bρ 14) (7174131 / 200000000000 : ℝ) ≤ @@ -850,26 +730,21 @@ lemma U_1_14 : have hlg : Real.log (3374557626289937 / 20000000000000000 : ℝ) ≤ (-(8897340153662197454051 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3374557626289937 / 20000000000000000 : ℝ) = - (3374557626289937 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3374557626289937 / 2500000000000000 : ℚ)) - (U := (1499867550837802545949 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3374557626289937 / 2500000000000000 : ℝ) ≤ - (1499867550837802545949 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (53316076869937 / 10000000000000000 : ℝ)) (q := - (3374557626289937 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [aρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3374557626289937 / 20000000000000000 : ℚ)) + (r' := (3374557626289937 / 2500000000000000 : ℚ)) + (U := (-(8897340153662197454051 / 5000000000000000000000 : ℚ))) + (U' := (1499867550837802545949 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 14) (t := (7174131 / 200000000000 : ℚ)) + (s := (53316076869937 / 10000000000000000 : ℚ)) + (q := (3374557626289937 / 20000000000000000 : ℚ)) + (U := (-(8897340153662197454051 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_15 : Uω (aρ 15) (bρ 15) (7174131 / 200000000000 : ℝ) ≤ @@ -877,26 +752,21 @@ lemma U_1_15 : have hlg : Real.log (3633158069658803 / 20000000000000000 : ℝ) ≤ (-(8528150055396143754779 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3633158069658803 / 20000000000000000 : ℝ) = - (3633158069658803 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3633158069658803 / 2500000000000000 : ℚ)) - (U := (1869057649103856245221 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3633158069658803 / 2500000000000000 : ℝ) ≤ - (1869057649103856245221 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (52343242823803 / 10000000000000000 : ℝ)) (q := - (3633158069658803 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [aρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3633158069658803 / 20000000000000000 : ℚ)) + (r' := (3633158069658803 / 2500000000000000 : ℚ)) + (U := (-(8528150055396143754779 / 5000000000000000000000 : ℚ))) + (U' := (1869057649103856245221 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 15) (t := (7174131 / 200000000000 : ℚ)) + (s := (52343242823803 / 10000000000000000 : ℚ)) + (q := (3633158069658803 / 20000000000000000 : ℚ)) + (U := (-(8528150055396143754779 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1_16 : Uω (aρ 16) (bρ 16) (7174131 / 200000000000 : ℝ) ≤ @@ -904,26 +774,21 @@ lemma U_1_16 : have hlg : Real.log (3784936920023489 / 20000000000000000 : ℝ) ≤ (-(16647030518034101616959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3784936920023489 / 20000000000000000 : ℝ) = - (3784936920023489 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3784936920023489 / 2500000000000000 : ℚ)) - (U := (4147384890965898383041 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3784936920023489 / 2500000000000000 : ℝ) ≤ - (4147384890965898383041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (51750441678489 / 10000000000000000 : ℝ)) (q := - (3784936920023489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [aρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3784936920023489 / 20000000000000000 : ℚ)) + (r' := (3784936920023489 / 2500000000000000 : ℚ)) + (U := (-(16647030518034101616959 / 10000000000000000000000 : ℚ))) + (U' := (4147384890965898383041 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 16) (t := (7174131 / 200000000000 : ℚ)) + (s := (51750441678489 / 10000000000000000 : ℚ)) + (q := (3784936920023489 / 20000000000000000 : ℚ)) + (U := (-(16647030518034101616959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_1 : Uρ (7174131 / 200000000000 : ℝ) ≤ @@ -1016,24 +881,21 @@ lemma U_2_1 : have hlg : Real.log (30661408404607 / 5000000000000000 : ℝ) ≤ (-(25470941903623612969977 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (30661408404607 / 5000000000000000 : ℝ) = (30661408404607 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30661408404607 / 19531250000000 : ℚ)) - (U := (2254945308376387030023 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (30661408404607 / 19531250000000 : ℝ) ≤ - (2254945308376387030023 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14671618839607 / 2500000000000000 : ℝ)) (q := - (30661408404607 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30661408404607 / 5000000000000000 : ℚ)) + (r' := (30661408404607 / 19531250000000 : ℚ)) + (U := (-(25470941903623612969977 / 5000000000000000000000 : ℚ))) + (U' := (2254945308376387030023 / 5000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (21522393 / 400000000000 : ℚ)) + (s := (14671618839607 / 2500000000000000 : ℚ)) + (q := (30661408404607 / 5000000000000000 : ℚ)) + (U := (-(25470941903623612969977 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_2 : Uω (aρ 2) (bρ 2) (21522393 / 400000000000 : ℝ) ≤ @@ -1041,24 +903,21 @@ lemma U_2_2 : have hlg : Real.log (18310794199513 / 2500000000000000 : ℝ) ≤ (-(49165552758527775040867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (18310794199513 / 2500000000000000 : ℝ) = (18310794199513 / 9765625000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18310794199513 / 9765625000000 : ℚ)) - (U := (6286221665472224959133 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18310794199513 / 9765625000000 : ℝ) ≤ - (6286221665472224959133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7344772853263 / 1250000000000000 : ℝ)) (q := - (18310794199513 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18310794199513 / 2500000000000000 : ℚ)) + (r' := (18310794199513 / 9765625000000 : ℚ)) + (U := (-(49165552758527775040867 / 10000000000000000000000 : ℚ))) + (U' := (6286221665472224959133 / 10000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (21522393 / 400000000000 : ℚ)) + (s := (7344772853263 / 1250000000000000 : ℚ)) + (q := (18310794199513 / 2500000000000000 : ℚ)) + (U := (-(49165552758527775040867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_3 : Uω (aρ 3) (bρ 3) (21522393 / 400000000000 : ℝ) ≤ @@ -1066,24 +925,21 @@ lemma U_2_3 : have hlg : Real.log (38793303976897 / 4000000000000000 : ℝ) ≤ (-(46358019844614904236579 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (38793303976897 / 4000000000000000 : ℝ) = (38793303976897 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38793303976897 / 31250000000000 : ℚ)) - (U := (2162282776385095763421 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (38793303976897 / 31250000000000 : ℝ) ≤ - (2162282776385095763421 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11768448552897 / 2000000000000000 : ℝ)) (q := - (38793303976897 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38793303976897 / 4000000000000000 : ℚ)) + (r' := (38793303976897 / 31250000000000 : ℚ)) + (U := (-(46358019844614904236579 / 10000000000000000000000 : ℚ))) + (U' := (2162282776385095763421 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (21522393 / 400000000000 : ℚ)) + (s := (11768448552897 / 2000000000000000 : ℚ)) + (q := (38793303976897 / 4000000000000000 : ℚ)) + (U := (-(46358019844614904236579 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_4 : Uω (aρ 4) (bρ 4) (21522393 / 400000000000 : ℝ) ≤ @@ -1091,25 +947,21 @@ lemma U_2_4 : have hlg : Real.log (272285430885961 / 20000000000000000 : ℝ) ≤ (-(2148318328187890160217 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (272285430885961 / 20000000000000000 : ℝ) = - (272285430885961 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (272285430885961 / 156250000000000 : ℚ)) - (U := (277696802862109839783 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (272285430885961 / 156250000000000 : ℝ) ≤ - (277696802862109839783 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58866972700961 / 10000000000000000 : ℝ)) (q := - (272285430885961 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (272285430885961 / 20000000000000000 : ℚ)) + (r' := (272285430885961 / 156250000000000 : ℚ)) + (U := (-(2148318328187890160217 / 500000000000000000000 : ℚ))) + (U' := (277696802862109839783 / 500000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (21522393 / 400000000000 : ℚ)) + (s := (58866972700961 / 10000000000000000 : ℚ)) + (q := (272285430885961 / 20000000000000000 : ℚ)) + (U := (-(2148318328187890160217 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_5 : Uω (aρ 5) (bρ 5) (21522393 / 400000000000 : ℝ) ≤ @@ -1117,24 +969,21 @@ lemma U_2_5 : have hlg : Real.log (48793514003197 / 2500000000000000 : ℝ) ≤ (-(19682243075206791475787 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (48793514003197 / 2500000000000000 : ℝ) = (48793514003197 / 39062500000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48793514003197 / 39062500000000 : ℚ)) - (U := (1112172333793208524213 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48793514003197 / 39062500000000 : ℝ) ≤ - (1112172333793208524213 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7342466813197 / 1250000000000000 : ℝ)) (q := - (48793514003197 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48793514003197 / 2500000000000000 : ℚ)) + (r' := (48793514003197 / 39062500000000 : ℚ)) + (U := (-(19682243075206791475787 / 5000000000000000000000 : ℚ))) + (U' := (1112172333793208524213 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (21522393 / 400000000000 : ℚ)) + (s := (7342466813197 / 1250000000000000 : ℚ)) + (q := (48793514003197 / 2500000000000000 : ℚ)) + (U := (-(19682243075206791475787 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_6 : Uω (aρ 6) (bρ 6) (21522393 / 400000000000 : ℝ) ≤ @@ -1142,25 +991,21 @@ lemma U_2_6 : have hlg : Real.log (139301499171973 / 5000000000000000 : ℝ) ≤ (-(35805525469465709732703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (139301499171973 / 5000000000000000 : ℝ) = - (139301499171973 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (139301499171973 / 78125000000000 : ℚ)) - (U := (5783305348534290267297 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (139301499171973 / 78125000000000 : ℝ) ≤ - (5783305348534290267297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14589311006973 / 2500000000000000 : ℝ)) (q := - (139301499171973 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (139301499171973 / 5000000000000000 : ℚ)) + (r' := (139301499171973 / 78125000000000 : ℚ)) + (U := (-(35805525469465709732703 / 10000000000000000000000 : ℚ))) + (U' := (5783305348534290267297 / 10000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (21522393 / 400000000000 : ℚ)) + (s := (14589311006973 / 2500000000000000 : ℚ)) + (q := (139301499171973 / 5000000000000000 : ℚ)) + (U := (-(35805525469465709732703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_7 : Uω (aρ 7) (bρ 7) (21522393 / 400000000000 : ℝ) ≤ @@ -1168,25 +1013,21 @@ lemma U_2_7 : have hlg : Real.log (390063798273459 / 10000000000000000 : ℝ) ≤ (-(2027518787259263390593 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (390063798273459 / 10000000000000000 : ℝ) = - (390063798273459 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (390063798273459 / 312500000000000 : ℚ)) - (U := (138566151178236609407 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (390063798273459 / 312500000000000 : ℝ) ≤ - (138566151178236609407 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28808731563459 / 5000000000000000 : ℝ)) (q := - (390063798273459 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (390063798273459 / 10000000000000000 : ℚ)) + (r' := (390063798273459 / 312500000000000 : ℚ)) + (U := (-(2027518787259263390593 / 625000000000000000000 : ℚ))) + (U' := (138566151178236609407 / 625000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (21522393 / 400000000000 : ℚ)) + (s := (28808731563459 / 5000000000000000 : ℚ)) + (q := (390063798273459 / 10000000000000000 : ℚ)) + (U := (-(2027518787259263390593 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_8 : Uω (aρ 8) (bρ 8) (21522393 / 400000000000 : ℝ) ≤ @@ -1194,25 +1035,21 @@ lemma U_2_8 : have hlg : Real.log (1062484639786859 / 20000000000000000 : ℝ) ≤ (-(183445131700844988143 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1062484639786859 / 20000000000000000 : ℝ) = - (1062484639786859 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1062484639786859 / 625000000000000 : ℚ)) - (U := (33163362142905011857 / 62500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1062484639786859 / 625000000000000 : ℝ) ≤ - (33163362142905011857 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (56432855026859 / 10000000000000000 : ℝ)) (q := - (1062484639786859 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1062484639786859 / 20000000000000000 : ℚ)) + (r' := (1062484639786859 / 625000000000000 : ℚ)) + (U := (-(183445131700844988143 / 62500000000000000000 : ℚ))) + (U' := (33163362142905011857 / 62500000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (21522393 / 400000000000 : ℚ)) + (s := (56432855026859 / 10000000000000000 : ℚ)) + (q := (1062484639786859 / 20000000000000000 : ℚ)) + (U := (-(183445131700844988143 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_9 : Uω (aρ 9) (bρ 9) (21522393 / 400000000000 : ℝ) ≤ @@ -1220,25 +1057,21 @@ lemma U_2_9 : have hlg : Real.log (700881131857547 / 10000000000000000 : ℝ) ≤ (-(13290010338352078837471 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (700881131857547 / 10000000000000000 : ℝ) = - (700881131857547 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (700881131857547 / 625000000000000 : ℚ)) - (U := (572933267647921162529 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (700881131857547 / 625000000000000 : ℝ) ≤ - (572933267647921162529 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (27372425297547 / 5000000000000000 : ℝ)) (q := - (700881131857547 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (700881131857547 / 10000000000000000 : ℚ)) + (r' := (700881131857547 / 625000000000000 : ℚ)) + (U := (-(13290010338352078837471 / 5000000000000000000000 : ℚ))) + (U' := (572933267647921162529 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (21522393 / 400000000000 : ℚ)) + (s := (27372425297547 / 5000000000000000 : ℚ)) + (q := (700881131857547 / 10000000000000000 : ℚ)) + (U := (-(13290010338352078837471 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_10 : Uω (aρ 10) (bρ 10) (21522393 / 400000000000 : ℝ) ≤ @@ -1246,26 +1079,21 @@ lemma U_2_10 : have hlg : Real.log (1788115596139249 / 20000000000000000 : ℝ) ≤ (-(24145699467680874899253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1788115596139249 / 20000000000000000 : ℝ) = - (1788115596139249 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1788115596139249 / 1250000000000000 : ℚ)) - (U := (3580187744319125100747 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1788115596139249 / 1250000000000000 : ℝ) ≤ - (3580187744319125100747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (52539149524249 / 10000000000000000 : ℝ)) (q := - (1788115596139249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1788115596139249 / 20000000000000000 : ℚ)) + (r' := (1788115596139249 / 1250000000000000 : ℚ)) + (U := (-(24145699467680874899253 / 10000000000000000000000 : ℚ))) + (U' := (3580187744319125100747 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (21522393 / 400000000000 : ℚ)) + (s := (52539149524249 / 10000000000000000 : ℚ)) + (q := (1788115596139249 / 20000000000000000 : ℚ)) + (U := (-(24145699467680874899253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_11 : Uω (aρ 11) (bρ 11) (21522393 / 400000000000 : ℝ) ≤ @@ -1273,26 +1101,21 @@ lemma U_2_11 : have hlg : Real.log (2203914271090737 / 20000000000000000 : ℝ) ≤ (-(22054972789443236367197 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2203914271090737 / 20000000000000000 : ℝ) = - (2203914271090737 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2203914271090737 / 1250000000000000 : ℚ)) - (U := (5670914422556763632803 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2203914271090737 / 1250000000000000 : ℝ) ≤ - (5670914422556763632803 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (49861198270737 / 10000000000000000 : ℝ)) (q := - (2203914271090737 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2203914271090737 / 20000000000000000 : ℚ)) + (r' := (2203914271090737 / 1250000000000000 : ℚ)) + (U := (-(22054972789443236367197 / 10000000000000000000000 : ℚ))) + (U' := (5670914422556763632803 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (21522393 / 400000000000 : ℚ)) + (s := (49861198270737 / 10000000000000000 : ℚ)) + (q := (2203914271090737 / 20000000000000000 : ℚ)) + (U := (-(22054972789443236367197 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_12 : Uω (aρ 12) (bρ 12) (21522393 / 400000000000 : ℝ) ≤ @@ -1300,25 +1123,21 @@ lemma U_2_12 : have hlg : Real.log (656146049612939 / 5000000000000000 : ℝ) ≤ (-(20308097898670736143723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (656146049612939 / 5000000000000000 : ℝ) = - (656146049612939 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (656146049612939 / 625000000000000 : ℚ)) - (U := (486317510329263856277 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (656146049612939 / 625000000000000 : ℝ) ≤ - (486317510329263856277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11707757236689 / 2500000000000000 : ℝ)) (q := - (656146049612939 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [aρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (656146049612939 / 5000000000000000 : ℚ)) + (r' := (656146049612939 / 625000000000000 : ℚ)) + (U := (-(20308097898670736143723 / 10000000000000000000000 : ℚ))) + (U' := (486317510329263856277 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (21522393 / 400000000000 : ℚ)) + (s := (11707757236689 / 2500000000000000 : ℚ)) + (q := (656146049612939 / 5000000000000000 : ℚ)) + (U := (-(20308097898670736143723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_13 : Uω (aρ 13) (bρ 13) (21522393 / 400000000000 : ℝ) ≤ @@ -1326,25 +1145,21 @@ lemma U_2_13 : have hlg : Real.log (755197706355697 / 5000000000000000 : ℝ) ≤ (-(18902136129446577859961 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (755197706355697 / 5000000000000000 : ℝ) = - (755197706355697 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (755197706355697 / 625000000000000 : ℚ)) - (U := (1892279279553422140039 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (755197706355697 / 625000000000000 : ℝ) ≤ - (1892279279553422140039 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10913978580697 / 2500000000000000 : ℝ)) (q := - (755197706355697 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [aρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (755197706355697 / 5000000000000000 : ℚ)) + (r' := (755197706355697 / 625000000000000 : ℚ)) + (U := (-(18902136129446577859961 / 10000000000000000000000 : ℚ))) + (U' := (1892279279553422140039 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (21522393 / 400000000000 : ℚ)) + (s := (10913978580697 / 2500000000000000 : ℚ)) + (q := (755197706355697 / 5000000000000000 : ℚ)) + (U := (-(18902136129446577859961 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_14 : Uω (aρ 14) (bρ 14) (21522393 / 400000000000 : ℝ) ≤ @@ -1352,25 +1167,21 @@ lemma U_2_14 : have hlg : Real.log (840424550963387 / 5000000000000000 : ℝ) ≤ (-(17832860086660498318657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (840424550963387 / 5000000000000000 : ℝ) = - (840424550963387 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (840424550963387 / 625000000000000 : ℚ)) - (U := (2961555322339501681343 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (840424550963387 / 625000000000000 : ℝ) ≤ - (2961555322339501681343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10159001927137 / 2500000000000000 : ℝ)) (q := - (840424550963387 / 5000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [aρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (840424550963387 / 5000000000000000 : ℚ)) + (r' := (840424550963387 / 625000000000000 : ℚ)) + (U := (-(17832860086660498318657 / 10000000000000000000000 : ℚ))) + (U' := (2961555322339501681343 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 14) (t := (21522393 / 400000000000 : ℚ)) + (s := (10159001927137 / 2500000000000000 : ℚ)) + (q := (840424550963387 / 5000000000000000 : ℚ)) + (U := (-(17832860086660498318657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_15 : Uω (aρ 15) (bρ 15) (21522393 / 400000000000 : ℝ) ≤ @@ -1378,25 +1189,21 @@ lemma U_2_15 : have hlg : Real.log (723756997736773 / 4000000000000000 : ℝ) ≤ (-(17095939417607986453457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (723756997736773 / 4000000000000000 : ℝ) = - (723756997736773 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (723756997736773 / 500000000000000 : ℚ)) - (U := (3698475991392013546543 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (723756997736773 / 500000000000000 : ℝ) ≤ - (3698475991392013546543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7629903024773 / 2000000000000000 : ℝ)) (q := - (723756997736773 / 4000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [aρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (723756997736773 / 4000000000000000 : ℚ)) + (r' := (723756997736773 / 500000000000000 : ℚ)) + (U := (-(17095939417607986453457 / 10000000000000000000000 : ℚ))) + (U' := (3698475991392013546543 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 15) (t := (21522393 / 400000000000 : ℚ)) + (s := (7629903024773 / 2000000000000000 : ℚ)) + (q := (723756997736773 / 4000000000000000 : ℚ)) + (U := (-(17095939417607986453457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2_16 : Uω (aρ 16) (bρ 16) (21522393 / 400000000000 : ℝ) ≤ @@ -1404,26 +1211,21 @@ lemma U_2_16 : have hlg : Real.log (1884799886888283 / 10000000000000000 : ℝ) ≤ (-(4171908594379160841333 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1884799886888283 / 10000000000000000 : ℝ) = - (1884799886888283 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1884799886888283 / 1250000000000000 : ℚ)) - (U := (1026695257870839158667 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1884799886888283 / 1250000000000000 : ℝ) ≤ - (1026695257870839158667 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (18296324353283 / 5000000000000000 : ℝ)) (q := - (1884799886888283 / 10000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [aρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1884799886888283 / 10000000000000000 : ℚ)) + (r' := (1884799886888283 / 1250000000000000 : ℚ)) + (U := (-(4171908594379160841333 / 2500000000000000000000 : ℚ))) + (U' := (1026695257870839158667 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 16) (t := (21522393 / 400000000000 : ℚ)) + (s := (18296324353283 / 5000000000000000 : ℚ)) + (q := (1884799886888283 / 10000000000000000 : ℚ)) + (U := (-(4171908594379160841333 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_2 : Uρ (21522393 / 400000000000 : ℝ) ≤ @@ -1516,24 +1318,21 @@ lemma U_3_1 : have hlg : Real.log (61135380726717 / 10000000000000000 : ℝ) ≤ (-(50972496086807483658427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (61135380726717 / 10000000000000000 : ℝ) = (61135380726717 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (61135380726717 / 39062500000000 : ℚ)) - (U := (4479278337192516341573 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (61135380726717 / 39062500000000 : ℝ) ≤ - (4479278337192516341573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (29245478234217 / 5000000000000000 : ℝ)) (q := - (61135380726717 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (61135380726717 / 10000000000000000 : ℚ)) + (r' := (61135380726717 / 39062500000000 : ℚ)) + (U := (-(50972496086807483658427 / 10000000000000000000000 : ℚ))) + (U' := (4479278337192516341573 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (7174131 / 100000000000 : ℚ)) + (s := (29245478234217 / 5000000000000000 : ℚ)) + (q := (61135380726717 / 10000000000000000 : ℚ)) + (U := (-(50972496086807483658427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_2 : Uω (aρ 2) (bρ 2) (7174131 / 100000000000 : ℝ) ≤ @@ -1541,25 +1340,21 @@ lemma U_3_2 : have hlg : Real.log (146038881156689 / 20000000000000000 : ℝ) ≤ (-(49196146549098639705941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (146038881156689 / 20000000000000000 : ℝ) = - (146038881156689 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (146038881156689 / 78125000000000 : ℚ)) - (U := (6255627874901360294059 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (146038881156689 / 78125000000000 : ℝ) ≤ - (6255627874901360294059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58490063661689 / 10000000000000000 : ℝ)) (q := - (146038881156689 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (146038881156689 / 20000000000000000 : ℚ)) + (r' := (146038881156689 / 78125000000000 : ℚ)) + (U := (-(49196146549098639705941 / 10000000000000000000000 : ℚ))) + (U' := (6255627874901360294059 / 10000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (7174131 / 100000000000 : ℚ)) + (s := (58490063661689 / 10000000000000000 : ℚ)) + (q := (146038881156689 / 20000000000000000 : ℚ)) + (U := (-(49196146549098639705941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_3 : Uω (aρ 3) (bρ 3) (7174131 / 100000000000 : ℝ) ≤ @@ -1567,25 +1362,21 @@ lemma U_3_3 : have hlg : Real.log (193374126628239 / 20000000000000000 : ℝ) ≤ (-(11597151895750616494561 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (193374126628239 / 20000000000000000 : ℝ) = - (193374126628239 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (193374126628239 / 156250000000000 : ℚ)) - (U := (532923759499383505439 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (193374126628239 / 156250000000000 : ℝ) ≤ - (532923759499383505439 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58429202783239 / 10000000000000000 : ℝ)) (q := - (193374126628239 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (193374126628239 / 20000000000000000 : ℚ)) + (r' := (193374126628239 / 156250000000000 : ℚ)) + (U := (-(11597151895750616494561 / 2500000000000000000000 : ℚ))) + (U' := (532923759499383505439 / 2500000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (7174131 / 100000000000 : ℚ)) + (s := (58429202783239 / 10000000000000000 : ℚ)) + (q := (193374126628239 / 20000000000000000 : ℚ)) + (U := (-(11597151895750616494561 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_4 : Uω (aρ 4) (bρ 4) (7174131 / 100000000000 : ℝ) ≤ @@ -1593,25 +1384,21 @@ lemma U_3_4 : have hlg : Real.log (271452488626557 / 20000000000000000 : ℝ) ≤ (-(429970042250669996509 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (271452488626557 / 20000000000000000 : ℝ) = - (271452488626557 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (271452488626557 / 156250000000000 : ℚ)) - (U := (55232983959330003491 / 100000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (271452488626557 / 156250000000000 : ℝ) ≤ - (55232983959330003491 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58213383716557 / 10000000000000000 : ℝ)) (q := - (271452488626557 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (271452488626557 / 20000000000000000 : ℚ)) + (r' := (271452488626557 / 156250000000000 : ℚ)) + (U := (-(429970042250669996509 / 100000000000000000000 : ℚ))) + (U' := (55232983959330003491 / 100000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (7174131 / 100000000000 : ℚ)) + (s := (58213383716557 / 10000000000000000 : ℚ)) + (q := (271452488626557 / 20000000000000000 : ℚ)) + (U := (-(429970042250669996509 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_5 : Uω (aρ 5) (bρ 5) (7174131 / 100000000000 : ℝ) ≤ @@ -1619,25 +1406,21 @@ lemma U_3_5 : have hlg : Real.log (194573819461431 / 10000000000000000 : ℝ) ≤ (-(9848821862142350549383 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (194573819461431 / 10000000000000000 : ℝ) = - (194573819461431 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194573819461431 / 156250000000000 : ℚ)) - (U := (548385842357649450617 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194573819461431 / 156250000000000 : ℝ) ≤ - (548385842357649450617 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28859307338931 / 5000000000000000 : ℝ)) (q := - (194573819461431 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194573819461431 / 10000000000000000 : ℚ)) + (r' := (194573819461431 / 156250000000000 : ℚ)) + (U := (-(9848821862142350549383 / 2500000000000000000000 : ℚ))) + (U' := (548385842357649450617 / 2500000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (7174131 / 100000000000 : ℚ)) + (s := (28859307338931 / 5000000000000000 : ℚ)) + (q := (194573819461431 / 10000000000000000 : ℚ)) + (U := (-(9848821862142350549383 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_6 : Uω (aρ 6) (bρ 6) (7174131 / 100000000000 : ℝ) ≤ @@ -1645,25 +1428,21 @@ lemma U_3_6 : have hlg : Real.log (277736547269241 / 10000000000000000 : ℝ) ≤ (-(17918336888719840156369 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (277736547269241 / 10000000000000000 : ℝ) = - (277736547269241 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (277736547269241 / 156250000000000 : ℚ)) - (U := (2876078520280159843631 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (277736547269241 / 156250000000000 : ℝ) ≤ - (2876078520280159843631 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28401847576741 / 5000000000000000 : ℝ)) (q := - (277736547269241 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (277736547269241 / 10000000000000000 : ℚ)) + (r' := (277736547269241 / 156250000000000 : ℚ)) + (U := (-(17918336888719840156369 / 5000000000000000000000 : ℚ))) + (U' := (2876078520280159843631 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (7174131 / 100000000000 : ℚ)) + (s := (28401847576741 / 5000000000000000 : ℚ)) + (q := (277736547269241 / 10000000000000000 : ℚ)) + (U := (-(17918336888719840156369 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_7 : Uω (aρ 7) (bρ 7) (7174131 / 100000000000 : ℝ) ≤ @@ -1671,24 +1450,21 @@ lemma U_3_7 : have hlg : Real.log (77765378718077 / 2000000000000000 : ℝ) ≤ (-(32472061297251956228297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (77765378718077 / 2000000000000000 : ℝ) = (77765378718077 / 62500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77765378718077 / 62500000000000 : ℚ)) - (U := (2185297717748043771703 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (77765378718077 / 62500000000000 : ℝ) ≤ - (2185297717748043771703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (5532300703577 / 1000000000000000 : ℝ)) (q := - (77765378718077 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77765378718077 / 2000000000000000 : ℚ)) + (r' := (77765378718077 / 62500000000000 : ℚ)) + (U := (-(32472061297251956228297 / 10000000000000000000000 : ℚ))) + (U' := (2185297717748043771703 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (7174131 / 100000000000 : ℚ)) + (s := (5532300703577 / 1000000000000000 : ℚ)) + (q := (77765378718077 / 2000000000000000 : ℚ)) + (U := (-(32472061297251956228297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_8 : Uω (aρ 8) (bρ 8) (7174131 / 100000000000 : ℝ) ≤ @@ -1696,25 +1472,21 @@ lemma U_3_8 : have hlg : Real.log (211802415407127 / 4000000000000000 : ℝ) ≤ (-(14691979007557547771577 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (211802415407127 / 4000000000000000 : ℝ) = - (211802415407127 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (211802415407127 / 125000000000000 : ℚ)) - (U := (2636700499942452228423 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (211802415407127 / 125000000000000 : ℝ) ≤ - (2636700499942452228423 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10627929110127 / 2000000000000000 : ℝ)) (q := - (211802415407127 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (211802415407127 / 4000000000000000 : ℚ)) + (r' := (211802415407127 / 125000000000000 : ℚ)) + (U := (-(14691979007557547771577 / 5000000000000000000000 : ℚ))) + (U' := (2636700499942452228423 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (7174131 / 100000000000 : ℚ)) + (s := (10627929110127 / 2000000000000000 : ℚ)) + (q := (211802415407127 / 4000000000000000 : ℚ)) + (U := (-(14691979007557547771577 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_9 : Uω (aρ 9) (bρ 9) (7174131 / 100000000000 : ℝ) ≤ @@ -1722,25 +1494,21 @@ lemma U_3_9 : have hlg : Real.log (698488168645371 / 10000000000000000 : ℝ) ≤ (-(26614221306142328686011 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (698488168645371 / 10000000000000000 : ℝ) = - (698488168645371 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (698488168645371 / 625000000000000 : ℚ)) - (U := (1111665905857671313989 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (698488168645371 / 625000000000000 : ℝ) ≤ - (1111665905857671313989 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (25069138722871 / 5000000000000000 : ℝ)) (q := - (698488168645371 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (698488168645371 / 10000000000000000 : ℚ)) + (r' := (698488168645371 / 625000000000000 : ℚ)) + (U := (-(26614221306142328686011 / 10000000000000000000000 : ℚ))) + (U' := (1111665905857671313989 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (7174131 / 100000000000 : ℚ)) + (s := (25069138722871 / 5000000000000000 : ℚ)) + (q := (698488168645371 / 10000000000000000 : ℚ)) + (U := (-(26614221306142328686011 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_10 : Uω (aρ 10) (bρ 10) (7174131 / 100000000000 : ℝ) ≤ @@ -1748,24 +1516,21 @@ lemma U_3_10 : have hlg : Real.log (89081689306903 / 1000000000000000 : ℝ) ≤ (-(24182014718027931878799 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (89081689306903 / 1000000000000000 : ℝ) = (89081689306903 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (89081689306903 / 62500000000000 : ℚ)) - (U := (3543872493972068121201 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (89081689306903 / 62500000000000 : ℝ) ≤ - (3543872493972068121201 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2311834639903 / 500000000000000 : ℝ)) (q := - (89081689306903 / 1000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [aρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (89081689306903 / 1000000000000000 : ℚ)) + (r' := (89081689306903 / 62500000000000 : ℚ)) + (U := (-(24182014718027931878799 / 10000000000000000000000 : ℚ))) + (U' := (3543872493972068121201 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (7174131 / 100000000000 : ℚ)) + (s := (2311834639903 / 500000000000000 : ℚ)) + (q := (89081689306903 / 1000000000000000 : ℚ)) + (U := (-(24182014718027931878799 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_11 : Uω (aρ 11) (bρ 11) (7174131 / 100000000000 : ℝ) ≤ @@ -1773,26 +1538,21 @@ lemma U_3_11 : have hlg : Real.log (2195268143255481 / 20000000000000000 : ℝ) ≤ (-(22094280725116768354743 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2195268143255481 / 20000000000000000 : ℝ) = - (2195268143255481 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2195268143255481 / 1250000000000000 : ℚ)) - (U := (5631606486883231645257 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2195268143255481 / 1250000000000000 : ℝ) ≤ - (5631606486883231645257 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (41394423710481 / 10000000000000000 : ℝ)) (q := - (2195268143255481 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2195268143255481 / 20000000000000000 : ℚ)) + (r' := (2195268143255481 / 1250000000000000 : ℚ)) + (U := (-(22094280725116768354743 / 10000000000000000000000 : ℚ))) + (U' := (5631606486883231645257 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (7174131 / 100000000000 : ℚ)) + (s := (41394423710481 / 10000000000000000 : ℚ)) + (q := (2195268143255481 / 20000000000000000 : ℚ)) + (U := (-(22094280725116768354743 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_12 : Uω (aρ 12) (bρ 12) (7174131 / 100000000000 : ℝ) ≤ @@ -1800,25 +1560,21 @@ lemma U_3_12 : have hlg : Real.log (653297527892073 / 5000000000000000 : ℝ) ≤ (-(20351605328285829232061 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (653297527892073 / 5000000000000000 : ℝ) = - (653297527892073 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (653297527892073 / 625000000000000 : ℚ)) - (U := (442810080714170767939 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (653297527892073 / 625000000000000 : ℝ) ≤ - (442810080714170767939 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (8904073834573 / 2500000000000000 : ℝ)) (q := - (653297527892073 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [aρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (653297527892073 / 5000000000000000 : ℚ)) + (r' := (653297527892073 / 625000000000000 : ℚ)) + (U := (-(20351605328285829232061 / 10000000000000000000000 : ℚ))) + (U' := (442810080714170767939 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (7174131 / 100000000000 : ℚ)) + (s := (8904073834573 / 2500000000000000 : ℚ)) + (q := (653297527892073 / 5000000000000000 : ℚ)) + (U := (-(20351605328285829232061 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_13 : Uω (aρ 13) (bρ 13) (7174131 / 100000000000 : ℝ) ≤ @@ -1826,26 +1582,21 @@ lemma U_3_13 : have hlg : Real.log (1502951489823239 / 10000000000000000 : ℝ) ≤ (-(18951542575309468805869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1502951489823239 / 10000000000000000 : ℝ) = - (1502951489823239 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1502951489823239 / 1250000000000000 : ℚ)) - (U := (1842872833690531194131 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1502951489823239 / 1250000000000000 : ℝ) ≤ - (1842872833690531194131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14473710910739 / 5000000000000000 : ℝ)) (q := - (1502951489823239 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [aρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1502951489823239 / 10000000000000000 : ℚ)) + (r' := (1502951489823239 / 1250000000000000 : ℚ)) + (U := (-(18951542575309468805869 / 10000000000000000000000 : ℚ))) + (U' := (1842872833690531194131 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (7174131 / 100000000000 : ℚ)) + (s := (14473710910739 / 5000000000000000 : ℚ)) + (q := (1502951489823239 / 10000000000000000 : ℚ)) + (U := (-(18951542575309468805869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_14 : Uω (aρ 14) (bρ 14) (7174131 / 100000000000 : ℝ) ≤ @@ -1853,26 +1604,21 @@ lemma U_3_14 : have hlg : Real.log (3342331165120743 / 20000000000000000 : ℝ) ≤ (-(4472659389032352227177 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3342331165120743 / 20000000000000000 : ℝ) = - (3342331165120743 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3342331165120743 / 2500000000000000 : ℚ)) - (U := (725944463217647772823 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3342331165120743 / 2500000000000000 : ℝ) ≤ - (725944463217647772823 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (21448322250743 / 10000000000000000 : ℝ)) (q := - (3342331165120743 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [aρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3342331165120743 / 20000000000000000 : ℚ)) + (r' := (3342331165120743 / 2500000000000000 : ℚ)) + (U := (-(4472659389032352227177 / 2500000000000000000000 : ℚ))) + (U' := (725944463217647772823 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 14) (t := (7174131 / 100000000000 : ℚ)) + (s := (21448322250743 / 10000000000000000 : ℚ)) + (q := (3342331165120743 / 20000000000000000 : ℚ)) + (U := (-(4472659389032352227177 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_15 : Uω (aρ 15) (bρ 15) (7174131 / 100000000000 : ℝ) ≤ @@ -1880,25 +1626,21 @@ lemma U_3_15 : have hlg : Real.log (898383398074539 / 5000000000000000 : ℝ) ≤ (-(17165962668190914916479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (898383398074539 / 5000000000000000 : ℝ) = - (898383398074539 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (898383398074539 / 625000000000000 : ℚ)) - (U := (3628452740809085083521 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (898383398074539 / 625000000000000 : ℝ) ≤ - (3628452740809085083521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (3269368003289 / 2500000000000000 : ℝ)) (q := - (898383398074539 / 5000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [aρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (898383398074539 / 5000000000000000 : ℚ)) + (r' := (898383398074539 / 625000000000000 : ℚ)) + (U := (-(17165962668190914916479 / 10000000000000000000000 : ℚ))) + (U' := (3628452740809085083521 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 15) (t := (7174131 / 100000000000 : ℚ)) + (s := (3269368003289 / 2500000000000000 : ℚ)) + (q := (898383398074539 / 5000000000000000 : ℚ)) + (U := (-(17165962668190914916479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_3_16 : Uω (aρ 16) (bρ 16) (7174131 / 100000000000 : ℝ) ≤ @@ -1996,24 +1738,21 @@ lemma U_4_1 : have hlg : Real.log (61110417965973 / 10000000000000000 : ℝ) ≤ (-(50976580114456355348677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (61110417965973 / 10000000000000000 : ℝ) = (61110417965973 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (61110417965973 / 39062500000000 : ℚ)) - (U := (4475194309543644651323 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (61110417965973 / 39062500000000 : ℝ) ≤ - (4475194309543644651323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (29232456748473 / 5000000000000000 : ℝ)) (q := - (61110417965973 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (61110417965973 / 10000000000000000 : ℚ)) + (r' := (61110417965973 / 39062500000000 : ℚ)) + (U := (-(50976580114456355348677 / 10000000000000000000000 : ℚ))) + (U' := (4475194309543644651323 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (14825913 / 200000000000 : ℚ)) + (s := (29232456748473 / 5000000000000000 : ℚ)) + (q := (61110417965973 / 10000000000000000 : ℚ)) + (U := (-(50976580114456355348677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_2 : Uω (aρ 2) (bρ 2) (14825913 / 200000000000 : ℝ) ≤ @@ -2021,25 +1760,21 @@ lemma U_4_2 : have hlg : Real.log (145979244790401 / 20000000000000000 : ℝ) ≤ (-(1968009239129451754533 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (145979244790401 / 20000000000000000 : ℝ) = - (145979244790401 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145979244790401 / 78125000000000 : ℚ)) - (U := (250061737830548245467 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (145979244790401 / 78125000000000 : ℝ) ≤ - (250061737830548245467 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58454309845401 / 10000000000000000 : ℝ)) (q := - (145979244790401 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145979244790401 / 20000000000000000 : ℚ)) + (r' := (145979244790401 / 78125000000000 : ℚ)) + (U := (-(1968009239129451754533 / 400000000000000000000 : ℚ))) + (U' := (250061737830548245467 / 400000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (14825913 / 200000000000 : ℚ)) + (s := (58454309845401 / 10000000000000000 : ℚ)) + (q := (145979244790401 / 20000000000000000 : ℚ)) + (U := (-(1968009239129451754533 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_3 : Uω (aρ 3) (bρ 3) (14825913 / 200000000000 : ℝ) ≤ @@ -2047,25 +1782,21 @@ lemma U_4_3 : have hlg : Real.log (193295065059677 / 20000000000000000 : ℝ) ≤ (-(46392696947832317425569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (193295065059677 / 20000000000000000 : ℝ) = - (193295065059677 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (193295065059677 / 156250000000000 : ℚ)) - (U := (2127605673167682574431 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (193295065059677 / 156250000000000 : ℝ) ≤ - (2127605673167682574431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58374023764677 / 10000000000000000 : ℝ)) (q := - (193295065059677 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (193295065059677 / 20000000000000000 : ℚ)) + (r' := (193295065059677 / 156250000000000 : ℚ)) + (U := (-(46392696947832317425569 / 10000000000000000000000 : ℚ))) + (U' := (2127605673167682574431 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (14825913 / 200000000000 : ℚ)) + (s := (58374023764677 / 10000000000000000 : ℚ)) + (q := (193295065059677 / 20000000000000000 : ℚ)) + (U := (-(46392696947832317425569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_4 : Uω (aρ 4) (bρ 4) (14825913 / 200000000000 : ℝ) ≤ @@ -2073,24 +1804,21 @@ lemma U_4_4 : have hlg : Real.log (54268212388099 / 4000000000000000 : ℝ) ≤ (-(21500554949887790778621 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (54268212388099 / 4000000000000000 : ℝ) = (54268212388099 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54268212388099 / 31250000000000 : ℚ)) - (U := (2759596360612209221379 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (54268212388099 / 31250000000000 : ℝ) ≤ - (2759596360612209221379 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11625167916099 / 2000000000000000 : ℝ)) (q := - (54268212388099 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54268212388099 / 4000000000000000 : ℚ)) + (r' := (54268212388099 / 31250000000000 : ℚ)) + (U := (-(21500554949887790778621 / 5000000000000000000000 : ℚ))) + (U' := (2759596360612209221379 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (14825913 / 200000000000 : ℚ)) + (s := (11625167916099 / 2000000000000000 : ℚ)) + (q := (54268212388099 / 4000000000000000 : ℚ)) + (U := (-(21500554949887790778621 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_5 : Uω (aρ 5) (bρ 5) (14825913 / 200000000000 : ℝ) ≤ @@ -2098,25 +1826,21 @@ lemma U_4_5 : have hlg : Real.log (194493230401519 / 10000000000000000 : ℝ) ≤ (-(9849857532743252544909 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (194493230401519 / 10000000000000000 : ℝ) = - (194493230401519 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194493230401519 / 156250000000000 : ℚ)) - (U := (547350171756747455091 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194493230401519 / 156250000000000 : ℝ) ≤ - (547350171756747455091 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28790659554019 / 5000000000000000 : ℝ)) (q := - (194493230401519 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194493230401519 / 10000000000000000 : ℚ)) + (r' := (194493230401519 / 156250000000000 : ℚ)) + (U := (-(9849857532743252544909 / 2500000000000000000000 : ℚ))) + (U' := (547350171756747455091 / 2500000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (14825913 / 200000000000 : ℚ)) + (s := (28790659554019 / 5000000000000000 : ℚ)) + (q := (194493230401519 / 10000000000000000 : ℚ)) + (U := (-(9849857532743252544909 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_6 : Uω (aρ 6) (bρ 6) (14825913 / 200000000000 : ℝ) ≤ @@ -2124,25 +1848,21 @@ lemma U_4_6 : have hlg : Real.log (277619584033359 / 10000000000000000 : ℝ) ≤ (-(17920442983008148696533 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (277619584033359 / 10000000000000000 : ℝ) = - (277619584033359 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (277619584033359 / 156250000000000 : ℚ)) - (U := (2873972425991851303467 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (277619584033359 / 156250000000000 : ℝ) ≤ - (2873972425991851303467 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28296825615859 / 5000000000000000 : ℝ)) (q := - (277619584033359 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (277619584033359 / 10000000000000000 : ℚ)) + (r' := (277619584033359 / 156250000000000 : ℚ)) + (U := (-(17920442983008148696533 / 5000000000000000000000 : ℚ))) + (U' := (2873972425991851303467 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (14825913 / 200000000000 : ℚ)) + (s := (28296825615859 / 5000000000000000 : ℚ)) + (q := (277619584033359 / 10000000000000000 : ℚ)) + (U := (-(17920442983008148696533 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_7 : Uω (aρ 7) (bρ 7) (14825913 / 200000000000 : ℝ) ≤ @@ -2150,25 +1870,21 @@ lemma U_4_7 : have hlg : Real.log (194329300239091 / 5000000000000000 : ℝ) ≤ (-(8119097615340380036387 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (194329300239091 / 5000000000000000 : ℝ) = - (194329300239091 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194329300239091 / 156250000000000 : ℚ)) - (U := (545242138409619963613 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194329300239091 / 156250000000000 : ℝ) ≤ - (545242138409619963613 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13752575840341 / 2500000000000000 : ℝ)) (q := - (194329300239091 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194329300239091 / 5000000000000000 : ℚ)) + (r' := (194329300239091 / 156250000000000 : ℚ)) + (U := (-(8119097615340380036387 / 2500000000000000000000 : ℚ))) + (U' := (545242138409619963613 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (14825913 / 200000000000 : ℚ)) + (s := (13752575840341 / 2500000000000000 : ℚ)) + (q := (194329300239091 / 5000000000000000 : ℚ)) + (U := (-(8119097615340380036387 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_8 : Uω (aρ 8) (bρ 8) (14825913 / 200000000000 : ℝ) ≤ @@ -2176,25 +1892,21 @@ lemma U_4_8 : have hlg : Real.log (264633547803489 / 5000000000000000 : ℝ) ≤ (-(2938847159611171861641 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (264633547803489 / 5000000000000000 : ℝ) = - (264633547803489 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (264633547803489 / 156250000000000 : ℚ)) - (U := (526888741888828138359 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (264633547803489 / 156250000000000 : ℝ) ≤ - (526888741888828138359 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13171410569739 / 2500000000000000 : ℝ)) (q := - (264633547803489 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (264633547803489 / 5000000000000000 : ℚ)) + (r' := (264633547803489 / 156250000000000 : ℚ)) + (U := (-(2938847159611171861641 / 1000000000000000000000 : ℚ))) + (U' := (526888741888828138359 / 1000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (14825913 / 200000000000 : ℚ)) + (s := (13171410569739 / 2500000000000000 : ℚ)) + (q := (264633547803489 / 5000000000000000 : ℚ)) + (U := (-(2938847159611171861641 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_9 : Uω (aρ 9) (bρ 9) (14825913 / 200000000000 : ℝ) ≤ @@ -2202,25 +1914,21 @@ lemma U_4_9 : have hlg : Real.log (1396306758365197 / 20000000000000000 : ℝ) ≤ (-(26619015513642536754779 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1396306758365197 / 20000000000000000 : ℝ) = - (1396306758365197 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1396306758365197 / 1250000000000000 : ℚ)) - (U := (1106871698357463245221 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1396306758365197 / 1250000000000000 : ℝ) ≤ - (1106871698357463245221 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (49492581070197 / 10000000000000000 : ℝ)) (q := - (1396306758365197 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1396306758365197 / 20000000000000000 : ℚ)) + (r' := (1396306758365197 / 1250000000000000 : ℚ)) + (U := (-(26619015513642536754779 / 10000000000000000000000 : ℚ))) + (U' := (1106871698357463245221 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (14825913 / 200000000000 : ℚ)) + (s := (49492581070197 / 10000000000000000 : ℚ)) + (q := (1396306758365197 / 20000000000000000 : ℚ)) + (U := (-(26619015513642536754779 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_10 : Uω (aρ 10) (bρ 10) (14825913 / 200000000000 : ℝ) ≤ @@ -2228,26 +1936,21 @@ lemma U_4_10 : have hlg : Real.log (890352333463911 / 10000000000000000 : ℝ) ≤ (-(24187231062536165434337 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (890352333463911 / 10000000000000000 : ℝ) = - (890352333463911 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (890352333463911 / 625000000000000 : ℚ)) - (U := (3538656149463834565663 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (890352333463911 / 625000000000000 : ℝ) ≤ - (3538656149463834565663 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (22665728068911 / 5000000000000000 : ℝ)) (q := - (890352333463911 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (890352333463911 / 10000000000000000 : ℚ)) + (r' := (890352333463911 / 625000000000000 : ℚ)) + (U := (-(24187231062536165434337 / 10000000000000000000000 : ℚ))) + (U' := (3538656149463834565663 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (14825913 / 200000000000 : ℚ)) + (s := (22665728068911 / 5000000000000000 : ℚ)) + (q := (890352333463911 / 10000000000000000 : ℚ)) + (U := (-(24187231062536165434337 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_11 : Uω (aρ 11) (bρ 11) (14825913 / 200000000000 : ℝ) ≤ @@ -2255,26 +1958,21 @@ lemma U_4_11 : have hlg : Real.log (2193982353625503 / 20000000000000000 : ℝ) ≤ (-(22100139537083282243419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2193982353625503 / 20000000000000000 : ℝ) = - (2193982353625503 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2193982353625503 / 1250000000000000 : ℚ)) - (U := (5625747674916717756581 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2193982353625503 / 1250000000000000 : ℝ) ≤ - (5625747674916717756581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (40132516630503 / 10000000000000000 : ℝ)) (q := - (2193982353625503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2193982353625503 / 20000000000000000 : ℚ)) + (r' := (2193982353625503 / 1250000000000000 : ℚ)) + (U := (-(22100139537083282243419 / 10000000000000000000000 : ℚ))) + (U' := (5625747674916717756581 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (14825913 / 200000000000 : ℚ)) + (s := (40132516630503 / 10000000000000000 : ℚ)) + (q := (2193982353625503 / 20000000000000000 : ℚ)) + (U := (-(22100139537083282243419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_12 : Uω (aρ 12) (bρ 12) (14825913 / 200000000000 : ℝ) ≤ @@ -2282,26 +1980,21 @@ lemma U_4_12 : have hlg : Real.log (2611393736553067 / 20000000000000000 : ℝ) ≤ (-(20358481952867747024019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2611393736553067 / 20000000000000000 : ℝ) = - (2611393736553067 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2611393736553067 / 2500000000000000 : ℚ)) - (U := (435933456132252975981 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2611393736553067 / 2500000000000000 : ℝ) ≤ - (435933456132252975981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (33843802873067 / 10000000000000000 : ℝ)) (q := - (2611393736553067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [aρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2611393736553067 / 20000000000000000 : ℚ)) + (r' := (2611393736553067 / 2500000000000000 : ℚ)) + (U := (-(20358481952867747024019 / 10000000000000000000000 : ℚ))) + (U' := (435933456132252975981 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (14825913 / 200000000000 : ℚ)) + (s := (33843802873067 / 10000000000000000 : ℚ)) + (q := (2611393736553067 / 20000000000000000 : ℚ)) + (U := (-(20358481952867747024019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_13 : Uω (aρ 13) (bρ 13) (14825913 / 200000000000 : ℝ) ≤ @@ -2309,25 +2002,21 @@ lemma U_4_13 : have hlg : Real.log (750827230859117 / 5000000000000000 : ℝ) ≤ (-(1896017617456667321 / 1000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (750827230859117 / 5000000000000000 : ℝ) = - (750827230859117 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (750827230859117 / 625000000000000 : ℚ)) - (U := (183423923443332679 / 1000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (750827230859117 / 625000000000000 : ℝ) ≤ - (183423923443332679 / 1000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6594312040367 / 2500000000000000 : ℝ)) (q := - (750827230859117 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [aρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (750827230859117 / 5000000000000000 : ℚ)) + (r' := (750827230859117 / 625000000000000 : ℚ)) + (U := (-(1896017617456667321 / 1000000000000000000 : ℚ))) + (U' := (183423923443332679 / 1000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (14825913 / 200000000000 : ℚ)) + (s := (6594312040367 / 2500000000000000 : ℚ)) + (q := (750827230859117 / 5000000000000000 : ℚ)) + (U := (-(1896017617456667321 / 1000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_14 : Uω (aρ 14) (bρ 14) (14825913 / 200000000000 : ℝ) ≤ @@ -2335,26 +2024,21 @@ lemma U_4_14 : have hlg : Real.log (3338220089219641 / 20000000000000000 : ℝ) ≤ (-(8951472576252204766649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3338220089219641 / 20000000000000000 : ℝ) = - (3338220089219641 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3338220089219641 / 2500000000000000 : ℚ)) - (U := (1445735128247795233351 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3338220089219641 / 2500000000000000 : ℝ) ≤ - (1445735128247795233351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (17361128899641 / 10000000000000000 : ℝ)) (q := - (3338220089219641 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [aρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3338220089219641 / 20000000000000000 : ℚ)) + (r' := (3338220089219641 / 2500000000000000 : ℚ)) + (U := (-(8951472576252204766649 / 5000000000000000000000 : ℚ))) + (U' := (1445735128247795233351 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 14) (t := (14825913 / 200000000000 : ℚ)) + (s := (17361128899641 / 10000000000000000 : ℚ)) + (q := (3338220089219641 / 20000000000000000 : ℚ)) + (U := (-(8951472576252204766649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_4_15 : Uω (aρ 15) (bρ 15) (14825913 / 200000000000 : ℝ) ≤ @@ -2457,24 +2141,21 @@ lemma U_5_1 : have hlg : Real.log (24425192541173 / 4000000000000000 : ℝ) ≤ (-(50984345571698067906027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (24425192541173 / 4000000000000000 : ℝ) = (24425192541173 / 15625000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24425192541173 / 15625000000000 : ℚ)) - (U := (4467428852301932093973 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (24425192541173 / 15625000000000 : ℝ) ≤ - (4467428852301932093973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11683084346173 / 2000000000000000 : ℝ)) (q := - (24425192541173 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24425192541173 / 4000000000000000 : ℚ)) + (r' := (24425192541173 / 15625000000000 : ℚ)) + (U := (-(50984345571698067906027 / 10000000000000000000000 : ℚ))) + (U' := (4467428852301932093973 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (78667711 / 1000000000000 : ℚ)) + (s := (11683084346173 / 2000000000000000 : ℚ)) + (q := (24425192541173 / 4000000000000000 : ℚ)) + (U := (-(50984345571698067906027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_2 : Uω (aρ 2) (bρ 2) (78667711 / 1000000000000 : ℝ) ≤ @@ -2482,25 +2163,21 @@ lemma U_5_2 : have hlg : Real.log (145865890759319 / 20000000000000000 : ℝ) ≤ (-(24603999536613700227217 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (145865890759319 / 20000000000000000 : ℝ) = - (145865890759319 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145865890759319 / 78125000000000 : ℚ)) - (U := (3121887675386299772783 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (145865890759319 / 78125000000000 : ℝ) ≤ - (3121887675386299772783 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58386337274319 / 10000000000000000 : ℝ)) (q := - (145865890759319 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145865890759319 / 20000000000000000 : ℚ)) + (r' := (145865890759319 / 78125000000000 : ℚ)) + (U := (-(24603999536613700227217 / 5000000000000000000000 : ℚ))) + (U' := (3121887675386299772783 / 5000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (78667711 / 1000000000000 : ℚ)) + (s := (58386337274319 / 10000000000000000 : ℚ)) + (q := (145865890759319 / 20000000000000000 : ℚ)) + (U := (-(24603999536613700227217 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_3 : Uω (aρ 3) (bρ 3) (78667711 / 1000000000000 : ℝ) ≤ @@ -2508,25 +2185,21 @@ lemma U_5_3 : have hlg : Real.log (193144715793361 / 20000000000000000 : ℝ) ≤ (-(11600119550061847085141 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (193144715793361 / 20000000000000000 : ℝ) = - (193144715793361 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (193144715793361 / 156250000000000 : ℚ)) - (U := (529956105188152914859 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (193144715793361 / 156250000000000 : ℝ) ≤ - (529956105188152914859 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58269055958361 / 10000000000000000 : ℝ)) (q := - (193144715793361 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (193144715793361 / 20000000000000000 : ℚ)) + (r' := (193144715793361 / 156250000000000 : ℚ)) + (U := (-(11600119550061847085141 / 2500000000000000000000 : ℚ))) + (U' := (529956105188152914859 / 2500000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (78667711 / 1000000000000 : ℚ)) + (s := (58269055958361 / 10000000000000000 : ℚ)) + (q := (193144715793361 / 20000000000000000 : ℚ)) + (U := (-(11600119550061847085141 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_4 : Uω (aρ 4) (bρ 4) (78667711 / 1000000000000 : ℝ) ≤ @@ -2534,25 +2207,21 @@ lemma U_5_4 : have hlg : Real.log (271128992465947 / 20000000000000000 : ℝ) ≤ (-(10752232140308635873551 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (271128992465947 / 20000000000000000 : ℝ) = - (271128992465947 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (271128992465947 / 156250000000000 : ℚ)) - (U := (1377843514941364126449 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (271128992465947 / 156250000000000 : ℝ) ≤ - (1377843514941364126449 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (57959151565947 / 10000000000000000 : ℝ)) (q := - (271128992465947 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (271128992465947 / 20000000000000000 : ℚ)) + (r' := (271128992465947 / 156250000000000 : ℚ)) + (U := (-(10752232140308635873551 / 2500000000000000000000 : ℚ))) + (U' := (1377843514941364126449 / 2500000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (78667711 / 1000000000000 : ℚ)) + (s := (57959151565947 / 10000000000000000 : ℚ)) + (q := (271128992465947 / 20000000000000000 : ℚ)) + (U := (-(10752232140308635873551 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_5 : Uω (aρ 5) (bρ 5) (78667711 / 1000000000000 : ℝ) ≤ @@ -2560,25 +2229,21 @@ lemma U_5_5 : have hlg : Real.log (388679312495423 / 20000000000000000 : ℝ) ≤ (-(1231479042758063468317 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (388679312495423 / 20000000000000000 : ℝ) = - (388679312495423 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (388679312495423 / 312500000000000 : ℚ)) - (U := (68171920304436531683 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (388679312495423 / 312500000000000 : ℝ) ≤ - (68171920304436531683 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (57319552260423 / 10000000000000000 : ℝ)) (q := - (388679312495423 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (388679312495423 / 20000000000000000 : ℚ)) + (r' := (388679312495423 / 312500000000000 : ℚ)) + (U := (-(1231479042758063468317 / 312500000000000000000 : ℚ))) + (U' := (68171920304436531683 / 312500000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (78667711 / 1000000000000 : ℚ)) + (s := (57319552260423 / 10000000000000000 : ℚ)) + (q := (388679312495423 / 20000000000000000 : ℚ)) + (U := (-(1231479042758063468317 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_6 : Uω (aρ 6) (bρ 6) (78667711 / 1000000000000 : ℝ) ≤ @@ -2586,24 +2251,21 @@ lemma U_5_6 : have hlg : Real.log (22191701086949 / 800000000000000 : ℝ) ≤ (-(17924466660160898289283 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (22191701086949 / 800000000000000 : ℝ) = (22191701086949 / 12500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22191701086949 / 12500000000000 : ℚ)) - (U := (2869948748839101710717 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (22191701086949 / 12500000000000 : ℝ) ≤ - (2869948748839101710717 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2247695671949 / 400000000000000 : ℝ)) (q := - (22191701086949 / 800000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22191701086949 / 800000000000000 : ℚ)) + (r' := (22191701086949 / 12500000000000 : ℚ)) + (U := (-(17924466660160898289283 / 5000000000000000000000 : ℚ))) + (U' := (2869948748839101710717 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (78667711 / 1000000000000 : ℚ)) + (s := (2247695671949 / 400000000000000 : ℚ)) + (q := (22191701086949 / 800000000000000 : ℚ)) + (U := (-(17924466660160898289283 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_7 : Uω (aρ 7) (bρ 7) (78667711 / 1000000000000 : ℝ) ≤ @@ -2611,25 +2273,21 @@ lemma U_5_7 : have hlg : Real.log (776672699289057 / 20000000000000000 : ℝ) ≤ (-(32484685260499643578059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (776672699289057 / 20000000000000000 : ℝ) = - (776672699289057 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (776672699289057 / 625000000000000 : ℚ)) - (U := (2172673754500356421941 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (776672699289057 / 625000000000000 : ℝ) ≤ - (2172673754500356421941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (54411183154057 / 10000000000000000 : ℝ)) (q := - (776672699289057 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (776672699289057 / 20000000000000000 : ℚ)) + (r' := (776672699289057 / 625000000000000 : ℚ)) + (U := (-(32484685260499643578059 / 10000000000000000000000 : ℚ))) + (U' := (2172673754500356421941 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (78667711 / 1000000000000 : ℚ)) + (s := (54411183154057 / 10000000000000000 : ℚ)) + (q := (776672699289057 / 20000000000000000 : ℚ)) + (U := (-(32484685260499643578059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_8 : Uω (aρ 8) (bρ 8) (78667711 / 1000000000000 : ℝ) ≤ @@ -2637,25 +2295,21 @@ lemma U_5_8 : have hlg : Real.log (1057615185486693 / 20000000000000000 : ℝ) ≤ (-(29397157238015419786121 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1057615185486693 / 20000000000000000 : ℝ) = - (1057615185486693 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1057615185486693 / 625000000000000 : ℚ)) - (U := (5260201776984580213879 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1057615185486693 / 625000000000000 : ℝ) ≤ - (5260201776984580213879 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (51812018011693 / 10000000000000000 : ℝ)) (q := - (1057615185486693 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1057615185486693 / 20000000000000000 : ℚ)) + (r' := (1057615185486693 / 625000000000000 : ℚ)) + (U := (-(29397157238015419786121 / 10000000000000000000000 : ℚ))) + (U' := (5260201776984580213879 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (78667711 / 1000000000000 : ℚ)) + (s := (51812018011693 / 10000000000000000 : ℚ)) + (q := (1057615185486693 / 20000000000000000 : ℚ)) + (U := (-(29397157238015419786121 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_9 : Uω (aρ 9) (bρ 9) (78667711 / 1000000000000 : ℝ) ≤ @@ -2663,25 +2317,21 @@ lemma U_5_9 : have hlg : Real.log (348752663432181 / 5000000000000000 : ℝ) ≤ (-(13314151100942602912333 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (348752663432181 / 5000000000000000 : ℝ) = - (348752663432181 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (348752663432181 / 312500000000000 : ℚ)) - (U := (548792505057397087667 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (348752663432181 / 312500000000000 : ℝ) ≤ - (548792505057397087667 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (12060464473431 / 2500000000000000 : ℝ)) (q := - (348752663432181 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (348752663432181 / 5000000000000000 : ℚ)) + (r' := (348752663432181 / 312500000000000 : ℚ)) + (U := (-(13314151100942602912333 / 5000000000000000000000 : ℚ))) + (U' := (548792505057397087667 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (78667711 / 1000000000000 : ℚ)) + (s := (12060464473431 / 2500000000000000 : ℚ)) + (q := (348752663432181 / 5000000000000000 : ℚ)) + (U := (-(13314151100942602912333 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_10 : Uω (aρ 10) (bρ 10) (78667711 / 1000000000000 : ℝ) ≤ @@ -2689,25 +2339,21 @@ lemma U_5_10 : have hlg : Real.log (177888739125561 / 2000000000000000 : ℝ) ≤ (-(12098720823673483752803 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (177888739125561 / 2000000000000000 : ℝ) = - (177888739125561 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (177888739125561 / 125000000000000 : ℚ)) - (U := (1764222782326516247197 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (177888739125561 / 125000000000000 : ℝ) ≤ - (1764222782326516247197 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4355956192561 / 1000000000000000 : ℝ)) (q := - (177888739125561 / 2000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [aρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (177888739125561 / 2000000000000000 : ℚ)) + (r' := (177888739125561 / 125000000000000 : ℚ)) + (U := (-(12098720823673483752803 / 5000000000000000000000 : ℚ))) + (U' := (1764222782326516247197 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (78667711 / 1000000000000 : ℚ)) + (s := (4355956192561 / 1000000000000000 : ℚ)) + (q := (177888739125561 / 2000000000000000 : ℚ)) + (U := (-(12098720823673483752803 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_11 : Uω (aρ 11) (bρ 11) (78667711 / 1000000000000 : ℝ) ≤ @@ -2715,26 +2361,21 @@ lemma U_5_11 : have hlg : Real.log (2191422685824679 / 20000000000000000 : ℝ) ≤ (-(22111813113724319814737 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2191422685824679 / 20000000000000000 : ℝ) = - (2191422685824679 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2191422685824679 / 1250000000000000 : ℚ)) - (U := (5614074098275680185263 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2191422685824679 / 1250000000000000 : ℝ) ≤ - (5614074098275680185263 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (37618230289679 / 10000000000000000 : ℝ)) (q := - (2191422685824679 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2191422685824679 / 20000000000000000 : ℚ)) + (r' := (2191422685824679 / 1250000000000000 : ℚ)) + (U := (-(22111813113724319814737 / 10000000000000000000000 : ℚ))) + (U' := (5614074098275680185263 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (78667711 / 1000000000000 : ℚ)) + (s := (37618230289679 / 10000000000000000 : ℚ)) + (q := (2191422685824679 / 20000000000000000 : ℚ)) + (U := (-(22111813113724319814737 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_12 : Uω (aρ 12) (bρ 12) (78667711 / 1000000000000 : ℝ) ≤ @@ -2742,26 +2383,21 @@ lemma U_5_12 : have hlg : Real.log (2607694933038421 / 20000000000000000 : ℝ) ≤ (-(20372656090798980590323 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2607694933038421 / 20000000000000000 : ℝ) = - (2607694933038421 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2607694933038421 / 2500000000000000 : ℚ)) - (U := (421759318201019409677 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2607694933038421 / 2500000000000000 : ℝ) ≤ - (421759318201019409677 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (30190380818421 / 10000000000000000 : ℝ)) (q := - (2607694933038421 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [aρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2607694933038421 / 20000000000000000 : ℚ)) + (r' := (2607694933038421 / 2500000000000000 : ℚ)) + (U := (-(20372656090798980590323 / 10000000000000000000000 : ℚ))) + (U' := (421759318201019409677 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (78667711 / 1000000000000 : ℚ)) + (s := (30190380818421 / 10000000000000000 : ℚ)) + (q := (2607694933038421 / 20000000000000000 : ℚ)) + (U := (-(20372656090798980590323 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_13 : Uω (aρ 13) (bρ 13) (78667711 / 1000000000000 : ℝ) ≤ @@ -2769,26 +2405,21 @@ lemma U_5_13 : have hlg : Real.log (2997515551401257 / 20000000000000000 : ℝ) ≤ (-(74138612372821309739 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2997515551401257 / 20000000000000000 : ℝ) = - (2997515551401257 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2997515551401257 / 2500000000000000 : ℚ)) - (U := (7089572818584940261 / 39062500000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2997515551401257 / 2500000000000000 : ℝ) ≤ - (7089572818584940261 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (20629257586257 / 10000000000000000 : ℝ)) (q := - (2997515551401257 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [aρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2997515551401257 / 20000000000000000 : ℚ)) + (r' := (2997515551401257 / 2500000000000000 : ℚ)) + (U := (-(74138612372821309739 / 39062500000000000000 : ℚ))) + (U' := (7089572818584940261 / 39062500000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 13) (t := (78667711 / 1000000000000 : ℚ)) + (s := (20629257586257 / 10000000000000000 : ℚ)) + (q := (2997515551401257 / 20000000000000000 : ℚ)) + (U := (-(74138612372821309739 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_5_14 : Uω (aρ 14) (bρ 14) (78667711 / 1000000000000 : ℝ) ≤ @@ -2895,24 +2526,21 @@ lemma U_6_1 : have hlg : Real.log (12197651654253 / 2000000000000000 : ℝ) ≤ (-(10199318023215378615661 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (12197651654253 / 2000000000000000 : ℝ) = (12197651654253 / 7812500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12197651654253 / 7812500000000 : ℚ)) - (U := (891036861584621384339 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12197651654253 / 7812500000000 : ℝ) ≤ - (891036861584621384339 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (5833745484753 / 1000000000000000 : ℝ)) (q := - (12197651654253 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12197651654253 / 2000000000000000 : ℚ)) + (r' := (12197651654253 / 7812500000000 : ℚ)) + (U := (-(10199318023215378615661 / 2000000000000000000000 : ℚ))) + (U' := (891036861584621384339 / 2000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (85815639 / 1000000000000 : ℚ)) + (s := (5833745484753 / 1000000000000000 : ℚ)) + (q := (12197651654253 / 2000000000000000 : ℚ)) + (U := (-(10199318023215378615661 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_2 : Uω (aρ 2) (bρ 2) (85815639 / 1000000000000 : ℝ) ≤ @@ -2920,23 +2548,21 @@ lemma U_6_2 : have hlg : Real.log (7284363017877 / 1000000000000000 : ℝ) ≤ (-(49220252785694328798381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (7284363017877 / 1000000000000000 : ℝ) = (7284363017877 / 3906250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7284363017877 / 3906250000000 : ℚ)) - (U := (6231521638305671201619 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7284363017877 / 3906250000000 : ℝ) ≤ - (6231521638305671201619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2913959307627 / 500000000000000 : ℝ)) (q := - (7284363017877 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7284363017877 / 1000000000000000 : ℚ)) + (r' := (7284363017877 / 3906250000000 : ℚ)) + (U := (-(49220252785694328798381 / 10000000000000000000000 : ℚ))) + (U' := (6231521638305671201619 / 10000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (85815639 / 1000000000000 : ℚ)) + (s := (2913959307627 / 500000000000000 : ℚ)) + (q := (7284363017877 / 1000000000000000 : ℚ)) + (U := (-(49220252785694328798381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_3 : Uω (aρ 3) (bρ 3) (85815639 / 1000000000000 : ℝ) ≤ @@ -2944,24 +2570,21 @@ lemma U_6_3 : have hlg : Real.log (38581518296581 / 4000000000000000 : ℝ) ≤ (-(23206381385399735792023 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (38581518296581 / 4000000000000000 : ℝ) = (38581518296581 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38581518296581 / 31250000000000 : ℚ)) - (U := (1053769925100264207977 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (38581518296581 / 31250000000000 : ℝ) ≤ - (1053769925100264207977 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11620682185581 / 2000000000000000 : ℝ)) (q := - (38581518296581 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38581518296581 / 4000000000000000 : ℚ)) + (r' := (38581518296581 / 31250000000000 : ℚ)) + (U := (-(23206381385399735792023 / 5000000000000000000000 : ℚ))) + (U' := (1053769925100264207977 / 5000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (85815639 / 1000000000000 : ℚ)) + (s := (11620682185581 / 2000000000000000 : ℚ)) + (q := (38581518296581 / 4000000000000000 : ℚ)) + (U := (-(23206381385399735792023 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_4 : Uω (aρ 4) (bρ 4) (85815639 / 1000000000000 : ℝ) ≤ @@ -2969,25 +2592,21 @@ lemma U_6_4 : have hlg : Real.log (135397031276029 / 10000000000000000 : ℝ) ≤ (-(21510644677510011539679 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (135397031276029 / 10000000000000000 : ℝ) = - (135397031276029 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (135397031276029 / 78125000000000 : ℚ)) - (U := (2749506632989988460321 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (135397031276029 / 78125000000000 : ℝ) ≤ - (2749506632989988460321 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28847850466029 / 5000000000000000 : ℝ)) (q := - (135397031276029 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (135397031276029 / 10000000000000000 : ℚ)) + (r' := (135397031276029 / 78125000000000 : ℚ)) + (U := (-(21510644677510011539679 / 5000000000000000000000 : ℚ))) + (U' := (2749506632989988460321 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (85815639 / 1000000000000 : ℚ)) + (s := (28847850466029 / 5000000000000000 : ℚ)) + (q := (135397031276029 / 10000000000000000 : ℚ)) + (U := (-(21510644677510011539679 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_5 : Uω (aρ 5) (bρ 5) (85815639 / 1000000000000 : ℝ) ≤ @@ -2995,25 +2614,21 @@ lemma U_6_5 : have hlg : Real.log (194096580910869 / 10000000000000000 : ℝ) ≤ (-(315358759639002277023 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (194096580910869 / 10000000000000000 : ℝ) = - (194096580910869 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194096580910869 / 156250000000000 : ℚ)) - (U := (17351886904997722977 / 80000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194096580910869 / 156250000000000 : ℝ) ≤ - (17351886904997722977 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28452440433369 / 5000000000000000 : ℝ)) (q := - (194096580910869 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194096580910869 / 10000000000000000 : ℚ)) + (r' := (194096580910869 / 156250000000000 : ℚ)) + (U := (-(315358759639002277023 / 80000000000000000000 : ℚ))) + (U' := (17351886904997722977 / 80000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (85815639 / 1000000000000 : ℚ)) + (s := (28452440433369 / 5000000000000000 : ℚ)) + (q := (194096580910869 / 10000000000000000 : ℚ)) + (U := (-(315358759639002277023 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_6 : Uω (aρ 6) (bρ 6) (85815639 / 1000000000000 : ℝ) ≤ @@ -3021,24 +2636,21 @@ lemma U_6_6 : have hlg : Real.log (11081664629919 / 400000000000000 : ℝ) ≤ (-(35861726381563634540717 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (11081664629919 / 400000000000000 : ℝ) = (11081664629919 / 6250000000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11081664629919 / 6250000000000 : ℚ)) - (U := (5727104436436365459283 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (11081664629919 / 6250000000000 : ℝ) ≤ - (5727104436436365459283 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1111091508019 / 200000000000000 : ℝ)) (q := - (11081664629919 / 400000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11081664629919 / 400000000000000 : ℚ)) + (r' := (11081664629919 / 6250000000000 : ℚ)) + (U := (-(35861726381563634540717 / 10000000000000000000000 : ℚ))) + (U' := (5727104436436365459283 / 10000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (85815639 / 1000000000000 : ℚ)) + (s := (1111091508019 / 200000000000000 : ℚ)) + (q := (11081664629919 / 400000000000000 : ℚ)) + (U := (-(35861726381563634540717 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_7 : Uω (aρ 7) (bρ 7) (85815639 / 1000000000000 : ℝ) ≤ @@ -3046,25 +2658,21 @@ lemma U_6_7 : have hlg : Real.log (775644021694503 / 20000000000000000 : ℝ) ≤ (-(32497938712340042706679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (775644021694503 / 20000000000000000 : ℝ) = - (775644021694503 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (775644021694503 / 625000000000000 : ℚ)) - (U := (2159420302659957293321 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (775644021694503 / 625000000000000 : ℝ) ≤ - (2159420302659957293321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (53453984839503 / 10000000000000000 : ℝ)) (q := - (775644021694503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (775644021694503 / 20000000000000000 : ℚ)) + (r' := (775644021694503 / 625000000000000 : ℚ)) + (U := (-(32497938712340042706679 / 10000000000000000000000 : ℚ))) + (U' := (2159420302659957293321 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (85815639 / 1000000000000 : ℚ)) + (s := (53453984839503 / 10000000000000000 : ℚ)) + (q := (775644021694503 / 20000000000000000 : ℚ)) + (U := (-(32497938712340042706679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_8 : Uω (aρ 8) (bρ 8) (85815639 / 1000000000000 : ℝ) ≤ @@ -3072,25 +2680,21 @@ lemma U_6_8 : have hlg : Real.log (1056137066353147 / 20000000000000000 : ℝ) ≤ (-(29411142977102807541847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1056137066353147 / 20000000000000000 : ℝ) = - (1056137066353147 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1056137066353147 / 625000000000000 : ℚ)) - (U := (5246216037897192458153 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1056137066353147 / 625000000000000 : ℝ) ≤ - (5246216037897192458153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (50405378158147 / 10000000000000000 : ℝ)) (q := - (1056137066353147 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1056137066353147 / 20000000000000000 : ℚ)) + (r' := (1056137066353147 / 625000000000000 : ℚ)) + (U := (-(29411142977102807541847 / 10000000000000000000000 : ℚ))) + (U' := (5246216037897192458153 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (85815639 / 1000000000000 : ℚ)) + (s := (50405378158147 / 10000000000000000 : ℚ)) + (q := (1056137066353147 / 20000000000000000 : ℚ)) + (U := (-(29411142977102807541847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_9 : Uω (aρ 9) (bρ 9) (85815639 / 1000000000000 : ℝ) ≤ @@ -3098,25 +2702,21 @@ lemma U_6_9 : have hlg : Real.log (1392900669621853 / 20000000000000000 : ℝ) ≤ (-(6660859717657794390429 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1392900669621853 / 20000000000000000 : ℝ) = - (1392900669621853 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1392900669621853 / 1250000000000000 : ℚ)) - (U := (270612085342205609571 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1392900669621853 / 1250000000000000 : ℝ) ≤ - (270612085342205609571 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (46203353066853 / 10000000000000000 : ℝ)) (q := - (1392900669621853 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1392900669621853 / 20000000000000000 : ℚ)) + (r' := (1392900669621853 / 1250000000000000 : ℚ)) + (U := (-(6660859717657794390429 / 2500000000000000000000 : ℚ))) + (U' := (270612085342205609571 / 2500000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (85815639 / 1000000000000 : ℚ)) + (s := (46203353066853 / 10000000000000000 : ℚ)) + (q := (1392900669621853 / 20000000000000000 : ℚ)) + (U := (-(6660859717657794390429 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_10 : Uω (aρ 10) (bρ 10) (85815639 / 1000000000000 : ℝ) ≤ @@ -3124,26 +2724,21 @@ lemma U_6_10 : have hlg : Real.log (887934335277677 / 10000000000000000 : ℝ) ≤ (-(4842885154875601165287 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (887934335277677 / 10000000000000000 : ℝ) = - (887934335277677 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (887934335277677 / 625000000000000 : ℚ)) - (U := (702292287524398834713 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (887934335277677 / 625000000000000 : ℝ) ≤ - (702292287524398834713 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (20306160252677 / 5000000000000000 : ℝ)) (q := - (887934335277677 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (887934335277677 / 10000000000000000 : ℚ)) + (r' := (887934335277677 / 625000000000000 : ℚ)) + (U := (-(4842885154875601165287 / 2000000000000000000000 : ℚ))) + (U' := (702292287524398834713 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (85815639 / 1000000000000 : ℚ)) + (s := (20306160252677 / 5000000000000000 : ℚ)) + (q := (887934335277677 / 10000000000000000 : ℚ)) + (U := (-(4842885154875601165287 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_11 : Uω (aρ 11) (bρ 11) (85815639 / 1000000000000 : ℝ) ≤ @@ -3151,26 +2746,21 @@ lemma U_6_11 : have hlg : Real.log (1093504032837657 / 10000000000000000 : ℝ) ≤ (-(4426395685635096752489 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1093504032837657 / 10000000000000000 : ℝ) = - (1093504032837657 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1093504032837657 / 625000000000000 : ℚ)) - (U := (1118781756764903247511 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1093504032837657 / 625000000000000 : ℝ) ≤ - (1118781756764903247511 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (16637544710157 / 5000000000000000 : ℝ)) (q := - (1093504032837657 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1093504032837657 / 10000000000000000 : ℚ)) + (r' := (1093504032837657 / 625000000000000 : ℚ)) + (U := (-(4426395685635096752489 / 2000000000000000000000 : ℚ))) + (U' := (1118781756764903247511 / 2000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (85815639 / 1000000000000 : ℚ)) + (s := (16637544710157 / 5000000000000000 : ℚ)) + (q := (1093504032837657 / 10000000000000000 : ℚ)) + (U := (-(4426395685635096752489 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_12 : Uω (aρ 12) (bρ 12) (85815639 / 1000000000000 : ℝ) ≤ @@ -3178,26 +2768,21 @@ lemma U_6_12 : have hlg : Real.log (2600735172932703 / 20000000000000000 : ℝ) ≤ (-(5099845272237973435631 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2600735172932703 / 20000000000000000 : ℝ) = - (2600735172932703 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2600735172932703 / 2500000000000000 : ℚ)) - (U := (98758580012026564369 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2600735172932703 / 2500000000000000 : ℝ) ≤ - (98758580012026564369 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (23302099992703 / 10000000000000000 : ℝ)) (q := - (2600735172932703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [aρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2600735172932703 / 20000000000000000 : ℚ)) + (r' := (2600735172932703 / 2500000000000000 : ℚ)) + (U := (-(5099845272237973435631 / 2500000000000000000000 : ℚ))) + (U' := (98758580012026564369 / 2500000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 12) (t := (85815639 / 1000000000000 : ℚ)) + (s := (23302099992703 / 10000000000000000 : ℚ)) + (q := (2600735172932703 / 20000000000000000 : ℚ)) + (U := (-(5099845272237973435631 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_6_13 : Uω (aρ 13) (bρ 13) (85815639 / 1000000000000 : ℝ) ≤ @@ -3309,23 +2894,21 @@ lemma U_7_1 : have hlg : Real.log (6087812562877 / 1000000000000000 : ℝ) ≤ (-(25507332223904240133213 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (6087812562877 / 1000000000000000 : ℝ) = (6087812562877 / 3906250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6087812562877 / 3906250000000 : ℚ)) - (U := (2218554988095759866787 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6087812562877 / 3906250000000 : ℝ) ≤ - (2218554988095759866787 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2911126336127 / 500000000000000 : ℝ)) (q := - (6087812562877 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6087812562877 / 1000000000000000 : ℚ)) + (r' := (6087812562877 / 3906250000000 : ℚ)) + (U := (-(25507332223904240133213 / 5000000000000000000000 : ℚ))) + (U' := (2218554988095759866787 / 5000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (19269871 / 200000000000 : ℚ)) + (s := (2911126336127 / 500000000000000 : ℚ)) + (q := (6087812562877 / 1000000000000000 : ℚ)) + (U := (-(25507332223904240133213 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_2 : Uω (aρ 2) (bρ 2) (19269871 / 200000000000 : ℝ) ≤ @@ -3333,25 +2916,21 @@ lemma U_7_2 : have hlg : Real.log (145423817540153 / 20000000000000000 : ℝ) ≤ (-(30773969948474174723 / 6250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (145423817540153 / 20000000000000000 : ℝ) = - (145423817540153 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145423817540153 / 78125000000000 : ℚ)) - (U := (3883389066525825277 / 6250000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (145423817540153 / 78125000000000 : ℝ) ≤ - (3883389066525825277 / 6250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (58121080495153 / 10000000000000000 : ℝ)) (q := - (145423817540153 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145423817540153 / 20000000000000000 : ℚ)) + (r' := (145423817540153 / 78125000000000 : ℚ)) + (U := (-(30773969948474174723 / 6250000000000000000 : ℚ))) + (U' := (3883389066525825277 / 6250000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (19269871 / 200000000000 : ℚ)) + (s := (58121080495153 / 10000000000000000 : ℚ)) + (q := (145423817540153 / 20000000000000000 : ℚ)) + (U := (-(30773969948474174723 / 6250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_3 : Uω (aρ 3) (bρ 3) (19269871 / 200000000000 : ℝ) ≤ @@ -3359,25 +2938,21 @@ lemma U_7_3 : have hlg : Real.log (192557444123869 / 20000000000000000 : ℝ) ≤ (-(23215465152356514085683 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (192557444123869 / 20000000000000000 : ℝ) = - (192557444123869 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192557444123869 / 156250000000000 : ℚ)) - (U := (1044686158143485914317 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (192557444123869 / 156250000000000 : ℝ) ≤ - (1044686158143485914317 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (57858600728869 / 10000000000000000 : ℝ)) (q := - (192557444123869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192557444123869 / 20000000000000000 : ℚ)) + (r' := (192557444123869 / 156250000000000 : ℚ)) + (U := (-(23215465152356514085683 / 5000000000000000000000 : ℚ))) + (U' := (1044686158143485914317 / 5000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (19269871 / 200000000000 : ℚ)) + (s := (57858600728869 / 10000000000000000 : ℚ)) + (q := (192557444123869 / 20000000000000000 : ℚ)) + (U := (-(23215465152356514085683 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_4 : Uω (aρ 4) (bρ 4) (19269871 / 200000000000 : ℝ) ≤ @@ -3385,24 +2960,21 @@ lemma U_7_4 : have hlg : Real.log (13514921999703 / 1000000000000000 : ℝ) ≤ (-(21519804344189444452201 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (13514921999703 / 1000000000000000 : ℝ) = (13514921999703 / 7812500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13514921999703 / 7812500000000 : ℚ)) - (U := (2740346966310555547799 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (13514921999703 / 7812500000000 : ℝ) ≤ - (2740346966310555547799 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (2865270776703 / 500000000000000 : ℝ)) (q := - (13514921999703 / 1000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13514921999703 / 1000000000000000 : ℚ)) + (r' := (13514921999703 / 7812500000000 : ℚ)) + (U := (-(21519804344189444452201 / 5000000000000000000000 : ℚ))) + (U' := (2740346966310555547799 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (19269871 / 200000000000 : ℚ)) + (s := (2865270776703 / 500000000000000 : ℚ)) + (q := (13514921999703 / 1000000000000000 : ℚ)) + (U := (-(21519804344189444452201 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_5 : Uω (aρ 5) (bρ 5) (19269871 / 200000000000 : ℝ) ≤ @@ -3410,24 +2982,21 @@ lemma U_7_5 : have hlg : Real.log (77494266368633 / 4000000000000000 : ℝ) ≤ (-(315507654980808174019 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (77494266368633 / 4000000000000000 : ℝ) = (77494266368633 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77494266368633 / 62500000000000 : ℚ)) - (U := (17202991563191825981 / 80000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (77494266368633 / 62500000000000 : ℝ) ≤ - (17202991563191825981 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11257677609633 / 2000000000000000 : ℝ)) (q := - (77494266368633 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77494266368633 / 4000000000000000 : ℚ)) + (r' := (77494266368633 / 62500000000000 : ℚ)) + (U := (-(315507654980808174019 / 80000000000000000000 : ℚ))) + (U' := (17202991563191825981 / 80000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (19269871 / 200000000000 : ℚ)) + (s := (11257677609633 / 2000000000000000 : ℚ)) + (q := (77494266368633 / 4000000000000000 : ℚ)) + (U := (-(315507654980808174019 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_6 : Uω (aρ 6) (bρ 6) (19269871 / 200000000000 : ℝ) ≤ @@ -3435,25 +3004,21 @@ lemma U_7_6 : have hlg : Real.log (553024552971181 / 20000000000000000 : ℝ) ≤ (-(8970212877133828550347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (553024552971181 / 20000000000000000 : ℝ) = - (553024552971181 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (553024552971181 / 312500000000000 : ℚ)) - (U := (1426994827366171449653 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (553024552971181 / 312500000000000 : ℝ) ≤ - (1426994827366171449653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (54601234036181 / 10000000000000000 : ℝ)) (q := - (553024552971181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (553024552971181 / 20000000000000000 : ℚ)) + (r' := (553024552971181 / 312500000000000 : ℚ)) + (U := (-(8970212877133828550347 / 2500000000000000000000 : ℚ))) + (U' := (1426994827366171449653 / 2500000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (19269871 / 200000000000 : ℚ)) + (s := (54601234036181 / 10000000000000000 : ℚ)) + (q := (553024552971181 / 20000000000000000 : ℚ)) + (U := (-(8970212877133828550347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_7 : Uω (aρ 7) (bρ 7) (19269871 / 200000000000 : ℝ) ≤ @@ -3461,25 +3026,21 @@ lemma U_7_7 : have hlg : Real.log (154819233332697 / 4000000000000000 : ℝ) ≤ (-(32517914390293590790913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (154819233332697 / 4000000000000000 : ℝ) = - (154819233332697 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (154819233332697 / 125000000000000 : ℚ)) - (U := (2139444624706409209087 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (154819233332697 / 125000000000000 : ℝ) ≤ - (2139444624706409209087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10402293393697 / 2000000000000000 : ℝ)) (q := - (154819233332697 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (154819233332697 / 4000000000000000 : ℚ)) + (r' := (154819233332697 / 125000000000000 : ℚ)) + (U := (-(32517914390293590790913 / 10000000000000000000000 : ℚ))) + (U' := (2139444624706409209087 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (19269871 / 200000000000 : ℚ)) + (s := (10402293393697 / 2000000000000000 : ℚ)) + (q := (154819233332697 / 4000000000000000 : ℚ)) + (U := (-(32517914390293590790913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_8 : Uω (aρ 8) (bρ 8) (19269871 / 200000000000 : ℝ) ≤ @@ -3487,25 +3048,21 @@ lemma U_7_8 : have hlg : Real.log (210776863658177 / 4000000000000000 : ℝ) ≤ (-(5886499166201685248543 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (210776863658177 / 4000000000000000 : ℝ) = - (210776863658177 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (210776863658177 / 125000000000000 : ℚ)) - (U := (1044972636798314751457 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (210776863658177 / 125000000000000 : ℝ) ≤ - (1044972636798314751457 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (9651593451177 / 2000000000000000 : ℝ)) (q := - (210776863658177 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (210776863658177 / 4000000000000000 : ℚ)) + (r' := (210776863658177 / 125000000000000 : ℚ)) + (U := (-(5886499166201685248543 / 2000000000000000000000 : ℚ))) + (U' := (1044972636798314751457 / 2000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (19269871 / 200000000000 : ℚ)) + (s := (9651593451177 / 2000000000000000 : ℚ)) + (q := (210776863658177 / 4000000000000000 : ℚ)) + (U := (-(5886499166201685248543 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_9 : Uω (aρ 9) (bρ 9) (19269871 / 200000000000 : ℝ) ≤ @@ -3513,25 +3070,21 @@ lemma U_7_9 : have hlg : Real.log (694807884018587 / 10000000000000000 : ℝ) ≤ (-(42667279831309115271 / 16000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (694807884018587 / 10000000000000000 : ℝ) = - (694807884018587 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (694807884018587 / 625000000000000 : ℚ)) - (U := (1694139707890884729 / 16000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (694807884018587 / 625000000000000 : ℝ) ≤ - (1694139707890884729 / 16000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (21511894321087 / 5000000000000000 : ℝ)) (q := - (694807884018587 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (694807884018587 / 10000000000000000 : ℚ)) + (r' := (694807884018587 / 625000000000000 : ℚ)) + (U := (-(42667279831309115271 / 16000000000000000000 : ℚ))) + (U' := (1694139707890884729 / 16000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (19269871 / 200000000000 : ℚ)) + (s := (21511894321087 / 5000000000000000 : ℚ)) + (q := (694807884018587 / 10000000000000000 : ℚ)) + (U := (-(42667279831309115271 / 16000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_10 : Uω (aρ 10) (bρ 10) (19269871 / 200000000000 : ℝ) ≤ @@ -3539,26 +3092,21 @@ lemma U_7_10 : have hlg : Real.log (885490567993697 / 10000000000000000 : ℝ) ≤ (-(606049641346655113191 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (885490567993697 / 10000000000000000 : ℝ) = - (885490567993697 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (885490567993697 / 625000000000000 : ℚ)) - (U := (87097538953344886809 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (885490567993697 / 625000000000000 : ℝ) ≤ - (87097538953344886809 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (17915061548697 / 5000000000000000 : ℝ)) (q := - (885490567993697 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (885490567993697 / 10000000000000000 : ℚ)) + (r' := (885490567993697 / 625000000000000 : ℚ)) + (U := (-(606049641346655113191 / 250000000000000000000 : ℚ))) + (U' := (87097538953344886809 / 250000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (19269871 / 200000000000 : ℚ)) + (s := (17915061548697 / 5000000000000000 : ℚ)) + (q := (885490567993697 / 10000000000000000 : ℚ)) + (U := (-(606049641346655113191 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_11 : Uω (aρ 11) (bρ 11) (19269871 / 200000000000 : ℝ) ≤ @@ -3566,26 +3114,21 @@ lemma U_7_11 : have hlg : Real.log (2179191411148691 / 20000000000000000 : ℝ) ≤ (-(22167783768353140953257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2179191411148691 / 20000000000000000 : ℝ) = - (2179191411148691 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2179191411148691 / 1250000000000000 : ℚ)) - (U := (5558103443646859046743 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2179191411148691 / 1250000000000000 : ℝ) ≤ - (5558103443646859046743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (25563772053691 / 10000000000000000 : ℝ)) (q := - (2179191411148691 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [aρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2179191411148691 / 20000000000000000 : ℚ)) + (r' := (2179191411148691 / 1250000000000000 : ℚ)) + (U := (-(22167783768353140953257 / 10000000000000000000000 : ℚ))) + (U' := (5558103443646859046743 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 11) (t := (19269871 / 200000000000 : ℚ)) + (s := (25563772053691 / 10000000000000000 : ℚ)) + (q := (2179191411148691 / 20000000000000000 : ℚ)) + (U := (-(22167783768353140953257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_7_12 : Uω (aρ 12) (bρ 12) (19269871 / 200000000000 : ℝ) ≤ @@ -3699,24 +3242,21 @@ lemma U_8_1 : have hlg : Real.log (30359729325639 / 5000000000000000 : ℝ) ≤ (-(51040761523417755773563 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (30359729325639 / 5000000000000000 : ℝ) = (30359729325639 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30359729325639 / 19531250000000 : ℚ)) - (U := (4411012900582244226437 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (30359729325639 / 19531250000000 : ℝ) ≤ - (4411012900582244226437 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14514230089389 / 2500000000000000 : ℝ)) (q := - (30359729325639 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30359729325639 / 5000000000000000 : ℚ)) + (r' := (30359729325639 / 19531250000000 : ℚ)) + (U := (-(51040761523417755773563 / 10000000000000000000000 : ℚ))) + (U' := (4411012900582244226437 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (55761057 / 500000000000 : ℚ)) + (s := (14514230089389 / 2500000000000000 : ℚ)) + (q := (30359729325639 / 5000000000000000 : ℚ)) + (U := (-(51040761523417755773563 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_2 : Uω (aρ 2) (bρ 2) (55761057 / 500000000000 : ℝ) ≤ @@ -3724,23 +3264,21 @@ lemma U_8_2 : have hlg : Real.log (9065245788109 / 1250000000000000 : ℝ) ≤ (-(12316127176026878844577 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (9065245788109 / 1250000000000000 : ℝ) = (9065245788109 / 4882812500000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9065245788109 / 4882812500000 : ℚ)) - (U := (1546816429973121155423 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9065245788109 / 4882812500000 : ℝ) ≤ - (1546816429973121155423 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7236615394343 / 1250000000000000 : ℝ)) (q := - (9065245788109 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9065245788109 / 1250000000000000 : ℚ)) + (r' := (9065245788109 / 4882812500000 : ℚ)) + (U := (-(12316127176026878844577 / 2500000000000000000000 : ℚ))) + (U' := (1546816429973121155423 / 2500000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (55761057 / 500000000000 : ℚ)) + (s := (7236615394343 / 1250000000000000 : ℚ)) + (q := (9065245788109 / 1250000000000000 : ℚ)) + (U := (-(12316127176026878844577 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_3 : Uω (aρ 3) (bρ 3) (55761057 / 500000000000 : ℝ) ≤ @@ -3748,24 +3286,21 @@ lemma U_8_3 : have hlg : Real.log (96025799718557 / 10000000000000000 : ℝ) ≤ (-(46457234677264518279157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (96025799718557 / 10000000000000000 : ℝ) = (96025799718557 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96025799718557 / 78125000000000 : ℚ)) - (U := (2063067943735481720843 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (96025799718557 / 78125000000000 : ℝ) ≤ - (2063067943735481720843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28752241816057 / 5000000000000000 : ℝ)) (q := - (96025799718557 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96025799718557 / 10000000000000000 : ℚ)) + (r' := (96025799718557 / 78125000000000 : ℚ)) + (U := (-(46457234677264518279157 / 10000000000000000000000 : ℚ))) + (U' := (2063067943735481720843 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (55761057 / 500000000000 : ℚ)) + (s := (28752241816057 / 5000000000000000 : ℚ)) + (q := (96025799718557 / 10000000000000000 : ℚ)) + (U := (-(46457234677264518279157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_4 : Uω (aρ 4) (bρ 4) (55761057 / 500000000000 : ℝ) ≤ @@ -3773,25 +3308,21 @@ lemma U_8_4 : have hlg : Real.log (269580170970713 / 20000000000000000 : ℝ) ≤ (-(21533108620975871780131 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (269580170970713 / 20000000000000000 : ℝ) = - (269580170970713 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (269580170970713 / 156250000000000 : ℚ)) - (U := (2727042689524128219869 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (269580170970713 / 156250000000000 : ℝ) ≤ - (2727042689524128219869 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (56738874100713 / 10000000000000000 : ℝ)) (q := - (269580170970713 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (269580170970713 / 20000000000000000 : ℚ)) + (r' := (269580170970713 / 156250000000000 : ℚ)) + (U := (-(21533108620975871780131 / 5000000000000000000000 : ℚ))) + (U' := (2727042689524128219869 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (55761057 / 500000000000 : ℚ)) + (s := (56738874100713 / 10000000000000000 : ℚ)) + (q := (269580170970713 / 20000000000000000 : ℚ)) + (U := (-(21533108620975871780131 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_5 : Uω (aρ 5) (bρ 5) (55761057 / 500000000000 : ℝ) ≤ @@ -3799,24 +3330,21 @@ lemma U_8_5 : have hlg : Real.log (96604975401611 / 5000000000000000 : ℝ) ≤ (-(1578625177908711877893 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (96604975401611 / 5000000000000000 : ℝ) = (96604975401611 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96604975401611 / 78125000000000 : ℚ)) - (U := (84928054811288122107 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (96604975401611 / 78125000000000 : ℝ) ≤ - (84928054811288122107 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13847171350361 / 2500000000000000 : ℝ)) (q := - (96604975401611 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96604975401611 / 5000000000000000 : ℚ)) + (r' := (96604975401611 / 78125000000000 : ℚ)) + (U := (-(1578625177908711877893 / 400000000000000000000 : ℚ))) + (U' := (84928054811288122107 / 400000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (55761057 / 500000000000 : ℚ)) + (s := (13847171350361 / 2500000000000000 : ℚ)) + (q := (96604975401611 / 5000000000000000 : ℚ)) + (U := (-(1578625177908711877893 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_6 : Uω (aρ 6) (bρ 6) (55761057 / 500000000000 : ℝ) ≤ @@ -3824,25 +3352,21 @@ lemma U_8_6 : have hlg : Real.log (275734990404539 / 10000000000000000 : ℝ) ≤ (-(897725036415218135001 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (275734990404539 / 10000000000000000 : ℝ) = - (275734990404539 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (275734990404539 / 156250000000000 : ℚ)) - (U := (141995734034781864999 / 250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (275734990404539 / 156250000000000 : ℝ) ≤ - (141995734034781864999 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (26599194732039 / 5000000000000000 : ℝ)) (q := - (275734990404539 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (275734990404539 / 10000000000000000 : ℚ)) + (r' := (275734990404539 / 156250000000000 : ℚ)) + (U := (-(897725036415218135001 / 250000000000000000000 : ℚ))) + (U' := (141995734034781864999 / 250000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (55761057 / 500000000000 : ℚ)) + (s := (26599194732039 / 5000000000000000 : ℚ)) + (q := (275734990404539 / 10000000000000000 : ℚ)) + (U := (-(897725036415218135001 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_7 : Uω (aρ 7) (bρ 7) (55761057 / 500000000000 : ℝ) ≤ @@ -3850,24 +3374,21 @@ lemma U_8_7 : have hlg : Real.log (96474216497051 / 2500000000000000 : ℝ) ≤ (-(16273851117356851483897 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (96474216497051 / 2500000000000000 : ℝ) = (96474216497051 / 78125000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96474216497051 / 78125000000000 : ℚ)) - (U := (1054828390143148516103 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (96474216497051 / 78125000000000 : ℝ) ≤ - (1054828390143148516103 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (3116297491963 / 625000000000000 : ℝ)) (q := - (96474216497051 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96474216497051 / 2500000000000000 : ℚ)) + (r' := (96474216497051 / 78125000000000 : ℚ)) + (U := (-(16273851117356851483897 / 5000000000000000000000 : ℚ))) + (U' := (1054828390143148516103 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (55761057 / 500000000000 : ℚ)) + (s := (3116297491963 / 625000000000000 : ℚ)) + (q := (96474216497051 / 2500000000000000 : ℚ)) + (U := (-(16273851117356851483897 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_8 : Uω (aρ 8) (bρ 8) (55761057 / 500000000000 : ℝ) ≤ @@ -3875,25 +3396,21 @@ lemma U_8_8 : have hlg : Real.log (525230043323873 / 10000000000000000 : ℝ) ≤ (-(7366260065742286983877 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (525230043323873 / 10000000000000000 : ℝ) = - (525230043323873 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (525230043323873 / 312500000000000 : ℚ)) - (U := (1298079688007713016123 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (525230043323873 / 312500000000000 : ℝ) ≤ - (1298079688007713016123 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (22492731601373 / 5000000000000000 : ℝ)) (q := - (525230043323873 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (525230043323873 / 10000000000000000 : ℚ)) + (r' := (525230043323873 / 312500000000000 : ℚ)) + (U := (-(7366260065742286983877 / 2500000000000000000000 : ℚ))) + (U' := (1298079688007713016123 / 2500000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (55761057 / 500000000000 : ℚ)) + (s := (22492731601373 / 5000000000000000 : ℚ)) + (q := (525230043323873 / 10000000000000000 : ℚ)) + (U := (-(7366260065742286983877 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_9 : Uω (aρ 9) (bρ 9) (55761057 / 500000000000 : ℝ) ≤ @@ -3901,25 +3418,21 @@ lemma U_8_9 : have hlg : Real.log (276883941615867 / 4000000000000000 : ℝ) ≤ (-(26704512040091709661141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (276883941615867 / 4000000000000000 : ℝ) = - (276883941615867 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (276883941615867 / 250000000000000 : ℚ)) - (U := (1021375171908290338859 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (276883941615867 / 250000000000000 : ℝ) ≤ - (1021375171908290338859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7595891254867 / 2000000000000000 : ℝ)) (q := - (276883941615867 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (276883941615867 / 4000000000000000 : ℚ)) + (r' := (276883941615867 / 250000000000000 : ℚ)) + (U := (-(26704512040091709661141 / 10000000000000000000000 : ℚ))) + (U' := (1021375171908290338859 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (55761057 / 500000000000 : ℚ)) + (s := (7595891254867 / 2000000000000000 : ℚ)) + (q := (276883941615867 / 4000000000000000 : ℚ)) + (U := (-(26704512040091709661141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_10 : Uω (aρ 10) (bρ 10) (55761057 / 500000000000 : ℝ) ≤ @@ -3927,26 +3440,21 @@ lemma U_8_10 : have hlg : Real.log (1762518009461781 / 20000000000000000 : ℝ) ≤ (-(24289887987277840384009 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1762518009461781 / 20000000000000000 : ℝ) = - (1762518009461781 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1762518009461781 / 1250000000000000 : ℚ)) - (U := (3435999224722159615991 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1762518009461781 / 1250000000000000 : ℝ) ≤ - (3435999224722159615991 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (27518724161781 / 10000000000000000 : ℝ)) (q := - (1762518009461781 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [aρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1762518009461781 / 20000000000000000 : ℚ)) + (r' := (1762518009461781 / 1250000000000000 : ℚ)) + (U := (-(24289887987277840384009 / 10000000000000000000000 : ℚ))) + (U' := (3435999224722159615991 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 10) (t := (55761057 / 500000000000 : ℚ)) + (s := (27518724161781 / 10000000000000000 : ℚ)) + (q := (1762518009461781 / 20000000000000000 : ℚ)) + (U := (-(24289887987277840384009 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_8_11 : Uω (aρ 11) (bρ 11) (55761057 / 500000000000 : ℝ) ≤ @@ -4068,24 +3576,21 @@ lemma U_9_1 : have hlg : Real.log (30245579911641 / 5000000000000000 : ℝ) ≤ (-(10215686268319257150869 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (30245579911641 / 5000000000000000 : ℝ) = (30245579911641 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30245579911641 / 19531250000000 : ℚ)) - (U := (874668616480742849131 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30245579911641 / 19531250000000 : ℝ) ≤ - (874668616480742849131 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (14454643220391 / 2500000000000000 : ℝ)) (q := - (30245579911641 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30245579911641 / 5000000000000000 : ℚ)) + (r' := (30245579911641 / 19531250000000 : ℚ)) + (U := (-(10215686268319257150869 / 2000000000000000000000 : ℚ))) + (U' := (874668616480742849131 / 2000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (33336783 / 250000000000 : ℚ)) + (s := (14454643220391 / 2500000000000000 : ℚ)) + (q := (30245579911641 / 5000000000000000 : ℚ)) + (U := (-(10215686268319257150869 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_2 : Uω (aρ 2) (bρ 2) (33336783 / 250000000000 : ℝ) ≤ @@ -4093,24 +3598,21 @@ lemma U_9_2 : have hlg : Real.log (72248304249749 / 10000000000000000 : ℝ) ≤ (-(9860463027542453411111 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (72248304249749 / 10000000000000000 : ℝ) = (72248304249749 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (72248304249749 / 39062500000000 : ℚ)) - (U := (1229891857257546588889 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (72248304249749 / 39062500000000 : ℝ) ≤ - (1229891857257546588889 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (28781924612249 / 5000000000000000 : ℝ)) (q := - (72248304249749 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (72248304249749 / 10000000000000000 : ℚ)) + (r' := (72248304249749 / 39062500000000 : ℚ)) + (U := (-(9860463027542453411111 / 2000000000000000000000 : ℚ))) + (U' := (1229891857257546588889 / 2000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (33336783 / 250000000000 : ℚ)) + (s := (28781924612249 / 5000000000000000 : ℚ)) + (q := (72248304249749 / 10000000000000000 : ℚ)) + (U := (-(9860463027542453411111 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_3 : Uω (aρ 3) (bρ 3) (33336783 / 250000000000 : ℝ) ≤ @@ -4118,23 +3620,21 @@ lemma U_9_3 : have hlg : Real.log (4783020619089 / 500000000000000 : ℝ) ≤ (-(46495358210023539812961 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (4783020619089 / 500000000000000 : ℝ) = (4783020619089 / 3906250000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4783020619089 / 3906250000000 : ℚ)) - (U := (2024944410976460187039 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4783020619089 / 3906250000000 : ℝ) ≤ - (2024944410976460187039 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (44524968077 / 7812500000000 : ℝ)) (q := - (4783020619089 / 500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4783020619089 / 500000000000000 : ℚ)) + (r' := (4783020619089 / 3906250000000 : ℚ)) + (U := (-(46495358210023539812961 / 10000000000000000000000 : ℚ))) + (U' := (2024944410976460187039 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (33336783 / 250000000000 : ℚ)) + (s := (44524968077 / 7812500000000 : ℚ)) + (q := (4783020619089 / 500000000000000 : ℚ)) + (U := (-(46495358210023539812961 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_4 : Uω (aρ 4) (bρ 4) (33336783 / 250000000000 : ℝ) ≤ @@ -4142,24 +3642,21 @@ lemma U_9_4 : have hlg : Real.log (67134410938101 / 5000000000000000 : ℝ) ≤ (-(21552482231997735895661 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (67134410938101 / 5000000000000000 : ℝ) = (67134410938101 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (67134410938101 / 39062500000000 : ℚ)) - (U := (2707669078502264104339 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (67134410938101 / 39062500000000 : ℝ) ≤ - (2707669078502264104339 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13978649265601 / 2500000000000000 : ℝ)) (q := - (67134410938101 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (67134410938101 / 5000000000000000 : ℚ)) + (r' := (67134410938101 / 39062500000000 : ℚ)) + (U := (-(21552482231997735895661 / 5000000000000000000000 : ℚ))) + (U' := (2707669078502264104339 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (33336783 / 250000000000 : ℚ)) + (s := (13978649265601 / 2500000000000000 : ℚ)) + (q := (67134410938101 / 5000000000000000 : ℚ)) + (U := (-(21552482231997735895661 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_5 : Uω (aρ 5) (bρ 5) (33336783 / 250000000000 : ℝ) ≤ @@ -4167,23 +3664,21 @@ lemma U_9_5 : have hlg : Real.log (240551240889 / 12500000000000 : ℝ) ≤ (-(19752753975247025066761 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show (240551240889 / 12500000000000 : ℝ) = (240551240889 / 195312500000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (240551240889 / 195312500000 : ℚ)) - (U := (1041661433752974933239 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (240551240889 / 195312500000 : ℝ) ≤ - (1041661433752974933239 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (270345096987 / 50000000000000 : ℝ)) (q := - (240551240889 / 12500000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (240551240889 / 12500000000000 : ℚ)) + (r' := (240551240889 / 195312500000 : ℚ)) + (U := (-(19752753975247025066761 / 5000000000000000000000 : ℚ))) + (U' := (1041661433752974933239 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (33336783 / 250000000000 : ℚ)) + (s := (270345096987 / 50000000000000 : ℚ)) + (q := (240551240889 / 12500000000000 : ℚ)) + (U := (-(19752753975247025066761 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_6 : Uω (aρ 6) (bρ 6) (33336783 / 250000000000 : ℝ) ≤ @@ -4191,24 +3686,21 @@ lemma U_9_6 : have hlg : Real.log (13729178527969 / 500000000000000 : ℝ) ≤ (-(17975423546595465917579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (13729178527969 / 500000000000000 : ℝ) = (13729178527969 / 7812500000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13729178527969 / 7812500000000 : ℚ)) - (U := (2818991862404534082421 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (13729178527969 / 7812500000000 : ℝ) ≤ - (2818991862404534082421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (319461249711 / 62500000000000 : ℝ)) (q := - (13729178527969 / 500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13729178527969 / 500000000000000 : ℚ)) + (r' := (13729178527969 / 7812500000000 : ℚ)) + (U := (-(17975423546595465917579 / 5000000000000000000000 : ℚ))) + (U' := (2818991862404534082421 / 5000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (33336783 / 250000000000 : ℚ)) + (s := (319461249711 / 62500000000000 : ℚ)) + (q := (13729178527969 / 500000000000000 : ℚ)) + (U := (-(17975423546595465917579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_7 : Uω (aρ 7) (bρ 7) (33336783 / 250000000000 : ℝ) ≤ @@ -4216,25 +3708,21 @@ lemma U_9_7 : have hlg : Real.log (768308916905443 / 20000000000000000 : ℝ) ≤ (-(6518591326819602089771 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (768308916905443 / 20000000000000000 : ℝ) = - (768308916905443 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (768308916905443 / 625000000000000 : ℚ)) - (U := (412880476180397910229 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (768308916905443 / 625000000000000 : ℝ) ≤ - (412880476180397910229 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (46594194980443 / 10000000000000000 : ℝ)) (q := - (768308916905443 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (768308916905443 / 20000000000000000 : ℚ)) + (r' := (768308916905443 / 625000000000000 : ℚ)) + (U := (-(6518591326819602089771 / 2000000000000000000000 : ℚ))) + (U' := (412880476180397910229 / 2000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (33336783 / 250000000000 : ℚ)) + (s := (46594194980443 / 10000000000000000 : ℚ)) + (q := (768308916905443 / 20000000000000000 : ℚ)) + (U := (-(6518591326819602089771 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_8 : Uω (aρ 8) (bρ 8) (33336783 / 250000000000 : ℝ) ≤ @@ -4242,25 +3730,21 @@ lemma U_9_8 : have hlg : Real.log (1045066541533949 / 20000000000000000 : ℝ) ≤ (-(14758258563778426940663 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1045066541533949 / 20000000000000000 : ℝ) = - (1045066541533949 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1045066541533949 / 625000000000000 : ℚ)) - (U := (2570420943721573059337 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1045066541533949 / 625000000000000 : ℝ) ≤ - (2570420943721573059337 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (39810168268949 / 10000000000000000 : ℝ)) (q := - (1045066541533949 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1045066541533949 / 20000000000000000 : ℚ)) + (r' := (1045066541533949 / 625000000000000 : ℚ)) + (U := (-(14758258563778426940663 / 5000000000000000000000 : ℚ))) + (U' := (2570420943721573059337 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (33336783 / 250000000000 : ℚ)) + (s := (39810168268949 / 10000000000000000 : ℚ)) + (q := (1045066541533949 / 20000000000000000 : ℚ)) + (U := (-(14758258563778426940663 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_9 : Uω (aρ 9) (bρ 9) (33336783 / 250000000000 : ℝ) ≤ @@ -4268,25 +3752,21 @@ lemma U_9_9 : have hlg : Real.log (1375458367291817 / 20000000000000000 : ℝ) ≤ (-(5353890477833411319021 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1375458367291817 / 20000000000000000 : ℝ) = - (1375458367291817 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1375458367291817 / 1250000000000000 : ℚ)) - (U := (191286964566588680979 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1375458367291817 / 1250000000000000 : ℝ) ≤ - (191286964566588680979 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (29236365666817 / 10000000000000000 : ℝ)) (q := - (1375458367291817 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [aρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1375458367291817 / 20000000000000000 : ℚ)) + (r' := (1375458367291817 / 1250000000000000 : ℚ)) + (U := (-(5353890477833411319021 / 2000000000000000000000 : ℚ))) + (U' := (191286964566588680979 / 2000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 9) (t := (33336783 / 250000000000 : ℚ)) + (s := (29236365666817 / 10000000000000000 : ℚ)) + (q := (1375458367291817 / 20000000000000000 : ℚ)) + (U := (-(5353890477833411319021 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_9_10 : Uω (aρ 10) (bρ 10) (33336783 / 250000000000 : ℝ) ≤ @@ -4413,24 +3893,21 @@ lemma U_10_1 : have hlg : Real.log (24063557272999 / 4000000000000000 : ℝ) ≤ (-(51133510883215947535941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (24063557272999 / 4000000000000000 : ℝ) = (24063557272999 / 15625000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24063557272999 / 15625000000000 : ℚ)) - (U := (4318263540784052464059 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (24063557272999 / 15625000000000 : ℝ) ≤ - (4318263540784052464059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11494309027999 / 2000000000000000 : ℝ)) (q := - (24063557272999 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24063557272999 / 4000000000000000 : ℚ)) + (r' := (24063557272999 / 15625000000000 : ℚ)) + (U := (-(51133510883215947535941 / 10000000000000000000000 : ℚ))) + (U' := (4318263540784052464059 / 10000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (82548843 / 500000000000 : ℚ)) + (s := (11494309027999 / 2000000000000000 : ℚ)) + (q := (24063557272999 / 4000000000000000 : ℚ)) + (U := (-(51133510883215947535941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_2 : Uω (aρ 2) (bρ 2) (82548843 / 500000000000 : ℝ) ≤ @@ -4438,25 +3915,21 @@ lemma U_10_2 : have hlg : Real.log (143698476155901 / 20000000000000000 : ℝ) ≤ (-(24678851808854408309657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (143698476155901 / 20000000000000000 : ℝ) = - (143698476155901 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (143698476155901 / 78125000000000 : ℚ)) - (U := (3047035403145591690343 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (143698476155901 / 78125000000000 : ℝ) ≤ - (3047035403145591690343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (57083222420901 / 10000000000000000 : ℝ)) (q := - (143698476155901 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (143698476155901 / 20000000000000000 : ℚ)) + (r' := (143698476155901 / 78125000000000 : ℚ)) + (U := (-(24678851808854408309657 / 5000000000000000000000 : ℚ))) + (U' := (3047035403145591690343 / 5000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (82548843 / 500000000000 : ℚ)) + (s := (57083222420901 / 10000000000000000 : ℚ)) + (q := (143698476155901 / 20000000000000000 : ℚ)) + (U := (-(24678851808854408309657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_3 : Uω (aρ 3) (bρ 3) (82548843 / 500000000000 : ℝ) ≤ @@ -4464,24 +3937,21 @@ lemma U_10_3 : have hlg : Real.log (23781360331077 / 2500000000000000 : ℝ) ≤ (-(5818929893213673684367 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (23781360331077 / 2500000000000000 : ℝ) = (23781360331077 / 19531250000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23781360331077 / 19531250000000 : ℚ)) - (U := (246107934411326315633 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23781360331077 / 19531250000000 : ℝ) ≤ - (246107934411326315633 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1757485080113 / 312500000000000 : ℝ)) (q := - (23781360331077 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23781360331077 / 2500000000000000 : ℚ)) + (r' := (23781360331077 / 19531250000000 : ℚ)) + (U := (-(5818929893213673684367 / 1250000000000000000000 : ℚ))) + (U' := (246107934411326315633 / 1250000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (82548843 / 500000000000 : ℚ)) + (s := (1757485080113 / 312500000000000 : ℚ)) + (q := (23781360331077 / 2500000000000000 : ℚ)) + (U := (-(5818929893213673684367 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_4 : Uω (aρ 4) (bρ 4) (82548843 / 500000000000 : ℝ) ≤ @@ -4489,25 +3959,21 @@ lemma U_10_4 : have hlg : Real.log (133500188112619 / 10000000000000000 : ℝ) ≤ (-(43162374832339657159807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (133500188112619 / 10000000000000000 : ℝ) = - (133500188112619 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (133500188112619 / 78125000000000 : ℚ)) - (U := (5357927788660342840193 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (133500188112619 / 78125000000000 : ℝ) ≤ - (5357927788660342840193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (27347417537619 / 5000000000000000 : ℝ)) (q := - (133500188112619 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (133500188112619 / 10000000000000000 : ℚ)) + (r' := (133500188112619 / 78125000000000 : ℚ)) + (U := (-(43162374832339657159807 / 10000000000000000000000 : ℚ))) + (U' := (5357927788660342840193 / 10000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (82548843 / 500000000000 : ℚ)) + (s := (27347417537619 / 5000000000000000 : ℚ)) + (q := (133500188112619 / 10000000000000000 : ℚ)) + (U := (-(43162374832339657159807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_5 : Uω (aρ 5) (bρ 5) (82548843 / 500000000000 : ℝ) ≤ @@ -4515,24 +3981,21 @@ lemma U_10_5 : have hlg : Real.log (95646657087479 / 5000000000000000 : ℝ) ≤ (-(39565324440062555612331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (95646657087479 / 5000000000000000 : ℝ) = (95646657087479 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (95646657087479 / 78125000000000 : ℚ)) - (U := (2023506377937444387669 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (95646657087479 / 78125000000000 : ℝ) ≤ - (2023506377937444387669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13022791966229 / 2500000000000000 : ℝ)) (q := - (95646657087479 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (95646657087479 / 5000000000000000 : ℚ)) + (r' := (95646657087479 / 78125000000000 : ℚ)) + (U := (-(39565324440062555612331 / 10000000000000000000000 : ℚ))) + (U' := (2023506377937444387669 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (82548843 / 500000000000 : ℚ)) + (s := (13022791966229 / 2500000000000000 : ℚ)) + (q := (95646657087479 / 5000000000000000 : ℚ)) + (U := (-(39565324440062555612331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_6 : Uω (aρ 6) (bρ 6) (82548843 / 500000000000 : ℝ) ≤ @@ -4540,25 +4003,21 @@ lemma U_10_6 : have hlg : Real.log (272828572881853 / 10000000000000000 : ℝ) ≤ (-(36014967106290014530057 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (272828572881853 / 10000000000000000 : ℝ) = - (272828572881853 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (272828572881853 / 156250000000000 : ℚ)) - (U := (5573863711709985469943 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (272828572881853 / 156250000000000 : ℝ) ≤ - (5573863711709985469943 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (23960655069353 / 5000000000000000 : ℝ)) (q := - (272828572881853 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (272828572881853 / 10000000000000000 : ℚ)) + (r' := (272828572881853 / 156250000000000 : ℚ)) + (U := (-(36014967106290014530057 / 10000000000000000000000 : ℚ))) + (U' := (5573863711709985469943 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (82548843 / 500000000000 : ℚ)) + (s := (23960655069353 / 5000000000000000 : ℚ)) + (q := (272828572881853 / 10000000000000000 : ℚ)) + (U := (-(36014967106290014530057 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_7 : Uω (aρ 7) (bρ 7) (82548843 / 500000000000 : ℝ) ≤ @@ -4566,25 +4025,21 @@ lemma U_10_7 : have hlg : Real.log (762783481867911 / 20000000000000000 : ℝ) ≤ (-(8166283330872021732883 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (762783481867911 / 20000000000000000 : ℝ) = - (762783481867911 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (762783481867911 / 625000000000000 : ℚ)) - (U := (498056422877978267117 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (762783481867911 / 625000000000000 : ℝ) ≤ - (498056422877978267117 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (41386265482911 / 10000000000000000 : ℝ)) (q := - (762783481867911 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (762783481867911 / 20000000000000000 : ℚ)) + (r' := (762783481867911 / 625000000000000 : ℚ)) + (U := (-(8166283330872021732883 / 2500000000000000000000 : ℚ))) + (U' := (498056422877978267117 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (82548843 / 500000000000 : ℚ)) + (s := (41386265482911 / 10000000000000000 : ℚ)) + (q := (762783481867911 / 20000000000000000 : ℚ)) + (U := (-(8166283330872021732883 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_8 : Uω (aρ 8) (bρ 8) (82548843 / 500000000000 : ℝ) ≤ @@ -4592,25 +4047,21 @@ lemma U_10_8 : have hlg : Real.log (517852877658559 / 10000000000000000 : ℝ) ≤ (-(592129837744490728151 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (517852877658559 / 10000000000000000 : ℝ) = - (517852877658559 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (517852877658559 / 312500000000000 : ℚ)) - (U := (101017342555509271849 / 200000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (517852877658559 / 312500000000000 : ℝ) ≤ - (101017342555509271849 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (15383443796059 / 5000000000000000 : ℝ)) (q := - (517852877658559 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [aρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (517852877658559 / 10000000000000000 : ℚ)) + (r' := (517852877658559 / 312500000000000 : ℚ)) + (U := (-(592129837744490728151 / 200000000000000000000 : ℚ))) + (U' := (101017342555509271849 / 200000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 8) (t := (82548843 / 500000000000 : ℚ)) + (s := (15383443796059 / 5000000000000000 : ℚ)) + (q := (517852877658559 / 10000000000000000 : ℚ)) + (U := (-(592129837744490728151 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_10_9 : Uω (aρ 9) (bρ 9) (82548843 / 500000000000 : ℝ) ≤ @@ -4742,25 +4193,21 @@ lemma U_11_1 : have hlg : Real.log (119331179383113 / 20000000000000000 : ℝ) ≤ (-(10243169805498114481613 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (119331179383113 / 20000000000000000 : ℝ) = - (119331179383113 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (119331179383113 / 78125000000000 : ℚ)) - (U := (847185079301885518387 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (119331179383113 / 78125000000000 : ℝ) ≤ - (847185079301885518387 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (56956023178113 / 10000000000000000 : ℝ)) (q := - (119331179383113 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (119331179383113 / 20000000000000000 : ℚ)) + (r' := (119331179383113 / 78125000000000 : ℚ)) + (U := (-(10243169805498114481613 / 2000000000000000000000 : ℚ))) + (U' := (847185079301885518387 / 2000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (53051547 / 250000000000 : ℚ)) + (s := (56956023178113 / 10000000000000000 : ℚ)) + (q := (119331179383113 / 20000000000000000 : ℚ)) + (U := (-(10243169805498114481613 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_2 : Uω (aρ 2) (bρ 2) (53051547 / 250000000000 : ℝ) ≤ @@ -4768,24 +4215,21 @@ lemma U_11_2 : have hlg : Real.log (17813753292691 / 2500000000000000 : ℝ) ≤ (-(24720375964658024966207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (17813753292691 / 2500000000000000 : ℝ) = (17813753292691 / 9765625000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17813753292691 / 9765625000000 : ℚ)) - (U := (3005511247341975033793 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17813753292691 / 9765625000000 : ℝ) ≤ - (3005511247341975033793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1761433050829 / 312500000000000 : ℝ)) (q := - (17813753292691 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17813753292691 / 2500000000000000 : ℚ)) + (r' := (17813753292691 / 9765625000000 : ℚ)) + (U := (-(24720375964658024966207 / 5000000000000000000000 : ℚ))) + (U' := (3005511247341975033793 / 5000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (53051547 / 250000000000 : ℚ)) + (s := (1761433050829 / 312500000000000 : ℚ)) + (q := (17813753292691 / 2500000000000000 : ℚ)) + (U := (-(24720375964658024966207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_3 : Uω (aρ 3) (bρ 3) (53051547 / 250000000000 : ℝ) ≤ @@ -4793,24 +4237,21 @@ lemma U_11_3 : have hlg : Real.log (94323922802349 / 10000000000000000 : ℝ) ≤ (-(46636055244366115624033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (94323922802349 / 10000000000000000 : ℝ) = (94323922802349 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (94323922802349 / 78125000000000 : ℚ)) - (U := (1884247376633884375967 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (94323922802349 / 78125000000000 : ℝ) ≤ - (1884247376633884375967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (27553785269849 / 5000000000000000 : ℝ)) (q := - (94323922802349 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (94323922802349 / 10000000000000000 : ℚ)) + (r' := (94323922802349 / 78125000000000 : ℚ)) + (U := (-(46636055244366115624033 / 10000000000000000000000 : ℚ))) + (U' := (1884247376633884375967 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (53051547 / 250000000000 : ℚ)) + (s := (27553785269849 / 5000000000000000 : ℚ)) + (q := (94323922802349 / 10000000000000000 : ℚ)) + (U := (-(46636055244366115624033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_4 : Uω (aρ 4) (bρ 4) (53051547 / 250000000000 : ℝ) ≤ @@ -4818,24 +4259,21 @@ lemma U_11_4 : have hlg : Real.log (33083897021511 / 2500000000000000 : ℝ) ≤ (-(21624996699245277221649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (33083897021511 / 2500000000000000 : ℝ) = (33083897021511 / 19531250000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33083897021511 / 19531250000000 : ℚ)) - (U := (2635154611254722778351 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33083897021511 / 19531250000000 : ℝ) ≤ - (2635154611254722778351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6604590005261 / 1250000000000000 : ℝ)) (q := - (33083897021511 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33083897021511 / 2500000000000000 : ℚ)) + (r' := (33083897021511 / 19531250000000 : ℚ)) + (U := (-(21624996699245277221649 / 5000000000000000000000 : ℚ))) + (U' := (2635154611254722778351 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (53051547 / 250000000000 : ℚ)) + (s := (6604590005261 / 1250000000000000 : ℚ)) + (q := (33083897021511 / 2500000000000000 : ℚ)) + (U := (-(21624996699245277221649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_5 : Uω (aρ 5) (bρ 5) (53051547 / 250000000000 : ℝ) ≤ @@ -4843,25 +4281,21 @@ lemma U_11_5 : have hlg : Real.log (189518966230509 / 10000000000000000 : ℝ) ≤ (-(39658512652531402453443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (189518966230509 / 10000000000000000 : ℝ) = - (189518966230509 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (189518966230509 / 156250000000000 : ℚ)) - (U := (1930318165468597546557 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (189518966230509 / 156250000000000 : ℝ) ≤ - (1930318165468597546557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (24506778498009 / 5000000000000000 : ℝ)) (q := - (189518966230509 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (189518966230509 / 10000000000000000 : ℚ)) + (r' := (189518966230509 / 156250000000000 : ℚ)) + (U := (-(39658512652531402453443 / 10000000000000000000000 : ℚ))) + (U' := (1930318165468597546557 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (53051547 / 250000000000 : ℚ)) + (s := (24506778498009 / 5000000000000000 : ℚ)) + (q := (189518966230509 / 10000000000000000 : ℚ)) + (U := (-(39658512652531402453443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_6 : Uω (aρ 6) (bρ 6) (53051547 / 250000000000 : ℝ) ≤ @@ -4869,25 +4303,21 @@ lemma U_11_6 : have hlg : Real.log (135004154291197 / 5000000000000000 : ℝ) ≤ (-(18059438196821077208529 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (135004154291197 / 5000000000000000 : ℝ) = - (135004154291197 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (135004154291197 / 78125000000000 : ℚ)) - (U := (2734977212178922791471 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (135004154291197 / 78125000000000 : ℝ) ≤ - (2734977212178922791471 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10687966639947 / 2500000000000000 : ℝ)) (q := - (135004154291197 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (135004154291197 / 5000000000000000 : ℚ)) + (r' := (135004154291197 / 78125000000000 : ℚ)) + (U := (-(18059438196821077208529 / 5000000000000000000000 : ℚ))) + (U' := (2734977212178922791471 / 5000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (53051547 / 250000000000 : ℚ)) + (s := (10687966639947 / 2500000000000000 : ℚ)) + (q := (135004154291197 / 5000000000000000 : ℚ)) + (U := (-(18059438196821077208529 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_7 : Uω (aρ 7) (bρ 7) (53051547 / 250000000000 : ℝ) ≤ @@ -4895,25 +4325,21 @@ lemma U_11_7 : have hlg : Real.log (150614428548557 / 4000000000000000 : ℝ) ≤ (-(6558653041860765113421 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (150614428548557 / 4000000000000000 : ℝ) = - (150614428548557 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (150614428548557 / 125000000000000 : ℚ)) - (U := (372818761139234886579 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (150614428548557 / 125000000000000 : ℝ) ≤ - (372818761139234886579 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6429202275557 / 2000000000000000 : ℝ)) (q := - (150614428548557 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (150614428548557 / 4000000000000000 : ℚ)) + (r' := (150614428548557 / 125000000000000 : ℚ)) + (U := (-(6558653041860765113421 / 2000000000000000000000 : ℚ))) + (U' := (372818761139234886579 / 2000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (53051547 / 250000000000 : ℚ)) + (s := (6429202275557 / 2000000000000000 : ℚ)) + (q := (150614428548557 / 4000000000000000 : ℚ)) + (U := (-(6558653041860765113421 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_11_8 : Uω (aρ 8) (bρ 8) (53051547 / 250000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U01.lean b/LeanPool/Zeta5Irrational/Table/U01.lean index 0737d75e5e..1de3f77fa0 100644 --- a/LeanPool/Zeta5Irrational/Table/U01.lean +++ b/LeanPool/Zeta5Irrational/Table/U01.lean @@ -24,24 +24,21 @@ lemma U_12_1 : have hlg : Real.log (14822473832053 / 2500000000000000 : ℝ) ≤ (-(51279014775995128440791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (14822473832053 / 2500000000000000 : ℝ) = (14822473832053 / 9765625000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14822473832053 / 9765625000000 : ℚ)) - (U := (4172759648004871559209 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14822473832053 / 9765625000000 : ℝ) ≤ - (4172759648004871559209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7070394933303 / 1250000000000000 : ℝ)) (q := - (14822473832053 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14822473832053 / 2500000000000000 : ℚ)) + (r' := (14822473832053 / 9765625000000 : ℚ)) + (U := (-(51279014775995128440791 / 10000000000000000000000 : ℚ))) + (U' := (4172759648004871559209 / 10000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (496117379 / 2000000000000 : ℚ)) + (s := (7070394933303 / 1250000000000000 : ℚ)) + (q := (14822473832053 / 2500000000000000 : ℚ)) + (U := (-(51279014775995128440791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_2 : Uω (aρ 2) (bρ 2) (496117379 / 2000000000000 : ℝ) ≤ @@ -49,25 +46,21 @@ lemma U_12_2 : have hlg : Real.log (141602028099197 / 20000000000000000 : ℝ) ≤ (-(3094041904103170921061 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (141602028099197 / 20000000000000000 : ℝ) = - (141602028099197 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (141602028099197 / 78125000000000 : ℚ)) - (U := (371693997396829078939 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (141602028099197 / 78125000000000 : ℝ) ≤ - (371693997396829078939 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (55816384399197 / 10000000000000000 : ℝ)) (q := - (141602028099197 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (141602028099197 / 20000000000000000 : ℚ)) + (r' := (141602028099197 / 78125000000000 : ℚ)) + (U := (-(3094041904103170921061 / 625000000000000000000 : ℚ))) + (U' := (371693997396829078939 / 625000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (496117379 / 2000000000000 : ℚ)) + (s := (55816384399197 / 10000000000000000 : ℚ)) + (q := (141602028099197 / 20000000000000000 : ℚ)) + (U := (-(3094041904103170921061 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_3 : Uω (aρ 3) (bρ 3) (496117379 / 2000000000000 : ℝ) ≤ @@ -75,25 +68,21 @@ lemma U_12_3 : have hlg : Real.log (187414745659063 / 20000000000000000 : ℝ) ≤ (-(23350817492635683984117 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (187414745659063 / 20000000000000000 : ℝ) = - (187414745659063 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (187414745659063 / 156250000000000 : ℚ)) - (U := (909333817864316015883 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (187414745659063 / 156250000000000 : ℝ) ≤ - (909333817864316015883 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (54232995609063 / 10000000000000000 : ℝ)) (q := - (187414745659063 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (187414745659063 / 20000000000000000 : ℚ)) + (r' := (187414745659063 / 156250000000000 : ℚ)) + (U := (-(23350817492635683984117 / 5000000000000000000000 : ℚ))) + (U' := (909333817864316015883 / 5000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (496117379 / 2000000000000 : ℚ)) + (s := (54232995609063 / 10000000000000000 : ℚ)) + (q := (187414745659063 / 20000000000000000 : ℚ)) + (U := (-(23350817492635683984117 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_4 : Uω (aρ 4) (bρ 4) (496117379 / 2000000000000 : ℝ) ≤ @@ -101,25 +90,21 @@ lemma U_12_4 : have hlg : Real.log (131428195324229 / 10000000000000000 : ℝ) ≤ (-(8663759421672724895473 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (131428195324229 / 10000000000000000 : ℝ) = - (131428195324229 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (131428195324229 / 78125000000000 : ℚ)) - (U := (1040301102527275104527 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (131428195324229 / 78125000000000 : ℝ) ≤ - (1040301102527275104527 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (25690229766729 / 5000000000000000 : ℝ)) (q := - (131428195324229 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (131428195324229 / 10000000000000000 : ℚ)) + (r' := (131428195324229 / 78125000000000 : ℚ)) + (U := (-(8663759421672724895473 / 2000000000000000000000 : ℚ))) + (U' := (1040301102527275104527 / 2000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (496117379 / 2000000000000 : ℚ)) + (s := (25690229766729 / 5000000000000000 : ℚ)) + (q := (131428195324229 / 10000000000000000 : ℚ)) + (U := (-(8663759421672724895473 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_5 : Uω (aρ 5) (bρ 5) (496117379 / 2000000000000 : ℝ) ≤ @@ -127,25 +112,21 @@ lemma U_12_5 : have hlg : Real.log (376204149959763 / 20000000000000000 : ℝ) ≤ (-(39733556029110319524967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (376204149959763 / 20000000000000000 : ℝ) = - (376204149959763 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (376204149959763 / 312500000000000 : ℚ)) - (U := (1855274788889680475033 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (376204149959763 / 312500000000000 : ℝ) ≤ - (1855274788889680475033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (46538299509763 / 10000000000000000 : ℝ)) (q := - (376204149959763 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (376204149959763 / 20000000000000000 : ℚ)) + (r' := (376204149959763 / 312500000000000 : ℚ)) + (U := (-(39733556029110319524967 / 10000000000000000000000 : ℚ))) + (U' := (1855274788889680475033 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (496117379 / 2000000000000 : ℚ)) + (s := (46538299509763 / 10000000000000000 : ℚ)) + (q := (376204149959763 / 20000000000000000 : ℚ)) + (U := (-(39733556029110319524967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_6 : Uω (aρ 6) (bρ 6) (496117379 / 2000000000000 : ℝ) ≤ @@ -153,25 +134,21 @@ lemma U_12_6 : have hlg : Real.log (535263583817503 / 20000000000000000 : ℝ) ≤ (-(36207282453746924592843 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (535263583817503 / 20000000000000000 : ℝ) = - (535263583817503 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (535263583817503 / 312500000000000 : ℚ)) - (U := (5381548364253075407157 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (535263583817503 / 312500000000000 : ℝ) ≤ - (5381548364253075407157 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (38357358227503 / 10000000000000000 : ℝ)) (q := - (535263583817503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (535263583817503 / 20000000000000000 : ℚ)) + (r' := (535263583817503 / 312500000000000 : ℚ)) + (U := (-(36207282453746924592843 / 10000000000000000000000 : ℚ))) + (U' := (5381548364253075407157 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (496117379 / 2000000000000 : ℚ)) + (s := (38357358227503 / 10000000000000000 : ℚ)) + (q := (535263583817503 / 20000000000000000 : ℚ)) + (U := (-(36207282453746924592843 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_7 : Uω (aρ 7) (bρ 7) (496117379 / 2000000000000 : ℝ) ≤ @@ -179,25 +156,21 @@ lemma U_12_7 : have hlg : Real.log (743295441345089 / 20000000000000000 : ℝ) ≤ (-(32923939525185939772853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (743295441345089 / 20000000000000000 : ℝ) = - (743295441345089 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (743295441345089 / 625000000000000 : ℚ)) - (U := (1733419489814060227147 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (743295441345089 / 625000000000000 : ℝ) ≤ - (1733419489814060227147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (22727834995089 / 10000000000000000 : ℝ)) (q := - (743295441345089 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [aρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (743295441345089 / 20000000000000000 : ℚ)) + (r' := (743295441345089 / 625000000000000 : ℚ)) + (U := (-(32923939525185939772853 / 10000000000000000000000 : ℚ))) + (U' := (1733419489814060227147 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 7) (t := (496117379 / 2000000000000 : ℚ)) + (s := (22727834995089 / 10000000000000000 : ℚ)) + (q := (743295441345089 / 20000000000000000 : ℚ)) + (U := (-(32923939525185939772853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_12_8 : Uω (aρ 8) (bρ 8) (496117379 / 2000000000000 : ℝ) ≤ @@ -335,25 +308,21 @@ lemma U_13_1 : have hlg : Real.log (117827942579917 / 20000000000000000 : ℝ) ≤ (-(25671310519013681683207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (117827942579917 / 20000000000000000 : ℝ) = - (117827942579917 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (117827942579917 / 78125000000000 : ℚ)) - (U := (2054576692986318316793 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (117827942579917 / 78125000000000 : ℝ) ≤ - (2054576692986318316793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (56169836404917 / 10000000000000000 : ℝ)) (q := - (117827942579917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (117827942579917 / 20000000000000000 : ℚ)) + (r' := (117827942579917 / 78125000000000 : ℚ)) + (U := (-(25671310519013681683207 / 5000000000000000000000 : ℚ))) + (U' := (2054576692986318316793 / 5000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (283911191 / 1000000000000 : ℚ)) + (s := (56169836404917 / 10000000000000000 : ℚ)) + (q := (117827942579917 / 20000000000000000 : ℚ)) + (U := (-(25671310519013681683207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_2 : Uω (aρ 2) (bρ 2) (283911191 / 1000000000000 : ℝ) ≤ @@ -361,24 +330,21 @@ lemma U_13_2 : have hlg : Real.log (28138178523381 / 4000000000000000 : ℝ) ≤ (-(9913844635044356752717 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (28138178523381 / 4000000000000000 : ℝ) = (28138178523381 / 15625000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28138178523381 / 15625000000000 : ℚ)) - (U := (1176510249755643247283 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (28138178523381 / 15625000000000 : ℝ) ≤ - (1176510249755643247283 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (11052754786381 / 2000000000000000 : ℝ)) (q := - (28138178523381 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28138178523381 / 4000000000000000 : ℚ)) + (r' := (28138178523381 / 15625000000000 : ℚ)) + (U := (-(9913844635044356752717 / 2000000000000000000000 : ℚ))) + (U' := (1176510249755643247283 / 2000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (283911191 / 1000000000000 : ℚ)) + (s := (11052754786381 / 2000000000000000 : ℚ)) + (q := (28138178523381 / 4000000000000000 : ℚ)) + (U := (-(9913844635044356752717 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_3 : Uω (aρ 3) (bρ 3) (283911191 / 1000000000000 : ℝ) ≤ @@ -386,24 +352,21 @@ lemma U_13_3 : have hlg : Real.log (46542429648523 / 5000000000000000 : ℝ) ≤ (-(46768288274873095600687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (46542429648523 / 5000000000000000 : ℝ) = (46542429648523 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46542429648523 / 39062500000000 : ℚ)) - (U := (1752014346126904399313 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (46542429648523 / 39062500000000 : ℝ) ≤ - (1752014346126904399313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13336623389773 / 2500000000000000 : ℝ)) (q := - (46542429648523 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46542429648523 / 5000000000000000 : ℚ)) + (r' := (46542429648523 / 39062500000000 : ℚ)) + (U := (-(46768288274873095600687 / 10000000000000000000000 : ℚ))) + (U' := (1752014346126904399313 / 10000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (283911191 / 1000000000000 : ℚ)) + (s := (13336623389773 / 2500000000000000 : ℚ)) + (q := (46542429648523 / 5000000000000000 : ℚ)) + (U := (-(46768288274873095600687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_4 : Uω (aρ 4) (bρ 4) (283911191 / 1000000000000 : ℝ) ≤ @@ -411,24 +374,21 @@ lemma U_13_4 : have hlg : Real.log (65250421395167 / 5000000000000000 : ℝ) ≤ (-(5423700856563990487439 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (65250421395167 / 5000000000000000 : ℝ) = (65250421395167 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65250421395167 / 39062500000000 : ℚ)) - (U := (641336971061009512561 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (65250421395167 / 39062500000000 : ℝ) ≤ - (641336971061009512561 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (12471069870167 / 2500000000000000 : ℝ)) (q := - (65250421395167 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65250421395167 / 5000000000000000 : ℚ)) + (r' := (65250421395167 / 39062500000000 : ℚ)) + (U := (-(5423700856563990487439 / 1250000000000000000000 : ℚ))) + (U' := (641336971061009512561 / 1250000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (283911191 / 1000000000000 : ℚ)) + (s := (12471069870167 / 2500000000000000 : ℚ)) + (q := (65250421395167 / 5000000000000000 : ℚ)) + (U := (-(5423700856563990487439 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_5 : Uω (aρ 5) (bρ 5) (283911191 / 1000000000000 : ℝ) ≤ @@ -436,24 +396,21 @@ lemma U_13_5 : have hlg : Real.log (93308506303549 / 5000000000000000 : ℝ) ≤ (-(39812819146312822009509 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (93308506303549 / 5000000000000000 : ℝ) = (93308506303549 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (93308506303549 / 78125000000000 : ℚ)) - (U := (1776011671687177990491 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (93308506303549 / 78125000000000 : ℝ) ≤ - (1776011671687177990491 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10981674944799 / 2500000000000000 : ℝ)) (q := - (93308506303549 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (93308506303549 / 5000000000000000 : ℚ)) + (r' := (93308506303549 / 78125000000000 : ℚ)) + (U := (-(39812819146312822009509 / 10000000000000000000000 : ℚ))) + (U' := (1776011671687177990491 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (283911191 / 1000000000000 : ℚ)) + (s := (10981674944799 / 2500000000000000 : ℚ)) + (q := (93308506303549 / 5000000000000000 : ℚ)) + (U := (-(39812819146312822009509 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_6 : Uω (aρ 6) (bρ 6) (283911191 / 1000000000000 : ℝ) ≤ @@ -461,25 +418,21 @@ lemma U_13_6 : have hlg : Real.log (529940946095807 / 20000000000000000 : ℝ) ≤ (-(18153609865494868493647 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (529940946095807 / 20000000000000000 : ℝ) = - (529940946095807 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (529940946095807 / 312500000000000 : ℚ)) - (U := (2640805543505131506353 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (529940946095807 / 312500000000000 : ℝ) ≤ - (2640805543505131506353 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (33393245520807 / 10000000000000000 : ℝ)) (q := - (529940946095807 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (529940946095807 / 20000000000000000 : ℚ)) + (r' := (529940946095807 / 312500000000000 : ℚ)) + (U := (-(18153609865494868493647 / 5000000000000000000000 : ℚ))) + (U' := (2640805543505131506353 / 5000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (283911191 / 1000000000000 : ℚ)) + (s := (33393245520807 / 10000000000000000 : ℚ)) + (q := (529940946095807 / 20000000000000000 : ℚ)) + (U := (-(18153609865494868493647 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_13_7 : Uω (aρ 7) (bρ 7) (283911191 / 1000000000000 : ℝ) ≤ @@ -621,24 +574,21 @@ lemma U_14_1 : have hlg : Real.log (29162076708097 / 5000000000000000 : ℝ) ≤ (-(5144324067033277739057 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (29162076708097 / 5000000000000000 : ℝ) = (29162076708097 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29162076708097 / 19531250000000 : ℚ)) - (U := (400853375366722260943 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29162076708097 / 19531250000000 : ℝ) ≤ - (400853375366722260943 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13888066941847 / 2500000000000000 : ℝ)) (q := - (29162076708097 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29162076708097 / 5000000000000000 : ℚ)) + (r' := (29162076708097 / 19531250000000 : ℚ)) + (U := (-(5144324067033277739057 / 1000000000000000000000 : ℚ))) + (U' := (400853375366722260943 / 1000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (170058951 / 500000000000 : ℚ)) + (s := (13888066941847 / 2500000000000000 : ℚ)) + (q := (29162076708097 / 5000000000000000 : ℚ)) + (U := (-(5144324067033277739057 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_2 : Uω (aρ 2) (bρ 2) (170058951 / 500000000000 : ℝ) ≤ @@ -646,24 +596,21 @@ lemma U_14_2 : have hlg : Real.log (13925594310293 / 2000000000000000 : ℝ) ≤ (-(496717399318518904317 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (13925594310293 / 2000000000000000 : ℝ) = (13925594310293 / 7812500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13925594310293 / 7812500000000 : ℚ)) - (U := (57800344921481095683 / 100000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (13925594310293 / 7812500000000 : ℝ) ≤ - (57800344921481095683 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (5439089152793 / 1000000000000000 : ℝ)) (q := - (13925594310293 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13925594310293 / 2000000000000000 : ℚ)) + (r' := (13925594310293 / 7812500000000 : ℚ)) + (U := (-(496717399318518904317 / 100000000000000000000 : ℚ))) + (U' := (57800344921481095683 / 100000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (170058951 / 500000000000 : ℚ)) + (s := (5439089152793 / 1000000000000000 : ℚ)) + (q := (13925594310293 / 2000000000000000 : ℚ)) + (U := (-(496717399318518904317 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_3 : Uω (aρ 3) (bρ 3) (170058951 / 500000000000 : ℝ) ≤ @@ -671,23 +618,21 @@ lemma U_14_3 : have hlg : Real.log (5756012276917 / 625000000000000 : ℝ) ≤ (-(1875002690401424918243 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (5756012276917 / 625000000000000 : ℝ) = (5756012276917 / 4882812500000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5756012276917 / 4882812500000 : ℚ)) - (U := (65809414438575081757 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5756012276917 / 4882812500000 : ℝ) ≤ - (65809414438575081757 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6491404367043 / 1250000000000000 : ℝ)) (q := - (5756012276917 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5756012276917 / 625000000000000 : ℚ)) + (r' := (5756012276917 / 4882812500000 : ℚ)) + (U := (-(1875002690401424918243 / 400000000000000000000 : ℚ))) + (U' := (65809414438575081757 / 400000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (170058951 / 500000000000 : ℚ)) + (s := (6491404367043 / 1250000000000000 : ℚ)) + (q := (5756012276917 / 625000000000000 : ℚ)) + (U := (-(1875002690401424918243 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_4 : Uω (aρ 4) (bρ 4) (170058951 / 500000000000 : ℝ) ≤ @@ -695,24 +640,21 @@ lemma U_14_4 : have hlg : Real.log (51600921238611 / 4000000000000000 : ℝ) ≤ (-(5438137640616013885629 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (51600921238611 / 4000000000000000 : ℝ) = (51600921238611 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51600921238611 / 31250000000000 : ℚ)) - (U := (626900187008986114371 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (51600921238611 / 31250000000000 : ℝ) ≤ - (626900187008986114371 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (9489853440611 / 2000000000000000 : ℝ)) (q := - (51600921238611 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51600921238611 / 4000000000000000 : ℚ)) + (r' := (51600921238611 / 31250000000000 : ℚ)) + (U := (-(5438137640616013885629 / 1250000000000000000000 : ℚ))) + (U' := (626900187008986114371 / 1250000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (170058951 / 500000000000 : ℚ)) + (s := (9489853440611 / 2000000000000000 : ℚ)) + (q := (51600921238611 / 4000000000000000 : ℚ)) + (U := (-(5438137640616013885629 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_5 : Uω (aρ 5) (bρ 5) (170058951 / 500000000000 : ℝ) ≤ @@ -720,25 +662,21 @@ lemma U_14_5 : have hlg : Real.log (368238108811001 / 20000000000000000 : ℝ) ≤ (-(39947577872317960521831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (368238108811001 / 20000000000000000 : ℝ) = - (368238108811001 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (368238108811001 / 312500000000000 : ℚ)) - (U := (1641252945682039478169 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (368238108811001 / 312500000000000 : ℝ) ≤ - (1641252945682039478169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (39492850486001 / 10000000000000000 : ℝ)) (q := - (368238108811001 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (368238108811001 / 20000000000000000 : ℚ)) + (r' := (368238108811001 / 312500000000000 : ℚ)) + (U := (-(39947577872317960521831 / 10000000000000000000000 : ℚ))) + (U' := (1641252945682039478169 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (170058951 / 500000000000 : ℚ)) + (s := (39492850486001 / 10000000000000000 : ℚ)) + (q := (368238108811001 / 20000000000000000 : ℚ)) + (U := (-(39947577872317960521831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_6 : Uω (aρ 6) (bρ 6) (170058951 / 500000000000 : ℝ) ≤ @@ -746,25 +684,21 @@ lemma U_14_6 : have hlg : Real.log (519591533231167 / 20000000000000000 : ℝ) ≤ (-(36504445610949767396391 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (519591533231167 / 20000000000000000 : ℝ) = - (519591533231167 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (519591533231167 / 312500000000000 : ℚ)) - (U := (5084385207050232603609 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (519591533231167 / 312500000000000 : ℝ) ≤ - (5084385207050232603609 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (23605899766167 / 10000000000000000 : ℝ)) (q := - (519591533231167 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [aρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (519591533231167 / 20000000000000000 : ℚ)) + (r' := (519591533231167 / 312500000000000 : ℚ)) + (U := (-(36504445610949767396391 / 10000000000000000000000 : ℚ))) + (U' := (5084385207050232603609 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 6) (t := (170058951 / 500000000000 : ℚ)) + (s := (23605899766167 / 10000000000000000 : ℚ)) + (q := (519591533231167 / 20000000000000000 : ℚ)) + (U := (-(36504445610949767396391 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_14_7 : Uω (aρ 7) (bρ 7) (170058951 / 500000000000 : ℝ) ≤ @@ -906,23 +840,21 @@ lemma U_15_1 : have hlg : Real.log (2886686981611 / 500000000000000 : ℝ) ≤ (-(10308997249903148058101 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (2886686981611 / 500000000000000 : ℝ) = (2886686981611 / 1953125000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2886686981611 / 1953125000000 : ℚ)) - (U := (781357634896851941899 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2886686981611 / 1953125000000 : ℝ) ≤ - (781357634896851941899 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (85833605171 / 15625000000000 : ℝ)) (q := - (2886686981611 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2886686981611 / 500000000000000 : ℚ)) + (r' := (2886686981611 / 1953125000000 : ℚ)) + (U := (-(10308997249903148058101 / 2000000000000000000000 : ℚ))) + (U' := (781357634896851941899 / 2000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (396324613 / 1000000000000 : ℚ)) + (s := (85833605171 / 15625000000000 : ℚ)) + (q := (2886686981611 / 500000000000000 : ℚ)) + (U := (-(10308997249903148058101 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_15_2 : Uω (aρ 2) (bρ 2) (396324613 / 1000000000000 : ℝ) ≤ @@ -930,25 +862,21 @@ lemma U_15_2 : have hlg : Real.log (137812659217157 / 20000000000000000 : ℝ) ≤ (-(24887961647494144053291 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (137812659217157 / 20000000000000000 : ℝ) = - (137812659217157 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (137812659217157 / 78125000000000 : ℚ)) - (U := (2837925564505855946709 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (137812659217157 / 78125000000000 : ℝ) ≤ - (2837925564505855946709 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (53509674752157 / 10000000000000000 : ℝ)) (q := - (137812659217157 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (137812659217157 / 20000000000000000 : ℚ)) + (r' := (137812659217157 / 78125000000000 : ℚ)) + (U := (-(24887961647494144053291 / 5000000000000000000000 : ℚ))) + (U' := (2837925564505855946709 / 5000000000000000000000 : ℚ)) + 8 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (396324613 / 1000000000000 : ℚ)) + (s := (53509674752157 / 10000000000000000 : ℚ)) + (q := (137812659217157 / 20000000000000000 : ℚ)) + (U := (-(24887961647494144053291 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_15_3 : Uω (aρ 3) (bρ 3) (396324613 / 1000000000000 : ℝ) ≤ @@ -956,25 +884,21 @@ lemma U_15_3 : have hlg : Real.log (182181659963663 / 20000000000000000 : ℝ) ≤ (-(11746208074433576911541 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (182181659963663 / 20000000000000000 : ℝ) = - (182181659963663 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (182181659963663 / 156250000000000 : ℚ)) - (U := (383867580816423088459 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (182181659963663 / 156250000000000 : ℝ) ≤ - (383867580816423088459 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (50482569148663 / 10000000000000000 : ℝ)) (q := - (182181659963663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (182181659963663 / 20000000000000000 : ℚ)) + (r' := (182181659963663 / 156250000000000 : ℚ)) + (U := (-(11746208074433576911541 / 2500000000000000000000 : ℚ))) + (U' := (383867580816423088459 / 2500000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (396324613 / 1000000000000 : ℚ)) + (s := (50482569148663 / 10000000000000000 : ℚ)) + (q := (182181659963663 / 20000000000000000 : ℚ)) + (U := (-(11746208074433576911541 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_15_4 : Uω (aρ 4) (bρ 4) (396324613 / 1000000000000 : ℝ) ≤ @@ -982,23 +906,21 @@ lemma U_15_4 : have hlg : Real.log (5097653032921 / 400000000000000 : ℝ) ≤ (-(43626843011011594664449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (5097653032921 / 400000000000000 : ℝ) = (5097653032921 / 3125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5097653032921 / 3125000000000 : ℚ)) - (U := (4893459609988405335551 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (5097653032921 / 3125000000000 : ℝ) ≤ - (4893459609988405335551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (897787595321 / 200000000000000 : ℝ)) (q := - (5097653032921 / 400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5097653032921 / 400000000000000 : ℚ)) + (r' := (5097653032921 / 3125000000000 : ℚ)) + (U := (-(43626843011011594664449 / 10000000000000000000000 : ℚ))) + (U' := (4893459609988405335551 / 10000000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (396324613 / 1000000000000 : ℚ)) + (s := (897787595321 / 200000000000000 : ℚ)) + (q := (5097653032921 / 400000000000000 : ℚ)) + (U := (-(43626843011011594664449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_15_5 : Uω (aρ 5) (bρ 5) (396324613 / 1000000000000 : ℝ) ≤ @@ -1006,25 +928,21 @@ lemma U_15_5 : have hlg : Real.log (362686051450057 / 20000000000000000 : ℝ) ≤ (-(20049749814838098711663 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (362686051450057 / 20000000000000000 : ℝ) = - (362686051450057 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (362686051450057 / 312500000000000 : ℚ)) - (U := (744665594161901288337 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (362686051450057 / 312500000000000 : ℝ) ≤ - (744665594161901288337 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (34502860235057 / 10000000000000000 : ℝ)) (q := - (362686051450057 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (362686051450057 / 20000000000000000 : ℚ)) + (r' := (362686051450057 / 312500000000000 : ℚ)) + (U := (-(20049749814838098711663 / 5000000000000000000000 : ℚ))) + (U' := (744665594161901288337 / 5000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (396324613 / 1000000000000 : ℚ)) + (s := (34502860235057 / 10000000000000000 : ℚ)) + (q := (362686051450057 / 20000000000000000 : ℚ)) + (U := (-(20049749814838098711663 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_15_6 : Uω (aρ 6) (bρ 6) (396324613 / 1000000000000 : ℝ) ≤ @@ -1171,23 +1089,21 @@ lemma U_16_1 : have hlg : Real.log (1774287399843 / 312500000000000 : ℝ) ≤ (-(51712055896552965688933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (1774287399843 / 312500000000000 : ℝ) = (1774287399843 / 1220703125000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1774287399843 / 1220703125000 : ℚ)) - (U := (3739718527447034311067 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1774287399843 / 1220703125000 : ℝ) ≤ - (3739718527447034311067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (3370611756247 / 625000000000000 : ℝ)) (q := - (1774287399843 / 312500000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1774287399843 / 312500000000000 : ℚ)) + (r' := (1774287399843 / 1220703125000 : ℚ)) + (U := (-(51712055896552965688933 / 10000000000000000000000 : ℚ))) + (U' := (3739718527447034311067 / 10000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (974522519 / 2000000000000 : ℚ)) + (s := (3370611756247 / 625000000000000 : ℚ)) + (q := (1774287399843 / 312500000000000 : ℚ)) + (U := (-(51712055896552965688933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_16_2 : Uω (aρ 2) (bρ 2) (974522519 / 2000000000000 : ℝ) ≤ @@ -1195,25 +1111,21 @@ lemma U_16_2 : have hlg : Real.log (135458842723471 / 20000000000000000 : ℝ) ≤ (-(49948197000145039205691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (135458842723471 / 20000000000000000 : ℝ) = - (135458842723471 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (135458842723471 / 78125000000000 : ℚ)) - (U := (5503577423854960794309 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (135458842723471 / 78125000000000 : ℝ) ≤ - (5503577423854960794309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (52065224723471 / 10000000000000000 : ℝ)) (q := - (135458842723471 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (135458842723471 / 20000000000000000 : ℚ)) + (r' := (135458842723471 / 78125000000000 : ℚ)) + (U := (-(49948197000145039205691 / 10000000000000000000000 : ℚ))) + (U' := (5503577423854960794309 / 10000000000000000000000 : ℚ)) + 8 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (974522519 / 2000000000000 : ℚ)) + (s := (52065224723471 / 10000000000000000 : ℚ)) + (q := (135458842723471 / 20000000000000000 : ℚ)) + (U := (-(49948197000145039205691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_16_3 : Uω (aρ 3) (bρ 3) (974522519 / 2000000000000 : ℝ) ≤ @@ -1221,23 +1133,21 @@ lemma U_16_3 : have hlg : Real.log (2794531439597 / 312500000000000 : ℝ) ≤ (-(11792350042914402417241 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (2794531439597 / 312500000000000 : ℝ) = (2794531439597 / 2441406250000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2794531439597 / 2441406250000 : ℚ)) - (U := (337725612335597582759 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2794531439597 / 2441406250000 : ℝ) ≤ - (337725612335597582759 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (3003767986513 / 625000000000000 : ℝ)) (q := - (2794531439597 / 312500000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2794531439597 / 312500000000000 : ℚ)) + (r' := (2794531439597 / 2441406250000 : ℚ)) + (U := (-(11792350042914402417241 / 2500000000000000000000 : ℚ))) + (U' := (337725612335597582759 / 2500000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (974522519 / 2000000000000 : ℚ)) + (s := (3003767986513 / 625000000000000 : ℚ)) + (q := (2794531439597 / 312500000000000 : ℚ)) + (U := (-(11792350042914402417241 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_16_4 : Uω (aρ 4) (bρ 4) (974522519 / 2000000000000 : ℝ) ≤ @@ -1245,25 +1155,21 @@ lemma U_16_4 : have hlg : Real.log (124753098670197 / 10000000000000000 : ℝ) ≤ (-(219200189839688302473 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (124753098670197 / 10000000000000000 : ℝ) = - (124753098670197 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (124753098670197 / 78125000000000 : ℚ)) - (U := (23401323265311697527 / 50000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (124753098670197 / 78125000000000 : ℝ) ≤ - (23401323265311697527 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (20211145962697 / 5000000000000000 : ℝ)) (q := - (124753098670197 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (124753098670197 / 10000000000000000 : ℚ)) + (r' := (124753098670197 / 78125000000000 : ℚ)) + (U := (-(219200189839688302473 / 50000000000000000000 : ℚ))) + (U' := (23401323265311697527 / 50000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (974522519 / 2000000000000 : ℚ)) + (s := (20211145962697 / 5000000000000000 : ℚ)) + (q := (124753098670197 / 10000000000000000 : ℚ)) + (U := (-(219200189839688302473 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_16_5 : Uω (aρ 5) (bρ 5) (974522519 / 2000000000000 : ℝ) ≤ @@ -1271,25 +1177,21 @@ lemma U_16_5 : have hlg : Real.log (351654077718997 / 20000000000000000 : ℝ) ≤ (-(808167918466123975469 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (351654077718997 / 20000000000000000 : ℝ) = - (351654077718997 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (351654077718997 / 312500000000000 : ℚ)) - (U := (23608697893876024531 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (351654077718997 / 312500000000000 : ℝ) ≤ - (23608697893876024531 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (24380252968997 / 10000000000000000 : ℝ)) (q := - (351654077718997 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [aρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (351654077718997 / 20000000000000000 : ℚ)) + (r' := (351654077718997 / 312500000000000 : ℚ)) + (U := (-(808167918466123975469 / 200000000000000000000 : ℚ))) + (U' := (23608697893876024531 / 200000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 5) (t := (974522519 / 2000000000000 : ℚ)) + (s := (24380252968997 / 10000000000000000 : ℚ)) + (q := (351654077718997 / 20000000000000000 : ℚ)) + (U := (-(808167918466123975469 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_16_6 : Uω (aρ 6) (bρ 6) (974522519 / 2000000000000 : ℝ) ≤ @@ -1435,24 +1337,21 @@ lemma U_17_1 : have hlg : Real.log (27909474323909 / 5000000000000000 : ℝ) ≤ (-(1037645395330397781579 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (27909474323909 / 5000000000000000 : ℝ) = (27909474323909 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27909474323909 / 19531250000000 : ℚ)) - (U := (71390093149602218421 / 200000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27909474323909 / 19531250000000 : ℝ) ≤ - (71390093149602218421 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (13230664567659 / 2500000000000000 : ℝ)) (q := - (27909474323909 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27909474323909 / 5000000000000000 : ℚ)) + (r' := (27909474323909 / 19531250000000 : ℚ)) + (U := (-(1037645395330397781579 / 200000000000000000000 : ℚ))) + (U' := (71390093149602218421 / 200000000000000000000 : ℚ)) + 8 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (289098953 / 500000000000 : ℚ)) + (s := (13230664567659 / 2500000000000000 : ℚ)) + (q := (27909474323909 / 5000000000000000 : ℚ)) + (U := (-(1037645395330397781579 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_17_2 : Uω (aρ 2) (bρ 2) (289098953 / 500000000000 : ℝ) ≤ @@ -1460,25 +1359,21 @@ lemma U_17_2 : have hlg : Real.log (133080139249959 / 20000000000000000 : ℝ) ≤ (-(50125360529440552437197 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (133080139249959 / 20000000000000000 : ℝ) = - (133080139249959 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (133080139249959 / 78125000000000 : ℚ)) - (U := (5326413894559447562803 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (133080139249959 / 78125000000000 : ℝ) ≤ - (5326413894559447562803 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (50595887714959 / 10000000000000000 : ℝ)) (q := - (133080139249959 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (133080139249959 / 20000000000000000 : ℚ)) + (r' := (133080139249959 / 78125000000000 : ℚ)) + (U := (-(50125360529440552437197 / 10000000000000000000000 : ℚ))) + (U' := (5326413894559447562803 / 10000000000000000000000 : ℚ)) + 8 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (289098953 / 500000000000 : ℚ)) + (s := (50595887714959 / 10000000000000000 : ℚ)) + (q := (133080139249959 / 20000000000000000 : ℚ)) + (U := (-(50125360529440552437197 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_17_3 : Uω (aρ 3) (bρ 3) (289098953 / 500000000000 : ℝ) ≤ @@ -1486,25 +1381,21 @@ lemma U_17_3 : have hlg : Real.log (175407785120543 / 20000000000000000 : ℝ) ≤ (-(47363740868116265483369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (175407785120543 / 20000000000000000 : ℝ) = - (175407785120543 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (175407785120543 / 156250000000000 : ℚ)) - (U := (1156561752883734516631 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (175407785120543 / 156250000000000 : ℝ) ≤ - (1156561752883734516631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (45527427235543 / 10000000000000000 : ℝ)) (q := - (175407785120543 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (175407785120543 / 20000000000000000 : ℚ)) + (r' := (175407785120543 / 156250000000000 : ℚ)) + (U := (-(47363740868116265483369 / 10000000000000000000000 : ℚ))) + (U' := (1156561752883734516631 / 10000000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (289098953 / 500000000000 : ℚ)) + (s := (45527427235543 / 10000000000000000 : ℚ)) + (q := (175407785120543 / 20000000000000000 : ℚ)) + (U := (-(47363740868116265483369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_17_4 : Uω (aρ 4) (bρ 4) (289098953 / 500000000000 : ℝ) ≤ @@ -1512,24 +1403,21 @@ lemma U_17_4 : have hlg : Real.log (48718750950201 / 4000000000000000 : ℝ) ≤ (-(11019964131301389298539 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (48718750950201 / 4000000000000000 : ℝ) = (48718750950201 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48718750950201 / 31250000000000 : ℚ)) - (U := (1110111523948610701461 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (48718750950201 / 31250000000000 : ℝ) ≤ - (1110111523948610701461 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7083843160201 / 2000000000000000 : ℝ)) (q := - (48718750950201 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48718750950201 / 4000000000000000 : ℚ)) + (r' := (48718750950201 / 31250000000000 : ℚ)) + (U := (-(11019964131301389298539 / 2500000000000000000000 : ℚ))) + (U' := (1110111523948610701461 / 2500000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (289098953 / 500000000000 : ℚ)) + (s := (7083843160201 / 2000000000000000 : ℚ)) + (q := (48718750950201 / 4000000000000000 : ℚ)) + (U := (-(11019964131301389298539 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_17_5 : Uω (aρ 5) (bρ 5) (289098953 / 500000000000 : ℝ) ≤ @@ -1681,24 +1569,21 @@ lemma U_18_1 : have hlg : Real.log (54215661123871 / 10000000000000000 : ℝ) ≤ (-(52173705525642853674791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (54215661123871 / 10000000000000000 : ℝ) = (54215661123871 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54215661123871 / 39062500000000 : ℚ)) - (U := (3278068898357146325209 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54215661123871 / 39062500000000 : ℝ) ≤ - (3278068898357146325209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (25616860236371 / 5000000000000000 : ℝ)) (q := - (54215661123871 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54215661123871 / 10000000000000000 : ℚ)) + (r' := (54215661123871 / 39062500000000 : ℚ)) + (U := (-(52173705525642853674791 / 10000000000000000000000 : ℚ))) + (U' := (3278068898357146325209 / 10000000000000000000000 : ℚ)) + 8 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (729961631 / 1000000000000 : ℚ)) + (s := (25616860236371 / 5000000000000000 : ℚ)) + (q := (54215661123871 / 10000000000000000 : ℚ)) + (U := (-(52173705525642853674791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_18_2 : Uω (aρ 2) (bρ 2) (729961631 / 1000000000000 : ℝ) ≤ @@ -1706,25 +1591,21 @@ lemma U_18_2 : have hlg : Real.log (129048676752739 / 20000000000000000 : ℝ) ≤ (-(157603058690652939389 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (129048676752739 / 20000000000000000 : ℝ) = - (129048676752739 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (129048676752739 / 78125000000000 : ℚ)) - (U := (15683736384347060611 / 31250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (129048676752739 / 78125000000000 : ℝ) ≤ - (15683736384347060611 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (48082062467739 / 10000000000000000 : ℝ)) (q := - (129048676752739 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (129048676752739 / 20000000000000000 : ℚ)) + (r' := (129048676752739 / 78125000000000 : ℚ)) + (U := (-(157603058690652939389 / 31250000000000000000 : ℚ))) + (U' := (15683736384347060611 / 31250000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (729961631 / 1000000000000 : ℚ)) + (s := (48082062467739 / 10000000000000000 : ℚ)) + (q := (129048676752739 / 20000000000000000 : ℚ)) + (U := (-(157603058690652939389 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_18_3 : Uω (aρ 3) (bρ 3) (729961631 / 1000000000000 : ℝ) ≤ @@ -1732,24 +1613,21 @@ lemma U_18_3 : have hlg : Real.log (33872122933673 / 4000000000000000 : ℝ) ≤ (-(5964321618170938271907 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (33872122933673 / 4000000000000000 : ℝ) = (33872122933673 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33872122933673 / 31250000000000 : ℚ)) - (U := (100716209454061728093 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (33872122933673 / 31250000000000 : ℝ) ≤ - (100716209454061728093 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (8199578806673 / 2000000000000000 : ℝ)) (q := - (33872122933673 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33872122933673 / 4000000000000000 : ℚ)) + (r' := (33872122933673 / 31250000000000 : ℚ)) + (U := (-(5964321618170938271907 / 1250000000000000000000 : ℚ))) + (U' := (100716209454061728093 / 1250000000000000000000 : ℚ)) + 7 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (729961631 / 1000000000000 : ℚ)) + (s := (8199578806673 / 2000000000000000 : ℚ)) + (q := (33872122933673 / 4000000000000000 : ℚ)) + (U := (-(5964321618170938271907 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_18_4 : Uω (aρ 4) (bρ 4) (729961631 / 1000000000000 : ℝ) ≤ @@ -1757,24 +1635,21 @@ lemma U_18_4 : have hlg : Real.log (57914011427119 / 5000000000000000 : ℝ) ≤ (-(44582338407334756483981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (57914011427119 / 5000000000000000 : ℝ) = (57914011427119 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57914011427119 / 39062500000000 : ℚ)) - (U := (3937964213665243516019 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (57914011427119 / 39062500000000 : ℝ) ≤ - (3937964213665243516019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6249786002119 / 2500000000000000 : ℝ)) (q := - (57914011427119 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57914011427119 / 5000000000000000 : ℚ)) + (r' := (57914011427119 / 39062500000000 : ℚ)) + (U := (-(44582338407334756483981 / 10000000000000000000000 : ℚ))) + (U' := (3937964213665243516019 / 10000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (729961631 / 1000000000000 : ℚ)) + (s := (6249786002119 / 2500000000000000 : ℚ)) + (q := (57914011427119 / 5000000000000000 : ℚ)) + (U := (-(44582338407334756483981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_18_5 : Uω (aρ 5) (bρ 5) (729961631 / 1000000000000 : ℝ) ≤ @@ -1926,24 +1801,21 @@ lemma U_19_1 : have hlg : Real.log (26705986680359 / 5000000000000000 : ℝ) ≤ (-(26161527144129535042071 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (26705986680359 / 5000000000000000 : ℝ) = (26705986680359 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26705986680359 / 19531250000000 : ℚ)) - (U := (1564360067870464957929 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (26705986680359 / 19531250000000 : ℝ) ≤ - (1564360067870464957929 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (12596290892859 / 2500000000000000 : ℝ)) (q := - (26705986680359 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26705986680359 / 5000000000000000 : ℚ)) + (r' := (26705986680359 / 19531250000000 : ℚ)) + (U := (-(26161527144129535042071 / 5000000000000000000000 : ℚ))) + (U' := (1564360067870464957929 / 5000000000000000000000 : ℚ)) + 8 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (1611686987 / 2000000000000 : ℚ)) + (s := (12596290892859 / 2500000000000000 : ℚ)) + (q := (26705986680359 / 5000000000000000 : ℚ)) + (U := (-(26161527144129535042071 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_19_2 : Uω (aρ 2) (bρ 2) (1611686987 / 2000000000000 : ℝ) ≤ @@ -1951,25 +1823,21 @@ lemma U_19_2 : have hlg : Real.log (127000771489839 / 20000000000000000 : ℝ) ≤ (-(10118588778586567237301 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (127000771489839 / 20000000000000000 : ℝ) = - (127000771489839 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (127000771489839 / 78125000000000 : ℚ)) - (U := (971766106213432762699 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (127000771489839 / 78125000000000 : ℝ) ≤ - (971766106213432762699 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (46792975829839 / 10000000000000000 : ℝ)) (q := - (127000771489839 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (127000771489839 / 20000000000000000 : ℚ)) + (r' := (127000771489839 / 78125000000000 : ℚ)) + (U := (-(10118588778586567237301 / 2000000000000000000000 : ℚ))) + (U' := (971766106213432762699 / 2000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (1611686987 / 2000000000000 : ℚ)) + (s := (46792975829839 / 10000000000000000 : ℚ)) + (q := (127000771489839 / 20000000000000000 : ℚ)) + (U := (-(10118588778586567237301 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_19_3 : Uω (aρ 3) (bρ 3) (1611686987 / 2000000000000 : ℝ) ≤ @@ -1977,24 +1845,21 @@ lemma U_19_3 : have hlg : Real.log (33232058051079 / 4000000000000000 : ℝ) ≤ (-(47905346243074077148493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (33232058051079 / 4000000000000000 : ℝ) = (33232058051079 / 31250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33232058051079 / 31250000000000 : ℚ)) - (U := (614956377925922851507 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (33232058051079 / 31250000000000 : ℝ) ≤ - (614956377925922851507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7711277649079 / 2000000000000000 : ℝ)) (q := - (33232058051079 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33232058051079 / 4000000000000000 : ℚ)) + (r' := (33232058051079 / 31250000000000 : ℚ)) + (U := (-(47905346243074077148493 / 10000000000000000000000 : ℚ))) + (U' := (614956377925922851507 / 10000000000000000000000 : ℚ)) + 7 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (1611686987 / 2000000000000 : ℚ)) + (s := (7711277649079 / 2000000000000000 : ℚ)) + (q := (33232058051079 / 4000000000000000 : ℚ)) + (U := (-(47905346243074077148493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_19_4 : Uω (aρ 4) (bρ 4) (1611686987 / 2000000000000 : ℝ) ≤ @@ -2002,24 +1867,21 @@ lemma U_19_4 : have hlg : Real.log (55889713253743 / 5000000000000000 : ℝ) ≤ (-(8987625693749818873013 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (55889713253743 / 5000000000000000 : ℝ) = (55889713253743 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55889713253743 / 39062500000000 : ℚ)) - (U := (716434830450181126987 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55889713253743 / 39062500000000 : ℝ) ≤ - (716434830450181126987 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4415192484993 / 2500000000000000 : ℝ)) (q := - (55889713253743 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [aρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55889713253743 / 5000000000000000 : ℚ)) + (r' := (55889713253743 / 39062500000000 : ℚ)) + (U := (-(8987625693749818873013 / 2000000000000000000000 : ℚ))) + (U' := (716434830450181126987 / 2000000000000000000000 : ℚ)) + 7 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 4) (t := (1611686987 / 2000000000000 : ℚ)) + (s := (4415192484993 / 2500000000000000 : ℚ)) + (q := (55889713253743 / 5000000000000000 : ℚ)) + (U := (-(8987625693749818873013 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_19_5 : Uω (aρ 5) (bρ 5) (1611686987 / 2000000000000 : ℝ) ≤ @@ -2171,24 +2033,21 @@ lemma U_20_1 : have hlg : Real.log (52606829630367 / 10000000000000000 : ℝ) ≤ (-(10494988835400103718169 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (52606829630367 / 10000000000000000 : ℝ) = (52606829630367 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52606829630367 / 39062500000000 : ℚ)) - (U := (595366049399896281831 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52606829630367 / 39062500000000 : ℝ) ≤ - (595366049399896281831 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (24766847367867 / 5000000000000000 : ℝ)) (q := - (52606829630367 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52606829630367 / 10000000000000000 : ℚ)) + (r' := (52606829630367 / 39062500000000 : ℚ)) + (U := (-(10494988835400103718169 / 2000000000000000000000 : ℚ))) + (U' := (595366049399896281831 / 2000000000000000000000 : ℚ)) + 8 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (220431339 / 250000000000 : ℚ)) + (s := (24766847367867 / 5000000000000000 : ℚ)) + (q := (52606829630367 / 10000000000000000 : ℚ)) + (U := (-(10494988835400103718169 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_20_2 : Uω (aρ 2) (bρ 2) (220431339 / 250000000000 : ℝ) ≤ @@ -2196,24 +2055,21 @@ lemma U_20_2 : have hlg : Real.log (12492899522193 / 2000000000000000 : ℝ) ≤ (-(50757420127736585768143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (12492899522193 / 2000000000000000 : ℝ) = (12492899522193 / 7812500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12492899522193 / 7812500000000 : ℚ)) - (U := (4694354296263414231857 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12492899522193 / 7812500000000 : ℝ) ≤ - (4694354296263414231857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4548001818693 / 1000000000000000 : ℝ)) (q := - (12492899522193 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12492899522193 / 2000000000000000 : ℚ)) + (r' := (12492899522193 / 7812500000000 : ℚ)) + (U := (-(50757420127736585768143 / 10000000000000000000000 : ℚ))) + (U' := (4694354296263414231857 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (220431339 / 250000000000 : ℚ)) + (s := (4548001818693 / 1000000000000000 : ℚ)) + (q := (12492899522193 / 2000000000000000 : ℚ)) + (U := (-(50757420127736585768143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_20_3 : Uω (aρ 3) (bρ 3) (220431339 / 250000000000 : ℝ) ≤ @@ -2221,25 +2077,21 @@ lemma U_20_3 : have hlg : Real.log (162810545224097 / 20000000000000000 : ℝ) ≤ (-(24054501625710163523737 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (162810545224097 / 20000000000000000 : ℝ) = - (162810545224097 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (162810545224097 / 156250000000000 : ℚ)) - (U := (205649684789836476263 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (162810545224097 / 156250000000000 : ℝ) ≤ - (205649684789836476263 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (35965461839097 / 10000000000000000 : ℝ)) (q := - (162810545224097 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (162810545224097 / 20000000000000000 : ℚ)) + (r' := (162810545224097 / 156250000000000 : ℚ)) + (U := (-(24054501625710163523737 / 5000000000000000000000 : ℚ))) + (U' := (205649684789836476263 / 5000000000000000000000 : ℚ)) + 7 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (220431339 / 250000000000 : ℚ)) + (s := (35965461839097 / 10000000000000000 : ℚ)) + (q := (162810545224097 / 20000000000000000 : ℚ)) + (U := (-(24054501625710163523737 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_20_4 : Uω (aρ 4) (bρ 4) (220431339 / 250000000000 : ℝ) ≤ @@ -2396,25 +2248,21 @@ lemma U_21_1 : have hlg : Real.log (102444728028721 / 20000000000000000 : ℝ) ≤ (-(329635258503986697477 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (102444728028721 / 20000000000000000 : ℝ) = - (102444728028721 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (102444728028721 / 78125000000000 : ℚ)) - (U := (16938331646013302523 / 62500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (102444728028721 / 78125000000000 : ℝ) ≤ - (16938331646013302523 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (48066166776221 / 10000000000000000 : ℝ)) (q := - (102444728028721 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (102444728028721 / 20000000000000000 : ℚ)) + (r' := (102444728028721 / 78125000000000 : ℚ)) + (U := (-(329635258503986697477 / 62500000000000000000 : ℚ))) + (U' := (16938331646013302523 / 62500000000000000000 : ℚ)) + 8 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (4047462733 / 4000000000000 : ℚ)) + (s := (48066166776221 / 10000000000000000 : ℚ)) + (q := (102444728028721 / 20000000000000000 : ℚ)) + (U := (-(329635258503986697477 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_21_2 : Uω (aρ 2) (bρ 2) (4047462733 / 4000000000000 : ℝ) ≤ @@ -2422,24 +2270,21 @@ lemma U_21_2 : have hlg : Real.log (12131394246941 / 2000000000000000 : ℝ) ≤ (-(25525528995361187317657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (12131394246941 / 2000000000000000 : ℝ) = (12131394246941 / 7812500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12131394246941 / 7812500000000 : ℚ)) - (U := (2200358216638812682343 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12131394246941 / 7812500000000 : ℝ) ≤ - (2200358216638812682343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4316636870691 / 1000000000000000 : ℝ)) (q := - (12131394246941 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12131394246941 / 2000000000000000 : ℚ)) + (r' := (12131394246941 / 7812500000000 : ℚ)) + (U := (-(25525528995361187317657 / 5000000000000000000000 : ℚ))) + (U' := (2200358216638812682343 / 5000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (4047462733 / 4000000000000 : ℚ)) + (s := (4316636870691 / 1000000000000000 : ℚ)) + (q := (12131394246941 / 2000000000000000 : ℚ)) + (U := (-(25525528995361187317657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_21_3 : Uω (aρ 3) (bρ 3) (4047462733 / 4000000000000 : ℝ) ≤ @@ -2447,24 +2292,21 @@ lemma U_21_3 : have hlg : Real.log (78304506299861 / 10000000000000000 : ℝ) ≤ (-(48497352170934822805119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (78304506299861 / 10000000000000000 : ℝ) = (78304506299861 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78304506299861 / 78125000000000 : ℚ)) - (U := (22950450065177194881 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (78304506299861 / 78125000000000 : ℝ) ≤ - (22950450065177194881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (15532666243611 / 5000000000000000 : ℝ)) (q := - (78304506299861 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78304506299861 / 10000000000000000 : ℚ)) + (r' := (78304506299861 / 78125000000000 : ℚ)) + (U := (-(48497352170934822805119 / 10000000000000000000000 : ℚ))) + (U' := (22950450065177194881 / 10000000000000000000000 : ℚ)) + 7 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (4047462733 / 4000000000000 : ℚ)) + (s := (15532666243611 / 5000000000000000 : ℚ)) + (q := (78304506299861 / 10000000000000000 : ℚ)) + (U := (-(48497352170934822805119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_21_4 : Uω (aρ 4) (bρ 4) (4047462733 / 4000000000000 : ℝ) ≤ @@ -2621,24 +2463,21 @@ lemma U_22_1 : have hlg : Real.log (49832962239517 / 10000000000000000 : ℝ) ≤ (-(2650831856230185575557 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (49832962239517 / 10000000000000000 : ℝ) = (49832962239517 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49832962239517 / 39062500000000 : ℚ)) - (U := (121756864969814424443 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (49832962239517 / 39062500000000 : ℝ) ≤ - (121756864969814424443 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (23294383249517 / 5000000000000000 : ℝ)) (q := - (49832962239517 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49832962239517 / 10000000000000000 : ℚ)) + (r' := (49832962239517 / 39062500000000 : ℚ)) + (U := (-(2650831856230185575557 / 500000000000000000000 : ℚ))) + (U' := (121756864969814424443 / 500000000000000000000 : ℚ)) + 8 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (2284012021 / 2000000000000 : ℚ)) + (s := (23294383249517 / 5000000000000000 : ℚ)) + (q := (49832962239517 / 10000000000000000 : ℚ)) + (U := (-(2650831856230185575557 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_22_2 : Uω (aρ 2) (bρ 2) (2284012021 / 2000000000000 : ℝ) ≤ @@ -2646,24 +2485,21 @@ lemma U_22_2 : have hlg : Real.log (58804608871521 / 10000000000000000 : ℝ) ≤ (-(51361201358950362094901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (58804608871521 / 10000000000000000 : ℝ) = (58804608871521 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58804608871521 / 39062500000000 : ℚ)) - (U := (4090573065049637905099 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58804608871521 / 39062500000000 : ℝ) ≤ - (4090573065049637905099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (20381523626521 / 5000000000000000 : ℝ)) (q := - (58804608871521 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58804608871521 / 10000000000000000 : ℚ)) + (r' := (58804608871521 / 39062500000000 : ℚ)) + (U := (-(51361201358950362094901 / 10000000000000000000000 : ℚ))) + (U' := (4090573065049637905099 / 10000000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (2284012021 / 2000000000000 : ℚ)) + (s := (20381523626521 / 5000000000000000 : ℚ)) + (q := (58804608871521 / 10000000000000000 : ℚ)) + (U := (-(51361201358950362094901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_22_3 : Uω (aρ 3) (bρ 3) (2284012021 / 2000000000000 : ℝ) ≤ @@ -2671,24 +2507,21 @@ lemma U_22_3 : have hlg : Real.log (37385038657803 / 5000000000000000 : ℝ) ≤ (-(979184520167902038687 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (37385038657803 / 5000000000000000 : ℝ) = (37385038657803 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37385038657803 / 19531250000000 : ℚ)) - (U := (129850968312097961313 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37385038657803 / 19531250000000 : ℝ) ≤ - (129850968312097961313 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (6324469447803 / 2500000000000000 : ℝ)) (q := - (37385038657803 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37385038657803 / 5000000000000000 : ℚ)) + (r' := (37385038657803 / 19531250000000 : ℚ)) + (U := (-(979184520167902038687 / 200000000000000000000 : ℚ))) + (U' := (129850968312097961313 / 200000000000000000000 : ℚ)) + 8 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (2284012021 / 2000000000000 : ℚ)) + (s := (6324469447803 / 2500000000000000 : ℚ)) + (q := (37385038657803 / 5000000000000000 : ℚ)) + (U := (-(979184520167902038687 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_22_4 : Uω (aρ 4) (bρ 4) (2284012021 / 2000000000000 : ℝ) ≤ @@ -2845,24 +2678,21 @@ lemma U_23_1 : have hlg : Real.log (48438139215859 / 10000000000000000 : ℝ) ≤ (-(26650264330778109932447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (48438139215859 / 10000000000000000 : ℝ) = (48438139215859 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48438139215859 / 39062500000000 : ℚ)) - (U := (1075622881221890067553 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48438139215859 / 39062500000000 : ℝ) ≤ - (1075622881221890067553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (22550261862109 / 5000000000000000 : ℝ)) (q := - (48438139215859 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48438139215859 / 10000000000000000 : ℚ)) + (r' := (48438139215859 / 39062500000000 : ℚ)) + (U := (-(26650264330778109932447 / 5000000000000000000000 : ℚ))) + (U' := (1075622881221890067553 / 5000000000000000000000 : ℚ)) + 8 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (5088585351 / 4000000000000 : ℚ)) + (s := (22550261862109 / 5000000000000000 : ℚ)) + (q := (48438139215859 / 10000000000000000 : ℚ)) + (U := (-(26650264330778109932447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_23_2 : Uω (aρ 2) (bρ 2) (5088585351 / 4000000000000 : ℝ) ≤ @@ -2870,23 +2700,21 @@ lemma U_23_2 : have hlg : Real.log (4551916935163 / 800000000000000 : ℝ) ≤ (-(206762531076714809157 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (4551916935163 / 800000000000000 : ℝ) = (4551916935163 / 3125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4551916935163 / 3125000000000 : ℚ)) - (U := (15044566619285190843 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (4551916935163 / 3125000000000 : ℝ) ≤ - (15044566619285190843 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1530126246463 / 400000000000000 : ℝ)) (q := - (4551916935163 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4551916935163 / 800000000000000 : ℚ)) + (r' := (4551916935163 / 3125000000000 : ℚ)) + (U := (-(206762531076714809157 / 40000000000000000000 : ℚ))) + (U' := (15044566619285190843 / 40000000000000000000 : ℚ)) + 8 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (5088585351 / 4000000000000 : ℚ)) + (s := (1530126246463 / 400000000000000 : ℚ)) + (q := (4551916935163 / 800000000000000 : ℚ)) + (U := (-(206762531076714809157 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_23_3 : Uω (aρ 3) (bρ 3) (5088585351 / 4000000000000 : ℝ) ≤ @@ -2894,24 +2722,21 @@ lemma U_23_3 : have hlg : Real.log (35195443021111 / 5000000000000000 : ℝ) ≤ (-(49562765747407728412987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (35195443021111 / 5000000000000000 : ℝ) = (35195443021111 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35195443021111 / 19531250000000 : ℚ)) - (U := (5889008676592271587013 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35195443021111 / 19531250000000 : ℝ) ≤ - (5889008676592271587013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1115056157309 / 625000000000000 : ℝ)) (q := - (35195443021111 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [aρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35195443021111 / 5000000000000000 : ℚ)) + (r' := (35195443021111 / 19531250000000 : ℚ)) + (U := (-(49562765747407728412987 / 10000000000000000000000 : ℚ))) + (U' := (5889008676592271587013 / 10000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 3) (t := (5088585351 / 4000000000000 : ℚ)) + (s := (1115056157309 / 625000000000000 : ℚ)) + (q := (35195443021111 / 5000000000000000 : ℚ)) + (U := (-(49562765747407728412987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_23_4 : Uω (aρ 4) (bρ 4) (5088585351 / 4000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U02.lean b/LeanPool/Zeta5Irrational/Table/U02.lean index 4f37004813..ca819e389b 100644 --- a/LeanPool/Zeta5Irrational/Table/U02.lean +++ b/LeanPool/Zeta5Irrational/Table/U02.lean @@ -24,24 +24,21 @@ lemma U_24_1 : have hlg : Real.log (23518669903887 / 5000000000000000 : ℝ) ≤ (-(53593986196108414589993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (23518669903887 / 5000000000000000 : ℝ) = (23518669903887 / 19531250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23518669903887 / 19531250000000 : ℚ)) - (U := (1857788227891585410007 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23518669903887 / 19531250000000 : ℝ) ≤ - (1857788227891585410007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (10900082045137 / 2500000000000000 : ℝ)) (q := - (23518669903887 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23518669903887 / 5000000000000000 : ℚ)) + (r' := (23518669903887 / 19531250000000 : ℚ)) + (U := (-(53593986196108414589993 / 10000000000000000000000 : ℚ))) + (U' := (1857788227891585410007 / 10000000000000000000000 : ℚ)) + 8 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (280457333 / 200000000000 : ℚ)) + (s := (10900082045137 / 2500000000000000 : ℚ)) + (q := (23518669903887 / 5000000000000000 : ℚ)) + (U := (-(53593986196108414589993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_24_2 : Uω (aρ 2) (bρ 2) (280457333 / 200000000000 : ℝ) ≤ @@ -49,25 +46,21 @@ lemma U_24_2 : have hlg : Real.log (109857535172831 / 20000000000000000 : ℝ) ≤ (-(52043031588685060884247 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (109857535172831 / 20000000000000000 : ℝ) = - (109857535172831 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (109857535172831 / 78125000000000 : ℚ)) - (U := (3408742835314939115753 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (109857535172831 / 78125000000000 : ℝ) ≤ - (3408742835314939115753 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (35614171227831 / 10000000000000000 : ℝ)) (q := - (109857535172831 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (109857535172831 / 20000000000000000 : ℚ)) + (r' := (109857535172831 / 78125000000000 : ℚ)) + (U := (-(52043031588685060884247 / 10000000000000000000000 : ℚ))) + (U' := (3408742835314939115753 / 10000000000000000000000 : ℚ)) + 8 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (280457333 / 200000000000 : ℚ)) + (s := (35614171227831 / 10000000000000000 : ℚ)) + (q := (109857535172831 / 20000000000000000 : ℚ)) + (U := (-(52043031588685060884247 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_24_3 : Uω (aρ 3) (bρ 3) (280457333 / 200000000000 : ℝ) ≤ @@ -230,23 +223,21 @@ lemma U_25_1 : have hlg : Real.log (8914471820163 / 2000000000000000 : ℝ) ≤ (-(27066132270492516043287 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (8914471820163 / 2000000000000000 : ℝ) = (8914471820163 / 7812500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8914471820163 / 7812500000000 : ℚ)) - (U := (659754941507483956713 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8914471820163 / 7812500000000 : ℝ) ≤ - (659754941507483956713 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4094527076413 / 1000000000000000 : ℝ)) (q := - (8914471820163 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8914471820163 / 2000000000000000 : ℚ)) + (r' := (8914471820163 / 7812500000000 : ℚ)) + (U := (-(27066132270492516043287 / 5000000000000000000000 : ℚ))) + (U' := (659754941507483956713 / 5000000000000000000000 : ℚ)) + 8 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (6519108259 / 4000000000000 : ℚ)) + (s := (4094527076413 / 1000000000000000 : ℚ)) + (q := (8914471820163 / 2000000000000000 : ℚ)) + (U := (-(27066132270492516043287 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_25_2 : Uω (aρ 2) (bρ 2) (6519108259 / 4000000000000 : ℝ) ≤ @@ -254,25 +245,21 @@ lemma U_25_2 : have hlg : Real.log (102558512735791 / 20000000000000000 : ℝ) ≤ (-(52730540587954460599153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (102558512735791 / 20000000000000000 : ℝ) = - (102558512735791 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (102558512735791 / 78125000000000 : ℚ)) - (U := (2721233836045539400847 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (102558512735791 / 78125000000000 : ℝ) ≤ - (2721233836045539400847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (30590052788291 / 10000000000000000 : ℝ)) (q := - (102558512735791 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (102558512735791 / 20000000000000000 : ℚ)) + (r' := (102558512735791 / 78125000000000 : ℚ)) + (U := (-(52730540587954460599153 / 10000000000000000000000 : ℚ))) + (U' := (2721233836045539400847 / 10000000000000000000000 : ℚ)) + 8 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (6519108259 / 4000000000000 : ℚ)) + (s := (30590052788291 / 10000000000000000 : ℚ)) + (q := (102558512735791 / 20000000000000000 : ℚ)) + (U := (-(52730540587954460599153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_25_3 : Uω (aρ 3) (bρ 3) (6519108259 / 4000000000000 : ℝ) ≤ @@ -434,23 +421,21 @@ lemma U_26_1 : have hlg : Real.log (4208288987711 / 1000000000000000 : ℝ) ≤ (-(13676747820096012817053 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (4208288987711 / 1000000000000000 : ℝ) = (4208288987711 / 3906250000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4208288987711 / 3906250000000 : ℚ)) - (U := (186195785903987182947 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4208288987711 / 3906250000000 : ℝ) ≤ - (186195785903987182947 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (1912061815711 / 500000000000000 : ℝ)) (q := - (4208288987711 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4208288987711 / 1000000000000000 : ℚ)) + (r' := (4208288987711 / 3906250000000 : ℚ)) + (U := (-(13676747820096012817053 / 2500000000000000000000 : ℚ))) + (U' := (186195785903987182947 / 2500000000000000000000 : ℚ)) + 8 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (3714534929 / 2000000000000 : ℚ)) + (s := (1912061815711 / 500000000000000 : ℚ)) + (q := (4208288987711 / 1000000000000000 : ℚ)) + (U := (-(13676747820096012817053 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_26_2 : Uω (aρ 2) (bρ 2) (3714534929 / 2000000000000 : ℝ) ≤ @@ -458,24 +443,21 @@ lemma U_26_2 : have hlg : Real.log (94462161952989 / 20000000000000000 : ℝ) ≤ (-(26776440993766361792693 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (94462161952989 / 20000000000000000 : ℝ) = (94462161952989 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (94462161952989 / 78125000000000 : ℚ)) - (U := (949446218233638207307 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (94462161952989 / 78125000000000 : ℝ) ≤ - (949446218233638207307 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (24768606002989 / 10000000000000000 : ℝ)) (q := - (94462161952989 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (94462161952989 / 20000000000000000 : ℚ)) + (r' := (94462161952989 / 78125000000000 : ℚ)) + (U := (-(26776440993766361792693 / 5000000000000000000000 : ℚ))) + (U' := (949446218233638207307 / 5000000000000000000000 : ℚ)) + 8 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (3714534929 / 2000000000000 : ℚ)) + (s := (24768606002989 / 10000000000000000 : ℚ)) + (q := (94462161952989 / 20000000000000000 : ℚ)) + (U := (-(26776440993766361792693 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_26_3 : Uω (aρ 3) (bρ 3) (3714534929 / 2000000000000 : ℝ) ≤ @@ -637,23 +619,21 @@ lemma U_27_1 : have hlg : Real.log (2472708345429 / 625000000000000 : ℝ) ≤ (-(55324376016046487597617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (2472708345429 / 625000000000000 : ℝ) = (2472708345429 / 2441406250000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2472708345429 / 2441406250000 : ℚ)) - (U := (127398407953512402383 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2472708345429 / 2441406250000 : ℝ) ≤ - (127398407953512402383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (8869256902807 / 2500000000000000 : ℝ)) (q := - (2472708345429 / 625000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2472708345429 / 625000000000000 : ℚ)) + (r' := (2472708345429 / 2441406250000 : ℚ)) + (U := (-(55324376016046487597617 / 10000000000000000000000 : ℚ))) + (U' := (127398407953512402383 / 10000000000000000000000 : ℚ)) + 8 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (8339031457 / 4000000000000 : ℚ)) + (s := (8869256902807 / 2500000000000000 : ℚ)) + (q := (2472708345429 / 625000000000000 : ℚ)) + (U := (-(55324376016046487597617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_27_2 : Uω (aρ 2) (bρ 2) (8339031457 / 4000000000000 : ℝ) ≤ @@ -661,24 +641,21 @@ lemma U_27_2 : have hlg : Real.log (84784328831557 / 20000000000000000 : ℝ) ≤ (-(10926753652502540317131 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (84784328831557 / 20000000000000000 : ℝ) = (84784328831557 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84784328831557 / 78125000000000 : ℚ)) - (U := (163601232297459682869 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84784328831557 / 78125000000000 : ℝ) ≤ - (163601232297459682869 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (17365676879057 / 10000000000000000 : ℝ)) (q := - (84784328831557 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [aρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84784328831557 / 20000000000000000 : ℚ)) + (r' := (84784328831557 / 78125000000000 : ℚ)) + (U := (-(10926753652502540317131 / 2000000000000000000000 : ℚ))) + (U' := (163601232297459682869 / 2000000000000000000000 : ℚ)) + 8 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 2) (t := (8339031457 / 4000000000000 : ℚ)) + (s := (17365676879057 / 10000000000000000 : ℚ)) + (q := (84784328831557 / 20000000000000000 : ℚ)) + (U := (-(10926753652502540317131 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_27_3 : Uω (aρ 3) (bρ 3) (8339031457 / 4000000000000 : ℝ) ≤ @@ -841,23 +818,21 @@ lemma U_28_1 : have hlg : Real.log (578219487291 / 156250000000000 : ℝ) ≤ (-(27996295164352877284557 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show (578219487291 / 156250000000000 : ℝ) = (578219487291 / 305175781250 : ℝ) / 2 ^ 9 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (578219487291 / 305175781250 : ℚ)) - (U := (3195327949147122715443 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (578219487291 / 305175781250 : ℝ) ≤ - (3195327949147122715443 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (4079669866031 / 1250000000000000 : ℝ)) (q := - (578219487291 / 156250000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (578219487291 / 156250000000000 : ℚ)) + (r' := (578219487291 / 305175781250 : ℚ)) + (U := (-(27996295164352877284557 / 5000000000000000000000 : ℚ))) + (U' := (3195327949147122715443 / 5000000000000000000000 : ℚ)) + 9 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (289031033 / 125000000000 : ℚ)) + (s := (4079669866031 / 1250000000000000 : ℚ)) + (q := (578219487291 / 156250000000000 : ℚ)) + (U := (-(27996295164352877284557 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_28_2 : Uω (aρ 2) (bρ 2) (289031033 / 125000000000 : ℝ) ≤ @@ -1024,24 +999,21 @@ lemma U_29_1 : have hlg : Real.log (13764879544613 / 5000000000000000 : ℝ) ≤ (-(14737682003414632220873 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show - (13764879544613 / 5000000000000000 : ℝ) = (13764879544613 / 9765625000000 : ℝ) / 2 ^ 9 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13764879544613 / 9765625000000 : ℚ)) - (U := (858129553335367779127 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13764879544613 / 9765625000000 : ℝ) ≤ - (858129553335367779127 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (5414320460863 / 2500000000000000 : ℝ)) (q := - (13764879544613 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13764879544613 / 5000000000000000 : ℚ)) + (r' := (13764879544613 / 9765625000000 : ℚ)) + (U := (-(14737682003414632220873 / 2500000000000000000000 : ℚ))) + (U' := (858129553335367779127 / 2500000000000000000000 : ℚ)) + 9 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (124379927 / 40000000000 : ℚ)) + (s := (5414320460863 / 2500000000000000 : ℚ)) + (q := (13764879544613 / 5000000000000000 : ℚ)) + (U := (-(14737682003414632220873 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_29_2 : Uω (aρ 2) (bρ 2) (124379927 / 40000000000 : ℝ) ≤ @@ -1207,24 +1179,21 @@ lemma U_30_1 : have hlg : Real.log (22101043215827 / 10000000000000000 : ℝ) ≤ (-(1910848611840935650757 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show - (22101043215827 / 10000000000000000 : ℝ) = (22101043215827 / 19531250000000 : ℝ) / 2 ^ 9 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22101043215827 / 19531250000000 : ℚ)) - (U := (38627832752814349243 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22101043215827 / 19531250000000 : ℝ) ≤ - (38627832752814349243 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_left_certificate (s := (7393049825827 / 5000000000000000 : ℝ)) (q := - (22101043215827 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [aρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22101043215827 / 10000000000000000 : ℚ)) + (r' := (22101043215827 / 19531250000000 : ℚ)) + (U := (-(1910848611840935650757 / 312500000000000000000 : ℚ))) + (U' := (38627832752814349243 / 312500000000000000000 : ℚ)) + 9 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_left_certificate_rational + (j := 1) (t := (7016246261 / 2000000000000 : ℚ)) + (s := (7393049825827 / 5000000000000000 : ℚ)) + (q := (22101043215827 / 10000000000000000 : ℚ)) + (U := (-(1910848611840935650757 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_30_2 : Uω (aρ 2) (bρ 2) (7016246261 / 2000000000000 : ℝ) ≤ @@ -1391,24 +1360,21 @@ lemma U_35_1 : have hlg : Real.log (27482550300017 / 10000000000000000 : ℝ) ≤ (-(5896789100911232295581 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show - (27482550300017 / 10000000000000000 : ℝ) = (27482550300017 / 19531250000000 : ℝ) / 2 ^ 9 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27482550300017 / 19531250000000 : ℚ)) - (U := (341535521788767704419 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27482550300017 / 19531250000000 : ℝ) ≤ - (341535521788767704419 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (10799992735017 / 5000000000000000 : ℝ)) (q := - (27482550300017 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27482550300017 / 10000000000000000 : ℚ)) + (r' := (27482550300017 / 19531250000000 : ℚ)) + (U := (-(5896789100911232295581 / 1000000000000000000000 : ℚ))) + (U' := (341535521788767704419 / 1000000000000000000000 : ℚ)) + 9 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19572466643 / 2000000000000 : ℚ)) + (s := (10799992735017 / 5000000000000000 : ℚ)) + (q := (27482550300017 / 10000000000000000 : ℚ)) + (U := (-(5896789100911232295581 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_35_2 : Uω (aρ 2) (bρ 2) (19572466643 / 2000000000000 : ℝ) ≤ @@ -1575,24 +1541,21 @@ lemma U_36_1 : have hlg : Real.log (64665325468751 / 20000000000000000 : ℝ) ≤ (-(28671312100952179027439 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show - (64665325468751 / 20000000000000000 : ℝ) = (64665325468751 / 39062500000000 : ℝ) / 2 ^ 9 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64665325468751 / 39062500000000 : ℚ)) - (U := (2520311012547820972561 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64665325468751 / 39062500000000 : ℝ) ≤ - (2520311012547820972561 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27332521386251 / 10000000000000000 : ℝ)) (q := - (64665325468751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64665325468751 / 20000000000000000 : ℚ)) + (r' := (64665325468751 / 39062500000000 : ℚ)) + (U := (-(28671312100952179027439 / 5000000000000000000000 : ℚ))) + (U' := (2520311012547820972561 / 5000000000000000000000 : ℚ)) + 9 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40732008867 / 4000000000000 : ℚ)) + (s := (27332521386251 / 10000000000000000 : ℚ)) + (q := (64665325468751 / 20000000000000000 : ℚ)) + (U := (-(28671312100952179027439 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_36_2 : Uω (aρ 2) (bρ 2) (40732008867 / 4000000000000 : ℝ) ≤ @@ -1759,24 +1722,21 @@ lemma U_37_1 : have hlg : Real.log (18460920659749 / 5000000000000000 : ℝ) ≤ (-(437620085001547802181 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 9 - (show - (18460920659749 / 5000000000000000 : ℝ) = (18460920659749 / 9765625000000 : ℝ) / 2 ^ 9 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18460920659749 / 9765625000000 : ℚ)) - (U := (49749026146889697819 / 78125000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18460920659749 / 9765625000000 : ℝ) ≤ - (49749026146889697819 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8135797400999 / 2500000000000000 : ℝ)) (q := - (18460920659749 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18460920659749 / 5000000000000000 : ℚ)) + (r' := (18460920659749 / 9765625000000 : ℚ)) + (U := (-(437620085001547802181 / 78125000000000000000 : ℚ))) + (U' := (49749026146889697819 / 78125000000000000000 : ℚ)) + 9 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1322471389 / 125000000000 : ℚ)) + (s := (8135797400999 / 2500000000000000 : ℚ)) + (q := (18460920659749 / 5000000000000000 : ℚ)) + (U := (-(437620085001547802181 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_37_2 : Uω (aρ 2) (bρ 2) (1322471389 / 125000000000 : ℝ) ≤ @@ -1943,24 +1903,21 @@ lemma U_38_1 : have hlg : Real.log (91396272407347 / 20000000000000000 : ℝ) ≤ (-(53882828561175423362757 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (91396272407347 / 20000000000000000 : ℝ) = (91396272407347 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (91396272407347 / 78125000000000 : ℚ)) - (U := (1568945862824576637243 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (91396272407347 / 78125000000000 : ℝ) ≤ - (1568945862824576637243 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (42160401467347 / 10000000000000000 : ℝ)) (q := - (91396272407347 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (91396272407347 / 20000000000000000 : ℚ)) + (r' := (91396272407347 / 78125000000000 : ℚ)) + (U := (-(53882828561175423362757 / 10000000000000000000000 : ℚ))) + (U' := (1568945862824576637243 / 10000000000000000000000 : ℚ)) + 8 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4549323561 / 400000000000 : ℚ)) + (s := (42160401467347 / 10000000000000000 : ℚ)) + (q := (91396272407347 / 20000000000000000 : ℚ)) + (U := (-(53882828561175423362757 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_38_2 : Uω (aρ 2) (bρ 2) (4549323561 / 400000000000 : ℝ) ≤ @@ -2127,24 +2084,21 @@ lemma U_39_1 : have hlg : Real.log (54187773546961 / 10000000000000000 : ℝ) ≤ (-(52178850672124585216629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (54187773546961 / 10000000000000000 : ℝ) = (54187773546961 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54187773546961 / 39062500000000 : ℚ)) - (U := (3272923751875414783371 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54187773546961 / 39062500000000 : ℝ) ≤ - (3272923751875414783371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25602149124461 / 5000000000000000 : ℝ)) (q := - (54187773546961 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54187773546961 / 10000000000000000 : ℚ)) + (r' := (54187773546961 / 39062500000000 : ℚ)) + (U := (-(52178850672124585216629 / 10000000000000000000000 : ℚ))) + (U' := (3272923751875414783371 / 10000000000000000000000 : ℚ)) + 8 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12166846693 / 1000000000000 : ℚ)) + (s := (25602149124461 / 5000000000000000 : ℚ)) + (q := (54187773546961 / 10000000000000000 : ℚ)) + (U := (-(52178850672124585216629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_39_2 : Uω (aρ 2) (bρ 2) (12166846693 / 1000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U03.lean b/LeanPool/Zeta5Irrational/Table/U03.lean index 7987ed11aa..25de963798 100644 --- a/LeanPool/Zeta5Irrational/Table/U03.lean +++ b/LeanPool/Zeta5Irrational/Table/U03.lean @@ -24,25 +24,21 @@ lemma U_40_1 : have hlg : Real.log (174111395654621 / 20000000000000000 : ℝ) ≤ (-(47437922514341080202681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (174111395654621 / 20000000000000000 : ℝ) = - (174111395654621 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (174111395654621 / 156250000000000 : ℚ)) - (U := (1082380106658919797319 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (174111395654621 / 156250000000000 : ℝ) ≤ - (1082380106658919797319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85198635189621 / 10000000000000000 : ℝ)) (q := - (174111395654621 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (174111395654621 / 20000000000000000 : ℚ)) + (r' := (174111395654621 / 156250000000000 : ℚ)) + (U := (-(47437922514341080202681 / 10000000000000000000000 : ℚ))) + (U' := (1082380106658919797319 / 10000000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3068199571 / 200000000000 : ℚ)) + (s := (85198635189621 / 10000000000000000 : ℚ)) + (q := (174111395654621 / 20000000000000000 : ℚ)) + (U := (-(47437922514341080202681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_40_2 : Uω (aρ 2) (bρ 2) (3068199571 / 200000000000 : ℝ) ≤ @@ -210,23 +206,21 @@ lemma U_41_1 : have hlg : Real.log (7494420682899 / 800000000000000 : ℝ) ≤ (-(23352264455452045399363 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (7494420682899 / 800000000000000 : ℝ) = (7494420682899 / 6250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7494420682899 / 6250000000000 : ℚ)) - (U := (907886855047954600637 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (7494420682899 / 6250000000000 : ℝ) ≤ - (907886855047954600637 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1839090346287 / 200000000000000 : ℝ)) (q := - (7494420682899 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7494420682899 / 800000000000000 : ℚ)) + (r' := (7494420682899 / 6250000000000 : ℚ)) + (U := (-(23352264455452045399363 / 5000000000000000000000 : ℚ))) + (U' := (907886855047954600637 / 5000000000000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (255845148549 / 16000000000000 : ℚ)) + (s := (1839090346287 / 200000000000000 : ℚ)) + (q := (7494420682899 / 800000000000000 : ℚ)) + (U := (-(23352264455452045399363 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_41_2 : Uω (aρ 2) (bρ 2) (255845148549 / 16000000000000 : ℝ) ≤ @@ -234,25 +228,21 @@ lemma U_41_2 : have hlg : Real.log (101438833572867 / 20000000000000000 : ℝ) ≤ (-(2113612623409580587049 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (101438833572867 / 20000000000000000 : ℝ) = - (101438833572867 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (101438833572867 / 78125000000000 : ℚ)) - (U := (104458353550419412951 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (101438833572867 / 78125000000000 : ℝ) ≤ - (104458353550419412951 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14900923162371 / 5000000000000000 : ℝ)) (q := - (101438833572867 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (101438833572867 / 20000000000000000 : ℚ)) + (r' := (101438833572867 / 78125000000000 : ℚ)) + (U := (-(2113612623409580587049 / 400000000000000000000 : ℚ))) + (U' := (104458353550419412951 / 400000000000000000000 : ℚ)) + 8 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (255845148549 / 16000000000000 : ℚ)) + (s := (14900923162371 / 5000000000000000 : ℚ)) + (q := (101438833572867 / 20000000000000000 : ℚ)) + (U := (-(2113612623409580587049 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_41_3 : Uω (aρ 3) (bρ 3) (255845148549 / 16000000000000 : ℝ) ≤ @@ -414,24 +404,21 @@ lemma U_42_1 : have hlg : Real.log (12535898731833 / 1250000000000000 : ℝ) ≤ (-(23011512008219083613497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (12535898731833 / 1250000000000000 : ℝ) = (12535898731833 / 9765625000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12535898731833 / 9765625000000 : ℚ)) - (U := (1248639302280916386503 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12535898731833 / 9765625000000 : ℝ) ≤ - (1248639302280916386503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (49337570329039 / 5000000000000000 : ℝ)) (q := - (12535898731833 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12535898731833 / 1250000000000000 : ℚ)) + (r' := (12535898731833 / 9765625000000 : ℚ)) + (U := (-(23011512008219083613497 / 5000000000000000000000 : ℚ))) + (U' := (1248639302280916386503 / 5000000000000000000000 : ℚ)) + 7 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (133117165709 / 8000000000000 : ℚ)) + (s := (49337570329039 / 5000000000000000 : ℚ)) + (q := (12535898731833 / 1250000000000000 : ℚ)) + (U := (-(23011512008219083613497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_42_2 : Uω (aρ 2) (bρ 2) (133117165709 / 8000000000000 : ℝ) ≤ @@ -439,24 +426,21 @@ lemma U_42_2 : have hlg : Real.log (60632591112057 / 10000000000000000 : ℝ) ≤ (-(51055078142581221338421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (60632591112057 / 10000000000000000 : ℝ) = (60632591112057 / 39062500000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (60632591112057 / 39062500000000 : ℚ)) - (U := (4396696281418778661579 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (60632591112057 / 39062500000000 : ℝ) ≤ - (4396696281418778661579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2695934730179 / 625000000000000 : ℝ)) (q := - (60632591112057 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (60632591112057 / 10000000000000000 : ℚ)) + (r' := (60632591112057 / 39062500000000 : ℚ)) + (U := (-(51055078142581221338421 / 10000000000000000000000 : ℚ))) + (U' := (4396696281418778661579 / 10000000000000000000000 : ℚ)) + 8 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (133117165709 / 8000000000000 : ℚ)) + (s := (2695934730179 / 625000000000000 : ℚ)) + (q := (60632591112057 / 10000000000000000 : ℚ)) + (U := (-(51055078142581221338421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_42_3 : Uω (aρ 3) (bρ 3) (133117165709 / 8000000000000 : ℝ) ≤ @@ -618,25 +602,21 @@ lemma U_43_1 : have hlg : Real.log (414340535730533 / 40000000000000000 : ℝ) ≤ (-(22849732727431537692483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (414340535730533 / 40000000000000000 : ℝ) = - (414340535730533 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (414340535730533 / 312500000000000 : ℚ)) - (U := (1410418583068462307517 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (414340535730533 / 312500000000000 : ℝ) ≤ - (1410418583068462307517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (51012204583727 / 5000000000000000 : ℝ)) (q := - (414340535730533 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (414340535730533 / 40000000000000000 : ℚ)) + (r' := (414340535730533 / 312500000000000 : ℚ)) + (U := (-(22849732727431537692483 / 5000000000000000000000 : ℚ))) + (U' := (1410418583068462307517 / 5000000000000000000000 : ℚ)) + 7 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (108571569141 / 6400000000000 : ℚ)) + (s := (51012204583727 / 5000000000000000 : ℚ)) + (q := (414340535730533 / 40000000000000000 : ℚ)) + (U := (-(22849732727431537692483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_43_2 : Uω (aρ 2) (bρ 2) (108571569141 / 6400000000000 : ℝ) ≤ @@ -644,25 +624,21 @@ lemma U_43_2 : have hlg : Real.log (260293083348717 / 40000000000000000 : ℝ) ≤ (-(5034826491214142248959 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (260293083348717 / 40000000000000000 : ℝ) = - (260293083348717 / 156250000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (260293083348717 / 156250000000000 : ℚ)) - (U := (510350951185857751041 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (260293083348717 / 156250000000000 : ℝ) ≤ - (510350951185857751041 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24384847743273 / 5000000000000000 : ℝ)) (q := - (260293083348717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (260293083348717 / 40000000000000000 : ℚ)) + (r' := (260293083348717 / 156250000000000 : ℚ)) + (U := (-(5034826491214142248959 / 1000000000000000000000 : ℚ))) + (U' := (510350951185857751041 / 1000000000000000000000 : ℚ)) + 8 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (108571569141 / 6400000000000 : ℚ)) + (s := (24384847743273 / 5000000000000000 : ℚ)) + (q := (260293083348717 / 40000000000000000 : ℚ)) + (U := (-(5034826491214142248959 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_43_3 : Uω (aρ 3) (bρ 3) (108571569141 / 6400000000000 : ℝ) ≤ @@ -824,24 +800,21 @@ lemma U_44_1 : have hlg : Real.log (53439932624379 / 5000000000000000 : ℝ) ≤ (-(45386349211403757950859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (53439932624379 / 5000000000000000 : ℝ) = (53439932624379 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53439932624379 / 39062500000000 : ℚ)) - (U := (3133953409596242049141 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (53439932624379 / 39062500000000 : ℝ) ≤ - (3133953409596242049141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105367252153141 / 10000000000000000 : ℝ)) (q := - (53439932624379 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53439932624379 / 5000000000000000 : ℚ)) + (r' := (53439932624379 / 39062500000000 : ℚ)) + (U := (-(45386349211403757950859 / 10000000000000000000000 : ℚ))) + (U' := (3133953409596242049141 / 10000000000000000000000 : ℚ)) + 7 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (276623514287 / 16000000000000 : ℚ)) + (s := (105367252153141 / 10000000000000000 : ℚ)) + (q := (53439932624379 / 5000000000000000 : ℚ)) + (U := (-(45386349211403757950859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_44_2 : Uω (aρ 2) (bρ 2) (276623514287 / 16000000000000 : ℝ) ≤ @@ -849,25 +822,21 @@ lemma U_44_2 : have hlg : Real.log (138636640821569 / 20000000000000000 : ℝ) ≤ (-(49716311348467284244491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (138636640821569 / 20000000000000000 : ℝ) = - (138636640821569 / 78125000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (138636640821569 / 78125000000000 : ℚ)) - (U := (5735463075532715755509 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (138636640821569 / 78125000000000 : ℝ) ≤ - (5735463075532715755509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27006587493597 / 5000000000000000 : ℝ)) (q := - (138636640821569 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (138636640821569 / 20000000000000000 : ℚ)) + (r' := (138636640821569 / 78125000000000 : ℚ)) + (U := (-(49716311348467284244491 / 10000000000000000000000 : ℚ))) + (U' := (5735463075532715755509 / 10000000000000000000000 : ℚ)) + 8 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (276623514287 / 16000000000000 : ℚ)) + (s := (27006587493597 / 5000000000000000 : ℚ)) + (q := (138636640821569 / 20000000000000000 : ℚ)) + (U := (-(49716311348467284244491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_44_3 : Uω (aρ 3) (bρ 3) (276623514287 / 16000000000000 : ℝ) ≤ @@ -1030,25 +999,21 @@ lemma U_45_1 : have hlg : Real.log (440686720790797 / 40000000000000000 : ℝ) ≤ (-(45083004919660055486503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (440686720790797 / 40000000000000000 : ℝ) = - (440686720790797 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (440686720790797 / 312500000000000 : ℚ)) - (U := (3437297701339944513497 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (440686720790797 / 312500000000000 : ℝ) ≤ - (3437297701339944513497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (108704262404461 / 10000000000000000 : ℝ)) (q := - (440686720790797 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (440686720790797 / 40000000000000000 : ℚ)) + (r' := (440686720790797 / 312500000000000 : ℚ)) + (U := (-(45083004919660055486503 / 10000000000000000000000 : ℚ))) + (U' := (3437297701339944513497 / 10000000000000000000000 : ℚ)) + 7 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (563636211443 / 32000000000000 : ℚ)) + (s := (108704262404461 / 10000000000000000 : ℚ)) + (q := (440686720790797 / 40000000000000000 : ℚ)) + (U := (-(45083004919660055486503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_45_2 : Uω (aρ 2) (bρ 2) (563636211443 / 32000000000000 : ℝ) ≤ @@ -1056,25 +1021,21 @@ lemma U_45_2 : have hlg : Real.log (293679884795729 / 40000000000000000 : ℝ) ≤ (-(9828288768212480750473 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show - (293679884795729 / 40000000000000000 : ℝ) = - (293679884795729 / 156250000000000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (293679884795729 / 156250000000000 : ℚ)) - (U := (1262066116587519249527 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (293679884795729 / 156250000000000 : ℝ) ≤ - (1262066116587519249527 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58969856916927 / 10000000000000000 : ℝ)) (q := - (293679884795729 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (293679884795729 / 40000000000000000 : ℚ)) + (r' := (293679884795729 / 156250000000000 : ℚ)) + (U := (-(9828288768212480750473 / 2000000000000000000000 : ℚ))) + (U' := (1262066116587519249527 / 2000000000000000000000 : ℚ)) + 8 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (563636211443 / 32000000000000 : ℚ)) + (s := (58969856916927 / 10000000000000000 : ℚ)) + (q := (293679884795729 / 40000000000000000 : ℚ)) + (U := (-(9828288768212480750473 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_45_3 : Uω (aρ 3) (bρ 3) (563636211443 / 32000000000000 : ℝ) ≤ @@ -1237,25 +1198,21 @@ lemma U_46_1 : have hlg : Real.log (226921678747097 / 20000000000000000 : ℝ) ≤ (-(44788826203166347861371 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (226921678747097 / 20000000000000000 : ℝ) = - (226921678747097 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (226921678747097 / 156250000000000 : ℚ)) - (U := (3731476417833652138629 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (226921678747097 / 156250000000000 : ℝ) ≤ - (3731476417833652138629 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (112035961109597 / 10000000000000000 : ℝ)) (q := - (226921678747097 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (226921678747097 / 20000000000000000 : ℚ)) + (r' := (226921678747097 / 156250000000000 : ℚ)) + (U := (-(44788826203166347861371 / 10000000000000000000000 : ℚ))) + (U' := (3731476417833652138629 / 10000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (71753174289 / 4000000000000 : ℚ)) + (s := (112035961109597 / 10000000000000000 : ℚ)) + (q := (226921678747097 / 20000000000000000 : ℚ)) + (U := (-(44788826203166347861371 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_46_2 : Uω (aρ 2) (bρ 2) (71753174289 / 4000000000000 : ℝ) ≤ @@ -1263,23 +1220,21 @@ lemma U_46_2 : have hlg : Real.log (2419116003209 / 312500000000000 : ℝ) ≤ (-(24306011407961759067497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 8 - (show (2419116003209 / 312500000000000 : ℝ) = (2419116003209 / 1220703125000 : ℝ) / 2 ^ 8 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2419116003209 / 1220703125000 : ℚ)) - (U := (3419875804038240932503 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2419116003209 / 1220703125000 : ℝ) ≤ - (3419875804038240932503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (15926679769469 / 2500000000000000 : ℝ)) (q := - (2419116003209 / 312500000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2419116003209 / 312500000000000 : ℚ)) + (r' := (2419116003209 / 1220703125000 : ℚ)) + (U := (-(24306011407961759067497 / 5000000000000000000000 : ℚ))) + (U' := (3419875804038240932503 / 5000000000000000000000 : ℚ)) + 8 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (71753174289 / 4000000000000 : ℚ)) + (s := (15926679769469 / 2500000000000000 : ℚ)) + (q := (2419116003209 / 312500000000000 : ℚ)) + (U := (-(24306011407961759067497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_46_3 : Uω (aρ 3) (bρ 3) (71753174289 / 4000000000000 : ℝ) ≤ @@ -1442,25 +1397,21 @@ lemma U_47_1 : have hlg : Real.log (466990291497527 / 40000000000000000 : ℝ) ≤ (-(4450326262908179514767 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (466990291497527 / 40000000000000000 : ℝ) = - (466990291497527 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (466990291497527 / 312500000000000 : ℚ)) - (U := (401703999191820485233 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (466990291497527 / 312500000000000 : ℝ) ≤ - (401703999191820485233 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (115362808464701 / 10000000000000000 : ℝ)) (q := - (466990291497527 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (466990291497527 / 40000000000000000 : ℚ)) + (r' := (466990291497527 / 312500000000000 : ℚ)) + (U := (-(4450326262908179514767 / 1000000000000000000000 : ℚ))) + (U' := (401703999191820485233 / 1000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (584414577181 / 32000000000000 : ℚ)) + (s := (115362808464701 / 10000000000000000 : ℚ)) + (q := (466990291497527 / 40000000000000000 : ℚ)) + (U := (-(4450326262908179514767 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_47_2 : Uω (aρ 2) (bρ 2) (584414577181 / 32000000000000 : ℝ) ≤ @@ -1468,25 +1419,21 @@ lemma U_47_2 : have hlg : Real.log (325265715969291 / 40000000000000000 : ℝ) ≤ (-(48119922953915799270603 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (325265715969291 / 40000000000000000 : ℝ) = - (325265715969291 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (325265715969291 / 312500000000000 : ℚ)) - (U := (400379667084200729397 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (325265715969291 / 312500000000000 : ℝ) ≤ - (400379667084200729397 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68269533210583 / 10000000000000000 : ℝ)) (q := - (325265715969291 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (325265715969291 / 40000000000000000 : ℚ)) + (r' := (325265715969291 / 312500000000000 : ℚ)) + (U := (-(48119922953915799270603 / 10000000000000000000000 : ℚ))) + (U' := (400379667084200729397 / 10000000000000000000000 : ℚ)) + 7 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (584414577181 / 32000000000000 : ℚ)) + (s := (68269533210583 / 10000000000000000 : ℚ)) + (q := (325265715969291 / 40000000000000000 : ℚ)) + (U := (-(48119922953915799270603 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_47_3 : Uω (aρ 3) (bρ 3) (584414577181 / 32000000000000 : ℝ) ≤ @@ -1648,24 +1595,21 @@ lemma U_48_1 : have hlg : Real.log (24006416936349 / 2000000000000000 : ℝ) ≤ (-(44225812907642607522863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (24006416936349 / 2000000000000000 : ℝ) = (24006416936349 / 15625000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24006416936349 / 15625000000000 : ℚ)) - (U := (4294489713357392477137 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (24006416936349 / 15625000000000 : ℝ) ≤ - (4294489713357392477137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23737042486573 / 2000000000000000 : ℝ)) (q := - (24006416936349 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24006416936349 / 2000000000000000 : ℚ)) + (r' := (24006416936349 / 15625000000000 : ℚ)) + (U := (-(44225812907642607522863 / 10000000000000000000000 : ℚ))) + (U' := (4294489713357392477137 / 10000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11896075201 / 640000000000 : ℚ)) + (s := (23737042486573 / 2000000000000000 : ℚ)) + (q := (24006416936349 / 2000000000000000 : ℚ)) + (U := (-(44225812907642607522863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_48_2 : Uω (aρ 2) (bρ 2) (11896075201 / 640000000000 : ℝ) ≤ @@ -1673,23 +1617,21 @@ lemma U_48_2 : have hlg : Real.log (8515051303781 / 1000000000000000 : ℝ) ≤ (-(47659199379596186942369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (8515051303781 / 1000000000000000 : ℝ) = (8515051303781 / 7812500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8515051303781 / 7812500000000 : ℚ)) - (U := (861103241403813057631 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8515051303781 / 7812500000000 : ℝ) ≤ - (861103241403813057631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14538216330999 / 2000000000000000 : ℝ)) (q := - (8515051303781 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8515051303781 / 1000000000000000 : ℚ)) + (r' := (8515051303781 / 7812500000000 : ℚ)) + (U := (-(47659199379596186942369 / 10000000000000000000000 : ℚ))) + (U' := (861103241403813057631 / 10000000000000000000000 : ℚ)) + 7 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11896075201 / 640000000000 : ℚ)) + (s := (14538216330999 / 2000000000000000 : ℚ)) + (q := (8515051303781 / 1000000000000000 : ℚ)) + (U := (-(47659199379596186942369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_48_3 : Uω (aρ 3) (bρ 3) (11896075201 / 640000000000 : ℝ) ≤ @@ -1852,24 +1794,21 @@ lemma U_49_1 : have hlg : Real.log (98651645039663 / 8000000000000000 : ℝ) ≤ (-(21978009554983345102107 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (98651645039663 / 8000000000000000 : ℝ) = (98651645039663 / 62500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (98651645039663 / 62500000000000 : ℚ)) - (U := (2282141755516654897893 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (98651645039663 / 62500000000000 : ℝ) ≤ - (2282141755516654897893 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12200353602197 / 1000000000000000 : ℝ)) (q := - (98651645039663 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (98651645039663 / 8000000000000000 : ℚ)) + (r' := (98651645039663 / 62500000000000 : ℚ)) + (U := (-(21978009554983345102107 / 5000000000000000000000 : ℚ))) + (U' := (2282141755516654897893 / 5000000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (605192942919 / 32000000000000 : ℚ)) + (s := (12200353602197 / 1000000000000000 : ℚ)) + (q := (98651645039663 / 8000000000000000 : ℚ)) + (U := (-(21978009554983345102107 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_49_2 : Uω (aρ 2) (bρ 2) (605192942919 / 32000000000000 : ℝ) ≤ @@ -1877,25 +1816,21 @@ lemma U_49_2 : have hlg : Real.log (355704538515791 / 40000000000000000 : ℝ) ≤ (-(47225342930112879030383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (355704538515791 / 40000000000000000 : ℝ) = - (355704538515791 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (355704538515791 / 312500000000000 : ℚ)) - (U := (1294959690887120969617 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (355704538515791 / 312500000000000 : ℝ) ≤ - (1294959690887120969617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19248926297677 / 2500000000000000 : ℝ)) (q := - (355704538515791 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (355704538515791 / 40000000000000000 : ℚ)) + (r' := (355704538515791 / 312500000000000 : ℚ)) + (U := (-(47225342930112879030383 / 10000000000000000000000 : ℚ))) + (U' := (1294959690887120969617 / 10000000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (605192942919 / 32000000000000 : ℚ)) + (s := (19248926297677 / 2500000000000000 : ℚ)) + (q := (355704538515791 / 40000000000000000 : ℚ)) + (U := (-(47225342930112879030383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_49_3 : Uω (aρ 3) (bρ 3) (605192942919 / 32000000000000 : ℝ) ≤ @@ -2057,25 +1992,21 @@ lemma U_50_1 : have hlg : Real.log (253190299591751 / 20000000000000000 : ℝ) ≤ (-(10923365431073482723193 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (253190299591751 / 20000000000000000 : ℝ) = - (253190299591751 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (253190299591751 / 156250000000000 : ℚ)) - (U := (1206710224176517276807 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (253190299591751 / 156250000000000 : ℝ) ≤ - (1206710224176517276807 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (125318103368001 / 10000000000000000 : ℝ)) (q := - (253190299591751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (253190299591751 / 20000000000000000 : ℚ)) + (r' := (253190299591751 / 156250000000000 : ℚ)) + (U := (-(10923365431073482723193 / 2500000000000000000000 : ℚ))) + (U' := (1206710224176517276807 / 2500000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (153895531447 / 8000000000000 : ℚ)) + (s := (125318103368001 / 10000000000000000 : ℚ)) + (q := (253190299591751 / 20000000000000000 : ℚ)) + (U := (-(10923365431073482723193 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_50_2 : Uω (aρ 2) (bρ 2) (153895531447 / 8000000000000 : ℝ) ≤ @@ -2083,24 +2014,21 @@ lemma U_50_2 : have hlg : Real.log (92652592342437 / 10000000000000000 : ℝ) ≤ (-(182870446791635865959 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (92652592342437 / 10000000000000000 : ℝ) = (92652592342437 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (92652592342437 / 78125000000000 : ℚ)) - (U := (6661985321645384041 / 39062500000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (92652592342437 / 78125000000000 : ℝ) ≤ - (6661985321645384041 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (20300500242781 / 2500000000000000 : ℝ)) (q := - (92652592342437 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (92652592342437 / 10000000000000000 : ℚ)) + (r' := (92652592342437 / 78125000000000 : ℚ)) + (U := (-(182870446791635865959 / 39062500000000000000 : ℚ))) + (U' := (6661985321645384041 / 39062500000000000000 : ℚ)) + 7 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (153895531447 / 8000000000000 : ℚ)) + (s := (20300500242781 / 2500000000000000 : ℚ)) + (q := (92652592342437 / 10000000000000000 : ℚ)) + (U := (-(182870446791635865959 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_50_3 : Uω (aρ 3) (bρ 3) (153895531447 / 8000000000000 : ℝ) ≤ @@ -2261,25 +2189,21 @@ lemma U_51_1 : have hlg : Real.log (266302536918669 / 20000000000000000 : ℝ) ≤ (-(21594272656989974022877 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (266302536918669 / 20000000000000000 : ℝ) = - (266302536918669 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (266302536918669 / 156250000000000 : ℚ)) - (U := (2665878653510025977123 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (266302536918669 / 156250000000000 : ℝ) ≤ - (2665878653510025977123 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (65968550700897 / 5000000000000000 : ℝ)) (q := - (266302536918669 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (266302536918669 / 20000000000000000 : ℚ)) + (r' := (266302536918669 / 156250000000000 : ℚ)) + (U := (-(21594272656989974022877 / 5000000000000000000000 : ℚ))) + (U' := (2665878653510025977123 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (318180245763 / 16000000000000 : ℚ)) + (s := (65968550700897 / 5000000000000000 : ℚ)) + (q := (266302536918669 / 20000000000000000 : ℚ)) + (U := (-(21594272656989974022877 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_51_2 : Uω (aρ 2) (bρ 2) (318180245763 / 16000000000000 : ℝ) ≤ @@ -2287,25 +2211,21 @@ lemma U_51_2 : have hlg : Real.log (199971256625133 / 20000000000000000 : ℝ) ≤ (-(9210627822742137523341 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (199971256625133 / 20000000000000000 : ℝ) = - (199971256625133 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (199971256625133 / 156250000000000 : ℚ)) - (U := (493432701457862476659 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (199971256625133 / 156250000000000 : ℝ) ≤ - (493432701457862476659 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44687416809129 / 5000000000000000 : ℝ)) (q := - (199971256625133 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (199971256625133 / 20000000000000000 : ℚ)) + (r' := (199971256625133 / 156250000000000 : ℚ)) + (U := (-(9210627822742137523341 / 2000000000000000000000 : ℚ))) + (U' := (493432701457862476659 / 2000000000000000000000 : ℚ)) + 7 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (318180245763 / 16000000000000 : ℚ)) + (s := (44687416809129 / 5000000000000000 : ℚ)) + (q := (199971256625133 / 20000000000000000 : ℚ)) + (U := (-(9210627822742137523341 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_51_3 : Uω (aρ 3) (bρ 3) (318180245763 / 16000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U04.lean b/LeanPool/Zeta5Irrational/Table/U04.lean index 9204ad42b5..94516e4860 100644 --- a/LeanPool/Zeta5Irrational/Table/U04.lean +++ b/LeanPool/Zeta5Irrational/Table/U04.lean @@ -24,23 +24,21 @@ lemma U_52_1 : have hlg : Real.log (2235222980587 / 160000000000000 : ℝ) ≤ (-(10677082056811715580897 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (2235222980587 / 160000000000000 : ℝ) = (2235222980587 / 1250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2235222980587 / 1250000000000 : ℚ)) - (U := (1452993598438284419103 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2235222980587 / 1250000000000 : ℝ) ≤ - (1452993598438284419103 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1108353582107 / 80000000000000 : ℝ)) (q := - (2235222980587 / 160000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2235222980587 / 160000000000000 : ℚ)) + (r' := (2235222980587 / 1250000000000 : ℚ)) + (U := (-(10677082056811715580897 / 2500000000000000000000 : ℚ))) + (U' := (1452993598438284419103 / 2500000000000000000000 : ℚ)) + 7 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (41071178579 / 2000000000000 : ℚ)) + (s := (1108353582107 / 80000000000000 : ℚ)) + (q := (2235222980587 / 160000000000000 : ℚ)) + (U := (-(10677082056811715580897 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_52_2 : Uω (aρ 2) (bρ 2) (41071178579 / 2000000000000 : ℝ) ≤ @@ -48,23 +46,21 @@ lemma U_52_2 : have hlg : Real.log (1674878732681 / 156250000000000 : ℝ) ≤ (-(45357165225401575594487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (1674878732681 / 156250000000000 : ℝ) = (1674878732681 / 1220703125000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1674878732681 / 1220703125000 : ℚ)) - (U := (3163137395598424405513 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1674878732681 / 1220703125000 : ℝ) ≤ - (3163137395598424405513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3040462983849 / 312500000000000 : ℝ)) (q := - (1674878732681 / 156250000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1674878732681 / 156250000000000 : ℚ)) + (r' := (1674878732681 / 1220703125000 : ℚ)) + (U := (-(45357165225401575594487 / 10000000000000000000000 : ℚ))) + (U' := (3163137395598424405513 / 10000000000000000000000 : ℚ)) + 7 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (41071178579 / 2000000000000 : ℚ)) + (s := (3040462983849 / 312500000000000 : ℚ)) + (q := (1674878732681 / 156250000000000 : ℚ)) + (U := (-(45357165225401575594487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_52_3 : Uω (aρ 3) (bρ 3) (41071178579 / 2000000000000 : ℝ) ≤ @@ -226,25 +222,21 @@ lemma U_53_1 : have hlg : Real.log (152787027675153 / 10000000000000000 : ℝ) ≤ (-(8362590788884110065771 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (152787027675153 / 10000000000000000 : ℝ) = - (152787027675153 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (152787027675153 / 78125000000000 : ℚ)) - (U := (1341469735315889934229 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (152787027675153 / 78125000000000 : ℝ) ≤ - (1341469735315889934229 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18966112744257 / 1250000000000000 : ℝ)) (q := - (152787027675153 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (152787027675153 / 10000000000000000 : ℚ)) + (r' := (152787027675153 / 78125000000000 : ℚ)) + (U := (-(8362590788884110065771 / 2000000000000000000000 : ℚ))) + (U' := (1341469735315889934229 / 2000000000000000000000 : ℚ)) + 7 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34934779437 / 1600000000000 : ℚ)) + (s := (18966112744257 / 1250000000000000 : ℚ)) + (q := (152787027675153 / 10000000000000000 : ℚ)) + (U := (-(8362590788884110065771 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_53_2 : Uω (aρ 2) (bρ 2) (34934779437 / 1600000000000 : ℝ) ≤ @@ -252,25 +244,21 @@ lemma U_53_2 : have hlg : Real.log (121332152126361 / 10000000000000000 : ℝ) ≤ (-(1764723410583048654431 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (121332152126361 / 10000000000000000 : ℝ) = - (121332152126361 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (121332152126361 / 78125000000000 : ℚ)) - (U := (176088694256951345569 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (121332152126361 / 78125000000000 : ℝ) ≤ - (176088694256951345569 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14073520420809 / 1250000000000000 : ℝ)) (q := - (121332152126361 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (121332152126361 / 10000000000000000 : ℚ)) + (r' := (121332152126361 / 78125000000000 : ℚ)) + (U := (-(1764723410583048654431 / 400000000000000000000 : ℚ))) + (U' := (176088694256951345569 / 400000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34934779437 / 1600000000000 : ℚ)) + (s := (14073520420809 / 1250000000000000 : ℚ)) + (q := (121332152126361 / 10000000000000000 : ℚ)) + (U := (-(1764723410583048654431 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_53_3 : Uω (aρ 3) (bρ 3) (34934779437 / 1600000000000 : ℝ) ≤ @@ -432,23 +420,21 @@ lemma U_54_1 : have hlg : Real.log (8292844436299 / 500000000000000 : ℝ) ≤ (-(20496075350021699854459 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show (8292844436299 / 500000000000000 : ℝ) = (8292844436299 / 7812500000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8292844436299 / 7812500000000 : ℚ)) - (U := (298340058978300145541 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8292844436299 / 7812500000000 : ℝ) ≤ - (298340058978300145541 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8244107273473 / 500000000000000 : ℝ)) (q := - (8292844436299 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8292844436299 / 500000000000000 : ℚ)) + (r' := (8292844436299 / 7812500000000 : ℚ)) + (U := (-(20496075350021699854459 / 5000000000000000000000 : ℚ))) + (U' := (298340058978300145541 / 5000000000000000000000 : ℚ)) + 6 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (92531540027 / 4000000000000 : ℚ)) + (s := (8244107273473 / 500000000000000 : ℚ)) + (q := (8292844436299 / 500000000000000 : ℚ)) + (U := (-(20496075350021699854459 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_54_2 : Uω (aρ 2) (bρ 2) (92531540027 / 4000000000000 : ℝ) ≤ @@ -456,25 +442,21 @@ lemma U_54_2 : have hlg : Real.log (135216483035671 / 10000000000000000 : ℝ) ≤ (-(21517316490172672414011 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (135216483035671 / 10000000000000000 : ℝ) = - (135216483035671 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (135216483035671 / 78125000000000 : ℚ)) - (U := (2742834820327327585989 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (135216483035671 / 78125000000000 : ℝ) ≤ - (2742834820327327585989 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63685173299421 / 5000000000000000 : ℝ)) (q := - (135216483035671 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (135216483035671 / 10000000000000000 : ℚ)) + (r' := (135216483035671 / 78125000000000 : ℚ)) + (U := (-(21517316490172672414011 / 5000000000000000000000 : ℚ))) + (U' := (2742834820327327585989 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (92531540027 / 4000000000000 : ℚ)) + (s := (63685173299421 / 5000000000000000 : ℚ)) + (q := (135216483035671 / 10000000000000000 : ℚ)) + (U := (-(21517316490172672414011 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_54_3 : Uω (aρ 3) (bρ 3) (92531540027 / 4000000000000 : ℝ) ≤ @@ -636,24 +618,21 @@ lemma U_55_1 : have hlg : Real.log (76784961606559 / 4000000000000000 : ℝ) ≤ (-(19765204149885397770799 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (76784961606559 / 4000000000000000 : ℝ) = (76784961606559 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (76784961606559 / 62500000000000 : ℚ)) - (U := (1029211259114602229201 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (76784961606559 / 62500000000000 : ℝ) ≤ - (1029211259114602229201 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38224043775559 / 2000000000000000 : ℝ)) (q := - (76784961606559 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (76784961606559 / 4000000000000000 : ℚ)) + (r' := (76784961606559 / 62500000000000 : ℚ)) + (U := (-(19765204149885397770799 / 5000000000000000000000 : ℚ))) + (U' := (1029211259114602229201 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6432545181 / 250000000000 : ℚ)) + (s := (38224043775559 / 2000000000000000 : ℚ)) + (q := (76784961606559 / 4000000000000000 : ℚ)) + (U := (-(19765204149885397770799 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_55_2 : Uω (aρ 2) (bρ 2) (6432545181 / 250000000000 : ℝ) ≤ @@ -661,25 +640,21 @@ lemma U_55_2 : have hlg : Real.log (325014159386617 / 20000000000000000 : ℝ) ≤ (-(20598094011261554616851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (325014159386617 / 20000000000000000 : ℝ) = - (325014159386617 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (325014159386617 / 312500000000000 : ℚ)) - (U := (196321397738445383149 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (325014159386617 / 312500000000000 : ℝ) ≤ - (196321397738445383149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (155978582741617 / 10000000000000000 : ℝ)) (q := - (325014159386617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (325014159386617 / 20000000000000000 : ℚ)) + (r' := (325014159386617 / 312500000000000 : ℚ)) + (U := (-(20598094011261554616851 / 5000000000000000000000 : ℚ))) + (U' := (196321397738445383149 / 5000000000000000000000 : ℚ)) + 6 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6432545181 / 250000000000 : ℚ)) + (s := (155978582741617 / 10000000000000000 : ℚ)) + (q := (325014159386617 / 20000000000000000 : ℚ)) + (U := (-(20598094011261554616851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_55_3 : Uω (aρ 3) (bρ 3) (6432545181 / 250000000000 : ℝ) ≤ @@ -841,25 +816,21 @@ lemma U_56_1 : have hlg : Real.log (101058419601983 / 5000000000000000 : ℝ) ≤ (-(19507472141650856272829 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (101058419601983 / 5000000000000000 : ℝ) = - (101058419601983 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (101058419601983 / 78125000000000 : ℚ)) - (U := (1286943267349143727171 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (101058419601983 / 78125000000000 : ℝ) ≤ - (1286943267349143727171 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100658482900841 / 5000000000000000 : ℝ)) (q := - (101058419601983 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (101058419601983 / 5000000000000000 : ℚ)) + (r' := (101058419601983 / 78125000000000 : ℚ)) + (U := (-(19507472141650856272829 / 5000000000000000000000 : ℚ))) + (U' := (1286943267349143727171 / 5000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (213931144553 / 8000000000000 : ℚ)) + (s := (100658482900841 / 5000000000000000 : ℚ)) + (q := (101058419601983 / 5000000000000000 : ℚ)) + (U := (-(19507472141650856272829 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_56_2 : Uω (aρ 2) (bρ 2) (213931144553 / 8000000000000 : ℝ) ≤ @@ -867,24 +838,21 @@ lemma U_56_2 : have hlg : Real.log (43253932961601 / 2500000000000000 : ℝ) ≤ (-(40569578445247696299549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (43253932961601 / 2500000000000000 : ℝ) = (43253932961601 / 39062500000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43253932961601 / 39062500000000 : ℚ)) - (U := (1019252372752303700451 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (43253932961601 / 39062500000000 : ℝ) ≤ - (1019252372752303700451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83441881798279 / 5000000000000000 : ℝ)) (q := - (43253932961601 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43253932961601 / 2500000000000000 : ℚ)) + (r' := (43253932961601 / 39062500000000 : ℚ)) + (U := (-(40569578445247696299549 / 10000000000000000000000 : ℚ))) + (U' := (1019252372752303700451 / 10000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (213931144553 / 8000000000000 : ℚ)) + (s := (83441881798279 / 5000000000000000 : ℚ)) + (q := (43253932961601 / 2500000000000000 : ℚ)) + (U := (-(40569578445247696299549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_56_3 : Uω (aρ 3) (bρ 3) (213931144553 / 8000000000000 : ℝ) ≤ @@ -892,23 +860,21 @@ lemma U_56_3 : have hlg : Real.log (729483898519 / 80000000000000 : ℝ) ≤ (-(46974446160582055541859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (729483898519 / 80000000000000 : ℝ) = (729483898519 / 625000000000 : ℝ) / 2 ^ 7 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (729483898519 / 625000000000 : ℚ)) - (U := (1545856460417944458141 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (729483898519 / 625000000000 : ℝ) ≤ - (1545856460417944458141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101238761767 / 20000000000000 : ℝ)) (q := - (729483898519 / 80000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (729483898519 / 80000000000000 : ℚ)) + (r' := (729483898519 / 625000000000 : ℚ)) + (U := (-(46974446160582055541859 / 10000000000000000000000 : ℚ))) + (U' := (1545856460417944458141 / 10000000000000000000000 : ℚ)) + 7 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (213931144553 / 8000000000000 : ℚ)) + (s := (101238761767 / 20000000000000 : ℚ)) + (q := (729483898519 / 80000000000000 : ℚ)) + (U := (-(46974446160582055541859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_56_4 : Uω (aρ 4) (bρ 4) (213931144553 / 8000000000000 : ℝ) ≤ @@ -1065,25 +1031,21 @@ lemma U_57_1 : have hlg : Real.log (103596247833641 / 5000000000000000 : ℝ) ≤ (-(38766920785090621061557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (103596247833641 / 5000000000000000 : ℝ) = - (103596247833641 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (103596247833641 / 78125000000000 : ℚ)) - (U := (2821910032909378938443 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (103596247833641 / 78125000000000 : ℝ) ≤ - (2821910032909378938443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (206412217002689 / 10000000000000000 : ℝ)) (q := - (103596247833641 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (103596247833641 / 5000000000000000 : ℚ)) + (r' := (103596247833641 / 78125000000000 : ℚ)) + (U := (-(38766920785090621061557 / 10000000000000000000000 : ℚ))) + (U' := (2821910032909378938443 / 10000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (435951987867 / 16000000000000 : ℚ)) + (s := (206412217002689 / 10000000000000000 : ℚ)) + (q := (103596247833641 / 5000000000000000 : ℚ)) + (U := (-(38766920785090621061557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_57_2 : Uω (aρ 2) (bρ 2) (435951987867 / 16000000000000 : ℝ) ≤ @@ -1091,24 +1053,21 @@ lemma U_57_2 : have hlg : Real.log (11140745093543 / 625000000000000 : ℝ) ≤ (-(8054285062790282216923 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (11140745093543 / 625000000000000 : ℝ) = (11140745093543 / 9765625000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11140745093543 / 9765625000000 : ℚ)) - (U := (263481100809717783077 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11140745093543 / 9765625000000 : ℝ) ≤ - (263481100809717783077 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (172300081171501 / 10000000000000000 : ℝ)) (q := - (11140745093543 / 625000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11140745093543 / 625000000000000 : ℚ)) + (r' := (11140745093543 / 9765625000000 : ℚ)) + (U := (-(8054285062790282216923 / 2000000000000000000000 : ℚ))) + (U' := (263481100809717783077 / 2000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (435951987867 / 16000000000000 : ℚ)) + (s := (172300081171501 / 10000000000000000 : ℚ)) + (q := (11140745093543 / 625000000000000 : ℚ)) + (U := (-(8054285062790282216923 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_57_3 : Uω (aρ 3) (bρ 3) (435951987867 / 16000000000000 : ℝ) ≤ @@ -1116,24 +1075,21 @@ lemma U_57_3 : have hlg : Real.log (99709473640723 / 10000000000000000 : ℝ) ≤ (-(46080796762313820607457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (99709473640723 / 10000000000000000 : ℝ) = (99709473640723 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (99709473640723 / 78125000000000 : ℚ)) - (U := (2439505858686179392543 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (99709473640723 / 78125000000000 : ℝ) ≤ - (2439505858686179392543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62611291809571 / 10000000000000000 : ℝ)) (q := - (99709473640723 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (99709473640723 / 10000000000000000 : ℚ)) + (r' := (99709473640723 / 78125000000000 : ℚ)) + (U := (-(46080796762313820607457 / 10000000000000000000000 : ℚ))) + (U' := (2439505858686179392543 / 10000000000000000000000 : ℚ)) + 7 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (435951987867 / 16000000000000 : ℚ)) + (s := (62611291809571 / 10000000000000000 : ℚ)) + (q := (99709473640723 / 10000000000000000 : ℚ)) + (U := (-(46080796762313820607457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_57_4 : Uω (aρ 4) (bρ 4) (435951987867 / 16000000000000 : ℝ) ≤ @@ -1291,24 +1247,21 @@ lemma U_58_1 : have hlg : Real.log (21226721167587 / 1000000000000000 : ℝ) ≤ (-(38524944569892604705309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (21226721167587 / 1000000000000000 : ℝ) = (21226721167587 / 15625000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21226721167587 / 15625000000000 : ℚ)) - (U := (3063886248107395294691 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (21226721167587 / 15625000000000 : ℝ) ≤ - (3063886248107395294691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1321909920589 / 62500000000000 : ℝ)) (q := - (21226721167587 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21226721167587 / 1000000000000000 : ℚ)) + (r' := (21226721167587 / 15625000000000 : ℚ)) + (U := (-(38524944569892604705309 / 10000000000000000000000 : ℚ))) + (U' := (3063886248107395294691 / 10000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (111010421657 / 4000000000000 : ℚ)) + (s := (1321909920589 / 62500000000000 : ℚ)) + (q := (21226721167587 / 1000000000000000 : ℚ)) + (U := (-(38524944569892604705309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_58_2 : Uω (aρ 2) (bρ 2) (111010421657 / 4000000000000 : ℝ) ≤ @@ -1316,24 +1269,21 @@ lemma U_58_2 : have hlg : Real.log (91738748014241 / 5000000000000000 : ℝ) ≤ (-(19991241739447185349551 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (91738748014241 / 5000000000000000 : ℝ) = (91738748014241 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (91738748014241 / 78125000000000 : ℚ)) - (U := (803173669552814650449 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (91738748014241 / 78125000000000 : ℝ) ≤ - (803173669552814650449 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (22211896063683 / 1250000000000000 : ℝ)) (q := - (91738748014241 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (91738748014241 / 5000000000000000 : ℚ)) + (r' := (91738748014241 / 78125000000000 : ℚ)) + (U := (-(19991241739447185349551 / 5000000000000000000000 : ℚ))) + (U' := (803173669552814650449 / 5000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (111010421657 / 4000000000000 : ℚ)) + (s := (22211896063683 / 1250000000000000 : ℚ)) + (q := (91738748014241 / 5000000000000000 : ℚ)) + (U := (-(19991241739447185349551 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_58_3 : Uω (aρ 3) (bρ 3) (111010421657 / 4000000000000 : ℝ) ≤ @@ -1341,25 +1291,21 @@ lemma U_58_3 : have hlg : Real.log (214864768720367 / 20000000000000000 : ℝ) ≤ (-(45334787031774164684501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (214864768720367 / 20000000000000000 : ℝ) = - (214864768720367 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (214864768720367 / 156250000000000 : ℚ)) - (U := (3185515589225835315499 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (214864768720367 / 156250000000000 : ℝ) ≤ - (3185515589225835315499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73001051522867 / 10000000000000000 : ℝ)) (q := - (214864768720367 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (214864768720367 / 20000000000000000 : ℚ)) + (r' := (214864768720367 / 156250000000000 : ℚ)) + (U := (-(45334787031774164684501 / 10000000000000000000000 : ℚ))) + (U' := (3185515589225835315499 / 10000000000000000000000 : ℚ)) + 7 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (111010421657 / 4000000000000 : ℚ)) + (s := (73001051522867 / 10000000000000000 : ℚ)) + (q := (214864768720367 / 20000000000000000 : ℚ)) + (U := (-(45334787031774164684501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_58_4 : Uω (aρ 4) (bρ 4) (111010421657 / 4000000000000 : ℝ) ≤ @@ -1517,25 +1463,21 @@ lemma U_59_1 : have hlg : Real.log (217341053575261 / 10000000000000000 : ℝ) ≤ (-(19144362876016614852763 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (217341053575261 / 10000000000000000 : ℝ) = - (217341053575261 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (217341053575261 / 156250000000000 : ℚ)) - (U := (1650052532983385147237 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (217341053575261 / 156250000000000 : ℝ) ≤ - (1650052532983385147237 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216597209367397 / 10000000000000000 : ℝ)) (q := - (217341053575261 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (217341053575261 / 10000000000000000 : ℚ)) + (r' := (217341053575261 / 156250000000000 : ℚ)) + (U := (-(19144362876016614852763 / 5000000000000000000000 : ℚ))) + (U' := (1650052532983385147237 / 5000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (452131385389 / 16000000000000 : ℚ)) + (s := (216597209367397 / 10000000000000000 : ℚ)) + (q := (217341053575261 / 10000000000000000 : ℚ)) + (U := (-(19144362876016614852763 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_59_2 : Uω (aρ 2) (bρ 2) (452131385389 / 16000000000000 : ℝ) ≤ @@ -1543,25 +1485,21 @@ lemma U_59_2 : have hlg : Real.log (377386787854213 / 20000000000000000 : ℝ) ≤ (-(7940433853980462156227 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (377386787854213 / 20000000000000000 : ℝ) = - (377386787854213 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (377386787854213 / 312500000000000 : ℚ)) - (U := (377332309619537843773 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (377386787854213 / 312500000000000 : ℝ) ≤ - (377332309619537843773 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5720965705659 / 312500000000000 : ℝ)) (q := - (377386787854213 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (377386787854213 / 20000000000000000 : ℚ)) + (r' := (377386787854213 / 312500000000000 : ℚ)) + (U := (-(7940433853980462156227 / 2000000000000000000000 : ℚ))) + (U' := (377332309619537843773 / 2000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (452131385389 / 16000000000000 : ℚ)) + (s := (5720965705659 / 312500000000000 : ℚ)) + (q := (377386787854213 / 20000000000000000 : ℚ)) + (U := (-(7940433853980462156227 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_59_3 : Uω (aρ 3) (bρ 3) (452131385389 / 16000000000000 : ℝ) ≤ @@ -1569,25 +1507,21 @@ lemma U_59_3 : have hlg : Real.log (114658374582899 / 10000000000000000 : ℝ) ≤ (-(44683833187501300822249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (114658374582899 / 10000000000000000 : ℝ) = - (114658374582899 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (114658374582899 / 78125000000000 : ℚ)) - (U := (3836469433498699177751 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (114658374582899 / 78125000000000 : ℝ) ≤ - (3836469433498699177751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (82396970242673 / 10000000000000000 : ℝ)) (q := - (114658374582899 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (114658374582899 / 10000000000000000 : ℚ)) + (r' := (114658374582899 / 78125000000000 : ℚ)) + (U := (-(44683833187501300822249 / 10000000000000000000000 : ℚ))) + (U' := (3836469433498699177751 / 10000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (452131385389 / 16000000000000 : ℚ)) + (s := (82396970242673 / 10000000000000000 : ℚ)) + (q := (114658374582899 / 10000000000000000 : ℚ)) + (U := (-(44683833187501300822249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_59_4 : Uω (aρ 4) (bρ 4) (452131385389 / 16000000000000 : ℝ) ≤ @@ -1744,25 +1678,21 @@ lemma U_60_1 : have hlg : Real.log (879510663099267 / 40000000000000000 : ℝ) ≤ (-(19086345216926816612793 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (879510663099267 / 40000000000000000 : ℝ) = - (879510663099267 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (879510663099267 / 625000000000000 : ℚ)) - (U := (1708070192073183387207 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (879510663099267 / 625000000000000 : ℝ) ≤ - (1708070192073183387207 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13696400181481 / 625000000000000 : ℝ)) (q := - (879510663099267 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (879510663099267 / 40000000000000000 : ℚ)) + (r' := (879510663099267 / 625000000000000 : ℚ)) + (U := (-(19086345216926816612793 / 5000000000000000000000 : ℚ))) + (U' := (1708070192073183387207 / 5000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (912352469539 / 32000000000000 : ℚ)) + (s := (13696400181481 / 625000000000000 : ℚ)) + (q := (879510663099267 / 40000000000000000 : ℚ)) + (U := (-(19086345216926816612793 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_60_2 : Uω (aρ 2) (bρ 2) (912352469539 / 32000000000000 : ℝ) ≤ @@ -1770,25 +1700,21 @@ lemma U_60_2 : have hlg : Real.log (765191907200309 / 40000000000000000 : ℝ) ≤ (-(791301614016874710873 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (765191907200309 / 40000000000000000 : ℝ) = - (765191907200309 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (765191907200309 / 625000000000000 : ℚ)) - (U := (40475002343125289127 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (765191907200309 / 625000000000000 : ℝ) ≤ - (40475002343125289127 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (185752037464217 / 10000000000000000 : ℝ)) (q := - (765191907200309 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (765191907200309 / 40000000000000000 : ℚ)) + (r' := (765191907200309 / 625000000000000 : ℚ)) + (U := (-(791301614016874710873 / 200000000000000000000 : ℚ))) + (U' := (40475002343125289127 / 200000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (912352469539 / 32000000000000 : ℚ)) + (s := (185752037464217 / 10000000000000000 : ℚ)) + (q := (765191907200309 / 40000000000000000 : ℚ)) + (U := (-(791301614016874710873 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_60_3 : Uω (aρ 3) (bρ 3) (912352469539 / 32000000000000 : ℝ) ≤ @@ -1796,25 +1722,21 @@ lemma U_60_3 : have hlg : Real.log (472544542588009 / 40000000000000000 : ℝ) ≤ (-(22192513593791331396327 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (472544542588009 / 40000000000000000 : ℝ) = - (472544542588009 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (472544542588009 / 312500000000000 : ℚ)) - (U := (2067637716708668603673 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (472544542588009 / 312500000000000 : ℝ) ≤ - (2067637716708668603673 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86824461508067 / 10000000000000000 : ℝ)) (q := - (472544542588009 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (472544542588009 / 40000000000000000 : ℚ)) + (r' := (472544542588009 / 312500000000000 : ℚ)) + (U := (-(22192513593791331396327 / 5000000000000000000000 : ℚ))) + (U' := (2067637716708668603673 / 5000000000000000000000 : ℚ)) + 7 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (912352469539 / 32000000000000 : ℚ)) + (s := (86824461508067 / 10000000000000000 : ℚ)) + (q := (472544542588009 / 40000000000000000 : ℚ)) + (U := (-(22192513593791331396327 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_60_4 : Uω (aρ 4) (bρ 4) (912352469539 / 32000000000000 : ℝ) ≤ @@ -1971,24 +1893,21 @@ lemma U_61_1 : have hlg : Real.log (13900880099627 / 625000000000000 : ℝ) ≤ (-(19028997467622808750993 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (13900880099627 / 625000000000000 : ℝ) = (13900880099627 / 9765625000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13900880099627 / 9765625000000 : ℚ)) - (U := (1765417941377191249007 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13900880099627 / 9765625000000 : ℝ) ≤ - (1765417941377191249007 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110843601839657 / 5000000000000000 : ℝ)) (q := - (13900880099627 / 625000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13900880099627 / 625000000000000 : ℚ)) + (r' := (13900880099627 / 9765625000000 : ℚ)) + (U := (-(19028997467622808750993 / 5000000000000000000000 : ℚ))) + (U' := (1765417941377191249007 / 5000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9204421683 / 320000000000 : ℚ)) + (s := (110843601839657 / 5000000000000000 : ℚ)) + (q := (13900880099627 / 625000000000000 : ℚ)) + (U := (-(19028997467622808750993 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_61_2 : Uω (aρ 2) (bρ 2) (9204421683 / 320000000000 : ℝ) ≤ @@ -1996,25 +1915,21 @@ lemma U_61_2 : have hlg : Real.log (387800886794229 / 20000000000000000 : ℝ) ≤ (-(19714977607198277378769 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (387800886794229 / 20000000000000000 : ℝ) = - (387800886794229 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (387800886794229 / 312500000000000 : ℚ)) - (U := (1079437801801722621231 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (387800886794229 / 312500000000000 : ℝ) ≤ - (1079437801801722621231 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188428939795479 / 10000000000000000 : ℝ)) (q := - (387800886794229 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (387800886794229 / 20000000000000000 : ℚ)) + (r' := (387800886794229 / 312500000000000 : ℚ)) + (U := (-(19714977607198277378769 / 5000000000000000000000 : ℚ))) + (U' := (1079437801801722621231 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9204421683 / 320000000000 : ℚ)) + (s := (188428939795479 / 10000000000000000 : ℚ)) + (q := (387800886794229 / 20000000000000000 : ℚ)) + (U := (-(19714977607198277378769 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_61_3 : Uω (aρ 3) (bρ 3) (9204421683 / 320000000000 : ℝ) ≤ @@ -2022,24 +1937,21 @@ lemma U_61_3 : have hlg : Real.log (15192680956257 / 1250000000000000 : ℝ) ≤ (-(22050425163131483974353 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (15192680956257 / 1250000000000000 : ℝ) = (15192680956257 / 9765625000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15192680956257 / 9765625000000 : ℚ)) - (U := (2209726147368516025647 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15192680956257 / 9765625000000 : ℝ) ≤ - (2209726147368516025647 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45553527325681 / 5000000000000000 : ℝ)) (q := - (15192680956257 / 1250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15192680956257 / 1250000000000000 : ℚ)) + (r' := (15192680956257 / 9765625000000 : ℚ)) + (U := (-(22050425163131483974353 / 5000000000000000000000 : ℚ))) + (U' := (2209726147368516025647 / 5000000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9204421683 / 320000000000 : ℚ)) + (s := (45553527325681 / 5000000000000000 : ℚ)) + (q := (15192680956257 / 1250000000000000 : ℚ)) + (U := (-(22050425163131483974353 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_61_4 : Uω (aρ 4) (bρ 4) (9204421683 / 320000000000 : ℝ) ≤ @@ -2196,25 +2108,21 @@ lemma U_62_1 : have hlg : Real.log (899801230876237 / 40000000000000000 : ℝ) ≤ (-(7588921694372028541901 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (899801230876237 / 40000000000000000 : ℝ) = - (899801230876237 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (899801230876237 / 625000000000000 : ℚ)) - (U := (728844469227971458099 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (899801230876237 / 625000000000000 : ℝ) ≤ - (728844469227971458099 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56057906266639 / 2500000000000000 : ℝ)) (q := - (899801230876237 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (899801230876237 / 40000000000000000 : ℚ)) + (r' := (899801230876237 / 625000000000000 : ℚ)) + (U := (-(7588921694372028541901 / 2000000000000000000000 : ℚ))) + (U' := (728844469227971458099 / 2000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (928531867061 / 32000000000000 : ℚ)) + (s := (56057906266639 / 2500000000000000 : ℚ)) + (q := (899801230876237 / 40000000000000000 : ℚ)) + (U := (-(7588921694372028541901 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_62_2 : Uω (aρ 2) (bρ 2) (928531867061 / 32000000000000 : ℝ) ≤ @@ -2222,25 +2130,21 @@ lemma U_62_2 : have hlg : Real.log (786003530603713 / 40000000000000000 : ℝ) ≤ (-(39296734472550530549671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (786003530603713 / 40000000000000000 : ℝ) = - (786003530603713 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (786003530603713 / 625000000000000 : ℚ)) - (U := (2292096345449469450329 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (786003530603713 / 625000000000000 : ℝ) ≤ - (2292096345449469450329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95550893720147 / 5000000000000000 : ℝ)) (q := - (786003530603713 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (786003530603713 / 40000000000000000 : ℚ)) + (r' := (786003530603713 / 625000000000000 : ℚ)) + (U := (-(39296734472550530549671 / 10000000000000000000000 : ℚ))) + (U' := (2292096345449469450329 / 10000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (928531867061 / 32000000000000 : ℚ)) + (s := (95550893720147 / 5000000000000000 : ℚ)) + (q := (786003530603713 / 40000000000000000 : ℚ)) + (U := (-(39296734472550530549671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_62_3 : Uω (aρ 3) (bρ 3) (928531867061 / 32000000000000 : ℝ) ≤ @@ -2248,25 +2152,21 @@ lemma U_62_3 : have hlg : Real.log (499536329628007 / 40000000000000000 : ℝ) ≤ (-(2739346502402930483743 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (499536329628007 / 40000000000000000 : ℝ) = - (499536329628007 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (499536329628007 / 312500000000000 : ℚ)) - (U := (293172411409569516257 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (499536329628007 / 312500000000000 : ℝ) ≤ - (293172411409569516257 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95264293302441 / 10000000000000000 : ℝ)) (q := - (499536329628007 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (499536329628007 / 40000000000000000 : ℚ)) + (r' := (499536329628007 / 312500000000000 : ℚ)) + (U := (-(2739346502402930483743 / 625000000000000000000 : ℚ))) + (U' := (293172411409569516257 / 625000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (928531867061 / 32000000000000 : ℚ)) + (s := (95264293302441 / 10000000000000000 : ℚ)) + (q := (499536329628007 / 40000000000000000 : ℚ)) + (U := (-(2739346502402930483743 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_62_4 : Uω (aρ 4) (bρ 4) (928531867061 / 32000000000000 : ℝ) ≤ @@ -2423,23 +2323,21 @@ lemma U_63_1 : have hlg : Real.log (45497270107 / 2000000000000 : ℝ) ≤ (-(4729062664342235400103 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show (45497270107 / 2000000000000 : ℝ) = (45497270107 / 31250000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45497270107 / 31250000000 : ℚ)) - (U := (469541187907764599897 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (45497270107 / 31250000000 : ℝ) ≤ - (469541187907764599897 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (362841087737 / 16000000000000 : ℝ)) (q := - (45497270107 / 2000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45497270107 / 2000000000000 : ℚ)) + (r' := (45497270107 / 31250000000 : ℚ)) + (U := (-(4729062664342235400103 / 1250000000000000000000 : ℚ))) + (U' := (469541187907764599897 / 1250000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (468310782911 / 16000000000000 : ℚ)) + (s := (362841087737 / 16000000000000 : ℚ)) + (q := (45497270107 / 2000000000000 : ℚ)) + (U := (-(4729062664342235400103 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_63_2 : Uω (aρ 2) (bρ 2) (468310782911 / 16000000000000 : ℝ) ≤ @@ -2447,25 +2345,21 @@ lemma U_63_2 : have hlg : Real.log (398198756912509 / 20000000000000000 : ℝ) ≤ (-(9791340702794776363367 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (398198756912509 / 20000000000000000 : ℝ) = - (398198756912509 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (398198756912509 / 312500000000000 : ℚ)) - (U := (605867001705223636633 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (398198756912509 / 312500000000000 : ℝ) ≤ - (605867001705223636633 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (96885374094067 / 5000000000000000 : ℝ)) (q := - (398198756912509 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (398198756912509 / 20000000000000000 : ℚ)) + (r' := (398198756912509 / 312500000000000 : ℚ)) + (U := (-(9791340702794776363367 / 2500000000000000000000 : ℚ))) + (U' := (605867001705223636633 / 2500000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (468310782911 / 16000000000000 : ℚ)) + (s := (96885374094067 / 5000000000000000 : ℚ)) + (q := (398198756912509 / 20000000000000000 : ℚ)) + (U := (-(9791340702794776363367 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_63_3 : Uω (aρ 3) (bρ 3) (468310782911 / 16000000000000 : ℝ) ≤ @@ -2473,25 +2367,21 @@ lemma U_63_3 : have hlg : Real.log (128171911629181 / 10000000000000000 : ℝ) ≤ (-(43569679477317919277667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (128171911629181 / 10000000000000000 : ℝ) = - (128171911629181 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (128171911629181 / 78125000000000 : ℚ)) - (U := (4950623143682080722333 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (128171911629181 / 78125000000000 : ℝ) ≤ - (4950623143682080722333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99311920883987 / 10000000000000000 : ℝ)) (q := - (128171911629181 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (128171911629181 / 10000000000000000 : ℚ)) + (r' := (128171911629181 / 78125000000000 : ℚ)) + (U := (-(43569679477317919277667 / 10000000000000000000000 : ℚ))) + (U' := (4950623143682080722333 / 10000000000000000000000 : ℚ)) + 7 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (468310782911 / 16000000000000 : ℚ)) + (s := (99311920883987 / 10000000000000000 : ℚ)) + (q := (128171911629181 / 10000000000000000 : ℚ)) + (U := (-(43569679477317919277667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_63_4 : Uω (aρ 4) (bρ 4) (468310782911 / 16000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U05.lean b/LeanPool/Zeta5Irrational/Table/U05.lean index ff17739d49..196f75bda2 100644 --- a/LeanPool/Zeta5Irrational/Table/U05.lean +++ b/LeanPool/Zeta5Irrational/Table/U05.lean @@ -24,25 +24,21 @@ lemma U_64_1 : have hlg : Real.log (920088864570853 / 40000000000000000 : ℝ) ≤ (-(18860822371165874400701 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (920088864570853 / 40000000000000000 : ℝ) = - (920088864570853 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (920088864570853 / 625000000000000 : ℚ)) - (U := (1933593037834125599299 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (920088864570853 / 625000000000000 : ℝ) ≤ - (1933593037834125599299 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (229319380188239 / 10000000000000000 : ℝ)) (q := - (920088864570853 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (920088864570853 / 40000000000000000 : ℚ)) + (r' := (920088864570853 / 625000000000000 : ℚ)) + (U := (-(18860822371165874400701 / 5000000000000000000000 : ℚ))) + (U' := (1933593037834125599299 / 5000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (944711264583 / 32000000000000 : ℚ)) + (s := (229319380188239 / 10000000000000000 : ℚ)) + (q := (920088864570853 / 40000000000000000 : ℚ)) + (U := (-(18860822371165874400701 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_64_2 : Uω (aρ 2) (bρ 2) (944711264583 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_64_2 : have hlg : Real.log (806784040118343 / 40000000000000000 : ℝ) ≤ (-(19517893536797811818607 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (806784040118343 / 40000000000000000 : ℝ) = - (806784040118343 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (806784040118343 / 625000000000000 : ℚ)) - (U := (1276521872202188181393 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (806784040118343 / 625000000000000 : ℝ) ≤ - (1276521872202188181393 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12277248779499 / 625000000000000 : ℝ)) (q := - (806784040118343 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (806784040118343 / 40000000000000000 : ℚ)) + (r' := (806784040118343 / 625000000000000 : ℚ)) + (U := (-(19517893536797811818607 / 5000000000000000000000 : ℚ))) + (U' := (1276521872202188181393 / 5000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (944711264583 / 32000000000000 : ℚ)) + (s := (12277248779499 / 625000000000000 : ℚ)) + (q := (806784040118343 / 40000000000000000 : ℚ)) + (U := (-(19517893536797811818607 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_64_3 : Uω (aρ 3) (bρ 3) (944711264583 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_64_3 : have hlg : Real.log (525645521645909 / 40000000000000000 : ℝ) ≤ (-(21660038294705195113549 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (525645521645909 / 40000000000000000 : ℝ) = - (525645521645909 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (525645521645909 / 312500000000000 : ℚ)) - (U := (2600113015794804886451 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (525645521645909 / 312500000000000 : ℝ) ≤ - (2600113015794804886451 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103262827585767 / 10000000000000000 : ℝ)) (q := - (525645521645909 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (525645521645909 / 40000000000000000 : ℚ)) + (r' := (525645521645909 / 312500000000000 : ℚ)) + (U := (-(21660038294705195113549 / 5000000000000000000000 : ℚ))) + (U' := (2600113015794804886451 / 5000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (944711264583 / 32000000000000 : ℚ)) + (s := (103262827585767 / 10000000000000000 : ℚ)) + (q := (525645521645909 / 40000000000000000 : ℚ)) + (U := (-(21660038294705195113549 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_64_4 : Uω (aρ 4) (bρ 4) (944711264583 / 32000000000000 : ℝ) ≤ @@ -251,24 +239,21 @@ lemma U_65_1 : have hlg : Real.log (93023164149801 / 4000000000000000 : ℝ) ≤ (-(37612010995240153131751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (93023164149801 / 4000000000000000 : ℝ) = (93023164149801 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (93023164149801 / 62500000000000 : ℚ)) - (U := (3976819822759846868249 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (93023164149801 / 62500000000000 : ℝ) ≤ - (3976819822759846868249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46372547557801 / 2000000000000000 : ℝ)) (q := - (93023164149801 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (93023164149801 / 4000000000000000 : ℚ)) + (r' := (93023164149801 / 62500000000000 : ℚ)) + (U := (-(37612010995240153131751 / 10000000000000000000000 : ℚ))) + (U' := (3976819822759846868249 / 10000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (59550060209 / 2000000000000 : ℚ)) + (s := (46372547557801 / 2000000000000000 : ℚ)) + (q := (93023164149801 / 4000000000000000 : ℚ)) + (U := (-(37612010995240153131751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_65_2 : Uω (aρ 2) (bρ 2) (59550060209 / 2000000000000 : ℝ) ≤ @@ -276,25 +261,21 @@ lemma U_65_2 : have hlg : Real.log (408581704475813 / 20000000000000000 : ℝ) ≤ (-(7781591291438441479693 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (408581704475813 / 20000000000000000 : ℝ) = - (408581704475813 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (408581704475813 / 312500000000000 : ℚ)) - (U := (536174872161558520307 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (408581704475813 / 312500000000000 : ℝ) ≤ - (536174872161558520307 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (199097634025813 / 10000000000000000 : ℝ)) (q := - (408581704475813 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (408581704475813 / 20000000000000000 : ℚ)) + (r' := (408581704475813 / 312500000000000 : ℚ)) + (U := (-(7781591291438441479693 / 2000000000000000000000 : ℚ))) + (U' := (536174872161558520307 / 2000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (59550060209 / 2000000000000 : ℚ)) + (s := (199097634025813 / 10000000000000000 : ℚ)) + (q := (408581704475813 / 20000000000000000 : ℚ)) + (U := (-(7781591291438441479693 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_65_3 : Uω (aρ 3) (bρ 3) (59550060209 / 2000000000000 : ℝ) ≤ @@ -302,25 +283,21 @@ lemma U_65_3 : have hlg : Real.log (134607839669749 / 10000000000000000 : ℝ) ≤ (-(43079747104388786598999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (134607839669749 / 10000000000000000 : ℝ) = - (134607839669749 / 78125000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (134607839669749 / 78125000000000 : ℚ)) - (U := (5440555516611213401001 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (134607839669749 / 78125000000000 : ℝ) ≤ - (5440555516611213401001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53563857619749 / 5000000000000000 : ℝ)) (q := - (134607839669749 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (134607839669749 / 10000000000000000 : ℚ)) + (r' := (134607839669749 / 78125000000000 : ℚ)) + (U := (-(43079747104388786598999 / 10000000000000000000000 : ℚ))) + (U' := (5440555516611213401001 / 10000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (59550060209 / 2000000000000 : ℚ)) + (s := (53563857619749 / 5000000000000000 : ℚ)) + (q := (134607839669749 / 10000000000000000 : ℚ)) + (U := (-(43079747104388786598999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_65_4 : Uω (aρ 4) (bρ 4) (59550060209 / 2000000000000 : ℝ) ≤ @@ -478,25 +455,21 @@ lemma U_66_1 : have hlg : Real.log (940373755235099 / 40000000000000000 : ℝ) ≤ (-(37503573233468039420779 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (940373755235099 / 40000000000000000 : ℝ) = - (940373755235099 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (940373755235099 / 625000000000000 : ℚ)) - (U := (4085257584531960579221 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (940373755235099 / 625000000000000 : ℝ) ≤ - (4085257584531960579221 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (234405763794737 / 10000000000000000 : ℝ)) (q := - (940373755235099 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (940373755235099 / 40000000000000000 : ℚ)) + (r' := (940373755235099 / 625000000000000 : ℚ)) + (U := (-(37503573233468039420779 / 10000000000000000000000 : ℚ))) + (U' := (4085257584531960579221 / 10000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (192178132421 / 6400000000000 : ℚ)) + (s := (234405763794737 / 10000000000000000 : ℚ)) + (q := (940373755235099 / 40000000000000000 : ℚ)) + (U := (-(37503573233468039420779 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_66_2 : Uω (aρ 2) (bρ 2) (192178132421 / 6400000000000 : ℝ) ≤ @@ -504,24 +477,21 @@ lemma U_66_2 : have hlg : Real.log (33101436143929 / 1600000000000000 : ℝ) ≤ (-(4847727796490385371113 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (33101436143929 / 1600000000000000 : ℝ) = (33101436143929 / 25000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33101436143929 / 25000000000000 : ℚ)) - (U := (350876055759614628887 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (33101436143929 / 25000000000000 : ℝ) ≤ - (350876055759614628887 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2017558504863 / 100000000000000 : ℝ)) (q := - (33101436143929 / 1600000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33101436143929 / 1600000000000000 : ℚ)) + (r' := (33101436143929 / 25000000000000 : ℚ)) + (U := (-(4847727796490385371113 / 1250000000000000000000 : ℚ))) + (U' := (350876055759614628887 / 1250000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (192178132421 / 6400000000000 : ℚ)) + (s := (2017558504863 / 100000000000000 : ℚ)) + (q := (33101436143929 / 1600000000000000 : ℚ)) + (U := (-(4847727796490385371113 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_66_3 : Uω (aρ 3) (bρ 3) (192178132421 / 6400000000000 : ℝ) ≤ @@ -529,25 +499,21 @@ lemma U_66_3 : have hlg : Real.log (551063142507483 / 40000000000000000 : ℝ) ≤ (-(42847853324868564028227 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (551063142507483 / 40000000000000000 : ℝ) = - (551063142507483 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (551063142507483 / 312500000000000 : ℚ)) - (U := (5672449296131435971773 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (551063142507483 / 312500000000000 : ℝ) ≤ - (5672449296131435971773 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110915576290929 / 10000000000000000 : ℝ)) (q := - (551063142507483 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (551063142507483 / 40000000000000000 : ℚ)) + (r' := (551063142507483 / 312500000000000 : ℚ)) + (U := (-(42847853324868564028227 / 10000000000000000000000 : ℚ))) + (U' := (5672449296131435971773 / 10000000000000000000000 : ℚ)) + 7 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (192178132421 / 6400000000000 : ℚ)) + (s := (110915576290929 / 10000000000000000 : ℚ)) + (q := (551063142507483 / 40000000000000000 : ℚ)) + (U := (-(42847853324868564028227 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_66_4 : Uω (aρ 4) (bρ 4) (192178132421 / 6400000000000 : ℝ) ≤ @@ -705,24 +671,21 @@ lemma U_67_1 : have hlg : Real.log (95051522713499 / 4000000000000000 : ℝ) ≤ (-(37396305496047393699967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (95051522713499 / 4000000000000000 : ℝ) = (95051522713499 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (95051522713499 / 62500000000000 : ℚ)) - (U := (4192525321952606300033 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (95051522713499 / 62500000000000 : ℝ) ≤ - (4192525321952606300033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23694846888187 / 1000000000000000 : ℝ)) (q := - (95051522713499 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (95051522713499 / 4000000000000000 : ℚ)) + (r' := (95051522713499 / 62500000000000 : ℚ)) + (U := (-(37396305496047393699967 / 10000000000000000000000 : ℚ))) + (U' := (4192525321952606300033 / 10000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (484490180433 / 16000000000000 : ℚ)) + (s := (23694846888187 / 1000000000000000 : ℚ)) + (q := (95051522713499 / 4000000000000000 : ℚ)) + (U := (-(37396305496047393699967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_67_2 : Uω (aρ 2) (bρ 2) (484490180433 / 16000000000000 : ℝ) ≤ @@ -730,24 +693,21 @@ lemma U_67_2 : have hlg : Real.log (41895089611997 / 2000000000000000 : ℝ) ≤ (-(19328669154765280711259 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (41895089611997 / 2000000000000000 : ℝ) = (41895089611997 / 31250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41895089611997 / 31250000000000 : ℚ)) - (U := (1465746254234719288741 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (41895089611997 / 31250000000000 : ℝ) ≤ - (1465746254234719288741 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40882152788869 / 2000000000000000 : ℝ)) (q := - (41895089611997 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41895089611997 / 2000000000000000 : ℚ)) + (r' := (41895089611997 / 31250000000000 : ℚ)) + (U := (-(19328669154765280711259 / 5000000000000000000000 : ℚ))) + (U' := (1465746254234719288741 / 5000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (484490180433 / 16000000000000 : ℚ)) + (s := (40882152788869 / 2000000000000000 : ℚ)) + (q := (41895089611997 / 2000000000000000 : ℚ)) + (U := (-(19328669154765280711259 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_67_3 : Uω (aρ 3) (bρ 3) (484490180433 / 16000000000000 : ℝ) ≤ @@ -755,23 +715,21 @@ lemma U_67_3 : have hlg : Real.log (8805564762709 / 625000000000000 : ℝ) ≤ (-(1704947106755531654199 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show (8805564762709 / 625000000000000 : ℝ) = (8805564762709 / 4882812500000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8805564762709 / 4882812500000 : ℚ)) - (U := (235864998084468345801 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8805564762709 / 4882812500000 : ℝ) ≤ - (235864998084468345801 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114634046581063 / 10000000000000000 : ℝ)) (q := - (8805564762709 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8805564762709 / 625000000000000 : ℚ)) + (r' := (8805564762709 / 4882812500000 : ℚ)) + (U := (-(1704947106755531654199 / 400000000000000000000 : ℚ))) + (U' := (235864998084468345801 / 400000000000000000000 : ℚ)) + 7 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (484490180433 / 16000000000000 : ℚ)) + (s := (114634046581063 / 10000000000000000 : ℚ)) + (q := (8805564762709 / 625000000000000 : ℚ)) + (U := (-(1704947106755531654199 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_67_4 : Uω (aρ 4) (bρ 4) (484490180433 / 16000000000000 : ℝ) ≤ @@ -929,25 +887,21 @@ lemma U_68_1 : have hlg : Real.log (960656077641081 / 40000000000000000 : ℝ) ≤ (-(37290182662862082118669 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (960656077641081 / 40000000000000000 : ℝ) = - (960656077641081 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (960656077641081 / 625000000000000 : ℚ)) - (U := (4298648155137917881331 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (960656077641081 / 625000000000000 : ℝ) ≤ - (4298648155137917881331 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239490863272103 / 10000000000000000 : ℝ)) (q := - (960656077641081 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (960656077641081 / 40000000000000000 : ℚ)) + (r' := (960656077641081 / 625000000000000 : ℚ)) + (U := (-(37290182662862082118669 / 10000000000000000000000 : ℚ))) + (U' := (4298648155137917881331 / 10000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (977070059627 / 32000000000000 : ℚ)) + (s := (239490863272103 / 10000000000000000 : ℚ)) + (q := (960656077641081 / 40000000000000000 : ℚ)) + (U := (-(37290182662862082118669 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_68_2 : Uω (aρ 2) (bρ 2) (977070059627 / 32000000000000 : ℝ) ≤ @@ -955,25 +909,21 @@ lemma U_68_2 : have hlg : Real.log (848261328979417 / 40000000000000000 : ℝ) ≤ (-(19267229861265618418229 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (848261328979417 / 40000000000000000 : ℝ) = - (848261328979417 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (848261328979417 / 625000000000000 : ℚ)) - (U := (1527185547734381581771 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (848261328979417 / 625000000000000 : ℝ) ≤ - (1527185547734381581771 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207062501451271 / 10000000000000000 : ℝ)) (q := - (848261328979417 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (848261328979417 / 40000000000000000 : ℚ)) + (r' := (848261328979417 / 625000000000000 : ℚ)) + (U := (-(19267229861265618418229 / 5000000000000000000000 : ℚ))) + (U' := (1527185547734381581771 / 5000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (977070059627 / 32000000000000 : ℚ)) + (s := (207062501451271 / 10000000000000000 : ℚ)) + (q := (848261328979417 / 40000000000000000 : ℚ)) + (U := (-(19267229861265618418229 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_68_3 : Uω (aρ 3) (bρ 3) (977070059627 / 32000000000000 : ℝ) ≤ @@ -981,25 +931,21 @@ lemma U_68_3 : have hlg : Real.log (575923453871657 / 40000000000000000 : ℝ) ≤ (-(42406599719954955895771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (575923453871657 / 40000000000000000 : ℝ) = - (575923453871657 / 312500000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (575923453871657 / 312500000000000 : ℚ)) - (U := (6113702901045044104229 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (575923453871657 / 312500000000000 : ℝ) ≤ - (6113702901045044104229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (118289670247391 / 10000000000000000 : ℝ)) (q := - (575923453871657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (575923453871657 / 40000000000000000 : ℚ)) + (r' := (575923453871657 / 312500000000000 : ℚ)) + (U := (-(42406599719954955895771 / 10000000000000000000000 : ℚ))) + (U' := (6113702901045044104229 / 10000000000000000000000 : ℚ)) + 7 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (977070059627 / 32000000000000 : ℚ)) + (s := (118289670247391 / 10000000000000000 : ℚ)) + (q := (575923453871657 / 40000000000000000 : ℚ)) + (U := (-(42406599719954955895771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_68_4 : Uω (aρ 4) (bρ 4) (977070059627 / 32000000000000 : ℝ) ≤ @@ -1157,25 +1103,21 @@ lemma U_69_1 : have hlg : Real.log (485398163167677 / 20000000000000000 : ℝ) ≤ (-(37185180418532968481481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (485398163167677 / 20000000000000000 : ℝ) = - (485398163167677 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (485398163167677 / 312500000000000 : ℚ)) - (U := (4403650399467031518519 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (485398163167677 / 312500000000000 : ℝ) ≤ - (4403650399467031518519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242032956756427 / 10000000000000000 : ℝ)) (q := - (485398163167677 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (485398163167677 / 20000000000000000 : ℚ)) + (r' := (485398163167677 / 312500000000000 : ℚ)) + (U := (-(37185180418532968481481 / 10000000000000000000000 : ℚ))) + (U' := (4403650399467031518519 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (246289939597 / 8000000000000 : ℚ)) + (s := (242032956756427 / 10000000000000000 : ℚ)) + (q := (485398163167677 / 20000000000000000 : ℚ)) + (U := (-(37185180418532968481481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_69_2 : Uω (aρ 2) (bρ 2) (246289939597 / 8000000000000 : ℝ) ≤ @@ -1183,24 +1125,21 @@ lemma U_69_2 : have hlg : Real.log (17172295095413 / 800000000000000 : ℝ) ≤ (-(4801642989010586665173 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (17172295095413 / 800000000000000 : ℝ) = (17172295095413 / 12500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17172295095413 / 12500000000000 : ℚ)) - (U := (396960863239413334827 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (17172295095413 / 12500000000000 : ℝ) ≤ - (396960863239413334827 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8388447339363 / 400000000000000 : ℝ)) (q := - (17172295095413 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17172295095413 / 800000000000000 : ℚ)) + (r' := (17172295095413 / 12500000000000 : ℚ)) + (U := (-(4801642989010586665173 / 1250000000000000000000 : ℚ))) + (U' := (396960863239413334827 / 1250000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (246289939597 / 8000000000000 : ℚ)) + (s := (8388447339363 / 400000000000000 : ℚ)) + (q := (17172295095413 / 800000000000000 : ℚ)) + (U := (-(4801642989010586665173 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_69_3 : Uω (aρ 3) (bρ 3) (246289939597 / 8000000000000 : ℝ) ≤ @@ -1208,25 +1147,21 @@ lemma U_69_3 : have hlg : Real.log (294088189591647 / 20000000000000000 : ℝ) ≤ (-(10549019659401938900341 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (294088189591647 / 20000000000000000 : ℝ) = - (294088189591647 / 156250000000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (294088189591647 / 156250000000000 : ℚ)) - (U := (1581055995848061099659 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (294088189591647 / 156250000000000 : ℝ) ≤ - (1581055995848061099659 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121888102040397 / 10000000000000000 : ℝ)) (q := - (294088189591647 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (294088189591647 / 20000000000000000 : ℚ)) + (r' := (294088189591647 / 156250000000000 : ℚ)) + (U := (-(10549019659401938900341 / 2500000000000000000000 : ℚ))) + (U' := (1581055995848061099659 / 2500000000000000000000 : ℚ)) + 7 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (246289939597 / 8000000000000 : ℚ)) + (s := (121888102040397 / 10000000000000000 : ℚ)) + (q := (294088189591647 / 20000000000000000 : ℚ)) + (U := (-(10549019659401938900341 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_69_4 : Uω (aρ 4) (bρ 4) (246289939597 / 8000000000000 : ℝ) ≤ @@ -1384,25 +1319,21 @@ lemma U_70_1 : have hlg : Real.log (247768773144139 / 10000000000000000 : ℝ) ≤ (-(7395688851059352324481 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (247768773144139 / 10000000000000000 : ℝ) = - (247768773144139 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (247768773144139 / 156250000000000 : ℚ)) - (U := (922077312540647675519 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (247768773144139 / 156250000000000 : ℝ) ≤ - (922077312540647675519 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (247116278151403 / 10000000000000000 : ℝ)) (q := - (247768773144139 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (247768773144139 / 10000000000000000 : ℚ)) + (r' := (247768773144139 / 156250000000000 : ℚ)) + (U := (-(7395688851059352324481 / 2000000000000000000000 : ℚ))) + (U' := (922077312540647675519 / 2000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (100133915591 / 3200000000000 : ℚ)) + (s := (247116278151403 / 10000000000000000 : ℚ)) + (q := (247768773144139 / 10000000000000000 : ℚ)) + (U := (-(7395688851059352324481 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_70_2 : Uω (aρ 2) (bρ 2) (100133915591 / 3200000000000 : ℝ) ≤ @@ -1410,25 +1341,21 @@ lemma U_70_2 : have hlg : Real.log (109913022081481 / 5000000000000000 : ℝ) ≤ (-(3817503845189056183093 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (109913022081481 / 5000000000000000 : ℝ) = - (109913022081481 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (109913022081481 / 78125000000000 : ℚ)) - (U := (341379236610943816907 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (109913022081481 / 78125000000000 : ℝ) ≤ - (341379236610943816907 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (214999832699049 / 10000000000000000 : ℝ)) (q := - (109913022081481 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (109913022081481 / 5000000000000000 : ℚ)) + (r' := (109913022081481 / 78125000000000 : ℚ)) + (U := (-(3817503845189056183093 / 1000000000000000000000 : ℚ))) + (U' := (341379236610943816907 / 1000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (100133915591 / 3200000000000 : ℚ)) + (s := (214999832699049 / 10000000000000000 : ℚ)) + (q := (109913022081481 / 5000000000000000 : ℚ)) + (U := (-(3817503845189056183093 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_70_3 : Uω (aρ 3) (bρ 3) (100133915591 / 3200000000000 : ℝ) ≤ @@ -1436,24 +1363,21 @@ lemma U_70_3 : have hlg : Real.log (76547154724709 / 5000000000000000 : ℝ) ≤ (-(2612053898144625343839 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (76547154724709 / 5000000000000000 : ℝ) = (76547154724709 / 39062500000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (76547154724709 / 39062500000000 : ℚ)) - (U := (420465015667874656161 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (76547154724709 / 39062500000000 : ℝ) ≤ - (420465015667874656161 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128932469621961 / 10000000000000000 : ℝ)) (q := - (76547154724709 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (76547154724709 / 5000000000000000 : ℚ)) + (r' := (76547154724709 / 39062500000000 : ℚ)) + (U := (-(2612053898144625343839 / 625000000000000000000 : ℚ))) + (U' := (420465015667874656161 / 625000000000000000000 : ℚ)) + 7 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (100133915591 / 3200000000000 : ℚ)) + (s := (128932469621961 / 10000000000000000 : ℚ)) + (q := (76547154724709 / 5000000000000000 : ℚ)) + (U := (-(2612053898144625343839 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_70_4 : Uω (aρ 4) (bρ 4) (100133915591 / 3200000000000 : ℝ) ≤ @@ -1610,25 +1534,21 @@ lemma U_71_1 : have hlg : Real.log (505675833464109 / 20000000000000000 : ℝ) ≤ (-(18387958661588722880311 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (505675833464109 / 20000000000000000 : ℝ) = - (505675833464109 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (505675833464109 / 312500000000000 : ℚ)) - (U := (2406456747411277119689 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (505675833464109 / 312500000000000 : ℝ) ≤ - (2406456747411277119689 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252198503601609 / 10000000000000000 : ℝ)) (q := - (505675833464109 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (505675833464109 / 20000000000000000 : ℚ)) + (r' := (505675833464109 / 312500000000000 : ℚ)) + (U := (-(18387958661588722880311 / 5000000000000000000000 : ℚ))) + (U' := (2406456747411277119689 / 5000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (127189819179 / 4000000000000 : ℚ)) + (s := (252198503601609 / 10000000000000000 : ℚ)) + (q := (505675833464109 / 20000000000000000 : ℚ)) + (U := (-(18387958661588722880311 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_71_2 : Uω (aρ 2) (bρ 2) (127189819179 / 4000000000000 : ℝ) ≤ @@ -1636,25 +1556,21 @@ lemma U_71_2 : have hlg : Real.log (224992938362713 / 10000000000000000 : ℝ) ≤ (-(7588542707518441531123 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (224992938362713 / 10000000000000000 : ℝ) = - (224992938362713 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (224992938362713 / 156250000000000 : ℚ)) - (U := (729223456081558468877 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (224992938362713 / 156250000000000 : ℝ) ≤ - (729223456081558468877 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110138779686463 / 5000000000000000 : ℝ)) (q := - (224992938362713 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (224992938362713 / 10000000000000000 : ℚ)) + (r' := (224992938362713 / 156250000000000 : ℚ)) + (U := (-(7588542707518441531123 / 2000000000000000000000 : ℚ))) + (U' := (729223456081558468877 / 2000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (127189819179 / 4000000000000 : ℚ)) + (s := (110138779686463 / 5000000000000000 : ℚ)) + (q := (224992938362713 / 10000000000000000 : ℚ)) + (U := (-(7588542707518441531123 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_71_3 : Uω (aρ 3) (bρ 3) (127189819179 / 4000000000000 : ℝ) ≤ @@ -1662,24 +1578,21 @@ lemma U_71_3 : have hlg : Real.log (79527998946249 / 5000000000000000 : ℝ) ≤ (-(1656433616878713809077 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (79527998946249 / 5000000000000000 : ℝ) = (79527998946249 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (79527998946249 / 78125000000000 : ℚ)) - (U := (7119615841286190923 / 400000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (79527998946249 / 78125000000000 : ℝ) ≤ - (7119615841286190923 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4243743274453 / 312500000000000 : ℝ)) (q := - (79527998946249 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (79527998946249 / 5000000000000000 : ℚ)) + (r' := (79527998946249 / 78125000000000 : ℚ)) + (U := (-(1656433616878713809077 / 400000000000000000000 : ℚ))) + (U' := (7119615841286190923 / 400000000000000000000 : ℚ)) + 6 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (127189819179 / 4000000000000 : ℚ)) + (s := (4243743274453 / 312500000000000 : ℚ)) + (q := (79527998946249 / 5000000000000000 : ℚ)) + (U := (-(1656433616878713809077 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_71_4 : Uω (aρ 4) (bρ 4) (127189819179 / 4000000000000 : ℝ) ≤ @@ -1836,25 +1749,21 @@ lemma U_72_1 : have hlg : Real.log (257906544821033 / 10000000000000000 : ℝ) ≤ (-(36577430804916419226009 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (257906544821033 / 10000000000000000 : ℝ) = - (257906544821033 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (257906544821033 / 156250000000000 : ℚ)) - (U := (5011400013083580773991 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (257906544821033 / 156250000000000 : ℝ) ≤ - (5011400013083580773991 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (257279698053941 / 10000000000000000 : ℝ)) (q := - (257906544821033 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (257906544821033 / 10000000000000000 : ℚ)) + (r' := (257906544821033 / 156250000000000 : ℚ)) + (U := (-(36577430804916419226009 / 10000000000000000000000 : ℚ))) + (U' := (5011400013083580773991 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (516848975477 / 16000000000000 : ℚ)) + (s := (257279698053941 / 10000000000000000 : ℚ)) + (q := (257906544821033 / 10000000000000000 : ℚ)) + (U := (-(36577430804916419226009 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_72_2 : Uω (aρ 2) (bρ 2) (516848975477 / 16000000000000 : ℝ) ≤ @@ -1862,25 +1771,21 @@ lemma U_72_2 : have hlg : Real.log (460309509343253 / 20000000000000000 : ℝ) ≤ (-(9428971103386477538939 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (460309509343253 / 20000000000000000 : ℝ) = - (460309509343253 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (460309509343253 / 312500000000000 : ℚ)) - (U := (968236601113522461061 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (460309509343253 / 312500000000000 : ℝ) ≤ - (968236601113522461061 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28193141283141 / 1250000000000000 : ℝ)) (q := - (460309509343253 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (460309509343253 / 20000000000000000 : ℚ)) + (r' := (460309509343253 / 312500000000000 : ℚ)) + (U := (-(9428971103386477538939 / 2500000000000000000000 : ℚ))) + (U' := (968236601113522461061 / 2500000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (516848975477 / 16000000000000 : ℚ)) + (s := (28193141283141 / 1250000000000000 : ℚ)) + (q := (460309509343253 / 20000000000000000 : ℚ)) + (U := (-(9428971103386477538939 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_72_3 : Uω (aρ 3) (bρ 3) (516848975477 / 16000000000000 : ℝ) ≤ @@ -1888,24 +1793,21 @@ lemma U_72_3 : have hlg : Real.log (65976783420521 / 4000000000000000 : ℝ) ≤ (-(41047467247559701779401 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (65976783420521 / 4000000000000000 : ℝ) = (65976783420521 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65976783420521 / 62500000000000 : ℚ)) - (U := (541363570440298220599 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (65976783420521 / 62500000000000 : ℝ) ≤ - (541363570440298220599 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1781445554681 / 125000000000000 : ℝ)) (q := - (65976783420521 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65976783420521 / 4000000000000000 : ℚ)) + (r' := (65976783420521 / 62500000000000 : ℚ)) + (U := (-(41047467247559701779401 / 10000000000000000000000 : ℚ))) + (U' := (541363570440298220599 / 10000000000000000000000 : ℚ)) + 6 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (516848975477 / 16000000000000 : ℚ)) + (s := (1781445554681 / 125000000000000 : ℚ)) + (q := (65976783420521 / 4000000000000000 : ℚ)) + (U := (-(41047467247559701779401 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_72_4 : Uω (aρ 4) (bρ 4) (516848975477 / 16000000000000 : ℝ) ≤ @@ -2063,25 +1965,21 @@ lemma U_73_1 : have hlg : Real.log (262974687362493 / 10000000000000000 : ℝ) ≤ (-(1455313035456262498261 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (262974687362493 / 10000000000000000 : ℝ) = - (262974687362493 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (262974687362493 / 156250000000000 : ℚ)) - (U := (208240197263737501739 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (262974687362493 / 156250000000000 : ℝ) ≤ - (208240197263737501739 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (65589980352809 / 2500000000000000 : ℝ)) (q := - (262974687362493 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (262974687362493 / 10000000000000000 : ℚ)) + (r' := (262974687362493 / 156250000000000 : ℚ)) + (U := (-(1455313035456262498261 / 400000000000000000000 : ℚ))) + (U' := (208240197263737501739 / 400000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (262469337119 / 8000000000000 : ℚ)) + (s := (65589980352809 / 2500000000000000 : ℚ)) + (q := (262974687362493 / 10000000000000000 : ℚ)) + (U := (-(1455313035456262498261 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_73_2 : Uω (aρ 2) (bρ 2) (262469337119 / 8000000000000 : ℝ) ≤ @@ -2089,25 +1987,21 @@ lemma U_73_2 : have hlg : Real.log (235311840764937 / 10000000000000000 : ℝ) ≤ (-(9373571884890926660439 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (235311840764937 / 10000000000000000 : ℝ) = - (235311840764937 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (235311840764937 / 156250000000000 : ℚ)) - (U := (1023635819609073339561 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (235311840764937 / 156250000000000 : ℝ) ≤ - (1023635819609073339561 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57700810181531 / 2500000000000000 : ℝ)) (q := - (235311840764937 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (235311840764937 / 10000000000000000 : ℚ)) + (r' := (235311840764937 / 156250000000000 : ℚ)) + (U := (-(9373571884890926660439 / 2500000000000000000000 : ℚ))) + (U' := (1023635819609073339561 / 2500000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (262469337119 / 8000000000000 : ℚ)) + (s := (57700810181531 / 2500000000000000 : ℚ)) + (q := (235311840764937 / 10000000000000000 : ℚ)) + (U := (-(9373571884890926660439 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_73_3 : Uω (aρ 3) (bρ 3) (262469337119 / 8000000000000 : ℝ) ≤ @@ -2115,25 +2009,21 @@ lemma U_73_3 : have hlg : Real.log (341524850067617 / 20000000000000000 : ℝ) ≤ (-(8140134214423032915029 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (341524850067617 / 20000000000000000 : ℝ) = - (341524850067617 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (341524850067617 / 312500000000000 : ℚ)) - (U := (177631949176967084971 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (341524850067617 / 312500000000000 : ℝ) ≤ - (177631949176967084971 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (149100515613867 / 10000000000000000 : ℝ)) (q := - (341524850067617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (341524850067617 / 20000000000000000 : ℚ)) + (r' := (341524850067617 / 312500000000000 : ℚ)) + (U := (-(8140134214423032915029 / 2000000000000000000000 : ℚ))) + (U' := (177631949176967084971 / 2000000000000000000000 : ℚ)) + 6 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (262469337119 / 8000000000000 : ℚ)) + (s := (149100515613867 / 10000000000000000 : ℚ)) + (q := (341524850067617 / 20000000000000000 : ℚ)) + (U := (-(8140134214423032915029 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_73_4 : Uω (aρ 4) (bρ 4) (262469337119 / 8000000000000 : ℝ) ≤ @@ -2290,24 +2180,21 @@ lemma U_74_1 : have hlg : Real.log (13655481220777 / 500000000000000 : ℝ) ≤ (-(36004671011973596596201 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (13655481220777 / 500000000000000 : ℝ) = (13655481220777 / 7812500000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13655481220777 / 7812500000000 : ℚ)) - (U := (5584159806026403403799 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (13655481220777 / 7812500000000 : ℝ) ≤ - (5584159806026403403799 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1703235450413 / 62500000000000 : ℝ)) (q := - (13655481220777 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13655481220777 / 500000000000000 : ℚ)) + (r' := (13655481220777 / 7812500000000 : ℚ)) + (U := (-(36004671011973596596201 / 10000000000000000000000 : ℚ))) + (U' := (5584159806026403403799 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6763975897 / 200000000000 : ℚ)) + (s := (1703235450413 / 62500000000000 : ℚ)) + (q := (13655481220777 / 500000000000000 : ℚ)) + (U := (-(36004671011973596596201 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_74_2 : Uω (aρ 2) (bρ 2) (6763975897 / 200000000000 : ℝ) ≤ @@ -2315,24 +2202,21 @@ lemma U_74_2 : have hlg : Real.log (30701632335961 / 1250000000000000 : ℝ) ≤ (-(18532915025022758161627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (30701632335961 / 1250000000000000 : ℝ) = (30701632335961 / 19531250000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30701632335961 / 19531250000000 : ℚ)) - (U := (2261500383977241838373 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (30701632335961 / 19531250000000 : ℝ) ≤ - (2261500383977241838373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (30161694140047 / 1250000000000000 : ℝ)) (q := - (30701632335961 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30701632335961 / 1250000000000000 : ℚ)) + (r' := (30701632335961 / 19531250000000 : ℚ)) + (U := (-(18532915025022758161627 / 5000000000000000000000 : ℚ))) + (U' := (2261500383977241838373 / 5000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6763975897 / 200000000000 : ℚ)) + (s := (30161694140047 / 1250000000000000 : ℚ)) + (q := (30701632335961 / 1250000000000000 : ℚ)) + (U := (-(18532915025022758161627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_74_3 : Uω (aρ 3) (bρ 3) (6763975897 / 200000000000 : ℝ) ≤ @@ -2340,25 +2224,21 @@ lemma U_74_3 : have hlg : Real.log (364477360851279 / 20000000000000000 : ℝ) ≤ (-(801004622320808228037 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (364477360851279 / 20000000000000000 : ℝ) = - (364477360851279 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (364477360851279 / 312500000000000 : ℚ)) - (U := (30771994039191771963 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (364477360851279 / 312500000000000 : ℝ) ≤ - (30771994039191771963 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (161940902946279 / 10000000000000000 : ℝ)) (q := - (364477360851279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (364477360851279 / 20000000000000000 : ℚ)) + (r' := (364477360851279 / 312500000000000 : ℚ)) + (U := (-(801004622320808228037 / 200000000000000000000 : ℚ))) + (U' := (30771994039191771963 / 200000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6763975897 / 200000000000 : ℚ)) + (s := (161940902946279 / 10000000000000000 : ℚ)) + (q := (364477360851279 / 20000000000000000 : ℚ)) + (U := (-(801004622320808228037 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_74_4 : Uω (aρ 4) (bρ 4) (6763975897 / 200000000000 : ℝ) ≤ @@ -2516,25 +2396,21 @@ lemma U_75_1 : have hlg : Real.log (113297170223489 / 4000000000000000 : ℝ) ≤ (-(35640354467824444665873 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (113297170223489 / 4000000000000000 : ℝ) = - (113297170223489 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (113297170223489 / 62500000000000 : ℚ)) - (U := (5948476350175555334127 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (113297170223489 / 62500000000000 : ℝ) ≤ - (5948476350175555334127 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56534430180239 / 2000000000000000 : ℝ)) (q := - (113297170223489 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (113297170223489 / 4000000000000000 : ℚ)) + (r' := (113297170223489 / 62500000000000 : ℚ)) + (U := (-(35640354467824444665873 / 10000000000000000000000 : ℚ))) + (U' := (5948476350175555334127 / 10000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (278648734641 / 8000000000000 : ℚ)) + (s := (56534430180239 / 2000000000000000 : ℚ)) + (q := (113297170223489 / 4000000000000000 : ℚ)) + (U := (-(35640354467824444665873 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_75_2 : Uω (aρ 2) (bρ 2) (278648734641 / 8000000000000 : ℝ) ≤ @@ -2542,25 +2418,21 @@ lemma U_75_2 : have hlg : Real.log (511797605676663 / 20000000000000000 : ℝ) ≤ (-(36655583055019159093507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (511797605676663 / 20000000000000000 : ℝ) = - (511797605676663 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (511797605676663 / 312500000000000 : ℚ)) - (U := (4933247762980840906493 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (511797605676663 / 312500000000000 : ℝ) ≤ - (4933247762980840906493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (251752917970413 / 10000000000000000 : ℝ)) (q := - (511797605676663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (511797605676663 / 20000000000000000 : ℚ)) + (r' := (511797605676663 / 312500000000000 : ℚ)) + (U := (-(36655583055019159093507 / 10000000000000000000000 : ℚ))) + (U' := (4933247762980840906493 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (278648734641 / 8000000000000 : ℚ)) + (s := (251752917970413 / 10000000000000000 : ℚ)) + (q := (511797605676663 / 20000000000000000 : ℚ)) + (U := (-(36655583055019159093507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_75_3 : Uω (aρ 3) (bρ 3) (278648734641 / 8000000000000 : ℝ) ≤ @@ -2568,25 +2440,21 @@ lemma U_75_3 : have hlg : Real.log (387071224436723 / 20000000000000000 : ℝ) ≤ (-(19724394162041300263193 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (387071224436723 / 20000000000000000 : ℝ) = - (387071224436723 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (387071224436723 / 312500000000000 : ℚ)) - (U := (1070021246958699736807 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (387071224436723 / 312500000000000 : ℝ) ≤ - (1070021246958699736807 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (174422643080473 / 10000000000000000 : ℝ)) (q := - (387071224436723 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (387071224436723 / 20000000000000000 : ℚ)) + (r' := (387071224436723 / 312500000000000 : ℚ)) + (U := (-(19724394162041300263193 / 5000000000000000000000 : ℚ))) + (U' := (1070021246958699736807 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (278648734641 / 8000000000000 : ℚ)) + (s := (174422643080473 / 10000000000000000 : ℚ)) + (q := (387071224436723 / 20000000000000000 : ℚ)) + (U := (-(19724394162041300263193 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_75_4 : Uω (aρ 4) (bρ 4) (278648734641 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U06.lean b/LeanPool/Zeta5Irrational/Table/U06.lean index 85605dc26c..0e3d2ecba8 100644 --- a/LeanPool/Zeta5Irrational/Table/U06.lean +++ b/LeanPool/Zeta5Irrational/Table/U06.lean @@ -24,25 +24,21 @@ lemma U_76_1 : have hlg : Real.log (293374760981357 / 10000000000000000 : ℝ) ≤ (-(17644447654831053876417 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (293374760981357 / 10000000000000000 : ℝ) = - (293374760981357 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (293374760981357 / 156250000000000 : ℚ)) - (U := (3149967754168946123583 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (293374760981357 / 156250000000000 : ℝ) ≤ - (3149967754168946123583 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (146411849147607 / 5000000000000000 : ℝ)) (q := - (293374760981357 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (293374760981357 / 10000000000000000 : ℚ)) + (r' := (293374760981357 / 156250000000000 : ℚ)) + (U := (-(17644447654831053876417 / 5000000000000000000000 : ℚ))) + (U' := (3149967754168946123583 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (143369216701 / 4000000000000 : ℚ)) + (s := (146411849147607 / 5000000000000000 : ℚ)) + (q := (293374760981357 / 10000000000000000 : ℚ)) + (U := (-(17644447654831053876417 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_76_2 : Uω (aρ 2) (bρ 2) (143369216701 / 4000000000000 : ℝ) ≤ @@ -50,24 +46,21 @@ lemma U_76_2 : have hlg : Real.log (16635682819909 / 625000000000000 : ℝ) ≤ (-(36262016923645122436277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (16635682819909 / 625000000000000 : ℝ) = (16635682819909 / 9765625000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16635682819909 / 9765625000000 : ℚ)) - (U := (5326813894354877563723 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16635682819909 / 9765625000000 : ℝ) ≤ - (5326813894354877563723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (65546259769897 / 2500000000000000 : ℝ)) (q := - (16635682819909 / 625000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16635682819909 / 625000000000000 : ℚ)) + (r' := (16635682819909 / 9765625000000 : ℚ)) + (U := (-(36262016923645122436277 / 10000000000000000000000 : ℚ))) + (U' := (5326813894354877563723 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (143369216701 / 4000000000000 : ℚ)) + (s := (65546259769897 / 2500000000000000 : ℚ)) + (q := (16635682819909 / 625000000000000 : ℚ)) + (U := (-(36262016923645122436277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_76_3 : Uω (aρ 3) (bρ 3) (143369216701 / 4000000000000 : ℝ) ≤ @@ -75,24 +68,21 @@ lemma U_76_3 : have hlg : Real.log (51172302248489 / 2500000000000000 : ℝ) ≤ (-(38888475953383457362861 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (51172302248489 / 2500000000000000 : ℝ) = (51172302248489 / 39062500000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51172302248489 / 39062500000000 : ℚ)) - (U := (2700354864616542637139 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51172302248489 / 39062500000000 : ℝ) ≤ - (2700354864616542637139 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46654428295103 / 2500000000000000 : ℝ)) (q := - (51172302248489 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51172302248489 / 2500000000000000 : ℚ)) + (r' := (51172302248489 / 39062500000000 : ℚ)) + (U := (-(38888475953383457362861 / 10000000000000000000000 : ℚ))) + (U' := (2700354864616542637139 / 10000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (143369216701 / 4000000000000 : ℚ)) + (s := (46654428295103 / 2500000000000000 : ℚ)) + (q := (51172302248489 / 2500000000000000 : ℚ)) + (U := (-(38888475953383457362861 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_76_4 : Uω (aρ 4) (bρ 4) (143369216701 / 4000000000000 : ℝ) ≤ @@ -249,25 +239,21 @@ lemma U_77_1 : have hlg : Real.log (313634604861411 / 10000000000000000 : ℝ) ≤ (-(17310558705766996086987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (313634604861411 / 10000000000000000 : ℝ) = - (313634604861411 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (313634604861411 / 312500000000000 : ℚ)) - (U := (18120801733003913013 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (313634604861411 / 312500000000000 : ℝ) ≤ - (18120801733003913013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156559569576411 / 5000000000000000 : ℝ)) (q := - (313634604861411 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (313634604861411 / 10000000000000000 : ℚ)) + (r' := (313634604861411 / 312500000000000 : ℚ)) + (U := (-(17310558705766996086987 / 5000000000000000000000 : ℚ))) + (U' := (18120801733003913013 / 5000000000000000000000 : ℚ)) + 5 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (75729457731 / 2000000000000 : ℚ)) + (s := (156559569576411 / 5000000000000000 : ℚ)) + (q := (313634604861411 / 10000000000000000 : ℚ)) + (U := (-(17310558705766996086987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_77_2 : Uω (aρ 2) (bρ 2) (75729457731 / 2000000000000 : ℝ) ≤ @@ -275,25 +261,21 @@ lemma U_77_2 : have hlg : Real.log (573360652699651 / 20000000000000000 : ℝ) ≤ (-(17759863104573821333591 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (573360652699651 / 20000000000000000 : ℝ) = - (573360652699651 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (573360652699651 / 312500000000000 : ℚ)) - (U := (3034552304426178666409 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (573360652699651 / 312500000000000 : ℝ) ≤ - (3034552304426178666409 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (282979594639651 / 10000000000000000 : ℝ)) (q := - (573360652699651 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (573360652699651 / 20000000000000000 : ℚ)) + (r' := (573360652699651 / 312500000000000 : ℚ)) + (U := (-(17759863104573821333591 / 5000000000000000000000 : ℚ))) + (U' := (3034552304426178666409 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (75729457731 / 2000000000000 : ℚ)) + (s := (282979594639651 / 10000000000000000 : ℚ)) + (q := (573360652699651 / 20000000000000000 : ℚ)) + (U := (-(17759863104573821333591 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_77_3 : Uω (aρ 3) (bρ 3) (75729457731 / 2000000000000 : ℝ) ≤ @@ -301,25 +283,21 @@ lemma U_77_3 : have hlg : Real.log (453331156866793 / 20000000000000000 : ℝ) ≤ (-(1893432330977563126623 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (453331156866793 / 20000000000000000 : ℝ) = - (453331156866793 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (453331156866793 / 312500000000000 : ℚ)) - (U := (186009209922436873377 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (453331156866793 / 312500000000000 : ℝ) ≤ - (186009209922436873377 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (210346205156793 / 10000000000000000 : ℝ)) (q := - (453331156866793 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (453331156866793 / 20000000000000000 : ℚ)) + (r' := (453331156866793 / 312500000000000 : ℚ)) + (U := (-(1893432330977563126623 / 500000000000000000000 : ℚ))) + (U' := (186009209922436873377 / 500000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (75729457731 / 2000000000000 : ℚ)) + (s := (210346205156793 / 10000000000000000 : ℚ)) + (q := (453331156866793 / 20000000000000000 : ℚ)) + (U := (-(1893432330977563126623 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_77_4 : Uω (aρ 4) (bρ 4) (75729457731 / 2000000000000 : ℝ) ≤ @@ -476,25 +454,21 @@ lemma U_78_1 : have hlg : Real.log (354142058631351 / 10000000000000000 : ℝ) ≤ (-(16703211212357127756093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (354142058631351 / 10000000000000000 : ℝ) = - (354142058631351 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (354142058631351 / 312500000000000 : ℚ)) - (U := (625468295142872243907 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (354142058631351 / 312500000000000 : ℝ) ≤ - (625468295142872243907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (176842776443851 / 5000000000000000 : ℝ)) (q := - (354142058631351 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (354142058631351 / 10000000000000000 : ℚ)) + (r' := (354142058631351 / 312500000000000 : ℚ)) + (U := (-(16703211212357127756093 / 5000000000000000000000 : ℚ))) + (U' := (625468295142872243907 / 5000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20954789123 / 500000000000 : ℚ)) + (s := (176842776443851 / 5000000000000000 : ℚ)) + (q := (354142058631351 / 10000000000000000 : ℚ)) + (U := (-(16703211212357127756093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_78_2 : Uω (aρ 2) (bρ 2) (20954789123 / 500000000000 : ℝ) ≤ @@ -502,25 +476,21 @@ lemma U_78_2 : have hlg : Real.log (655181959732697 / 20000000000000000 : ℝ) ≤ (-(8546436382655285391233 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (655181959732697 / 20000000000000000 : ℝ) = - (655181959732697 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (655181959732697 / 625000000000000 : ℚ)) - (U := (117903371094714608767 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (655181959732697 / 625000000000000 : ℝ) ≤ - (117903371094714608767 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (324352407867697 / 10000000000000000 : ℝ)) (q := - (655181959732697 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (655181959732697 / 20000000000000000 : ℚ)) + (r' := (655181959732697 / 625000000000000 : ℚ)) + (U := (-(8546436382655285391233 / 2500000000000000000000 : ℚ))) + (U' := (117903371094714608767 / 2500000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20954789123 / 500000000000 : ℚ)) + (s := (324352407867697 / 10000000000000000 : ℚ)) + (q := (655181959732697 / 20000000000000000 : ℚ)) + (U := (-(8546436382655285391233 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_78_3 : Uω (aρ 3) (bρ 3) (20954789123 / 500000000000 : ℝ) ≤ @@ -528,25 +498,21 @@ lemma U_78_3 : have hlg : Real.log (539438049580741 / 20000000000000000 : ℝ) ≤ (-(36129596021937323314463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (539438049580741 / 20000000000000000 : ℝ) = - (539438049580741 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (539438049580741 / 312500000000000 : ℚ)) - (U := (5459234796062676685537 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (539438049580741 / 312500000000000 : ℝ) ≤ - (5459234796062676685537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256004604065741 / 10000000000000000 : ℝ)) (q := - (539438049580741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (539438049580741 / 20000000000000000 : ℚ)) + (r' := (539438049580741 / 312500000000000 : ℚ)) + (U := (-(36129596021937323314463 / 10000000000000000000000 : ℚ))) + (U' := (5459234796062676685537 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20954789123 / 500000000000 : ℚ)) + (s := (256004604065741 / 10000000000000000 : ℚ)) + (q := (539438049580741 / 20000000000000000 : ℚ)) + (U := (-(36129596021937323314463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_78_4 : Uω (aρ 4) (bρ 4) (20954789123 / 500000000000 : ℝ) ≤ @@ -703,25 +669,21 @@ lemma U_79_1 : have hlg : Real.log (147649612727507 / 4000000000000000 : ℝ) ≤ (-(8248019133811670168773 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (147649612727507 / 4000000000000000 : ℝ) = - (147649612727507 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (147649612727507 / 125000000000000 : ℚ)) - (U := (416320619938329831227 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (147649612727507 / 125000000000000 : ℝ) ≤ - (416320619938329831227 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36868605468941 / 1000000000000000 : ℝ)) (q := - (147649612727507 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (147649612727507 / 4000000000000000 : ℚ)) + (r' := (147649612727507 / 125000000000000 : ℚ)) + (U := (-(8248019133811670168773 / 2500000000000000000000 : ℚ))) + (U' := (416320619938329831227 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (694494763253 / 16000000000000 : ℚ)) + (s := (36868605468941 / 1000000000000000 : ℚ)) + (q := (147649612727507 / 4000000000000000 : ℚ)) + (U := (-(8248019133811670168773 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_79_2 : Uω (aρ 2) (bρ 2) (694494763253 / 16000000000000 : ℝ) ≤ @@ -729,24 +691,21 @@ lemma U_79_2 : have hlg : Real.log (27415774538689 / 800000000000000 : ℝ) ≤ (-(33734931655425398758109 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (27415774538689 / 800000000000000 : ℝ) = (27415774538689 / 25000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27415774538689 / 25000000000000 : ℚ)) - (U := (922427359574601241891 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (27415774538689 / 25000000000000 : ℝ) ≤ - (922427359574601241891 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3396013670291 / 100000000000000 : ℝ)) (q := - (27415774538689 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27415774538689 / 800000000000000 : ℚ)) + (r' := (27415774538689 / 25000000000000 : ℚ)) + (U := (-(33734931655425398758109 / 10000000000000000000000 : ℚ))) + (U' := (922427359574601241891 / 10000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (694494763253 / 16000000000000 : ℚ)) + (s := (3396013670291 / 100000000000000 : ℚ)) + (q := (27415774538689 / 800000000000000 : ℚ)) + (U := (-(33734931655425398758109 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_79_3 : Uω (aρ 3) (bρ 3) (694494763253 / 16000000000000 : ℝ) ≤ @@ -754,25 +713,21 @@ lemma U_79_3 : have hlg : Real.log (285437704511201 / 10000000000000000 : ℝ) ≤ (-(17781582814941265651163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (285437704511201 / 10000000000000000 : ℝ) = - (285437704511201 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (285437704511201 / 156250000000000 : ℚ)) - (U := (3012832594058734348837 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (285437704511201 / 156250000000000 : ℝ) ≤ - (3012832594058734348837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (272478518934277 / 10000000000000000 : ℝ)) (q := - (285437704511201 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (285437704511201 / 10000000000000000 : ℚ)) + (r' := (285437704511201 / 156250000000000 : ℚ)) + (U := (-(17781582814941265651163 / 5000000000000000000000 : ℚ))) + (U' := (3012832594058734348837 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (694494763253 / 16000000000000 : ℚ)) + (s := (272478518934277 / 10000000000000000 : ℚ)) + (q := (285437704511201 / 10000000000000000 : ℚ)) + (U := (-(17781582814941265651163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_79_4 : Uω (aρ 4) (bρ 4) (694494763253 / 16000000000000 : ℝ) ≤ @@ -780,24 +735,21 @@ lemma U_79_4 : have hlg : Real.log (37483956842069 / 2500000000000000 : ℝ) ≤ (-(2625083115715732209859 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 7 - (show - (37483956842069 / 2500000000000000 : ℝ) = (37483956842069 / 19531250000000 : ℝ) / 2 ^ 7 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37483956842069 / 19531250000000 : ℚ)) - (U := (407435798096767790141 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37483956842069 / 19531250000000 : ℝ) ≤ - (407435798096767790141 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79768945713427 / 10000000000000000 : ℝ)) (q := - (37483956842069 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37483956842069 / 2500000000000000 : ℚ)) + (r' := (37483956842069 / 19531250000000 : ℚ)) + (U := (-(2625083115715732209859 / 625000000000000000000 : ℚ))) + (U' := (407435798096767790141 / 625000000000000000000 : ℚ)) + 7 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (694494763253 / 16000000000000 : ℚ)) + (s := (79768945713427 / 10000000000000000 : ℚ)) + (q := (37483956842069 / 2500000000000000 : ℚ)) + (U := (-(2625083115715732209859 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_79_5 : Uω (aρ 5) (bρ 5) (694494763253 / 16000000000000 : ℝ) ≤ @@ -949,25 +901,21 @@ lemma U_80_1 : have hlg : Real.log (1506457859888209 / 40000000000000000 : ℝ) ≤ (-(6558236691624471248019 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1506457859888209 / 40000000000000000 : ℝ) = - (1506457859888209 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1506457859888209 / 1250000000000000 : ℚ)) - (U := (373235111375528751981 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1506457859888209 / 1250000000000000 : ℝ) ≤ - (373235111375528751981 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (376185198709417 / 10000000000000000 : ℝ)) (q := - (1506457859888209 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1506457859888209 / 40000000000000000 : ℚ)) + (r' := (1506457859888209 / 1250000000000000 : ℚ)) + (U := (-(6558236691624471248019 / 2000000000000000000000 : ℚ))) + (U' := (373235111375528751981 / 2000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1412931037823 / 32000000000000 : ℚ)) + (s := (376185198709417 / 10000000000000000 : ℚ)) + (q := (1506457859888209 / 40000000000000000 : ℚ)) + (U := (-(6558236691624471248019 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_80_2 : Uω (aρ 2) (bρ 2) (1412931037823 / 32000000000000 : ℝ) ≤ @@ -975,25 +923,21 @@ lemma U_80_2 : have hlg : Real.log (1400982498276359 / 40000000000000000 : ℝ) ≤ (-(33517056778454642676983 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1400982498276359 / 40000000000000000 : ℝ) = - (1400982498276359 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1400982498276359 / 1250000000000000 : ℚ)) - (U := (1140302236545357323017 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1400982498276359 / 1250000000000000 : ℝ) ≤ - (1140302236545357323017 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86804132603373 / 2500000000000000 : ℝ)) (q := - (1400982498276359 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1400982498276359 / 40000000000000000 : ℚ)) + (r' := (1400982498276359 / 1250000000000000 : ℚ)) + (U := (-(33517056778454642676983 / 10000000000000000000000 : ℚ))) + (U' := (1140302236545357323017 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1412931037823 / 32000000000000 : ℚ)) + (s := (86804132603373 / 2500000000000000 : ℚ)) + (q := (1400982498276359 / 40000000000000000 : ℚ)) + (U := (-(33517056778454642676983 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_80_3 : Uω (aρ 3) (bρ 3) (1412931037823 / 32000000000000 : ℝ) ≤ @@ -1001,25 +945,21 @@ lemma U_80_3 : have hlg : Real.log (1173061294838367 / 40000000000000000 : ℝ) ≤ (-(27572364292843690767 / 7812500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1173061294838367 / 40000000000000000 : ℝ) = - (1173061294838367 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1173061294838367 / 625000000000000 : ℚ)) - (U := (4918909783718809233 / 7812500000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1173061294838367 / 625000000000000 : ℝ) ≤ - (4918909783718809233 / 7812500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17540752190281 / 625000000000000 : ℝ)) (q := - (1173061294838367 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1173061294838367 / 40000000000000000 : ℚ)) + (r' := (1173061294838367 / 625000000000000 : ℚ)) + (U := (-(27572364292843690767 / 7812500000000000000 : ℚ))) + (U' := (4918909783718809233 / 7812500000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1412931037823 / 32000000000000 : ℚ)) + (s := (17540752190281 / 625000000000000 : ℚ)) + (q := (1173061294838367 / 40000000000000000 : ℚ)) + (U := (-(27572364292843690767 / 7812500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_80_4 : Uω (aρ 4) (bρ 4) (1412931037823 / 32000000000000 : ℝ) ≤ @@ -1027,25 +967,21 @@ lemma U_80_4 : have hlg : Real.log (652273459780041 / 40000000000000000 : ℝ) ≤ (-(20580854203499261973059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (652273459780041 / 40000000000000000 : ℝ) = - (652273459780041 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (652273459780041 / 625000000000000 : ℚ)) - (U := (213561205500738026941 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (652273459780041 / 625000000000000 : ℝ) ≤ - (213561205500738026941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98552298580333 / 10000000000000000 : ℝ)) (q := - (652273459780041 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (652273459780041 / 40000000000000000 : ℚ)) + (r' := (652273459780041 / 625000000000000 : ℚ)) + (U := (-(20580854203499261973059 / 5000000000000000000000 : ℚ))) + (U' := (213561205500738026941 / 5000000000000000000000 : ℚ)) + 6 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1412931037823 / 32000000000000 : ℚ)) + (s := (98552298580333 / 10000000000000000 : ℚ)) + (q := (652273459780041 / 40000000000000000 : ℚ)) + (U := (-(20580854203499261973059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_80_5 : Uω (aρ 5) (bρ 5) (1412931037823 / 32000000000000 : ℝ) ≤ @@ -1196,25 +1132,21 @@ lemma U_81_1 : have hlg : Real.log (192052279005631 / 5000000000000000 : ℝ) ≤ (-(3259425568664305827969 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (192052279005631 / 5000000000000000 : ℝ) = - (192052279005631 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192052279005631 / 156250000000000 : ℚ)) - (U := (206310332835694172031 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (192052279005631 / 156250000000000 : ℝ) ≤ - (206310332835694172031 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (191841831250637 / 5000000000000000 : ℝ)) (q := - (192052279005631 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192052279005631 / 5000000000000000 : ℚ)) + (r' := (192052279005631 / 156250000000000 : ℚ)) + (U := (-(3259425568664305827969 / 1000000000000000000000 : ℚ))) + (U' := (206310332835694172031 / 1000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (71843627457 / 1600000000000 : ℚ)) + (s := (191841831250637 / 5000000000000000 : ℚ)) + (q := (192052279005631 / 5000000000000000 : ℚ)) + (U := (-(3259425568664305827969 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_81_2 : Uω (aρ 2) (bρ 2) (71843627457 / 1600000000000 : ℝ) ≤ @@ -1222,25 +1154,21 @@ lemma U_81_2 : have hlg : Real.log (715582457297373 / 20000000000000000 : ℝ) ≤ (-(6660781429157999445921 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (715582457297373 / 20000000000000000 : ℝ) = - (715582457297373 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (715582457297373 / 625000000000000 : ℚ)) - (U := (270690373842000554079 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (715582457297373 / 625000000000000 : ℝ) ≤ - (270690373842000554079 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (354826016286123 / 10000000000000000 : ℝ)) (q := - (715582457297373 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (715582457297373 / 20000000000000000 : ℚ)) + (r' := (715582457297373 / 625000000000000 : ℚ)) + (U := (-(6660781429157999445921 / 2000000000000000000000 : ℚ))) + (U' := (270690373842000554079 / 2000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (71843627457 / 1600000000000 : ℚ)) + (s := (354826016286123 / 10000000000000000 : ℚ)) + (q := (715582457297373 / 20000000000000000 : ℚ)) + (U := (-(6660781429157999445921 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_81_3 : Uω (aρ 3) (bρ 3) (71843627457 / 1600000000000 : ℝ) ≤ @@ -1248,25 +1176,21 @@ lemma U_81_3 : have hlg : Real.log (120429677203231 / 4000000000000000 : ℝ) ≤ (-(35029836476419809769441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (120429677203231 / 4000000000000000 : ℝ) = - (120429677203231 / 62500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (120429677203231 / 62500000000000 : ℚ)) - (U := (6558994341580190230559 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (120429677203231 / 62500000000000 : ℝ) ≤ - (6558994341580190230559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57757610270981 / 2000000000000000 : ℝ)) (q := - (120429677203231 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (120429677203231 / 4000000000000000 : ℚ)) + (r' := (120429677203231 / 62500000000000 : ℚ)) + (U := (-(35029836476419809769441 / 10000000000000000000000 : ℚ))) + (U' := (6558994341580190230559 / 10000000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (71843627457 / 1600000000000 : ℚ)) + (s := (57757610270981 / 2000000000000000 : ℚ)) + (q := (120429677203231 / 4000000000000000 : ℚ)) + (U := (-(35029836476419809769441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_81_4 : Uω (aρ 4) (bρ 4) (71843627457 / 1600000000000 : ℝ) ≤ @@ -1274,24 +1198,21 @@ lemma U_81_4 : have hlg : Real.log (10932628365517 / 625000000000000 : ℝ) ≤ (-(8091999804594550308781 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (10932628365517 / 625000000000000 : ℝ) = (10932628365517 / 9765625000000 : ℝ) / 2 ^ 6 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10932628365517 / 9765625000000 : ℚ)) - (U := (225766359005449691219 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (10932628365517 / 9765625000000 : ℝ) ≤ - (225766359005449691219 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57388977050147 / 5000000000000000 : ℝ)) (q := - (10932628365517 / 625000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10932628365517 / 625000000000000 : ℚ)) + (r' := (10932628365517 / 9765625000000 : ℚ)) + (U := (-(8091999804594550308781 / 2000000000000000000000 : ℚ))) + (U' := (225766359005449691219 / 2000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (71843627457 / 1600000000000 : ℚ)) + (s := (57388977050147 / 5000000000000000 : ℚ)) + (q := (10932628365517 / 625000000000000 : ℚ)) + (U := (-(8091999804594550308781 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_81_5 : Uω (aρ 5) (bρ 5) (71843627457 / 1600000000000 : ℝ) ≤ @@ -1443,25 +1364,21 @@ lemma U_82_1 : have hlg : Real.log (3102795865275137 / 80000000000000000 : ℝ) ≤ (-(32497230363190579783231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3102795865275137 / 80000000000000000 : ℝ) = - (3102795865275137 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3102795865275137 / 2500000000000000 : ℚ)) - (U := (2160128651809420216769 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3102795865275137 / 2500000000000000 : ℝ) ≤ - (2160128651809420216769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (387432651654253 / 10000000000000000 : ℝ)) (q := - (3102795865275137 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3102795865275137 / 80000000000000000 : ℚ)) + (r' := (3102795865275137 / 2500000000000000 : ℚ)) + (U := (-(32497230363190579783231 / 10000000000000000000000 : ℚ))) + (U' := (2160128651809420216769 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2897686609597 / 64000000000000 : ℚ)) + (s := (387432651654253 / 10000000000000000 : ℚ)) + (q := (3102795865275137 / 80000000000000000 : ℚ)) + (U := (-(32497230363190579783231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_82_2 : Uω (aρ 2) (bρ 2) (2897686609597 / 64000000000000 : ℝ) ≤ @@ -1469,25 +1386,21 @@ lemma U_82_2 : have hlg : Real.log (578500836206773 / 16000000000000000 : ℝ) ≤ (-(6639808015630789086519 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (578500836206773 / 16000000000000000 : ℝ) = - (578500836206773 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (578500836206773 / 500000000000000 : ℚ)) - (U := (291663787369210913481 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (578500836206773 / 500000000000000 : ℝ) ≤ - (291663787369210913481 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (71725748620787 / 2000000000000000 : ℝ)) (q := - (578500836206773 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (578500836206773 / 16000000000000000 : ℚ)) + (r' := (578500836206773 / 500000000000000 : ℚ)) + (U := (-(6639808015630789086519 / 2000000000000000000000 : ℚ))) + (U' := (291663787369210913481 / 2000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2897686609597 / 64000000000000 : ℚ)) + (s := (71725748620787 / 2000000000000000 : ℚ)) + (q := (578500836206773 / 16000000000000000 : ℚ)) + (U := (-(6639808015630789086519 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_82_3 : Uω (aρ 3) (bρ 3) (2897686609597 / 64000000000000 : ℝ) ≤ @@ -1495,25 +1408,21 @@ lemma U_82_3 : have hlg : Real.log (2439776680760601 / 80000000000000000 : ℝ) ≤ (-(87253003056903595321 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (2439776680760601 / 80000000000000000 : ℝ) = - (2439776680760601 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2439776680760601 / 1250000000000000 : ℚ)) - (U := (16719073988096404679 / 25000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2439776680760601 / 1250000000000000 : ℝ) ≤ - (16719073988096404679 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292842974385619 / 10000000000000000 : ℝ)) (q := - (2439776680760601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2439776680760601 / 80000000000000000 : ℚ)) + (r' := (2439776680760601 / 1250000000000000 : ℚ)) + (U := (-(87253003056903595321 / 25000000000000000000 : ℚ))) + (U' := (16719073988096404679 / 25000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2897686609597 / 64000000000000 : ℚ)) + (s := (292842974385619 / 10000000000000000 : ℚ)) + (q := (2439776680760601 / 80000000000000000 : ℚ)) + (U := (-(87253003056903595321 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_82_4 : Uω (aρ 4) (bρ 4) (2897686609597 / 64000000000000 : ℝ) ≤ @@ -1521,25 +1430,21 @@ lemma U_82_4 : have hlg : Real.log (1444254397221741 / 80000000000000000 : ℝ) ≤ (-(20072167163996576495227 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1444254397221741 / 80000000000000000 : ℝ) = - (1444254397221741 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1444254397221741 / 1250000000000000 : ℚ)) - (U := (722248245003423504773 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1444254397221741 / 1250000000000000 : ℝ) ≤ - (722248245003423504773 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7641036535369 / 625000000000000 : ℝ)) (q := - (1444254397221741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1444254397221741 / 80000000000000000 : ℚ)) + (r' := (1444254397221741 / 1250000000000000 : ℚ)) + (U := (-(20072167163996576495227 / 5000000000000000000000 : ℚ))) + (U' := (722248245003423504773 / 5000000000000000000000 : ℚ)) + 6 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2897686609597 / 64000000000000 : ℚ)) + (s := (7641036535369 / 625000000000000 : ℚ)) + (q := (1444254397221741 / 80000000000000000 : ℚ)) + (U := (-(20072167163996576495227 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_82_5 : Uω (aρ 5) (bρ 5) (2897686609597 / 64000000000000 : ℝ) ≤ @@ -1691,25 +1596,21 @@ lemma U_83_1 : have hlg : Real.log (1566377321980367 / 40000000000000000 : ℝ) ≤ (-(8100284844802228771499 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1566377321980367 / 40000000000000000 : ℝ) = - (1566377321980367 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1566377321980367 / 1250000000000000 : ℚ)) - (U := (564054908947771228501 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1566377321980367 / 1250000000000000 : ℝ) ≤ - (564054908947771228501 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (391181485182371 / 10000000000000000 : ℝ)) (q := - (1566377321980367 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1566377321980367 / 40000000000000000 : ℚ)) + (r' := (1566377321980367 / 1250000000000000 : ℚ)) + (U := (-(8100284844802228771499 / 2500000000000000000000 : ℚ))) + (U' := (564054908947771228501 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1460814060457 / 32000000000000 : ℚ)) + (s := (391181485182371 / 10000000000000000 : ℚ)) + (q := (1566377321980367 / 40000000000000000 : ℚ)) + (U := (-(8100284844802228771499 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_83_2 : Uω (aρ 2) (bρ 2) (1460814060457 / 32000000000000 : ℝ) ≤ @@ -1717,25 +1618,21 @@ lemma U_83_2 : have hlg : Real.log (1461336691110951 / 40000000000000000 : ℝ) ≤ (-(4136909867612453369687 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1461336691110951 / 40000000000000000 : ℝ) = - (1461336691110951 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1461336691110951 / 1250000000000000 : ℚ)) - (U := (195260009262546630313 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1461336691110951 / 1250000000000000 : ℝ) ≤ - (195260009262546630313 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (362430182257663 / 10000000000000000 : ℝ)) (q := - (1461336691110951 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1461336691110951 / 40000000000000000 : ℚ)) + (r' := (1461336691110951 / 1250000000000000 : ℚ)) + (U := (-(4136909867612453369687 / 1250000000000000000000 : ℚ))) + (U' := (195260009262546630313 / 1250000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1460814060457 / 32000000000000 : ℚ)) + (s := (362430182257663 / 10000000000000000 : ℚ)) + (q := (1461336691110951 / 40000000000000000 : ℚ)) + (U := (-(4136909867612453369687 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_83_3 : Uω (aρ 3) (bρ 3) (1460814060457 / 32000000000000 : ℝ) ≤ @@ -1743,25 +1640,21 @@ lemma U_83_3 : have hlg : Real.log (1235463415565381 / 40000000000000000 : ℝ) ≤ (-(34774333175818615317637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1235463415565381 / 40000000000000000 : ℝ) = - (1235463415565381 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1235463415565381 / 625000000000000 : ℚ)) - (U := (6814497642181384682363 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1235463415565381 / 625000000000000 : ℝ) ≤ - (6814497642181384682363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (148444825417439 / 5000000000000000 : ℝ)) (q := - (1235463415565381 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1235463415565381 / 40000000000000000 : ℚ)) + (r' := (1235463415565381 / 625000000000000 : ℚ)) + (U := (-(34774333175818615317637 / 10000000000000000000000 : ℚ))) + (U' := (6814497642181384682363 / 10000000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1460814060457 / 32000000000000 : ℚ)) + (s := (148444825417439 / 5000000000000000 : ℚ)) + (q := (1235463415565381 / 40000000000000000 : ℚ)) + (U := (-(34774333175818615317637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_83_4 : Uω (aρ 4) (bρ 4) (1460814060457 / 32000000000000 : ℝ) ≤ @@ -1769,25 +1662,21 @@ lemma U_83_4 : have hlg : Real.log (743918890423493 / 40000000000000000 : ℝ) ≤ (-(19923513604471120193173 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (743918890423493 / 40000000000000000 : ℝ) = - (743918890423493 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (743918890423493 / 625000000000000 : ℚ)) - (U := (870901804528879806827 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (743918890423493 / 625000000000000 : ℝ) ≤ - (870901804528879806827 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (64705784664467 / 5000000000000000 : ℝ)) (q := - (743918890423493 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (743918890423493 / 40000000000000000 : ℚ)) + (r' := (743918890423493 / 625000000000000 : ℚ)) + (U := (-(19923513604471120193173 / 5000000000000000000000 : ℚ))) + (U' := (870901804528879806827 / 5000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1460814060457 / 32000000000000 : ℚ)) + (s := (64705784664467 / 5000000000000000 : ℚ)) + (q := (743918890423493 / 40000000000000000 : ℚ)) + (U := (-(19923513604471120193173 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_83_5 : Uω (aρ 5) (bρ 5) (1460814060457 / 32000000000000 : ℝ) ≤ @@ -1939,25 +1828,21 @@ lemma U_84_1 : have hlg : Real.log (3162712817873931 / 80000000000000000 : ℝ) ≤ (-(16152982436976417664993 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3162712817873931 / 80000000000000000 : ℝ) = - (3162712817873931 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3162712817873931 / 2500000000000000 : ℚ)) - (U := (1175697070523582335007 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3162712817873931 / 2500000000000000 : ℝ) ≤ - (1175697070523582335007 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (394930167517389 / 10000000000000000 : ℝ)) (q := - (3162712817873931 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3162712817873931 / 80000000000000000 : ℚ)) + (r' := (3162712817873931 / 2500000000000000 : ℚ)) + (U := (-(16152982436976417664993 / 5000000000000000000000 : ℚ))) + (U' := (1175697070523582335007 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2945569632231 / 64000000000000 : ℚ)) + (s := (394930167517389 / 10000000000000000 : ℚ)) + (q := (3162712817873931 / 80000000000000000 : ℚ)) + (U := (-(16152982436976417664993 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_84_2 : Uω (aρ 2) (bρ 2) (2945569632231 / 64000000000000 : ℝ) ≤ @@ -1965,25 +1850,21 @@ lemma U_84_2 : have hlg : Real.log (2952837593143699 / 80000000000000000 : ℝ) ≤ (-(16496300146835009040687 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2952837593143699 / 80000000000000000 : ℝ) = - (2952837593143699 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2952837593143699 / 2500000000000000 : ℚ)) - (U := (832379360664990959313 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2952837593143699 / 2500000000000000 : ℝ) ≤ - (832379360664990959313 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (366230373844831 / 10000000000000000 : ℝ)) (q := - (2952837593143699 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2952837593143699 / 80000000000000000 : ℚ)) + (r' := (2952837593143699 / 2500000000000000 : ℚ)) + (U := (-(16496300146835009040687 / 5000000000000000000000 : ℚ))) + (U' := (832379360664990959313 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2945569632231 / 64000000000000 : ℚ)) + (s := (366230373844831 / 10000000000000000 : ℚ)) + (q := (2952837593143699 / 80000000000000000 : ℚ)) + (U := (-(16496300146835009040687 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_84_3 : Uω (aρ 3) (bρ 3) (2945569632231 / 64000000000000 : ℝ) ≤ @@ -1991,25 +1872,21 @@ lemma U_84_3 : have hlg : Real.log (2502045325907491 / 80000000000000000 : ℝ) ≤ (-(34649181056232259045777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2502045325907491 / 80000000000000000 : ℝ) = - (2502045325907491 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2502045325907491 / 2500000000000000 : ℚ)) - (U := (8177958767740954223 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (2502045325907491 / 2500000000000000 : ℝ) ≤ - (8177958767740954223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (300928413385779 / 10000000000000000 : ℝ)) (q := - (2502045325907491 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2502045325907491 / 80000000000000000 : ℚ)) + (r' := (2502045325907491 / 2500000000000000 : ℚ)) + (U := (-(34649181056232259045777 / 10000000000000000000000 : ℚ))) + (U' := (8177958767740954223 / 10000000000000000000000 : ℚ)) + 5 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2945569632231 / 64000000000000 : ℚ)) + (s := (300928413385779 / 10000000000000000 : ℚ)) + (q := (2502045325907491 / 80000000000000000 : ℚ)) + (U := (-(34649181056232259045777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_84_4 : Uω (aρ 4) (bρ 4) (2945569632231 / 64000000000000 : ℝ) ≤ @@ -2017,25 +1894,21 @@ lemma U_84_4 : have hlg : Real.log (1530330503929419 / 80000000000000000 : ℝ) ≤ (-(494567863174717687381 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1530330503929419 / 80000000000000000 : ℝ) = - (1530330503929419 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1530330503929419 / 1250000000000000 : ℚ)) - (U := (25292522050282312619 / 125000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1530330503929419 / 1250000000000000 : ℝ) ≤ - (25292522050282312619 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (136293888956261 / 10000000000000000 : ℝ)) (q := - (1530330503929419 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1530330503929419 / 80000000000000000 : ℚ)) + (r' := (1530330503929419 / 1250000000000000 : ℚ)) + (U := (-(494567863174717687381 / 125000000000000000000 : ℚ))) + (U' := (25292522050282312619 / 125000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2945569632231 / 64000000000000 : ℚ)) + (s := (136293888956261 / 10000000000000000 : ℚ)) + (q := (1530330503929419 / 80000000000000000 : ℚ)) + (U := (-(494567863174717687381 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_84_5 : Uω (aρ 5) (bρ 5) (2945569632231 / 64000000000000 : ℝ) ≤ @@ -2186,24 +2059,21 @@ lemma U_85_1 : have hlg : Real.log (39908380050929 / 1000000000000000 : ℝ) ≤ (-(16105844747499819637607 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (39908380050929 / 1000000000000000 : ℝ) = (39908380050929 / 31250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39908380050929 / 31250000000000 : ℚ)) - (U := (1222834760000180362393 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (39908380050929 / 31250000000000 : ℝ) ≤ - (1222834760000180362393 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79735740584841 / 2000000000000000 : ℝ)) (q := - (39908380050929 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39908380050929 / 1000000000000000 : ℚ)) + (r' := (39908380050929 / 31250000000000 : ℚ)) + (U := (-(16105844747499819637607 / 5000000000000000000000 : ℚ))) + (U' := (1222834760000180362393 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (742377785887 / 16000000000000 : ℚ)) + (s := (79735740584841 / 2000000000000000 : ℚ)) + (q := (39908380050929 / 1000000000000000 : ℚ)) + (U := (-(16105844747499819637607 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_85_2 : Uω (aρ 2) (bρ 2) (742377785887 / 16000000000000 : ℝ) ≤ @@ -2211,24 +2081,21 @@ lemma U_85_2 : have hlg : Real.log (18643731047181 / 500000000000000 : ℝ) ≤ (-(8222745361049200402393 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (18643731047181 / 500000000000000 : ℝ) = (18643731047181 / 15625000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18643731047181 / 15625000000000 : ℚ)) - (U := (441594392700799597607 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (18643731047181 / 15625000000000 : ℝ) ≤ - (441594392700799597607 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (74005871260573 / 2000000000000000 : ℝ)) (q := - (18643731047181 / 500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18643731047181 / 500000000000000 : ℚ)) + (r' := (18643731047181 / 15625000000000 : ℚ)) + (U := (-(8222745361049200402393 / 2500000000000000000000 : ℚ))) + (U' := (441594392700799597607 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (742377785887 / 16000000000000 : ℚ)) + (s := (74005871260573 / 2000000000000000 : ℚ)) + (q := (18643731047181 / 500000000000000 : ℚ)) + (U := (-(8222745361049200402393 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_85_3 : Uω (aρ 3) (bρ 3) (742377785887 / 16000000000000 : ℝ) ≤ @@ -2236,25 +2103,21 @@ lemma U_85_3 : have hlg : Real.log (158320838924591 / 5000000000000000 : ℝ) ≤ (-(17262847949594570677381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (158320838924591 / 5000000000000000 : ℝ) = - (158320838924591 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (158320838924591 / 156250000000000 : ℚ)) - (U := (65831557905429322619 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (158320838924591 / 156250000000000 : ℝ) ≤ - (65831557905429322619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (304959576463989 / 10000000000000000 : ℝ)) (q := - (158320838924591 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (158320838924591 / 5000000000000000 : ℚ)) + (r' := (158320838924591 / 156250000000000 : ℚ)) + (U := (-(17262847949594570677381 / 5000000000000000000000 : ℚ))) + (U' := (65831557905429322619 / 5000000000000000000000 : ℚ)) + 5 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (742377785887 / 16000000000000 : ℚ)) + (s := (304959576463989 / 10000000000000000 : ℚ)) + (q := (158320838924591 / 5000000000000000 : ℚ)) + (U := (-(17262847949594570677381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_85_4 : Uω (aρ 4) (bρ 4) (742377785887 / 16000000000000 : ℝ) ≤ @@ -2262,25 +2125,21 @@ lemma U_85_4 : have hlg : Real.log (392972531333811 / 20000000000000000 : ℝ) ≤ (-(7859495672749720896173 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (392972531333811 / 20000000000000000 : ℝ) = - (392972531333811 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (392972531333811 / 312500000000000 : ℚ)) - (U := (458270490850279103827 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (392972531333811 / 312500000000000 : ℝ) ≤ - (458270490850279103827 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35735733291109 / 2500000000000000 : ℝ)) (q := - (392972531333811 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (392972531333811 / 20000000000000000 : ℚ)) + (r' := (392972531333811 / 312500000000000 : ℚ)) + (U := (-(7859495672749720896173 / 2000000000000000000000 : ℚ))) + (U' := (458270490850279103827 / 2000000000000000000000 : ℚ)) + 6 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (742377785887 / 16000000000000 : ℚ)) + (s := (35735733291109 / 2500000000000000 : ℚ)) + (q := (392972531333811 / 20000000000000000 : ℚ)) + (U := (-(7859495672749720896173 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_85_5 : Uω (aρ 5) (bρ 5) (742377785887 / 16000000000000 : ℝ) ≤ @@ -2432,25 +2291,21 @@ lemma U_86_1 : have hlg : Real.log (3222627418985217 / 80000000000000000 : ℝ) ≤ (-(16059148189551546355899 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3222627418985217 / 80000000000000000 : ℝ) = - (3222627418985217 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3222627418985217 / 2500000000000000 : ℚ)) - (U := (1269531317948453644101 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3222627418985217 / 2500000000000000 : ℝ) ≤ - (1269531317948453644101 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (50303386938581 / 1250000000000000 : ℝ)) (q := - (3222627418985217 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3222627418985217 / 80000000000000000 : ℚ)) + (r' := (3222627418985217 / 2500000000000000 : ℚ)) + (U := (-(16059148189551546355899 / 5000000000000000000000 : ℚ))) + (U' := (1269531317948453644101 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (598690530973 / 12800000000000 : ℚ)) + (s := (50303386938581 / 1250000000000000 : ℚ)) + (q := (3222627418985217 / 80000000000000000 : ℚ)) + (U := (-(16059148189551546355899 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_86_2 : Uω (aρ 2) (bρ 2) (598690530973 / 12800000000000 : ℝ) ≤ @@ -2458,25 +2313,21 @@ lemma U_86_2 : have hlg : Real.log (3013151652889589 / 80000000000000000 : ℝ) ≤ (-(1024700013012026515809 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3013151652889589 / 80000000000000000 : ℝ) = - (3013151652889589 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3013151652889589 / 2500000000000000 : ℚ)) - (U := (58342456206723484191 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3013151652889589 / 2500000000000000 : ℝ) ≤ - (58342456206723484191 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (373827166494741 / 10000000000000000 : ℝ)) (q := - (3013151652889589 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3013151652889589 / 80000000000000000 : ℚ)) + (r' := (3013151652889589 / 2500000000000000 : ℚ)) + (U := (-(1024700013012026515809 / 312500000000000000000 : ℚ))) + (U' := (58342456206723484191 / 312500000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (598690530973 / 12800000000000 : ℚ)) + (s := (373827166494741 / 10000000000000000 : ℚ)) + (q := (3013151652889589 / 80000000000000000 : ℚ)) + (U := (-(1024700013012026515809 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_86_3 : Uω (aρ 3) (bρ 3) (598690530973 / 12800000000000 : ℝ) ≤ @@ -2484,25 +2335,21 @@ lemma U_86_3 : have hlg : Real.log (2564192311550617 / 80000000000000000 : ℝ) ≤ (-(6880766185247015737031 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2564192311550617 / 80000000000000000 : ℝ) = - (2564192311550617 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2564192311550617 / 2500000000000000 : ℚ)) - (U := (50705617752984262969 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2564192311550617 / 2500000000000000 : ℝ) ≤ - (50705617752984262969 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154491718754999 / 5000000000000000 : ℝ)) (q := - (2564192311550617 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2564192311550617 / 80000000000000000 : ℚ)) + (r' := (2564192311550617 / 2500000000000000 : ℚ)) + (U := (-(6880766185247015737031 / 2000000000000000000000 : ℚ))) + (U' := (50705617752984262969 / 2000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (598690530973 / 12800000000000 : ℚ)) + (s := (154491718754999 / 5000000000000000 : ℚ)) + (q := (2564192311550617 / 80000000000000000 : ℚ)) + (U := (-(6880766185247015737031 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_86_4 : Uω (aρ 4) (bρ 4) (598690530973 / 12800000000000 : ℝ) ≤ @@ -2510,25 +2357,21 @@ lemma U_86_4 : have hlg : Real.log (1612641249535897 / 80000000000000000 : ℝ) ≤ (-(39041532706513693929033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1612641249535897 / 80000000000000000 : ℝ) = - (1612641249535897 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1612641249535897 / 1250000000000000 : ℚ)) - (U := (2547298111486306070967 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1612641249535897 / 1250000000000000 : ℝ) ≤ - (2547298111486306070967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (74694926535659 / 5000000000000000 : ℝ)) (q := - (1612641249535897 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1612641249535897 / 80000000000000000 : ℚ)) + (r' := (1612641249535897 / 1250000000000000 : ℚ)) + (U := (-(39041532706513693929033 / 10000000000000000000000 : ℚ))) + (U' := (2547298111486306070967 / 10000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (598690530973 / 12800000000000 : ℚ)) + (s := (74694926535659 / 5000000000000000 : ℚ)) + (q := (1612641249535897 / 80000000000000000 : ℚ)) + (U := (-(39041532706513693929033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_86_5 : Uω (aρ 5) (bρ 5) (598690530973 / 12800000000000 : ℝ) ≤ @@ -2680,25 +2523,21 @@ lemma U_87_1 : have hlg : Real.log (1626291939211537 / 40000000000000000 : ℝ) ≤ (-(6405153826788440415589 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1626291939211537 / 40000000000000000 : ℝ) = - (1626291939211537 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1626291939211537 / 1250000000000000 : ℚ)) - (U := (526317976211559584411 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1626291939211537 / 1250000000000000 : ℝ) ≤ - (526317976211559584411 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (406175349224831 / 10000000000000000 : ℝ)) (q := - (1626291939211537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1626291939211537 / 40000000000000000 : ℚ)) + (r' := (1626291939211537 / 1250000000000000 : ℚ)) + (U := (-(6405153826788440415589 / 2000000000000000000000 : ℚ))) + (U' := (526317976211559584411 / 2000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1508697083091 / 32000000000000 : ℚ)) + (s := (406175349224831 / 10000000000000000 : ℚ)) + (q := (1626291939211537 / 40000000000000000 : ℚ)) + (U := (-(6405153826788440415589 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_87_2 : Uω (aρ 2) (bρ 2) (1508697083091 / 32000000000000 : ℝ) ≤ @@ -2706,25 +2545,21 @@ lemma U_87_2 : have hlg : Real.log (1521650895320563 / 40000000000000000 : ℝ) ≤ (-(6538167184020175693239 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1521650895320563 / 40000000000000000 : ℝ) = - (1521650895320563 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1521650895320563 / 1250000000000000 : ℚ)) - (U := (393304618979824306761 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1521650895320563 / 1250000000000000 : ℝ) ≤ - (393304618979824306761 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11800744993417 / 312500000000000 : ℝ)) (q := - (1521650895320563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1521650895320563 / 40000000000000000 : ℚ)) + (r' := (1521650895320563 / 1250000000000000 : ℚ)) + (U := (-(6538167184020175693239 / 2000000000000000000000 : ℚ))) + (U' := (393304618979824306761 / 2000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1508697083091 / 32000000000000 : ℚ)) + (s := (11800744993417 / 312500000000000 : ℚ)) + (q := (1521650895320563 / 40000000000000000 : ℚ)) + (U := (-(6538167184020175693239 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_87_3 : Uω (aρ 3) (bρ 3) (1508697083091 / 32000000000000 : ℝ) ≤ @@ -2732,25 +2567,21 @@ lemma U_87_3 : have hlg : Real.log (1297611559329427 / 40000000000000000 : ℝ) ≤ (-(34283541402370319659499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1297611559329427 / 40000000000000000 : ℝ) = - (1297611559329427 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1297611559329427 / 1250000000000000 : ℚ)) - (U := (373817612629680340501 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1297611559329427 / 1250000000000000 : ℝ) ≤ - (373817612629680340501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9781258691993 / 312500000000000 : ℝ)) (q := - (1297611559329427 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1297611559329427 / 40000000000000000 : ℚ)) + (r' := (1297611559329427 / 1250000000000000 : ℚ)) + (U := (-(34283541402370319659499 / 10000000000000000000000 : ℚ))) + (U' := (373817612629680340501 / 10000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1508697083091 / 32000000000000 : ℚ)) + (s := (9781258691993 / 312500000000000 : ℚ)) + (q := (1297611559329427 / 40000000000000000 : ℚ)) + (U := (-(34283541402370319659499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_87_4 : Uω (aρ 4) (bρ 4) (1508697083091 / 32000000000000 : ℝ) ≤ @@ -2758,25 +2589,21 @@ lemma U_87_4 : have hlg : Real.log (165268434059053 / 8000000000000000 : ℝ) ≤ (-(1551850317616410832219 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (165268434059053 / 8000000000000000 : ℝ) = - (165268434059053 / 125000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (165268434059053 / 125000000000000 : ℚ)) - (U := (111702915103589167781 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (165268434059053 / 125000000000000 : ℝ) ≤ - (111702915103589167781 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (31131952938339 / 2000000000000000 : ℝ)) (q := - (165268434059053 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (165268434059053 / 8000000000000000 : ℚ)) + (r' := (165268434059053 / 125000000000000 : ℚ)) + (U := (-(1551850317616410832219 / 400000000000000000000 : ℚ))) + (U' := (111702915103589167781 / 400000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1508697083091 / 32000000000000 : ℚ)) + (s := (31131952938339 / 2000000000000000 : ℚ)) + (q := (165268434059053 / 8000000000000000 : ℚ)) + (U := (-(1551850317616410832219 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_87_5 : Uω (aρ 5) (bρ 5) (1508697083091 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U07.lean b/LeanPool/Zeta5Irrational/Table/U07.lean index 6a8edfdb9f..a810cd99f1 100644 --- a/LeanPool/Zeta5Irrational/Table/U07.lean +++ b/LeanPool/Zeta5Irrational/Table/U07.lean @@ -24,25 +24,21 @@ lemma U_88_1 : have hlg : Real.log (131301591905011 / 3200000000000000 : ℝ) ≤ (-(31934091820714900994499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (131301591905011 / 3200000000000000 : ℝ) = - (131301591905011 / 100000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (131301591905011 / 100000000000000 : ℚ)) - (U := (2723267194285099005501 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (131301591905011 / 100000000000000 : ℝ) ≤ - (2723267194285099005501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4099234678821 / 100000000000000 : ℝ)) (q := - (131301591905011 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (131301591905011 / 3200000000000000 : ℚ)) + (r' := (131301591905011 / 100000000000000 : ℚ)) + (U := (-(31934091820714900994499 / 10000000000000000000000 : ℚ))) + (U' := (2723267194285099005501 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3041335677499 / 64000000000000 : ℚ)) + (s := (4099234678821 / 100000000000000 : ℚ)) + (q := (131301591905011 / 3200000000000000 : ℚ)) + (U := (-(31934091820714900994499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_88_2 : Uω (aρ 2) (bρ 2) (3041335677499 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_88_2 : have hlg : Real.log (614689503320911 / 16000000000000000 : ℝ) ≤ (-(254627088457477178169 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (614689503320911 / 16000000000000000 : ℝ) = - (614689503320911 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (614689503320911 / 500000000000000 : ℚ)) - (U := (16133528847210321831 / 78125000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (614689503320911 / 500000000000000 : ℝ) ≤ - (16133528847210321831 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9535485253423 / 250000000000000 : ℝ)) (q := - (614689503320911 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (614689503320911 / 16000000000000000 : ℚ)) + (r' := (614689503320911 / 500000000000000 : ℚ)) + (U := (-(254627088457477178169 / 78125000000000000000 : ℚ))) + (U' := (16133528847210321831 / 78125000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3041335677499 / 64000000000000 : ℚ)) + (s := (9535485253423 / 250000000000000 : ℚ)) + (q := (614689503320911 / 16000000000000000 : ℚ)) + (U := (-(254627088457477178169 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_88_3 : Uω (aρ 3) (bρ 3) (3041335677499 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_88_3 : have hlg : Real.log (2626226911586943 / 80000000000000000 : ℝ) ≤ (-(34164784516352722640813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2626226911586943 / 80000000000000000 : ℝ) = - (2626226911586943 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2626226911586943 / 2500000000000000 : ℚ)) - (U := (492574498647277359187 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2626226911586943 / 2500000000000000 : ℝ) ≤ - (492574498647277359187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (317010365232517 / 10000000000000000 : ℝ)) (q := - (2626226911586943 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2626226911586943 / 80000000000000000 : ℚ)) + (r' := (2626226911586943 / 2500000000000000 : ℚ)) + (U := (-(34164784516352722640813 / 10000000000000000000000 : ℚ))) + (U' := (492574498647277359187 / 10000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3041335677499 / 64000000000000 : ℚ)) + (s := (317010365232517 / 10000000000000000 : ℚ)) + (q := (2626226911586943 / 80000000000000000 : ℚ)) + (U := (-(34164784516352722640813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_88_4 : Uω (aρ 4) (bρ 4) (3041335677499 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_88_4 : have hlg : Real.log (1692101728321819 / 80000000000000000 : ℝ) ≤ (-(1928027625307929110733 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1692101728321819 / 80000000000000000 : ℝ) = - (1692101728321819 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1692101728321819 / 1250000000000000 : ℚ)) - (U := (151413915592070889267 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1692101728321819 / 1250000000000000 : ℝ) ≤ - (151413915592070889267 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40443312620309 / 2500000000000000 : ℝ)) (q := - (1692101728321819 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1692101728321819 / 80000000000000000 : ℚ)) + (r' := (1692101728321819 / 1250000000000000 : ℚ)) + (U := (-(1928027625307929110733 / 500000000000000000000 : ℚ))) + (U' := (151413915592070889267 / 500000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3041335677499 / 64000000000000 : ℚ)) + (s := (40443312620309 / 2500000000000000 : ℚ)) + (q := (1692101728321819 / 80000000000000000 : ℚ)) + (U := (-(1928027625307929110733 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_88_5 : Uω (aρ 5) (bρ 5) (3041335677499 / 64000000000000 : ℝ) ≤ @@ -272,25 +256,21 @@ lemma U_89_1 : have hlg : Real.log (414061898909553 / 10000000000000000 : ℝ) ≤ (-(796081223438251080513 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (414061898909553 / 10000000000000000 : ℝ) = - (414061898909553 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (414061898909553 / 312500000000000 : ℚ)) - (U := (70352751936748919487 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (414061898909553 / 312500000000000 : ℝ) ≤ - (70352751936748919487 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (206835727575803 / 5000000000000000 : ℝ)) (q := - (414061898909553 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (414061898909553 / 10000000000000000 : ℚ)) + (r' := (414061898909553 / 312500000000000 : ℚ)) + (U := (-(796081223438251080513 / 250000000000000000000 : ℚ))) + (U' := (70352751936748919487 / 250000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (191579824301 / 4000000000000 : ℚ)) + (s := (206835727575803 / 5000000000000000 : ℚ)) + (q := (414061898909553 / 10000000000000000 : ℚ)) + (U := (-(796081223438251080513 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_89_2 : Uω (aρ 2) (bρ 2) (191579824301 / 4000000000000 : ℝ) ≤ @@ -298,25 +278,21 @@ lemma U_89_2 : have hlg : Real.log (387948620148739 / 10000000000000000 : ℝ) ≤ (-(6498934924237707349841 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (387948620148739 / 10000000000000000 : ℝ) = - (387948620148739 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (387948620148739 / 312500000000000 : ℚ)) - (U := (432536878762292650159 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (387948620148739 / 312500000000000 : ℝ) ≤ - (432536878762292650159 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (192606955069989 / 5000000000000000 : ℝ)) (q := - (387948620148739 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (387948620148739 / 10000000000000000 : ℚ)) + (r' := (387948620148739 / 312500000000000 : ℚ)) + (U := (-(6498934924237707349841 / 2000000000000000000000 : ℚ))) + (U' := (432536878762292650159 / 2000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (191579824301 / 4000000000000 : ℚ)) + (s := (192606955069989 / 5000000000000000 : ℚ)) + (q := (387948620148739 / 10000000000000000 : ℚ)) + (U := (-(6498934924237707349841 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_89_3 : Uω (aρ 3) (bρ 3) (191579824301 / 4000000000000 : ℝ) ≤ @@ -324,23 +300,21 @@ lemma U_89_3 : have hlg : Real.log (1297463233747 / 39062500000000 : ℝ) ≤ (-(17023759633831421878791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show (1297463233747 / 39062500000000 : ℝ) = (1297463233747 / 1220703125000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1297463233747 / 1220703125000 : ℚ)) - (U := (304919873668578121209 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1297463233747 / 1220703125000 : ℝ) ≤ - (304919873668578121209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (80253487967741 / 2500000000000000 : ℝ)) (q := - (1297463233747 / 39062500000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1297463233747 / 39062500000000 : ℚ)) + (r' := (1297463233747 / 1220703125000 : ℚ)) + (U := (-(17023759633831421878791 / 5000000000000000000000 : ℚ))) + (U' := (304919873668578121209 / 5000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (191579824301 / 4000000000000 : ℚ)) + (s := (80253487967741 / 2500000000000000 : ℚ)) + (q := (1297463233747 / 39062500000000 : ℚ)) + (U := (-(17023759633831421878791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_89_4 : Uω (aρ 4) (bρ 4) (191579824301 / 4000000000000 : ℝ) ≤ @@ -348,25 +322,21 @@ lemma U_89_4 : have hlg : Real.log (216370228340183 / 10000000000000000 : ℝ) ≤ (-(19166747049474907076563 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (216370228340183 / 10000000000000000 : ℝ) = - (216370228340183 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (216370228340183 / 156250000000000 : ℚ)) - (U := (1627668359525092923437 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (216370228340183 / 156250000000000 : ℝ) ≤ - (1627668359525092923437 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83873706968933 / 5000000000000000 : ℝ)) (q := - (216370228340183 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (216370228340183 / 10000000000000000 : ℚ)) + (r' := (216370228340183 / 156250000000000 : ℚ)) + (U := (-(19166747049474907076563 / 5000000000000000000000 : ℚ))) + (U' := (1627668359525092923437 / 5000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (191579824301 / 4000000000000 : ℚ)) + (s := (83873706968933 / 5000000000000000 : ℚ)) + (q := (216370228340183 / 10000000000000000 : ℚ)) + (U := (-(19166747049474907076563 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_89_5 : Uω (aρ 5) (bρ 5) (191579824301 / 4000000000000 : ℝ) ≤ @@ -518,25 +488,21 @@ lemma U_90_1 : have hlg : Real.log (3342450073533213 / 80000000000000000 : ℝ) ≤ (-(31753225403554109637937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3342450073533213 / 80000000000000000 : ℝ) = - (3342450073533213 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3342450073533213 / 2500000000000000 : ℚ)) - (U := (2904133611445890362063 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3342450073533213 / 2500000000000000 : ℝ) ≤ - (2904133611445890362063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (208709657286261 / 5000000000000000 : ℝ)) (q := - (3342450073533213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3342450073533213 / 80000000000000000 : ℚ)) + (r' := (3342450073533213 / 2500000000000000 : ℚ)) + (U := (-(31753225403554109637937 / 10000000000000000000000 : ℚ))) + (U' := (2904133611445890362063 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3089218700133 / 64000000000000 : ℚ)) + (s := (208709657286261 / 5000000000000000 : ℚ)) + (q := (3342450073533213 / 80000000000000000 : ℚ)) + (U := (-(31753225403554109637937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_90_2 : Uω (aρ 2) (bρ 2) (3089218700133 / 64000000000000 : ℝ) ≤ @@ -544,25 +510,21 @@ lemma U_90_2 : have hlg : Real.log (3133726249682913 / 80000000000000000 : ℝ) ≤ (-(16199019208965554918851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3133726249682913 / 80000000000000000 : ℝ) = - (3133726249682913 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3133726249682913 / 2500000000000000 : ℚ)) - (U := (1129660298534445081149 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3133726249682913 / 2500000000000000 : ℝ) ≤ - (1129660298534445081149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (389007371119947 / 10000000000000000 : ℝ)) (q := - (3133726249682913 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3133726249682913 / 80000000000000000 : ℚ)) + (r' := (3133726249682913 / 2500000000000000 : ℚ)) + (U := (-(16199019208965554918851 / 5000000000000000000000 : ℚ))) + (U' := (1129660298534445081149 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3089218700133 / 64000000000000 : ℚ)) + (s := (389007371119947 / 10000000000000000 : ℚ)) + (q := (3133726249682913 / 80000000000000000 : ℚ)) + (U := (-(16199019208965554918851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_90_3 : Uω (aρ 3) (bρ 3) (3089218700133 / 64000000000000 : ℝ) ≤ @@ -570,25 +532,21 @@ lemma U_90_3 : have hlg : Real.log (2688157452933953 / 80000000000000000 : ℝ) ≤ (-(6786341272376926062427 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2688157452933953 / 80000000000000000 : ℝ) = - (2688157452933953 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2688157452933953 / 2500000000000000 : ℚ)) - (U := (145130530623073937573 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2688157452933953 / 2500000000000000 : ℝ) ≤ - (145130530623073937573 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325011278282707 / 10000000000000000 : ℝ)) (q := - (2688157452933953 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2688157452933953 / 80000000000000000 : ℚ)) + (r' := (2688157452933953 / 2500000000000000 : ℚ)) + (U := (-(6786341272376926062427 / 2000000000000000000000 : ℚ))) + (U' := (145130530623073937573 / 2000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3089218700133 / 64000000000000 : ℚ)) + (s := (325011278282707 / 10000000000000000 : ℚ)) + (q := (2688157452933953 / 80000000000000000 : ℚ)) + (U := (-(6786341272376926062427 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_90_4 : Uω (aρ 4) (bρ 4) (3089218700133 / 64000000000000 : ℝ) ≤ @@ -596,25 +554,21 @@ lemma U_90_4 : have hlg : Real.log (1769322173922313 / 80000000000000000 : ℝ) ≤ (-(9528575281149508014001 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1769322173922313 / 80000000000000000 : ℝ) = - (1769322173922313 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1769322173922313 / 1250000000000000 : ℚ)) - (U := (868632423350491985999 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1769322173922313 / 1250000000000000 : ℝ) ≤ - (868632423350491985999 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (173596639594797 / 10000000000000000 : ℝ)) (q := - (1769322173922313 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1769322173922313 / 80000000000000000 : ℚ)) + (r' := (1769322173922313 / 1250000000000000 : ℚ)) + (U := (-(9528575281149508014001 / 2500000000000000000000 : ℚ))) + (U' := (868632423350491985999 / 2500000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3089218700133 / 64000000000000 : ℚ)) + (s := (173596639594797 / 10000000000000000 : ℚ)) + (q := (1769322173922313 / 80000000000000000 : ℚ)) + (U := (-(9528575281149508014001 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_90_5 : Uω (aρ 5) (bρ 5) (3089218700133 / 64000000000000 : ℝ) ≤ @@ -767,24 +721,21 @@ lemma U_91_1 : have hlg : Real.log (67448089160959 / 1600000000000000 : ℝ) ≤ (-(1583200327193589922537 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (67448089160959 / 1600000000000000 : ℝ) = (67448089160959 / 50000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (67448089160959 / 50000000000000 : ℚ)) - (U := (149667623556410077463 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (67448089160959 / 50000000000000 : ℝ) ≤ - (149667623556410077463 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16846681982317 / 400000000000000 : ℝ)) (q := - (67448089160959 / 1600000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (67448089160959 / 1600000000000000 : ℚ)) + (r' := (67448089160959 / 50000000000000 : ℚ)) + (U := (-(1583200327193589922537 / 500000000000000000000 : ℚ))) + (U' := (149667623556410077463 / 500000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (62263204229 / 1280000000000 : ℚ)) + (s := (16846681982317 / 400000000000000 : ℚ)) + (q := (67448089160959 / 1600000000000000 : ℚ)) + (U := (-(1583200327193589922537 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_91_2 : Uω (aρ 2) (bρ 2) (62263204229 / 1280000000000 : ℝ) ≤ @@ -792,25 +743,21 @@ lemma U_91_2 : have hlg : Real.log (1581929751247923 / 40000000000000000 : ℝ) ≤ (-(16151169947406386751941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1581929751247923 / 40000000000000000 : ℝ) = - (1581929751247923 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1581929751247923 / 1250000000000000 : ℚ)) - (U := (1177509560093613248059 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1581929751247923 / 1250000000000000 : ℝ) ≤ - (1177509560093613248059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (392799823179899 / 10000000000000000 : ℝ)) (q := - (1581929751247923 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1581929751247923 / 40000000000000000 : ℚ)) + (r' := (1581929751247923 / 1250000000000000 : ℚ)) + (U := (-(16151169947406386751941 / 5000000000000000000000 : ℚ))) + (U' := (1177509560093613248059 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (62263204229 / 1280000000000 : ℚ)) + (s := (392799823179899 / 10000000000000000 : ℚ)) + (q := (1581929751247923 / 40000000000000000 : ℚ)) + (U := (-(16151169947406386751941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_91_3 : Uω (aρ 3) (bρ 3) (62263204229 / 1280000000000 : ℝ) ≤ @@ -818,25 +765,21 @@ lemma U_91_3 : have hlg : Real.log (271908607497609 / 8000000000000000 : ℝ) ≤ (-(1056790878554544750231 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (271908607497609 / 8000000000000000 : ℝ) = - (271908607497609 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (271908607497609 / 250000000000000 : ℚ)) - (U := (26251590664205249769 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (271908607497609 / 250000000000000 : ℝ) ≤ - (26251590664205249769 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8225064316249 / 250000000000000 : ℝ)) (q := - (271908607497609 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (271908607497609 / 8000000000000000 : ℚ)) + (r' := (271908607497609 / 250000000000000 : ℚ)) + (U := (-(1056790878554544750231 / 312500000000000000000 : ℚ))) + (U' := (26251590664205249769 / 312500000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (62263204229 / 1280000000000 : ℚ)) + (s := (8225064316249 / 250000000000000 : ℚ)) + (q := (271908607497609 / 8000000000000000 : ℚ)) + (U := (-(1056790878554544750231 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_91_4 : Uω (aρ 4) (bρ 4) (62263204229 / 1280000000000 : ℝ) ≤ @@ -844,25 +787,21 @@ lemma U_91_4 : have hlg : Real.log (903615836022631 / 40000000000000000 : ℝ) ≤ (-(37902304216173367332429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (903615836022631 / 40000000000000000 : ℝ) = - (903615836022631 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (903615836022631 / 625000000000000 : ℚ)) - (U := (3686526601826632667571 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (903615836022631 / 625000000000000 : ℝ) ≤ - (3686526601826632667571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (179333152982253 / 10000000000000000 : ℝ)) (q := - (903615836022631 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (903615836022631 / 40000000000000000 : ℚ)) + (r' := (903615836022631 / 625000000000000 : ℚ)) + (U := (-(37902304216173367332429 / 10000000000000000000000 : ℚ))) + (U' := (3686526601826632667571 / 10000000000000000000000 : ℚ)) + 6 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (62263204229 / 1280000000000 : ℚ)) + (s := (179333152982253 / 10000000000000000 : ℚ)) + (q := (903615836022631 / 40000000000000000 : ℚ)) + (U := (-(37902304216173367332429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_91_5 : Uω (aρ 5) (bρ 5) (62263204229 / 1280000000000 : ℝ) ≤ @@ -1014,25 +953,21 @@ lemma U_92_1 : have hlg : Real.log (3402358357990847 / 80000000000000000 : ℝ) ≤ (-(31575578075022150256599 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3402358357990847 / 80000000000000000 : ℝ) = - (3402358357990847 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3402358357990847 / 2500000000000000 : ℚ)) - (U := (3081780939977849743401 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3402358357990847 / 2500000000000000 : ℝ) ≤ - (3081780939977849743401 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26557166462523 / 625000000000000 : ℝ)) (q := - (3402358357990847 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3402358357990847 / 80000000000000000 : ℚ)) + (r' := (3402358357990847 / 2500000000000000 : ℚ)) + (U := (-(31575578075022150256599 / 10000000000000000000000 : ℚ))) + (U' := (3081780939977849743401 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3137101722767 / 64000000000000 : ℚ)) + (s := (26557166462523 / 625000000000000 : ℚ)) + (q := (3402358357990847 / 80000000000000000 : ℚ)) + (U := (-(31575578075022150256599 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_92_2 : Uω (aρ 2) (bρ 2) (3137101722767 / 64000000000000 : ℝ) ≤ @@ -1040,25 +975,21 @@ lemma U_92_2 : have hlg : Real.log (3193988835403747 / 80000000000000000 : ℝ) ≤ (-(16103780395389085637527 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3193988835403747 / 80000000000000000 : ℝ) = - (3193988835403747 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3193988835403747 / 2500000000000000 : ℚ)) - (U := (1224899112110914362473 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3193988835403747 / 2500000000000000 : ℝ) ≤ - (1224899112110914362473 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (396591295263593 / 10000000000000000 : ℝ)) (q := - (3193988835403747 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3193988835403747 / 80000000000000000 : ℚ)) + (r' := (3193988835403747 / 2500000000000000 : ℚ)) + (U := (-(16103780395389085637527 / 5000000000000000000000 : ℚ))) + (U' := (1224899112110914362473 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3137101722767 / 64000000000000 : ℚ)) + (s := (396591295263593 / 10000000000000000 : ℚ)) + (q := (3193988835403747 / 80000000000000000 : ℚ)) + (U := (-(16103780395389085637527 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_92_3 : Uω (aρ 3) (bρ 3) (3137101722767 / 64000000000000 : ℝ) ≤ @@ -1066,25 +997,21 @@ lemma U_92_3 : have hlg : Real.log (2749991436463211 / 80000000000000000 : ℝ) ≤ (-(33704288357139015076803 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2749991436463211 / 80000000000000000 : ℝ) = - (2749991436463211 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2749991436463211 / 2500000000000000 : ℚ)) - (U := (953070657860984923197 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2749991436463211 / 2500000000000000 : ℝ) ≤ - (953070657860984923197 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (332988051878459 / 10000000000000000 : ℝ)) (q := - (2749991436463211 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2749991436463211 / 80000000000000000 : ℚ)) + (r' := (2749991436463211 / 2500000000000000 : ℚ)) + (U := (-(33704288357139015076803 / 10000000000000000000000 : ℚ))) + (U' := (953070657860984923197 / 10000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3137101722767 / 64000000000000 : ℚ)) + (s := (332988051878459 / 10000000000000000 : ℚ)) + (q := (2749991436463211 / 80000000000000000 : ℚ)) + (U := (-(33704288357139015076803 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_92_4 : Uω (aρ 4) (bρ 4) (3137101722767 / 64000000000000 : ℝ) ≤ @@ -1092,25 +1019,21 @@ lemma U_92_4 : have hlg : Real.log (1844732269690687 / 80000000000000000 : ℝ) ≤ (-(18848462387150699761219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1844732269690687 / 80000000000000000 : ℝ) = - (1844732269690687 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1844732269690687 / 1250000000000000 : ℚ)) - (U := (1945953021849300238781 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1844732269690687 / 1250000000000000 : ℝ) ≤ - (1945953021849300238781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23120930156291 / 1250000000000000 : ℝ)) (q := - (1844732269690687 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1844732269690687 / 80000000000000000 : ℚ)) + (r' := (1844732269690687 / 1250000000000000 : ℚ)) + (U := (-(18848462387150699761219 / 5000000000000000000000 : ℚ))) + (U' := (1945953021849300238781 / 5000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3137101722767 / 64000000000000 : ℚ)) + (s := (23120930156291 / 1250000000000000 : ℚ)) + (q := (1844732269690687 / 80000000000000000 : ℚ)) + (U := (-(18848462387150699761219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_92_5 : Uω (aρ 5) (bρ 5) (3137101722767 / 64000000000000 : ℝ) ≤ @@ -1263,25 +1186,21 @@ lemma U_93_1 : have hlg : Real.log (429038973258891 / 10000000000000000 : ℝ) ≤ (-(31487926091174342905069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (429038973258891 / 10000000000000000 : ℝ) = - (429038973258891 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (429038973258891 / 312500000000000 : ℚ)) - (U := (3169432923825657094931 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (429038973258891 / 312500000000000 : ℝ) ≤ - (3169432923825657094931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (428662159277157 / 10000000000000000 : ℝ)) (q := - (429038973258891 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (429038973258891 / 10000000000000000 : ℚ)) + (r' := (429038973258891 / 312500000000000 : ℚ)) + (U := (-(31487926091174342905069 / 10000000000000000000000 : ℚ))) + (U' := (3169432923825657094931 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (790260808521 / 16000000000000 : ℚ)) + (s := (428662159277157 / 10000000000000000 : ℚ)) + (q := (429038973258891 / 10000000000000000 : ℚ)) + (U := (-(31487926091174342905069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_93_2 : Uω (aρ 2) (bρ 2) (790260808521 / 16000000000000 : ℝ) ≤ @@ -1289,24 +1208,21 @@ lemma U_93_2 : have hlg : Real.log (32241143597669 / 800000000000000 : ℝ) ≤ (-(32113683379671497832899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (32241143597669 / 800000000000000 : ℝ) = (32241143597669 / 25000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32241143597669 / 25000000000000 : ℚ)) - (U := (2543675635328502167101 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (32241143597669 / 25000000000000 : ℝ) ≤ - (2543675635328502167101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4003818152111 / 100000000000000 : ℝ)) (q := - (32241143597669 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32241143597669 / 800000000000000 : ℚ)) + (r' := (32241143597669 / 25000000000000 : ℚ)) + (U := (-(32113683379671497832899 / 10000000000000000000000 : ℚ))) + (U' := (2543675635328502167101 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (790260808521 / 16000000000000 : ℚ)) + (s := (4003818152111 / 100000000000000 : ℚ)) + (q := (32241143597669 / 800000000000000 : ℚ)) + (U := (-(32113683379671497832899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_93_3 : Uω (aρ 3) (bρ 3) (790260808521 / 16000000000000 : ℝ) ≤ @@ -1314,25 +1230,21 @@ lemma U_93_3 : have hlg : Real.log (139043718136819 / 4000000000000000 : ℝ) ≤ (-(1679630618076205600743 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (139043718136819 / 4000000000000000 : ℝ) = - (139043718136819 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (139043718136819 / 125000000000000 : ℚ)) - (U := (53237332673794399257 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (139043718136819 / 125000000000000 : ℝ) ≤ - (53237332673794399257 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33696792230347 / 1000000000000000 : ℝ)) (q := - (139043718136819 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (139043718136819 / 4000000000000000 : ℚ)) + (r' := (139043718136819 / 125000000000000 : ℚ)) + (U := (-(1679630618076205600743 / 500000000000000000000 : ℚ))) + (U' := (53237332673794399257 / 500000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (790260808521 / 16000000000000 : ℚ)) + (s := (33696792230347 / 1000000000000000 : ℚ)) + (q := (139043718136819 / 4000000000000000 : ℚ)) + (U := (-(1679630618076205600743 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_93_4 : Uω (aρ 4) (bρ 4) (790260808521 / 16000000000000 : ℝ) ≤ @@ -1340,25 +1252,21 @@ lemma U_93_4 : have hlg : Real.log (117616265462433 / 5000000000000000 : ℝ) ≤ (-(18748829261004226629189 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (117616265462433 / 5000000000000000 : ℝ) = - (117616265462433 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (117616265462433 / 78125000000000 : ℚ)) - (U := (2045586147995773370811 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (117616265462433 / 78125000000000 : ℝ) ≤ - (2045586147995773370811 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (190508574534107 / 10000000000000000 : ℝ)) (q := - (117616265462433 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (117616265462433 / 5000000000000000 : ℚ)) + (r' := (117616265462433 / 78125000000000 : ℚ)) + (U := (-(18748829261004226629189 / 5000000000000000000000 : ℚ))) + (U' := (2045586147995773370811 / 5000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (790260808521 / 16000000000000 : ℚ)) + (s := (190508574534107 / 10000000000000000 : ℚ)) + (q := (117616265462433 / 5000000000000000 : ℚ)) + (U := (-(18748829261004226629189 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_93_5 : Uω (aρ 5) (bρ 5) (790260808521 / 16000000000000 : ℝ) ≤ @@ -1511,25 +1419,21 @@ lemma U_94_1 : have hlg : Real.log (692452950911409 / 16000000000000000 : ℝ) ≤ (-(15700518525454701202457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (692452950911409 / 16000000000000000 : ℝ) = - (692452950911409 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (692452950911409 / 500000000000000 : ℚ)) - (U := (1628160982045298797543 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (692452950911409 / 500000000000000 : ℝ) ≤ - (1628160982045298797543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86481908051071 / 2000000000000000 : ℝ)) (q := - (692452950911409 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (692452950911409 / 16000000000000000 : ℚ)) + (r' := (692452950911409 / 500000000000000 : ℚ)) + (U := (-(15700518525454701202457 / 5000000000000000000000 : ℚ))) + (U' := (1628160982045298797543 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3184984745401 / 64000000000000 : ℚ)) + (s := (86481908051071 / 2000000000000000 : ℚ)) + (q := (692452950911409 / 16000000000000000 : ℚ)) + (U := (-(15700518525454701202457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_94_2 : Uω (aρ 2) (bρ 2) (3184984745401 / 64000000000000 : ℝ) ≤ @@ -1537,25 +1441,21 @@ lemma U_94_2 : have hlg : Real.log (3254236182740573 / 80000000000000000 : ℝ) ≤ (-(32020690449308287470393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3254236182740573 / 80000000000000000 : ℝ) = - (3254236182740573 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3254236182740573 / 2500000000000000 : ℚ)) - (U := (2636668565691712529607 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3254236182740573 / 2500000000000000 : ℝ) ≤ - (2636668565691712529607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404171409811237 / 10000000000000000 : ℝ)) (q := - (3254236182740573 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3254236182740573 / 80000000000000000 : ℚ)) + (r' := (3254236182740573 / 2500000000000000 : ℚ)) + (U := (-(32020690449308287470393 / 10000000000000000000000 : ℚ))) + (U' := (2636668565691712529607 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3184984745401 / 64000000000000 : ℚ)) + (s := (404171409811237 / 10000000000000000 : ℚ)) + (q := (3254236182740573 / 80000000000000000 : ℚ)) + (U := (-(32020690449308287470393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_94_3 : Uω (aρ 3) (bρ 3) (3184984745401 / 64000000000000 : ℝ) ≤ @@ -1563,25 +1463,21 @@ lemma U_94_3 : have hlg : Real.log (2811735639464453 / 80000000000000000 : ℝ) ≤ (-(6696449350830705340347 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2811735639464453 / 80000000000000000 : ℝ) = - (2811735639464453 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2811735639464453 / 2500000000000000 : ℚ)) - (U := (235022452169294659653 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2811735639464453 / 2500000000000000 : ℝ) ≤ - (235022452169294659653 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (340942380342207 / 10000000000000000 : ℝ)) (q := - (2811735639464453 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2811735639464453 / 80000000000000000 : ℚ)) + (r' := (2811735639464453 / 2500000000000000 : ℚ)) + (U := (-(6696449350830705340347 / 2000000000000000000000 : ℚ))) + (U' := (235022452169294659653 / 2000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3184984745401 / 64000000000000 : ℚ)) + (s := (340942380342207 / 10000000000000000 : ℚ)) + (q := (2811735639464453 / 80000000000000000 : ℚ)) + (U := (-(6696449350830705340347 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_94_4 : Uω (aρ 4) (bρ 4) (3184984745401 / 64000000000000 : ℝ) ≤ @@ -1589,25 +1485,21 @@ lemma U_94_4 : have hlg : Real.log (1918647214652921 / 80000000000000000 : ℝ) ≤ (-(37304062711062346239319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1918647214652921 / 80000000000000000 : ℝ) = - (1918647214652921 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1918647214652921 / 1250000000000000 : ℚ)) - (U := (4284768106937653760681 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1918647214652921 / 1250000000000000 : ℝ) ≤ - (4284768106937653760681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48991113801081 / 2500000000000000 : ℝ)) (q := - (1918647214652921 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1918647214652921 / 80000000000000000 : ℚ)) + (r' := (1918647214652921 / 1250000000000000 : ℚ)) + (U := (-(37304062711062346239319 / 10000000000000000000000 : ℚ))) + (U' := (4284768106937653760681 / 10000000000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3184984745401 / 64000000000000 : ℚ)) + (s := (48991113801081 / 2500000000000000 : ℚ)) + (q := (1918647214652921 / 80000000000000000 : ℚ)) + (U := (-(37304062711062346239319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_94_5 : Uω (aρ 5) (bρ 5) (3184984745401 / 64000000000000 : ℝ) ≤ @@ -1759,25 +1651,21 @@ lemma U_95_1 : have hlg : Real.log (1746108637647431 / 40000000000000000 : ℝ) ≤ (-(31314897764576203369223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1746108637647431 / 40000000000000000 : ℝ) = - (1746108637647431 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1746108637647431 / 1250000000000000 : ℚ)) - (U := (3342461250423796630777 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1746108637647431 / 1250000000000000 : ℝ) ≤ - (3342461250423796630777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27259800581033 / 625000000000000 : ℝ)) (q := - (1746108637647431 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1746108637647431 / 40000000000000000 : ℚ)) + (r' := (1746108637647431 / 1250000000000000 : ℚ)) + (U := (-(31314897764576203369223 / 10000000000000000000000 : ℚ))) + (U' := (3342461250423796630777 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1604463128359 / 32000000000000 : ℚ)) + (s := (27259800581033 / 625000000000000 : ℚ)) + (q := (1746108637647431 / 40000000000000000 : ℚ)) + (U := (-(31314897764576203369223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_95_2 : Uω (aρ 2) (bρ 2) (1604463128359 / 32000000000000 : ℝ) ≤ @@ -1785,25 +1673,21 @@ lemma U_95_2 : have hlg : Real.log (1642177203736419 / 40000000000000000 : ℝ) ≤ (-(1995535330098219433187 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1642177203736419 / 40000000000000000 : ℝ) = - (1642177203736419 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1642177203736419 / 1250000000000000 : ℚ)) - (U := (170549608339280566813 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1642177203736419 / 1250000000000000 : ℝ) ≤ - (170549608339280566813 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203980052425511 / 5000000000000000 : ℝ)) (q := - (1642177203736419 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1642177203736419 / 40000000000000000 : ℚ)) + (r' := (1642177203736419 / 1250000000000000 : ℚ)) + (U := (-(1995535330098219433187 / 625000000000000000000 : ℚ))) + (U' := (170549608339280566813 / 625000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1604463128359 / 32000000000000 : ℚ)) + (s := (203980052425511 / 5000000000000000 : ℚ)) + (q := (1642177203736419 / 40000000000000000 : ℚ)) + (U := (-(1995535330098219433187 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_95_3 : Uω (aρ 3) (bρ 3) (1604463128359 / 32000000000000 : ℝ) ≤ @@ -1811,25 +1695,21 @@ lemma U_95_3 : have hlg : Real.log (1421288007529287 / 40000000000000000 : ℝ) ≤ (-(33373159447642545139733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1421288007529287 / 40000000000000000 : ℝ) = - (1421288007529287 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1421288007529287 / 1250000000000000 : ℚ)) - (U := (1284199567357454860267 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1421288007529287 / 1250000000000000 : ℝ) ≤ - (1284199567357454860267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21556975818591 / 625000000000000 : ℝ)) (q := - (1421288007529287 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1421288007529287 / 40000000000000000 : ℚ)) + (r' := (1421288007529287 / 1250000000000000 : ℚ)) + (U := (-(33373159447642545139733 / 10000000000000000000000 : ℚ))) + (U' := (1284199567357454860267 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1604463128359 / 32000000000000 : ℚ)) + (s := (21556975818591 / 625000000000000 : ℚ)) + (q := (1421288007529287 / 40000000000000000 : ℚ)) + (U := (-(33373159447642545139733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_95_4 : Uω (aρ 4) (bρ 4) (1604463128359 / 32000000000000 : ℝ) ≤ @@ -1837,25 +1717,21 @@ lemma U_95_4 : have hlg : Real.log (977560446800329 / 40000000000000000 : ℝ) ≤ (-(37115746034298764438831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (977560446800329 / 40000000000000000 : ℝ) = - (977560446800329 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (977560446800329 / 625000000000000 : ℚ)) - (U := (4473084783701235561169 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (977560446800329 / 625000000000000 : ℝ) ≤ - (4473084783701235561169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (201342013797977 / 10000000000000000 : ℝ)) (q := - (977560446800329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (977560446800329 / 40000000000000000 : ℚ)) + (r' := (977560446800329 / 625000000000000 : ℚ)) + (U := (-(37115746034298764438831 / 10000000000000000000000 : ℚ))) + (U' := (4473084783701235561169 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1604463128359 / 32000000000000 : ℚ)) + (s := (201342013797977 / 10000000000000000 : ℚ)) + (q := (977560446800329 / 40000000000000000 : ℚ)) + (U := (-(37115746034298764438831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_95_5 : Uω (aρ 5) (bρ 5) (1604463128359 / 32000000000000 : ℝ) ≤ @@ -2008,25 +1884,21 @@ lemma U_96_1 : have hlg : Real.log (704433871945367 / 16000000000000000 : ℝ) ≤ (-(31229495382192123462893 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (704433871945367 / 16000000000000000 : ℝ) = - (704433871945367 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (704433871945367 / 500000000000000 : ℚ)) - (U := (3427863632807876537107 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (704433871945367 / 500000000000000 : ℝ) ≤ - (3427863632807876537107 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (10997599231531 / 250000000000000 : ℝ)) (q := - (704433871945367 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (704433871945367 / 16000000000000000 : ℚ)) + (r' := (704433871945367 / 500000000000000 : ℚ)) + (U := (-(31229495382192123462893 / 10000000000000000000000 : ℚ))) + (U' := (3427863632807876537107 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (646573553607 / 12800000000000 : ℚ)) + (s := (10997599231531 / 250000000000000 : ℚ)) + (q := (704433871945367 / 16000000000000000 : ℚ)) + (U := (-(31229495382192123462893 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_96_2 : Uω (aρ 2) (bρ 2) (646573553607 / 12800000000000 : ℝ) ≤ @@ -2034,25 +1906,21 @@ lemma U_96_2 : have hlg : Real.log (3314469133291263 / 80000000000000000 : ℝ) ≤ (-(31837291633471834828943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3314469133291263 / 80000000000000000 : ℝ) = - (3314469133291263 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3314469133291263 / 2500000000000000 : ℚ)) - (U := (2820067381528165171057 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3314469133291263 / 2500000000000000 : ℝ) ≤ - (2820067381528165171057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (411747925162347 / 10000000000000000 : ℝ)) (q := - (3314469133291263 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3314469133291263 / 80000000000000000 : ℚ)) + (r' := (3314469133291263 / 2500000000000000 : ℚ)) + (U := (-(31837291633471834828943 / 10000000000000000000000 : ℚ))) + (U' := (2820067381528165171057 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (646573553607 / 12800000000000 : ℚ)) + (s := (411747925162347 / 10000000000000000 : ℚ)) + (q := (3314469133291263 / 80000000000000000 : ℚ)) + (U := (-(31837291633471834828943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_96_3 : Uω (aρ 3) (bρ 3) (646573553607 / 12800000000000 : ℝ) ≤ @@ -2060,25 +1928,21 @@ lemma U_96_3 : have hlg : Real.log (574679240581723 / 16000000000000000 : ℝ) ≤ (-(33265319572434076398587 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (574679240581723 / 16000000000000000 : ℝ) = - (574679240581723 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (574679240581723 / 500000000000000 : ℚ)) - (U := (1392039442565923601413 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (574679240581723 / 500000000000000 : ℝ) ≤ - (1392039442565923601413 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (69775159783337 / 2000000000000000 : ℝ)) (q := - (574679240581723 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (574679240581723 / 16000000000000000 : ℚ)) + (r' := (574679240581723 / 500000000000000 : ℚ)) + (U := (-(33265319572434076398587 / 10000000000000000000000 : ℚ))) + (U' := (1392039442565923601413 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (646573553607 / 12800000000000 : ℚ)) + (s := (69775159783337 / 2000000000000000 : ℚ)) + (q := (574679240581723 / 16000000000000000 : ℚ)) + (U := (-(33265319572434076398587 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_96_4 : Uω (aρ 4) (bρ 4) (646573553607 / 12800000000000 : ℝ) ≤ @@ -2086,25 +1950,21 @@ lemma U_96_4 : have hlg : Real.log (1991305742591499 / 80000000000000000 : ℝ) ≤ (-(18466180287477100611297 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1991305742591499 / 80000000000000000 : ℝ) = - (1991305742591499 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1991305742591499 / 1250000000000000 : ℚ)) - (U := (2328235121522899388703 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1991305742591499 / 1250000000000000 : ℝ) ≤ - (2328235121522899388703 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103323682451203 / 5000000000000000 : ℝ)) (q := - (1991305742591499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1991305742591499 / 80000000000000000 : ℚ)) + (r' := (1991305742591499 / 1250000000000000 : ℚ)) + (U := (-(18466180287477100611297 / 5000000000000000000000 : ℚ))) + (U' := (2328235121522899388703 / 5000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (646573553607 / 12800000000000 : ℚ)) + (s := (103323682451203 / 5000000000000000 : ℚ)) + (q := (1991305742591499 / 80000000000000000 : ℚ)) + (U := (-(18466180287477100611297 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_96_5 : Uω (aρ 5) (bρ 5) (646573553607 / 12800000000000 : ℝ) ≤ @@ -2257,25 +2117,21 @@ lemma U_97_1 : have hlg : Real.log (222007563681771 / 5000000000000000 : ℝ) ≤ (-(31144817381860143498661 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (222007563681771 / 5000000000000000 : ℝ) = - (222007563681771 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (222007563681771 / 156250000000000 : ℚ)) - (U := (3512541633139856501339 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (222007563681771 / 156250000000000 : ℝ) ≤ - (3512541633139856501339 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221825511456667 / 5000000000000000 : ℝ)) (q := - (222007563681771 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (222007563681771 / 5000000000000000 : ℚ)) + (r' := (222007563681771 / 156250000000000 : ℚ)) + (U := (-(31144817381860143498661 / 10000000000000000000000 : ℚ))) + (U' := (3512541633139856501339 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (407101159919 / 8000000000000 : ℚ)) + (s := (221825511456667 / 5000000000000000 : ℚ)) + (q := (222007563681771 / 5000000000000000 : ℚ)) + (U := (-(31144817381860143498661 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_97_2 : Uω (aρ 2) (bρ 2) (407101159919 / 8000000000000 : ℝ) ≤ @@ -2283,23 +2139,21 @@ lemma U_97_2 : have hlg : Real.log (4180725569849 / 100000000000000 : ℝ) ≤ (-(1984178357444751687497 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show (4180725569849 / 100000000000000 : ℝ) = (4180725569849 / 3125000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4180725569849 / 3125000000000 : ℚ)) - (U := (181906580992748312503 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (4180725569849 / 3125000000000 : ℝ) ≤ - (181906580992748312503 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8310697893321 / 200000000000000 : ℝ)) (q := - (4180725569849 / 100000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4180725569849 / 100000000000000 : ℚ)) + (r' := (4180725569849 / 3125000000000 : ℚ)) + (U := (-(1984178357444751687497 / 625000000000000000000 : ℚ))) + (U' := (181906580992748312503 / 625000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (407101159919 / 8000000000000 : ℚ)) + (s := (8310697893321 / 200000000000000 : ℚ)) + (q := (4180725569849 / 100000000000000 : ℚ)) + (U := (-(1984178357444751687497 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_97_3 : Uω (aρ 3) (bρ 3) (407101159919 / 8000000000000 : ℝ) ≤ @@ -2307,23 +2161,21 @@ lemma U_97_3 : have hlg : Real.log (9075615260803 / 250000000000000 : ℝ) ≤ (-(3315869741376076852277 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show (9075615260803 / 250000000000000 : ℝ) = (9075615260803 / 7812500000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9075615260803 / 7812500000000 : ℚ)) - (U := (149866160123923147723 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9075615260803 / 7812500000000 : ℝ) ≤ - (149866160123923147723 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35283510791049 / 1000000000000000 : ℝ)) (q := - (9075615260803 / 250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9075615260803 / 250000000000000 : ℚ)) + (r' := (9075615260803 / 7812500000000 : ℚ)) + (U := (-(3315869741376076852277 / 1000000000000000000000 : ℚ))) + (U' := (149866160123923147723 / 1000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (407101159919 / 8000000000000 : ℚ)) + (s := (35283510791049 / 1000000000000000 : ℚ)) + (q := (9075615260803 / 250000000000000 : ℚ)) + (U := (-(3315869741376076852277 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_97_4 : Uω (aρ 4) (bρ 4) (407101159919 / 8000000000000 : ℝ) ≤ @@ -2331,25 +2183,21 @@ lemma U_97_4 : have hlg : Real.log (506805864423637 / 20000000000000000 : ℝ) ≤ (-(36753595311212100745499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (506805864423637 / 20000000000000000 : ℝ) = - (506805864423637 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (506805864423637 / 312500000000000 : ℚ)) - (U := (4835235506787899254501 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (506805864423637 / 312500000000000 : ℝ) ≤ - (4835235506787899254501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (211885932534887 / 10000000000000000 : ℝ)) (q := - (506805864423637 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (506805864423637 / 20000000000000000 : ℚ)) + (r' := (506805864423637 / 312500000000000 : ℚ)) + (U := (-(36753595311212100745499 / 10000000000000000000000 : ℚ))) + (U' := (4835235506787899254501 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (407101159919 / 8000000000000 : ℚ)) + (s := (211885932534887 / 10000000000000000 : ℚ)) + (q := (506805864423637 / 20000000000000000 : ℚ)) + (U := (-(36753595311212100745499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_97_5 : Uω (aρ 5) (bρ 5) (407101159919 / 8000000000000 : ℝ) ≤ @@ -2502,25 +2350,21 @@ lemma U_98_1 : have hlg : Real.log (1806011551951707 / 40000000000000000 : ℝ) ≤ (-(15488793007051782660579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1806011551951707 / 40000000000000000 : ℝ) = - (1806011551951707 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1806011551951707 / 1250000000000000 : ℚ)) - (U := (1839886500448217339421 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1806011551951707 / 1250000000000000 : ℝ) ≤ - (1839886500448217339421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (451144821875541 / 10000000000000000 : ℝ)) (q := - (1806011551951707 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1806011551951707 / 40000000000000000 : ℚ)) + (r' := (1806011551951707 / 1250000000000000 : ℚ)) + (U := (-(15488793007051782660579 / 5000000000000000000000 : ℚ))) + (U' := (1839886500448217339421 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1652346150993 / 32000000000000 : ℚ)) + (s := (451144821875541 / 10000000000000000 : ℚ)) + (q := (1806011551951707 / 40000000000000000 : ℚ)) + (U := (-(15488793007051782660579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_98_2 : Uω (aρ 2) (bρ 2) (1652346150993 / 32000000000000 : ℝ) ≤ @@ -2528,25 +2372,21 @@ lemma U_98_2 : have hlg : Real.log (1702396628433119 / 40000000000000000 : ℝ) ≤ (-(789210603282412178031 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1702396628433119 / 40000000000000000 : ℝ) = - (1702396628433119 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1702396628433119 / 1250000000000000 : ℚ)) - (U := (77223372092587821969 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1702396628433119 / 1250000000000000 : ℝ) ≤ - (77223372092587821969 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (423106372626247 / 10000000000000000 : ℝ)) (q := - (1702396628433119 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1702396628433119 / 40000000000000000 : ℚ)) + (r' := (1702396628433119 / 1250000000000000 : ℚ)) + (U := (-(789210603282412178031 / 250000000000000000000 : ℚ))) + (U' := (77223372092587821969 / 250000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1652346150993 / 32000000000000 : ℚ)) + (s := (423106372626247 / 10000000000000000 : ℚ)) + (q := (1702396628433119 / 40000000000000000 : ℚ)) + (U := (-(789210603282412178031 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_98_3 : Uω (aρ 3) (bρ 3) (1652346150993 / 32000000000000 : ℝ) ≤ @@ -2554,25 +2394,21 @@ lemma U_98_3 : have hlg : Real.log (1482871145547441 / 40000000000000000 : ℝ) ≤ (-(32948992811289585472047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1482871145547441 / 40000000000000000 : ℝ) = - (1482871145547441 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1482871145547441 / 1250000000000000 : ℚ)) - (U := (1708366203710414527953 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1482871145547441 / 1250000000000000 : ℝ) ≤ - (1708366203710414527953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11273116797919 / 312500000000000 : ℝ)) (q := - (1482871145547441 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1482871145547441 / 40000000000000000 : ℚ)) + (r' := (1482871145547441 / 1250000000000000 : ℚ)) + (U := (-(32948992811289585472047 / 10000000000000000000000 : ℚ))) + (U' := (1708366203710414527953 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1652346150993 / 32000000000000 : ℚ)) + (s := (11273116797919 / 312500000000000 : ℚ)) + (q := (1482871145547441 / 40000000000000000 : ℚ)) + (U := (-(32948992811289585472047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_98_4 : Uω (aρ 4) (bρ 4) (1652346150993 / 32000000000000 : ℝ) ≤ @@ -2580,25 +2416,21 @@ lemma U_98_4 : have hlg : Real.log (1049166414959979 / 40000000000000000 : ℝ) ≤ (-(9102208735492745651249 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1049166414959979 / 40000000000000000 : ℝ) = - (1049166414959979 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1049166414959979 / 625000000000000 : ℚ)) - (U := (1294998969007254348751 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1049166414959979 / 625000000000000 : ℝ) ≤ - (1294998969007254348751 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (222181553304677 / 10000000000000000 : ℝ)) (q := - (1049166414959979 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1049166414959979 / 40000000000000000 : ℚ)) + (r' := (1049166414959979 / 625000000000000 : ℚ)) + (U := (-(9102208735492745651249 / 2500000000000000000000 : ℚ))) + (U' := (1294998969007254348751 / 2500000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1652346150993 / 32000000000000 : ℚ)) + (s := (222181553304677 / 10000000000000000 : ℚ)) + (q := (1049166414959979 / 40000000000000000 : ℚ)) + (U := (-(9102208735492745651249 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_98_5 : Uω (aρ 5) (bρ 5) (1652346150993 / 32000000000000 : ℝ) ≤ @@ -2750,25 +2582,21 @@ lemma U_99_1 : have hlg : Real.log (183596180579089 / 4000000000000000 : ℝ) ≤ (-(30813109637784336635283 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (183596180579089 / 4000000000000000 : ℝ) = - (183596180579089 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (183596180579089 / 125000000000000 : ℚ)) - (U := (3844249377215663364717 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (183596180579089 / 125000000000000 : ℝ) ≤ - (3844249377215663364717 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45863822650857 / 1000000000000000 : ℝ)) (q := - (183596180579089 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (183596180579089 / 4000000000000000 : ℚ)) + (r' := (183596180579089 / 125000000000000 : ℚ)) + (U := (-(30813109637784336635283 / 10000000000000000000000 : ℚ))) + (U' := (3844249377215663364717 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (167628766231 / 3200000000000 : ℚ)) + (s := (45863822650857 / 1000000000000000 : ℚ)) + (q := (183596180579089 / 4000000000000000 : ℚ)) + (U := (-(30813109637784336635283 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_99_2 : Uω (aρ 2) (bρ 2) (167628766231 / 3200000000000 : ℝ) ≤ @@ -2776,24 +2604,21 @@ lemma U_99_2 : have hlg : Real.log (43312418864037 / 1000000000000000 : ℝ) ≤ (-(31393158740030300939493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (43312418864037 / 1000000000000000 : ℝ) = (43312418864037 / 31250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43312418864037 / 31250000000000 : ℚ)) - (U := (3264200274969699060507 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (43312418864037 / 31250000000000 : ℝ) ≤ - (3264200274969699060507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86134942680773 / 2000000000000000 : ℝ)) (q := - (43312418864037 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43312418864037 / 1000000000000000 : ℚ)) + (r' := (43312418864037 / 31250000000000 : ℚ)) + (U := (-(31393158740030300939493 / 10000000000000000000000 : ℚ))) + (U' := (3264200274969699060507 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (167628766231 / 3200000000000 : ℚ)) + (s := (86134942680773 / 2000000000000000 : ℚ)) + (q := (43312418864037 / 1000000000000000 : ℚ)) + (U := (-(31393158740030300939493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_99_3 : Uω (aρ 3) (bρ 3) (167628766231 / 3200000000000 : ℝ) ≤ @@ -2801,24 +2626,21 @@ lemma U_99_3 : have hlg : Real.log (75680427309953 / 2000000000000000 : ℝ) ≤ (-(8185957218103774495557 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (75680427309953 / 2000000000000000 : ℝ) = (75680427309953 / 62500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (75680427309953 / 62500000000000 : ℚ)) - (U := (478382535646225504443 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (75680427309953 / 62500000000000 : ℝ) ≤ - (478382535646225504443 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73725343114531 / 2000000000000000 : ℝ)) (q := - (75680427309953 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (75680427309953 / 2000000000000000 : ℚ)) + (r' := (75680427309953 / 62500000000000 : ℚ)) + (U := (-(8185957218103774495557 / 2500000000000000000000 : ℚ))) + (U' := (478382535646225504443 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (167628766231 / 3200000000000 : ℚ)) + (s := (73725343114531 / 2000000000000000 : ℚ)) + (q := (75680427309953 / 2000000000000000 : ℚ)) + (U := (-(8185957218103774495557 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_99_4 : Uω (aρ 4) (bρ 4) (167628766231 / 3200000000000 : ℝ) ≤ @@ -2826,25 +2648,21 @@ lemma U_99_4 : have hlg : Real.log (542145274302063 / 20000000000000000 : ℝ) ≤ (-(9019883879209497377887 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (542145274302063 / 20000000000000000 : ℝ) = - (542145274302063 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (542145274302063 / 312500000000000 : ℚ)) - (U := (1377323825290502622113 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (542145274302063 / 312500000000000 : ℝ) ≤ - (1377323825290502622113 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58065474460047 / 2500000000000000 : ℝ)) (q := - (542145274302063 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (542145274302063 / 20000000000000000 : ℚ)) + (r' := (542145274302063 / 312500000000000 : ℚ)) + (U := (-(9019883879209497377887 / 2500000000000000000000 : ℚ))) + (U' := (1377323825290502622113 / 2500000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (167628766231 / 3200000000000 : ℚ)) + (s := (58065474460047 / 2500000000000000 : ℚ)) + (q := (542145274302063 / 20000000000000000 : ℚ)) + (U := (-(9019883879209497377887 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_99_5 : Uω (aρ 5) (bρ 5) (167628766231 / 3200000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U08.lean b/LeanPool/Zeta5Irrational/Table/U08.lean index d8cdb38684..69f036a368 100644 --- a/LeanPool/Zeta5Irrational/Table/U08.lean +++ b/LeanPool/Zeta5Irrational/Table/U08.lean @@ -24,25 +24,21 @@ lemma U_100_1 : have hlg : Real.log (373182261801303 / 8000000000000000 : ℝ) ≤ (-(30651298815258709468093 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (373182261801303 / 8000000000000000 : ℝ) = - (373182261801303 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (373182261801303 / 250000000000000 : ℚ)) - (U := (4006060199741290531907 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (373182261801303 / 250000000000000 : ℝ) ≤ - (4006060199741290531907 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23306562791491 / 500000000000000 : ℝ)) (q := - (373182261801303 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (373182261801303 / 8000000000000000 : ℚ)) + (r' := (373182261801303 / 250000000000000 : ℚ)) + (U := (-(30651298815258709468093 / 10000000000000000000000 : ℚ))) + (U' := (4006060199741290531907 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1700229173627 / 32000000000000 : ℚ)) + (s := (23306562791491 / 500000000000000 : ℚ)) + (q := (373182261801303 / 8000000000000000 : ℚ)) + (U := (-(30651298815258709468093 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_100_2 : Uω (aρ 2) (bρ 2) (1700229173627 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_100_2 : have hlg : Real.log (1762590931396799 / 40000000000000000 : ℝ) ≤ (-(78052365153972182917 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1762590931396799 / 40000000000000000 : ℝ) = - (1762590931396799 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1762590931396799 / 1250000000000000 : ℚ)) - (U := (8591032383527817083 / 25000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1762590931396799 / 1250000000000000 : ℝ) ≤ - (8591032383527817083 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (219120039767481 / 5000000000000000 : ℝ)) (q := - (1762590931396799 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1762590931396799 / 40000000000000000 : ℚ)) + (r' := (1762590931396799 / 1250000000000000 : ℚ)) + (U := (-(78052365153972182917 / 25000000000000000000 : ℚ))) + (U' := (8591032383527817083 / 25000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1700229173627 / 32000000000000 : ℚ)) + (s := (219120039767481 / 5000000000000000 : ℚ)) + (q := (1762590931396799 / 40000000000000000 : ℚ)) + (U := (-(78052365153972182917 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_100_3 : Uω (aρ 3) (bρ 3) (1700229173627 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_100_3 : have hlg : Real.log (1544312862311407 / 40000000000000000 : ℝ) ≤ (-(16271501953539078684187 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1544312862311407 / 40000000000000000 : ℝ) = - (1544312862311407 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1544312862311407 / 1250000000000000 : ℚ)) - (U := (1057177553960921315813 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1544312862311407 / 1250000000000000 : ℝ) ≤ - (1057177553960921315813 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188248575671133 / 5000000000000000 : ℝ)) (q := - (1544312862311407 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1544312862311407 / 40000000000000000 : ℚ)) + (r' := (1544312862311407 / 1250000000000000 : ℚ)) + (U := (-(16271501953539078684187 / 5000000000000000000000 : ℚ))) + (U' := (1057177553960921315813 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1700229173627 / 32000000000000 : ℚ)) + (s := (188248575671133 / 5000000000000000 : ℚ)) + (q := (1544312862311407 / 40000000000000000 : ℚ)) + (U := (-(16271501953539078684187 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_100_4 : Uω (aρ 4) (bρ 4) (1700229173627 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_100_4 : have hlg : Real.log (1119037901687173 / 40000000000000000 : ℝ) ≤ (-(35764101527639732941787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1119037901687173 / 40000000000000000 : ℝ) = - (1119037901687173 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1119037901687173 / 625000000000000 : ℚ)) - (U := (5824729290360267058213 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1119037901687173 / 625000000000000 : ℝ) ≤ - (5824729290360267058213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242153852095149 / 10000000000000000 : ℝ)) (q := - (1119037901687173 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1119037901687173 / 40000000000000000 : ℚ)) + (r' := (1119037901687173 / 625000000000000 : ℚ)) + (U := (-(35764101527639732941787 / 10000000000000000000000 : ℚ))) + (U' := (5824729290360267058213 / 10000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1700229173627 / 32000000000000 : ℚ)) + (s := (242153852095149 / 10000000000000000 : ℚ)) + (q := (1119037901687173 / 40000000000000000 : ℚ)) + (U := (-(35764101527639732941787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_100_5 : Uω (aρ 5) (bρ 5) (1700229173627 / 32000000000000 : ℝ) ≤ @@ -272,23 +256,21 @@ lemma U_101_1 : have hlg : Real.log (9479300486123 / 200000000000000 : ℝ) ≤ (-(3049206840087526189059 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show (9479300486123 / 200000000000000 : ℝ) = (9479300486123 / 6250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9479300486123 / 6250000000000 : ℚ)) - (U := (416529061412473810941 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (9479300486123 / 6250000000000 : ℝ) ≤ - (416529061412473810941 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4736239276523 / 100000000000000 : ℝ)) (q := - (9479300486123 / 200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9479300486123 / 200000000000000 : ℚ)) + (r' := (9479300486123 / 6250000000000 : ℚ)) + (U := (-(3049206840087526189059 / 1000000000000000000000 : ℚ))) + (U' := (416529061412473810941 / 1000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (107760667809 / 2000000000000 : ℚ)) + (s := (4736239276523 / 100000000000000 : ℚ)) + (q := (9479300486123 / 200000000000000 : ℚ)) + (U := (-(3049206840087526189059 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_101_2 : Uω (aρ 2) (bρ 2) (107760667809 / 2000000000000 : ℝ) ≤ @@ -296,24 +278,21 @@ lemma U_101_2 : have hlg : Real.log (89633973091073 / 2000000000000000 : ℝ) ≤ (-(3881460057703866310033 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (89633973091073 / 2000000000000000 : ℝ) = (89633973091073 / 62500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (89633973091073 / 62500000000000 : ℚ)) - (U := (450709819171133689967 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (89633973091073 / 62500000000000 : ℝ) ≤ - (450709819171133689967 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44580262246073 / 1000000000000000 : ℝ)) (q := - (89633973091073 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (89633973091073 / 2000000000000000 : ℚ)) + (r' := (89633973091073 / 62500000000000 : ℚ)) + (U := (-(3881460057703866310033 / 1250000000000000000000 : ℚ))) + (U' := (450709819171133689967 / 1250000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (107760667809 / 2000000000000 : ℚ)) + (s := (44580262246073 / 1000000000000000 : ℚ)) + (q := (89633973091073 / 2000000000000000 : ℚ)) + (U := (-(3881460057703866310033 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_101_3 : Uω (aρ 3) (bρ 3) (107760667809 / 2000000000000 : ℝ) ≤ @@ -321,25 +300,21 @@ lemma U_101_3 : have hlg : Real.log (787493063159317 / 20000000000000000 : ℝ) ≤ (-(126352851143046549433 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (787493063159317 / 20000000000000000 : ℝ) = - (787493063159317 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (787493063159317 / 625000000000000 : ℚ)) - (U := (9027457509297200567 / 39062500000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (787493063159317 / 625000000000000 : ℝ) ≤ - (9027457509297200567 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (384352061059317 / 10000000000000000 : ℝ)) (q := - (787493063159317 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (787493063159317 / 20000000000000000 : ℚ)) + (r' := (787493063159317 / 625000000000000 : ℚ)) + (U := (-(126352851143046549433 / 39062500000000000000 : ℚ))) + (U' := (9027457509297200567 / 39062500000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (107760667809 / 2000000000000 : ℚ)) + (s := (384352061059317 / 10000000000000000 : ℚ)) + (q := (787493063159317 / 20000000000000000 : ℚ)) + (U := (-(126352851143046549433 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_101_4 : Uω (aρ 4) (bρ 4) (107760667809 / 2000000000000 : ℝ) ≤ @@ -347,25 +322,21 @@ lemma U_101_4 : have hlg : Real.log (288363216890881 / 10000000000000000 : ℝ) ≤ (-(2216324696954452647823 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (288363216890881 / 10000000000000000 : ℝ) = - (288363216890881 / 156250000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (288363216890881 / 156250000000000 : ℚ)) - (U := (382977229170547352177 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (288363216890881 / 156250000000000 : ℝ) ≤ - (382977229170547352177 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (125939806373381 / 5000000000000000 : ℝ)) (q := - (288363216890881 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (288363216890881 / 10000000000000000 : ℚ)) + (r' := (288363216890881 / 156250000000000 : ℚ)) + (U := (-(2216324696954452647823 / 625000000000000000000 : ℚ))) + (U' := (382977229170547352177 / 625000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (107760667809 / 2000000000000 : ℚ)) + (s := (125939806373381 / 5000000000000000 : ℚ)) + (q := (288363216890881 / 10000000000000000 : ℚ)) + (U := (-(2216324696954452647823 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_101_5 : Uω (aρ 5) (bρ 5) (107760667809 / 2000000000000 : ℝ) ≤ @@ -516,25 +487,21 @@ lemma U_102_1 : have hlg : Real.log (488938915059511 / 10000000000000000 : ℝ) ≤ (-(7545257017708016980781 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (488938915059511 / 10000000000000000 : ℝ) = - (488938915059511 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (488938915059511 / 312500000000000 : ℚ)) - (U := (1119082736041983019219 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (488938915059511 / 312500000000000 : ℝ) ≤ - (1119082736041983019219 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (488608264585897 / 10000000000000000 : ℝ)) (q := - (488938915059511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (488938915059511 / 10000000000000000 : ℚ)) + (r' := (488938915059511 / 312500000000000 : ℚ)) + (U := (-(7545257017708016980781 / 2500000000000000000000 : ℚ))) + (U' := (1119082736041983019219 / 2500000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (886026853789 / 16000000000000 : ℚ)) + (s := (488608264585897 / 10000000000000000 : ℚ)) + (q := (488938915059511 / 10000000000000000 : ℚ)) + (U := (-(7545257017708016980781 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_102_2 : Uω (aρ 2) (bρ 2) (886026853789 / 16000000000000 : ℝ) ≤ @@ -542,25 +509,21 @@ lemma U_102_2 : have hlg : Real.log (926420347528863 / 20000000000000000 : ℝ) ≤ (-(30721594805733174632861 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (926420347528863 / 20000000000000000 : ℝ) = - (926420347528863 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (926420347528863 / 625000000000000 : ℚ)) - (U := (3935764209266825367139 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (926420347528863 / 625000000000000 : ℝ) ≤ - (3935764209266825367139 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (230459897252869 / 5000000000000000 : ℝ)) (q := - (926420347528863 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (926420347528863 / 20000000000000000 : ℚ)) + (r' := (926420347528863 / 625000000000000 : ℚ)) + (U := (-(30721594805733174632861 / 10000000000000000000000 : ℚ))) + (U' := (3935764209266825367139 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (886026853789 / 16000000000000 : ℚ)) + (s := (230459897252869 / 5000000000000000 : ℚ)) + (q := (926420347528863 / 20000000000000000 : ℚ)) + (U := (-(30721594805733174632861 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_102_3 : Uω (aρ 3) (bρ 3) (886026853789 / 16000000000000 : ℝ) ≤ @@ -568,24 +531,21 @@ lemma U_102_3 : have hlg : Real.log (10226542571457 / 250000000000000 : ℝ) ≤ (-(15982371816390557011147 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (10226542571457 / 250000000000000 : ℝ) = (10226542571457 / 7812500000000 : ℝ) / 2 ^ 5 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10226542571457 / 7812500000000 : ℚ)) - (U := (1346307691109442988853 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10226542571457 / 7812500000000 : ℝ) ≤ - (1346307691109442988853 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (80003791808687 / 2000000000000000 : ℝ)) (q := - (10226542571457 / 250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10226542571457 / 250000000000000 : ℚ)) + (r' := (10226542571457 / 7812500000000 : ℚ)) + (U := (-(15982371816390557011147 / 5000000000000000000000 : ℚ))) + (U' := (1346307691109442988853 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (886026853789 / 16000000000000 : ℚ)) + (s := (80003791808687 / 2000000000000000 : ℚ)) + (q := (10226542571457 / 250000000000000 : ℚ)) + (U := (-(15982371816390557011147 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_102_4 : Uω (aρ 4) (bρ 4) (886026853789 / 16000000000000 : ℝ) ≤ @@ -593,25 +553,21 @@ lemma U_102_4 : have hlg : Real.log (610714120865997 / 20000000000000000 : ℝ) ≤ (-(34888585885879677851941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (610714120865997 / 20000000000000000 : ℝ) = - (610714120865997 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (610714120865997 / 312500000000000 : ℚ)) - (U := (6700244932120322148059 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (610714120865997 / 312500000000000 : ℝ) ≤ - (6700244932120322148059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16931490953617 / 625000000000000 : ℝ)) (q := - (610714120865997 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (610714120865997 / 20000000000000000 : ℚ)) + (r' := (610714120865997 / 312500000000000 : ℚ)) + (U := (-(34888585885879677851941 / 10000000000000000000000 : ℚ))) + (U' := (6700244932120322148059 / 10000000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (886026853789 / 16000000000000 : ℚ)) + (s := (16931490953617 / 625000000000000 : ℚ)) + (q := (610714120865997 / 20000000000000000 : ℚ)) + (U := (-(34888585885879677851941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_102_5 : Uω (aρ 5) (bρ 5) (886026853789 / 16000000000000 : ℝ) ≤ @@ -763,24 +719,21 @@ lemma U_103_1 : have hlg : Real.log (31494511537239 / 625000000000000 : ℝ) ≤ (-(14939691773495747728407 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (31494511537239 / 625000000000000 : ℝ) = (31494511537239 / 19531250000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31494511537239 / 19531250000000 : ℚ)) - (U := (2388987734004252271593 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31494511537239 / 19531250000000 : ℝ) ≤ - (2388987734004252271593 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (251795679542699 / 5000000000000000 : ℝ)) (q := - (31494511537239 / 625000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31494511537239 / 625000000000000 : ℚ)) + (r' := (31494511537239 / 19531250000000 : ℚ)) + (U := (-(14939691773495747728407 / 5000000000000000000000 : ℚ))) + (U' := (2388987734004252271593 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (454984182553 / 8000000000000 : ℚ)) + (s := (251795679542699 / 5000000000000000 : ℚ)) + (q := (31494511537239 / 625000000000000 : ℚ)) + (U := (-(14939691773495747728407 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_103_2 : Uω (aρ 2) (bρ 2) (454984182553 / 8000000000000 : ℝ) ≤ @@ -788,25 +741,21 @@ lemma U_103_2 : have hlg : Real.log (478245625030189 / 10000000000000000 : ℝ) ≤ (-(7600539775674981056863 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (478245625030189 / 10000000000000000 : ℝ) = - (478245625030189 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (478245625030189 / 312500000000000 : ℚ)) - (U := (1063799978075018943137 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (478245625030189 / 312500000000000 : ℝ) ≤ - (1063799978075018943137 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (929740727469 / 19531250000000 : ℝ)) (q := - (478245625030189 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (478245625030189 / 10000000000000000 : ℚ)) + (r' := (478245625030189 / 312500000000000 : ℚ)) + (U := (-(7600539775674981056863 / 2500000000000000000000 : ℚ))) + (U' := (1063799978075018943137 / 2500000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (454984182553 / 8000000000000 : ℚ)) + (s := (929740727469 / 19531250000000 : ℚ)) + (q := (478245625030189 / 10000000000000000 : ℚ)) + (U := (-(7600539775674981056863 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_103_3 : Uω (aρ 3) (bρ 3) (454984182553 / 8000000000000 : ℝ) ≤ @@ -814,25 +763,21 @@ lemma U_103_3 : have hlg : Real.log (848701910179767 / 20000000000000000 : ℝ) ≤ (-(1974862208469201710963 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (848701910179767 / 20000000000000000 : ℝ) = - (848701910179767 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (848701910179767 / 625000000000000 : ℚ)) - (U := (191222729968298289037 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (848701910179767 / 625000000000000 : ℝ) ≤ - (191222729968298289037 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (415634018933517 / 10000000000000000 : ℝ)) (q := - (848701910179767 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (848701910179767 / 20000000000000000 : ℚ)) + (r' := (848701910179767 / 625000000000000 : ℚ)) + (U := (-(1974862208469201710963 / 625000000000000000000 : ℚ))) + (U' := (191222729968298289037 / 625000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (454984182553 / 8000000000000 : ℚ)) + (s := (415634018933517 / 10000000000000000 : ℚ)) + (q := (848701910179767 / 20000000000000000 : ℚ)) + (U := (-(1974862208469201710963 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_103_4 : Uω (aρ 4) (bρ 4) (454984182553 / 8000000000000 : ℝ) ≤ @@ -840,25 +785,21 @@ lemma U_103_4 : have hlg : Real.log (322112688666289 / 10000000000000000 : ℝ) ≤ (-(17177194607766529470513 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (322112688666289 / 10000000000000000 : ℝ) = - (322112688666289 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (322112688666289 / 312500000000000 : ℚ)) - (U := (151484899733470529487 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (322112688666289 / 312500000000000 : ℝ) ≤ - (151484899733470529487 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9045364598479 / 312500000000000 : ℝ)) (q := - (322112688666289 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (322112688666289 / 10000000000000000 : ℚ)) + (r' := (322112688666289 / 312500000000000 : ℚ)) + (U := (-(17177194607766529470513 / 5000000000000000000000 : ℚ))) + (U' := (151484899733470529487 / 5000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (454984182553 / 8000000000000 : ℚ)) + (s := (9045364598479 / 312500000000000 : ℚ)) + (q := (322112688666289 / 10000000000000000 : ℚ)) + (U := (-(17177194607766529470513 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_103_5 : Uω (aρ 5) (bρ 5) (454984182553 / 8000000000000 : ℝ) ≤ @@ -1010,25 +951,21 @@ lemma U_104_1 : have hlg : Real.log (533857069350801 / 10000000000000000 : ℝ) ≤ (-(3662765284919319541649 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (533857069350801 / 10000000000000000 : ℝ) = - (533857069350801 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (533857069350801 / 312500000000000 : ℚ)) - (U := (669404591955680458351 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (533857069350801 / 312500000000000 : ℝ) ≤ - (669404591955680458351 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (266777119724551 / 5000000000000000 : ℝ)) (q := - (533857069350801 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (533857069350801 / 10000000000000000 : ℚ)) + (r' := (533857069350801 / 312500000000000 : ℚ)) + (U := (-(3662765284919319541649 / 1250000000000000000000 : ℚ))) + (U' := (669404591955680458351 / 1250000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47892569387 / 800000000000 : ℚ)) + (s := (266777119724551 / 5000000000000000 : ℚ)) + (q := (533857069350801 / 10000000000000000 : ℚ)) + (U := (-(3662765284919319541649 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_104_2 : Uω (aρ 2) (bρ 2) (47892569387 / 800000000000 : ℝ) ≤ @@ -1036,25 +973,21 @@ lemma U_104_2 : have hlg : Real.log (508303695593581 / 10000000000000000 : ℝ) ≤ (-(3724076594691395072657 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (508303695593581 / 10000000000000000 : ℝ) = - (508303695593581 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (508303695593581 / 312500000000000 : ℚ)) - (U := (608093282183604927343 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (508303695593581 / 312500000000000 : ℝ) ≤ - (608093282183604927343 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253108252222331 / 5000000000000000 : ℝ)) (q := - (508303695593581 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (508303695593581 / 10000000000000000 : ℚ)) + (r' := (508303695593581 / 312500000000000 : ℚ)) + (U := (-(3724076594691395072657 / 1250000000000000000000 : ℚ))) + (U' := (608093282183604927343 / 1250000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47892569387 / 800000000000 : ℚ)) + (s := (253108252222331 / 5000000000000000 : ℚ)) + (q := (508303695593581 / 10000000000000000 : ℚ)) + (U := (-(3724076594691395072657 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_104_3 : Uω (aρ 3) (bρ 3) (47892569387 / 800000000000 : ℝ) ≤ @@ -1062,25 +995,21 @@ lemma U_104_3 : have hlg : Real.log (181945026151459 / 4000000000000000 : ℝ) ≤ (-(6180690102931800358943 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (181945026151459 / 4000000000000000 : ℝ) = - (181945026151459 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (181945026151459 / 125000000000000 : ℚ)) - (U := (750781700068199641057 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (181945026151459 / 125000000000000 : ℝ) ≤ - (750781700068199641057 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89346070072959 / 2000000000000000 : ℝ)) (q := - (181945026151459 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (181945026151459 / 4000000000000000 : ℚ)) + (r' := (181945026151459 / 125000000000000 : ℚ)) + (U := (-(6180690102931800358943 / 2000000000000000000000 : ℚ))) + (U' := (750781700068199641057 / 2000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47892569387 / 800000000000 : ℚ)) + (s := (89346070072959 / 2000000000000000 : ℚ)) + (q := (181945026151459 / 4000000000000000 : ℚ)) + (U := (-(6180690102931800358943 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_104_4 : Uω (aρ 4) (bρ 4) (47892569387 / 800000000000 : ℝ) ≤ @@ -1088,25 +1017,21 @@ lemma U_104_4 : have hlg : Real.log (710142503980007 / 20000000000000000 : ℝ) ≤ (-(33380218915095679924057 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (710142503980007 / 20000000000000000 : ℝ) = - (710142503980007 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (710142503980007 / 625000000000000 : ℚ)) - (U := (1277140099904320075943 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (710142503980007 / 625000000000000 : ℝ) ≤ - (1277140099904320075943 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325441904652507 / 10000000000000000 : ℝ)) (q := - (710142503980007 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (710142503980007 / 20000000000000000 : ℚ)) + (r' := (710142503980007 / 625000000000000 : ℚ)) + (U := (-(33380218915095679924057 / 10000000000000000000000 : ℚ))) + (U' := (1277140099904320075943 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47892569387 / 800000000000 : ℚ)) + (s := (325441904652507 / 10000000000000000 : ℚ)) + (q := (710142503980007 / 20000000000000000 : ℚ)) + (U := (-(33380218915095679924057 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_104_5 : Uω (aρ 5) (bρ 5) (47892569387 / 800000000000 : ℝ) ≤ @@ -1258,25 +1183,21 @@ lemma U_105_1 : have hlg : Real.log (1127600083104993 / 20000000000000000 : ℝ) ≤ (-(7189101795739181296169 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1127600083104993 / 20000000000000000 : ℝ) = - (1127600083104993 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1127600083104993 / 625000000000000 : ℚ)) - (U := (1475237958010818703831 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1127600083104993 / 625000000000000 : ℝ) ≤ - (1475237958010818703831 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (563513294706243 / 10000000000000000 : ℝ)) (q := - (1127600083104993 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1127600083104993 / 20000000000000000 : ℚ)) + (r' := (1127600083104993 / 625000000000000 : ℚ)) + (U := (-(7189101795739181296169 / 2500000000000000000000 : ℚ))) + (U' := (1475237958010818703831 / 2500000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (502867205187 / 8000000000000 : ℚ)) + (s := (563513294706243 / 10000000000000000 : ℚ)) + (q := (1127600083104993 / 20000000000000000 : ℚ)) + (U := (-(7189101795739181296169 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_105_2 : Uω (aρ 2) (bρ 2) (502867205187 / 8000000000000 : ℝ) ≤ @@ -1284,25 +1205,21 @@ lemma U_105_2 : have hlg : Real.log (1076694127943669 / 20000000000000000 : ℝ) ≤ (-(1826148073864402492947 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1076694127943669 / 20000000000000000 : ℝ) = - (1076694127943669 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1076694127943669 / 625000000000000 : ℚ)) - (U := (339936864573097507053 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1076694127943669 / 625000000000000 : ℝ) ≤ - (339936864573097507053 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (536376352054919 / 10000000000000000 : ℝ)) (q := - (1076694127943669 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1076694127943669 / 20000000000000000 : ℚ)) + (r' := (1076694127943669 / 625000000000000 : ℚ)) + (U := (-(1826148073864402492947 / 625000000000000000000 : ℚ))) + (U' := (339936864573097507053 / 625000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (502867205187 / 8000000000000 : ℚ)) + (s := (536376352054919 / 10000000000000000 : ℚ)) + (q := (1076694127943669 / 20000000000000000 : ℚ)) + (U := (-(1826148073864402492947 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_105_3 : Uω (aρ 3) (bρ 3) (502867205187 / 8000000000000 : ℝ) ≤ @@ -1310,25 +1227,21 @@ lemma U_105_3 : have hlg : Real.log (970598978574067 / 20000000000000000 : ℝ) ≤ (-(1210229666652526991207 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (970598978574067 / 20000000000000000 : ℝ) = - (970598978574067 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (970598978574067 / 625000000000000 : ℚ)) - (U := (176064693947473008793 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (970598978574067 / 625000000000000 : ℝ) ≤ - (176064693947473008793 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (477677309035317 / 10000000000000000 : ℝ)) (q := - (970598978574067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (970598978574067 / 20000000000000000 : ℚ)) + (r' := (970598978574067 / 625000000000000 : ℚ)) + (U := (-(1210229666652526991207 / 400000000000000000000 : ℚ))) + (U' := (176064693947473008793 / 400000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (502867205187 / 8000000000000 : ℚ)) + (s := (477677309035317 / 10000000000000000 : ℚ)) + (q := (970598978574067 / 20000000000000000 : ℚ)) + (U := (-(1210229666652526991207 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_105_4 : Uω (aρ 4) (bρ 4) (502867205187 / 8000000000000 : ℝ) ≤ @@ -1336,24 +1249,21 @@ lemma U_105_4 : have hlg : Real.log (38747605742901 / 1000000000000000 : ℝ) ≤ (-(16253431555359706555137 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (38747605742901 / 1000000000000000 : ℝ) = (38747605742901 / 31250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38747605742901 / 31250000000000 : ℚ)) - (U := (1075247952140293444863 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (38747605742901 / 31250000000000 : ℝ) ≤ - (1075247952140293444863 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36032462638427 / 1000000000000000 : ℝ)) (q := - (38747605742901 / 1000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38747605742901 / 1000000000000000 : ℚ)) + (r' := (38747605742901 / 31250000000000 : ℚ)) + (U := (-(16253431555359706555137 / 5000000000000000000000 : ℚ))) + (U' := (1075247952140293444863 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (502867205187 / 8000000000000 : ℚ)) + (s := (36032462638427 / 1000000000000000 : ℚ)) + (q := (38747605742901 / 1000000000000000 : ℚ)) + (U := (-(16253431555359706555137 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_105_5 : Uω (aρ 5) (bρ 5) (502867205187 / 8000000000000 : ℝ) ≤ @@ -1505,25 +1415,21 @@ lemma U_106_1 : have hlg : Real.log (1187482781690451 / 20000000000000000 : ℝ) ≤ (-(28238965150618197558677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1187482781690451 / 20000000000000000 : ℝ) = - (1187482781690451 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1187482781690451 / 625000000000000 : ℚ)) - (U := (6418393864381802441323 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1187482781690451 / 625000000000000 : ℝ) ≤ - (6418393864381802441323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (593469104145451 / 10000000000000000 : ℝ)) (q := - (1187482781690451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1187482781690451 / 20000000000000000 : ℚ)) + (r' := (1187482781690451 / 625000000000000 : ℚ)) + (U := (-(28238965150618197558677 / 10000000000000000000000 : ℚ))) + (U' := (6418393864381802441323 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (65851089563 / 1000000000000 : ℚ)) + (s := (593469104145451 / 10000000000000000 : ℚ)) + (q := (1187482781690451 / 20000000000000000 : ℚ)) + (U := (-(28238965150618197558677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_106_2 : Uω (aρ 2) (bρ 2) (65851089563 / 1000000000000 : ℝ) ≤ @@ -1531,25 +1437,21 @@ lemma U_106_2 : have hlg : Real.log (568378078312381 / 10000000000000000 : ℝ) ≤ (-(28675535425575934481119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (568378078312381 / 10000000000000000 : ℝ) = - (568378078312381 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (568378078312381 / 312500000000000 : ℚ)) - (U := (5981823589424065518881 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (568378078312381 / 312500000000000 : ℝ) ≤ - (5981823589424065518881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (283255745794881 / 5000000000000000 : ℝ)) (q := - (568378078312381 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (568378078312381 / 10000000000000000 : ℚ)) + (r' := (568378078312381 / 312500000000000 : ℚ)) + (U := (-(28675535425575934481119 / 10000000000000000000000 : ℚ))) + (U' := (5981823589424065518881 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (65851089563 / 1000000000000 : ℚ)) + (s := (283255745794881 / 5000000000000000 : ℚ)) + (q := (568378078312381 / 10000000000000000 : ℚ)) + (U := (-(28675535425575934481119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_106_3 : Uω (aρ 3) (bρ 3) (65851089563 / 1000000000000 : ℝ) ≤ @@ -1557,25 +1459,21 @@ lemma U_106_3 : have hlg : Real.log (1031350726414239 / 20000000000000000 : ℝ) ≤ (-(29648629442586589394293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1031350726414239 / 20000000000000000 : ℝ) = - (1031350726414239 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1031350726414239 / 625000000000000 : ℚ)) - (U := (5008729572413410605707 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1031350726414239 / 625000000000000 : ℝ) ≤ - (5008729572413410605707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (508502167729239 / 10000000000000000 : ℝ)) (q := - (1031350726414239 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1031350726414239 / 20000000000000000 : ℚ)) + (r' := (1031350726414239 / 625000000000000 : ℚ)) + (U := (-(29648629442586589394293 / 10000000000000000000000 : ℚ))) + (U' := (5008729572413410605707 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (65851089563 / 1000000000000 : ℚ)) + (s := (508502167729239 / 10000000000000000 : ℚ)) + (q := (1031350726414239 / 20000000000000000 : ℚ)) + (U := (-(29648629442586589394293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_106_4 : Uω (aρ 4) (bρ 4) (65851089563 / 1000000000000 : ℝ) ≤ @@ -1583,25 +1481,21 @@ lemma U_106_4 : have hlg : Real.log (419474093477657 / 10000000000000000 : ℝ) ≤ (-(7928346505977301990569 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (419474093477657 / 10000000000000000 : ℝ) = - (419474093477657 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (419474093477657 / 312500000000000 : ℚ)) - (U := (735993247772698009431 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (419474093477657 / 312500000000000 : ℝ) ≤ - (735993247772698009431 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (197196904667657 / 5000000000000000 : ℝ)) (q := - (419474093477657 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (419474093477657 / 10000000000000000 : ℚ)) + (r' := (419474093477657 / 312500000000000 : ℚ)) + (U := (-(7928346505977301990569 / 2500000000000000000000 : ℚ))) + (U' := (735993247772698009431 / 2500000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (65851089563 / 1000000000000 : ℚ)) + (s := (197196904667657 / 5000000000000000 : ℚ)) + (q := (419474093477657 / 10000000000000000 : ℚ)) + (U := (-(7928346505977301990569 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_106_5 : Uω (aρ 5) (bρ 5) (65851089563 / 1000000000000 : ℝ) ≤ @@ -1754,25 +1648,21 @@ lemma U_107_1 : have hlg : Real.log (483404390005741 / 8000000000000000 : ℝ) ≤ (-(7015858174040562655969 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (483404390005741 / 8000000000000000 : ℝ) = - (483404390005741 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (483404390005741 / 250000000000000 : ℚ)) - (U := (1648481579709437344031 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (483404390005741 / 250000000000000 : ℝ) ≤ - (1648481579709437344031 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3774924616369 / 62500000000000 : ℝ)) (q := - (483404390005741 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (483404390005741 / 8000000000000000 : ℚ)) + (r' := (483404390005741 / 250000000000000 : ℚ)) + (U := (-(7015858174040562655969 / 2500000000000000000000 : ℚ))) + (U' := (1648481579709437344031 / 2500000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2140864814337 / 32000000000000 : ℚ)) + (s := (3774924616369 / 62500000000000 : ℚ)) + (q := (483404390005741 / 8000000000000000 : ℚ)) + (U := (-(7015858174040562655969 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_107_2 : Uω (aρ 2) (bρ 2) (2140864814337 / 32000000000000 : ℝ) ≤ @@ -1780,25 +1670,21 @@ lemma U_107_2 : have hlg : Real.log (463137145245269 / 8000000000000000 : ℝ) ≤ (-(3561466998880705627953 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (463137145245269 / 8000000000000000 : ℝ) = - (463137145245269 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (463137145245269 / 250000000000000 : ℚ)) - (U := (770702877994294372047 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (463137145245269 / 250000000000000 : ℝ) ≤ - (770702877994294372047 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28854441961393 / 500000000000000 : ℝ)) (q := - (463137145245269 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (463137145245269 / 8000000000000000 : ℚ)) + (r' := (463137145245269 / 250000000000000 : ℚ)) + (U := (-(3561466998880705627953 / 1250000000000000000000 : ℚ))) + (U' := (770702877994294372047 / 1250000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2140864814337 / 32000000000000 : ℚ)) + (s := (28854441961393 / 500000000000000 : ℚ)) + (q := (463137145245269 / 8000000000000000 : ℚ)) + (U := (-(3561466998880705627953 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_107_3 : Uω (aρ 3) (bρ 3) (2140864814337 / 32000000000000 : ℝ) ≤ @@ -1806,25 +1692,21 @@ lemma U_107_3 : have hlg : Real.log (421063944006301 / 8000000000000000 : ℝ) ≤ (-(14722060556063304097267 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (421063944006301 / 8000000000000000 : ℝ) = - (421063944006301 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (421063944006301 / 250000000000000 : ℚ)) - (U := (2606618951436695902733 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (421063944006301 / 250000000000000 : ℝ) ≤ - (2606618951436695902733 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12982548562011 / 250000000000000 : ℝ)) (q := - (421063944006301 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (421063944006301 / 8000000000000000 : ℚ)) + (r' := (421063944006301 / 250000000000000 : ℚ)) + (U := (-(14722060556063304097267 / 5000000000000000000000 : ℚ))) + (U' := (2606618951436695902733 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2140864814337 / 32000000000000 : ℚ)) + (s := (12982548562011 / 250000000000000 : ℚ)) + (q := (421063944006301 / 8000000000000000 : ℚ)) + (U := (-(14722060556063304097267 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_107_4 : Uω (aρ 4) (bρ 4) (2140864814337 / 32000000000000 : ℝ) ≤ @@ -1832,25 +1714,21 @@ lemma U_107_4 : have hlg : Real.log (1722533495644141 / 40000000000000000 : ℝ) ≤ (-(6290166566300702968681 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1722533495644141 / 40000000000000000 : ℝ) = - (1722533495644141 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1722533495644141 / 1250000000000000 : ℚ)) - (U := (641305236699297031319 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1722533495644141 / 1250000000000000 : ℝ) ≤ - (641305236699297031319 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203101505675879 / 5000000000000000 : ℝ)) (q := - (1722533495644141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1722533495644141 / 40000000000000000 : ℚ)) + (r' := (1722533495644141 / 1250000000000000 : ℚ)) + (U := (-(6290166566300702968681 / 2000000000000000000000 : ℚ))) + (U' := (641305236699297031319 / 2000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2140864814337 / 32000000000000 : ℚ)) + (s := (203101505675879 / 5000000000000000 : ℚ)) + (q := (1722533495644141 / 40000000000000000 : ℚ)) + (U := (-(6290166566300702968681 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_107_5 : Uω (aρ 5) (bρ 5) (2140864814337 / 32000000000000 : ℝ) ≤ @@ -1858,25 +1736,21 @@ lemma U_107_5 : have hlg : Real.log (840723189842747 / 40000000000000000 : ℝ) ≤ (-(38623722698065706631519 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (840723189842747 / 40000000000000000 : ℝ) = - (840723189842747 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (840723189842747 / 625000000000000 : ℚ)) - (U := (2965108119934293368481 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (840723189842747 / 625000000000000 : ℝ) ≤ - (2965108119934293368481 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83487777786061 / 10000000000000000 : ℝ)) (q := - (840723189842747 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (840723189842747 / 40000000000000000 : ℚ)) + (r' := (840723189842747 / 625000000000000 : ℚ)) + (U := (-(38623722698065706631519 / 10000000000000000000000 : ℚ))) + (U' := (2965108119934293368481 / 10000000000000000000000 : ℚ)) + 6 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2140864814337 / 32000000000000 : ℚ)) + (s := (83487777786061 / 10000000000000000 : ℚ)) + (q := (840723189842747 / 40000000000000000 : ℚ)) + (U := (-(38623722698065706631519 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_107_6 : Uω (aρ 6) (bρ 6) (2140864814337 / 32000000000000 : ℝ) ≤ @@ -2023,25 +1897,21 @@ lemma U_108_1 : have hlg : Real.log (1229538844085863 / 20000000000000000 : ℝ) ≤ (-(13945465483393786464533 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1229538844085863 / 20000000000000000 : ℝ) = - (1229538844085863 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1229538844085863 / 625000000000000 : ℚ)) - (U := (3383214024106213535467 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1229538844085863 / 625000000000000 : ℝ) ≤ - (3383214024106213535467 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (307253224420119 / 5000000000000000 : ℝ)) (q := - (1229538844085863 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1229538844085863 / 20000000000000000 : ℚ)) + (r' := (1229538844085863 / 625000000000000 : ℚ)) + (U := (-(13945465483393786464533 / 5000000000000000000000 : ℚ))) + (U' := (3383214024106213535467 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1087247381329 / 16000000000000 : ℚ)) + (s := (307253224420119 / 5000000000000000 : ℚ)) + (q := (1229538844085863 / 20000000000000000 : ℚ)) + (U := (-(13945465483393786464533 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_108_2 : Uω (aρ 2) (bρ 2) (1087247381329 / 16000000000000 : ℝ) ≤ @@ -2049,25 +1919,21 @@ lemma U_108_2 : have hlg : Real.log (1178927130014927 / 20000000000000000 : ℝ) ≤ (-(14155637296061263611593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1178927130014927 / 20000000000000000 : ℝ) = - (1178927130014927 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1178927130014927 / 625000000000000 : ℚ)) - (U := (3173042211438736388407 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1178927130014927 / 625000000000000 : ℝ) ≤ - (3173042211438736388407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (293831873639651 / 5000000000000000 : ℝ)) (q := - (1178927130014927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1178927130014927 / 20000000000000000 : ℚ)) + (r' := (1178927130014927 / 625000000000000 : ℚ)) + (U := (-(14155637296061263611593 / 5000000000000000000000 : ℚ))) + (U' := (3173042211438736388407 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1087247381329 / 16000000000000 : ℚ)) + (s := (293831873639651 / 5000000000000000 : ℚ)) + (q := (1178927130014927 / 20000000000000000 : ℚ)) + (U := (-(14155637296061263611593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_108_3 : Uω (aρ 3) (bρ 3) (1087247381329 / 16000000000000 : ℝ) ≤ @@ -2075,25 +1941,21 @@ lemma U_108_3 : have hlg : Real.log (1073957319292933 / 20000000000000000 : ℝ) ≤ (-(29243820169079584143899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1073957319292933 / 20000000000000000 : ℝ) = - (1073957319292933 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1073957319292933 / 625000000000000 : ℚ)) - (U := (5413538845920415856101 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1073957319292933 / 625000000000000 : ℝ) ≤ - (5413538845920415856101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (132522510726827 / 2500000000000000 : ℝ)) (q := - (1073957319292933 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1073957319292933 / 20000000000000000 : ℚ)) + (r' := (1073957319292933 / 625000000000000 : ℚ)) + (U := (-(29243820169079584143899 / 10000000000000000000000 : ℚ))) + (U' := (5413538845920415856101 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1087247381329 / 16000000000000 : ℚ)) + (s := (132522510726827 / 2500000000000000 : ℚ)) + (q := (1073957319292933 / 20000000000000000 : ℚ)) + (U := (-(29243820169079584143899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_108_4 : Uω (aρ 4) (bρ 4) (1087247381329 / 16000000000000 : ℝ) ≤ @@ -2101,25 +1963,21 @@ lemma U_108_4 : have hlg : Real.log (883515901536191 / 20000000000000000 : ℝ) ≤ (-(31195782612954482994049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (883515901536191 / 20000000000000000 : ℝ) = - (883515901536191 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (883515901536191 / 625000000000000 : ℚ)) - (U := (3461576402045517005951 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (883515901536191 / 625000000000000 : ℝ) ≤ - (3461576402045517005951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (208971403107783 / 5000000000000000 : ℝ)) (q := - (883515901536191 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (883515901536191 / 20000000000000000 : ℚ)) + (r' := (883515901536191 / 625000000000000 : ℚ)) + (U := (-(31195782612954482994049 / 10000000000000000000000 : ℚ))) + (U' := (3461576402045517005951 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1087247381329 / 16000000000000 : ℚ)) + (s := (208971403107783 / 5000000000000000 : ℚ)) + (q := (883515901536191 / 20000000000000000 : ℚ)) + (U := (-(31195782612954482994049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_108_5 : Uω (aρ 5) (bρ 5) (1087247381329 / 16000000000000 : ℝ) ≤ @@ -2127,25 +1985,21 @@ lemma U_108_5 : have hlg : Real.log (466384484071707 / 20000000000000000 : ℝ) ≤ (-(1174524119975398790487 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (466384484071707 / 20000000000000000 : ℝ) = - (466384484071707 / 312500000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (466384484071707 / 312500000000000 : ℚ)) - (U := (125126843087101209513 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (466384484071707 / 312500000000000 : ℝ) ≤ - (125126843087101209513 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59500654043041 / 5000000000000000 : ℝ)) (q := - (466384484071707 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (466384484071707 / 20000000000000000 : ℚ)) + (r' := (466384484071707 / 312500000000000 : ℚ)) + (U := (-(1174524119975398790487 / 312500000000000000000 : ℚ))) + (U' := (125126843087101209513 / 312500000000000000000 : ℚ)) + 6 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1087247381329 / 16000000000000 : ℚ)) + (s := (59500654043041 / 5000000000000000 : ℚ)) + (q := (466384484071707 / 20000000000000000 : ℚ)) + (U := (-(1174524119975398790487 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_108_6 : Uω (aρ 6) (bρ 6) (1087247381329 / 16000000000000 : ℝ) ≤ @@ -2291,25 +2145,21 @@ lemma U_109_1 : have hlg : Real.log (2501132810550933 / 40000000000000000 : ℝ) ≤ (-(13860678498047024113487 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2501132810550933 / 40000000000000000 : ℝ) = - (2501132810550933 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2501132810550933 / 2500000000000000 : ℚ)) - (U := (2265107952975886513 / 5000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (2501132810550933 / 2500000000000000 : ℝ) ≤ - (2265107952975886513 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (625024651179529 / 10000000000000000 : ℝ)) (q := - (2501132810550933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2501132810550933 / 40000000000000000 : ℚ)) + (r' := (2501132810550933 / 2500000000000000 : ℚ)) + (U := (-(13860678498047024113487 / 5000000000000000000000 : ℚ))) + (U' := (2265107952975886513 / 5000000000000000000000 : ℚ)) + 4 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2208124710979 / 32000000000000 : ℚ)) + (s := (625024651179529 / 10000000000000000 : ℚ)) + (q := (2501132810550933 / 40000000000000000 : ℚ)) + (U := (-(13860678498047024113487 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_109_2 : Uω (aρ 2) (bρ 2) (2208124710979 / 32000000000000 : ℝ) ≤ @@ -2317,25 +2167,21 @@ lemma U_109_2 : have hlg : Real.log (2400018173404683 / 40000000000000000 : ℝ) ≤ (-(7033507858092569809221 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2400018173404683 / 40000000000000000 : ℝ) = - (2400018173404683 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2400018173404683 / 1250000000000000 : ℚ)) - (U := (1630831895657430190779 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2400018173404683 / 1250000000000000 : ℝ) ≤ - (1630831895657430190779 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (149559086279101 / 2500000000000000 : ℝ)) (q := - (2400018173404683 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2400018173404683 / 40000000000000000 : ℚ)) + (r' := (2400018173404683 / 1250000000000000 : ℚ)) + (U := (-(7033507858092569809221 / 2500000000000000000000 : ℚ))) + (U' := (1630831895657430190779 / 2500000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2208124710979 / 32000000000000 : ℚ)) + (s := (149559086279101 / 2500000000000000 : ℚ)) + (q := (2400018173404683 / 40000000000000000 : ℚ)) + (U := (-(7033507858092569809221 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_109_3 : Uω (aρ 3) (bρ 3) (2208124710979 / 32000000000000 : ℝ) ≤ @@ -2343,25 +2189,21 @@ lemma U_109_3 : have hlg : Real.log (2190487605624223 / 40000000000000000 : ℝ) ≤ (-(29047552827988840937373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2190487605624223 / 40000000000000000 : ℝ) = - (2190487605624223 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2190487605624223 / 1250000000000000 : ℚ)) - (U := (5609806187011159062627 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2190487605624223 / 1250000000000000 : ℝ) ≤ - (5609806187011159062627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (270433583788087 / 5000000000000000 : ℝ)) (q := - (2190487605624223 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2190487605624223 / 40000000000000000 : ℚ)) + (r' := (2190487605624223 / 1250000000000000 : ℚ)) + (U := (-(29047552827988840937373 / 10000000000000000000000 : ℚ))) + (U' := (5609806187011159062627 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2208124710979 / 32000000000000 : ℚ)) + (s := (270433583788087 / 5000000000000000 : ℚ)) + (q := (2190487605624223 / 40000000000000000 : ℚ)) + (U := (-(29047552827988840937373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_109_4 : Uω (aρ 4) (bρ 4) (2208124710979 / 32000000000000 : ℝ) ≤ @@ -2369,25 +2211,21 @@ lemma U_109_4 : have hlg : Real.log (1811402676018173 / 40000000000000000 : ℝ) ≤ (-(7736944871340474206587 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1811402676018173 / 40000000000000000 : ℝ) = - (1811402676018173 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1811402676018173 / 1250000000000000 : ℚ)) - (U := (927394882409525793413 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1811402676018173 / 1250000000000000 : ℝ) ≤ - (927394882409525793413 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (429618883838149 / 10000000000000000 : ℝ)) (q := - (1811402676018173 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1811402676018173 / 40000000000000000 : ℚ)) + (r' := (1811402676018173 / 1250000000000000 : ℚ)) + (U := (-(7736944871340474206587 / 2500000000000000000000 : ℚ))) + (U' := (927394882409525793413 / 2500000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2208124710979 / 32000000000000 : ℚ)) + (s := (429618883838149 / 10000000000000000 : ℚ)) + (q := (1811402676018173 / 40000000000000000 : ℚ)) + (U := (-(7736944871340474206587 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_109_5 : Uω (aρ 5) (bρ 5) (2208124710979 / 32000000000000 : ℝ) ≤ @@ -2395,25 +2233,21 @@ lemma U_109_5 : have hlg : Real.log (1009542158843399 / 40000000000000000 : ℝ) ≤ (-(36793825325521051304251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (1009542158843399 / 40000000000000000 : ℝ) = - (1009542158843399 / 625000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1009542158843399 / 625000000000000 : ℚ)) - (U := (4795005492478948695749 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1009542158843399 / 625000000000000 : ℝ) ≤ - (4795005492478948695749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73439272292881 / 5000000000000000 : ℝ)) (q := - (1009542158843399 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1009542158843399 / 40000000000000000 : ℚ)) + (r' := (1009542158843399 / 625000000000000 : ℚ)) + (U := (-(36793825325521051304251 / 10000000000000000000000 : ℚ))) + (U' := (4795005492478948695749 / 10000000000000000000000 : ℚ)) + 6 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2208124710979 / 32000000000000 : ℚ)) + (s := (73439272292881 / 5000000000000000 : ℚ)) + (q := (1009542158843399 / 40000000000000000 : ℚ)) + (U := (-(36793825325521051304251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_109_6 : Uω (aρ 6) (bρ 6) (2208124710979 / 32000000000000 : ℝ) ≤ @@ -2560,25 +2394,21 @@ lemma U_110_1 : have hlg : Real.log (5044320300925587 / 80000000000000000 : ℝ) ≤ (-(3454704645218149241057 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5044320300925587 / 80000000000000000 : ℝ) = - (5044320300925587 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5044320300925587 / 5000000000000000 : ℚ)) - (U := (11031256281850758943 / 1250000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5044320300925587 / 5000000000000000 : ℝ) ≤ - (11031256281850758943 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (630283641710303 / 10000000000000000 : ℝ)) (q := - (5044320300925587 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5044320300925587 / 80000000000000000 : ℚ)) + (r' := (5044320300925587 / 5000000000000000 : ℚ)) + (U := (-(3454704645218149241057 / 1250000000000000000000 : ℚ))) + (U' := (11031256281850758943 / 1250000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4449879370279 / 64000000000000 : ℚ)) + (s := (630283641710303 / 10000000000000000 : ℚ)) + (q := (5044320300925587 / 80000000000000000 : ℚ)) + (U := (-(3454704645218149241057 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_110_2 : Uω (aρ 2) (bρ 2) (4449879370279 / 64000000000000 : ℝ) ≤ @@ -2586,25 +2416,21 @@ lemma U_110_2 : have hlg : Real.log (4842196946632063 / 80000000000000000 : ℝ) ≤ (-(28046581010402783172551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4842196946632063 / 80000000000000000 : ℝ) = - (4842196946632063 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4842196946632063 / 2500000000000000 : ℚ)) - (U := (6610778004597216827449 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4842196946632063 / 2500000000000000 : ℝ) ≤ - (6610778004597216827449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (301760907823461 / 5000000000000000 : ℝ)) (q := - (4842196946632063 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4842196946632063 / 80000000000000000 : ℚ)) + (r' := (4842196946632063 / 2500000000000000 : ℚ)) + (U := (-(28046581010402783172551 / 10000000000000000000000 : ℚ))) + (U' := (6610778004597216827449 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4449879370279 / 64000000000000 : ℚ)) + (s := (301760907823461 / 5000000000000000 : ℚ)) + (q := (4842196946632063 / 80000000000000000 : ℚ)) + (U := (-(28046581010402783172551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_110_3 : Uω (aρ 3) (bρ 3) (4449879370279 / 64000000000000 : ℝ) ≤ @@ -2612,25 +2438,21 @@ lemma U_110_3 : have hlg : Real.log (4423532526790299 / 80000000000000000 : ℝ) ≤ (-(28950880422802094840081 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4423532526790299 / 80000000000000000 : ℝ) = - (4423532526790299 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4423532526790299 / 2500000000000000 : ℚ)) - (U := (5706478592197905159919 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4423532526790299 / 2500000000000000 : ℝ) ≤ - (5706478592197905159919 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (546251817036481 / 10000000000000000 : ℝ)) (q := - (4423532526790299 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4423532526790299 / 80000000000000000 : ℚ)) + (r' := (4423532526790299 / 2500000000000000 : ℚ)) + (U := (-(28950880422802094840081 / 10000000000000000000000 : ℚ))) + (U' := (5706478592197905159919 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4449879370279 / 64000000000000 : ℚ)) + (s := (546251817036481 / 10000000000000000 : ℚ)) + (q := (4423532526790299 / 80000000000000000 : ℚ)) + (U := (-(28950880422802094840081 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_110_4 : Uω (aρ 4) (bρ 4) (4449879370279 / 64000000000000 : ℝ) ≤ @@ -2638,25 +2460,21 @@ lemma U_110_4 : have hlg : Real.log (3667087060613467 / 80000000000000000 : ℝ) ≤ (-(30826290029214530827127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3667087060613467 / 80000000000000000 : ℝ) = - (3667087060613467 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3667087060613467 / 2500000000000000 : ℚ)) - (U := (3831068985785469172873 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3667087060613467 / 2500000000000000 : ℝ) ≤ - (3831068985785469172873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (435434631557273 / 10000000000000000 : ℝ)) (q := - (3667087060613467 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3667087060613467 / 80000000000000000 : ℚ)) + (r' := (3667087060613467 / 2500000000000000 : ℚ)) + (U := (-(30826290029214530827127 / 10000000000000000000000 : ℚ))) + (U' := (3831068985785469172873 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4449879370279 / 64000000000000 : ℚ)) + (s := (435434631557273 / 10000000000000000 : ℚ)) + (q := (3667087060613467 / 80000000000000000 : ℚ)) + (U := (-(30826290029214530827127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_110_5 : Uω (aρ 5) (bρ 5) (4449879370279 / 64000000000000 : ℝ) ≤ @@ -2664,25 +2482,21 @@ lemma U_110_5 : have hlg : Real.log (417921732650731 / 16000000000000000 : ℝ) ≤ (-(36450498271319145357943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (417921732650731 / 16000000000000000 : ℝ) = - (417921732650731 / 250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (417921732650731 / 250000000000000 : ℚ)) - (U := (5138332546680854642057 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (417921732650731 / 250000000000000 : ℝ) ≤ - (5138332546680854642057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (497671723601 / 31250000000000 : ℝ)) (q := - (417921732650731 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (417921732650731 / 16000000000000000 : ℚ)) + (r' := (417921732650731 / 250000000000000 : ℚ)) + (U := (-(36450498271319145357943 / 10000000000000000000000 : ℚ))) + (U' := (5138332546680854642057 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4449879370279 / 64000000000000 : ℚ)) + (s := (497671723601 / 31250000000000 : ℚ)) + (q := (417921732650731 / 16000000000000000 : ℚ)) + (U := (-(36450498271319145357943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_110_6 : Uω (aρ 6) (bρ 6) (4449879370279 / 64000000000000 : ℝ) ≤ @@ -2829,24 +2643,21 @@ lemma U_111_1 : have hlg : Real.log (63579683693473 / 1000000000000000 : ℝ) ≤ (-(27554612974095860072559 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (63579683693473 / 1000000000000000 : ℝ) = (63579683693473 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63579683693473 / 62500000000000 : ℚ)) - (U := (171274237904139927441 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (63579683693473 / 62500000000000 : ℝ) ≤ - (171274237904139927441 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63554256092321 / 1000000000000000 : ℝ)) (q := - (63579683693473 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63579683693473 / 1000000000000000 : ℚ)) + (r' := (63579683693473 / 62500000000000 : ℚ)) + (U := (-(27554612974095860072559 / 10000000000000000000000 : ℚ))) + (U' := (171274237904139927441 / 10000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22417546593 / 320000000000 : ℚ)) + (s := (63554256092321 / 1000000000000000 : ℚ)) + (q := (63579683693473 / 1000000000000000 : ℚ)) + (U := (-(27554612974095860072559 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_111_2 : Uω (aρ 2) (bρ 2) (22417546593 / 320000000000 : ℝ) ≤ @@ -2854,25 +2665,21 @@ lemma U_111_2 : have hlg : Real.log (610544426766827 / 10000000000000000 : ℝ) ≤ (-(2795989308656552345633 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (610544426766827 / 10000000000000000 : ℝ) = - (610544426766827 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (610544426766827 / 312500000000000 : ℚ)) - (U := (669746592843447654367 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (610544426766827 / 312500000000000 : ℝ) ≤ - (669746592843447654367 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152201688274351 / 2500000000000000 : ℝ)) (q := - (610544426766827 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (610544426766827 / 10000000000000000 : ℚ)) + (r' := (610544426766827 / 312500000000000 : ℚ)) + (U := (-(2795989308656552345633 / 1000000000000000000000 : ℚ))) + (U' := (669746592843447654367 / 1000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22417546593 / 320000000000 : ℚ)) + (s := (152201688274351 / 2500000000000000 : ℚ)) + (q := (610544426766827 / 10000000000000000 : ℚ)) + (U := (-(2795989308656552345633 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_111_3 : Uω (aρ 3) (bρ 3) (22417546593 / 320000000000 : ℝ) ≤ @@ -2880,25 +2687,21 @@ lemma U_111_3 : have hlg : Real.log (1116519953864983 / 20000000000000000 : ℝ) ≤ (-(14427578041578170897611 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1116519953864983 / 20000000000000000 : ℝ) = - (1116519953864983 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1116519953864983 / 625000000000000 : ℚ)) - (U := (2901101465921829102389 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1116519953864983 / 625000000000000 : ℝ) ≤ - (2901101465921829102389 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (551633959778733 / 10000000000000000 : ℝ)) (q := - (1116519953864983 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1116519953864983 / 20000000000000000 : ℚ)) + (r' := (1116519953864983 / 625000000000000 : ℚ)) + (U := (-(14427578041578170897611 / 5000000000000000000000 : ℚ))) + (U' := (2901101465921829102389 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22417546593 / 320000000000 : ℚ)) + (s := (551633959778733 / 10000000000000000 : ℚ)) + (q := (1116519953864983 / 20000000000000000 : ℚ)) + (U := (-(14427578041578170897611 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_111_4 : Uω (aρ 4) (bρ 4) (22417546593 / 320000000000 : ℝ) ≤ @@ -2906,25 +2709,21 @@ lemma U_111_4 : have hlg : Real.log (927828115562441 / 20000000000000000 : ℝ) ≤ (-(3838301319880865820711 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (927828115562441 / 20000000000000000 : ℝ) = - (927828115562441 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (927828115562441 / 625000000000000 : ℚ)) - (U := (493868556994134179289 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (927828115562441 / 625000000000000 : ℝ) ≤ - (493868556994134179289 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (441236302541191 / 10000000000000000 : ℝ)) (q := - (927828115562441 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (927828115562441 / 20000000000000000 : ℚ)) + (r' := (927828115562441 / 625000000000000 : ℚ)) + (U := (-(3838301319880865820711 / 1250000000000000000000 : ℚ))) + (U' := (493868556994134179289 / 1250000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22417546593 / 320000000000 : ℚ)) + (s := (441236302541191 / 10000000000000000 : ℚ)) + (q := (927828115562441 / 20000000000000000 : ℚ)) + (U := (-(3838301319880865820711 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_111_5 : Uω (aρ 5) (bρ 5) (22417546593 / 320000000000 : ℝ) ≤ @@ -2932,25 +2731,21 @@ lemma U_111_5 : have hlg : Real.log (134825024062817 / 5000000000000000 : ℝ) ≤ (-(36132153701588461327473 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (134825024062817 / 5000000000000000 : ℝ) = - (134825024062817 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (134825024062817 / 78125000000000 : ℚ)) - (U := (5456677116411538672527 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (134825024062817 / 78125000000000 : ℝ) ≤ - (5456677116411538672527 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85449101282509 / 5000000000000000 : ℝ)) (q := - (134825024062817 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (134825024062817 / 5000000000000000 : ℚ)) + (r' := (134825024062817 / 78125000000000 : ℚ)) + (U := (-(36132153701588461327473 / 10000000000000000000000 : ℚ))) + (U' := (5456677116411538672527 / 10000000000000000000000 : ℚ)) + 6 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22417546593 / 320000000000 : ℚ)) + (s := (85449101282509 / 5000000000000000 : ℚ)) + (q := (134825024062817 / 5000000000000000 : ℚ)) + (U := (-(36132153701588461327473 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_111_6 : Uω (aρ 6) (bρ 6) (22417546593 / 320000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U09.lean b/LeanPool/Zeta5Irrational/Table/U09.lean index 7010c21cb6..b0463585d0 100644 --- a/LeanPool/Zeta5Irrational/Table/U09.lean +++ b/LeanPool/Zeta5Irrational/Table/U09.lean @@ -24,25 +24,21 @@ lemma U_112_1 : have hlg : Real.log (5128428811782121 / 80000000000000000 : ℝ) ≤ (-(5494454591738893614821 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5128428811782121 / 80000000000000000 : ℝ) = - (5128428811782121 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5128428811782121 / 5000000000000000 : ℚ)) - (U := (50722850661106385179 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5128428811782121 / 5000000000000000 : ℝ) ≤ - (50722850661106385179 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160200352643531 / 2500000000000000 : ℝ)) (q := - (5128428811782121 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5128428811782121 / 80000000000000000 : ℚ)) + (r' := (5128428811782121 / 5000000000000000 : ℚ)) + (U := (-(5494454591738893614821 / 2000000000000000000000 : ℚ))) + (U' := (50722850661106385179 / 2000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4517139266921 / 64000000000000 : ℚ)) + (s := (160200352643531 / 2500000000000000 : ℚ)) + (q := (5128428811782121 / 80000000000000000 : ℚ)) + (U := (-(5494454591738893614821 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_112_2 : Uω (aρ 2) (bρ 2) (4517139266921 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_112_2 : have hlg : Real.log (985302360873997 / 16000000000000000 : ℝ) ≤ (-(27873954405000162249769 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (985302360873997 / 16000000000000000 : ℝ) = - (985302360873997 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (985302360873997 / 500000000000000 : ℚ)) - (U := (6783404609999837750231 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (985302360873997 / 500000000000000 : ℝ) ≤ - (6783404609999837750231 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61409117123109 / 1000000000000000 : ℝ)) (q := - (985302360873997 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (985302360873997 / 16000000000000000 : ℚ)) + (r' := (985302360873997 / 500000000000000 : ℚ)) + (U := (-(27873954405000162249769 / 10000000000000000000000 : ℚ))) + (U' := (6783404609999837750231 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4517139266921 / 64000000000000 : ℚ)) + (s := (61409117123109 / 1000000000000000 : ℚ)) + (q := (985302360873997 / 16000000000000000 : ℚ)) + (U := (-(27873954405000162249769 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_112_3 : Uω (aρ 3) (bρ 3) (4517139266921 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_112_3 : have hlg : Real.log (4508617367911213 / 80000000000000000 : ℝ) ≤ (-(179752256073111659559 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4508617367911213 / 80000000000000000 : ℝ) = - (4508617367911213 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4508617367911213 / 2500000000000000 : ℚ)) - (U := (36856237770638340441 / 62500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4508617367911213 / 2500000000000000 : ℝ) ≤ - (36856237770638340441 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (557013668466397 / 10000000000000000 : ℝ)) (q := - (4508617367911213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4508617367911213 / 80000000000000000 : ℚ)) + (r' := (4508617367911213 / 2500000000000000 : ℚ)) + (U := (-(179752256073111659559 / 62500000000000000000 : ℚ))) + (U' := (36856237770638340441 / 62500000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4517139266921 / 64000000000000 : ℚ)) + (s := (557013668466397 / 10000000000000000 : ℚ)) + (q := (4508617367911213 / 80000000000000000 : ℚ)) + (U := (-(179752256073111659559 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_112_4 : Uω (aρ 4) (bρ 4) (4517139266921 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_112_4 : have hlg : Real.log (3755483749271957 / 80000000000000000 : ℝ) ≤ (-(15294047642102670013741 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3755483749271957 / 80000000000000000 : ℝ) = - (3755483749271957 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3755483749271957 / 2500000000000000 : ℚ)) - (U := (2034631865397329986259 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3755483749271957 / 2500000000000000 : ℝ) ≤ - (2034631865397329986259 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (447024444871583 / 10000000000000000 : ℝ)) (q := - (3755483749271957 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3755483749271957 / 80000000000000000 : ℚ)) + (r' := (3755483749271957 / 2500000000000000 : ℚ)) + (U := (-(15294047642102670013741 / 5000000000000000000000 : ℚ))) + (U' := (2034631865397329986259 / 5000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4517139266921 / 64000000000000 : ℚ)) + (s := (447024444871583 / 10000000000000000 : ℚ)) + (q := (3755483749271957 / 80000000000000000 : ℚ)) + (U := (-(15294047642102670013741 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_112_5 : Uω (aρ 5) (bρ 5) (4517139266921 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_112_5 : have hlg : Real.log (444484538504269 / 16000000000000000 : ℝ) ≤ (-(35834287293306577019241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (444484538504269 / 16000000000000000 : ℝ) = - (444484538504269 / 250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (444484538504269 / 250000000000000 : ℚ)) - (U := (5754543524693422980759 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (444484538504269 / 250000000000000 : ℝ) ≤ - (5754543524693422980759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18194910001893 / 1000000000000000 : ℝ)) (q := - (444484538504269 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (444484538504269 / 16000000000000000 : ℚ)) + (r' := (444484538504269 / 250000000000000 : ℚ)) + (U := (-(35834287293306577019241 / 10000000000000000000000 : ℚ))) + (U' := (5754543524693422980759 / 10000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4517139266921 / 64000000000000 : ℚ)) + (s := (18194910001893 / 1000000000000000 : ℚ)) + (q := (444484538504269 / 16000000000000000 : ℚ)) + (U := (-(35834287293306577019241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_112_6 : Uω (aρ 6) (bρ 6) (4517139266921 / 64000000000000 : ℝ) ≤ @@ -292,25 +272,21 @@ lemma U_113_1 : have hlg : Real.log (517048265663313 / 8000000000000000 : ℝ) ≤ (-(27390605922888495679481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (517048265663313 / 8000000000000000 : ℝ) = - (517048265663313 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (517048265663313 / 500000000000000 : ℚ)) - (U := (335281289111504320519 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (517048265663313 / 500000000000000 : ℝ) ≤ - (335281289111504320519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16151504809043 / 250000000000000 : ℝ)) (q := - (517048265663313 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (517048265663313 / 8000000000000000 : ℚ)) + (r' := (517048265663313 / 500000000000000 : ℚ)) + (U := (-(27390605922888495679481 / 10000000000000000000000 : ℚ))) + (U' := (335281289111504320519 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2275384607621 / 32000000000000 : ℚ)) + (s := (16151504809043 / 250000000000000 : ℚ)) + (q := (517048265663313 / 8000000000000000 : ℚ)) + (U := (-(27390605922888495679481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_113_2 : Uω (aρ 2) (bρ 2) (2275384607621 / 32000000000000 : ℝ) ≤ @@ -318,25 +294,21 @@ lemma U_113_2 : have hlg : Real.log (2484333085253499 / 40000000000000000 : ℝ) ≤ (-(13894376027202381802373 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2484333085253499 / 40000000000000000 : ℝ) = - (2484333085253499 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2484333085253499 / 1250000000000000 : ℚ)) - (U := (3434303480297618197627 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2484333085253499 / 1250000000000000 : ℝ) ≤ - (3434303480297618197627 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (619375083340187 / 10000000000000000 : ℝ)) (q := - (2484333085253499 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2484333085253499 / 40000000000000000 : ℚ)) + (r' := (2484333085253499 / 1250000000000000 : ℚ)) + (U := (-(13894376027202381802373 / 5000000000000000000000 : ℚ))) + (U' := (3434303480297618197627 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2275384607621 / 32000000000000 : ℚ)) + (s := (619375083340187 / 10000000000000000 : ℚ)) + (q := (2484333085253499 / 40000000000000000 : ℚ)) + (U := (-(13894376027202381802373 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_113_3 : Uω (aρ 3) (bρ 3) (2275384607621 / 32000000000000 : ℝ) ≤ @@ -344,25 +316,21 @@ lemma U_113_3 : have hlg : Real.log (2275572731773867 / 40000000000000000 : ℝ) ≤ (-(14333238409323982707187 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2275572731773867 / 40000000000000000 : ℝ) = - (2275572731773867 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2275572731773867 / 1250000000000000 : ℚ)) - (U := (2995441098176017292813 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2275572731773867 / 1250000000000000 : ℝ) ≤ - (2995441098176017292813 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (562391012950371 / 10000000000000000 : ℝ)) (q := - (2275572731773867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2275572731773867 / 40000000000000000 : ℚ)) + (r' := (2275572731773867 / 1250000000000000 : ℚ)) + (U := (-(14333238409323982707187 / 5000000000000000000000 : ℚ))) + (U' := (2995441098176017292813 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2275384607621 / 32000000000000 : ℚ)) + (s := (562391012950371 / 10000000000000000 : ℚ)) + (q := (2275572731773867 / 40000000000000000 : ℚ)) + (U := (-(14333238409323982707187 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_113_4 : Uω (aρ 4) (bρ 4) (2275384607621 / 32000000000000 : ℝ) ≤ @@ -370,25 +338,21 @@ lemma U_113_4 : have hlg : Real.log (1899801498462243 / 40000000000000000 : ℝ) ≤ (-(15235650232966056679897 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1899801498462243 / 40000000000000000 : ℝ) = - (1899801498462243 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1899801498462243 / 1250000000000000 : ℚ)) - (U := (2093029274533943320103 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1899801498462243 / 1250000000000000 : ℝ) ≤ - (2093029274533943320103 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (452799577359559 / 10000000000000000 : ℝ)) (q := - (1899801498462243 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1899801498462243 / 40000000000000000 : ℚ)) + (r' := (1899801498462243 / 1250000000000000 : ℚ)) + (U := (-(15235650232966056679897 / 5000000000000000000000 : ℚ))) + (U' := (2093029274533943320103 / 5000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2275384607621 / 32000000000000 : ℚ)) + (s := (452799577359559 / 10000000000000000 : ℚ)) + (q := (1899801498462243 / 40000000000000000 : ℚ)) + (U := (-(15235650232966056679897 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_113_5 : Uω (aρ 5) (bρ 5) (2275384607621 / 32000000000000 : ℝ) ≤ @@ -396,25 +360,21 @@ lemma U_113_5 : have hlg : Real.log (228568373818183 / 8000000000000000 : ℝ) ≤ (-(17776807122822487646779 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (228568373818183 / 8000000000000000 : ℝ) = - (228568373818183 / 125000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (228568373818183 / 125000000000000 : ℚ)) - (U := (3017608286177512353221 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (228568373818183 / 125000000000000 : ℝ) ≤ - (3017608286177512353221 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38501936401779 / 2000000000000000 : ℝ)) (q := - (228568373818183 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (228568373818183 / 8000000000000000 : ℚ)) + (r' := (228568373818183 / 125000000000000 : ℚ)) + (U := (-(17776807122822487646779 / 5000000000000000000000 : ℚ))) + (U' := (3017608286177512353221 / 5000000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2275384607621 / 32000000000000 : ℚ)) + (s := (38501936401779 / 2000000000000000 : ℚ)) + (q := (228568373818183 / 8000000000000000 : ℚ)) + (U := (-(17776807122822487646779 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_113_6 : Uω (aρ 6) (bρ 6) (2275384607621 / 32000000000000 : ℝ) ≤ @@ -562,25 +522,21 @@ lemma U_114_1 : have hlg : Real.log (5212536236606059 / 80000000000000000 : ℝ) ≤ (-(853425029583273381449 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5212536236606059 / 80000000000000000 : ℝ) = - (5212536236606059 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5212536236606059 / 5000000000000000 : ℚ)) - (U := (13008945791726618551 / 312500000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5212536236606059 / 5000000000000000 : ℝ) ≤ - (13008945791726618551 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (162829726982449 / 2500000000000000 : ℝ)) (q := - (5212536236606059 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5212536236606059 / 80000000000000000 : ℚ)) + (r' := (5212536236606059 / 5000000000000000 : ℚ)) + (U := (-(853425029583273381449 / 312500000000000000000 : ℚ))) + (U' := (13008945791726618551 / 312500000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4584399163563 / 64000000000000 : ℚ)) + (s := (162829726982449 / 2500000000000000 : ℚ)) + (q := (5212536236606059 / 80000000000000000 : ℚ)) + (U := (-(853425029583273381449 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_114_2 : Uω (aρ 2) (bρ 2) (4584399163563 / 64000000000000 : ℝ) ≤ @@ -588,25 +544,21 @@ lemma U_114_2 : have hlg : Real.log (200432742556419 / 3200000000000000 : ℝ) ≤ (-(13852136729366462766811 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (200432742556419 / 3200000000000000 : ℝ) = - (200432742556419 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (200432742556419 / 200000000000000 : ℚ)) - (U := (10806876633537233189 / 5000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (200432742556419 / 200000000000000 : ℝ) ≤ - (10806876633537233189 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6246585022659 / 100000000000000 : ℝ)) (q := - (200432742556419 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (200432742556419 / 3200000000000000 : ℚ)) + (r' := (200432742556419 / 200000000000000 : ℚ)) + (U := (-(13852136729366462766811 / 5000000000000000000000 : ℚ))) + (U' := (10806876633537233189 / 5000000000000000000000 : ℚ)) + 4 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4584399163563 / 64000000000000 : ℚ)) + (s := (6246585022659 / 100000000000000 : ℚ)) + (q := (200432742556419 / 3200000000000000 : ℚ)) + (U := (-(13852136729366462766811 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_114_3 : Uω (aρ 3) (bρ 3) (4584399163563 / 64000000000000 : ℝ) ≤ @@ -614,25 +566,21 @@ lemma U_114_3 : have hlg : Real.log (918732874213519 / 16000000000000000 : ℝ) ≤ (-(3571685737350867667193 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (918732874213519 / 16000000000000000 : ℝ) = - (918732874213519 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (918732874213519 / 500000000000000 : ℚ)) - (U := (760484139524132332807 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (918732874213519 / 500000000000000 : ℝ) ≤ - (760484139524132332807 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28388303020259 / 500000000000000 : ℝ)) (q := - (918732874213519 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (918732874213519 / 16000000000000000 : ℚ)) + (r' := (918732874213519 / 500000000000000 : ℚ)) + (U := (-(3571685737350867667193 / 1250000000000000000000 : ℚ))) + (U' := (760484139524132332807 / 1250000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4584399163563 / 64000000000000 : ℚ)) + (s := (28388303020259 / 500000000000000 : ℚ)) + (q := (918732874213519 / 16000000000000000 : ℚ)) + (U := (-(3571685737350867667193 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_114_4 : Uω (aρ 4) (bρ 4) (4584399163563 / 64000000000000 : ℝ) ≤ @@ -640,25 +588,21 @@ lemma U_114_4 : have hlg : Real.log (3843672171359951 / 80000000000000000 : ℝ) ≤ (-(30355984291079358506601 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3843672171359951 / 80000000000000000 : ℝ) = - (3843672171359951 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3843672171359951 / 2500000000000000 : ℚ)) - (U := (4301374723920641493399 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3843672171359951 / 2500000000000000 : ℝ) ≤ - (4301374723920641493399 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (458562191543269 / 10000000000000000 : ℝ)) (q := - (3843672171359951 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3843672171359951 / 80000000000000000 : ℚ)) + (r' := (3843672171359951 / 2500000000000000 : ℚ)) + (U := (-(30355984291079358506601 / 10000000000000000000000 : ℚ))) + (U' := (4301374723920641493399 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4584399163563 / 64000000000000 : ℚ)) + (s := (458562191543269 / 10000000000000000 : ℚ)) + (q := (3843672171359951 / 80000000000000000 : ℚ)) + (U := (-(30355984291079358506601 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_114_5 : Uω (aρ 5) (bρ 5) (4584399163563 / 64000000000000 : ℝ) ≤ @@ -666,25 +610,21 @@ lemma U_114_5 : have hlg : Real.log (2347290188291931 / 80000000000000000 : ℝ) ≤ (-(8821912704169286925593 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (2347290188291931 / 80000000000000000 : ℝ) = - (2347290188291931 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2347290188291931 / 1250000000000000 : ℚ)) - (U := (1575295000330713074407 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2347290188291931 / 1250000000000000 : ℝ) ≤ - (1575295000330713074407 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6333019222227 / 312500000000000 : ℝ)) (q := - (2347290188291931 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2347290188291931 / 80000000000000000 : ℚ)) + (r' := (2347290188291931 / 1250000000000000 : ℚ)) + (U := (-(8821912704169286925593 / 2500000000000000000000 : ℚ))) + (U' := (1575295000330713074407 / 2500000000000000000000 : ℚ)) + 6 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4584399163563 / 64000000000000 : ℚ)) + (s := (6333019222227 / 312500000000000 : ℚ)) + (q := (2347290188291931 / 80000000000000000 : ℚ)) + (U := (-(8821912704169286925593 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_114_6 : Uω (aρ 6) (bρ 6) (4584399163563 / 64000000000000 : ℝ) ≤ @@ -831,25 +771,21 @@ lemma U_115_1 : have hlg : Real.log (1313647389516337 / 20000000000000000 : ℝ) ≤ (-(13614623686929618077151 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1313647389516337 / 20000000000000000 : ℝ) = - (1313647389516337 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1313647389516337 / 1250000000000000 : ℚ)) - (U := (248319919070381922849 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1313647389516337 / 1250000000000000 : ℝ) ≤ - (248319919070381922849 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (328288779434731 / 5000000000000000 : ℝ)) (q := - (1313647389516337 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1313647389516337 / 20000000000000000 : ℚ)) + (r' := (1313647389516337 / 1250000000000000 : ℚ)) + (U := (-(13614623686929618077151 / 5000000000000000000000 : ℚ))) + (U' := (248319919070381922849 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1154507277971 / 16000000000000 : ℚ)) + (s := (328288779434731 / 5000000000000000 : ℚ)) + (q := (1313647389516337 / 20000000000000000 : ℚ)) + (U := (-(13614623686929618077151 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_115_2 : Uω (aρ 2) (bρ 2) (1154507277971 / 16000000000000 : ℝ) ≤ @@ -857,25 +793,21 @@ lemma U_115_2 : have hlg : Real.log (631621129277163 / 10000000000000000 : ℝ) ≤ (-(27620506355407504983373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (631621129277163 / 10000000000000000 : ℝ) = - (631621129277163 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (631621129277163 / 625000000000000 : ℚ)) - (U := (105380856592495016627 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (631621129277163 / 625000000000000 : ℝ) ≤ - (105380856592495016627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (629941440417451 / 10000000000000000 : ℝ)) (q := - (631621129277163 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (631621129277163 / 10000000000000000 : ℚ)) + (r' := (631621129277163 / 625000000000000 : ℚ)) + (U := (-(27620506355407504983373 / 10000000000000000000000 : ℚ))) + (U' := (105380856592495016627 / 10000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1154507277971 / 16000000000000 : ℚ)) + (s := (629941440417451 / 10000000000000000 : ℚ)) + (q := (631621129277163 / 10000000000000000 : ℚ)) + (U := (-(27620506355407504983373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_115_3 : Uω (aρ 3) (bρ 3) (1154507277971 / 16000000000000 : ℝ) ≤ @@ -883,25 +815,21 @@ lemma U_115_3 : have hlg : Real.log (1159043587244137 / 20000000000000000 : ℝ) ≤ (-(28481371009729646648441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1159043587244137 / 20000000000000000 : ℝ) = - (1159043587244137 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1159043587244137 / 625000000000000 : ℚ)) - (U := (6175988005270353351559 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1159043587244137 / 625000000000000 : ℝ) ≤ - (6175988005270353351559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (286569437728631 / 5000000000000000 : ℝ)) (q := - (1159043587244137 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1159043587244137 / 20000000000000000 : ℚ)) + (r' := (1159043587244137 / 625000000000000 : ℚ)) + (U := (-(28481371009729646648441 / 10000000000000000000000 : ℚ))) + (U' := (6175988005270353351559 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1154507277971 / 16000000000000 : ℚ)) + (s := (286569437728631 / 5000000000000000 : ℚ)) + (q := (1159043587244137 / 20000000000000000 : ℚ)) + (U := (-(28481371009729646648441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_115_4 : Uω (aρ 4) (bρ 4) (1154507277971 / 16000000000000 : ℝ) ≤ @@ -909,25 +837,21 @@ lemma U_115_4 : have hlg : Real.log (971923284241157 / 20000000000000000 : ℝ) ≤ (-(15121053377842898206551 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (971923284241157 / 20000000000000000 : ℝ) = - (971923284241157 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (971923284241157 / 625000000000000 : ℚ)) - (U := (2207626129657101793449 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (971923284241157 / 625000000000000 : ℝ) ≤ - (2207626129657101793449 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (232156376759641 / 5000000000000000 : ℝ)) (q := - (971923284241157 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (971923284241157 / 20000000000000000 : ℚ)) + (r' := (971923284241157 / 625000000000000 : ℚ)) + (U := (-(15121053377842898206551 / 5000000000000000000000 : ℚ))) + (U' := (2207626129657101793449 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1154507277971 / 16000000000000 : ℚ)) + (s := (232156376759641 / 5000000000000000 : ℚ)) + (q := (971923284241157 / 20000000000000000 : ℚ)) + (U := (-(15121053377842898206551 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_115_5 : Uω (aρ 5) (bρ 5) (1154507277971 / 16000000000000 : ℝ) ≤ @@ -935,25 +859,21 @@ lemma U_115_5 : have hlg : Real.log (150467447175143 / 5000000000000000 : ℝ) ≤ (-(8758616067257419857111 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (150467447175143 / 5000000000000000 : ℝ) = - (150467447175143 / 78125000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (150467447175143 / 78125000000000 : ℚ)) - (U := (1638591637242580142889 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (150467447175143 / 78125000000000 : ℝ) ≤ - (1638591637242580142889 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (212449177313697 / 10000000000000000 : ℝ)) (q := - (150467447175143 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (150467447175143 / 5000000000000000 : ℚ)) + (r' := (150467447175143 / 78125000000000 : ℚ)) + (U := (-(8758616067257419857111 / 2500000000000000000000 : ℚ))) + (U' := (1638591637242580142889 / 2500000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1154507277971 / 16000000000000 : ℚ)) + (s := (212449177313697 / 10000000000000000 : ℚ)) + (q := (150467447175143 / 5000000000000000 : ℚ)) + (U := (-(8758616067257419857111 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_115_6 : Uω (aρ 6) (bρ 6) (1154507277971 / 16000000000000 : ℝ) ≤ @@ -1100,25 +1020,21 @@ lemma U_116_1 : have hlg : Real.log (1059328525434621 / 16000000000000000 : ℝ) ≤ (-(6787383700929643976333 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1059328525434621 / 16000000000000000 : ℝ) = - (1059328525434621 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1059328525434621 / 1000000000000000 : ℚ)) - (U := (144088102070356023667 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1059328525434621 / 1000000000000000 : ℝ) ≤ - (144088102070356023667 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (132367229344249 / 2000000000000000 : ℝ)) (q := - (1059328525434621 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1059328525434621 / 16000000000000000 : ℚ)) + (r' := (1059328525434621 / 1000000000000000 : ℚ)) + (U := (-(6787383700929643976333 / 2500000000000000000000 : ℚ))) + (U' := (144088102070356023667 / 2500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (930331812041 / 12800000000000 : ℚ)) + (s := (132367229344249 / 2000000000000000 : ℚ)) + (q := (1059328525434621 / 16000000000000000 : ℚ)) + (U := (-(6787383700929643976333 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_116_2 : Uω (aρ 2) (bρ 2) (930331812041 / 12800000000000 : ℝ) ≤ @@ -1126,25 +1042,21 @@ lemma U_116_2 : have hlg : Real.log (5095117629408681 / 80000000000000000 : ℝ) ≤ (-(3442179850001808571531 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5095117629408681 / 80000000000000000 : ℝ) = - (5095117629408681 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5095117629408681 / 5000000000000000 : ℚ)) - (U := (23556051498191428469 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5095117629408681 / 5000000000000000 : ℝ) ≤ - (23556051498191428469 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (635223909790139 / 10000000000000000 : ℝ)) (q := - (5095117629408681 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5095117629408681 / 80000000000000000 : ℚ)) + (r' := (5095117629408681 / 5000000000000000 : ℚ)) + (U := (-(3442179850001808571531 / 1250000000000000000000 : ℚ))) + (U' := (23556051498191428469 / 1250000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (930331812041 / 12800000000000 : ℚ)) + (s := (635223909790139 / 10000000000000000 : ℚ)) + (q := (5095117629408681 / 80000000000000000 : ℚ)) + (U := (-(3442179850001808571531 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_116_3 : Uω (aρ 3) (bρ 3) (930331812041 / 12800000000000 : ℝ) ≤ @@ -1152,25 +1064,21 @@ lemma U_116_3 : have hlg : Real.log (4678675646071621 / 80000000000000000 : ℝ) ≤ (-(14195057725500391424769 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4678675646071621 / 80000000000000000 : ℝ) = - (4678675646071621 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4678675646071621 / 2500000000000000 : ℚ)) - (U := (3133621781999608575231 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4678675646071621 / 2500000000000000 : ℝ) ≤ - (3133621781999608575231 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (289254760152937 / 5000000000000000 : ℝ)) (q := - (4678675646071621 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4678675646071621 / 80000000000000000 : ℚ)) + (r' := (4678675646071621 / 2500000000000000 : ℚ)) + (U := (-(14195057725500391424769 / 5000000000000000000000 : ℚ))) + (U' := (3133621781999608575231 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (930331812041 / 12800000000000 : ℚ)) + (s := (289254760152937 / 5000000000000000 : ℚ)) + (q := (4678675646071621 / 80000000000000000 : ℚ)) + (U := (-(14195057725500391424769 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_116_4 : Uω (aρ 4) (bρ 4) (930331812041 / 12800000000000 : ℝ) ≤ @@ -1178,25 +1086,21 @@ lemma U_116_4 : have hlg : Real.log (3931667663084301 / 80000000000000000 : ℝ) ≤ (-(30129629557487540673771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3931667663084301 / 80000000000000000 : ℝ) = - (3931667663084301 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3931667663084301 / 2500000000000000 : ℚ)) - (U := (4527729457512459326229 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3931667663084301 / 2500000000000000 : ℝ) ≤ - (4527729457512459326229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117512926406011 / 2500000000000000 : ℝ)) (q := - (3931667663084301 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3931667663084301 / 80000000000000000 : ℚ)) + (r' := (3931667663084301 / 2500000000000000 : ℚ)) + (U := (-(30129629557487540673771 / 10000000000000000000000 : ℚ))) + (U' := (4527729457512459326229 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (930331812041 / 12800000000000 : ℚ)) + (s := (117512926406011 / 2500000000000000 : ℚ)) + (q := (3931667663084301 / 80000000000000000 : ℚ)) + (U := (-(30129629557487540673771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_116_5 : Uω (aρ 5) (bρ 5) (930331812041 / 12800000000000 : ℝ) ≤ @@ -1204,25 +1108,21 @@ lemma U_116_5 : have hlg : Real.log (2466438291419753 / 80000000000000000 : ℝ) ≤ (-(34792515104179698616019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 6 - (show - (2466438291419753 / 80000000000000000 : ℝ) = - (2466438291419753 / 1250000000000000 : ℝ) / 2 ^ 6 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2466438291419753 / 1250000000000000 : ℚ)) - (U := (6796315713820301383981 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2466438291419753 / 1250000000000000 : ℝ) ≤ - (6796315713820301383981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221934282042907 / 10000000000000000 : ℝ)) (q := - (2466438291419753 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2466438291419753 / 80000000000000000 : ℚ)) + (r' := (2466438291419753 / 1250000000000000 : ℚ)) + (U := (-(34792515104179698616019 / 10000000000000000000000 : ℚ))) + (U' := (6796315713820301383981 / 10000000000000000000000 : ℚ)) + 6 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (930331812041 / 12800000000000 : ℚ)) + (s := (221934282042907 / 10000000000000000 : ℚ)) + (q := (2466438291419753 / 80000000000000000 : ℚ)) + (U := (-(34792515104179698616019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_116_6 : Uω (aρ 6) (bρ 6) (930331812041 / 12800000000000 : ℝ) ≤ @@ -1369,25 +1269,21 @@ lemma U_117_1 : have hlg : Real.log (106773908997941 / 1600000000000000 : ℝ) ≤ (-(13535226541398232719239 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (106773908997941 / 1600000000000000 : ℝ) = - (106773908997941 / 100000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (106773908997941 / 100000000000000 : ℚ)) - (U := (327717064601767280761 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (106773908997941 / 100000000000000 : ℝ) ≤ - (327717064601767280761 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26683786919083 / 400000000000000 : ℝ)) (q := - (106773908997941 / 1600000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (106773908997941 / 1600000000000000 : ℚ)) + (r' := (106773908997941 / 100000000000000 : ℚ)) + (U := (-(13535226541398232719239 / 5000000000000000000000 : ℚ))) + (U' := (327717064601767280761 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2342644504263 / 32000000000000 : ℚ)) + (s := (26683786919083 / 400000000000000 : ℚ)) + (q := (106773908997941 / 1600000000000000 : ℚ)) + (U := (-(13535226541398232719239 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_117_2 : Uω (aρ 2) (bρ 2) (2342644504263 / 32000000000000 : ℝ) ≤ @@ -1395,25 +1291,21 @@ lemma U_117_2 : have hlg : Real.log (2568632197939373 / 40000000000000000 : ℝ) ≤ (-(6863764786365759850067 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2568632197939373 / 40000000000000000 : ℝ) = - (2568632197939373 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2568632197939373 / 2500000000000000 : ℚ)) - (U := (67707016634240149933 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2568632197939373 / 2500000000000000 : ℝ) ≤ - (67707016634240149933 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (640505921982499 / 10000000000000000 : ℝ)) (q := - (2568632197939373 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2568632197939373 / 40000000000000000 : ℚ)) + (r' := (2568632197939373 / 2500000000000000 : ℚ)) + (U := (-(6863764786365759850067 / 2500000000000000000000 : ℚ))) + (U' := (67707016634240149933 / 2500000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2342644504263 / 32000000000000 : ℚ)) + (s := (640505921982499 / 10000000000000000 : ℚ)) + (q := (2568632197939373 / 40000000000000000 : ℚ)) + (U := (-(6863764786365759850067 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_117_3 : Uω (aρ 3) (bρ 3) (2342644504263 / 32000000000000 : ℝ) ≤ @@ -1421,25 +1313,21 @@ lemma U_117_3 : have hlg : Real.log (472116850189721 / 8000000000000000 : ℝ) ≤ (-(14149851502271592942073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (472116850189721 / 8000000000000000 : ℝ) = - (472116850189721 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (472116850189721 / 250000000000000 : ℚ)) - (U := (3178828005228407057927 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (472116850189721 / 250000000000000 : ℝ) ≤ - (3178828005228407057927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (116775610967423 / 2000000000000000 : ℝ)) (q := - (472116850189721 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (472116850189721 / 8000000000000000 : ℚ)) + (r' := (472116850189721 / 250000000000000 : ℚ)) + (U := (-(14149851502271592942073 / 5000000000000000000000 : ℚ))) + (U' := (3178828005228407057927 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2342644504263 / 32000000000000 : ℚ)) + (s := (116775610967423 / 2000000000000000 : ℚ)) + (q := (472116850189721 / 8000000000000000 : ℚ)) + (U := (-(14149851502271592942073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_117_4 : Uω (aρ 4) (bρ 4) (2342644504263 / 32000000000000 : ℝ) ≤ @@ -1447,25 +1335,21 @@ lemma U_117_4 : have hlg : Real.log (1987798715104119 / 40000000000000000 : ℝ) ≤ (-(30018515996535756825573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1987798715104119 / 40000000000000000 : ℝ) = - (1987798715104119 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1987798715104119 / 1250000000000000 : ℚ)) - (U := (4638843018464243174427 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1987798715104119 / 1250000000000000 : ℝ) ≤ - (4638843018464243174427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14868108374371 / 312500000000000 : ℝ)) (q := - (1987798715104119 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1987798715104119 / 40000000000000000 : ℚ)) + (r' := (1987798715104119 / 1250000000000000 : ℚ)) + (U := (-(30018515996535756825573 / 10000000000000000000000 : ℚ))) + (U' := (4638843018464243174427 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2342644504263 / 32000000000000 : ℚ)) + (s := (14868108374371 / 312500000000000 : ℚ)) + (q := (1987798715104119 / 40000000000000000 : ℚ)) + (U := (-(30018515996535756825573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_117_5 : Uω (aρ 5) (bρ 5) (2342644504263 / 32000000000000 : ℝ) ≤ @@ -1473,25 +1357,21 @@ lemma U_117_5 : have hlg : Real.log (1262159503365177 / 40000000000000000 : ℝ) ≤ (-(34560553073273099210261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1262159503365177 / 40000000000000000 : ℝ) = - (1262159503365177 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1262159503365177 / 1250000000000000 : ℚ)) - (U := (96805941726900789739 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1262159503365177 / 1250000000000000 : ℝ) ≤ - (96805941726900789739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231149781445401 / 10000000000000000 : ℝ)) (q := - (1262159503365177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1262159503365177 / 40000000000000000 : ℚ)) + (r' := (1262159503365177 / 1250000000000000 : ℚ)) + (U := (-(34560553073273099210261 / 10000000000000000000000 : ℚ))) + (U' := (96805941726900789739 / 10000000000000000000000 : ℚ)) + 5 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2342644504263 / 32000000000000 : ℚ)) + (s := (231149781445401 / 10000000000000000 : ℚ)) + (q := (1262159503365177 / 40000000000000000 : ℚ)) + (U := (-(34560553073273099210261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_117_6 : Uω (aρ 6) (bρ 6) (2342644504263 / 32000000000000 : ℝ) ≤ @@ -1638,25 +1518,21 @@ lemma U_118_1 : have hlg : Real.log (2143888708271497 / 32000000000000000 : ℝ) ≤ (-(6757786420885346854021 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2143888708271497 / 32000000000000000 : ℝ) = - (2143888708271497 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2143888708271497 / 2000000000000000 : ℚ)) - (U := (173685382114653145979 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2143888708271497 / 2000000000000000 : ℝ) ≤ - (173685382114653145979 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8371548918249 / 125000000000000 : ℝ)) (q := - (2143888708271497 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2143888708271497 / 32000000000000000 : ℚ)) + (r' := (2143888708271497 / 2000000000000000 : ℚ)) + (U := (-(6757786420885346854021 / 2500000000000000000000 : ℚ))) + (U' := (173685382114653145979 / 2500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9404207965373 / 128000000000000 : ℚ)) + (s := (8371548918249 / 125000000000000 : ℚ)) + (q := (2143888708271497 / 32000000000000000 : ℚ)) + (U := (-(6757786420885346854021 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_118_2 : Uω (aρ 2) (bρ 2) (9404207965373 / 128000000000000 : ℝ) ≤ @@ -1664,25 +1540,21 @@ lemma U_118_2 : have hlg : Real.log (10316674214847229 / 160000000000000000 : ℝ) ≤ (-(1096564948833060777743 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10316674214847229 / 160000000000000000 : ℝ) = - (10316674214847229 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10316674214847229 / 10000000000000000 : ℚ)) - (U := (12470539646939222257 / 400000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10316674214847229 / 10000000000000000 : ℝ) ≤ - (12470539646939222257 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (321573380078069 / 5000000000000000 : ℝ)) (q := - (10316674214847229 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10316674214847229 / 160000000000000000 : ℚ)) + (r' := (10316674214847229 / 10000000000000000 : ℚ)) + (U := (-(1096564948833060777743 / 400000000000000000000 : ℚ))) + (U' := (12470539646939222257 / 400000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9404207965373 / 128000000000000 : ℚ)) + (s := (321573380078069 / 5000000000000000 : ℚ)) + (q := (10316674214847229 / 160000000000000000 : ℚ)) + (U := (-(1096564948833060777743 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_118_3 : Uω (aρ 3) (bρ 3) (9404207965373 / 128000000000000 : ℝ) ≤ @@ -1690,25 +1562,21 @@ lemma U_118_3 : have hlg : Real.log (379392946941437 / 6400000000000000 : ℝ) ≤ (-(110370343779415330577 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (379392946941437 / 6400000000000000 : ℝ) = - (379392946941437 / 200000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (379392946941437 / 200000000000000 : ℚ)) - (U := (25009964872928419423 / 39062500000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (379392946941437 / 200000000000000 : ℝ) ≤ - (25009964872928419423 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23462461953689 / 400000000000000 : ℝ)) (q := - (379392946941437 / 6400000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (379392946941437 / 6400000000000000 : ℚ)) + (r' := (379392946941437 / 200000000000000 : ℚ)) + (U := (-(110370343779415330577 / 39062500000000000000 : ℚ))) + (U' := (25009964872928419423 / 39062500000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9404207965373 / 128000000000000 : ℚ)) + (s := (23462461953689 / 400000000000000 : ℚ)) + (q := (379392946941437 / 6400000000000000 : ℚ)) + (U := (-(110370343779415330577 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_118_4 : Uω (aρ 4) (bρ 4) (9404207965373 / 128000000000000 : ℝ) ≤ @@ -1716,25 +1584,21 @@ lemma U_118_4 : have hlg : Real.log (1599018412565393 / 32000000000000000 : ℝ) ≤ (-(1198538381065681381673 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1599018412565393 / 32000000000000000 : ℝ) = - (1599018412565393 / 1000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1599018412565393 / 1000000000000000 : ℚ)) - (U := (187755979534318618327 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1599018412565393 / 1000000000000000 : ℝ) ≤ - (187755979534318618327 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95727855713721 / 2000000000000000 : ℝ)) (q := - (1599018412565393 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1599018412565393 / 32000000000000000 : ℚ)) + (r' := (1599018412565393 / 1000000000000000 : ℚ)) + (U := (-(1198538381065681381673 / 400000000000000000000 : ℚ))) + (U' := (187755979534318618327 / 400000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9404207965373 / 128000000000000 : ℚ)) + (s := (95727855713721 / 2000000000000000 : ℚ)) + (q := (1599018412565393 / 32000000000000000 : ℚ)) + (U := (-(1198538381065681381673 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_118_5 : Uω (aρ 5) (bρ 5) (9404207965373 / 128000000000000 : ℝ) ≤ @@ -1742,25 +1606,21 @@ lemma U_118_5 : have hlg : Real.log (5105789273487933 / 160000000000000000 : ℝ) ≤ (-(34447987663370110448543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (5105789273487933 / 160000000000000000 : ℝ) = - (5105789273487933 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5105789273487933 / 5000000000000000 : ℚ)) - (U := (209371351629889551457 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5105789273487933 / 5000000000000000 : ℝ) ≤ - (209371351629889551457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117833174618113 / 5000000000000000 : ℝ)) (q := - (5105789273487933 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5105789273487933 / 160000000000000000 : ℚ)) + (r' := (5105789273487933 / 5000000000000000 : ℚ)) + (U := (-(34447987663370110448543 / 10000000000000000000000 : ℚ))) + (U' := (209371351629889551457 / 10000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9404207965373 / 128000000000000 : ℚ)) + (s := (117833174618113 / 5000000000000000 : ℚ)) + (q := (5105789273487933 / 160000000000000000 : ℚ)) + (U := (-(34447987663370110448543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_118_6 : Uω (aρ 6) (bρ 6) (9404207965373 / 128000000000000 : ℝ) ≤ @@ -1906,25 +1766,21 @@ lemma U_119_1 : have hlg : Real.log (5380748032018147 / 80000000000000000 : ℝ) ≤ (-(26991992297169125119499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5380748032018147 / 80000000000000000 : ℝ) = - (5380748032018147 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5380748032018147 / 5000000000000000 : ℚ)) - (U := (733894914830874880501 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5380748032018147 / 5000000000000000 : ℝ) ≤ - (733894914830874880501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (672353139082193 / 10000000000000000 : ℝ)) (q := - (5380748032018147 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5380748032018147 / 80000000000000000 : ℚ)) + (r' := (5380748032018147 / 5000000000000000 : ℚ)) + (U := (-(26991992297169125119499 / 10000000000000000000000 : ℚ))) + (U' := (733894914830874880501 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4718918956847 / 64000000000000 : ℚ)) + (s := (672353139082193 / 10000000000000000 : ℚ)) + (q := (5380748032018147 / 80000000000000000 : ℚ)) + (U := (-(26991992297169125119499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_119_2 : Uω (aρ 2) (bρ 2) (4718918956847 / 64000000000000 : ℝ) ≤ @@ -1932,25 +1788,21 @@ lemma U_119_2 : have hlg : Real.log (5179409378499819 / 80000000000000000 : ℝ) ≤ (-(27373356034580663451179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5179409378499819 / 80000000000000000 : ℝ) = - (5179409378499819 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5179409378499819 / 5000000000000000 : ℚ)) - (U := (352531177419336548821 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5179409378499819 / 5000000000000000 : ℝ) ≤ - (352531177419336548821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (645787488212611 / 10000000000000000 : ℝ)) (q := - (5179409378499819 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5179409378499819 / 80000000000000000 : ℚ)) + (r' := (5179409378499819 / 5000000000000000 : ℚ)) + (U := (-(27373356034580663451179 / 10000000000000000000000 : ℚ))) + (U' := (352531177419336548821 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4718918956847 / 64000000000000 : ℚ)) + (s := (645787488212611 / 10000000000000000 : ℚ)) + (q := (5179409378499819 / 80000000000000000 : ℚ)) + (U := (-(27373356034580663451179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_119_3 : Uω (aρ 3) (bρ 3) (4718918956847 / 64000000000000 : ℝ) ≤ @@ -1958,25 +1810,21 @@ lemma U_119_3 : have hlg : Real.log (4763653147175431 / 80000000000000000 : ℝ) ≤ (-(28210117915897178442261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4763653147175431 / 80000000000000000 : ℝ) = - (4763653147175431 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4763653147175431 / 2500000000000000 : ℚ)) - (U := (6447241099102821557739 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4763653147175431 / 2500000000000000 : ℝ) ≤ - (6447241099102821557739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (294622268365757 / 5000000000000000 : ℝ)) (q := - (4763653147175431 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4763653147175431 / 80000000000000000 : ℚ)) + (r' := (4763653147175431 / 2500000000000000 : ℚ)) + (U := (-(28210117915897178442261 / 10000000000000000000000 : ℚ))) + (U' := (6447241099102821557739 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4718918956847 / 64000000000000 : ℚ)) + (s := (294622268365757 / 5000000000000000 : ℚ)) + (q := (4763653147175431 / 80000000000000000 : ℚ)) + (U := (-(28210117915897178442261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_119_4 : Uω (aρ 4) (bρ 4) (4718918956847 / 64000000000000 : ℝ) ≤ @@ -1984,24 +1832,21 @@ lemma U_119_4 : have hlg : Real.log (32155872285303 / 640000000000000 : ℝ) ≤ (-(29908730883182997431499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (32155872285303 / 640000000000000 : ℝ) = (32155872285303 / 20000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32155872285303 / 20000000000000 : ℚ)) - (U := (4748628131817002568501 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32155872285303 / 20000000000000 : ℝ) ≤ - (4748628131817002568501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3851971519347 / 80000000000000 : ℝ)) (q := - (32155872285303 / 640000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32155872285303 / 640000000000000 : ℚ)) + (r' := (32155872285303 / 20000000000000 : ℚ)) + (U := (-(29908730883182997431499 / 10000000000000000000000 : ℚ))) + (U' := (4748628131817002568501 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4718918956847 / 64000000000000 : ℚ)) + (s := (3851971519347 / 80000000000000 : ℚ)) + (q := (32155872285303 / 640000000000000 : ℚ)) + (U := (-(29908730883182997431499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_119_5 : Uω (aρ 5) (bρ 5) (4718918956847 / 64000000000000 : ℝ) ≤ @@ -2009,25 +1854,21 @@ lemma U_119_5 : have hlg : Real.log (2581245470590107 / 80000000000000000 : ℝ) ≤ (-(34337546103835562865811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2581245470590107 / 80000000000000000 : ℝ) = - (2581245470590107 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2581245470590107 / 2500000000000000 : ℚ)) - (U := (319812911164437134189 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2581245470590107 / 2500000000000000 : ℝ) ≤ - (319812911164437134189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (240126717985183 / 10000000000000000 : ℝ)) (q := - (2581245470590107 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2581245470590107 / 80000000000000000 : ℚ)) + (r' := (2581245470590107 / 2500000000000000 : ℚ)) + (U := (-(34337546103835562865811 / 10000000000000000000000 : ℚ))) + (U' := (319812911164437134189 / 10000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4718918956847 / 64000000000000 : ℚ)) + (s := (240126717985183 / 10000000000000000 : ℚ)) + (q := (2581245470590107 / 80000000000000000 : ℚ)) + (U := (-(34337546103835562865811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_119_6 : Uω (aρ 6) (bρ 6) (4718918956847 / 64000000000000 : ℝ) ≤ @@ -2175,25 +2016,21 @@ lemma U_120_1 : have hlg : Real.log (10803548469219799 / 160000000000000000 : ℝ) ≤ (-(26952991720637376599691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10803548469219799 / 160000000000000000 : ℝ) = - (10803548469219799 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10803548469219799 / 10000000000000000 : ℚ)) - (U := (772895491362623400309 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10803548469219799 / 10000000000000000 : ℝ) ≤ - (772895491362623400309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (674982350017553 / 10000000000000000 : ℝ)) (q := - (10803548469219799 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10803548469219799 / 160000000000000000 : ℚ)) + (r' := (10803548469219799 / 10000000000000000 : ℚ)) + (U := (-(26952991720637376599691 / 10000000000000000000000 : ℚ))) + (U' := (772895491362623400309 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1894293572403 / 25600000000000 : ℚ)) + (s := (674982350017553 / 10000000000000000 : ℚ)) + (q := (10803548469219799 / 160000000000000000 : ℚ)) + (U := (-(26952991720637376599691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_120_2 : Uω (aρ 2) (bρ 2) (1894293572403 / 25600000000000 : ℝ) ≤ @@ -2201,25 +2038,21 @@ lemma U_120_2 : have hlg : Real.log (10400962428977599 / 160000000000000000 : ℝ) ≤ (-(13666377355402748850127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10400962428977599 / 160000000000000000 : ℝ) = - (10400962428977599 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10400962428977599 / 10000000000000000 : ℚ)) - (U := (196566250597251149873 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10400962428977599 / 10000000000000000 : ℝ) ≤ - (196566250597251149873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (324214053748639 / 5000000000000000 : ℝ)) (q := - (10400962428977599 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10400962428977599 / 160000000000000000 : ℚ)) + (r' := (10400962428977599 / 10000000000000000 : ℚ)) + (U := (-(13666377355402748850127 / 5000000000000000000000 : ℚ))) + (U' := (196566250597251149873 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1894293572403 / 25600000000000 : ℚ)) + (s := (324214053748639 / 5000000000000000 : ℚ)) + (q := (10400962428977599 / 160000000000000000 : ℚ)) + (U := (-(13666377355402748850127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_120_3 : Uω (aρ 3) (bρ 3) (1894293572403 / 25600000000000 : ℝ) ≤ @@ -2227,25 +2060,21 @@ lemma U_120_3 : have hlg : Real.log (1913956984259227 / 32000000000000000 : ℝ) ≤ (-(28165630829855142778867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1913956984259227 / 32000000000000000 : ℝ) = - (1913956984259227 / 1000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1913956984259227 / 1000000000000000 : ℚ)) - (U := (6491728185144857221133 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1913956984259227 / 1000000000000000 : ℝ) ≤ - (6491728185144857221133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (118385405077419 / 2000000000000000 : ℝ)) (q := - (1913956984259227 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1913956984259227 / 32000000000000000 : ℚ)) + (r' := (1913956984259227 / 1000000000000000 : ℚ)) + (U := (-(28165630829855142778867 / 10000000000000000000000 : ℚ))) + (U' := (6491728185144857221133 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1894293572403 / 25600000000000 : ℚ)) + (s := (118385405077419 / 2000000000000000 : ℚ)) + (q := (1913956984259227 / 32000000000000000 : ℚ)) + (U := (-(28165630829855142778867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_120_4 : Uω (aρ 4) (bρ 4) (1894293572403 / 25600000000000 : ℝ) ≤ @@ -2253,25 +2082,21 @@ lemma U_120_4 : have hlg : Real.log (8082823260978207 / 160000000000000000 : ℝ) ≤ (-(5970865177888741761793 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (8082823260978207 / 160000000000000000 : ℝ) = - (8082823260978207 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8082823260978207 / 5000000000000000 : ℚ)) - (U := (960606625111258238207 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8082823260978207 / 5000000000000000 : ℝ) ≤ - (960606625111258238207 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242175499456177 / 5000000000000000 : ℝ)) (q := - (8082823260978207 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8082823260978207 / 160000000000000000 : ℚ)) + (r' := (8082823260978207 / 5000000000000000 : ℚ)) + (U := (-(5970865177888741761793 / 2000000000000000000000 : ℚ))) + (U' := (960606625111258238207 / 2000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1894293572403 / 25600000000000 : ℚ)) + (s := (242175499456177 / 5000000000000000 : ℚ)) + (q := (8082823260978207 / 160000000000000000 : ℚ)) + (U := (-(5970865177888741761793 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_120_5 : Uω (aρ 5) (bρ 5) (1894293572403 / 25600000000000 : ℝ) ≤ @@ -2279,25 +2104,21 @@ lemma U_120_5 : have hlg : Real.log (1043753523753371 / 32000000000000000 : ℝ) ≤ (-(3422912528271636769997 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1043753523753371 / 32000000000000000 : ℝ) = - (1043753523753371 / 1000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1043753523753371 / 1000000000000000 : ℚ)) - (U := (42823373228363230003 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1043753523753371 / 1000000000000000 : ℝ) ≤ - (42823373228363230003 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48906792594187 / 2000000000000000 : ℝ)) (q := - (1043753523753371 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1043753523753371 / 32000000000000000 : ℚ)) + (r' := (1043753523753371 / 1000000000000000 : ℚ)) + (U := (-(3422912528271636769997 / 1000000000000000000000 : ℚ))) + (U' := (42823373228363230003 / 1000000000000000000000 : ℚ)) + 5 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1894293572403 / 25600000000000 : ℚ)) + (s := (48906792594187 / 2000000000000000 : ℚ)) + (q := (1043753523753371 / 32000000000000000 : ℚ)) + (U := (-(3422912528271636769997 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_120_6 : Uω (aρ 6) (bρ 6) (1894293572403 / 25600000000000 : ℝ) ≤ @@ -2445,25 +2266,21 @@ lemma U_121_1 : have hlg : Real.log (1355700094784461 / 20000000000000000 : ℝ) ≤ (-(6728535691238731355147 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1355700094784461 / 20000000000000000 : ℝ) = - (1355700094784461 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1355700094784461 / 1250000000000000 : ℚ)) - (U := (202936111761268644853 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1355700094784461 / 1250000000000000 : ℝ) ≤ - (202936111761268644853 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (677611546436961 / 10000000000000000 : ℝ)) (q := - (1355700094784461 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1355700094784461 / 20000000000000000 : ℚ)) + (r' := (1355700094784461 / 1250000000000000 : ℚ)) + (U := (-(6728535691238731355147 / 2500000000000000000000 : ℚ))) + (U' := (202936111761268644853 / 2500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (297034306573 / 4000000000000 : ℚ)) + (s := (677611546436961 / 10000000000000000 : ℚ)) + (q := (1355700094784461 / 20000000000000000 : ℚ)) + (U := (-(6728535691238731355147 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_121_2 : Uω (aρ 2) (bρ 2) (297034306573 / 4000000000000 : ℝ) ≤ @@ -2471,25 +2288,21 @@ lemma U_121_2 : have hlg : Real.log (652694077585557 / 10000000000000000 : ℝ) ≤ (-(3411539798815513981353 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (652694077585557 / 10000000000000000 : ℝ) = - (652694077585557 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (652694077585557 / 625000000000000 : ℚ)) - (U := (54196102684486018647 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (652694077585557 / 625000000000000 : ℝ) ≤ - (54196102684486018647 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325534309666807 / 5000000000000000 : ℝ)) (q := - (652694077585557 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (652694077585557 / 10000000000000000 : ℚ)) + (r' := (652694077585557 / 625000000000000 : ℚ)) + (U := (-(3411539798815513981353 / 1250000000000000000000 : ℚ))) + (U' := (54196102684486018647 / 1250000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (297034306573 / 4000000000000 : ℚ)) + (s := (325534309666807 / 5000000000000000 : ℚ)) + (q := (652694077585557 / 10000000000000000 : ℚ)) + (U := (-(3411539798815513981353 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_121_3 : Uω (aρ 3) (bρ 3) (297034306573 / 4000000000000 : ℝ) ≤ @@ -2497,25 +2310,21 @@ lemma U_121_3 : have hlg : Real.log (600766225526559 / 10000000000000000 : ℝ) ≤ (-(7030336219103306552713 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (600766225526559 / 10000000000000000 : ℝ) = - (600766225526559 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (600766225526559 / 312500000000000 : ℚ)) - (U := (1634003534646693447287 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (600766225526559 / 312500000000000 : ℝ) ≤ - (1634003534646693447287 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (297304510782809 / 5000000000000000 : ℝ)) (q := - (600766225526559 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (600766225526559 / 10000000000000000 : ℚ)) + (r' := (600766225526559 / 312500000000000 : ℚ)) + (U := (-(7030336219103306552713 / 2500000000000000000000 : ℚ))) + (U' := (1634003534646693447287 / 2500000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (297034306573 / 4000000000000 : ℚ)) + (s := (297304510782809 / 5000000000000000 : ℚ)) + (q := (600766225526559 / 10000000000000000 : ℚ)) + (U := (-(7030336219103306552713 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_121_4 : Uω (aρ 4) (bρ 4) (297034306573 / 4000000000000 : ℝ) ≤ @@ -2523,25 +2332,21 @@ lemma U_121_4 : have hlg : Real.log (507916124857619 / 10000000000000000 : ℝ) ≤ (-(3725030056597356522343 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (507916124857619 / 10000000000000000 : ℝ) = - (507916124857619 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (507916124857619 / 312500000000000 : ℚ)) - (U := (607139820277643477657 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (507916124857619 / 312500000000000 : ℝ) ≤ - (607139820277643477657 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243601500646369 / 5000000000000000 : ℝ)) (q := - (507916124857619 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (507916124857619 / 10000000000000000 : ℚ)) + (r' := (507916124857619 / 312500000000000 : ℚ)) + (U := (-(3725030056597356522343 / 1250000000000000000000 : ℚ))) + (U' := (607139820277643477657 / 1250000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (297034306573 / 4000000000000 : ℚ)) + (s := (243601500646369 / 5000000000000000 : ℚ)) + (q := (507916124857619 / 10000000000000000 : ℚ)) + (U := (-(3725030056597356522343 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_121_5 : Uω (aρ 5) (bρ 5) (297034306573 / 4000000000000 : ℝ) ≤ @@ -2549,24 +2354,21 @@ lemma U_121_5 : have hlg : Real.log (82416279421253 / 2500000000000000 : ℝ) ≤ (-(682452605272557036629 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (82416279421253 / 2500000000000000 : ℝ) = (82416279421253 / 78125000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82416279421253 / 78125000000000 : ℚ)) - (U := (10694575027442963371 / 200000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (82416279421253 / 78125000000000 : ℝ) ≤ - (10694575027442963371 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62222726570631 / 2500000000000000 : ℝ)) (q := - (82416279421253 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82416279421253 / 2500000000000000 : ℚ)) + (r' := (82416279421253 / 78125000000000 : ℚ)) + (U := (-(682452605272557036629 / 200000000000000000000 : ℚ))) + (U' := (10694575027442963371 / 200000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (297034306573 / 4000000000000 : ℚ)) + (s := (62222726570631 / 2500000000000000 : ℚ)) + (q := (82416279421253 / 2500000000000000 : ℚ)) + (U := (-(682452605272557036629 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_121_6 : Uω (aρ 6) (bρ 6) (297034306573 / 4000000000000 : ℝ) ≤ @@ -2712,25 +2514,21 @@ lemma U_122_1 : have hlg : Real.log (10887652932550481 / 160000000000000000 : ℝ) ≤ (-(26875444254963523057139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10887652932550481 / 160000000000000000 : ℝ) = - (10887652932550481 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10887652932550481 / 10000000000000000 : ℚ)) - (U := (850442957036476942861 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10887652932550481 / 10000000000000000 : ℝ) ≤ - (850442957036476942861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (170060182127183 / 2500000000000000 : ℝ)) (q := - (10887652932550481 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10887652932550481 / 160000000000000000 : ℚ)) + (r' := (10887652932550481 / 10000000000000000 : ℚ)) + (U := (-(26875444254963523057139 / 10000000000000000000000 : ℚ))) + (U' := (850442957036476942861 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9538727758657 / 128000000000000 : ℚ)) + (s := (170060182127183 / 2500000000000000 : ℚ)) + (q := (10887652932550481 / 160000000000000000 : ℚ)) + (U := (-(26875444254963523057139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_122_2 : Uω (aρ 2) (bρ 2) (9538727758657 / 128000000000000 : ℝ) ≤ @@ -2738,25 +2536,21 @@ lemma U_122_2 : have hlg : Real.log (10485247204589921 / 160000000000000000 : ℝ) ≤ (-(27252045731424229280841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10485247204589921 / 160000000000000000 : ℝ) = - (10485247204589921 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10485247204589921 / 10000000000000000 : ℚ)) - (U := (473841480575770719159 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10485247204589921 / 10000000000000000 : ℝ) ≤ - (473841480575770719159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (326854512511831 / 5000000000000000 : ℝ)) (q := - (10485247204589921 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10485247204589921 / 160000000000000000 : ℚ)) + (r' := (10485247204589921 / 10000000000000000 : ℚ)) + (U := (-(27252045731424229280841 / 10000000000000000000000 : ℚ))) + (U' := (473841480575770719159 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9538727758657 / 128000000000000 : ℚ)) + (s := (326854512511831 / 5000000000000000 : ℚ)) + (q := (10485247204589921 / 160000000000000000 : ℚ)) + (U := (-(27252045731424229280841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_122_3 : Uω (aρ 3) (bρ 3) (9538727758657 / 128000000000000 : ℝ) ≤ @@ -2764,25 +2558,21 @@ lemma U_122_3 : have hlg : Real.log (9654730408809841 / 160000000000000000 : ℝ) ≤ (-(28077258208867713837771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (9654730408809841 / 160000000000000000 : ℝ) = - (9654730408809841 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9654730408809841 / 5000000000000000 : ℚ)) - (U := (6580100806132286162229 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9654730408809841 / 5000000000000000 : ℝ) ≤ - (6580100806132286162229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18665329121911 / 312500000000000 : ℝ)) (q := - (9654730408809841 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9654730408809841 / 160000000000000000 : ℚ)) + (r' := (9654730408809841 / 5000000000000000 : ℚ)) + (U := (-(28077258208867713837771 / 10000000000000000000000 : ℚ))) + (U' := (6580100806132286162229 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9538727758657 / 128000000000000 : ℚ)) + (s := (18665329121911 / 312500000000000 : ℚ)) + (q := (9654730408809841 / 160000000000000000 : ℚ)) + (U := (-(28077258208867713837771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_122_4 : Uω (aρ 4) (bρ 4) (9538727758657 / 128000000000000 : ℝ) ≤ @@ -2790,25 +2580,21 @@ lemma U_122_4 : have hlg : Real.log (8170472638651729 / 160000000000000000 : ℝ) ≤ (-(14873235281136487034493 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (8170472638651729 / 160000000000000000 : ℝ) = - (8170472638651729 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8170472638651729 / 5000000000000000 : ℚ)) - (U := (2455444226363512965507 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8170472638651729 / 5000000000000000 : ℝ) ≤ - (2455444226363512965507 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (122513122924097 / 2500000000000000 : ℝ)) (q := - (8170472638651729 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8170472638651729 / 160000000000000000 : ℚ)) + (r' := (8170472638651729 / 5000000000000000 : ℚ)) + (U := (-(14873235281136487034493 / 5000000000000000000000 : ℚ))) + (U' := (2455444226363512965507 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9538727758657 / 128000000000000 : ℚ)) + (s := (122513122924097 / 2500000000000000 : ℚ)) + (q := (8170472638651729 / 160000000000000000 : ℚ)) + (U := (-(14873235281136487034493 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_122_5 : Uω (aρ 5) (bρ 5) (9538727758657 / 128000000000000 : ℝ) ≤ @@ -2816,25 +2602,21 @@ lemma U_122_5 : have hlg : Real.log (5330134507460841 / 160000000000000000 : ℝ) ≤ (-(6803594680306818344917 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (5330134507460841 / 160000000000000000 : ℝ) = - (5330134507460841 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5330134507460841 / 5000000000000000 : ℚ)) - (U := (127877122693181655083 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5330134507460841 / 5000000000000000 : ℝ) ≤ - (127877122693181655083 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253200144632527 / 10000000000000000 : ℝ)) (q := - (5330134507460841 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5330134507460841 / 160000000000000000 : ℚ)) + (r' := (5330134507460841 / 5000000000000000 : ℚ)) + (U := (-(6803594680306818344917 / 2000000000000000000000 : ℚ))) + (U' := (127877122693181655083 / 2000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9538727758657 / 128000000000000 : ℚ)) + (s := (253200144632527 / 10000000000000000 : ℚ)) + (q := (5330134507460841 / 160000000000000000 : ℚ)) + (U := (-(6803594680306818344917 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_122_6 : Uω (aρ 6) (bρ 6) (9538727758657 / 128000000000000 : ℝ) ≤ @@ -2982,25 +2764,21 @@ lemma U_123_1 : have hlg : Real.log (5464852496684989 / 80000000000000000 : ℝ) ≤ (-(5367379005824790420369 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5464852496684989 / 80000000000000000 : ℝ) = - (5464852496684989 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5464852496684989 / 5000000000000000 : ℚ)) - (U := (177798436575209579631 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5464852496684989 / 5000000000000000 : ℝ) ≤ - (177798436575209579631 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (682869896398591 / 10000000000000000 : ℝ)) (q := - (5464852496684989 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5464852496684989 / 80000000000000000 : ℚ)) + (r' := (5464852496684989 / 5000000000000000 : ℚ)) + (U := (-(5367379005824790420369 / 2000000000000000000000 : ℚ))) + (U' := (177798436575209579631 / 2000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4786178853489 / 64000000000000 : ℚ)) + (s := (682869896398591 / 10000000000000000 : ℚ)) + (q := (5464852496684989 / 80000000000000000 : ℚ)) + (U := (-(5367379005824790420369 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_123_2 : Uω (aρ 2) (bρ 2) (4786178853489 / 64000000000000 : ℝ) ≤ @@ -3008,25 +2786,21 @@ lemma U_123_2 : have hlg : Real.log (5263694164444461 / 80000000000000000 : ℝ) ≤ (-(27211935407585621453431 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5263694164444461 / 80000000000000000 : ℝ) = - (5263694164444461 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5263694164444461 / 5000000000000000 : ℚ)) - (U := (513951804414378546569 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5263694164444461 / 5000000000000000 : ℝ) ≤ - (513951804414378546569 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (656349325848459 / 10000000000000000 : ℝ)) (q := - (5263694164444461 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5263694164444461 / 80000000000000000 : ℚ)) + (r' := (5263694164444461 / 5000000000000000 : ℚ)) + (U := (-(27211935407585621453431 / 10000000000000000000000 : ℚ))) + (U' := (513951804414378546569 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4786178853489 / 64000000000000 : ℚ)) + (s := (656349325848459 / 10000000000000000 : ℚ)) + (q := (5263694164444461 / 80000000000000000 : ℚ)) + (U := (-(27211935407585621453431 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_123_3 : Uω (aρ 3) (bρ 3) (4786178853489 / 64000000000000 : ℝ) ≤ @@ -3034,25 +2808,21 @@ lemma U_123_3 : have hlg : Real.log (4848598687282497 / 80000000000000000 : ℝ) ≤ (-(14016684503152133467349 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4848598687282497 / 80000000000000000 : ℝ) = - (4848598687282497 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4848598687282497 / 2500000000000000 : ℚ)) - (U := (3311995004347866532651 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4848598687282497 / 2500000000000000 : ℝ) ≤ - (3311995004347866532651 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9374555670437 / 156250000000000 : ℝ)) (q := - (4848598687282497 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4848598687282497 / 80000000000000000 : ℚ)) + (r' := (4848598687282497 / 2500000000000000 : ℚ)) + (U := (-(14016684503152133467349 / 5000000000000000000000 : ℚ))) + (U' := (3311995004347866532651 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4786178853489 / 64000000000000 : ℚ)) + (s := (9374555670437 / 156250000000000 : ℚ)) + (q := (4848598687282497 / 80000000000000000 : ℚ)) + (U := (-(14016684503152133467349 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_123_4 : Uω (aρ 4) (bρ 4) (4786178853489 / 64000000000000 : ℝ) ≤ @@ -3060,25 +2830,21 @@ lemma U_123_4 : have hlg : Real.log (821426753229409 / 16000000000000000 : ℝ) ≤ (-(29693012286484085391417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (821426753229409 / 16000000000000000 : ℝ) = - (821426753229409 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (821426753229409 / 500000000000000 : ℚ)) - (U := (4964346728515914608583 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (821426753229409 / 500000000000000 : ℝ) ≤ - (4964346728515914608583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98579902737821 / 2000000000000000 : ℝ)) (q := - (821426753229409 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (821426753229409 / 16000000000000000 : ℚ)) + (r' := (821426753229409 / 500000000000000 : ℚ)) + (U := (-(29693012286484085391417 / 10000000000000000000000 : ℚ))) + (U' := (4964346728515914608583 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4786178853489 / 64000000000000 : ℚ)) + (s := (98579902737821 / 2000000000000000 : ℚ)) + (q := (821426753229409 / 16000000000000000 : ℚ)) + (U := (-(29693012286484085391417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_123_5 : Uω (aρ 5) (bρ 5) (4786178853489 / 64000000000000 : ℝ) ≤ @@ -3086,25 +2852,21 @@ lemma U_123_5 : have hlg : Real.log (2692632327572469 / 80000000000000000 : ℝ) ≤ (-(16957536789013437420659 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2692632327572469 / 80000000000000000 : ℝ) = - (2692632327572469 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2692632327572469 / 2500000000000000 : ℚ)) - (U := (371142718486562579341 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2692632327572469 / 2500000000000000 : ℝ) ≤ - (371142718486562579341 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (257464073380461 / 10000000000000000 : ℝ)) (q := - (2692632327572469 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2692632327572469 / 80000000000000000 : ℚ)) + (r' := (2692632327572469 / 2500000000000000 : ℚ)) + (U := (-(16957536789013437420659 / 5000000000000000000000 : ℚ))) + (U' := (371142718486562579341 / 5000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4786178853489 / 64000000000000 : ℚ)) + (s := (257464073380461 / 10000000000000000 : ℚ)) + (q := (2692632327572469 / 80000000000000000 : ℚ)) + (U := (-(16957536789013437420659 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_123_6 : Uω (aρ 6) (bρ 6) (4786178853489 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U10.lean b/LeanPool/Zeta5Irrational/Table/U10.lean index 432dacab04..07d9922890 100644 --- a/LeanPool/Zeta5Irrational/Table/U10.lean +++ b/LeanPool/Zeta5Irrational/Table/U10.lean @@ -24,25 +24,21 @@ lemma U_124_1 : have hlg : Real.log (10971756942039611 / 160000000000000000 : ℝ) ≤ (-(13399246969653145294021 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10971756942039611 / 160000000000000000 : ℝ) = - (10971756942039611 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10971756942039611 / 10000000000000000 : ℚ)) - (U := (463696636346854705979 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10971756942039611 / 10000000000000000 : ℝ) ≤ - (463696636346854705979 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (685499050269717 / 10000000000000000 : ℝ)) (q := - (10971756942039611 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10971756942039611 / 160000000000000000 : ℚ)) + (r' := (10971756942039611 / 10000000000000000 : ℚ)) + (U := (-(13399246969653145294021 / 5000000000000000000000 : ℚ))) + (U' := (463696636346854705979 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9605987655299 / 128000000000000 : ℚ)) + (s := (685499050269717 / 10000000000000000 : ℚ)) + (q := (10971756942039611 / 160000000000000000 : ℚ)) + (U := (-(13399246969653145294021 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_124_2 : Uω (aρ 2) (bρ 2) (9605987655299 / 128000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_124_2 : have hlg : Real.log (2113905724869911 / 32000000000000000 : ℝ) ≤ (-(27171986109213034869943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2113905724869911 / 32000000000000000 : ℝ) = - (2113905724869911 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2113905724869911 / 2000000000000000 : ℚ)) - (U := (553901102786965130057 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2113905724869911 / 2000000000000000 : ℝ) ≤ - (553901102786965130057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (32949476153423 / 500000000000000 : ℝ)) (q := - (2113905724869911 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2113905724869911 / 32000000000000000 : ℚ)) + (r' := (2113905724869911 / 2000000000000000 : ℚ)) + (U := (-(27171986109213034869943 / 10000000000000000000000 : ℚ))) + (U' := (553901102786965130057 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9605987655299 / 128000000000000 : ℚ)) + (s := (32949476153423 / 500000000000000 : ℚ)) + (q := (2113905724869911 / 32000000000000000 : ℚ)) + (U := (-(27171986109213034869943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_124_3 : Uω (aρ 3) (bρ 3) (9605987655299 / 128000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_124_3 : have hlg : Real.log (9739660556868003 / 160000000000000000 : ℝ) ≤ (-(13994837736555882275651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (9739660556868003 / 160000000000000000 : ℝ) = - (9739660556868003 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9739660556868003 / 5000000000000000 : ℚ)) - (U := (3333841770944117724349 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9739660556868003 / 5000000000000000 : ℝ) ≤ - (3333841770944117724349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (301326060491633 / 5000000000000000 : ℝ)) (q := - (9739660556868003 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9739660556868003 / 160000000000000000 : ℚ)) + (r' := (9739660556868003 / 5000000000000000 : ℚ)) + (U := (-(13994837736555882275651 / 5000000000000000000000 : ℚ))) + (U' := (3333841770944117724349 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9605987655299 / 128000000000000 : ℚ)) + (s := (301326060491633 / 5000000000000000 : ℚ)) + (q := (9739660556868003 / 160000000000000000 : ℚ)) + (U := (-(13994837736555882275651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_124_4 : Uω (aρ 4) (bρ 4) (9605987655299 / 128000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_124_4 : have hlg : Real.log (8258043018870651 / 160000000000000000 : ℝ) ≤ (-(14819930885633522672703 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (8258043018870651 / 160000000000000000 : ℝ) = - (8258043018870651 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8258043018870651 / 5000000000000000 : ℚ)) - (U := (2508748621866477327297 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8258043018870651 / 5000000000000000 : ℝ) ≤ - (2508748621866477327297 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (495744109798597 / 10000000000000000 : ℝ)) (q := - (8258043018870651 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8258043018870651 / 160000000000000000 : ℚ)) + (r' := (8258043018870651 / 5000000000000000 : ℚ)) + (U := (-(14819930885633522672703 / 5000000000000000000000 : ℚ))) + (U' := (2508748621866477327297 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9605987655299 / 128000000000000 : ℚ)) + (s := (495744109798597 / 10000000000000000 : ℚ)) + (q := (8258043018870651 / 160000000000000000 : ℚ)) + (U := (-(14819930885633522672703 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_124_5 : Uω (aρ 5) (bρ 5) (9605987655299 / 128000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_124_5 : have hlg : Real.log (1088010008964823 / 32000000000000000 : ℝ) ≤ (-(16906927768461829373233 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1088010008964823 / 32000000000000000 : ℝ) = - (1088010008964823 / 1000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1088010008964823 / 1000000000000000 : ℚ)) - (U := (421751739038170626767 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1088010008964823 / 1000000000000000 : ℝ) ≤ - (421751739038170626767 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13084245368889 / 500000000000000 : ℝ)) (q := - (1088010008964823 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1088010008964823 / 32000000000000000 : ℚ)) + (r' := (1088010008964823 / 1000000000000000 : ℚ)) + (U := (-(16906927768461829373233 / 5000000000000000000000 : ℚ))) + (U' := (421751739038170626767 / 5000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9605987655299 / 128000000000000 : ℚ)) + (s := (13084245368889 / 500000000000000 : ℚ)) + (q := (1088010008964823 / 32000000000000000 : ℚ)) + (U := (-(16906927768461829373233 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_124_6 : Uω (aρ 6) (bρ 6) (9605987655299 / 128000000000000 : ℝ) ≤ @@ -293,25 +273,21 @@ lemma U_125_1 : have hlg : Real.log (2753452194961219 / 40000000000000000 : ℝ) ≤ (-(6690059962646030184617 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2753452194961219 / 40000000000000000 : ℝ) = - (2753452194961219 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2753452194961219 / 2500000000000000 : ℚ)) - (U := (241411840353969815383 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2753452194961219 / 2500000000000000 : ℝ) ≤ - (241411840353969815383 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (688128190282797 / 10000000000000000 : ℝ)) (q := - (2753452194961219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2753452194961219 / 40000000000000000 : ℚ)) + (r' := (2753452194961219 / 2500000000000000 : ℚ)) + (U := (-(6690059962646030184617 / 2500000000000000000000 : ℚ))) + (U' := (241411840353969815383 / 2500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (481980880181 / 6400000000000 : ℚ)) + (s := (688128190282797 / 10000000000000000 : ℚ)) + (q := (2753452194961219 / 40000000000000000 : ℚ)) + (U := (-(6690059962646030184617 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_125_2 : Uω (aρ 2) (bρ 2) (481980880181 / 6400000000000 : ℝ) ≤ @@ -319,25 +295,21 @@ lemma U_125_2 : have hlg : Real.log (2652917025223531 / 40000000000000000 : ℝ) ≤ (-(1085287861694982018329 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2652917025223531 / 40000000000000000 : ℝ) = - (2652917025223531 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2652917025223531 / 2500000000000000 : ℚ)) - (U := (23747626785017981671 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2652917025223531 / 2500000000000000 : ℝ) ≤ - (23747626785017981671 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661629617923953 / 10000000000000000 : ℝ)) (q := - (2652917025223531 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2652917025223531 / 40000000000000000 : ℚ)) + (r' := (2652917025223531 / 2500000000000000 : ℚ)) + (U := (-(1085287861694982018329 / 400000000000000000000 : ℚ))) + (U' := (23747626785017981671 / 400000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (481980880181 / 6400000000000 : ℚ)) + (s := (661629617923953 / 10000000000000000 : ℚ)) + (q := (2652917025223531 / 40000000000000000 : ℚ)) + (U := (-(1085287861694982018329 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_125_3 : Uω (aρ 3) (bρ 3) (481980880181 / 6400000000000 : ℝ) ≤ @@ -345,25 +317,21 @@ lemma U_125_3 : have hlg : Real.log (2445530001495253 / 40000000000000000 : ℝ) ≤ (-(6986543959626957316373 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2445530001495253 / 40000000000000000 : ℝ) = - (2445530001495253 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2445530001495253 / 1250000000000000 : ℚ)) - (U := (1677795794123042683627 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2445530001495253 / 1250000000000000 : ℝ) ≤ - (1677795794123042683627 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (302666106204907 / 5000000000000000 : ℝ)) (q := - (2445530001495253 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2445530001495253 / 40000000000000000 : ℚ)) + (r' := (2445530001495253 / 1250000000000000 : ℚ)) + (U := (-(6986543959626957316373 / 2500000000000000000000 : ℚ))) + (U' := (1677795794123042683627 / 2500000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (481980880181 / 6400000000000 : ℚ)) + (s := (302666106204907 / 5000000000000000 : ℚ)) + (q := (2445530001495253 / 40000000000000000 : ℚ)) + (U := (-(6986543959626957316373 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_125_4 : Uω (aρ 4) (bρ 4) (481980880181 / 6400000000000 : ℝ) ≤ @@ -371,25 +339,21 @@ lemma U_125_4 : have hlg : Real.log (2075449857638049 / 40000000000000000 : ℝ) ≤ (-(1849188452354571814583 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2075449857638049 / 40000000000000000 : ℝ) = - (2075449857638049 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2075449857638049 / 1250000000000000 : ℚ)) - (U := (316896486082928185417 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2075449857638049 / 1250000000000000 : ℝ) ≤ - (316896486082928185417 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (124646580386553 / 2500000000000000 : ℝ)) (q := - (2075449857638049 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2075449857638049 / 40000000000000000 : ℚ)) + (r' := (2075449857638049 / 1250000000000000 : ℚ)) + (U := (-(1849188452354571814583 / 625000000000000000000 : ℚ))) + (U' := (316896486082928185417 / 625000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (481980880181 / 6400000000000 : ℚ)) + (s := (124646580386553 / 2500000000000000 : ℚ)) + (q := (2075449857638049 / 40000000000000000 : ℚ)) + (U := (-(1849188452354571814583 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_125_5 : Uω (aρ 5) (bρ 5) (481980880181 / 6400000000000 : ℝ) ≤ @@ -397,25 +361,21 @@ lemma U_125_5 : have hlg : Real.log (274725354828193 / 8000000000000000 : ℝ) ≤ (-(33714249304541786608363 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (274725354828193 / 8000000000000000 : ℝ) = - (274725354828193 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (274725354828193 / 250000000000000 : ℚ)) - (U := (943109710458213391637 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (274725354828193 / 250000000000000 : ℝ) ≤ - (943109710458213391637 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26586469913267 / 1000000000000000 : ℝ)) (q := - (274725354828193 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (274725354828193 / 8000000000000000 : ℚ)) + (r' := (274725354828193 / 250000000000000 : ℚ)) + (U := (-(33714249304541786608363 / 10000000000000000000000 : ℚ))) + (U' := (943109710458213391637 / 10000000000000000000000 : ℚ)) + 5 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (481980880181 / 6400000000000 : ℚ)) + (s := (26586469913267 / 1000000000000000 : ℚ)) + (q := (274725354828193 / 8000000000000000 : ℚ)) + (U := (-(33714249304541786608363 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_125_6 : Uω (aρ 6) (bρ 6) (481980880181 / 6400000000000 : ℝ) ≤ @@ -562,25 +522,21 @@ lemma U_126_1 : have hlg : Real.log (11055860508051669 / 160000000000000000 : ℝ) ≤ (-(26722131641032751290407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (11055860508051669 / 160000000000000000 : ℝ) = - (11055860508051669 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11055860508051669 / 10000000000000000 : ℚ)) - (U := (1003755570967248709593 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11055860508051669 / 10000000000000000 : ℝ) ≤ - (1003755570967248709593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (172689329149017 / 2500000000000000 : ℝ)) (q := - (11055860508051669 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11055860508051669 / 160000000000000000 : ℚ)) + (r' := (11055860508051669 / 10000000000000000 : ℚ)) + (U := (-(26722131641032751290407 / 10000000000000000000000 : ℚ))) + (U' := (1003755570967248709593 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9673247551941 / 128000000000000 : ℚ)) + (s := (172689329149017 / 2500000000000000 : ℚ)) + (q := (11055860508051669 / 160000000000000000 : ℚ)) + (U := (-(26722131641032751290407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_126_2 : Uω (aρ 2) (bρ 2) (9673247551941 / 128000000000000 : ℝ) ≤ @@ -588,25 +544,21 @@ lemma U_126_2 : have hlg : Real.log (10653806768286813 / 160000000000000000 : ℝ) ≤ (-(3386570678593159343237 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10653806768286813 / 160000000000000000 : ℝ) = - (10653806768286813 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10653806768286813 / 10000000000000000 : ℚ)) - (U := (79165222906840656763 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10653806768286813 / 10000000000000000 : ℝ) ≤ - (79165222906840656763 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (664269611635461 / 10000000000000000 : ℝ)) (q := - (10653806768286813 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10653806768286813 / 160000000000000000 : ℚ)) + (r' := (10653806768286813 / 10000000000000000 : ℚ)) + (U := (-(3386570678593159343237 / 1250000000000000000000 : ℚ))) + (U' := (79165222906840656763 / 1250000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9673247551941 / 128000000000000 : ℚ)) + (s := (664269611635461 / 10000000000000000 : ℚ)) + (q := (10653806768286813 / 160000000000000000 : ℚ)) + (U := (-(3386570678593159343237 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_126_3 : Uω (aρ 3) (bρ 3) (9673247551941 / 128000000000000 : ℝ) ≤ @@ -614,25 +566,21 @@ lemma U_126_3 : have hlg : Real.log (9824575771271253 / 160000000000000000 : ℝ) ≤ (-(697571708901889533809 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (9824575771271253 / 160000000000000000 : ℝ) = - (9824575771271253 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9824575771271253 / 5000000000000000 : ℚ)) - (U := (168862266473110466191 / 250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9824575771271253 / 5000000000000000 : ℝ) ≤ - (168862266473110466191 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152002960839629 / 2500000000000000 : ℝ)) (q := - (9824575771271253 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9824575771271253 / 160000000000000000 : ℚ)) + (r' := (9824575771271253 / 5000000000000000 : ℚ)) + (U := (-(697571708901889533809 / 250000000000000000000 : ℚ))) + (U' := (168862266473110466191 / 250000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9673247551941 / 128000000000000 : ℚ)) + (s := (152002960839629 / 2500000000000000 : ℚ)) + (q := (9824575771271253 / 160000000000000000 : ℚ)) + (U := (-(697571708901889533809 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_126_4 : Uω (aρ 4) (bρ 4) (9673247551941 / 128000000000000 : ℝ) ≤ @@ -640,25 +588,21 @@ lemma U_126_4 : have hlg : Real.log (8345537091702853 / 160000000000000000 : ℝ) ≤ (-(2953446897992292134223 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (8345537091702853 / 160000000000000000 : ℝ) = - (8345537091702853 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8345537091702853 / 5000000000000000 : ℚ)) - (U := (512289003507707865777 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8345537091702853 / 5000000000000000 : ℝ) ≤ - (512289003507707865777 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (250713094738733 / 5000000000000000 : ℝ)) (q := - (8345537091702853 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8345537091702853 / 160000000000000000 : ℚ)) + (r' := (8345537091702853 / 5000000000000000 : ℚ)) + (U := (-(2953446897992292134223 / 1000000000000000000000 : ℚ))) + (U' := (512289003507707865777 / 1000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9673247551941 / 128000000000000 : ℚ)) + (s := (250713094738733 / 5000000000000000 : ℚ)) + (q := (8345537091702853 / 160000000000000000 : ℚ)) + (U := (-(2953446897992292134223 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_126_5 : Uω (aρ 5) (bρ 5) (9673247551941 / 128000000000000 : ℝ) ≤ @@ -666,25 +610,21 @@ lemma U_126_5 : have hlg : Real.log (5548651058829061 / 160000000000000000 : ℝ) ≤ (-(6723237936362052732691 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (5548651058829061 / 160000000000000000 : ℝ) = - (5548651058829061 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5548651058829061 / 5000000000000000 : ℚ)) - (U := (208233866637947267309 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5548651058829061 / 5000000000000000 : ℝ) ≤ - (208233866637947267309 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (135002677351621 / 5000000000000000 : ℝ)) (q := - (5548651058829061 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5548651058829061 / 160000000000000000 : ℚ)) + (r' := (5548651058829061 / 5000000000000000 : ℚ)) + (U := (-(6723237936362052732691 / 2000000000000000000000 : ℚ))) + (U' := (208233866637947267309 / 2000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9673247551941 / 128000000000000 : ℚ)) + (s := (135002677351621 / 5000000000000000 : ℚ)) + (q := (5548651058829061 / 160000000000000000 : ℚ)) + (U := (-(6723237936362052732691 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_126_6 : Uω (aρ 6) (bρ 6) (9673247551941 / 128000000000000 : ℝ) ≤ @@ -832,25 +772,21 @@ lemma U_127_1 : have hlg : Real.log (5548956063953347 / 80000000000000000 : ℝ) ≤ (-(2668416820153121014947 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5548956063953347 / 80000000000000000 : ℝ) = - (5548956063953347 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5548956063953347 / 5000000000000000 : ℚ)) - (U := (104171901046878985053 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5548956063953347 / 5000000000000000 : ℝ) ≤ - (104171901046878985053 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86673303670671 / 1250000000000000 : ℝ)) (q := - (5548956063953347 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5548956063953347 / 80000000000000000 : ℚ)) + (r' := (5548956063953347 / 5000000000000000 : ℚ)) + (U := (-(2668416820153121014947 / 1000000000000000000000 : ℚ))) + (U' := (104171901046878985053 / 1000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4853438750131 / 64000000000000 : ℚ)) + (s := (86673303670671 / 1250000000000000 : ℚ)) + (q := (5548956063953347 / 80000000000000000 : ℚ)) + (U := (-(2668416820153121014947 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_127_2 : Uω (aρ 2) (bρ 2) (4853438750131 / 64000000000000 : ℝ) ≤ @@ -858,25 +794,21 @@ lemma U_127_2 : have hlg : Real.log (1069594463613683 / 16000000000000000 : ℝ) ≤ (-(13526545752678102531631 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1069594463613683 / 16000000000000000 : ℝ) = - (1069594463613683 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1069594463613683 / 1000000000000000 : ℚ)) - (U := (336397853321897468369 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1069594463613683 / 1000000000000000 : ℝ) ≤ - (336397853321897468369 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (133381901080827 / 2000000000000000 : ℝ)) (q := - (1069594463613683 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1069594463613683 / 16000000000000000 : ℚ)) + (r' := (1069594463613683 / 1000000000000000 : ℚ)) + (U := (-(13526545752678102531631 / 5000000000000000000000 : ℚ))) + (U' := (336397853321897468369 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4853438750131 / 64000000000000 : ℚ)) + (s := (133381901080827 / 2000000000000000 : ℚ)) + (q := (1069594463613683 / 16000000000000000 : ℚ)) + (U := (-(13526545752678102531631 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_127_3 : Uω (aρ 3) (bρ 3) (4853438750131 / 64000000000000 : ℝ) ≤ @@ -884,25 +816,21 @@ lemma U_127_3 : have hlg : Real.log (986702790123111 / 16000000000000000 : ℝ) ≤ (-(1392987565165561452741 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (986702790123111 / 16000000000000000 : ℝ) = - (986702790123111 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (986702790123111 / 500000000000000 : ℚ)) - (U := (339880385584438547259 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (986702790123111 / 500000000000000 : ℝ) ≤ - (339880385584438547259 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (15267275497273 / 250000000000000 : ℝ)) (q := - (986702790123111 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (986702790123111 / 16000000000000000 : ℚ)) + (r' := (986702790123111 / 500000000000000 : ℚ)) + (U := (-(1392987565165561452741 / 500000000000000000000 : ℚ))) + (U' := (339880385584438547259 / 500000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4853438750131 / 64000000000000 : ℚ)) + (s := (15267275497273 / 250000000000000 : ℚ)) + (q := (986702790123111 / 16000000000000000 : ℚ)) + (U := (-(1392987565165561452741 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_127_4 : Uω (aρ 4) (bρ 4) (4853438750131 / 64000000000000 : ℝ) ≤ @@ -910,25 +838,21 @@ lemma U_127_4 : have hlg : Real.log (4194628159557691 / 80000000000000000 : ℝ) ≤ (-(14741109681724341615633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4194628159557691 / 80000000000000000 : ℝ) = - (4194628159557691 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4194628159557691 / 2500000000000000 : ℚ)) - (U := (2587569825775658384367 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4194628159557691 / 2500000000000000 : ℝ) ≤ - (2587569825775658384367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252131876595727 / 5000000000000000 : ℝ)) (q := - (4194628159557691 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4194628159557691 / 80000000000000000 : ℚ)) + (r' := (4194628159557691 / 2500000000000000 : ℚ)) + (U := (-(14741109681724341615633 / 5000000000000000000000 : ℚ))) + (U' := (2587569825775658384367 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4853438750131 / 64000000000000 : ℚ)) + (s := (252131876595727 / 5000000000000000 : ℚ)) + (q := (4194628159557691 / 80000000000000000 : ℚ)) + (U := (-(14741109681724341615633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_127_5 : Uω (aρ 5) (bρ 5) (4853438750131 / 64000000000000 : ℝ) ≤ @@ -936,25 +860,21 @@ lemma U_127_5 : have hlg : Real.log (2801248060076399 / 80000000000000000 : ℝ) ≤ (-(33519615797620916311619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2801248060076399 / 80000000000000000 : ℝ) = - (2801248060076399 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2801248060076399 / 2500000000000000 : ℚ)) - (U := (1137743217379083688381 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2801248060076399 / 2500000000000000 : ℝ) ≤ - (1137743217379083688381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (274108647656131 / 10000000000000000 : ℝ)) (q := - (2801248060076399 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2801248060076399 / 80000000000000000 : ℚ)) + (r' := (2801248060076399 / 2500000000000000 : ℚ)) + (U := (-(33519615797620916311619 / 10000000000000000000000 : ℚ))) + (U' := (1137743217379083688381 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4853438750131 / 64000000000000 : ℚ)) + (s := (274108647656131 / 10000000000000000 : ℚ)) + (q := (2801248060076399 / 80000000000000000 : ℚ)) + (U := (-(33519615797620916311619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_127_6 : Uω (aρ 6) (bρ 6) (4853438750131 / 64000000000000 : ℝ) ≤ @@ -1101,25 +1021,21 @@ lemma U_128_1 : have hlg : Real.log (349437970232949 / 5000000000000000 : ℝ) ≤ (-(5321734251810154824021 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (349437970232949 / 5000000000000000 : ℝ) = - (349437970232949 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (349437970232949 / 312500000000000 : ℚ)) - (U := (223443190589845175979 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (349437970232949 / 312500000000000 : ℝ) ≤ - (223443190589845175979 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (698644614883671 / 10000000000000000 : ℝ)) (q := - (349437970232949 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (349437970232949 / 5000000000000000 : ℚ)) + (r' := (349437970232949 / 312500000000000 : ℚ)) + (U := (-(5321734251810154824021 / 2000000000000000000000 : ℚ))) + (U' := (223443190589845175979 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1221767174613 / 16000000000000 : ℚ)) + (s := (698644614883671 / 10000000000000000 : ℚ)) + (q := (349437970232949 / 5000000000000000 : ℚ)) + (U := (-(5321734251810154824021 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_128_2 : Uω (aρ 2) (bρ 2) (1221767174613 / 16000000000000 : ℝ) ≤ @@ -1127,25 +1043,21 @@ lemma U_128_2 : have hlg : Real.log (269505450272227 / 4000000000000000 : ℝ) ≤ (-(26974610252730626450719 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (269505450272227 / 4000000000000000 : ℝ) = - (269505450272227 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (269505450272227 / 250000000000000 : ℚ)) - (U := (751276959269373549281 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (269505450272227 / 250000000000000 : ℝ) ≤ - (751276959269373549281 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (67218899782301 / 1000000000000000 : ℝ)) (q := - (269505450272227 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (269505450272227 / 4000000000000000 : ℚ)) + (r' := (269505450272227 / 250000000000000 : ℚ)) + (U := (-(26974610252730626450719 / 10000000000000000000000 : ℚ))) + (U' := (751276959269373549281 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1221767174613 / 16000000000000 : ℚ)) + (s := (67218899782301 / 1000000000000000 : ℚ)) + (q := (269505450272227 / 4000000000000000 : ℚ)) + (U := (-(26974610252730626450719 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_128_3 : Uω (aρ 3) (bρ 3) (1221767174613 / 16000000000000 : ℝ) ≤ @@ -1153,25 +1065,21 @@ lemma U_128_3 : have hlg : Real.log (621995090304443 / 10000000000000000 : ℝ) ≤ (-(27774081713696468351641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (621995090304443 / 10000000000000000 : ℝ) = - (621995090304443 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (621995090304443 / 312500000000000 : ℚ)) - (U := (6883277301303531648359 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (621995090304443 / 312500000000000 : ℝ) ≤ - (6883277301303531648359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (616048033420761 / 10000000000000000 : ℝ)) (q := - (621995090304443 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (621995090304443 / 10000000000000000 : ℚ)) + (r' := (621995090304443 / 312500000000000 : ℚ)) + (U := (-(27774081713696468351641 / 10000000000000000000000 : ℚ))) + (U' := (6883277301303531648359 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1221767174613 / 16000000000000 : ℚ)) + (s := (616048033420761 / 10000000000000000 : ℚ)) + (q := (621995090304443 / 10000000000000000 : ℚ)) + (U := (-(27774081713696468351641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_128_4 : Uω (aρ 4) (bρ 4) (1221767174613 / 16000000000000 : ℝ) ≤ @@ -1179,25 +1087,21 @@ lemma U_128_4 : have hlg : Real.log (1059580087923863 / 20000000000000000 : ℝ) ≤ (-(14689297930419472306447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1059580087923863 / 20000000000000000 : ℝ) = - (1059580087923863 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1059580087923863 / 625000000000000 : ℚ)) - (U := (2639381577080527693553 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1059580087923863 / 625000000000000 : ℝ) ≤ - (2639381577080527693553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (254966060900369 / 5000000000000000 : ℝ)) (q := - (1059580087923863 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1059580087923863 / 20000000000000000 : ℚ)) + (r' := (1059580087923863 / 625000000000000 : ℚ)) + (U := (-(14689297930419472306447 / 5000000000000000000000 : ℚ))) + (U' := (2639381577080527693553 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1221767174613 / 16000000000000 : ℚ)) + (s := (254966060900369 / 5000000000000000 : ℚ)) + (q := (1059580087923863 / 20000000000000000 : ℚ)) + (U := (-(14689297930419472306447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_128_5 : Uω (aρ 5) (bρ 5) (1221767174613 / 16000000000000 : ℝ) ≤ @@ -1205,25 +1109,21 @@ lemma U_128_5 : have hlg : Real.log (356833848352817 / 10000000000000000 : ℝ) ≤ (-(33330701080104509943517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (356833848352817 / 10000000000000000 : ℝ) = - (356833848352817 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (356833848352817 / 312500000000000 : ℚ)) - (U := (1326657934895490056483 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (356833848352817 / 312500000000000 : ℝ) ≤ - (1326657934895490056483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (282209649917509 / 10000000000000000 : ℝ)) (q := - (356833848352817 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (356833848352817 / 10000000000000000 : ℚ)) + (r' := (356833848352817 / 312500000000000 : ℚ)) + (U := (-(33330701080104509943517 / 10000000000000000000000 : ℚ))) + (U' := (1326657934895490056483 / 10000000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1221767174613 / 16000000000000 : ℚ)) + (s := (282209649917509 / 10000000000000000 : ℚ)) + (q := (356833848352817 / 10000000000000000 : ℚ)) + (U := (-(33330701080104509943517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_128_6 : Uω (aρ 6) (bρ 6) (1221767174613 / 16000000000000 : ℝ) ≤ @@ -1370,25 +1270,21 @@ lemma U_129_1 : have hlg : Real.log (1126611754809097 / 16000000000000000 : ℝ) ≤ (-(26533740398960545318349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1126611754809097 / 16000000000000000 : ℝ) = - (1126611754809097 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1126611754809097 / 1000000000000000 : ℚ)) - (U := (1192146813039454681651 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1126611754809097 / 1000000000000000 : ℝ) ≤ - (1192146813039454681651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (70390274803809 / 1000000000000000 : ℝ)) (q := - (1126611754809097 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1126611754809097 / 16000000000000000 : ℚ)) + (r' := (1126611754809097 / 1000000000000000 : ℚ)) + (U := (-(26533740398960545318349 / 10000000000000000000000 : ℚ))) + (U' := (1192146813039454681651 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4920698646773 / 64000000000000 : ℚ)) + (s := (70390274803809 / 1000000000000000 : ℚ)) + (q := (1126611754809097 / 16000000000000000 : ℚ)) + (U := (-(26533740398960545318349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_129_2 : Uω (aρ 2) (bρ 2) (4920698646773 / 64000000000000 : ℝ) ≤ @@ -1396,25 +1292,21 @@ lemma U_129_2 : have hlg : Real.log (5432244149519873 / 80000000000000000 : ℝ) ≤ (-(26896742978634930657697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5432244149519873 / 80000000000000000 : ℝ) = - (5432244149519873 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5432244149519873 / 5000000000000000 : ℚ)) - (U := (829144233365069342303 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5432244149519873 / 5000000000000000 : ℝ) ≤ - (829144233365069342303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (677468104416687 / 10000000000000000 : ℝ)) (q := - (5432244149519873 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5432244149519873 / 80000000000000000 : ℚ)) + (r' := (5432244149519873 / 5000000000000000 : ℚ)) + (U := (-(26896742978634930657697 / 10000000000000000000000 : ℚ))) + (U' := (829144233365069342303 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4920698646773 / 64000000000000 : ℚ)) + (s := (677468104416687 / 10000000000000000 : ℚ)) + (q := (5432244149519873 / 80000000000000000 : ℚ)) + (U := (-(26896742978634930657697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_129_3 : Uω (aρ 3) (bρ 3) (4920698646773 / 64000000000000 : ℝ) ≤ @@ -1422,25 +1314,21 @@ lemma U_129_3 : have hlg : Real.log (1003680100806941 / 16000000000000000 : ℝ) ≤ (-(27689153753963773397029 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1003680100806941 / 16000000000000000 : ℝ) = - (1003680100806941 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1003680100806941 / 1000000000000000 : ℚ)) - (U := (36733458036226602971 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1003680100806941 / 1000000000000000 : ℝ) ≤ - (36733458036226602971 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (124280659879079 / 2000000000000000 : ℝ)) (q := - (1003680100806941 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1003680100806941 / 16000000000000000 : ℚ)) + (r' := (1003680100806941 / 1000000000000000 : ℚ)) + (U := (-(27689153753963773397029 / 10000000000000000000000 : ℚ))) + (U' := (36733458036226602971 / 10000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4920698646773 / 64000000000000 : ℚ)) + (s := (124280659879079 / 2000000000000000 : ℚ)) + (q := (1003680100806941 / 16000000000000000 : ℚ)) + (U := (-(27689153753963773397029 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_129_4 : Uω (aρ 4) (bρ 4) (4920698646773 / 64000000000000 : ℝ) ≤ @@ -1448,25 +1336,21 @@ lemma U_129_4 : have hlg : Real.log (4281977487348057 / 80000000000000000 : ℝ) ≤ (-(14638058503645561336247 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4281977487348057 / 80000000000000000 : ℝ) = - (4281977487348057 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4281977487348057 / 2500000000000000 : ℚ)) - (U := (2690621003854438663753 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4281977487348057 / 2500000000000000 : ℝ) ≤ - (2690621003854438663753 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (515591726288733 / 10000000000000000 : ℝ)) (q := - (4281977487348057 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4281977487348057 / 80000000000000000 : ℚ)) + (r' := (4281977487348057 / 2500000000000000 : ℚ)) + (U := (-(14638058503645561336247 / 5000000000000000000000 : ℚ))) + (U' := (2690621003854438663753 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4920698646773 / 64000000000000 : ℚ)) + (s := (515591726288733 / 10000000000000000 : ℚ)) + (q := (4281977487348057 / 80000000000000000 : ℚ)) + (U := (-(14638058503645561336247 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_129_5 : Uω (aρ 5) (bρ 5) (4920698646773 / 64000000000000 : ℝ) ≤ @@ -1474,25 +1358,21 @@ lemma U_129_5 : have hlg : Real.log (581513923481993 / 16000000000000000 : ℝ) ≤ (-(8286772710427584474673 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (581513923481993 / 16000000000000000 : ℝ) = - (581513923481993 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (581513923481993 / 500000000000000 : ℚ)) - (U := (377567043322415525327 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (581513923481993 / 500000000000000 : ℝ) ≤ - (377567043322415525327 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29017967813921 / 1000000000000000 : ℝ)) (q := - (581513923481993 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (581513923481993 / 16000000000000000 : ℚ)) + (r' := (581513923481993 / 500000000000000 : ℚ)) + (U := (-(8286772710427584474673 / 2500000000000000000000 : ℚ))) + (U' := (377567043322415525327 / 2500000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4920698646773 / 64000000000000 : ℚ)) + (s := (29017967813921 / 1000000000000000 : ℚ)) + (q := (581513923481993 / 16000000000000000 : ℚ)) + (U := (-(8286772710427584474673 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_129_6 : Uω (aρ 6) (bρ 6) (4920698646773 / 64000000000000 : ℝ) ≤ @@ -1640,25 +1520,21 @@ lemma U_130_1 : have hlg : Real.log (2837554909783663 / 40000000000000000 : ℝ) ≤ (-(5291873437976526183487 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2837554909783663 / 40000000000000000 : ℝ) = - (2837554909783663 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2837554909783663 / 2500000000000000 : ℚ)) - (U := (253304004423473816513 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2837554909783663 / 2500000000000000 : ℝ) ≤ - (253304004423473816513 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (354580414996697 / 5000000000000000 : ℝ)) (q := - (2837554909783663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2837554909783663 / 40000000000000000 : ℚ)) + (r' := (2837554909783663 / 2500000000000000 : ℚ)) + (U := (-(5291873437976526183487 / 2000000000000000000000 : ℚ))) + (U' := (253304004423473816513 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2477164297547 / 32000000000000 : ℚ)) + (s := (354580414996697 / 5000000000000000 : ℚ)) + (q := (2837554909783663 / 40000000000000000 : ℚ)) + (U := (-(5291873437976526183487 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_130_2 : Uω (aρ 2) (bρ 2) (2477164297547 / 32000000000000 : ℝ) ≤ @@ -1666,25 +1542,21 @@ lemma U_130_2 : have hlg : Real.log (2737188893046777 / 40000000000000000 : ℝ) ≤ (-(26819480107653810847137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2737188893046777 / 40000000000000000 : ℝ) = - (2737188893046777 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2737188893046777 / 2500000000000000 : ℚ)) - (U := (906407104346189152863 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2737188893046777 / 2500000000000000 : ℝ) ≤ - (906407104346189152863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (682746834134951 / 10000000000000000 : ℝ)) (q := - (2737188893046777 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2737188893046777 / 40000000000000000 : ℚ)) + (r' := (2737188893046777 / 2500000000000000 : ℚ)) + (U := (-(26819480107653810847137 / 10000000000000000000000 : ℚ))) + (U' := (906407104346189152863 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2477164297547 / 32000000000000 : ℚ)) + (s := (682746834134951 / 10000000000000000 : ℚ)) + (q := (2737188893046777 / 40000000000000000 : ℚ)) + (U := (-(26819480107653810847137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_130_3 : Uω (aρ 3) (bρ 3) (2477164297547 / 32000000000000 : ℝ) ≤ @@ -1692,25 +1564,21 @@ lemma U_130_3 : have hlg : Real.log (2530416737297469 / 40000000000000000 : ℝ) ≤ (-(13802477227999504398421 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2530416737297469 / 40000000000000000 : ℝ) = - (2530416737297469 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2530416737297469 / 2500000000000000 : ℚ)) - (U := (60466378000495601579 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2530416737297469 / 2500000000000000 : ℝ) ≤ - (60466378000495601579 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626756862610297 / 10000000000000000 : ℝ)) (q := - (2530416737297469 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2530416737297469 / 40000000000000000 : ℚ)) + (r' := (2530416737297469 / 2500000000000000 : ℚ)) + (U := (-(13802477227999504398421 / 5000000000000000000000 : ℚ))) + (U' := (60466378000495601579 / 5000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2477164297547 / 32000000000000 : ℚ)) + (s := (626756862610297 / 10000000000000000 : ℚ)) + (q := (2530416737297469 / 40000000000000000 : ℚ)) + (U := (-(13802477227999504398421 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_130_4 : Uω (aρ 4) (bρ 4) (2477164297547 / 32000000000000 : ℝ) ≤ @@ -1718,25 +1586,21 @@ lemma U_130_4 : have hlg : Real.log (2162800354217801 / 40000000000000000 : ℝ) ≤ (-(5834951221022183615197 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2162800354217801 / 40000000000000000 : ℝ) = - (2162800354217801 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2162800354217801 / 1250000000000000 : ℚ)) - (U := (1096520581977816384803 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2162800354217801 / 1250000000000000 : ℝ) ≤ - (1096520581977816384803 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (521242852135463 / 10000000000000000 : ℝ)) (q := - (2162800354217801 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2162800354217801 / 40000000000000000 : ℚ)) + (r' := (2162800354217801 / 1250000000000000 : ℚ)) + (U := (-(5834951221022183615197 / 2000000000000000000000 : ℚ))) + (U' := (1096520581977816384803 / 2000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2477164297547 / 32000000000000 : ℚ)) + (s := (521242852135463 / 10000000000000000 : ℚ)) + (q := (2162800354217801 / 40000000000000000 : ℚ)) + (U := (-(5834951221022183615197 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_130_5 : Uω (aρ 5) (bρ 5) (2477164297547 / 32000000000000 : ℝ) ≤ @@ -1744,25 +1608,21 @@ lemma U_130_5 : have hlg : Real.log (1479993291679967 / 40000000000000000 : ℝ) ≤ (-(8242104744242823723913 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1479993291679967 / 40000000000000000 : ℝ) = - (1479993291679967 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1479993291679967 / 1250000000000000 : ℚ)) - (U := (422235009507176276087 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1479993291679967 / 1250000000000000 : ℝ) ≤ - (422235009507176276087 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (149014620100773 / 5000000000000000 : ℝ)) (q := - (1479993291679967 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1479993291679967 / 40000000000000000 : ℚ)) + (r' := (1479993291679967 / 1250000000000000 : ℚ)) + (U := (-(8242104744242823723913 / 2500000000000000000000 : ℚ))) + (U' := (422235009507176276087 / 2500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2477164297547 / 32000000000000 : ℚ)) + (s := (149014620100773 / 5000000000000000 : ℚ)) + (q := (1479993291679967 / 40000000000000000 : ℚ)) + (U := (-(8242104744242823723913 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_130_6 : Uω (aρ 6) (bρ 6) (2477164297547 / 32000000000000 : ℝ) ≤ @@ -1909,25 +1769,21 @@ lemma U_131_1 : have hlg : Real.log (228686426592583 / 3200000000000000 : ℝ) ≤ (-(26385543387535192161299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (228686426592583 / 3200000000000000 : ℝ) = - (228686426592583 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (228686426592583 / 200000000000000 : ℚ)) - (U := (1340343824464807838701 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (228686426592583 / 200000000000000 : ℝ) ≤ - (1340343824464807838701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14288377237601 / 200000000000000 : ℝ)) (q := - (228686426592583 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (228686426592583 / 3200000000000000 : ℚ)) + (r' := (228686426592583 / 200000000000000 : ℚ)) + (U := (-(26385543387535192161299 / 10000000000000000000000 : ℚ))) + (U' := (1340343824464807838701 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (997591708683 / 12800000000000 : ℚ)) + (s := (14288377237601 / 200000000000000 : ℚ)) + (q := (228686426592583 / 3200000000000000 : ℚ)) + (U := (-(26385543387535192161299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_131_2 : Uω (aρ 2) (bρ 2) (997591708683 / 12800000000000 : ℝ) ≤ @@ -1935,25 +1791,21 @@ lemma U_131_2 : have hlg : Real.log (1103301989972711 / 16000000000000000 : ℝ) ≤ (-(1069712491504947096903 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1103301989972711 / 16000000000000000 : ℝ) = - (1103301989972711 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1103301989972711 / 1000000000000000 : ℚ)) - (U := (39322996975052903097 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1103301989972711 / 1000000000000000 : ℝ) ≤ - (39322996975052903097 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (137605039130459 / 2000000000000000 : ℝ)) (q := - (1103301989972711 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1103301989972711 / 16000000000000000 : ℚ)) + (r' := (1103301989972711 / 1000000000000000 : ℚ)) + (U := (-(1069712491504947096903 / 400000000000000000000 : ℚ))) + (U' := (39322996975052903097 / 400000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (997591708683 / 12800000000000 : ℚ)) + (s := (137605039130459 / 2000000000000000 : ℚ)) + (q := (1103301989972711 / 16000000000000000 : ℚ)) + (U := (-(1069712491504947096903 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_131_3 : Uω (aρ 3) (bρ 3) (997591708683 / 12800000000000 : ℝ) ≤ @@ -1961,23 +1813,21 @@ lemma U_131_3 : have hlg : Real.log (326608627659 / 5120000000000 : ℝ) ≤ (-(27521471202141578539429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (326608627659 / 5120000000000 : ℝ) = (326608627659 / 320000000000 : ℝ) / 2 ^ 4 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (326608627659 / 320000000000 : ℚ)) - (U := (204416009858421460571 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (326608627659 / 320000000000 : ℝ) ≤ - (204416009858421460571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1011374026127 / 16000000000000 : ℝ)) (q := - (326608627659 / 5120000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (326608627659 / 5120000000000 : ℚ)) + (r' := (326608627659 / 320000000000 : ℚ)) + (U := (-(27521471202141578539429 / 10000000000000000000000 : ℚ))) + (U' := (204416009858421460571 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (997591708683 / 12800000000000 : ℚ)) + (s := (1011374026127 / 16000000000000 : ℚ)) + (q := (326608627659 / 5120000000000 : ℚ)) + (U := (-(27521471202141578539429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_131_4 : Uω (aρ 4) (bρ 4) (997591708683 / 12800000000000 : ℝ) ≤ @@ -1985,25 +1835,21 @@ lemma U_131_4 : have hlg : Real.log (4369191106212779 / 80000000000000000 : ℝ) ≤ (-(1453724371476601447869 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4369191106212779 / 80000000000000000 : ℝ) = - (4369191106212779 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4369191106212779 / 2500000000000000 : ℚ)) - (U := (279143579273398552131 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4369191106212779 / 2500000000000000 : ℝ) ≤ - (279143579273398552131 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (526885772154601 / 10000000000000000 : ℝ)) (q := - (4369191106212779 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4369191106212779 / 80000000000000000 : ℚ)) + (r' := (4369191106212779 / 2500000000000000 : ℚ)) + (U := (-(1453724371476601447869 / 500000000000000000000 : ℚ))) + (U' := (279143579273398552131 / 500000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (997591708683 / 12800000000000 : ℚ)) + (s := (526885772154601 / 10000000000000000 : ℚ)) + (q := (4369191106212779 / 80000000000000000 : ℚ)) + (U := (-(1453724371476601447869 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_131_5 : Uω (aρ 5) (bρ 5) (997591708683 / 12800000000000 : ℝ) ≤ @@ -2011,25 +1857,21 @@ lemma U_131_5 : have hlg : Real.log (3011958796030119 / 80000000000000000 : ℝ) ≤ (-(32794360034669585926951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3011958796030119 / 80000000000000000 : ℝ) = - (3011958796030119 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3011958796030119 / 2500000000000000 : ℚ)) - (U := (1862998980330414073049 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3011958796030119 / 2500000000000000 : ℝ) ≤ - (1862998980330414073049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2388809483937 / 78125000000000 : ℝ)) (q := - (3011958796030119 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3011958796030119 / 80000000000000000 : ℚ)) + (r' := (3011958796030119 / 2500000000000000 : ℚ)) + (U := (-(32794360034669585926951 / 10000000000000000000000 : ℚ))) + (U' := (1862998980330414073049 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (997591708683 / 12800000000000 : ℚ)) + (s := (2388809483937 / 78125000000000 : ℚ)) + (q := (3011958796030119 / 80000000000000000 : ℚ)) + (U := (-(32794360034669585926951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_131_6 : Uω (aρ 6) (bρ 6) (997591708683 / 12800000000000 : ℝ) ≤ @@ -2177,25 +2019,21 @@ lemma U_132_1 : have hlg : Real.log (359950707136057 / 5000000000000000 : ℝ) ≤ (-(5262452185846792494703 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (359950707136057 / 5000000000000000 : ℝ) = - (359950707136057 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (359950707136057 / 312500000000000 : ℚ)) - (U := (282725256553207505297 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (359950707136057 / 312500000000000 : ℝ) ≤ - (282725256553207505297 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (359838422397739 / 5000000000000000 : ℝ)) (q := - (359950707136057 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (359950707136057 / 5000000000000000 : ℚ)) + (r' := (359950707136057 / 312500000000000 : ℚ)) + (U := (-(5262452185846792494703 / 2000000000000000000000 : ℚ))) + (U' := (282725256553207505297 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (627698561467 / 8000000000000 : ℚ)) + (s := (359838422397739 / 5000000000000000 : ℚ)) + (q := (359950707136057 / 5000000000000000 : ℚ)) + (U := (-(5262452185846792494703 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_132_2 : Uω (aρ 2) (bρ 2) (627698561467 / 8000000000000 : ℝ) ≤ @@ -2203,25 +2041,21 @@ lemma U_132_2 : have hlg : Real.log (1389660168617201 / 20000000000000000 : ℝ) ≤ (-(6666682595679150360093 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1389660168617201 / 20000000000000000 : ℝ) = - (1389660168617201 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1389660168617201 / 1250000000000000 : ℚ)) - (U := (264789207320849639907 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1389660168617201 / 1250000000000000 : ℝ) ≤ - (264789207320849639907 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (693303197378451 / 10000000000000000 : ℝ)) (q := - (1389660168617201 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1389660168617201 / 20000000000000000 : ℚ)) + (r' := (1389660168617201 / 1250000000000000 : ℚ)) + (U := (-(6666682595679150360093 / 2500000000000000000000 : ℚ))) + (U' := (264789207320849639907 / 2500000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (627698561467 / 8000000000000 : ℚ)) + (s := (693303197378451 / 10000000000000000 : ℚ)) + (q := (1389660168617201 / 20000000000000000 : ℚ)) + (U := (-(6666682595679150360093 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_132_3 : Uω (aρ 3) (bρ 3) (627698561467 / 8000000000000 : ℝ) ≤ @@ -2229,24 +2063,21 @@ lemma U_132_3 : have hlg : Real.log (64320995861959 / 1000000000000000 : ℝ) ≤ (-(3429836462828796430307 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (64320995861959 / 1000000000000000 : ℝ) = (64320995861959 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64320995861959 / 62500000000000 : ℚ)) - (U := (35899438671203569693 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (64320995861959 / 62500000000000 : ℝ) ≤ - (35899438671203569693 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63745905235043 / 1000000000000000 : ℝ)) (q := - (64320995861959 / 1000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64320995861959 / 1000000000000000 : ℚ)) + (r' := (64320995861959 / 62500000000000 : ℚ)) + (U := (-(3429836462828796430307 / 1250000000000000000000 : ℚ))) + (U' := (35899438671203569693 / 1250000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (627698561467 / 8000000000000 : ℚ)) + (s := (63745905235043 / 1000000000000000 : ℚ)) + (q := (64320995861959 / 1000000000000000 : ℚ)) + (U := (-(3429836462828796430307 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_132_4 : Uω (aρ 4) (bρ 4) (627698561467 / 8000000000000 : ℝ) ≤ @@ -2254,25 +2085,21 @@ lemma U_132_4 : have hlg : Real.log (1103187431032073 / 20000000000000000 : ℝ) ≤ (-(28975286180128640663519 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1103187431032073 / 20000000000000000 : ℝ) = - (1103187431032073 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1103187431032073 / 625000000000000 : ℚ)) - (U := (5682072834871359336481 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1103187431032073 / 625000000000000 : ℝ) ≤ - (5682072834871359336481 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (532520747208323 / 10000000000000000 : ℝ)) (q := - (1103187431032073 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1103187431032073 / 20000000000000000 : ℚ)) + (r' := (1103187431032073 / 625000000000000 : ℚ)) + (U := (-(28975286180128640663519 / 10000000000000000000000 : ℚ))) + (U' := (5682072834871359336481 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (627698561467 / 8000000000000 : ℚ)) + (s := (532520747208323 / 10000000000000000 : ℚ)) + (q := (1103187431032073 / 20000000000000000 : ℚ)) + (U := (-(28975286180128640663519 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_132_5 : Uω (aρ 5) (bρ 5) (627698561467 / 8000000000000 : ℝ) ≤ @@ -2280,24 +2107,21 @@ lemma U_132_5 : have hlg : Real.log (95734975020517 / 2500000000000000 : ℝ) ≤ (-(32624623126546358520591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (95734975020517 / 2500000000000000 : ℝ) = (95734975020517 / 78125000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (95734975020517 / 78125000000000 : ℚ)) - (U := (2032735888453641479409 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (95734975020517 / 78125000000000 : ℝ) ≤ - (2032735888453641479409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156701517837693 / 5000000000000000 : ℝ)) (q := - (95734975020517 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (95734975020517 / 2500000000000000 : ℚ)) + (r' := (95734975020517 / 78125000000000 : ℚ)) + (U := (-(32624623126546358520591 / 10000000000000000000000 : ℚ))) + (U' := (2032735888453641479409 / 10000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (627698561467 / 8000000000000 : ℚ)) + (s := (156701517837693 / 5000000000000000 : ℚ)) + (q := (95734975020517 / 2500000000000000 : ℚ)) + (U := (-(32624623126546358520591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_132_6 : Uω (aρ 6) (bρ 6) (627698561467 / 8000000000000 : ℝ) ≤ @@ -2444,24 +2268,21 @@ lemma U_133_1 : have hlg : Real.log (46410094175333 / 640000000000000 : ℝ) ≤ (-(5247902385718883216969 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (46410094175333 / 640000000000000 : ℝ) = (46410094175333 / 40000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46410094175333 / 40000000000000 : ℚ)) - (U := (297275056681116783031 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46410094175333 / 40000000000000 : ℝ) ≤ - (297275056681116783031 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2899739119221 / 40000000000000 : ℝ)) (q := - (46410094175333 / 640000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46410094175333 / 640000000000000 : ℚ)) + (r' := (46410094175333 / 40000000000000 : ℚ)) + (U := (-(5247902385718883216969 / 2000000000000000000000 : ℚ))) + (U' := (297275056681116783031 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5055218440057 / 64000000000000 : ℚ)) + (s := (2899739119221 / 40000000000000 : ℚ)) + (q := (46410094175333 / 640000000000000 : ℚ)) + (U := (-(5247902385718883216969 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_133_2 : Uω (aρ 2) (bρ 2) (5055218440057 / 64000000000000 : ℝ) ≤ @@ -2469,25 +2290,21 @@ lemma U_133_2 : have hlg : Real.log (5600769992529341 / 80000000000000000 : ℝ) ≤ (-(5318245093358236445799 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5600769992529341 / 80000000000000000 : ℝ) = - (5600769992529341 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5600769992529341 / 5000000000000000 : ℚ)) - (U := (226932349041763554201 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5600769992529341 / 5000000000000000 : ℝ) ≤ - (226932349041763554201 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (698580847468429 / 10000000000000000 : ℝ)) (q := - (5600769992529341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5600769992529341 / 80000000000000000 : ℚ)) + (r' := (5600769992529341 / 5000000000000000 : ℚ)) + (U := (-(5318245093358236445799 / 2000000000000000000000 : ℚ))) + (U' := (226932349041763554201 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5055218440057 / 64000000000000 : ℚ)) + (s := (698580847468429 / 10000000000000000 : ℚ)) + (q := (5600769992529341 / 80000000000000000 : ℚ)) + (U := (-(5318245093358236445799 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_133_3 : Uω (aρ 3) (bρ 3) (5055218440057 / 64000000000000 : ℝ) ≤ @@ -2495,25 +2312,21 @@ lemma U_133_3 : have hlg : Real.log (5188093221524637 / 80000000000000000 : ℝ) ≤ (-(27356603986588711129289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5188093221524637 / 80000000000000000 : ℝ) = - (5188093221524637 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5188093221524637 / 5000000000000000 : ℚ)) - (U := (369283225411288870711 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5188093221524637 / 5000000000000000 : ℝ) ≤ - (369283225411288870711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (642807761067253 / 10000000000000000 : ℝ)) (q := - (5188093221524637 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5188093221524637 / 80000000000000000 : ℚ)) + (r' := (5188093221524637 / 5000000000000000 : ℚ)) + (U := (-(27356603986588711129289 / 10000000000000000000000 : ℚ))) + (U' := (369283225411288870711 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5055218440057 / 64000000000000 : ℚ)) + (s := (642807761067253 / 10000000000000000 : ℚ)) + (q := (5188093221524637 / 80000000000000000 : ℚ)) + (U := (-(27356603986588711129289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_133_4 : Uω (aρ 4) (bρ 4) (5055218440057 / 64000000000000 : ℝ) ≤ @@ -2521,25 +2334,21 @@ lemma U_133_4 : have hlg : Real.log (4456277560487961 / 80000000000000000 : ℝ) ≤ (-(14438564217655403680117 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4456277560487961 / 80000000000000000 : ℝ) = - (4456277560487961 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4456277560487961 / 2500000000000000 : ℚ)) - (U := (2890115289844596319883 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4456277560487961 / 2500000000000000 : ℝ) ≤ - (2890115289844596319883 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (134537006718271 / 2500000000000000 : ℝ)) (q := - (4456277560487961 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4456277560487961 / 80000000000000000 : ℚ)) + (r' := (4456277560487961 / 2500000000000000 : ℚ)) + (U := (-(14438564217655403680117 / 5000000000000000000000 : ℚ))) + (U' := (2890115289844596319883 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5055218440057 / 64000000000000 : ℚ)) + (s := (134537006718271 / 2500000000000000 : ℚ)) + (q := (4456277560487961 / 80000000000000000 : ℚ)) + (U := (-(14438564217655403680117 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_133_5 : Uω (aρ 5) (bρ 5) (5055218440057 / 64000000000000 : ℝ) ≤ @@ -2547,25 +2356,21 @@ lemma U_133_5 : have hlg : Real.log (622939437810389 / 16000000000000000 : ℝ) ≤ (-(4057368370546522140043 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (622939437810389 / 16000000000000000 : ℝ) = - (622939437810389 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (622939437810389 / 500000000000000 : ℚ)) - (U := (274801506328477859957 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (622939437810389 / 500000000000000 : ℝ) ≤ - (274801506328477859957 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8023571333727 / 250000000000000 : ℝ)) (q := - (622939437810389 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (622939437810389 / 16000000000000000 : ℚ)) + (r' := (622939437810389 / 500000000000000 : ℚ)) + (U := (-(4057368370546522140043 / 1250000000000000000000 : ℚ))) + (U' := (274801506328477859957 / 1250000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5055218440057 / 64000000000000 : ℚ)) + (s := (8023571333727 / 250000000000000 : ℚ)) + (q := (622939437810389 / 16000000000000000 : ℚ)) + (U := (-(4057368370546522140043 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_133_6 : Uω (aρ 6) (bρ 6) (5055218440057 / 64000000000000 : ℝ) ≤ @@ -2712,25 +2517,21 @@ lemma U_134_1 : have hlg : Real.log (2921656021086593 / 40000000000000000 : ℝ) ≤ (-(26167288670425871360889 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2921656021086593 / 40000000000000000 : ℝ) = - (2921656021086593 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2921656021086593 / 2500000000000000 : ℚ)) - (U := (1558598541574128639111 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2921656021086593 / 2500000000000000 : ℝ) ≤ - (1558598541574128639111 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (365096333972117 / 5000000000000000 : ℝ)) (q := - (2921656021086593 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2921656021086593 / 40000000000000000 : ℚ)) + (r' := (2921656021086593 / 2500000000000000 : ℚ)) + (U := (-(26167288670425871360889 / 10000000000000000000000 : ℚ))) + (U' := (1558598541574128639111 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2544424194189 / 32000000000000 : ℚ)) + (s := (365096333972117 / 5000000000000000 : ℚ)) + (q := (2921656021086593 / 40000000000000000 : ℚ)) + (U := (-(26167288670425871360889 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_134_2 : Uω (aρ 2) (bρ 2) (2544424194189 / 32000000000000 : ℝ) ≤ @@ -2738,25 +2539,21 @@ lemma U_134_2 : have hlg : Real.log (2821448967842361 / 40000000000000000 : ℝ) ≤ (-(26516288816997824638059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2821448967842361 / 40000000000000000 : ℝ) = - (2821448967842361 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2821448967842361 / 2500000000000000 : ℚ)) - (U := (1209598395002175361941 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2821448967842361 / 2500000000000000 : ℝ) ≤ - (1209598395002175361941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (351929076916059 / 5000000000000000 : ℝ)) (q := - (2821448967842361 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2821448967842361 / 40000000000000000 : ℚ)) + (r' := (2821448967842361 / 2500000000000000 : ℚ)) + (U := (-(26516288816997824638059 / 10000000000000000000000 : ℚ))) + (U' := (1209598395002175361941 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2544424194189 / 32000000000000 : ℚ)) + (s := (351929076916059 / 5000000000000000 : ℚ)) + (q := (2821448967842361 / 40000000000000000 : ℚ)) + (U := (-(26516288816997824638059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_134_3 : Uω (aρ 3) (bρ 3) (2544424194189 / 32000000000000 : ℝ) ≤ @@ -2764,25 +2561,21 @@ lemma U_134_3 : have hlg : Real.log (2615250310535261 / 40000000000000000 : ℝ) ≤ (-(2727519639092246926631 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2615250310535261 / 40000000000000000 : ℝ) = - (2615250310535261 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2615250310535261 / 2500000000000000 : ℚ)) - (U := (45069082107753073369 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2615250310535261 / 2500000000000000 : ℝ) ≤ - (45069082107753073369 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (81019366441071 / 1250000000000000 : ℝ)) (q := - (2615250310535261 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2615250310535261 / 40000000000000000 : ℚ)) + (r' := (2615250310535261 / 2500000000000000 : ℚ)) + (U := (-(2727519639092246926631 / 1000000000000000000000 : ℚ))) + (U' := (45069082107753073369 / 1000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2544424194189 / 32000000000000 : ℚ)) + (s := (81019366441071 / 1250000000000000 : ℚ)) + (q := (2615250310535261 / 40000000000000000 : ℚ)) + (U := (-(2727519639092246926631 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_134_4 : Uω (aρ 4) (bρ 4) (2544424194189 / 32000000000000 : ℝ) ≤ @@ -2790,25 +2583,21 @@ lemma U_134_4 : have hlg : Real.log (2249887785468721 / 40000000000000000 : ℝ) ≤ (-(28779991109665995308087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2249887785468721 / 40000000000000000 : ℝ) = - (2249887785468721 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2249887785468721 / 1250000000000000 : ℚ)) - (U := (5877367905334004691913 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2249887785468721 / 1250000000000000 : ℝ) ≤ - (5877367905334004691913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (271883925030149 / 5000000000000000 : ℝ)) (q := - (2249887785468721 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2249887785468721 / 40000000000000000 : ℚ)) + (r' := (2249887785468721 / 1250000000000000 : ℚ)) + (U := (-(28779991109665995308087 / 10000000000000000000000 : ℚ))) + (U' := (5877367905334004691913 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2544424194189 / 32000000000000 : ℚ)) + (s := (271883925030149 / 5000000000000000 : ℚ)) + (q := (2249887785468721 / 40000000000000000 : ℚ)) + (U := (-(28779991109665995308087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_134_5 : Uω (aρ 5) (bρ 5) (2544424194189 / 32000000000000 : ℝ) ≤ @@ -2816,25 +2605,21 @@ lemma U_134_5 : have hlg : Real.log (1582759550979519 / 40000000000000000 : ℝ) ≤ (-(16148547889847596668857 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1582759550979519 / 40000000000000000 : ℝ) = - (1582759550979519 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1582759550979519 / 1250000000000000 : ℚ)) - (U := (1180131617652403331143 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1582759550979519 / 1250000000000000 : ℝ) ≤ - (1180131617652403331143 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (328393652150697 / 10000000000000000 : ℝ)) (q := - (1582759550979519 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1582759550979519 / 40000000000000000 : ℚ)) + (r' := (1582759550979519 / 1250000000000000 : ℚ)) + (U := (-(16148547889847596668857 / 5000000000000000000000 : ℚ))) + (U' := (1180131617652403331143 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2544424194189 / 32000000000000 : ℚ)) + (s := (328393652150697 / 10000000000000000 : ℚ)) + (q := (1582759550979519 / 40000000000000000 : ℚ)) + (U := (-(16148547889847596668857 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_134_6 : Uω (aρ 6) (bρ 6) (2544424194189 / 32000000000000 : ℝ) ≤ @@ -2982,25 +2767,21 @@ lemma U_135_1 : have hlg : Real.log (235414485158707 / 3200000000000000 : ℝ) ≤ (-(13047791802904571252103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (235414485158707 / 3200000000000000 : ℝ) = - (235414485158707 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (235414485158707 / 200000000000000 : ℚ)) - (U := (815151803095428747897 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (235414485158707 / 200000000000000 : ℝ) ≤ - (815151803095428747897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7354505102177 / 100000000000000 : ℝ)) (q := - (235414485158707 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (235414485158707 / 3200000000000000 : ℚ)) + (r' := (235414485158707 / 200000000000000 : ℚ)) + (U := (-(13047791802904571252103 / 5000000000000000000000 : ℚ))) + (U' := (815151803095428747897 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5122478336699 / 64000000000000 : ℚ)) + (s := (7354505102177 / 100000000000000 : ℚ)) + (q := (235414485158707 / 3200000000000000 : ℚ)) + (U := (-(13047791802904571252103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_135_2 : Uω (aρ 2) (bρ 2) (5122478336699 / 64000000000000 : ℝ) ≤ @@ -3008,25 +2789,21 @@ lemma U_135_2 : have hlg : Real.log (5685024534630623 / 80000000000000000 : ℝ) ≤ (-(13220955953813518373719 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5685024534630623 / 80000000000000000 : ℝ) = - (5685024534630623 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5685024534630623 / 5000000000000000 : ℚ)) - (U := (641987652186481626281 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5685024534630623 / 5000000000000000 : ℝ) ≤ - (641987652186481626281 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (709135124143437 / 10000000000000000 : ℝ)) (q := - (5685024534630623 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5685024534630623 / 80000000000000000 : ℚ)) + (r' := (5685024534630623 / 5000000000000000 : ℚ)) + (U := (-(13220955953813518373719 / 5000000000000000000000 : ℚ))) + (U' := (641987652186481626281 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5122478336699 / 64000000000000 : ℚ)) + (s := (709135124143437 / 10000000000000000 : ℚ)) + (q := (5685024534630623 / 80000000000000000 : ℚ)) + (U := (-(13220955953813518373719 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_135_3 : Uω (aρ 3) (bρ 3) (5122478336699 / 64000000000000 : ℝ) ≤ @@ -3034,25 +2811,21 @@ lemma U_135_3 : have hlg : Real.log (5272902018632919 / 80000000000000000 : ℝ) ≤ (-(13597228774851769235177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5272902018632919 / 80000000000000000 : ℝ) = - (5272902018632919 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5272902018632919 / 5000000000000000 : ℚ)) - (U := (265714831148230764823 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5272902018632919 / 5000000000000000 : ℝ) ≤ - (265714831148230764823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (653500601494011 / 10000000000000000 : ℝ)) (q := - (5272902018632919 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5272902018632919 / 80000000000000000 : ℚ)) + (r' := (5272902018632919 / 5000000000000000 : ℚ)) + (U := (-(13597228774851769235177 / 5000000000000000000000 : ℚ))) + (U' := (265714831148230764823 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5122478336699 / 64000000000000 : ℚ)) + (s := (653500601494011 / 10000000000000000 : ℚ)) + (q := (5272902018632919 / 80000000000000000 : ℚ)) + (U := (-(13597228774851769235177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_135_4 : Uω (aρ 4) (bρ 4) (5122478336699 / 64000000000000 : ℝ) ≤ @@ -3060,25 +2833,21 @@ lemma U_135_4 : have hlg : Real.log (4543244670778931 / 80000000000000000 : ℝ) ≤ (-(7170962978482870943403 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4543244670778931 / 80000000000000000 : ℝ) = - (4543244670778931 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4543244670778931 / 2500000000000000 : ℚ)) - (U := (1493376775267129056597 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4543244670778931 / 2500000000000000 : ℝ) ≤ - (1493376775267129056597 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (274690222797757 / 5000000000000000 : ℝ)) (q := - (4543244670778931 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4543244670778931 / 80000000000000000 : ℚ)) + (r' := (4543244670778931 / 2500000000000000 : ℚ)) + (U := (-(7170962978482870943403 / 2500000000000000000000 : ℚ))) + (U' := (1493376775267129056597 / 2500000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5122478336699 / 64000000000000 : ℚ)) + (s := (274690222797757 / 5000000000000000 : ℚ)) + (q := (4543244670778931 / 80000000000000000 : ℚ)) + (U := (-(7170962978482870943403 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_135_5 : Uω (aρ 5) (bρ 5) (5122478336699 / 64000000000000 : ℝ) ≤ @@ -3086,25 +2855,21 @@ lemma U_135_5 : have hlg : Real.log (3216008644341211 / 80000000000000000 : ℝ) ≤ (-(6427771188288008699121 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3216008644341211 / 80000000000000000 : ℝ) = - (3216008644341211 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3216008644341211 / 2500000000000000 : ℚ)) - (U := (503700614711991300879 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3216008644341211 / 2500000000000000 : ℝ) ≤ - (503700614711991300879 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83940339580271 / 2500000000000000 : ℝ)) (q := - (3216008644341211 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3216008644341211 / 80000000000000000 : ℚ)) + (r' := (3216008644341211 / 2500000000000000 : ℚ)) + (U := (-(6427771188288008699121 / 2000000000000000000000 : ℚ))) + (U' := (503700614711991300879 / 2000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5122478336699 / 64000000000000 : ℚ)) + (s := (83940339580271 / 2500000000000000 : ℚ)) + (q := (3216008644341211 / 80000000000000000 : ℚ)) + (U := (-(6427771188288008699121 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_135_6 : Uω (aρ 6) (bρ 6) (5122478336699 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U11.lean b/LeanPool/Zeta5Irrational/Table/U11.lean index 94199086dc..b59108f235 100644 --- a/LeanPool/Zeta5Irrational/Table/U11.lean +++ b/LeanPool/Zeta5Irrational/Table/U11.lean @@ -24,25 +24,21 @@ lemma U_136_1 : have hlg : Real.log (296370601810347 / 4000000000000000 : ℝ) ≤ (-(26024389347350076319563 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (296370601810347 / 4000000000000000 : ℝ) = - (296370601810347 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (296370601810347 / 250000000000000 : ℚ)) - (U := (1701497864649923680437 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (296370601810347 / 250000000000000 : ℝ) ≤ - (1701497864649923680437 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18517707690059 / 250000000000000 : ℝ)) (q := - (296370601810347 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (296370601810347 / 4000000000000000 : ℚ)) + (r' := (296370601810347 / 250000000000000 : ℚ)) + (U := (-(26024389347350076319563 / 10000000000000000000000 : ℚ))) + (U' := (1701497864649923680437 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (257805414251 / 3200000000000 : ℚ)) + (s := (18517707690059 / 250000000000000 : ℚ)) + (q := (296370601810347 / 4000000000000000 : ℚ)) + (U := (-(26024389347350076319563 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_136_2 : Uω (aρ 2) (bρ 2) (257805414251 / 3200000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_136_2 : have hlg : Real.log (1431787454788469 / 20000000000000000 : ℝ) ≤ (-(26368086404189464320953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1431787454788469 / 20000000000000000 : ℝ) = - (1431787454788469 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1431787454788469 / 1250000000000000 : ℚ)) - (U := (1357800807810535679047 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1431787454788469 / 1250000000000000 : ℝ) ≤ - (1357800807810535679047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (357205882924547 / 5000000000000000 : ℝ)) (q := - (1431787454788469 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1431787454788469 / 20000000000000000 : ℚ)) + (r' := (1431787454788469 / 1250000000000000 : ℚ)) + (U := (-(26368086404189464320953 / 10000000000000000000000 : ℚ))) + (U' := (1357800807810535679047 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (257805414251 / 3200000000000 : ℚ)) + (s := (357205882924547 / 5000000000000000 : ℚ)) + (q := (1431787454788469 / 20000000000000000 : ℚ)) + (U := (-(26368086404189464320953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_136_3 : Uω (aρ 3) (bρ 3) (257805414251 / 3200000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_136_3 : have hlg : Real.log (664412195038341 / 10000000000000000 : ℝ) ≤ (-(3389297048001651951123 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (664412195038341 / 10000000000000000 : ℝ) = - (664412195038341 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (664412195038341 / 625000000000000 : ℚ)) - (U := (76438853498348048877 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (664412195038341 / 625000000000000 : ℝ) ≤ - (76438853498348048877 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (658844807487307 / 10000000000000000 : ℝ)) (q := - (664412195038341 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (664412195038341 / 10000000000000000 : ℚ)) + (r' := (664412195038341 / 625000000000000 : ℚ)) + (U := (-(3389297048001651951123 / 1250000000000000000000 : ℚ))) + (U' := (76438853498348048877 / 1250000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (257805414251 / 3200000000000 : ℚ)) + (s := (658844807487307 / 10000000000000000 : ℚ)) + (q := (664412195038341 / 10000000000000000 : ℚ)) + (U := (-(3389297048001651951123 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_136_4 : Uω (aρ 4) (bρ 4) (257805414251 / 3200000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_136_4 : have hlg : Real.log (1146671434283737 / 20000000000000000 : ℝ) ≤ (-(7147172329350315520741 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1146671434283737 / 20000000000000000 : ℝ) = - (1146671434283737 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1146671434283737 / 625000000000000 : ℚ)) - (U := (1517167424399684479259 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1146671434283737 / 625000000000000 : ℝ) ≤ - (1517167424399684479259 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (277493016379681 / 5000000000000000 : ℝ)) (q := - (1146671434283737 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1146671434283737 / 20000000000000000 : ℚ)) + (r' := (1146671434283737 / 625000000000000 : ℚ)) + (U := (-(7147172329350315520741 / 2500000000000000000000 : ℚ))) + (U' := (1517167424399684479259 / 2500000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (257805414251 / 3200000000000 : ℚ)) + (s := (277493016379681 / 5000000000000000 : ℚ)) + (q := (1146671434283737 / 20000000000000000 : ℚ)) + (U := (-(7147172329350315520741 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_136_5 : Uω (aρ 5) (bρ 5) (257805414251 / 3200000000000 : ℝ) ≤ @@ -128,23 +112,21 @@ lemma U_136_5 : have hlg : Real.log (2551708774461 / 62500000000000 : ℝ) ≤ (-(31984033130623965837531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show (2551708774461 / 62500000000000 : ℝ) = (2551708774461 / 1953125000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2551708774461 / 1953125000000 : ℚ)) - (U := (2673325884376034162469 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2551708774461 / 1953125000000 : ℝ) ≤ - (2673325884376034162469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68610265127629 / 2000000000000000 : ℝ)) (q := - (2551708774461 / 62500000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2551708774461 / 62500000000000 : ℚ)) + (r' := (2551708774461 / 1953125000000 : ℚ)) + (U := (-(31984033130623965837531 / 10000000000000000000000 : ℚ))) + (U' := (2673325884376034162469 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (257805414251 / 3200000000000 : ℚ)) + (s := (68610265127629 / 2000000000000000 : ℚ)) + (q := (2551708774461 / 62500000000000 : ℚ)) + (U := (-(31984033130623965837531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_136_6 : Uω (aρ 6) (bρ 6) (257805414251 / 3200000000000 : ℝ) ≤ @@ -292,25 +274,21 @@ lemma U_137_1 : have hlg : Real.log (3005755663550111 / 40000000000000000 : ℝ) ≤ (-(25883504479644690843899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3005755663550111 / 40000000000000000 : ℝ) = - (3005755663550111 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3005755663550111 / 2500000000000000 : ℚ)) - (U := (1842382732355309156101 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3005755663550111 / 2500000000000000 : ℝ) ≤ - (1842382732355309156101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (93902971434421 / 1250000000000000 : ℝ)) (q := - (3005755663550111 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3005755663550111 / 40000000000000000 : ℚ)) + (r' := (3005755663550111 / 2500000000000000 : ℚ)) + (U := (-(25883504479644690843899 / 10000000000000000000000 : ℚ))) + (U' := (1842382732355309156101 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2611684090831 / 32000000000000 : ℚ)) + (s := (93902971434421 / 1250000000000000 : ℚ)) + (q := (3005755663550111 / 40000000000000000 : ℚ)) + (U := (-(25883504479644690843899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_137_2 : Uω (aρ 2) (bρ 2) (2611684090831 / 32000000000000 : ℝ) ≤ @@ -318,25 +296,21 @@ lemma U_137_2 : have hlg : Real.log (2905698279867373 / 40000000000000000 : ℝ) ≤ (-(5244411439855569471477 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2905698279867373 / 40000000000000000 : ℝ) = - (2905698279867373 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2905698279867373 / 2500000000000000 : ℚ)) - (U := (300766002544430528523 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2905698279867373 / 2500000000000000 : ℝ) ≤ - (300766002544430528523 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (724964092143999 / 10000000000000000 : ℝ)) (q := - (2905698279867373 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2905698279867373 / 40000000000000000 : ℚ)) + (r' := (2905698279867373 / 2500000000000000 : ℚ)) + (U := (-(5244411439855569471477 / 2000000000000000000000 : ℚ))) + (U' := (300766002544430528523 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2611684090831 / 32000000000000 : ℚ)) + (s := (724964092143999 / 10000000000000000 : ℚ)) + (q := (2905698279867373 / 40000000000000000 : ℚ)) + (U := (-(5244411439855569471477 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_137_3 : Uω (aρ 3) (bρ 3) (2611684090831 / 32000000000000 : ℝ) ≤ @@ -344,25 +318,21 @@ lemma U_137_3 : have hlg : Real.log (2700035818426691 / 40000000000000000 : ℝ) ≤ (-(26956144140679057589663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2700035818426691 / 40000000000000000 : ℝ) = - (2700035818426691 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2700035818426691 / 2500000000000000 : ℚ)) - (U := (769743071320942410337 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2700035818426691 / 2500000000000000 : ℝ) ≤ - (769743071320942410337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (334764483886829 / 5000000000000000 : ℝ)) (q := - (2700035818426691 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2700035818426691 / 40000000000000000 : ℚ)) + (r' := (2700035818426691 / 2500000000000000 : ℚ)) + (U := (-(26956144140679057589663 / 10000000000000000000000 : ℚ))) + (U' := (769743071320942410337 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2611684090831 / 32000000000000 : ℚ)) + (s := (334764483886829 / 5000000000000000 : ℚ)) + (q := (2700035818426691 / 40000000000000000 : ℚ)) + (U := (-(26956144140679057589663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_137_4 : Uω (aρ 4) (bρ 4) (2611684090831 / 32000000000000 : ℝ) ≤ @@ -370,25 +340,21 @@ lemma U_137_4 : have hlg : Real.log (2336743549494169 / 40000000000000000 : ℝ) ≤ (-(1136048455279144140469 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2336743549494169 / 40000000000000000 : ℝ) = - (2336743549494169 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2336743549494169 / 1250000000000000 : ℚ)) - (U := (250245905320855859531 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2336743549494169 / 1250000000000000 : ℝ) ≤ - (250245905320855859531 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (566177014372397 / 10000000000000000 : ℝ)) (q := - (2336743549494169 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2336743549494169 / 40000000000000000 : ℚ)) + (r' := (2336743549494169 / 1250000000000000 : ℚ)) + (U := (-(1136048455279144140469 / 400000000000000000000 : ℚ))) + (U' := (250245905320855859531 / 400000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2611684090831 / 32000000000000 : ℚ)) + (s := (566177014372397 / 10000000000000000 : ℚ)) + (q := (2336743549494169 / 40000000000000000 : ℚ)) + (U := (-(1136048455279144140469 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_137_5 : Uω (aρ 5) (bρ 5) (2611684090831 / 32000000000000 : ℝ) ≤ @@ -396,25 +362,21 @@ lemma U_137_5 : have hlg : Real.log (336568744601939 / 8000000000000000 : ℝ) ≤ (-(15841971990601673642843 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (336568744601939 / 8000000000000000 : ℝ) = - (336568744601939 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (336568744601939 / 250000000000000 : ℚ)) - (U := (1486707516898326357157 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (336568744601939 / 250000000000000 : ℝ) ≤ - (1486707516898326357157 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8935425511629 / 250000000000000 : ℝ)) (q := - (336568744601939 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (336568744601939 / 8000000000000000 : ℚ)) + (r' := (336568744601939 / 250000000000000 : ℚ)) + (U := (-(15841971990601673642843 / 5000000000000000000000 : ℚ))) + (U' := (1486707516898326357157 / 5000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2611684090831 / 32000000000000 : ℚ)) + (s := (8935425511629 / 250000000000000 : ℚ)) + (q := (336568744601939 / 8000000000000000 : ℚ)) + (U := (-(15841971990601673642843 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_137_6 : Uω (aρ 6) (bρ 6) (2611684090831 / 32000000000000 : ℝ) ≤ @@ -562,24 +524,21 @@ lemma U_138_1 : have hlg : Real.log (38097562149829 / 500000000000000 : ℝ) ≤ (-(25744578028657117086197 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (38097562149829 / 500000000000000 : ℝ) = (38097562149829 / 31250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38097562149829 / 31250000000000 : ℚ)) - (U := (1981309183342882913803 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (38097562149829 / 31250000000000 : ℝ) ≤ - (1981309183342882913803 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19043476671079 / 250000000000000 : ℝ)) (q := - (38097562149829 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38097562149829 / 500000000000000 : ℚ)) + (r' := (38097562149829 / 31250000000000 : ℚ)) + (U := (-(25744578028657117086197 / 10000000000000000000000 : ℚ))) + (U' := (1981309183342882913803 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (165332127447 / 2000000000000 : ℚ)) + (s := (19043476671079 / 250000000000000 : ℚ)) + (q := (38097562149829 / 500000000000000 : ℚ)) + (U := (-(25744578028657117086197 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_138_2 : Uω (aρ 2) (bρ 2) (165332127447 / 2000000000000 : ℝ) ≤ @@ -587,25 +546,21 @@ lemma U_138_2 : have hlg : Real.log (1473909594695023 / 20000000000000000 : ℝ) ≤ (-(3259767267427656465799 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1473909594695023 / 20000000000000000 : ℝ) = - (1473909594695023 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1473909594695023 / 1250000000000000 : ℚ)) - (U := (205968634072343534201 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1473909594695023 / 1250000000000000 : ℝ) ≤ - (205968634072343534201 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (735515188055023 / 10000000000000000 : ℝ)) (q := - (1473909594695023 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1473909594695023 / 20000000000000000 : ℚ)) + (r' := (1473909594695023 / 1250000000000000 : ℚ)) + (U := (-(3259767267427656465799 / 1250000000000000000000 : ℚ))) + (U' := (205968634072343534201 / 1250000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (165332127447 / 2000000000000 : ℚ)) + (s := (735515188055023 / 10000000000000000 : ℚ)) + (q := (1473909594695023 / 20000000000000000 : ℚ)) + (U := (-(3259767267427656465799 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_138_3 : Uω (aρ 3) (bρ 3) (165332127447 / 2000000000000 : ℝ) ≤ @@ -613,25 +568,21 @@ lemma U_138_3 : have hlg : Real.log (685602991004679 / 10000000000000000 : ℝ) ≤ (-(3350052051316778232639 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (685602991004679 / 10000000000000000 : ℝ) = - (685602991004679 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (685602991004679 / 625000000000000 : ℚ)) - (U := (115683850183221767361 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (685602991004679 / 625000000000000 : ℝ) ≤ - (115683850183221767361 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (340103840859679 / 5000000000000000 : ℝ)) (q := - (685602991004679 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (685602991004679 / 10000000000000000 : ℚ)) + (r' := (685602991004679 / 625000000000000 : ℚ)) + (U := (-(3350052051316778232639 / 1250000000000000000000 : ℚ))) + (U' := (115683850183221767361 / 1250000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (165332127447 / 2000000000000 : ℚ)) + (s := (340103840859679 / 5000000000000000 : ℚ)) + (q := (685602991004679 / 10000000000000000 : ℚ)) + (U := (-(3350052051316778232639 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_138_4 : Uω (aρ 4) (bρ 4) (165332127447 / 2000000000000 : ℝ) ≤ @@ -639,25 +590,21 @@ lemma U_138_4 : have hlg : Real.log (297511623973151 / 5000000000000000 : ℝ) ≤ (-(14108699468577326473109 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (297511623973151 / 5000000000000000 : ℝ) = - (297511623973151 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (297511623973151 / 156250000000000 : ℚ)) - (U := (3219980038922673526891 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (297511623973151 / 156250000000000 : ℝ) ≤ - (3219980038922673526891 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (144335594166901 / 2500000000000000 : ℝ)) (q := - (297511623973151 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (297511623973151 / 5000000000000000 : ℚ)) + (r' := (297511623973151 / 156250000000000 : ℚ)) + (U := (-(14108699468577326473109 / 5000000000000000000000 : ℚ))) + (U' := (3219980038922673526891 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (165332127447 / 2000000000000 : ℚ)) + (s := (144335594166901 / 2500000000000000 : ℚ)) + (q := (297511623973151 / 5000000000000000 : ℚ)) + (U := (-(14108699468577326473109 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_138_5 : Uω (aρ 5) (bρ 5) (165332127447 / 2000000000000 : ℝ) ≤ @@ -665,24 +612,21 @@ lemma U_138_5 : have hlg : Real.log (34641552310843 / 800000000000000 : ℝ) ≤ (-(627911566201869230741 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (34641552310843 / 800000000000000 : ℝ) = (34641552310843 / 25000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34641552310843 / 25000000000000 : ℚ)) - (U := (65235614098130769259 / 200000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (34641552310843 / 25000000000000 : ℝ) ≤ - (65235614098130769259 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14860984315243 / 400000000000000 : ℝ)) (q := - (34641552310843 / 800000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34641552310843 / 800000000000000 : ℚ)) + (r' := (34641552310843 / 25000000000000 : ℚ)) + (U := (-(627911566201869230741 / 200000000000000000000 : ℚ))) + (U' := (65235614098130769259 / 200000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (165332127447 / 2000000000000 : ℚ)) + (s := (14860984315243 / 400000000000000 : ℚ)) + (q := (34641552310843 / 800000000000000 : ℚ)) + (U := (-(627911566201869230741 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_138_6 : Uω (aρ 6) (bρ 6) (165332127447 / 2000000000000 : ℝ) ≤ @@ -829,25 +773,21 @@ lemma U_139_1 : have hlg : Real.log (3089853957178669 / 40000000000000000 : ℝ) ≤ (-(25607556263304084967409 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3089853957178669 / 40000000000000000 : ℝ) = - (3089853957178669 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3089853957178669 / 2500000000000000 : ℚ)) - (U := (2118330948695915032591 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3089853957178669 / 2500000000000000 : ℝ) ≤ - (2118330948695915032591 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (386127100294511 / 5000000000000000 : ℝ)) (q := - (3089853957178669 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3089853957178669 / 40000000000000000 : ℚ)) + (r' := (3089853957178669 / 2500000000000000 : ℚ)) + (U := (-(25607556263304084967409 / 10000000000000000000000 : ℚ))) + (U' := (2118330948695915032591 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2678943987473 / 32000000000000 : ℚ)) + (s := (386127100294511 / 5000000000000000 : ℚ)) + (q := (3089853957178669 / 40000000000000000 : ℚ)) + (U := (-(25607556263304084967409 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_139_2 : Uω (aρ 2) (bρ 2) (2678943987473 / 32000000000000 : ℝ) ≤ @@ -855,25 +795,21 @@ lemma U_139_2 : have hlg : Real.log (597987548509579 / 8000000000000000 : ℝ) ≤ (-(3242033609723343368109 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (597987548509579 / 8000000000000000 : ℝ) = - (597987548509579 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (597987548509579 / 500000000000000 : ℚ)) - (U := (223702291776656631891 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (597987548509579 / 500000000000000 : ℝ) ≤ - (223702291776656631891 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (149213021156727 / 2000000000000000 : ℝ)) (q := - (597987548509579 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (597987548509579 / 8000000000000000 : ℚ)) + (r' := (597987548509579 / 500000000000000 : ℚ)) + (U := (-(3242033609723343368109 / 1250000000000000000000 : ℚ))) + (U' := (223702291776656631891 / 1250000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2678943987473 / 32000000000000 : ℚ)) + (s := (149213021156727 / 2000000000000000 : ℚ)) + (q := (597987548509579 / 8000000000000000 : ℚ)) + (U := (-(3242033609723343368109 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_139_3 : Uω (aρ 3) (bρ 3) (2678943987473 / 32000000000000 : ℝ) ≤ @@ -881,25 +817,21 @@ lemma U_139_3 : have hlg : Real.log (2784777722022853 / 40000000000000000 : ℝ) ≤ (-(5329422790878437414709 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2784777722022853 / 40000000000000000 : ℝ) = - (2784777722022853 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2784777722022853 / 2500000000000000 : ℚ)) - (U := (215754651521562585291 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2784777722022853 / 2500000000000000 : ℝ) ≤ - (215754651521562585291 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (345440600935557 / 5000000000000000 : ℝ)) (q := - (2784777722022853 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2784777722022853 / 40000000000000000 : ℚ)) + (r' := (2784777722022853 / 2500000000000000 : ℚ)) + (U := (-(5329422790878437414709 / 2000000000000000000000 : ℚ))) + (U' := (215754651521562585291 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2678943987473 / 32000000000000 : ℚ)) + (s := (345440600935557 / 5000000000000000 : ℚ)) + (q := (2784777722022853 / 40000000000000000 : ℚ)) + (U := (-(5329422790878437414709 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_139_4 : Uω (aρ 4) (bρ 4) (2678943987473 / 32000000000000 : ℝ) ≤ @@ -907,25 +839,21 @@ lemma U_139_4 : have hlg : Real.log (2423394111912659 / 40000000000000000 : ℝ) ≤ (-(350463796210277297691 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2423394111912659 / 40000000000000000 : ℝ) = - (2423394111912659 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2423394111912659 / 1250000000000000 : ℚ)) - (U := (82753191477222702309 / 125000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2423394111912659 / 1250000000000000 : ℝ) ≤ - (82753191477222702309 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (588483577881017 / 10000000000000000 : ℝ)) (q := - (2423394111912659 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2423394111912659 / 40000000000000000 : ℚ)) + (r' := (2423394111912659 / 1250000000000000 : ℚ)) + (U := (-(350463796210277297691 / 125000000000000000000 : ℚ))) + (U' := (82753191477222702309 / 125000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2678943987473 / 32000000000000 : ℚ)) + (s := (588483577881017 / 10000000000000000 : ℚ)) + (q := (2423394111912659 / 40000000000000000 : ℚ)) + (U := (-(350463796210277297691 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_139_5 : Uω (aρ 5) (bρ 5) (2678943987473 / 32000000000000 : ℝ) ≤ @@ -933,25 +861,21 @@ lemma U_139_5 : have hlg : Real.log (356170396638393 / 8000000000000000 : ℝ) ≤ (-(15558937803900991527783 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (356170396638393 / 8000000000000000 : ℝ) = - (356170396638393 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (356170396638393 / 250000000000000 : ℚ)) - (U := (1769741703599008472217 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (356170396638393 / 250000000000000 : ℝ) ≤ - (1769741703599008472217 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38540243285567 / 1000000000000000 : ℝ)) (q := - (356170396638393 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (356170396638393 / 8000000000000000 : ℚ)) + (r' := (356170396638393 / 250000000000000 : ℚ)) + (U := (-(15558937803900991527783 / 5000000000000000000000 : ℚ))) + (U' := (1769741703599008472217 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2678943987473 / 32000000000000 : ℚ)) + (s := (38540243285567 / 1000000000000000 : ℚ)) + (q := (356170396638393 / 8000000000000000 : ℚ)) + (U := (-(15558937803900991527783 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_139_6 : Uω (aρ 6) (bρ 6) (2678943987473 / 32000000000000 : ℝ) ≤ @@ -1098,25 +1022,21 @@ lemma U_140_1 : have hlg : Real.log (1565951316076903 / 20000000000000000 : ℝ) ≤ (-(25472387635023400139573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1565951316076903 / 20000000000000000 : ℝ) = - (1565951316076903 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1565951316076903 / 1250000000000000 : ℚ)) - (U := (2253499576976599860427 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1565951316076903 / 1250000000000000 : ℝ) ≤ - (2253499576976599860427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (391384589613139 / 5000000000000000 : ℝ)) (q := - (1565951316076903 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1565951316076903 / 20000000000000000 : ℚ)) + (r' := (1565951316076903 / 1250000000000000 : ℚ)) + (U := (-(25472387635023400139573 / 10000000000000000000000 : ℚ))) + (U' := (2253499576976599860427 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1356286967897 / 16000000000000 : ℚ)) + (s := (391384589613139 / 5000000000000000 : ℚ)) + (q := (1565951316076903 / 20000000000000000 : ℚ)) + (U := (-(25472387635023400139573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_140_2 : Uω (aρ 2) (bρ 2) (1356286967897 / 16000000000000 : ℝ) ≤ @@ -1124,25 +1044,21 @@ lemma U_140_2 : have hlg : Real.log (1516027018954759 / 20000000000000000 : ℝ) ≤ (-(12898195814616624135193 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1516027018954759 / 20000000000000000 : ℝ) = - (1516027018954759 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1516027018954759 / 1250000000000000 : ℚ)) - (U := (964747791383375864807 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1516027018954759 / 1250000000000000 : ℝ) ≤ - (964747791383375864807 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (378306947307067 / 5000000000000000 : ℝ)) (q := - (1516027018954759 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1516027018954759 / 20000000000000000 : ℚ)) + (r' := (1516027018954759 / 1250000000000000 : ℚ)) + (U := (-(12898195814616624135193 / 5000000000000000000000 : ℚ))) + (U' := (964747791383375864807 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1356286967897 / 16000000000000 : ℚ)) + (s := (378306947307067 / 5000000000000000 : ℚ)) + (q := (1516027018954759 / 20000000000000000 : ℚ)) + (U := (-(12898195814616624135193 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_140_3 : Uω (aρ 3) (bρ 3) (1356286967897 / 16000000000000 : ℝ) ≤ @@ -1150,25 +1066,21 @@ lemma U_140_3 : have hlg : Real.log (141356678327789 / 2000000000000000 : ℝ) ≤ (-(26496161287310828503139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (141356678327789 / 2000000000000000 : ℝ) = - (141356678327789 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (141356678327789 / 125000000000000 : ℚ)) - (U := (1229725924689171496861 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (141356678327789 / 125000000000000 : ℝ) ≤ - (1229725924689171496861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (140309953057453 / 2000000000000000 : ℝ)) (q := - (141356678327789 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (141356678327789 / 2000000000000000 : ℚ)) + (r' := (141356678327789 / 125000000000000 : ℚ)) + (U := (-(26496161287310828503139 / 10000000000000000000000 : ℚ))) + (U' := (1229725924689171496861 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1356286967897 / 16000000000000 : ℚ)) + (s := (140309953057453 / 2000000000000000 : ℚ)) + (q := (141356678327789 / 2000000000000000 : ℚ)) + (U := (-(26496161287310828503139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_140_4 : Uω (aρ 4) (bρ 4) (1356286967897 / 16000000000000 : ℝ) ≤ @@ -1176,25 +1088,21 @@ lemma U_140_4 : have hlg : Real.log (246664960350121 / 4000000000000000 : ℝ) ≤ (-(217657707718408659519 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (246664960350121 / 4000000000000000 : ℝ) = - (246664960350121 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (246664960350121 / 125000000000000 : ℚ)) - (U := (53102909586278840481 / 78125000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (246664960350121 / 125000000000000 : ℝ) ≤ - (53102909586278840481 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29980098241249 / 500000000000000 : ℝ)) (q := - (246664960350121 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (246664960350121 / 4000000000000000 : ℚ)) + (r' := (246664960350121 / 125000000000000 : ℚ)) + (U := (-(217657707718408659519 / 78125000000000000000 : ℚ))) + (U' := (53102909586278840481 / 78125000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1356286967897 / 16000000000000 : ℚ)) + (s := (29980098241249 / 500000000000000 : ℚ)) + (q := (246664960350121 / 4000000000000000 : ℚ)) + (U := (-(217657707718408659519 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_140_5 : Uω (aρ 5) (bρ 5) (1356286967897 / 16000000000000 : ℝ) ≤ @@ -1202,25 +1110,21 @@ lemma U_140_5 : have hlg : Real.log (457303691842081 / 10000000000000000 : ℝ) ≤ (-(30849926669156202687773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (457303691842081 / 10000000000000000 : ℝ) = - (457303691842081 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (457303691842081 / 312500000000000 : ℚ)) - (U := (3807432345843797312227 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (457303691842081 / 312500000000000 : ℝ) ≤ - (3807432345843797312227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (399074466093537 / 10000000000000000 : ℝ)) (q := - (457303691842081 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (457303691842081 / 10000000000000000 : ℚ)) + (r' := (457303691842081 / 312500000000000 : ℚ)) + (U := (-(30849926669156202687773 / 10000000000000000000000 : ℚ))) + (U' := (3807432345843797312227 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1356286967897 / 16000000000000 : ℚ)) + (s := (399074466093537 / 10000000000000000 : ℚ)) + (q := (457303691842081 / 10000000000000000 : ℚ)) + (U := (-(30849926669156202687773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_140_6 : Uω (aρ 6) (bρ 6) (1356286967897 / 16000000000000 : ℝ) ≤ @@ -1367,25 +1271,21 @@ lemma U_141_1 : have hlg : Real.log (200999943759371 / 2500000000000000 : ℝ) ≤ (-(1260370690780799325851 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (200999943759371 / 2500000000000000 : ℝ) = - (200999943759371 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (200999943759371 / 156250000000000 : ℚ)) - (U := (125923669819200674149 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (200999943759371 / 156250000000000 : ℝ) ≤ - (125923669819200674149 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (401899347761859 / 5000000000000000 : ℝ)) (q := - (200999943759371 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (200999943759371 / 2500000000000000 : ℚ)) + (r' := (200999943759371 / 156250000000000 : ℚ)) + (U := (-(1260370690780799325851 / 500000000000000000000 : ℚ))) + (U' := (125923669819200674149 / 500000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (694958458109 / 8000000000000 : ℚ)) + (s := (401899347761859 / 5000000000000000 : ℚ)) + (q := (200999943759371 / 2500000000000000 : ℚ)) + (U := (-(1260370690780799325851 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_141_2 : Uω (aρ 2) (bρ 2) (694958458109 / 8000000000000 : ℝ) ≤ @@ -1393,25 +1293,21 @@ lemma U_141_2 : have hlg : Real.log (1558140111364829 / 20000000000000000 : ℝ) ≤ (-(3190299248545577399671 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1558140111364829 / 20000000000000000 : ℝ) = - (1558140111364829 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1558140111364829 / 1250000000000000 : ℚ)) - (U := (275436652954422600329 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1558140111364829 / 1250000000000000 : ℝ) ≤ - (275436652954422600329 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (777708269323579 / 10000000000000000 : ℝ)) (q := - (1558140111364829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1558140111364829 / 20000000000000000 : ℚ)) + (r' := (1558140111364829 / 1250000000000000 : ℚ)) + (U := (-(3190299248545577399671 / 1250000000000000000000 : ℚ))) + (U' := (275436652954422600329 / 1250000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (694958458109 / 8000000000000 : ℚ)) + (s := (777708269323579 / 10000000000000000 : ℚ)) + (q := (1558140111364829 / 20000000000000000 : ℚ)) + (U := (-(3190299248545577399671 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_141_3 : Uω (aρ 3) (bρ 3) (694958458109 / 8000000000000 : ℝ) ≤ @@ -1419,25 +1315,21 @@ lemma U_141_3 : have hlg : Real.log (727954317676977 / 10000000000000000 : ℝ) ≤ (-(3275127593940399875157 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (727954317676977 / 10000000000000000 : ℝ) = - (727954317676977 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (727954317676977 / 625000000000000 : ℚ)) - (U := (190608307559600124843 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (727954317676977 / 625000000000000 : ℝ) ≤ - (190608307559600124843 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45179556228919 / 625000000000000 : ℝ)) (q := - (727954317676977 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (727954317676977 / 10000000000000000 : ℚ)) + (r' := (727954317676977 / 625000000000000 : ℚ)) + (U := (-(3275127593940399875157 / 1250000000000000000000 : ℚ))) + (U' := (190608307559600124843 / 1250000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (694958458109 / 8000000000000 : ℚ)) + (s := (45179556228919 / 625000000000000 : ℚ)) + (q := (727954317676977 / 10000000000000000 : ℚ)) + (U := (-(3275127593940399875157 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_141_4 : Uω (aρ 4) (bρ 4) (694958458109 / 8000000000000 : ℝ) ≤ @@ -1445,25 +1337,21 @@ lemma U_141_4 : have hlg : Real.log (319129185882303 / 5000000000000000 : ℝ) ≤ (-(13757985990762632792871 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (319129185882303 / 5000000000000000 : ℝ) = - (319129185882303 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (319129185882303 / 312500000000000 : ℚ)) - (U := (104957615237367207129 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (319129185882303 / 312500000000000 : ℝ) ≤ - (104957615237367207129 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (310887594451481 / 5000000000000000 : ℝ)) (q := - (319129185882303 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (319129185882303 / 5000000000000000 : ℚ)) + (r' := (319129185882303 / 312500000000000 : ℚ)) + (U := (-(13757985990762632792871 / 5000000000000000000000 : ℚ))) + (U' := (104957615237367207129 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (694958458109 / 8000000000000 : ℚ)) + (s := (310887594451481 / 5000000000000000 : ℚ)) + (q := (319129185882303 / 5000000000000000 : ℚ)) + (U := (-(13757985990762632792871 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_141_5 : Uω (aρ 5) (bρ 5) (694958458109 / 8000000000000 : ℝ) ≤ @@ -1471,25 +1359,21 @@ lemma U_141_5 : have hlg : Real.log (240607945013181 / 5000000000000000 : ℝ) ≤ (-(30340243654537166784837 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (240607945013181 / 5000000000000000 : ℝ) = - (240607945013181 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (240607945013181 / 156250000000000 : ℚ)) - (U := (4317115360462833215163 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (240607945013181 / 156250000000000 : ℝ) ≤ - (4317115360462833215163 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (212940072380737 / 5000000000000000 : ℝ)) (q := - (240607945013181 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (240607945013181 / 5000000000000000 : ℚ)) + (r' := (240607945013181 / 156250000000000 : ℚ)) + (U := (-(30340243654537166784837 / 10000000000000000000000 : ℚ))) + (U' := (4317115360462833215163 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (694958458109 / 8000000000000 : ℚ)) + (s := (212940072380737 / 5000000000000000 : ℚ)) + (q := (240607945013181 / 5000000000000000 : ℚ)) + (U := (-(30340243654537166784837 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_141_6 : Uω (aρ 6) (bρ 6) (694958458109 / 8000000000000 : ℝ) ≤ @@ -1636,25 +1520,21 @@ lemma U_142_1 : have hlg : Real.log (1650047233580129 / 20000000000000000 : ℝ) ≤ (-(3118660448249061296987 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1650047233580129 / 20000000000000000 : ℝ) = - (1650047233580129 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1650047233580129 / 1250000000000000 : ℚ)) - (U := (347075453250938703013 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1650047233580129 / 1250000000000000 : ℝ) ≤ - (347075453250938703013 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (412413830664127 / 5000000000000000 : ℝ)) (q := - (1650047233580129 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1650047233580129 / 20000000000000000 : ℚ)) + (r' := (1650047233580129 / 1250000000000000 : ℚ)) + (U := (-(3118660448249061296987 / 1250000000000000000000 : ℚ))) + (U' := (347075453250938703013 / 1250000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1423546864539 / 16000000000000 : ℚ)) + (s := (412413830664127 / 5000000000000000 : ℚ)) + (q := (1650047233580129 / 20000000000000000 : ℚ)) + (U := (-(3118660448249061296987 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_142_2 : Uω (aρ 2) (bρ 2) (1423546864539 / 16000000000000 : ℝ) ≤ @@ -1662,25 +1542,21 @@ lemma U_142_2 : have hlg : Real.log (800124607553441 / 10000000000000000 : ℝ) ≤ (-(12627864479779576637511 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (800124607553441 / 10000000000000000 : ℝ) = - (800124607553441 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (800124607553441 / 625000000000000 : ℚ)) - (U := (1235079126220423362489 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (800124607553441 / 625000000000000 : ℝ) ≤ - (1235079126220423362489 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (798798655365007 / 10000000000000000 : ℝ)) (q := - (800124607553441 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (800124607553441 / 10000000000000000 : ℚ)) + (r' := (800124607553441 / 625000000000000 : ℚ)) + (U := (-(12627864479779576637511 / 5000000000000000000000 : ℚ))) + (U' := (1235079126220423362489 / 5000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1423546864539 / 16000000000000 : ℚ)) + (s := (798798655365007 / 10000000000000000 : ℚ)) + (q := (800124607553441 / 10000000000000000 : ℚ)) + (U := (-(12627864479779576637511 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_142_3 : Uω (aρ 3) (bρ 3) (1423546864539 / 16000000000000 : ℝ) ≤ @@ -1688,25 +1564,21 @@ lemma U_142_3 : have hlg : Real.log (1498233167106849 / 20000000000000000 : ℝ) ≤ (-(25914457472574753600061 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1498233167106849 / 20000000000000000 : ℝ) = - (1498233167106849 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1498233167106849 / 1250000000000000 : ℚ)) - (U := (1811429739425246399939 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1498233167106849 / 1250000000000000 : ℝ) ≤ - (1811429739425246399939 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (372089356857487 / 5000000000000000 : ℝ)) (q := - (1498233167106849 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1498233167106849 / 20000000000000000 : ℚ)) + (r' := (1498233167106849 / 1250000000000000 : ℚ)) + (U := (-(25914457472574753600061 / 10000000000000000000000 : ℚ))) + (U' := (1811429739425246399939 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1423546864539 / 16000000000000 : ℚ)) + (s := (372089356857487 / 5000000000000000 : ℚ)) + (q := (1498233167106849 / 20000000000000000 : ℚ)) + (U := (-(25914457472574753600061 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_142_4 : Uω (aρ 4) (bρ 4) (1423546864539 / 16000000000000 : ℝ) ≤ @@ -1714,23 +1586,21 @@ lemma U_142_4 : have hlg : Real.log (659815621873 / 10000000000000 : ℝ) ≤ (-(217470394859432947223 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (659815621873 / 10000000000000 : ℝ) = (659815621873 / 625000000000 : ℝ) / 2 ^ 4 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (659815621873 / 625000000000 : ℚ)) - (U := (4336702836567052777 / 80000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (659815621873 / 625000000000 : ℝ) ≤ - (4336702836567052777 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5150967771353 / 80000000000000 : ℝ)) (q := - (659815621873 / 10000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (659815621873 / 10000000000000 : ℚ)) + (r' := (659815621873 / 625000000000 : ℚ)) + (U := (-(217470394859432947223 / 80000000000000000000 : ℚ))) + (U' := (4336702836567052777 / 80000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1423546864539 / 16000000000000 : ℚ)) + (s := (5150967771353 / 80000000000000 : ℚ)) + (q := (659815621873 / 10000000000000 : ℚ)) + (U := (-(217470394859432947223 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_142_5 : Uω (aρ 5) (bρ 5) (1423546864539 / 16000000000000 : ℝ) ≤ @@ -1738,25 +1608,21 @@ lemma U_142_5 : have hlg : Real.log (252411098596889 / 5000000000000000 : ℝ) ≤ (-(7465335220405714049317 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (252411098596889 / 5000000000000000 : ℝ) = - (252411098596889 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (252411098596889 / 156250000000000 : ℚ)) - (U := (1199004533344285950683 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (252411098596889 / 156250000000000 : ℝ) ≤ - (1199004533344285950683 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (452074041395681 / 10000000000000000 : ℝ)) (q := - (252411098596889 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (252411098596889 / 5000000000000000 : ℚ)) + (r' := (252411098596889 / 156250000000000 : ℚ)) + (U := (-(7465335220405714049317 / 2500000000000000000000 : ℚ))) + (U' := (1199004533344285950683 / 2500000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1423546864539 / 16000000000000 : ℚ)) + (s := (452074041395681 / 10000000000000000 : ℚ)) + (q := (252411098596889 / 5000000000000000 : ℚ)) + (U := (-(7465335220405714049317 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_142_6 : Uω (aρ 6) (bρ 6) (1423546864539 / 16000000000000 : ℝ) ≤ @@ -1902,25 +1768,21 @@ lemma U_143_1 : have hlg : Real.log (423023601912517 / 5000000000000000 : ℝ) ≤ (-(4939530432806504756481 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (423023601912517 / 5000000000000000 : ℝ) = - (423023601912517 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (423023601912517 / 312500000000000 : ℚ)) - (U := (605647009593495243519 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (423023601912517 / 312500000000000 : ℝ) ≤ - (605647009593495243519 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26433003678049 / 312500000000000 : ℝ)) (q := - (423023601912517 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (423023601912517 / 5000000000000000 : ℚ)) + (r' := (423023601912517 / 312500000000000 : ℚ)) + (U := (-(4939530432806504756481 / 2000000000000000000000 : ℚ))) + (U' := (605647009593495243519 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (72858840643 / 800000000000 : ℚ)) + (s := (26433003678049 / 312500000000000 : ℚ)) + (q := (423023601912517 / 5000000000000000 : ℚ)) + (U := (-(4939530432806504756481 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_143_2 : Uω (aρ 2) (bρ 2) (72858840643 / 800000000000 : ℝ) ≤ @@ -1928,25 +1790,21 @@ lemma U_143_2 : have hlg : Real.log (410588659497357 / 5000000000000000 : ℝ) ≤ (-(12498006527585179078093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (410588659497357 / 5000000000000000 : ℝ) = - (410588659497357 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (410588659497357 / 312500000000000 : ℚ)) - (U := (1364937078414820921907 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (410588659497357 / 312500000000000 : ℝ) ≤ - (1364937078414820921907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (51242835034183 / 625000000000000 : ℝ)) (q := - (410588659497357 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (410588659497357 / 5000000000000000 : ℚ)) + (r' := (410588659497357 / 312500000000000 : ℚ)) + (U := (-(12498006527585179078093 / 5000000000000000000000 : ℚ))) + (U' := (1364937078414820921907 / 5000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (72858840643 / 800000000000 : ℚ)) + (s := (51242835034183 / 625000000000000 : ℚ)) + (q := (410588659497357 / 5000000000000000 : ℚ)) + (U := (-(12498006527585179078093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_143_3 : Uω (aρ 3) (bρ 3) (72858840643 / 800000000000 : ℝ) ≤ @@ -1954,25 +1812,21 @@ lemma U_143_3 : have hlg : Real.log (1540541824803243 / 20000000000000000 : ℝ) ≤ (-(25635980836800211611331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1540541824803243 / 20000000000000000 : ℝ) = - (1540541824803243 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1540541824803243 / 1250000000000000 : ℚ)) - (U := (2089906375199788388669 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1540541824803243 / 1250000000000000 : ℝ) ≤ - (2089906375199788388669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (765468653710743 / 10000000000000000 : ℝ)) (q := - (1540541824803243 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1540541824803243 / 20000000000000000 : ℚ)) + (r' := (1540541824803243 / 1250000000000000 : ℚ)) + (U := (-(25635980836800211611331 / 10000000000000000000000 : ℚ))) + (U' := (2089906375199788388669 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (72858840643 / 800000000000 : ℚ)) + (s := (765468653710743 / 10000000000000000 : ℚ)) + (q := (1540541824803243 / 20000000000000000 : ℚ)) + (U := (-(25635980836800211611331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_143_4 : Uω (aρ 4) (bρ 4) (72858840643 / 800000000000 : ℝ) ≤ @@ -1980,25 +1834,21 @@ lemma U_143_4 : have hlg : Real.log (1362676011438963 / 20000000000000000 : ℝ) ≤ (-(26862818505948193076349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1362676011438963 / 20000000000000000 : ℝ) = - (1362676011438963 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1362676011438963 / 1250000000000000 : ℚ)) - (U := (863068706051806923651 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1362676011438963 / 1250000000000000 : ℝ) ≤ - (863068706051806923651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (665897021411463 / 10000000000000000 : ℝ)) (q := - (1362676011438963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1362676011438963 / 20000000000000000 : ℚ)) + (r' := (1362676011438963 / 1250000000000000 : ℚ)) + (U := (-(26862818505948193076349 / 10000000000000000000000 : ℚ))) + (U' := (863068706051806923651 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (72858840643 / 800000000000 : ℚ)) + (s := (665897021411463 / 10000000000000000 : ℚ)) + (q := (1362676011438963 / 20000000000000000 : ℚ)) + (U := (-(26862818505948193076349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_143_5 : Uω (aρ 5) (bρ 5) (72858840643 / 800000000000 : ℝ) ≤ @@ -2006,25 +1856,21 @@ lemma U_143_5 : have hlg : Real.log (1056345863520347 / 20000000000000000 : ℝ) ≤ (-(3676145772901062746707 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1056345863520347 / 20000000000000000 : ℝ) = - (1056345863520347 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1056345863520347 / 625000000000000 : ℚ)) - (U := (656024103973937253293 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1056345863520347 / 625000000000000 : ℝ) ≤ - (656024103973937253293 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (477756792827847 / 10000000000000000 : ℝ)) (q := - (1056345863520347 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1056345863520347 / 20000000000000000 : ℚ)) + (r' := (1056345863520347 / 625000000000000 : ℚ)) + (U := (-(3676145772901062746707 / 1250000000000000000000 : ℚ))) + (U' := (656024103973937253293 / 1250000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (72858840643 / 800000000000 : ℚ)) + (s := (477756792827847 / 10000000000000000 : ℚ)) + (q := (1056345863520347 / 20000000000000000 : ℚ)) + (U := (-(3676145772901062746707 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_143_6 : Uω (aρ 6) (bρ 6) (72858840643 / 800000000000 : ℝ) ≤ @@ -2171,25 +2017,21 @@ lemma U_144_1 : have hlg : Real.log (1776187372263171 / 20000000000000000 : ℝ) ≤ (-(24212631311087841507319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1776187372263171 / 20000000000000000 : ℝ) = - (1776187372263171 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1776187372263171 / 1250000000000000 : ℚ)) - (U := (3513255900912158492681 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1776187372263171 / 1250000000000000 : ℝ) ≤ - (3513255900912158492681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (887911646909421 / 10000000000000000 : ℝ)) (q := - (1776187372263171 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1776187372263171 / 20000000000000000 : ℚ)) + (r' := (1776187372263171 / 1250000000000000 : ℚ)) + (U := (-(24212631311087841507319 / 10000000000000000000000 : ℚ))) + (U' := (3513255900912158492681 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (762218354751 / 8000000000000 : ℚ)) + (s := (887911646909421 / 10000000000000000 : ℚ)) + (q := (1776187372263171 / 20000000000000000 : ℚ)) + (U := (-(24212631311087841507319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_144_2 : Uω (aρ 2) (bρ 2) (762218354751 / 8000000000000 : ℝ) ≤ @@ -2197,25 +2039,21 @@ lemma U_144_2 : have hlg : Real.log (431638880396551 / 5000000000000000 : ℝ) ≤ (-(24496038767204679231087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (431638880396551 / 5000000000000000 : ℝ) = - (431638880396551 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (431638880396551 / 312500000000000 : ℚ)) - (U := (3229848444795320768913 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (431638880396551 / 312500000000000 : ℝ) ≤ - (3229848444795320768913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (431024404371227 / 5000000000000000 : ℝ)) (q := - (431638880396551 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (431638880396551 / 5000000000000000 : ℚ)) + (r' := (431638880396551 / 312500000000000 : ℚ)) + (U := (-(24496038767204679231087 / 10000000000000000000000 : ℚ))) + (U' := (3229848444795320768913 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (762218354751 / 8000000000000 : ℚ)) + (s := (431024404371227 / 5000000000000000 : ℚ)) + (q := (431638880396551 / 5000000000000000 : ℚ)) + (U := (-(24496038767204679231087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_144_3 : Uω (aρ 3) (bρ 3) (762218354751 / 8000000000000 : ℝ) ≤ @@ -2223,25 +2061,21 @@ lemma U_144_3 : have hlg : Real.log (406279134060903 / 5000000000000000 : ℝ) ≤ (-(25101527446924252214789 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (406279134060903 / 5000000000000000 : ℝ) = - (406279134060903 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (406279134060903 / 312500000000000 : ℚ)) - (U := (2624359765075747785211 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (406279134060903 / 312500000000000 : ℝ) ≤ - (2624359765075747785211 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404002964874931 / 5000000000000000 : ℝ)) (q := - (406279134060903 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (406279134060903 / 5000000000000000 : ℚ)) + (r' := (406279134060903 / 312500000000000 : ℚ)) + (U := (-(25101527446924252214789 / 10000000000000000000000 : ℚ))) + (U' := (2624359765075747785211 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (762218354751 / 8000000000000 : ℚ)) + (s := (404002964874931 / 5000000000000000 : ℚ)) + (q := (406279134060903 / 5000000000000000 : ℚ)) + (U := (-(25101527446924252214789 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_144_4 : Uω (aρ 4) (bρ 4) (762218354751 / 8000000000000 : ℝ) ≤ @@ -2249,25 +2083,21 @@ lemma U_144_4 : have hlg : Real.log (1448582297152821 / 20000000000000000 : ℝ) ≤ (-(13125734602345873881497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1448582297152821 / 20000000000000000 : ℝ) = - (1448582297152821 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1448582297152821 / 1250000000000000 : ℚ)) - (U := (737209003654126118503 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1448582297152821 / 1250000000000000 : ℝ) ≤ - (737209003654126118503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (709765871724071 / 10000000000000000 : ℝ)) (q := - (1448582297152821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1448582297152821 / 20000000000000000 : ℚ)) + (r' := (1448582297152821 / 1250000000000000 : ℚ)) + (U := (-(13125734602345873881497 / 5000000000000000000000 : ℚ))) + (U' := (737209003654126118503 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (762218354751 / 8000000000000 : ℚ)) + (s := (709765871724071 / 10000000000000000 : ℚ)) + (q := (1448582297152821 / 20000000000000000 : ℚ)) + (U := (-(13125734602345873881497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_144_5 : Uω (aρ 5) (bρ 5) (762218354751 / 8000000000000 : ℝ) ≤ @@ -2275,25 +2105,21 @@ lemma U_144_5 : have hlg : Real.log (1148512384323577 / 20000000000000000 : ℝ) ≤ (-(28572647461235244444859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1148512384323577 / 20000000000000000 : ℝ) = - (1148512384323577 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1148512384323577 / 625000000000000 : ℚ)) - (U := (6084711553764755555141 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1148512384323577 / 625000000000000 : ℝ) ≤ - (6084711553764755555141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (527885878229827 / 10000000000000000 : ℝ)) (q := - (1148512384323577 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1148512384323577 / 20000000000000000 : ℚ)) + (r' := (1148512384323577 / 625000000000000 : ℚ)) + (U := (-(28572647461235244444859 / 10000000000000000000000 : ℚ))) + (U' := (6084711553764755555141 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (762218354751 / 8000000000000 : ℚ)) + (s := (527885878229827 / 10000000000000000 : ℚ)) + (q := (1148512384323577 / 20000000000000000 : ℚ)) + (U := (-(28572647461235244444859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_144_6 : Uω (aρ 6) (bρ 6) (762218354751 / 8000000000000 : ℝ) ≤ @@ -2441,25 +2267,21 @@ lemma U_145_1 : have hlg : Real.log (1860278700728729 / 20000000000000000 : ℝ) ≤ (-(5937514892280973947171 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1860278700728729 / 20000000000000000 : ℝ) = - (1860278700728729 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1860278700728729 / 1250000000000000 : ℚ)) - (U := (993956910719026052829 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1860278700728729 / 1250000000000000 : ℝ) ≤ - (993956910719026052829 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (929965539973729 / 10000000000000000 : ℝ)) (q := - (1860278700728729 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1860278700728729 / 20000000000000000 : ℚ)) + (r' := (1860278700728729 / 1250000000000000 : ℚ)) + (U := (-(5937514892280973947171 / 2500000000000000000000 : ℚ))) + (U' := (993956910719026052829 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24870259471 / 250000000000 : ℚ)) + (s := (929965539973729 / 10000000000000000 : ℚ)) + (q := (1860278700728729 / 20000000000000000 : ℚ)) + (U := (-(5937514892280973947171 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_145_2 : Uω (aρ 2) (bρ 2) (24870259471 / 250000000000 : ℝ) ≤ @@ -2467,25 +2289,21 @@ lemma U_145_2 : have hlg : Real.log (181074467070649 / 2000000000000000 : ℝ) ≤ (-(24019940915667638914899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (181074467070649 / 2000000000000000 : ℝ) = - (181074467070649 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (181074467070649 / 125000000000000 : ℚ)) - (U := (3705946296332361085101 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (181074467070649 / 125000000000000 : ℝ) ≤ - (3705946296332361085101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90420052246149 / 1000000000000000 : ℝ)) (q := - (181074467070649 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (181074467070649 / 2000000000000000 : ℚ)) + (r' := (181074467070649 / 125000000000000 : ℚ)) + (U := (-(24019940915667638914899 / 10000000000000000000000 : ℚ))) + (U' := (3705946296332361085101 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24870259471 / 250000000000 : ℚ)) + (s := (90420052246149 / 1000000000000000 : ℚ)) + (q := (181074467070649 / 2000000000000000 : ℚ)) + (U := (-(24019940915667638914899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_145_3 : Uω (aρ 3) (bρ 3) (24870259471 / 250000000000 : ℝ) ≤ @@ -2493,25 +2311,21 @@ lemma U_145_3 : have hlg : Real.log (1709641544020893 / 20000000000000000 : ℝ) ≤ (-(12297242736766437788551 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1709641544020893 / 20000000000000000 : ℝ) = - (1709641544020893 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1709641544020893 / 1250000000000000 : ℚ)) - (U := (1565700869233562211449 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1709641544020893 / 1250000000000000 : ℝ) ≤ - (1565700869233562211449 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (850493502125893 / 10000000000000000 : ℝ)) (q := - (1709641544020893 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1709641544020893 / 20000000000000000 : ℚ)) + (r' := (1709641544020893 / 1250000000000000 : ℚ)) + (U := (-(12297242736766437788551 / 5000000000000000000000 : ℚ))) + (U' := (1565700869233562211449 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24870259471 / 250000000000 : ℚ)) + (s := (850493502125893 / 10000000000000000 : ℚ)) + (q := (1709641544020893 / 20000000000000000 : ℚ)) + (U := (-(12297242736766437788551 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_145_4 : Uω (aρ 4) (bρ 4) (24870259471 / 250000000000 : ℝ) ≤ @@ -2519,24 +2333,21 @@ lemma U_145_4 : have hlg : Real.log (95892487016369 / 1250000000000000 : ℝ) ≤ (-(25676711922883085692547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (95892487016369 / 1250000000000000 : ℝ) = (95892487016369 / 78125000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (95892487016369 / 78125000000000 : ℚ)) - (U := (2049175289116914307453 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (95892487016369 / 78125000000000 : ℝ) ≤ - (2049175289116914307453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23544560357247 / 312500000000000 : ℝ)) (q := - (95892487016369 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (95892487016369 / 1250000000000000 : ℚ)) + (r' := (95892487016369 / 78125000000000 : ℚ)) + (U := (-(25676711922883085692547 / 10000000000000000000000 : ℚ))) + (U' := (2049175289116914307453 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24870259471 / 250000000000 : ℚ)) + (s := (23544560357247 / 312500000000000 : ℚ)) + (q := (95892487016369 / 1250000000000000 : ℚ)) + (U := (-(25676711922883085692547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_145_5 : Uω (aρ 5) (bρ 5) (24870259471 / 250000000000 : ℝ) ≤ @@ -2544,25 +2355,21 @@ lemma U_145_5 : have hlg : Real.log (123938721978887 / 2000000000000000 : ℝ) ≤ (-(13905575961864639085561 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (123938721978887 / 2000000000000000 : ℝ) = - (123938721978887 / 62500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123938721978887 / 62500000000000 : ℚ)) - (U := (3423103545635360914439 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (123938721978887 / 62500000000000 : ℝ) ≤ - (3423103545635360914439 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57672327829387 / 1000000000000000 : ℝ)) (q := - (123938721978887 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123938721978887 / 2000000000000000 : ℚ)) + (r' := (123938721978887 / 62500000000000 : ℚ)) + (U := (-(13905575961864639085561 / 5000000000000000000000 : ℚ))) + (U' := (3423103545635360914439 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24870259471 / 250000000000 : ℚ)) + (s := (57672327829387 / 1000000000000000 : ℚ)) + (q := (123938721978887 / 2000000000000000 : ℚ)) + (U := (-(13905575961864639085561 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_145_6 : Uω (aρ 6) (bρ 6) (24870259471 / 250000000000 : ℝ) ≤ @@ -2709,24 +2516,21 @@ lemma U_146_1 : have hlg : Real.log (47207794808651 / 500000000000000 : ℝ) ≤ (-(23600490741746310132633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (47207794808651 / 500000000000000 : ℝ) = (47207794808651 / 31250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47207794808651 / 31250000000000 : ℚ)) - (U := (4125396470253689867367 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47207794808651 / 31250000000000 : ℝ) ≤ - (4125396470253689867367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188796933219833 / 2000000000000000 : ℝ)) (q := - (47207794808651 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47207794808651 / 500000000000000 : ℚ)) + (r' := (47207794808651 / 31250000000000 : ℚ)) + (U := (-(23600490741746310132633 / 10000000000000000000000 : ℚ))) + (U' := (4125396470253689867367 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (188796933219833 / 2000000000000000 : ℚ)) + (q := (47207794808651 / 500000000000000 : ℚ)) + (U := (-(23600490741746310132633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_2 : Uω (aρ 2) (bρ 2) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2734,25 +2538,21 @@ lemma U_146_2 : have hlg : Real.log (229851046232431 / 2500000000000000 : ℝ) ≤ (-(23866145357694081674823 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (229851046232431 / 2500000000000000 : ℝ) = - (229851046232431 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (229851046232431 / 156250000000000 : ℚ)) - (U := (3859741854305918325177 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (229851046232431 / 156250000000000 : ℝ) ≤ - (3859741854305918325177 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (918250256122573 / 10000000000000000 : ℝ)) (q := - (229851046232431 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (229851046232431 / 2500000000000000 : ℚ)) + (r' := (229851046232431 / 156250000000000 : ℚ)) + (U := (-(23866145357694081674823 / 10000000000000000000000 : ℚ))) + (U' := (3859741854305918325177 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (918250256122573 / 10000000000000000 : ℚ)) + (q := (229851046232431 / 2500000000000000 : ℚ)) + (U := (-(23866145357694081674823 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_3 : Uω (aρ 3) (bρ 3) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2760,25 +2560,21 @@ lemma U_146_3 : have hlg : Real.log (1737809756710397 / 20000000000000000 : ℝ) ≤ (-(4886213425407009894147 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1737809756710397 / 20000000000000000 : ℝ) = - (1737809756710397 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1737809756710397 / 1250000000000000 : ℚ)) - (U := (658964016992990105853 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1737809756710397 / 1250000000000000 : ℝ) ≤ - (658964016992990105853 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (432323874661761 / 5000000000000000 : ℝ)) (q := - (1737809756710397 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1737809756710397 / 20000000000000000 : ℚ)) + (r' := (1737809756710397 / 1250000000000000 : ℚ)) + (U := (-(4886213425407009894147 / 2000000000000000000000 : ℚ))) + (U' := (658964016992990105853 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (432323874661761 / 5000000000000000 : ℚ)) + (q := (1737809756710397 / 20000000000000000 : ℚ)) + (U := (-(4886213425407009894147 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_4 : Uω (aρ 4) (bρ 4) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2786,23 +2582,21 @@ lemma U_146_4 : have hlg : Real.log (3125616824483 / 40000000000000 : ℝ) ≤ (-(25492478055288563125353 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (3125616824483 / 40000000000000 : ℝ) = (3125616824483 / 2500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3125616824483 / 2500000000000 : ℚ)) - (U := (2233409156711436874647 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3125616824483 / 2500000000000 : ℝ) ≤ - (2233409156711436874647 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6143524687357 / 80000000000000 : ℝ)) (q := - (3125616824483 / 40000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3125616824483 / 40000000000000 : ℚ)) + (r' := (3125616824483 / 2500000000000 : ℚ)) + (U := (-(25492478055288563125353 / 10000000000000000000000 : ℚ))) + (U' := (2233409156711436874647 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (6143524687357 / 80000000000000 : ℚ)) + (q := (3125616824483 / 40000000000000 : ℚ)) + (U := (-(25492478055288563125353 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_5 : Uω (aρ 5) (bρ 5) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2810,25 +2604,21 @@ lemma U_146_5 : have hlg : Real.log (1269450401433503 / 20000000000000000 : ℝ) ≤ (-(27571482204858512832921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1269450401433503 / 20000000000000000 : ℝ) = - (1269450401433503 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1269450401433503 / 1250000000000000 : ℚ)) - (U := (154405007141487167079 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1269450401433503 / 1250000000000000 : ℝ) ≤ - (154405007141487167079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (148193123611657 / 2500000000000000 : ℝ)) (q := - (1269450401433503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1269450401433503 / 20000000000000000 : ℚ)) + (r' := (1269450401433503 / 1250000000000000 : ℚ)) + (U := (-(27571482204858512832921 / 10000000000000000000000 : ℚ))) + (U' := (154405007141487167079 / 10000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (148193123611657 / 2500000000000000 : ℚ)) + (q := (1269450401433503 / 20000000000000000 : ℚ)) + (U := (-(27571482204858512832921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_6 : Uω (aρ 6) (bρ 6) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2836,25 +2626,21 @@ lemma U_146_6 : have hlg : Real.log (125621101760153 / 4000000000000000 : ℝ) ≤ (-(17303896956176881585291 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (125621101760153 / 4000000000000000 : ℝ) = - (125621101760153 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (125621101760153 / 125000000000000 : ℚ)) - (U := (24782551323118414709 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (125621101760153 / 125000000000000 : ℝ) ≤ - (24782551323118414709 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11866797695389 / 1000000000000000 : ℝ)) (q := - (125621101760153 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (125621101760153 / 4000000000000000 : ℚ)) + (r' := (125621101760153 / 125000000000000 : ℚ)) + (U := (-(17303896956176881585291 / 5000000000000000000000 : ℚ))) + (U' := (24782551323118414709 / 5000000000000000000000 : ℚ)) + 5 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1614118950931 / 16000000000000 : ℚ)) + (s := (11866797695389 / 1000000000000000 : ℚ)) + (q := (125621101760153 / 4000000000000000 : ℚ)) + (U := (-(17303896956176881585291 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_146_7 : Uω (aρ 7) (bρ 7) (1614118950931 / 16000000000000 : ℝ) ≤ @@ -2997,25 +2783,21 @@ lemma U_147_1 : have hlg : Real.log (958172366476481 / 10000000000000000 : ℝ) ≤ (-(586328171474169128263 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (958172366476481 / 10000000000000000 : ℝ) = - (958172366476481 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (958172366476481 / 625000000000000 : ℚ)) - (U := (106819008825830871737 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (958172366476481 / 625000000000000 : ℝ) ≤ - (106819008825830871737 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239500910303553 / 2500000000000000 : ℝ)) (q := - (958172366476481 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (958172366476481 / 10000000000000000 : ℚ)) + (r' := (958172366476481 / 625000000000000 : ℚ)) + (U := (-(586328171474169128263 / 250000000000000000000 : ℚ))) + (U' := (106819008825830871737 / 250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (239500910303553 / 2500000000000000 : ℚ)) + (q := (958172366476481 / 10000000000000000 : ℚ)) + (U := (-(586328171474169128263 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_2 : Uω (aρ 2) (bρ 2) (818270647859 / 8000000000000 : ℝ) ≤ @@ -3023,25 +2805,21 @@ lemma U_147_2 : have hlg : Real.log (466717748083379 / 5000000000000000 : ℝ) ≤ (-(23714685092528748377319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (466717748083379 / 5000000000000000 : ℝ) = - (466717748083379 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (466717748083379 / 312500000000000 : ℚ)) - (U := (4011202119471251622681 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (466717748083379 / 312500000000000 : ℝ) ≤ - (4011202119471251622681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (466149456552383 / 5000000000000000 : ℝ)) (q := - (466717748083379 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (466717748083379 / 5000000000000000 : ℚ)) + (r' := (466717748083379 / 312500000000000 : ℚ)) + (U := (-(23714685092528748377319 / 10000000000000000000000 : ℚ))) + (U' := (4011202119471251622681 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (466149456552383 / 5000000000000000 : ℚ)) + (q := (466717748083379 / 5000000000000000 : ℚ)) + (U := (-(23714685092528748377319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_3 : Uω (aρ 3) (bρ 3) (818270647859 / 8000000000000 : ℝ) ≤ @@ -3049,25 +2827,21 @@ lemma U_147_3 : have hlg : Real.log (353194694588661 / 4000000000000000 : ℝ) ≤ (-(3033787739285829484113 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (353194694588661 / 4000000000000000 : ℝ) = - (353194694588661 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (353194694588661 / 250000000000000 : ℚ)) - (U := (431948162214170515887 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (353194694588661 / 250000000000000 : ℝ) ≤ - (431948162214170515887 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (175759500012911 / 2000000000000000 : ℝ)) (q := - (353194694588661 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (353194694588661 / 4000000000000000 : ℚ)) + (r' := (353194694588661 / 250000000000000 : ℚ)) + (U := (-(3033787739285829484113 / 1250000000000000000000 : ℚ))) + (U' := (431948162214170515887 / 1250000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (175759500012911 / 2000000000000000 : ℚ)) + (q := (353194694588661 / 4000000000000000 : ℚ)) + (U := (-(3033787739285829484113 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_4 : Uω (aρ 4) (bρ 4) (818270647859 / 8000000000000 : ℝ) ≤ @@ -3075,25 +2849,21 @@ lemma U_147_4 : have hlg : Real.log (795659388347077 / 10000000000000000 : ℝ) ≤ (-(25311691807556838955743 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (795659388347077 / 10000000000000000 : ℝ) = - (795659388347077 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (795659388347077 / 625000000000000 : ℚ)) - (U := (2414195404443161044257 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (795659388347077 / 625000000000000 : ℝ) ≤ - (2414195404443161044257 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (195609246220101 / 2500000000000000 : ℝ)) (q := - (795659388347077 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (795659388347077 / 10000000000000000 : ℚ)) + (r' := (795659388347077 / 625000000000000 : ℚ)) + (U := (-(25311691807556838955743 / 10000000000000000000000 : ℚ))) + (U' := (2414195404443161044257 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (195609246220101 / 2500000000000000 : ℚ)) + (q := (795659388347077 / 10000000000000000 : ℚ)) + (U := (-(25311691807556838955743 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_5 : Uω (aρ 5) (bρ 5) (818270647859 / 8000000000000 : ℝ) ≤ @@ -3101,25 +2871,21 @@ lemma U_147_5 : have hlg : Real.log (649706537778299 / 10000000000000000 : ℝ) ≤ (-(13669097951678662512941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (649706537778299 / 10000000000000000 : ℝ) = - (649706537778299 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (649706537778299 / 625000000000000 : ℚ)) - (U := (193845654321337487059 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (649706537778299 / 625000000000000 : ℝ) ≤ - (193845654321337487059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (76090150384731 / 1250000000000000 : ℝ)) (q := - (649706537778299 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (649706537778299 / 10000000000000000 : ℚ)) + (r' := (649706537778299 / 625000000000000 : ℚ)) + (U := (-(13669097951678662512941 / 5000000000000000000000 : ℚ))) + (U' := (193845654321337487059 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (76090150384731 / 1250000000000000 : ℚ)) + (q := (649706537778299 / 10000000000000000 : ℚ)) + (U := (-(13669097951678662512941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_6 : Uω (aρ 6) (bρ 6) (818270647859 / 8000000000000 : ℝ) ≤ @@ -3127,25 +2893,21 @@ lemma U_147_6 : have hlg : Real.log (346219772076763 / 10000000000000000 : ℝ) ≤ (-(2102041636154490140537 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (346219772076763 / 10000000000000000 : ℝ) = - (346219772076763 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (346219772076763 / 312500000000000 : ℚ)) - (U := (64043302283009859463 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (346219772076763 / 312500000000000 : ℝ) ≤ - (64043302283009859463 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21123505851847 / 1250000000000000 : ℝ)) (q := - (346219772076763 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (346219772076763 / 10000000000000000 : ℚ)) + (r' := (346219772076763 / 312500000000000 : ℚ)) + (U := (-(2102041636154490140537 / 625000000000000000000 : ℚ))) + (U' := (64043302283009859463 / 625000000000000000000 : ℚ)) + 5 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (818270647859 / 8000000000000 : ℚ)) + (s := (21123505851847 / 1250000000000000 : ℚ)) + (q := (346219772076763 / 10000000000000000 : ℚ)) + (U := (-(2102041636154490140537 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_147_7 : Uω (aρ 7) (bρ 7) (818270647859 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U12.lean b/LeanPool/Zeta5Irrational/Table/U12.lean index aa52a66ef0..ad0f3a6fd6 100644 --- a/LeanPool/Zeta5Irrational/Table/U12.lean +++ b/LeanPool/Zeta5Irrational/Table/U12.lean @@ -24,25 +24,21 @@ lemma U_148_1 : have hlg : Real.log (194437752908333 / 2000000000000000 : ℝ) ≤ (-(23307903831274102064587 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (194437752908333 / 2000000000000000 : ℝ) = - (194437752908333 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194437752908333 / 125000000000000 : ℚ)) - (U := (4417983380725897935413 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (194437752908333 / 125000000000000 : ℝ) ≤ - (4417983380725897935413 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (194404494370541 / 2000000000000000 : ℝ)) (q := - (194437752908333 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194437752908333 / 2000000000000000 : ℚ)) + (r' := (194437752908333 / 125000000000000 : ℚ)) + (U := (-(23307903831274102064587 / 10000000000000000000000 : ℚ))) + (U' := (4417983380725897935413 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (194404494370541 / 2000000000000000 : ℚ)) + (q := (194437752908333 / 2000000000000000 : ℚ)) + (U := (-(23307903831274102064587 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_2 : Uω (aρ 2) (bρ 2) (331792728101 / 3200000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_148_2 : have hlg : Real.log (947466293039537 / 10000000000000000 : ℝ) ≤ (-(1472843130775668236677 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (947466293039537 / 10000000000000000 : ℝ) = - (947466293039537 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (947466293039537 / 625000000000000 : ℚ)) - (U := (260024819974331763323 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (947466293039537 / 625000000000000 : ℝ) ≤ - (260024819974331763323 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (946346541358449 / 10000000000000000 : ℝ)) (q := - (947466293039537 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (947466293039537 / 10000000000000000 : ℚ)) + (r' := (947466293039537 / 625000000000000 : ℚ)) + (U := (-(1472843130775668236677 / 625000000000000000000 : ℚ))) + (U' := (260024819974331763323 / 625000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (946346541358449 / 10000000000000000 : ℚ)) + (q := (947466293039537 / 10000000000000000 : ℚ)) + (U := (-(1472843130775668236677 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_3 : Uω (aρ 3) (bρ 3) (331792728101 / 3200000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_148_3 : have hlg : Real.log (1794132906474863 / 20000000000000000 : ℝ) ≤ (-(24112104277449450185939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1794132906474863 / 20000000000000000 : ℝ) = - (1794132906474863 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1794132906474863 / 1250000000000000 : ℚ)) - (U := (3613782934550549814061 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1794132906474863 / 1250000000000000 : ℝ) ≤ - (3613782934550549814061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (446471484052119 / 5000000000000000 : ℝ)) (q := - (1794132906474863 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1794132906474863 / 20000000000000000 : ℚ)) + (r' := (1794132906474863 / 1250000000000000 : ℚ)) + (U := (-(24112104277449450185939 / 10000000000000000000000 : ℚ))) + (U' := (3613782934550549814061 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (446471484052119 / 5000000000000000 : ℚ)) + (q := (1794132906474863 / 20000000000000000 : ℚ)) + (U := (-(24112104277449450185939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_4 : Uω (aρ 4) (bρ 4) (331792728101 / 3200000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_148_4 : have hlg : Real.log (404952970464647 / 5000000000000000 : ℝ) ≤ (-(25134222523221480039377 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (404952970464647 / 5000000000000000 : ℝ) = - (404952970464647 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (404952970464647 / 312500000000000 : ℚ)) - (U := (2591664688778519960623 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (404952970464647 / 312500000000000 : ℝ) ≤ - (2591664688778519960623 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (796916124552963 / 10000000000000000 : ℝ)) (q := - (404952970464647 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (404952970464647 / 5000000000000000 : ℚ)) + (r' := (404952970464647 / 312500000000000 : ℚ)) + (U := (-(25134222523221480039377 / 10000000000000000000000 : ℚ))) + (U' := (2591664688778519960623 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (796916124552963 / 10000000000000000 : ℚ)) + (q := (404952970464647 / 5000000000000000 : ℚ)) + (U := (-(25134222523221480039377 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_5 : Uω (aρ 5) (bρ 5) (331792728101 / 3200000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_148_5 : have hlg : Real.log (664641470824081 / 10000000000000000 : ℝ) ≤ (-(13555463086437859904049 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (664641470824081 / 10000000000000000 : ℝ) = - (664641470824081 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (664641470824081 / 625000000000000 : ℚ)) - (U := (307480519562140095951 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (664641470824081 / 625000000000000 : ℝ) ≤ - (307480519562140095951 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (624577103677537 / 10000000000000000 : ℝ)) (q := - (664641470824081 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (664641470824081 / 10000000000000000 : ℚ)) + (r' := (664641470824081 / 625000000000000 : ℚ)) + (U := (-(13555463086437859904049 / 5000000000000000000000 : ℚ))) + (U' := (307480519562140095951 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (624577103677537 / 10000000000000000 : ℚ)) + (q := (664641470824081 / 10000000000000000 : ℚ)) + (U := (-(13555463086437859904049 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_6 : Uω (aρ 6) (bρ 6) (331792728101 / 3200000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_148_6 : have hlg : Real.log (745851195633597 / 20000000000000000 : ℝ) ≤ (-(1644480720294708417623 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (745851195633597 / 20000000000000000 : ℝ) = - (745851195633597 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (745851195633597 / 625000000000000 : ℚ)) - (U := (88387230455291582377 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (745851195633597 / 625000000000000 : ℝ) ≤ - (88387230455291582377 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (52096433200743 / 2500000000000000 : ℝ)) (q := - (745851195633597 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (745851195633597 / 20000000000000000 : ℚ)) + (r' := (745851195633597 / 625000000000000 : ℚ)) + (U := (-(1644480720294708417623 / 500000000000000000000 : ℚ))) + (U' := (88387230455291582377 / 500000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (331792728101 / 3200000000000 : ℚ)) + (s := (52096433200743 / 2500000000000000 : ℚ)) + (q := (745851195633597 / 20000000000000000 : ℚ)) + (U := (-(1644480720294708417623 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_148_7 : Uω (aρ 7) (bρ 7) (331792728101 / 3200000000000 : ℝ) ≤ @@ -315,25 +291,21 @@ lemma U_149_1 : have hlg : Real.log (3916787749818561 / 40000000000000000 : ℝ) ≤ (-(2904509483478323326409 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3916787749818561 / 40000000000000000 : ℝ) = - (3916787749818561 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3916787749818561 / 2500000000000000 : ℚ)) - (U := (561226418021676673591 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3916787749818561 / 2500000000000000 : ℝ) ≤ - (561226418021676673591 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (489515917466359 / 5000000000000000 : ℝ)) (q := - (3916787749818561 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3916787749818561 / 40000000000000000 : ℚ)) + (r' := (3916787749818561 / 2500000000000000 : ℚ)) + (U := (-(2904509483478323326409 / 1250000000000000000000 : ℚ))) + (U' := (561226418021676673591 / 1250000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (489515917466359 / 5000000000000000 : ℚ)) + (q := (3916787749818561 / 40000000000000000 : ℚ)) + (U := (-(2904509483478323326409 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_2 : Uω (aρ 2) (bρ 2) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -341,25 +313,21 @@ lemma U_149_2 : have hlg : Real.log (3817926022778861 / 40000000000000000 : ℝ) ≤ (-(2936465129834332087859 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3817926022778861 / 40000000000000000 : ℝ) = - (3817926022778861 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3817926022778861 / 2500000000000000 : ℚ)) - (U := (529270771665667912141 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3817926022778861 / 2500000000000000 : ℝ) ≤ - (529270771665667912141 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (238342495980717 / 2500000000000000 : ℝ)) (q := - (3817926022778861 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3817926022778861 / 40000000000000000 : ℚ)) + (r' := (3817926022778861 / 2500000000000000 : ℚ)) + (U := (-(2936465129834332087859 / 1250000000000000000000 : ℚ))) + (U' := (529270771665667912141 / 1250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (238342495980717 / 2500000000000000 : ℚ)) + (q := (3817926022778861 / 40000000000000000 : ℚ)) + (U := (-(2936465129834332087859 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_3 : Uω (aρ 3) (bρ 3) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -367,25 +335,21 @@ lemma U_149_3 : have hlg : Real.log (3616422160668097 / 40000000000000000 : ℝ) ≤ (-(6008485673465917970041 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3616422160668097 / 40000000000000000 : ℝ) = - (3616422160668097 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3616422160668097 / 2500000000000000 : ℚ)) - (U := (922986129534082029959 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3616422160668097 / 2500000000000000 : ℝ) ≤ - (922986129534082029959 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (450007079608743 / 5000000000000000 : ℝ)) (q := - (3616422160668097 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3616422160668097 / 40000000000000000 : ℚ)) + (r' := (3616422160668097 / 2500000000000000 : ℚ)) + (U := (-(6008485673465917970041 / 2500000000000000000000 : ℚ))) + (U' := (922986129534082029959 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (450007079608743 / 5000000000000000 : ℚ)) + (q := (3616422160668097 / 40000000000000000 : ℚ)) + (U := (-(6008485673465917970041 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_4 : Uω (aρ 4) (bρ 4) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -393,25 +357,21 @@ lemma U_149_4 : have hlg : Real.log (653620901436473 / 8000000000000000 : ℝ) ≤ (-(25046692976457419243763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (653620901436473 / 8000000000000000 : ℝ) = - (653620901436473 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (653620901436473 / 500000000000000 : ℚ)) - (U := (2679194235542580756237 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (653620901436473 / 500000000000000 : ℝ) ≤ - (2679194235542580756237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40207475676981 / 500000000000000 : ℝ)) (q := - (653620901436473 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (653620901436473 / 8000000000000000 : ℚ)) + (r' := (653620901436473 / 500000000000000 : ℚ)) + (U := (-(25046692976457419243763 / 10000000000000000000000 : ℚ))) + (U' := (2679194235542580756237 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (40207475676981 / 500000000000000 : ℚ)) + (q := (653620901436473 / 8000000000000000 : ℚ)) + (U := (-(25046692976457419243763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_5 : Uω (aρ 5) (bρ 5) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -419,25 +379,21 @@ lemma U_149_5 : have hlg : Real.log (2688370509070709 / 40000000000000000 : ℝ) ≤ (-(26999442017161149412787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2688370509070709 / 40000000000000000 : ℝ) = - (2688370509070709 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2688370509070709 / 2500000000000000 : ℚ)) - (U := (726445194838850587213 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2688370509070709 / 2500000000000000 : ℝ) ≤ - (726445194838850587213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79059054227349 / 1250000000000000 : ℝ)) (q := - (2688370509070709 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2688370509070709 / 40000000000000000 : ℚ)) + (r' := (2688370509070709 / 2500000000000000 : ℚ)) + (U := (-(26999442017161149412787 / 10000000000000000000000 : ℚ))) + (U' := (726445194838850587213 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (79059054227349 / 1250000000000000 : ℚ)) + (q := (2688370509070709 / 40000000000000000 : ℚ)) + (U := (-(26999442017161149412787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_6 : Uω (aρ 6) (bρ 6) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -445,25 +401,21 @@ lemma U_149_6 : have hlg : Real.log (1540633872166461 / 40000000000000000 : ℝ) ≤ (-(16283427578860002476577 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1540633872166461 / 40000000000000000 : ℝ) = - (1540633872166461 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1540633872166461 / 1250000000000000 : ℚ)) - (U := (1045251928639997523423 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1540633872166461 / 1250000000000000 : ℝ) ≤ - (1045251928639997523423 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56461122626667 / 2500000000000000 : ℝ)) (q := - (1540633872166461 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1540633872166461 / 40000000000000000 : ℚ)) + (r' := (1540633872166461 / 1250000000000000 : ℚ)) + (U := (-(16283427578860002476577 / 5000000000000000000000 : ℚ))) + (U' := (1045251928639997523423 / 5000000000000000000000 : ℚ)) + 5 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3340349625797 / 32000000000000 : ℚ)) + (s := (56461122626667 / 2500000000000000 : ℚ)) + (q := (1540633872166461 / 40000000000000000 : ℚ)) + (U := (-(16283427578860002476577 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_149_7 : Uω (aρ 7) (bρ 7) (3340349625797 / 32000000000000 : ℝ) ≤ @@ -605,25 +557,21 @@ lemma U_150_1 : have hlg : Real.log (246551273362417 / 2500000000000000 : ℝ) ≤ (-(5791190081092174150987 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (246551273362417 / 2500000000000000 : ℝ) = - (246551273362417 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (246551273362417 / 156250000000000 : ℚ)) - (U := (1140281721907825849013 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (246551273362417 / 156250000000000 : ℝ) ≤ - (1140281721907825849013 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (246510291044209 / 2500000000000000 : ℝ)) (q := - (246551273362417 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (246551273362417 / 2500000000000000 : ℚ)) + (r' := (246551273362417 / 156250000000000 : ℚ)) + (U := (-(5791190081092174150987 / 2500000000000000000000 : ℚ))) + (U' := (1140281721907825849013 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (246510291044209 / 2500000000000000 : ℚ)) + (q := (246551273362417 / 2500000000000000 : ℚ)) + (U := (-(5791190081092174150987 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_2 : Uω (aρ 2) (bρ 2) (420346496323 / 4000000000000 : ℝ) ≤ @@ -631,25 +579,21 @@ lemma U_150_2 : have hlg : Real.log (1922993196237621 / 20000000000000000 : ℝ) ≤ (-(2927311680014733944333 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1922993196237621 / 20000000000000000 : ℝ) = - (1922993196237621 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1922993196237621 / 1250000000000000 : ℚ)) - (U := (538424221485266055667 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1922993196237621 / 1250000000000000 : ℝ) ≤ - (538424221485266055667 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (960393186025121 / 10000000000000000 : ℝ)) (q := - (1922993196237621 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1922993196237621 / 20000000000000000 : ℚ)) + (r' := (1922993196237621 / 1250000000000000 : ℚ)) + (U := (-(2927311680014733944333 / 1250000000000000000000 : ℚ))) + (U' := (538424221485266055667 / 1250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (960393186025121 / 10000000000000000 : ℚ)) + (q := (1922993196237621 / 20000000000000000 : ℚ)) + (U := (-(2927311680014733944333 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_3 : Uω (aρ 3) (bρ 3) (420346496323 / 4000000000000 : ℝ) ≤ @@ -657,25 +601,21 @@ lemma U_150_3 : have hlg : Real.log (113893016104001 / 1250000000000000 : ℝ) ≤ (-(93579659246677020249 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (113893016104001 / 1250000000000000 : ℝ) = - (113893016104001 / 78125000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (113893016104001 / 78125000000000 : ℚ)) - (U := (14724587675197979751 / 39062500000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (113893016104001 / 78125000000000 : ℝ) ≤ - (14724587675197979751 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (226771088450379 / 2500000000000000 : ℝ)) (q := - (113893016104001 / 1250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (113893016104001 / 1250000000000000 : ℚ)) + (r' := (113893016104001 / 78125000000000 : ℚ)) + (U := (-(93579659246677020249 / 39062500000000000000 : ℚ))) + (U' := (14724587675197979751 / 39062500000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (226771088450379 / 2500000000000000 : ℚ)) + (q := (113893016104001 / 1250000000000000 : ℚ)) + (U := (-(93579659246677020249 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_4 : Uω (aρ 4) (bρ 4) (420346496323 / 4000000000000 : ℝ) ≤ @@ -683,25 +623,21 @@ lemma U_150_4 : have hlg : Real.log (1648288651716599 / 20000000000000000 : ℝ) ≤ (-(4991989407247450880853 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1648288651716599 / 20000000000000000 : ℝ) = - (1648288651716599 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1648288651716599 / 1250000000000000 : ℚ)) - (U := (553188035152549119147 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1648288651716599 / 1250000000000000 : ℝ) ≤ - (553188035152549119147 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (811378928919099 / 10000000000000000 : ℝ)) (q := - (1648288651716599 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1648288651716599 / 20000000000000000 : ℚ)) + (r' := (1648288651716599 / 1250000000000000 : ℚ)) + (U := (-(4991989407247450880853 / 2000000000000000000000 : ℚ))) + (U' := (553188035152549119147 / 2000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (811378928919099 / 10000000000000000 : ℚ)) + (q := (1648288651716599 / 20000000000000000 : ℚ)) + (U := (-(4991989407247450880853 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_5 : Uω (aρ 5) (bρ 5) (420346496323 / 4000000000000 : ℝ) ≤ @@ -709,25 +645,21 @@ lemma U_150_5 : have hlg : Real.log (1359066893920101 / 20000000000000000 : ℝ) ≤ (-(1344466957828672674537 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1359066893920101 / 20000000000000000 : ℝ) = - (1359066893920101 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1359066893920101 / 1250000000000000 : ℚ)) - (U := (41827402771327325463 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1359066893920101 / 1250000000000000 : ℝ) ≤ - (41827402771327325463 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (640347090457601 / 10000000000000000 : ℝ)) (q := - (1359066893920101 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1359066893920101 / 20000000000000000 : ℚ)) + (r' := (1359066893920101 / 1250000000000000 : ℚ)) + (U := (-(1344466957828672674537 / 500000000000000000000 : ℚ))) + (U' := (41827402771327325463 / 500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (640347090457601 / 10000000000000000 : ℚ)) + (q := (1359066893920101 / 20000000000000000 : ℚ)) + (U := (-(1344466957828672674537 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_6 : Uω (aρ 6) (bρ 6) (420346496323 / 4000000000000 : ℝ) ≤ @@ -735,25 +667,21 @@ lemma U_150_6 : have hlg : Real.log (793729402033551 / 20000000000000000 : ℝ) ≤ (-(3226744951560163699253 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (793729402033551 / 20000000000000000 : ℝ) = - (793729402033551 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (793729402033551 / 625000000000000 : ℚ)) - (U := (238990949939836300747 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (793729402033551 / 625000000000000 : ℝ) ≤ - (238990949939836300747 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242249973711051 / 10000000000000000 : ℝ)) (q := - (793729402033551 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (793729402033551 / 20000000000000000 : ℚ)) + (r' := (793729402033551 / 625000000000000 : ℚ)) + (U := (-(3226744951560163699253 / 1000000000000000000000 : ℚ))) + (U' := (238990949939836300747 / 1000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (420346496323 / 4000000000000 : ℚ)) + (s := (242249973711051 / 10000000000000000 : ℚ)) + (q := (793729402033551 / 20000000000000000 : ℚ)) + (U := (-(3226744951560163699253 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_150_7 : Uω (aρ 7) (bρ 7) (420346496323 / 4000000000000 : ℝ) ≤ @@ -893,25 +821,21 @@ lemma U_151_1 : have hlg : Real.log (794570586307991 / 8000000000000000 : ℝ) ≤ (-(2886743742383077728029 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (794570586307991 / 8000000000000000 : ℝ) = - (794570586307991 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (794570586307991 / 500000000000000 : ℚ)) - (U := (578992159116922271971 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (794570586307991 / 500000000000000 : ℝ) ≤ - (578992159116922271971 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (49652523015077 / 500000000000000 : ℝ)) (q := - (794570586307991 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (794570586307991 / 8000000000000000 : ℚ)) + (r' := (794570586307991 / 500000000000000 : ℚ)) + (U := (-(2886743742383077728029 / 1250000000000000000000 : ℚ))) + (U' := (578992159116922271971 / 1250000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (49652523015077 / 500000000000000 : ℚ)) + (q := (794570586307991 / 8000000000000000 : ℚ)) + (U := (-(2886743742383077728029 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_2 : Uω (aρ 2) (bρ 2) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -919,25 +843,21 @@ lemma U_151_2 : have hlg : Real.log (3874046291721471 / 40000000000000000 : ℝ) ≤ (-(4669159877652684528577 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3874046291721471 / 40000000000000000 : ℝ) = - (3874046291721471 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3874046291721471 / 2500000000000000 : ℚ)) - (U := (876017564747315471423 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3874046291721471 / 2500000000000000 : ℝ) ≤ - (876017564747315471423 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (483708076451149 / 5000000000000000 : ℝ)) (q := - (3874046291721471 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3874046291721471 / 40000000000000000 : ℚ)) + (r' := (3874046291721471 / 2500000000000000 : ℚ)) + (U := (-(4669159877652684528577 / 2000000000000000000000 : ℚ))) + (U' := (876017564747315471423 / 2000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (483708076451149 / 5000000000000000 : ℚ)) + (q := (3874046291721471 / 40000000000000000 : ℚ)) + (U := (-(4669159877652684528577 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_3 : Uω (aρ 3) (bρ 3) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -945,25 +865,21 @@ lemma U_151_3 : have hlg : Real.log (3672728923173331 / 40000000000000000 : ℝ) ≤ (-(23879444915266449414989 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3672728923173331 / 40000000000000000 : ℝ) = - (3672728923173331 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3672728923173331 / 2500000000000000 : ℚ)) - (U := (3846442296733550585011 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3672728923173331 / 2500000000000000 : ℝ) ≤ - (3846442296733550585011 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228538393744557 / 2500000000000000 : ℝ)) (q := - (3672728923173331 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3672728923173331 / 40000000000000000 : ℚ)) + (r' := (3672728923173331 / 2500000000000000 : ℚ)) + (U := (-(23879444915266449414989 / 10000000000000000000000 : ℚ))) + (U' := (3846442296733550585011 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (228538393744557 / 2500000000000000 : ℚ)) + (q := (3672728923173331 / 40000000000000000 : ℚ)) + (U := (-(23879444915266449414989 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_4 : Uω (aρ 4) (bρ 4) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -971,25 +887,21 @@ lemma U_151_4 : have hlg : Real.log (3325042363024537 / 40000000000000000 : ℝ) ≤ (-(24873970382882411377119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3325042363024537 / 40000000000000000 : ℝ) = - (3325042363024537 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3325042363024537 / 2500000000000000 : ℚ)) - (U := (2851916829117588622881 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3325042363024537 / 2500000000000000 : ℝ) ≤ - (2851916829117588622881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (818604475968831 / 10000000000000000 : ℝ)) (q := - (3325042363024537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3325042363024537 / 40000000000000000 : ℚ)) + (r' := (3325042363024537 / 2500000000000000 : ℚ)) + (U := (-(24873970382882411377119 / 10000000000000000000000 : ℚ))) + (U' := (2851916829117588622881 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (818604475968831 / 10000000000000000 : ℚ)) + (q := (3325042363024537 / 40000000000000000 : ℚ)) + (U := (-(24873970382882411377119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_5 : Uω (aρ 5) (bρ 5) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -997,25 +909,21 @@ lemma U_151_5 : have hlg : Real.log (549571445302699 / 8000000000000000 : ℝ) ≤ (-(26780580354809959357677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (549571445302699 / 8000000000000000 : ℝ) = - (549571445302699 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (549571445302699 / 500000000000000 : ℚ)) - (U := (945306857190040642323 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (549571445302699 / 500000000000000 : ℝ) ≤ - (945306857190040642323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (64820182704831 / 1000000000000000 : ℝ)) (q := - (549571445302699 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (549571445302699 / 8000000000000000 : ℚ)) + (r' := (549571445302699 / 500000000000000 : ℚ)) + (U := (-(26780580354809959357677 / 10000000000000000000000 : ℚ))) + (U' := (945306857190040642323 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (64820182704831 / 1000000000000000 : ℚ)) + (q := (549571445302699 / 8000000000000000 : ℚ)) + (U := (-(26780580354809959357677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_6 : Uω (aρ 6) (bρ 6) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -1023,25 +931,21 @@ lemma U_151_6 : have hlg : Real.log (1632579498774009 / 40000000000000000 : ℝ) ≤ (-(3198718174266971398463 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1632579498774009 / 40000000000000000 : ℝ) = - (1632579498774009 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1632579498774009 / 1250000000000000 : ℚ)) - (U := (267017727233028601537 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1632579498774009 / 1250000000000000 : ℝ) ≤ - (267017727233028601537 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (257803338318567 / 10000000000000000 : ℝ)) (q := - (1632579498774009 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1632579498774009 / 40000000000000000 : ℚ)) + (r' := (1632579498774009 / 1250000000000000 : ℚ)) + (U := (-(3198718174266971398463 / 1000000000000000000000 : ℚ))) + (U' := (267017727233028601537 / 1000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3385194315371 / 32000000000000 : ℚ)) + (s := (257803338318567 / 10000000000000000 : ℚ)) + (q := (1632579498774009 / 40000000000000000 : ℚ)) + (U := (-(3198718174266971398463 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_151_7 : Uω (aρ 7) (bρ 7) (3385194315371 / 32000000000000 : ℝ) ≤ @@ -1183,25 +1087,21 @@ lemma U_152_1 : have hlg : Real.log (2000442712217593 / 20000000000000000 : ℝ) ≤ (-(4604727520682233243737 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2000442712217593 / 20000000000000000 : ℝ) = - (2000442712217593 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2000442712217593 / 1250000000000000 : ℚ)) - (U := (940449921717766756263 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2000442712217593 / 1250000000000000 : ℝ) ≤ - (940449921717766756263 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (500029862001609 / 5000000000000000 : ℝ)) (q := - (2000442712217593 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2000442712217593 / 20000000000000000 : ℚ)) + (r' := (2000442712217593 / 1250000000000000 : ℚ)) + (U := (-(4604727520682233243737 / 2000000000000000000000 : ℚ))) + (U' := (940449921717766756263 / 2000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (500029862001609 / 5000000000000000 : ℚ)) + (q := (2000442712217593 / 20000000000000000 : ℚ)) + (U := (-(4604727520682233243737 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_2 : Uω (aρ 2) (bρ 2) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1209,25 +1109,21 @@ lemma U_152_2 : have hlg : Real.log (1951052865344707 / 20000000000000000 : ℝ) ≤ (-(5818407786757043322733 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1951052865344707 / 20000000000000000 : ℝ) = - (1951052865344707 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1951052865344707 / 1250000000000000 : ℚ)) - (U := (1113064016242956677267 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1951052865344707 / 1250000000000000 : ℝ) ≤ - (1113064016242956677267 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243609722410083 / 2500000000000000 : ℝ)) (q := - (1951052865344707 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1951052865344707 / 20000000000000000 : ℚ)) + (r' := (1951052865344707 / 1250000000000000 : ℚ)) + (U := (-(5818407786757043322733 / 2500000000000000000000 : ℚ))) + (U' := (1113064016242956677267 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (243609722410083 / 2500000000000000 : ℚ)) + (q := (1951052865344707 / 20000000000000000 : ℚ)) + (U := (-(5818407786757043322733 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_3 : Uω (aρ 3) (bρ 3) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1235,25 +1131,21 @@ lemma U_152_3 : have hlg : Real.log (925219857255517 / 10000000000000000 : ℝ) ≤ (-(11901544890733755628069 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (925219857255517 / 10000000000000000 : ℝ) = - (925219857255517 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (925219857255517 / 625000000000000 : ℚ)) - (U := (1961398715266244371931 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (925219857255517 / 625000000000000 : ℝ) ≤ - (1961398715266244371931 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (921221845156659 / 10000000000000000 : ℝ)) (q := - (925219857255517 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (925219857255517 / 10000000000000000 : ℚ)) + (r' := (925219857255517 / 625000000000000 : ℚ)) + (U := (-(11901544890733755628069 / 5000000000000000000000 : ℚ))) + (U' := (1961398715266244371931 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (921221845156659 / 10000000000000000 : ℚ)) + (q := (925219857255517 / 10000000000000000 : ℚ)) + (U := (-(11901544890733755628069 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_4 : Uω (aρ 4) (bρ 4) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1261,25 +1153,21 @@ lemma U_152_4 : have hlg : Real.log (1676749944515773 / 20000000000000000 : ℝ) ≤ (-(309859363700855048777 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1676749944515773 / 20000000000000000 : ℝ) = - (1676749944515773 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1676749944515773 / 1250000000000000 : ℚ)) - (U := (36714226449144951223 / 125000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1676749944515773 / 1250000000000000 : ℝ) ≤ - (36714226449144951223 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (412913128113199 / 5000000000000000 : ℝ)) (q := - (1676749944515773 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1676749944515773 / 20000000000000000 : ℚ)) + (r' := (1676749944515773 / 1250000000000000 : ℚ)) + (U := (-(309859363700855048777 / 125000000000000000000 : ℚ))) + (U' := (36714226449144951223 / 125000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (412913128113199 / 5000000000000000 : ℚ)) + (q := (1676749944515773 / 20000000000000000 : ℚ)) + (U := (-(309859363700855048777 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_5 : Uω (aρ 5) (bρ 5) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1287,25 +1175,21 @@ lemma U_152_5 : have hlg : Real.log (138877112805401 / 2000000000000000 : ℝ) ≤ (-(833535311543117281089 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (138877112805401 / 2000000000000000 : ℝ) = - (138877112805401 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (138877112805401 / 125000000000000 : ℚ)) - (U := (32898663831882718911 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (138877112805401 / 125000000000000 : ℝ) ≤ - (32898663831882718911 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (131207471819927 / 2000000000000000 : ℝ)) (q := - (138877112805401 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (138877112805401 / 2000000000000000 : ℚ)) + (r' := (138877112805401 / 125000000000000 : ℚ)) + (U := (-(833535311543117281089 / 312500000000000000000 : ℚ))) + (U' := (32898663831882718911 / 312500000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (131207471819927 / 2000000000000000 : ℚ)) + (q := (138877112805401 / 2000000000000000 : ℚ)) + (U := (-(833535311543117281089 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_6 : Uω (aρ 6) (bρ 6) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1313,25 +1197,21 @@ lemma U_152_6 : have hlg : Real.log (419071922331349 / 10000000000000000 : ℝ) ≤ (-(31722978131427743478867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (419071922331349 / 10000000000000000 : ℝ) = - (419071922331349 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (419071922331349 / 312500000000000 : ℚ)) - (U := (2934380883572256521133 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (419071922331349 / 312500000000000 : ℝ) ≤ - (2934380883572256521133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (272650450848323 / 10000000000000000 : ℝ)) (q := - (419071922331349 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (419071922331349 / 10000000000000000 : ℚ)) + (r' := (419071922331349 / 312500000000000 : ℚ)) + (U := (-(31722978131427743478867 / 10000000000000000000000 : ℚ))) + (U' := (2934380883572256521133 / 10000000000000000000000 : ℚ)) + 5 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1703808330079 / 16000000000000 : ℚ)) + (s := (272650450848323 / 10000000000000000 : ℚ)) + (q := (419071922331349 / 10000000000000000 : ℚ)) + (U := (-(31722978131427743478867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_152_7 : Uω (aρ 7) (bρ 7) (1703808330079 / 16000000000000 : ℝ) ≤ @@ -1471,25 +1351,21 @@ lemma U_153_1 : have hlg : Real.log (4028917853838367 / 40000000000000000 : ℝ) ≤ (-(286922704474371271327 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4028917853838367 / 40000000000000000 : ℝ) = - (4028917853838367 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4028917853838367 / 2500000000000000 : ℚ)) - (U := (59650885675628728673 / 125000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4028917853838367 / 2500000000000000 : ℝ) ≤ - (59650885675628728673 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1007068955958871 / 10000000000000000 : ℝ)) (q := - (4028917853838367 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4028917853838367 / 40000000000000000 : ℚ)) + (r' := (4028917853838367 / 2500000000000000 : ℚ)) + (U := (-(286922704474371271327 / 125000000000000000000 : ℚ))) + (U' := (59650885675628728673 / 125000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (1007068955958871 / 10000000000000000 : ℚ)) + (q := (4028917853838367 / 40000000000000000 : ℚ)) + (U := (-(286922704474371271327 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_2 : Uω (aρ 2) (bρ 2) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1497,25 +1373,21 @@ lemma U_153_2 : have hlg : Real.log (786032943851897 / 8000000000000000 : ℝ) ≤ (-(23201981147737440312697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (786032943851897 / 8000000000000000 : ℝ) = - (786032943851897 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (786032943851897 / 500000000000000 : ℚ)) - (U := (4523906064262559687303 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (786032943851897 / 500000000000000 : ℝ) ≤ - (4523906064262559687303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98146140117943 / 1000000000000000 : ℝ)) (q := - (786032943851897 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (786032943851897 / 8000000000000000 : ℚ)) + (r' := (786032943851897 / 500000000000000 : ℚ)) + (U := (-(23201981147737440312697 / 10000000000000000000000 : ℚ))) + (U' := (4523906064262559687303 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (98146140117943 / 1000000000000000 : ℚ)) + (q := (786032943851897 / 8000000000000000 : ℚ)) + (U := (-(23201981147737440312697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_3 : Uω (aρ 3) (bρ 3) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1523,25 +1395,21 @@ lemma U_153_3 : have hlg : Real.log (3729028076321347 / 40000000000000000 : ℝ) ≤ (-(949092729089347156587 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3729028076321347 / 40000000000000000 : ℝ) = - (3729028076321347 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3729028076321347 / 2500000000000000 : ℚ)) - (U := (159942759390652843413 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3729028076321347 / 2500000000000000 : ℝ) ≤ - (159942759390652843413 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (928289186060361 / 10000000000000000 : ℝ)) (q := - (3729028076321347 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3729028076321347 / 40000000000000000 : ℚ)) + (r' := (3729028076321347 / 2500000000000000 : ℚ)) + (U := (-(949092729089347156587 / 400000000000000000000 : ℚ))) + (U' := (159942759390652843413 / 400000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (928289186060361 / 10000000000000000 : ℚ)) + (q := (3729028076321347 / 40000000000000000 : ℚ)) + (U := (-(949092729089347156587 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_4 : Uω (aρ 4) (bρ 4) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1549,25 +1417,21 @@ lemma U_153_4 : have hlg : Real.log (3381950077383383 / 40000000000000000 : ℝ) ≤ (-(6176067409942879644687 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3381950077383383 / 40000000000000000 : ℝ) = - (3381950077383383 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3381950077383383 / 2500000000000000 : ℚ)) - (U := (755404393057120355313 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3381950077383383 / 2500000000000000 : ℝ) ≤ - (755404393057120355313 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (833044367656379 / 10000000000000000 : ℝ)) (q := - (3381950077383383 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3381950077383383 / 40000000000000000 : ℚ)) + (r' := (3381950077383383 / 2500000000000000 : ℚ)) + (U := (-(6176067409942879644687 / 2500000000000000000000 : ℚ))) + (U' := (755404393057120355313 / 2500000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (833044367656379 / 10000000000000000 : ℚ)) + (q := (3381950077383383 / 40000000000000000 : ℚ)) + (U := (-(6176067409942879644687 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_5 : Uω (aρ 5) (bρ 5) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1575,25 +1439,21 @@ lemma U_153_5 : have hlg : Real.log (2807190236661777 / 40000000000000000 : ℝ) ≤ (-(5313390771513018446107 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2807190236661777 / 40000000000000000 : ℝ) = - (2807190236661777 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2807190236661777 / 2500000000000000 : ℚ)) - (U := (231786670886981553893 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2807190236661777 / 2500000000000000 : ℝ) ≤ - (231786670886981553893 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (41490897914411 / 625000000000000 : ℝ)) (q := - (2807190236661777 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2807190236661777 / 40000000000000000 : ℚ)) + (r' := (2807190236661777 / 2500000000000000 : ℚ)) + (U := (-(5313390771513018446107 / 2000000000000000000000 : ℚ))) + (U' := (231786670886981553893 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (41490897914411 / 625000000000000 : ℚ)) + (q := (2807190236661777 / 40000000000000000 : ℚ)) + (U := (-(5313390771513018446107 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_6 : Uω (aρ 6) (bρ 6) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1601,25 +1461,21 @@ lemma U_153_6 : have hlg : Real.log (1718802708717827 / 40000000000000000 : ℝ) ≤ (-(15736257519806563902167 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1718802708717827 / 40000000000000000 : ℝ) = - (1718802708717827 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1718802708717827 / 1250000000000000 : ℚ)) - (U := (1592421987693436097833 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1718802708717827 / 1250000000000000 : ℝ) ≤ - (1592421987693436097833 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (286900977798601 / 10000000000000000 : ℝ)) (q := - (1718802708717827 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1718802708717827 / 40000000000000000 : ℚ)) + (r' := (1718802708717827 / 1250000000000000 : ℚ)) + (U := (-(15736257519806563902167 / 5000000000000000000000 : ℚ))) + (U' := (1592421987693436097833 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (686007800989 / 6400000000000 : ℚ)) + (s := (286900977798601 / 10000000000000000 : ℚ)) + (q := (1718802708717827 / 40000000000000000 : ℚ)) + (U := (-(15736257519806563902167 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_153_7 : Uω (aρ 7) (bρ 7) (686007800989 / 6400000000000 : ℝ) ≤ @@ -1761,25 +1617,21 @@ lemma U_154_1 : have hlg : Real.log (1014237555266513 / 10000000000000000 : ℝ) ≤ (-(22884479388127094268989 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1014237555266513 / 10000000000000000 : ℝ) = - (1014237555266513 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1014237555266513 / 625000000000000 : ℚ)) - (U := (4841407823872905731011 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1014237555266513 / 625000000000000 : ℝ) ≤ - (4841407823872905731011 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (126759769603347 / 1250000000000000 : ℝ)) (q := - (1014237555266513 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1014237555266513 / 10000000000000000 : ℚ)) + (r' := (1014237555266513 / 625000000000000 : ℚ)) + (U := (-(22884479388127094268989 / 10000000000000000000000 : ℚ))) + (U' := (4841407823872905731011 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (126759769603347 / 1250000000000000 : ℚ)) + (q := (1014237555266513 / 10000000000000000 : ℚ)) + (U := (-(22884479388127094268989 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_2 : Uω (aρ 2) (bρ 2) (863115337433 / 8000000000000 : ℝ) ≤ @@ -1787,25 +1639,21 @@ lemma U_154_2 : have hlg : Real.log (1979111633515501 / 20000000000000000 : ℝ) ≤ (-(2891355248039883648733 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1979111633515501 / 20000000000000000 : ℝ) = - (1979111633515501 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1979111633515501 / 1250000000000000 : ℚ)) - (U := (574380653460116351267 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1979111633515501 / 1250000000000000 : ℝ) ≤ - (574380653460116351267 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (988483692319251 / 10000000000000000 : ℝ)) (q := - (1979111633515501 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1979111633515501 / 20000000000000000 : ℚ)) + (r' := (1979111633515501 / 1250000000000000 : ℚ)) + (U := (-(2891355248039883648733 / 1250000000000000000000 : ℚ))) + (U' := (574380653460116351267 / 1250000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (988483692319251 / 10000000000000000 : ℚ)) + (q := (1979111633515501 / 20000000000000000 : ℚ)) + (U := (-(2891355248039883648733 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_3 : Uω (aρ 3) (bρ 3) (863115337433 / 8000000000000 : ℝ) ≤ @@ -1813,25 +1661,21 @@ lemma U_154_3 : have hlg : Real.log (1878587453599769 / 20000000000000000 : ℝ) ≤ (-(591303033137199082917 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1878587453599769 / 20000000000000000 : ℝ) = - (1878587453599769 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1878587453599769 / 1250000000000000 : ℚ)) - (U := (101844147162800917083 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1878587453599769 / 1250000000000000 : ℝ) ≤ - (101844147162800917083 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (935355618753519 / 10000000000000000 : ℝ)) (q := - (1878587453599769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1878587453599769 / 20000000000000000 : ℚ)) + (r' := (1878587453599769 / 1250000000000000 : ℚ)) + (U := (-(591303033137199082917 / 250000000000000000000 : ℚ))) + (U' := (101844147162800917083 / 250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (935355618753519 / 10000000000000000 : ℚ)) + (q := (1878587453599769 / 20000000000000000 : ℚ)) + (U := (-(591303033137199082917 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_4 : Uω (aρ 4) (bρ 4) (863115337433 / 8000000000000 : ℝ) ≤ @@ -1839,25 +1683,21 @@ lemma U_154_4 : have hlg : Real.log (852598279294741 / 10000000000000000 : ℝ) ≤ (-(24620518847931819427187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (852598279294741 / 10000000000000000 : ℝ) = - (852598279294741 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (852598279294741 / 625000000000000 : ℚ)) - (U := (3105368364068180572813 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (852598279294741 / 625000000000000 : ℝ) ≤ - (3105368364068180572813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105032363101029 / 1250000000000000 : ℝ)) (q := - (852598279294741 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (852598279294741 / 10000000000000000 : ℚ)) + (r' := (852598279294741 / 625000000000000 : ℚ)) + (U := (-(24620518847931819427187 / 10000000000000000000000 : ℚ))) + (U' := (3105368364068180572813 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (105032363101029 / 1250000000000000 : ℚ)) + (q := (852598279294741 / 10000000000000000 : ℚ)) + (U := (-(24620518847931819427187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_5 : Uω (aρ 5) (bρ 5) (863115337433 / 8000000000000 : ℝ) ≤ @@ -1865,25 +1705,21 @@ lemma U_154_5 : have hlg : Real.log (283680246175593 / 4000000000000000 : ℝ) ≤ (-(1653876205589663543733 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (283680246175593 / 4000000000000000 : ℝ) = - (283680246175593 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (283680246175593 / 250000000000000 : ℚ)) - (U := (78991745160336456267 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (283680246175593 / 250000000000000 : ℝ) ≤ - (78991745160336456267 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (134330699286343 / 2000000000000000 : ℝ)) (q := - (283680246175593 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (283680246175593 / 4000000000000000 : ℚ)) + (r' := (283680246175593 / 250000000000000 : ℚ)) + (U := (-(1653876205589663543733 / 625000000000000000000 : ℚ))) + (U' := (78991745160336456267 / 625000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (134330699286343 / 2000000000000000 : ℚ)) + (q := (283680246175593 / 4000000000000000 : ℚ)) + (U := (-(1653876205589663543733 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_6 : Uω (aρ 6) (bρ 6) (863115337433 / 8000000000000 : ℝ) ≤ @@ -1891,25 +1727,21 @@ lemma U_154_6 : have hlg : Real.log (880147126120617 / 20000000000000000 : ℝ) ≤ (-(15616992344826031747609 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (880147126120617 / 20000000000000000 : ℝ) = - (880147126120617 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (880147126120617 / 625000000000000 : ℚ)) - (U := (1711687162673968252391 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (880147126120617 / 625000000000000 : ℝ) ≤ - (1711687162673968252391 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (300639766814367 / 10000000000000000 : ℝ)) (q := - (880147126120617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (880147126120617 / 20000000000000000 : ℚ)) + (r' := (880147126120617 / 625000000000000 : ℚ)) + (U := (-(15616992344826031747609 / 5000000000000000000000 : ℚ))) + (U' := (1711687162673968252391 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (863115337433 / 8000000000000 : ℚ)) + (s := (300639766814367 / 10000000000000000 : ℚ)) + (q := (880147126120617 / 20000000000000000 : ℚ)) + (U := (-(15616992344826031747609 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_154_7 : Uω (aρ 7) (bρ 7) (863115337433 / 8000000000000 : ℝ) ≤ @@ -2051,25 +1883,21 @@ lemma U_155_1 : have hlg : Real.log (325677310541247 / 3200000000000000 : ℝ) ≤ (-(22849990415668781578591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (325677310541247 / 3200000000000000 : ℝ) = - (325677310541247 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (325677310541247 / 200000000000000 : ℚ)) - (U := (4875896796331218421409 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (325677310541247 / 200000000000000 : ℝ) ≤ - (4875896796331218421409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40703309832143 / 400000000000000 : ℝ)) (q := - (325677310541247 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (325677310541247 / 3200000000000000 : ℚ)) + (r' := (325677310541247 / 200000000000000 : ℚ)) + (U := (-(22849990415668781578591 / 10000000000000000000000 : ℚ))) + (U' := (4875896796331218421409 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (40703309832143 / 400000000000000 : ℚ)) + (q := (325677310541247 / 3200000000000000 : ℚ)) + (U := (-(22849990415668781578591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_2 : Uω (aρ 2) (bρ 2) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2077,25 +1905,21 @@ lemma U_155_2 : have hlg : Real.log (7944504757085371 / 80000000000000000 : ℝ) ≤ (-(23095461694982195708649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7944504757085371 / 80000000000000000 : ℝ) = - (7944504757085371 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7944504757085371 / 5000000000000000 : ℚ)) - (U := (4630425517017804291351 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7944504757085371 / 5000000000000000 : ℝ) ≤ - (4630425517017804291351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (247998689175531 / 2500000000000000 : ℝ)) (q := - (7944504757085371 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7944504757085371 / 80000000000000000 : ℚ)) + (r' := (7944504757085371 / 5000000000000000 : ℚ)) + (U := (-(23095461694982195708649 / 10000000000000000000000 : ℚ))) + (U' := (4630425517017804291351 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (247998689175531 / 2500000000000000 : ℚ)) + (q := (7944504757085371 / 80000000000000000 : ℚ)) + (U := (-(23095461694982195708649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_3 : Uω (aρ 3) (bρ 3) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2103,25 +1927,21 @@ lemma U_155_3 : have hlg : Real.log (1508499061719027 / 16000000000000000 : ℝ) ≤ (-(11807367817896096737809 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1508499061719027 / 16000000000000000 : ℝ) = - (1508499061719027 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1508499061719027 / 1000000000000000 : ℚ)) - (U := (2055575788103903262191 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1508499061719027 / 1000000000000000 : ℝ) ≤ - (2055575788103903262191 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (187777700185913 / 2000000000000000 : ℝ)) (q := - (1508499061719027 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1508499061719027 / 16000000000000000 : ℚ)) + (r' := (1508499061719027 / 1000000000000000 : ℚ)) + (U := (-(11807367817896096737809 / 5000000000000000000000 : ℚ))) + (U' := (2055575788103903262191 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (187777700185913 / 2000000000000000 : ℚ)) + (q := (1508499061719027 / 16000000000000000 : ℚ)) + (U := (-(11807367817896096737809 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_4 : Uω (aρ 4) (bρ 4) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2129,25 +1949,21 @@ lemma U_155_4 : have hlg : Real.log (6849224027335643 / 80000000000000000 : ℝ) ≤ (-(12289456342288177086599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6849224027335643 / 80000000000000000 : ℝ) = - (6849224027335643 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6849224027335643 / 5000000000000000 : ℚ)) - (U := (1573487263711822913401 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6849224027335643 / 5000000000000000 : ℝ) ≤ - (1573487263711822913401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (210966215419923 / 2500000000000000 : ℝ)) (q := - (6849224027335643 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6849224027335643 / 80000000000000000 : ℚ)) + (r' := (6849224027335643 / 5000000000000000 : ℚ)) + (U := (-(12289456342288177086599 / 5000000000000000000000 : ℚ))) + (U' := (1573487263711822913401 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (210966215419923 / 2500000000000000 : ℚ)) + (q := (6849224027335643 / 80000000000000000 : ℚ)) + (U := (-(12289456342288177086599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_5 : Uω (aρ 5) (bρ 5) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2155,25 +1971,21 @@ lemma U_155_5 : have hlg : Real.log (5703191106221687 / 80000000000000000 : ℝ) ≤ (-(5282001544501092498839 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5703191106221687 / 80000000000000000 : ℝ) = - (5703191106221687 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5703191106221687 / 5000000000000000 : ℚ)) - (U := (263175897898907501161 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5703191106221687 / 5000000000000000 : ℝ) ≤ - (263175897898907501161 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (675546550736203 / 10000000000000000 : ℝ)) (q := - (5703191106221687 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5703191106221687 / 80000000000000000 : ℚ)) + (r' := (5703191106221687 / 5000000000000000 : ℚ)) + (U := (-(5282001544501092498839 / 2000000000000000000000 : ℚ))) + (U' := (263175897898907501161 / 2000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (675546550736203 / 10000000000000000 : ℚ)) + (q := (5703191106221687 / 80000000000000000 : ℚ)) + (U := (-(5282001544501092498839 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_6 : Uω (aρ 6) (bρ 6) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2181,25 +1993,21 @@ lemma U_155_6 : have hlg : Real.log (712279725650911 / 16000000000000000 : ℝ) ≤ (-(31118732925594350230399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (712279725650911 / 16000000000000000 : ℝ) = - (712279725650911 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (712279725650911 / 500000000000000 : ℚ)) - (U := (3538626089405649769601 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (712279725650911 / 500000000000000 : ℝ) ≤ - (3538626089405649769601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (15366940319221 / 500000000000000 : ℝ)) (q := - (712279725650911 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (712279725650911 / 16000000000000000 : ℚ)) + (r' := (712279725650911 / 500000000000000 : ℚ)) + (U := (-(31118732925594350230399 / 10000000000000000000000 : ℚ))) + (U' := (3538626089405649769601 / 10000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6927345044251 / 64000000000000 : ℚ)) + (s := (15366940319221 / 500000000000000 : ℚ)) + (q := (712279725650911 / 16000000000000000 : ℚ)) + (U := (-(31118732925594350230399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_155_7 : Uω (aρ 7) (bρ 7) (6927345044251 / 64000000000000 : ℝ) ≤ @@ -2342,25 +2150,21 @@ lemma U_156_1 : have hlg : Real.log (4084982527398643 / 40000000000000000 : ℝ) ≤ (-(5703905005074826194883 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4084982527398643 / 40000000000000000 : ℝ) = - (4084982527398643 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4084982527398643 / 2500000000000000 : ℚ)) - (U := (1227566797925173805117 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4084982527398643 / 2500000000000000 : ℝ) ≤ - (1227566797925173805117 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (510543663623567 / 5000000000000000 : ℝ)) (q := - (4084982527398643 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4084982527398643 / 40000000000000000 : ℚ)) + (r' := (4084982527398643 / 2500000000000000 : ℚ)) + (U := (-(5703905005074826194883 / 2500000000000000000000 : ℚ))) + (U' := (1227566797925173805117 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (510543663623567 / 5000000000000000 : ℚ)) + (q := (4084982527398643 / 40000000000000000 : ℚ)) + (U := (-(5703905005074826194883 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_2 : Uω (aρ 2) (bρ 2) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2368,25 +2172,21 @@ lemma U_156_2 : have hlg : Real.log (797256276666427 / 8000000000000000 : ℝ) ≤ (-(115301032043345084123 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (797256276666427 / 8000000000000000 : ℝ) = - (797256276666427 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (797256276666427 / 500000000000000 : ℚ)) - (U := (23328404016654915877 / 50000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (797256276666427 / 500000000000000 : ℝ) ≤ - (23328404016654915877 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24887644193097 / 250000000000000 : ℝ)) (q := - (797256276666427 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (797256276666427 / 8000000000000000 : ℚ)) + (r' := (797256276666427 / 500000000000000 : ℚ)) + (U := (-(115301032043345084123 / 50000000000000000000 : ℚ))) + (U' := (23328404016654915877 / 50000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (24887644193097 / 250000000000000 : ℚ)) + (q := (797256276666427 / 8000000000000000 : ℚ)) + (U := (-(115301032043345084123 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_3 : Uω (aρ 3) (bρ 3) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2394,25 +2194,21 @@ lemma U_156_3 : have hlg : Real.log (3785319962516137 / 40000000000000000 : ℝ) ≤ (-(23577490354072033648947 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3785319962516137 / 40000000000000000 : ℝ) = - (3785319962516137 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3785319962516137 / 2500000000000000 : ℚ)) - (U := (4148396857927966351053 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3785319962516137 / 2500000000000000 : ℝ) ≤ - (4148396857927966351053 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (942421163665881 / 10000000000000000 : ℝ)) (q := - (3785319962516137 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3785319962516137 / 40000000000000000 : ℚ)) + (r' := (3785319962516137 / 2500000000000000 : ℚ)) + (U := (-(23577490354072033648947 / 10000000000000000000000 : ℚ))) + (U' := (4148396857927966351053 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (942421163665881 / 10000000000000000 : ℚ)) + (q := (3785319962516137 / 40000000000000000 : ℚ)) + (U := (-(23577490354072033648947 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_4 : Uω (aρ 4) (bρ 4) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2420,25 +2216,21 @@ lemma U_156_4 : have hlg : Real.log (687765838197183 / 8000000000000000 : ℝ) ≤ (-(24537483910791336289901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (687765838197183 / 8000000000000000 : ℝ) = - (687765838197183 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (687765838197183 / 500000000000000 : ℚ)) - (U := (3188403301208663710099 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (687765838197183 / 500000000000000 : ℝ) ≤ - (3188403301208663710099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84746995896577 / 1000000000000000 : ℝ)) (q := - (687765838197183 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (687765838197183 / 8000000000000000 : ℚ)) + (r' := (687765838197183 / 500000000000000 : ℚ)) + (U := (-(24537483910791336289901 / 10000000000000000000000 : ℚ))) + (U' := (3188403301208663710099 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (84746995896577 / 1000000000000000 : ℚ)) + (q := (687765838197183 / 8000000000000000 : ℚ)) + (U := (-(24537483910791336289901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_5 : Uω (aρ 5) (bρ 5) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2446,25 +2238,21 @@ lemma U_156_5 : have hlg : Real.log (2866380162684629 / 40000000000000000 : ℝ) ≤ (-(26358294867270100871003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2866380162684629 / 40000000000000000 : ℝ) = - (2866380162684629 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2866380162684629 / 2500000000000000 : ℚ)) - (U := (1367592344729899128997 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2866380162684629 / 2500000000000000 : ℝ) ≤ - (1367592344729899128997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (679435364150127 / 10000000000000000 : ℝ)) (q := - (2866380162684629 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2866380162684629 / 40000000000000000 : ℚ)) + (r' := (2866380162684629 / 2500000000000000 : ℚ)) + (U := (-(26358294867270100871003 / 10000000000000000000000 : ℚ))) + (U' := (1367592344729899128997 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (679435364150127 / 10000000000000000 : ℚ)) + (q := (2866380162684629 / 40000000000000000 : ℚ)) + (U := (-(26358294867270100871003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_6 : Uω (aρ 6) (bρ 6) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2472,25 +2260,21 @@ lemma U_156_6 : have hlg : Real.log (360179341265761 / 8000000000000000 : ℝ) ≤ (-(15502973708874956289793 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (360179341265761 / 8000000000000000 : ℝ) = - (360179341265761 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (360179341265761 / 250000000000000 : ℚ)) - (U := (1825705798625043710207 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (360179341265761 / 250000000000000 : ℝ) ≤ - (1825705798625043710207 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62786802222443 / 2000000000000000 : ℝ)) (q := - (360179341265761 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (360179341265761 / 8000000000000000 : ℚ)) + (r' := (360179341265761 / 250000000000000 : ℚ)) + (U := (-(15502973708874956289793 / 5000000000000000000000 : ℚ))) + (U' := (1825705798625043710207 / 5000000000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3474883694519 / 32000000000000 : ℚ)) + (s := (62786802222443 / 2000000000000000 : ℚ)) + (q := (360179341265761 / 8000000000000000 : ℚ)) + (U := (-(15502973708874956289793 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_156_7 : Uω (aρ 7) (bρ 7) (3474883694519 / 32000000000000 : ℝ) ≤ @@ -2631,25 +2415,21 @@ lemma U_157_1 : have hlg : Real.log (8197997316239641 / 80000000000000000 : ℝ) ≤ (-(22781367389197025760763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8197997316239641 / 80000000000000000 : ℝ) = - (8197997316239641 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8197997316239641 / 5000000000000000 : ℚ)) - (U := (4944519822802974239237 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8197997316239641 / 5000000000000000 : ℝ) ≤ - (4944519822802974239237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (512295950617377 / 5000000000000000 : ℝ)) (q := - (8197997316239641 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8197997316239641 / 80000000000000000 : ℚ)) + (r' := (8197997316239641 / 5000000000000000 : ℚ)) + (U := (-(22781367389197025760763 / 10000000000000000000000 : ℚ))) + (U' := (4944519822802974239237 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (512295950617377 / 5000000000000000 : ℚ)) + (q := (8197997316239641 / 80000000000000000 : ℚ)) + (U := (-(22781367389197025760763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_2 : Uω (aρ 2) (bρ 2) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2657,25 +2437,21 @@ lemma U_157_2 : have hlg : Real.log (8000620565049141 / 80000000000000000 : ℝ) ≤ (-(11512537621657838256657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8000620565049141 / 80000000000000000 : ℝ) = - (8000620565049141 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8000620565049141 / 5000000000000000 : ℚ)) - (U := (2350405984342161743343 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8000620565049141 / 5000000000000000 : ℝ) ≤ - (2350405984342161743343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (999016725947129 / 10000000000000000 : ℝ)) (q := - (8000620565049141 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8000620565049141 / 80000000000000000 : ℚ)) + (r' := (8000620565049141 / 5000000000000000 : ℚ)) + (U := (-(11512537621657838256657 / 5000000000000000000000 : ℚ))) + (U' := (2350405984342161743343 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (999016725947129 / 10000000000000000 : ℚ)) + (q := (8000620565049141 / 80000000000000000 : ℚ)) + (U := (-(11512537621657838256657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_3 : Uω (aρ 3) (bρ 3) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2683,25 +2459,21 @@ lemma U_157_3 : have hlg : Real.log (1519756734708893 / 16000000000000000 : ℝ) ≤ (-(2942548052630913630127 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1519756734708893 / 16000000000000000 : ℝ) = - (1519756734708893 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1519756734708893 / 1000000000000000 : ℚ)) - (U := (523187848869086369873 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1519756734708893 / 1000000000000000 : ℝ) ≤ - (523187848869086369873 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5912210058881 / 62500000000000 : ℝ)) (q := - (1519756734708893 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1519756734708893 / 16000000000000000 : ℚ)) + (r' := (1519756734708893 / 1000000000000000 : ℚ)) + (U := (-(2942548052630913630127 / 1250000000000000000000 : ℚ))) + (U' := (523187848869086369873 / 1250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (5912210058881 / 62500000000000 : ℚ)) + (q := (1519756734708893 / 16000000000000000 : ℚ)) + (U := (-(2942548052630913630127 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_4 : Uω (aρ 4) (bρ 4) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2709,25 +2481,21 @@ lemma U_157_4 : have hlg : Real.log (6906089341960289 / 80000000000000000 : ℝ) ≤ (-(3062028872361546944299 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6906089341960289 / 80000000000000000 : ℝ) = - (6906089341960289 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6906089341960289 / 5000000000000000 : ℚ)) - (U := (403707029138453055701 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6906089341960289 / 5000000000000000 : ℝ) ≤ - (403707029138453055701 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (212768551897479 / 2500000000000000 : ℝ)) (q := - (6906089341960289 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6906089341960289 / 80000000000000000 : ℚ)) + (r' := (6906089341960289 / 5000000000000000 : ℚ)) + (U := (-(3062028872361546944299 / 1250000000000000000000 : ℚ))) + (U' := (403707029138453055701 / 1250000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (212768551897479 / 2500000000000000 : ℚ)) + (q := (6906089341960289 / 80000000000000000 : ℚ)) + (U := (-(3062028872361546944299 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_5 : Uω (aρ 5) (bρ 5) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2735,25 +2503,21 @@ lemma U_157_5 : have hlg : Real.log (5762312870576409 / 80000000000000000 : ℝ) ≤ (-(26306876994912978474327 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5762312870576409 / 80000000000000000 : ℝ) = - (5762312870576409 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5762312870576409 / 5000000000000000 : ℚ)) - (U := (1419010217087021525673 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5762312870576409 / 5000000000000000 : ℝ) ≤ - (1419010217087021525673 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (341660004539473 / 5000000000000000 : ℝ)) (q := - (5762312870576409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5762312870576409 / 80000000000000000 : ℚ)) + (r' := (5762312870576409 / 5000000000000000 : ℚ)) + (U := (-(26306876994912978474327 / 10000000000000000000000 : ℚ))) + (U' := (1419010217087021525673 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (341660004539473 / 5000000000000000 : ℚ)) + (q := (5762312870576409 / 80000000000000000 : ℚ)) + (U := (-(26306876994912978474327 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_6 : Uω (aρ 6) (bρ 6) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2761,25 +2525,21 @@ lemma U_157_6 : have hlg : Real.log (3641798503794537 / 80000000000000000 : ℝ) ≤ (-(15447744896504633414501 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3641798503794537 / 80000000000000000 : ℝ) = - (3641798503794537 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3641798503794537 / 2500000000000000 : ℚ)) - (U := (1880934610995366585499 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3641798503794537 / 2500000000000000 : ℝ) ≤ - (1880934610995366585499 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160215896261739 / 5000000000000000 : ℝ)) (q := - (3641798503794537 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3641798503794537 / 80000000000000000 : ℚ)) + (r' := (3641798503794537 / 2500000000000000 : ℚ)) + (U := (-(15447744896504633414501 / 5000000000000000000000 : ℚ))) + (U' := (1880934610995366585499 / 5000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (278887589353 / 2560000000000 : ℚ)) + (s := (160215896261739 / 5000000000000000 : ℚ)) + (q := (3641798503794537 / 80000000000000000 : ℚ)) + (U := (-(15447744896504633414501 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_157_7 : Uω (aρ 7) (bρ 7) (278887589353 / 2560000000000 : ℝ) ≤ @@ -2922,25 +2682,21 @@ lemma U_158_1 : have hlg : Real.log (2056507387040809 / 20000000000000000 : ℝ) ≤ (-(11373615858935949105329 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2056507387040809 / 20000000000000000 : ℝ) = - (2056507387040809 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2056507387040809 / 1250000000000000 : ℚ)) - (U := (2489327747064050894671 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2056507387040809 / 1250000000000000 : ℝ) ≤ - (2489327747064050894671 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (257024116960671 / 2500000000000000 : ℝ)) (q := - (2056507387040809 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2056507387040809 / 20000000000000000 : ℚ)) + (r' := (2056507387040809 / 1250000000000000 : ℚ)) + (U := (-(11373615858935949105329 / 5000000000000000000000 : ℚ))) + (U' := (2489327747064050894671 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (257024116960671 / 2500000000000000 : ℚ)) + (q := (2056507387040809 / 20000000000000000 : ℚ)) + (U := (-(11373615858935949105329 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_2 : Uω (aρ 2) (bρ 2) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -2948,25 +2704,21 @@ lemma U_158_2 : have hlg : Real.log (250896192326839 / 2500000000000000 : ℝ) ≤ (-(22990067326181240245647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (250896192326839 / 2500000000000000 : ℝ) = - (250896192326839 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (250896192326839 / 156250000000000 : ℚ)) - (U := (4735819885818759754353 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (250896192326839 / 156250000000000 : ℝ) ≤ - (4735819885818759754353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1002527631926587 / 10000000000000000 : ℝ)) (q := - (250896192326839 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (250896192326839 / 2500000000000000 : ℚ)) + (r' := (250896192326839 / 156250000000000 : ℚ)) + (U := (-(22990067326181240245647 / 10000000000000000000000 : ℚ))) + (U' := (4735819885818759754353 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (1002527631926587 / 10000000000000000 : ℚ)) + (q := (250896192326839 / 2500000000000000 : ℚ)) + (U := (-(22990067326181240245647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_3 : Uω (aρ 3) (bρ 3) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -2974,25 +2726,21 @@ lemma U_158_3 : have hlg : Real.log (1906731640954683 / 20000000000000000 : ℝ) ≤ (-(1175170839473725169687 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1906731640954683 / 20000000000000000 : ℝ) = - (1906731640954683 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1906731640954683 / 1250000000000000 : ℚ)) - (U := (211123521126274830313 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1906731640954683 / 1250000000000000 : ℝ) ≤ - (211123521126274830313 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (474742920308279 / 5000000000000000 : ℝ)) (q := - (1906731640954683 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1906731640954683 / 20000000000000000 : ℚ)) + (r' := (1906731640954683 / 1250000000000000 : ℚ)) + (U := (-(1175170839473725169687 / 500000000000000000000 : ℚ))) + (U' := (211123521126274830313 / 500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (474742920308279 / 5000000000000000 : ℚ)) + (q := (1906731640954683 / 20000000000000000 : ℚ)) + (U := (-(1175170839473725169687 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_4 : Uω (aρ 4) (bρ 4) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -3000,25 +2748,21 @@ lemma U_158_4 : have hlg : Real.log (346725847512379 / 4000000000000000 : ℝ) ≤ (-(12227576180934471999219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (346725847512379 / 4000000000000000 : ℝ) = - (346725847512379 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (346725847512379 / 250000000000000 : ℚ)) - (U := (1635367425065528000781 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (346725847512379 / 250000000000000 : ℝ) ≤ - (1635367425065528000781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85467761828877 / 1000000000000000 : ℝ)) (q := - (346725847512379 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (346725847512379 / 4000000000000000 : ℚ)) + (r' := (346725847512379 / 250000000000000 : ℚ)) + (U := (-(12227576180934471999219 / 5000000000000000000000 : ℚ))) + (U' := (1635367425065528000781 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (85467761828877 / 1000000000000000 : ℚ)) + (q := (346725847512379 / 4000000000000000 : ℚ)) + (U := (-(12227576180934471999219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_5 : Uω (aρ 5) (bρ 5) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -3026,25 +2770,21 @@ lemma U_158_5 : have hlg : Real.log (1447962256152311 / 20000000000000000 : ℝ) ≤ (-(13127875225417848178601 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1447962256152311 / 20000000000000000 : ℝ) = - (1447962256152311 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1447962256152311 / 1250000000000000 : ℚ)) - (U := (735068380582151821399 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1447962256152311 / 1250000000000000 : ℝ) ≤ - (735068380582151821399 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (343600278107093 / 5000000000000000 : ℝ)) (q := - (1447962256152311 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1447962256152311 / 20000000000000000 : ℚ)) + (r' := (1447962256152311 / 1250000000000000 : ℚ)) + (U := (-(13127875225417848178601 / 5000000000000000000000 : ℚ))) + (U' := (735068380582151821399 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (343600278107093 / 5000000000000000 : ℚ)) + (q := (1447962256152311 / 20000000000000000 : ℚ)) + (U := (-(13127875225417848178601 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_6 : Uω (aρ 6) (bρ 6) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -3052,25 +2792,21 @@ lemma U_158_6 : have hlg : Real.log (230089821502913 / 5000000000000000 : ℝ) ≤ (-(30787234291560992907967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (230089821502913 / 5000000000000000 : ℝ) = - (230089821502913 / 156250000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (230089821502913 / 156250000000000 : ℚ)) - (U := (3870124723439007092033 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (230089821502913 / 156250000000000 : ℝ) ≤ - (3870124723439007092033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (326837961213527 / 10000000000000000 : ℝ)) (q := - (230089821502913 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (230089821502913 / 5000000000000000 : ℚ)) + (r' := (230089821502913 / 156250000000000 : ℚ)) + (U := (-(30787234291560992907967 / 10000000000000000000000 : ℚ))) + (U' := (3870124723439007092033 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1748653019653 / 16000000000000 : ℚ)) + (s := (326837961213527 / 10000000000000000 : ℚ)) + (q := (230089821502913 / 5000000000000000 : ℚ)) + (U := (-(30787234291560992907967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_158_7 : Uω (aρ 7) (bρ 7) (1748653019653 / 16000000000000 : ℝ) ≤ @@ -3212,25 +2948,21 @@ lemma U_159_1 : have hlg : Real.log (8254061750868911 / 80000000000000000 : ℝ) ≤ (-(5678303052512994256621 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8254061750868911 / 80000000000000000 : ℝ) = - (8254061750868911 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8254061750868911 / 5000000000000000 : ℚ)) - (U := (1253168750487005743379 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8254061750868911 / 5000000000000000 : ℝ) ≤ - (1253168750487005743379 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (515800513573067 / 5000000000000000 : ℝ)) (q := - (8254061750868911 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8254061750868911 / 80000000000000000 : ℚ)) + (r' := (8254061750868911 / 5000000000000000 : ℚ)) + (U := (-(5678303052512994256621 / 2500000000000000000000 : ℚ))) + (U' := (1253168750487005743379 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (515800513573067 / 5000000000000000 : ℚ)) + (q := (8254061750868911 / 80000000000000000 : ℚ)) + (U := (-(5678303052512994256621 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_2 : Uω (aρ 2) (bρ 2) (7017034423399 / 64000000000000 : ℝ) ≤ @@ -3238,25 +2970,21 @@ lemma U_159_2 : have hlg : Real.log (1611347107416251 / 16000000000000000 : ℝ) ≤ (-(22955181793716472346763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1611347107416251 / 16000000000000000 : ℝ) = - (1611347107416251 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1611347107416251 / 1000000000000000 : ℚ)) - (U := (4770705418283527653237 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1611347107416251 / 1000000000000000 : ℝ) ≤ - (4770705418283527653237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (50301924310461 / 500000000000000 : ℝ)) (q := - (1611347107416251 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1611347107416251 / 16000000000000000 : ℚ)) + (r' := (1611347107416251 / 1000000000000000 : ℚ)) + (U := (-(22955181793716472346763 / 10000000000000000000000 : ℚ))) + (U' := (4770705418283527653237 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (50301924310461 / 500000000000000 : ℚ)) + (q := (1611347107416251 / 16000000000000000 : ℚ)) + (U := (-(22955181793716472346763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_3 : Uω (aρ 3) (bρ 3) (7017034423399 / 64000000000000 : ℝ) ≤ @@ -3264,25 +2992,21 @@ lemma U_159_3 : have hlg : Real.log (7655068605397903 / 80000000000000000 : ℝ) ≤ (-(11733293211981849575587 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7655068605397903 / 80000000000000000 : ℝ) = - (7655068605397903 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7655068605397903 / 5000000000000000 : ℚ)) - (U := (2129650394018150424413 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7655068605397903 / 5000000000000000 : ℝ) ≤ - (2129650394018150424413 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (476508929819191 / 5000000000000000 : ℝ)) (q := - (7655068605397903 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7655068605397903 / 80000000000000000 : ℚ)) + (r' := (7655068605397903 / 5000000000000000 : ℚ)) + (U := (-(11733293211981849575587 / 5000000000000000000000 : ℚ))) + (U' := (2129650394018150424413 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (476508929819191 / 5000000000000000 : ℚ)) + (q := (7655068605397903 / 80000000000000000 : ℚ)) + (U := (-(11733293211981849575587 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_4 : Uω (aρ 4) (bρ 4) (7017034423399 / 64000000000000 : ℝ) ≤ @@ -3290,25 +3014,21 @@ lemma U_159_4 : have hlg : Real.log (6962941249049127 / 80000000000000000 : ℝ) ≤ (-(6103561638252420282721 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6962941249049127 / 80000000000000000 : ℝ) = - (6962941249049127 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6962941249049127 / 5000000000000000 : ℚ)) - (U := (827910164747579717279 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6962941249049127 / 5000000000000000 : ℝ) ≤ - (827910164747579717279 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (214570050404047 / 2500000000000000 : ℝ)) (q := - (6962941249049127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6962941249049127 / 80000000000000000 : ℚ)) + (r' := (6962941249049127 / 5000000000000000 : ℚ)) + (U := (-(6103561638252420282721 / 2500000000000000000000 : ℚ))) + (U' := (827910164747579717279 / 2500000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (214570050404047 / 2500000000000000 : ℚ)) + (q := (6962941249049127 / 80000000000000000 : ℚ)) + (U := (-(6103561638252420282721 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_5 : Uω (aρ 5) (bρ 5) (7017034423399 / 64000000000000 : ℝ) ≤ @@ -3316,25 +3036,21 @@ lemma U_159_5 : have hlg : Real.log (1164273812717547 / 16000000000000000 : ℝ) ≤ (-(6551227913151442296359 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1164273812717547 / 16000000000000000 : ℝ) = - (1164273812717547 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1164273812717547 / 1000000000000000 : ℚ)) - (U := (380243889848557703641 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1164273812717547 / 1000000000000000 : ℝ) ≤ - (380243889848557703641 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8638463432323 / 125000000000000 : ℝ)) (q := - (1164273812717547 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1164273812717547 / 16000000000000000 : ℚ)) + (r' := (1164273812717547 / 1000000000000000 : ℚ)) + (U := (-(6551227913151442296359 / 2500000000000000000000 : ℚ))) + (U' := (380243889848557703641 / 2500000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (8638463432323 / 125000000000000 : ℚ)) + (q := (1164273812717547 / 16000000000000000 : ℚ)) + (U := (-(6551227913151442296359 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_6 : Uω (aρ 6) (bρ 6) (7017034423399 / 64000000000000 : ℝ) ≤ @@ -3342,25 +3058,21 @@ lemma U_159_6 : have hlg : Real.log (3720730472628851 / 80000000000000000 : ℝ) ≤ (-(6136213241512007746819 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3720730472628851 / 80000000000000000 : ℝ) = - (3720730472628851 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3720730472628851 / 2500000000000000 : ℚ)) - (U := (795258561487992253181 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3720730472628851 / 2500000000000000 : ℝ) ≤ - (795258561487992253181 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (333157801986119 / 10000000000000000 : ℝ)) (q := - (3720730472628851 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3720730472628851 / 80000000000000000 : ℚ)) + (r' := (3720730472628851 / 2500000000000000 : ℚ)) + (U := (-(6136213241512007746819 / 2000000000000000000000 : ℚ))) + (U' := (795258561487992253181 / 2000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7017034423399 / 64000000000000 : ℚ)) + (s := (333157801986119 / 10000000000000000 : ℚ)) + (q := (3720730472628851 / 80000000000000000 : ℚ)) + (U := (-(6136213241512007746819 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_159_7 : Uω (aρ 7) (bρ 7) (7017034423399 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U13.lean b/LeanPool/Zeta5Irrational/Table/U13.lean index dd746d0723..4323599d7d 100644 --- a/LeanPool/Zeta5Irrational/Table/U13.lean +++ b/LeanPool/Zeta5Irrational/Table/U13.lean @@ -24,25 +24,21 @@ lemma U_160_1 : have hlg : Real.log (4141046962326717 / 40000000000000000 : ℝ) ≤ (-(22679308077571814145547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4141046962326717 / 40000000000000000 : ℝ) = - (4141046962326717 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4141046962326717 / 2500000000000000 : ℚ)) - (U := (5046579134428185854453 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4141046962326717 / 2500000000000000 : ℝ) ≤ - (5046579134428185854453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (32347049350603 / 312500000000000 : ℝ)) (q := - (4141046962326717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4141046962326717 / 40000000000000000 : ℚ)) + (r' := (4141046962326717 / 2500000000000000 : ℚ)) + (U := (-(22679308077571814145547 / 10000000000000000000000 : ℚ))) + (U' := (5046579134428185854453 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (32347049350603 / 312500000000000 : ℚ)) + (q := (4141046962326717 / 40000000000000000 : ℚ)) + (U := (-(22679308077571814145547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_2 : Uω (aρ 2) (bρ 2) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_160_2 : have hlg : Real.log (4042396357536883 / 40000000000000000 : ℝ) ≤ (-(22920417791434948469573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4042396357536883 / 40000000000000000 : ℝ) = - (4042396357536883 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4042396357536883 / 2500000000000000 : ℚ)) - (U := (4805469420565051530427 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4042396357536883 / 2500000000000000 : ℝ) ≤ - (4805469420565051530427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1009549289334379 / 10000000000000000 : ℝ)) (q := - (4042396357536883 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4042396357536883 / 40000000000000000 : ℚ)) + (r' := (4042396357536883 / 2500000000000000 : ℚ)) + (U := (-(22920417791434948469573 / 10000000000000000000000 : ℚ))) + (U' := (4805469420565051530427 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (1009549289334379 / 10000000000000000 : ℚ)) + (q := (4042396357536883 / 40000000000000000 : ℚ)) + (U := (-(22920417791434948469573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_3 : Uω (aρ 3) (bρ 3) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_160_3 : have hlg : Real.log (768320980768329 / 8000000000000000 : ℝ) ≤ (-(23429892300799022833847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (768320980768329 / 8000000000000000 : ℝ) = - (768320980768329 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (768320980768329 / 500000000000000 : ℚ)) - (U := (4295994911200977166153 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (768320980768329 / 500000000000000 : ℝ) ≤ - (4295994911200977166153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23913741720919 / 250000000000000 : ℝ)) (q := - (768320980768329 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (768320980768329 / 8000000000000000 : ℚ)) + (r' := (768320980768329 / 500000000000000 : ℚ)) + (U := (-(23429892300799022833847 / 10000000000000000000000 : ℚ))) + (U' := (4295994911200977166153 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (23913741720919 / 250000000000000 : ℚ)) + (q := (768320980768329 / 8000000000000000 : ℚ)) + (U := (-(23429892300799022833847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_4 : Uω (aρ 4) (bρ 4) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_160_4 : have hlg : Real.log (699136227986493 / 8000000000000000 : ℝ) ≤ (-(24373512065536270100317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (699136227986493 / 8000000000000000 : ℝ) = - (699136227986493 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (699136227986493 / 500000000000000 : ℚ)) - (U := (3352375146463729899683 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (699136227986493 / 500000000000000 : ℝ) ≤ - (3352375146463729899683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86188196794717 / 1000000000000000 : ℝ)) (q := - (699136227986493 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (699136227986493 / 8000000000000000 : ℚ)) + (r' := (699136227986493 / 500000000000000 : ℚ)) + (U := (-(24373512065536270100317 / 10000000000000000000000 : ℚ))) + (U' := (3352375146463729899683 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (86188196794717 / 1000000000000000 : ℚ)) + (q := (699136227986493 / 8000000000000000 : ℚ)) + (U := (-(24373512065536270100317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_5 : Uω (aρ 5) (bρ 5) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_160_5 : have hlg : Real.log (2925436628593717 / 40000000000000000 : ℝ) ≤ (-(26154357087978048520417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2925436628593717 / 40000000000000000 : ℝ) = - (2925436628593717 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2925436628593717 / 2500000000000000 : ℚ)) - (U := (1571530124021951479583 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2925436628593717 / 2500000000000000 : ℝ) ≤ - (1571530124021951479583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (173737407903199 / 2500000000000000 : ℝ)) (q := - (2925436628593717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2925436628593717 / 40000000000000000 : ℚ)) + (r' := (2925436628593717 / 2500000000000000 : ℚ)) + (U := (-(26154357087978048520417 / 10000000000000000000000 : ℚ))) + (U' := (1571530124021951479583 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (173737407903199 / 2500000000000000 : ℚ)) + (q := (2925436628593717 / 40000000000000000 : ℚ)) + (U := (-(26154357087978048520417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_6 : Uω (aρ 6) (bρ 6) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_160_6 : have hlg : Real.log (1879848889828579 / 40000000000000000 : ℝ) ≤ (-(30576880569535722827721 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1879848889828579 / 40000000000000000 : ℝ) = - (1879848889828579 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1879848889828579 / 1250000000000000 : ℚ)) - (U := (4080478445464277172279 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1879848889828579 / 1250000000000000 : ℝ) ≤ - (4080478445464277172279 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (339396137370227 / 10000000000000000 : ℝ)) (q := - (1879848889828579 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1879848889828579 / 40000000000000000 : ℚ)) + (r' := (1879848889828579 / 1250000000000000 : ℚ)) + (U := (-(30576880569535722827721 / 10000000000000000000000 : ℚ))) + (U' := (4080478445464277172279 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3519728384093 / 32000000000000 : ℚ)) + (s := (339396137370227 / 10000000000000000 : ℚ)) + (q := (1879848889828579 / 40000000000000000 : ℚ)) + (U := (-(30576880569535722827721 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_160_7 : Uω (aρ 7) (bρ 7) (3519728384093 / 32000000000000 : ℝ) ≤ @@ -315,25 +291,21 @@ lemma U_161_1 : have hlg : Real.log (8310126069809573 / 80000000000000000 : ℝ) ≤ (-(22645518540262755321593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8310126069809573 / 80000000000000000 : ℝ) = - (8310126069809573 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8310126069809573 / 5000000000000000 : ℚ)) - (U := (5080368671737244678407 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8310126069809573 / 5000000000000000 : ℝ) ≤ - (5080368671737244678407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (519305062067681 / 5000000000000000 : ℝ)) (q := - (8310126069809573 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8310126069809573 / 80000000000000000 : ℚ)) + (r' := (8310126069809573 / 5000000000000000 : ℚ)) + (U := (-(22645518540262755321593 / 10000000000000000000000 : ℚ))) + (U' := (5080368671737244678407 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (519305062067681 / 5000000000000000 : ℚ)) + (q := (8310126069809573 / 80000000000000000 : ℚ)) + (U := (-(22645518540262755321593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_2 : Uω (aρ 2) (bρ 2) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -341,25 +313,21 @@ lemma U_161_2 : have hlg : Real.log (8112849690563841 / 80000000000000000 : ℝ) ≤ (-(22885774473786439499311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8112849690563841 / 80000000000000000 : ℝ) = - (8112849690563841 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8112849690563841 / 5000000000000000 : ℚ)) - (U := (4840112738213560500689 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8112849690563841 / 5000000000000000 : ℝ) ≤ - (4840112738213560500689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1013060041833929 / 10000000000000000 : ℝ)) (q := - (8112849690563841 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8112849690563841 / 80000000000000000 : ℚ)) + (r' := (8112849690563841 / 5000000000000000 : ℚ)) + (U := (-(22885774473786439499311 / 10000000000000000000000 : ℚ))) + (U' := (4840112738213560500689 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (1013060041833929 / 10000000000000000 : ℚ)) + (q := (8112849690563841 / 80000000000000000 : ℚ)) + (U := (-(22885774473786439499311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_3 : Uω (aρ 3) (bρ 3) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -367,25 +335,21 @@ lemma U_161_3 : have hlg : Real.log (7711350179937309 / 80000000000000000 : ℝ) ≤ (-(4678666681552500330723 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7711350179937309 / 80000000000000000 : ℝ) = - (7711350179937309 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7711350179937309 / 5000000000000000 : ℚ)) - (U := (866510760847499669277 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7711350179937309 / 5000000000000000 : ℝ) ≤ - (866510760847499669277 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (15001269851989 / 156250000000000 : ℝ)) (q := - (7711350179937309 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7711350179937309 / 80000000000000000 : ℚ)) + (r' := (7711350179937309 / 5000000000000000 : ℚ)) + (U := (-(4678666681552500330723 / 2000000000000000000000 : ℚ))) + (U' := (866510760847499669277 / 2000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (15001269851989 / 156250000000000 : ℚ)) + (q := (7711350179937309 / 80000000000000000 : ℚ)) + (U := (-(4678666681552500330723 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_4 : Uω (aρ 4) (bρ 4) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -393,25 +357,21 @@ lemma U_161_4 : have hlg : Real.log (280791203339793 / 3200000000000000 : ℝ) ≤ (-(12166473716122874792837 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (280791203339793 / 3200000000000000 : ℝ) = - (280791203339793 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (280791203339793 / 200000000000000 : ℚ)) - (U := (1696469889877125207163 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (280791203339793 / 200000000000000 : ℝ) ≤ - (1696469889877125207163 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (34619317099267 / 400000000000000 : ℝ)) (q := - (280791203339793 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (280791203339793 / 3200000000000000 : ℚ)) + (r' := (280791203339793 / 200000000000000 : ℚ)) + (U := (-(12166473716122874792837 / 5000000000000000000000 : ℚ))) + (U' := (1696469889877125207163 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (34619317099267 / 400000000000000 : ℚ)) + (q := (280791203339793 / 3200000000000000 : ℚ)) + (U := (-(12166473716122874792837 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_5 : Uω (aρ 5) (bρ 5) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -419,25 +379,21 @@ lemma U_161_5 : have hlg : Real.log (5880361868833621 / 80000000000000000 : ℝ) ≤ (-(26104083312985725933909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5880361868833621 / 80000000000000000 : ℝ) = - (5880361868833621 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5880361868833621 / 5000000000000000 : ℚ)) - (U := (1621803899014274066091 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5880361868833621 / 5000000000000000 : ℝ) ≤ - (1621803899014274066091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (349409146575687 / 5000000000000000 : ℝ)) (q := - (5880361868833621 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5880361868833621 / 80000000000000000 : ℚ)) + (r' := (5880361868833621 / 5000000000000000 : ℚ)) + (U := (-(26104083312985725933909 / 10000000000000000000000 : ℚ))) + (U' := (1621803899014274066091 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (349409146575687 / 5000000000000000 : ℚ)) + (q := (5880361868833621 / 80000000000000000 : ℚ)) + (U := (-(26104083312985725933909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_6 : Uω (aρ 6) (bρ 6) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -445,25 +401,21 @@ lemma U_161_6 : have hlg : Real.log (3798356722211609 / 80000000000000000 : ℝ) ≤ (-(30474581016948763726831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3798356722211609 / 80000000000000000 : ℝ) = - (3798356722211609 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3798356722211609 / 2500000000000000 : ℚ)) - (U := (4182777998051236273169 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3798356722211609 / 2500000000000000 : ℝ) ≤ - (4182777998051236273169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (345557381635871 / 10000000000000000 : ℝ)) (q := - (3798356722211609 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3798356722211609 / 80000000000000000 : ℚ)) + (r' := (3798356722211609 / 2500000000000000 : ℚ)) + (U := (-(30474581016948763726831 / 10000000000000000000000 : ℚ))) + (U' := (4182777998051236273169 / 10000000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7061879112973 / 64000000000000 : ℚ)) + (s := (345557381635871 / 10000000000000000 : ℚ)) + (q := (3798356722211609 / 80000000000000000 : ℚ)) + (U := (-(30474581016948763726831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_161_7 : Uω (aρ 7) (bρ 7) (7061879112973 / 64000000000000 : ℝ) ≤ @@ -606,25 +558,21 @@ lemma U_162_1 : have hlg : Real.log (2084539546656537 / 20000000000000000 : ℝ) ≤ (-(22611842825845109650421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2084539546656537 / 20000000000000000 : ℝ) = - (2084539546656537 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2084539546656537 / 1250000000000000 : ℚ)) - (U := (5114044386154890349579 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2084539546656537 / 1250000000000000 : ℝ) ≤ - (5114044386154890349579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1042114661966537 / 10000000000000000 : ℝ)) (q := - (2084539546656537 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2084539546656537 / 20000000000000000 : ℚ)) + (r' := (2084539546656537 / 1250000000000000 : ℚ)) + (U := (-(22611842825845109650421 / 10000000000000000000000 : ℚ))) + (U' := (5114044386154890349579 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (44276884111 / 400000000000 : ℚ)) + (s := (1042114661966537 / 10000000000000000 : ℚ)) + (q := (2084539546656537 / 20000000000000000 : ℚ)) + (U := (-(22611842825845109650421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_2 : Uω (aρ 2) (bρ 2) (44276884111 / 400000000000 : ℝ) ≤ @@ -632,25 +580,21 @@ lemma U_162_2 : have hlg : Real.log (101761330820619 / 1000000000000000 : ℝ) ≤ (-(5712812751008120059167 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (101761330820619 / 1000000000000000 : ℝ) = - (101761330820619 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (101761330820619 / 62500000000000 : ℚ)) - (U := (1218659051991879940833 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (101761330820619 / 62500000000000 : ℝ) ≤ - (1218659051991879940833 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (50828537211619 / 500000000000000 : ℝ)) (q := - (101761330820619 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (101761330820619 / 1000000000000000 : ℚ)) + (r' := (101761330820619 / 62500000000000 : ℚ)) + (U := (-(5712812751008120059167 / 2500000000000000000000 : ℚ))) + (U' := (1218659051991879940833 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (44276884111 / 400000000000 : ℚ)) + (s := (50828537211619 / 500000000000000 : ℚ)) + (q := (101761330820619 / 1000000000000000 : ℚ)) + (U := (-(5712812751008120059167 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_3 : Uω (aρ 3) (bρ 3) (44276884111 / 400000000000 : ℝ) ≤ @@ -658,25 +602,21 @@ lemma U_162_3 : have hlg : Real.log (386974486564303 / 4000000000000000 : ℝ) ≤ (-(364951699124394211791 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (386974486564303 / 4000000000000000 : ℝ) = - (386974486564303 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (386974486564303 / 250000000000000 : ℚ)) - (U := (68265288563105788209 / 156250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (386974486564303 / 250000000000000 : ℝ) ≤ - (68265288563105788209 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (192722533398303 / 2000000000000000 : ℝ)) (q := - (386974486564303 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (386974486564303 / 4000000000000000 : ℚ)) + (r' := (386974486564303 / 250000000000000 : ℚ)) + (U := (-(364951699124394211791 / 156250000000000000000 : ℚ))) + (U' := (68265288563105788209 / 156250000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (44276884111 / 400000000000 : ℚ)) + (s := (192722533398303 / 2000000000000000 : ℚ)) + (q := (386974486564303 / 4000000000000000 : ℚ)) + (U := (-(364951699124394211791 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_4 : Uω (aρ 4) (bρ 4) (44276884111 / 400000000000 : ℝ) ≤ @@ -684,25 +624,21 @@ lemma U_162_4 : have hlg : Real.log (881024337506673 / 10000000000000000 : ℝ) ≤ (-(12146275602580457198217 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (881024337506673 / 10000000000000000 : ℝ) = - (881024337506673 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (881024337506673 / 625000000000000 : ℚ)) - (U := (1716668003419542801783 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (881024337506673 / 625000000000000 : ℝ) ≤ - (1716668003419542801783 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (434541545124173 / 5000000000000000 : ℝ)) (q := - (881024337506673 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (881024337506673 / 10000000000000000 : ℚ)) + (r' := (881024337506673 / 625000000000000 : ℚ)) + (U := (-(12146275602580457198217 / 5000000000000000000000 : ℚ))) + (U' := (1716668003419542801783 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (44276884111 / 400000000000 : ℚ)) + (s := (434541545124173 / 5000000000000000 : ℚ)) + (q := (881024337506673 / 10000000000000000 : ℚ)) + (U := (-(12146275602580457198217 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_5 : Uω (aρ 5) (bρ 5) (44276884111 / 400000000000 : ℝ) ≤ @@ -710,25 +646,21 @@ lemma U_162_5 : have hlg : Real.log (147745878897207 / 2000000000000000 : ℝ) ≤ (-(26054086950097842529433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (147745878897207 / 2000000000000000 : ℝ) = - (147745878897207 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (147745878897207 / 125000000000000 : ℚ)) - (U := (1671800261902157470567 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (147745878897207 / 125000000000000 : ℝ) ≤ - (1671800261902157470567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (70268312354207 / 1000000000000000 : ℝ)) (q := - (147745878897207 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (147745878897207 / 2000000000000000 : ℚ)) + (r' := (147745878897207 / 125000000000000 : ℚ)) + (U := (-(26054086950097842529433 / 10000000000000000000000 : ℚ))) + (U' := (1671800261902157470567 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (44276884111 / 400000000000 : ℚ)) + (s := (70268312354207 / 1000000000000000 : ℚ)) + (q := (147745878897207 / 2000000000000000 : ℚ)) + (U := (-(26054086950097842529433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_6 : Uω (aρ 6) (bρ 6) (44276884111 / 400000000000 : ℝ) ≤ @@ -736,25 +668,21 @@ lemma U_162_6 : have hlg : Real.log (959180877277593 / 20000000000000000 : ℝ) ≤ (-(7593519709594403117721 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (959180877277593 / 20000000000000000 : ℝ) = - (959180877277593 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (959180877277593 / 625000000000000 : ℚ)) - (U := (1070820044155596882279 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (959180877277593 / 625000000000000 : ℝ) ≤ - (1070820044155596882279 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (351645586987593 / 10000000000000000 : ℝ)) (q := - (959180877277593 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (959180877277593 / 20000000000000000 : ℚ)) + (r' := (959180877277593 / 625000000000000 : ℚ)) + (U := (-(7593519709594403117721 / 2500000000000000000000 : ℚ))) + (U' := (1070820044155596882279 / 2500000000000000000000 : ℚ)) + 5 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (44276884111 / 400000000000 : ℚ)) + (s := (351645586987593 / 10000000000000000 : ℚ)) + (q := (959180877277593 / 20000000000000000 : ℚ)) + (U := (-(7593519709594403117721 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_162_7 : Uω (aρ 7) (bρ 7) (44276884111 / 400000000000 : ℝ) ≤ @@ -897,25 +825,21 @@ lemma U_163_1 : have hlg : Real.log (1673238055077623 / 16000000000000000 : ℝ) ≤ (-(2822285021227761372561 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1673238055077623 / 16000000000000000 : ℝ) = - (1673238055077623 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1673238055077623 / 1000000000000000 : ℚ)) - (U := (643450880272238627439 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1673238055077623 / 1000000000000000 : ℝ) ≤ - (643450880272238627439 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (52280959639203 / 500000000000000 : ℝ)) (q := - (1673238055077623 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1673238055077623 / 16000000000000000 : ℚ)) + (r' := (1673238055077623 / 1000000000000000 : ℚ)) + (U := (-(2822285021227761372561 / 1250000000000000000000 : ℚ))) + (U' := (643450880272238627439 / 1250000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (52280959639203 / 500000000000000 : ℚ)) + (q := (1673238055077623 / 16000000000000000 : ℚ)) + (U := (-(2822285021227761372561 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_2 : Uω (aρ 2) (bρ 2) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -923,25 +847,21 @@ lemma U_163_2 : have hlg : Real.log (8168963042399931 / 80000000000000000 : ℝ) ≤ (-(22816846554124106986407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8168963042399931 / 80000000000000000 : ℝ) = - (8168963042399931 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8168963042399931 / 5000000000000000 : ℚ)) - (U := (4909040657875893013593 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8168963042399931 / 5000000000000000 : ℝ) ≤ - (4909040657875893013593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (510040698523507 / 5000000000000000 : ℝ)) (q := - (8168963042399931 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8168963042399931 / 80000000000000000 : ℚ)) + (r' := (8168963042399931 / 5000000000000000 : ℚ)) + (U := (-(22816846554124106986407 / 10000000000000000000000 : ℚ))) + (U' := (4909040657875893013593 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (510040698523507 / 5000000000000000 : ℚ)) + (q := (8168963042399931 / 80000000000000000 : ℚ)) + (U := (-(22816846554124106986407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_3 : Uω (aρ 3) (bρ 3) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -949,25 +869,21 @@ lemma U_163_3 : have hlg : Real.log (7767628470721819 / 80000000000000000 : ℝ) ≤ (-(23320617319657831171039 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7767628470721819 / 80000000000000000 : ℝ) = - (7767628470721819 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7767628470721819 / 5000000000000000 : ℚ)) - (U := (4405269892342168828961 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7767628470721819 / 5000000000000000 : ℝ) ≤ - (4405269892342168828961 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (483571930238743 / 5000000000000000 : ℝ)) (q := - (7767628470721819 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7767628470721819 / 80000000000000000 : ℚ)) + (r' := (7767628470721819 / 5000000000000000 : ℚ)) + (U := (-(23320617319657831171039 / 10000000000000000000000 : ℚ))) + (U' := (4405269892342168828961 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (483571930238743 / 5000000000000000 : ℚ)) + (q := (7767628470721819 / 80000000000000000 : ℚ)) + (U := (-(23320617319657831171039 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_4 : Uω (aρ 4) (bρ 4) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -975,25 +891,21 @@ lemma U_163_4 : have hlg : Real.log (7076606168984419 / 80000000000000000 : ℝ) ≤ (-(24252321955188649295791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7076606168984419 / 80000000000000000 : ℝ) = - (7076606168984419 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7076606168984419 / 5000000000000000 : ℚ)) - (U := (3473565256811350704209 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7076606168984419 / 5000000000000000 : ℝ) ≤ - (3473565256811350704209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109085308263517 / 1250000000000000 : ℝ)) (q := - (7076606168984419 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7076606168984419 / 80000000000000000 : ℚ)) + (r' := (7076606168984419 / 5000000000000000 : ℚ)) + (U := (-(24252321955188649295791 / 10000000000000000000000 : ℚ))) + (U' := (3473565256811350704209 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (109085308263517 / 1250000000000000 : ℚ)) + (q := (7076606168984419 / 80000000000000000 : ℚ)) + (U := (-(24252321955188649295791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_5 : Uω (aρ 5) (bρ 5) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -1001,25 +913,21 @@ lemma U_163_5 : have hlg : Real.log (5939293369830159 / 80000000000000000 : ℝ) ≤ (-(26004364686440584843293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5939293369830159 / 80000000000000000 : ℝ) = - (5939293369830159 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5939293369830159 / 5000000000000000 : ℚ)) - (U := (1721522525559415156707 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5939293369830159 / 5000000000000000 : ℝ) ≤ - (1721522525559415156707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (706544185654571 / 10000000000000000 : ℝ)) (q := - (5939293369830159 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5939293369830159 / 80000000000000000 : ℚ)) + (r' := (5939293369830159 / 5000000000000000 : ℚ)) + (U := (-(26004364686440584843293 / 10000000000000000000000 : ℚ))) + (U' := (1721522525559415156707 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (706544185654571 / 10000000000000000 : ℚ)) + (q := (5939293369830159 / 80000000000000000 : ℚ)) + (U := (-(26004364686440584843293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_6 : Uω (aρ 6) (bρ 6) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -1027,25 +935,21 @@ lemma U_163_6 : have hlg : Real.log (3874813059751239 / 80000000000000000 : ℝ) ≤ (-(15137646071887000568089 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3874813059751239 / 80000000000000000 : ℝ) = - (3874813059751239 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3874813059751239 / 2500000000000000 : ℚ)) - (U := (2191033435612999431911 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3874813059751239 / 2500000000000000 : ℝ) ≤ - (2191033435612999431911 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (357664483274841 / 10000000000000000 : ℝ)) (q := - (3874813059751239 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3874813059751239 / 80000000000000000 : ℚ)) + (r' := (3874813059751239 / 2500000000000000 : ℚ)) + (U := (-(15137646071887000568089 / 5000000000000000000000 : ℚ))) + (U' := (2191033435612999431911 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7106723802547 / 64000000000000 : ℚ)) + (s := (357664483274841 / 10000000000000000 : ℚ)) + (q := (3874813059751239 / 80000000000000000 : ℚ)) + (U := (-(15137646071887000568089 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_163_7 : Uω (aρ 7) (bρ 7) (7106723802547 / 64000000000000 : ℝ) ≤ @@ -1187,25 +1091,21 @@ lemma U_164_1 : have hlg : Real.log (4197111168188307 / 40000000000000000 : ℝ) ≤ (-(4508965963075115482201 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4197111168188307 / 40000000000000000 : ℝ) = - (4197111168188307 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4197111168188307 / 2500000000000000 : ℚ)) - (U := (1036211479324884517799 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4197111168188307 / 2500000000000000 : ℝ) ≤ - (1036211479324884517799 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (131140464582277 / 1250000000000000 : ℝ)) (q := - (4197111168188307 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4197111168188307 / 40000000000000000 : ℚ)) + (r' := (4197111168188307 / 2500000000000000 : ℚ)) + (U := (-(4508965963075115482201 / 2000000000000000000000 : ℚ))) + (U' := (1036211479324884517799 / 2000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (131140464582277 / 1250000000000000 : ℚ)) + (q := (4197111168188307 / 40000000000000000 : ℚ)) + (U := (-(4508965963075115482201 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_2 : Uω (aρ 2) (bρ 2) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1213,25 +1113,21 @@ lemma U_164_2 : have hlg : Real.log (4098509711427897 / 40000000000000000 : ℝ) ≤ (-(2278256030458170454529 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4098509711427897 / 40000000000000000 : ℝ) = - (4098509711427897 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4098509711427897 / 2500000000000000 : ℚ)) - (U := (494332690741829545471 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4098509711427897 / 2500000000000000 : ℝ) ≤ - (494332690741829545471 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1023592000788011 / 10000000000000000 : ℝ)) (q := - (4098509711427897 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4098509711427897 / 40000000000000000 : ℚ)) + (r' := (4098509711427897 / 2500000000000000 : ℚ)) + (U := (-(2278256030458170454529 / 1000000000000000000000 : ℚ))) + (U' := (494332690741829545471 / 1000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (1023592000788011 / 10000000000000000 : ℚ)) + (q := (4098509711427897 / 40000000000000000 : ℚ)) + (U := (-(2278256030458170454529 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_3 : Uω (aρ 3) (bρ 3) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1239,25 +1135,21 @@ lemma U_164_3 : have hlg : Real.log (3897883203552751 / 40000000000000000 : ℝ) ≤ (-(23284458156104073445189 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3897883203552751 / 40000000000000000 : ℝ) = - (3897883203552751 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3897883203552751 / 2500000000000000 : ℚ)) - (U := (4441429055895926554811 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3897883203552751 / 2500000000000000 : ℝ) ≤ - (4441429055895926554811 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (485337426600219 / 5000000000000000 : ℝ)) (q := - (3897883203552751 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3897883203552751 / 40000000000000000 : ℚ)) + (r' := (3897883203552751 / 2500000000000000 : ℚ)) + (U := (-(23284458156104073445189 / 10000000000000000000000 : ℚ))) + (U' := (4441429055895926554811 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (485337426600219 / 5000000000000000 : ℚ)) + (q := (3897883203552751 / 40000000000000000 : ℚ)) + (U := (-(23284458156104073445189 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_4 : Uω (aρ 4) (bρ 4) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1265,25 +1157,21 @@ lemma U_164_4 : have hlg : Real.log (3552507264537567 / 40000000000000000 : ℝ) ≤ (-(2421225827178593245939 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3552507264537567 / 40000000000000000 : ℝ) = - (3552507264537567 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3552507264537567 / 2500000000000000 : ℚ)) - (U := (351362894021406754061 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3552507264537567 / 2500000000000000 : ℝ) ≤ - (351362894021406754061 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (438140532378923 / 5000000000000000 : ℝ)) (q := - (3552507264537567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3552507264537567 / 40000000000000000 : ℚ)) + (r' := (3552507264537567 / 2500000000000000 : ℚ)) + (U := (-(2421225827178593245939 / 1000000000000000000000 : ℚ))) + (U' := (351362894021406754061 / 1000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (438140532378923 / 5000000000000000 : ℚ)) + (q := (3552507264537567 / 40000000000000000 : ℚ)) + (U := (-(2421225827178593245939 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_5 : Uω (aρ 5) (bρ 5) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1291,25 +1179,21 @@ lemma U_164_5 : have hlg : Real.log (2984368378214133 / 40000000000000000 : ℝ) ≤ (-(5190982654415919228157 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2984368378214133 / 40000000000000000 : ℝ) = - (2984368378214133 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2984368378214133 / 2500000000000000 : ℚ)) - (U := (354194787984080771843 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2984368378214133 / 2500000000000000 : ℝ) ≤ - (354194787984080771843 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (710401540931129 / 10000000000000000 : ℝ)) (q := - (2984368378214133 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2984368378214133 / 40000000000000000 : ℚ)) + (r' := (2984368378214133 / 2500000000000000 : ℚ)) + (U := (-(5190982654415919228157 / 2000000000000000000000 : ℚ))) + (U' := (354194787984080771843 / 2000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (710401540931129 / 10000000000000000 : ℚ)) + (q := (2984368378214133 / 40000000000000000 : ℚ)) + (U := (-(5190982654415919228157 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_6 : Uω (aρ 6) (bρ 6) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1317,25 +1201,21 @@ lemma U_164_6 : have hlg : Real.log (1956319570663707 / 40000000000000000 : ℝ) ≤ (-(30178145148616695910741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1956319570663707 / 40000000000000000 : ℝ) = - (1956319570663707 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1956319570663707 / 1250000000000000 : ℚ)) - (U := (4479213866383304089259 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1956319570663707 / 1250000000000000 : ℝ) ≤ - (4479213866383304089259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90904378073979 / 2500000000000000 : ℝ)) (q := - (1956319570663707 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1956319570663707 / 40000000000000000 : ℚ)) + (r' := (1956319570663707 / 1250000000000000 : ℚ)) + (U := (-(30178145148616695910741 / 10000000000000000000000 : ℚ))) + (U' := (4479213866383304089259 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3564573073667 / 32000000000000 : ℚ)) + (s := (90904378073979 / 2500000000000000 : ℚ)) + (q := (1956319570663707 / 40000000000000000 : ℚ)) + (U := (-(30178145148616695910741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_164_7 : Uω (aρ 7) (bρ 7) (3564573073667 / 32000000000000 : ℝ) ≤ @@ -1477,25 +1357,21 @@ lemma U_165_1 : have hlg : Real.log (8422254369869049 / 80000000000000000 : ℝ) ≤ (-(225114910132635713543 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8422254369869049 / 80000000000000000 : ℝ) = - (8422254369869049 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8422254369869049 / 5000000000000000 : ℚ)) - (U := (52143961987364286457 / 100000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8422254369869049 / 5000000000000000 : ℝ) ≤ - (52143961987364286457 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263157058414589 / 2500000000000000 : ℝ)) (q := - (8422254369869049 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8422254369869049 / 80000000000000000 : ℚ)) + (r' := (8422254369869049 / 5000000000000000 : ℚ)) + (U := (-(225114910132635713543 / 100000000000000000000 : ℚ))) + (U' := (52143961987364286457 / 100000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (263157058414589 / 2500000000000000 : ℚ)) + (q := (8422254369869049 / 80000000000000000 : ℚ)) + (U := (-(225114910132635713543 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_2 : Uω (aρ 2) (bρ 2) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1503,25 +1379,21 @@ lemma U_165_2 : have hlg : Real.log (8225075609029889 / 80000000000000000 : ℝ) ≤ (-(11374195722188479028337 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8225075609029889 / 80000000000000000 : ℝ) = - (8225075609029889 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8225075609029889 / 5000000000000000 : ℚ)) - (U := (2488747883811520971663 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8225075609029889 / 5000000000000000 : ℝ) ≤ - (2488747883811520971663 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (513551277979283 / 5000000000000000 : ℝ)) (q := - (8225075609029889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8225075609029889 / 80000000000000000 : ℚ)) + (r' := (8225075609029889 / 5000000000000000 : ℚ)) + (U := (-(11374195722188479028337 / 5000000000000000000000 : ℚ))) + (U' := (2488747883811520971663 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (513551277979283 / 5000000000000000 : ℚ)) + (q := (8225075609029889 / 80000000000000000 : ℚ)) + (U := (-(11374195722188479028337 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_3 : Uω (aρ 3) (bρ 3) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1529,25 +1401,21 @@ lemma U_165_3 : have hlg : Real.log (7823903549169049 / 80000000000000000 : ℝ) ≤ (-(23248430285377622815949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7823903549169049 / 80000000000000000 : ℝ) = - (7823903549169049 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7823903549169049 / 5000000000000000 : ℚ)) - (U := (4477456926622377184051 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7823903549169049 / 5000000000000000 : ℝ) ≤ - (4477456926622377184051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243551411835839 / 2500000000000000 : ℝ)) (q := - (7823903549169049 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7823903549169049 / 80000000000000000 : ℚ)) + (r' := (7823903549169049 / 5000000000000000 : ℚ)) + (U := (-(23248430285377622815949 / 10000000000000000000000 : ℚ))) + (U' := (4477456926622377184051 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (243551411835839 / 2500000000000000 : ℚ)) + (q := (7823903549169049 / 80000000000000000 : ℚ)) + (U := (-(23248430285377622815949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_4 : Uω (aρ 4) (bρ 4) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1555,25 +1423,21 @@ lemma U_165_4 : have hlg : Real.log (7133419818469869 / 80000000000000000 : ℝ) ≤ (-(24172358762633393102107 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7133419818469869 / 80000000000000000 : ℝ) = - (7133419818469869 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7133419818469869 / 5000000000000000 : ℚ)) - (U := (3553528449366606897893 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7133419818469869 / 5000000000000000 : ℝ) ≤ - (3553528449366606897893 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (879878895733561 / 10000000000000000 : ℝ)) (q := - (7133419818469869 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7133419818469869 / 80000000000000000 : ℚ)) + (r' := (7133419818469869 / 5000000000000000 : ℚ)) + (U := (-(24172358762633393102107 / 10000000000000000000000 : ℚ))) + (U' := (3553528449366606897893 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (879878895733561 / 10000000000000000 : ℚ)) + (q := (7133419818469869 / 80000000000000000 : ℚ)) + (U := (-(24172358762633393102107 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_5 : Uω (aρ 5) (bρ 5) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1581,25 +1445,21 @@ lemma U_165_5 : have hlg : Real.log (5998165555909053 / 80000000000000000 : ℝ) ≤ (-(25905729518360809311063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5998165555909053 / 80000000000000000 : ℝ) = - (5998165555909053 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5998165555909053 / 5000000000000000 : ℚ)) - (U := (1820157693639190688937 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5998165555909053 / 5000000000000000 : ℝ) ≤ - (1820157693639190688937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (714255249428357 / 10000000000000000 : ℝ)) (q := - (5998165555909053 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5998165555909053 / 80000000000000000 : ℚ)) + (r' := (5998165555909053 / 5000000000000000 : ℚ)) + (U := (-(25905729518360809311063 / 10000000000000000000000 : ℚ))) + (U' := (1820157693639190688937 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (714255249428357 / 10000000000000000 : ℚ)) + (q := (5998165555909053 / 80000000000000000 : ℚ)) + (U := (-(25905729518360809311063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_6 : Uω (aρ 6) (bρ 6) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1607,25 +1467,21 @@ lemma U_165_6 : have hlg : Real.log (3950214487904321 / 80000000000000000 : ℝ) ≤ (-(30082567552000849825557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (3950214487904321 / 80000000000000000 : ℝ) = - (3950214487904321 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3950214487904321 / 2500000000000000 : ℚ)) - (U := (4574791462999150174443 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3950214487904321 / 2500000000000000 : ℝ) ≤ - (4574791462999150174443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (184753928783587 / 5000000000000000 : ℝ)) (q := - (3950214487904321 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3950214487904321 / 80000000000000000 : ℚ)) + (r' := (3950214487904321 / 2500000000000000 : ℚ)) + (U := (-(30082567552000849825557 / 10000000000000000000000 : ℚ))) + (U' := (4574791462999150174443 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7151568492121 / 64000000000000 : ℚ)) + (s := (184753928783587 / 5000000000000000 : ℚ)) + (q := (3950214487904321 / 80000000000000000 : ℚ)) + (U := (-(30082567552000849825557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_165_7 : Uω (aρ 7) (bρ 7) (7151568492121 / 64000000000000 : ℝ) ≤ @@ -1767,25 +1623,21 @@ lemma U_166_1 : have hlg : Real.log (2112571594034783 / 20000000000000000 : ℝ) ≤ (-(22478263021719406875639 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2112571594034783 / 20000000000000000 : ℝ) = - (2112571594034783 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2112571594034783 / 1250000000000000 : ℚ)) - (U := (5247624190280593124361 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2112571594034783 / 1250000000000000 : ℝ) ≤ - (5247624190280593124361 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (264033185963227 / 2500000000000000 : ℝ)) (q := - (2112571594034783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2112571594034783 / 20000000000000000 : ℚ)) + (r' := (2112571594034783 / 1250000000000000 : ℚ)) + (U := (-(22478263021719406875639 / 10000000000000000000000 : ℚ))) + (U' := (5247624190280593124361 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (264033185963227 / 2500000000000000 : ℚ)) + (q := (2112571594034783 / 20000000000000000 : ℚ)) + (U := (-(22478263021719406875639 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_2 : Uω (aρ 2) (bρ 2) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -1793,25 +1645,21 @@ lemma U_166_2 : have hlg : Real.log (257910362590861 / 2500000000000000 : ℝ) ≤ (-(181714713366534310893 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (257910362590861 / 2500000000000000 : ℝ) = - (257910362590861 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (257910362590861 / 156250000000000 : ℚ)) - (U := (40092384329465689107 / 80000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (257910362590861 / 156250000000000 : ℝ) ≤ - (40092384329465689107 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1030613063055013 / 10000000000000000 : ℝ)) (q := - (257910362590861 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (257910362590861 / 2500000000000000 : ℚ)) + (r' := (257910362590861 / 156250000000000 : ℚ)) + (U := (-(181714713366534310893 / 80000000000000000000 : ℚ))) + (U' := (40092384329465689107 / 80000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (1030613063055013 / 10000000000000000 : ℚ)) + (q := (257910362590861 / 2500000000000000 : ℚ)) + (U := (-(181714713366534310893 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_3 : Uω (aρ 3) (bρ 3) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -1819,25 +1667,21 @@ lemma U_166_3 : have hlg : Real.log (1963009976379449 / 20000000000000000 : ℝ) ≤ (-(2901566593777723928731 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1963009976379449 / 20000000000000000 : ℝ) = - (1963009976379449 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1963009976379449 / 1250000000000000 : ℚ)) - (U := (564169307722276071269 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1963009976379449 / 1250000000000000 : ℝ) ≤ - (564169307722276071269 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (488868122528787 / 5000000000000000 : ℝ)) (q := - (1963009976379449 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1963009976379449 / 20000000000000000 : ℚ)) + (r' := (1963009976379449 / 1250000000000000 : ℚ)) + (U := (-(2901566593777723928731 / 1250000000000000000000 : ℚ))) + (U' := (564169307722276071269 / 1250000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (488868122528787 / 5000000000000000 : ℚ)) + (q := (1963009976379449 / 20000000000000000 : ℚ)) + (U := (-(2901566593777723928731 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_4 : Uω (aρ 4) (bρ 4) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -1845,25 +1689,21 @@ lemma U_166_4 : have hlg : Real.log (223806939833861 / 2500000000000000 : ℝ) ≤ (-(12066311026658035428937 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (223806939833861 / 2500000000000000 : ℝ) = - (223806939833861 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (223806939833861 / 156250000000000 : ℚ)) - (U := (1796632579341964571063 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (223806939833861 / 156250000000000 : ℝ) ≤ - (1796632579341964571063 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (883475968414013 / 10000000000000000 : ℝ)) (q := - (223806939833861 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (223806939833861 / 2500000000000000 : ℚ)) + (r' := (223806939833861 / 156250000000000 : ℚ)) + (U := (-(12066311026658035428937 / 5000000000000000000000 : ℚ))) + (U' := (1796632579341964571063 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (883475968414013 / 10000000000000000 : ℚ)) + (q := (223806939833861 / 2500000000000000 : ℚ)) + (U := (-(12066311026658035428937 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_5 : Uω (aρ 5) (bρ 5) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -1871,25 +1711,21 @@ lemma U_166_5 : have hlg : Real.log (1506895000779397 / 20000000000000000 : ℝ) ≤ (-(12928405148153663752511 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1506895000779397 / 20000000000000000 : ℝ) = - (1506895000779397 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1506895000779397 / 1250000000000000 : ℚ)) - (U := (934538457846336247489 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1506895000779397 / 1250000000000000 : ℝ) ≤ - (934538457846336247489 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (359052684928761 / 5000000000000000 : ℝ)) (q := - (1506895000779397 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1506895000779397 / 20000000000000000 : ℚ)) + (r' := (1506895000779397 / 1250000000000000 : ℚ)) + (U := (-(12928405148153663752511 / 5000000000000000000000 : ℚ))) + (U' := (934538457846336247489 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (359052684928761 / 5000000000000000 : ℚ)) + (q := (1506895000779397 / 20000000000000000 : ℚ)) + (U := (-(12928405148153663752511 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_6 : Uω (aρ 6) (bρ 6) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -1897,25 +1733,21 @@ lemma U_166_6 : have hlg : Real.log (996887726049841 / 20000000000000000 : ℝ) ≤ (-(14994246997006309491453 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (996887726049841 / 20000000000000000 : ℝ) = - (996887726049841 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (996887726049841 / 625000000000000 : ℚ)) - (U := (2334432510493690508547 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (996887726049841 / 625000000000000 : ℝ) ≤ - (2334432510493690508547 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (187669235133983 / 5000000000000000 : ℝ)) (q := - (996887726049841 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (996887726049841 / 20000000000000000 : ℚ)) + (r' := (996887726049841 / 625000000000000 : ℚ)) + (U := (-(14994246997006309491453 / 5000000000000000000000 : ℚ))) + (U' := (2334432510493690508547 / 5000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1793497709227 / 16000000000000 : ℚ)) + (s := (187669235133983 / 5000000000000000 : ℚ)) + (q := (996887726049841 / 20000000000000000 : ℚ)) + (U := (-(14994246997006309491453 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_166_7 : Uω (aρ 7) (bρ 7) (1793497709227 / 16000000000000 : ℝ) ≤ @@ -2057,25 +1889,21 @@ lemma U_167_1 : have hlg : Real.log (8478318355456963 / 80000000000000000 : ℝ) ≤ (-(22445145106352584507421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8478318355456963 / 80000000000000000 : ℝ) = - (8478318355456963 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8478318355456963 / 5000000000000000 : ℚ)) - (U := (5280742105647415492579 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8478318355456963 / 5000000000000000 : ℝ) ≤ - (5280742105647415492579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1059637247309397 / 10000000000000000 : ℝ)) (q := - (8478318355456963 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8478318355456963 / 80000000000000000 : ℚ)) + (r' := (8478318355456963 / 5000000000000000 : ℚ)) + (U := (-(22445145106352584507421 / 10000000000000000000000 : ℚ))) + (U' := (5280742105647415492579 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (1059637247309397 / 10000000000000000 : ℚ)) + (q := (8478318355456963 / 80000000000000000 : ℚ)) + (U := (-(22445145106352584507421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_2 : Uω (aρ 2) (bρ 2) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2083,25 +1911,21 @@ lemma U_167_2 : have hlg : Real.log (8281187406447127 / 80000000000000000 : ℝ) ≤ (-(2835050336178665111439 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8281187406447127 / 80000000000000000 : ℝ) = - (8281187406447127 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8281187406447127 / 5000000000000000 : ℚ)) - (U := (630685565321334888561 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8281187406447127 / 5000000000000000 : ℝ) ≤ - (630685565321334888561 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (517061761283469 / 5000000000000000 : ℝ)) (q := - (8281187406447127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8281187406447127 / 80000000000000000 : ℚ)) + (r' := (8281187406447127 / 5000000000000000 : ℚ)) + (U := (-(2835050336178665111439 / 1250000000000000000000 : ℚ))) + (U' := (630685565321334888561 / 1250000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (517061761283469 / 5000000000000000 : ℚ)) + (q := (8281187406447127 / 80000000000000000 : ℚ)) + (U := (-(2835050336178665111439 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_3 : Uω (aρ 3) (bρ 3) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2109,25 +1933,21 @@ lemma U_167_3 : have hlg : Real.log (7880175484632751 / 80000000000000000 : ℝ) ≤ (-(2317676460388831441057 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7880175484632751 / 80000000000000000 : ℝ) = - (7880175484632751 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7880175484632751 / 5000000000000000 : ℚ)) - (U := (454912260811168558943 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7880175484632751 / 5000000000000000 : ℝ) ≤ - (454912260811168558943 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61329165528959 / 625000000000000 : ℝ)) (q := - (7880175484632751 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7880175484632751 / 80000000000000000 : ℚ)) + (r' := (7880175484632751 / 5000000000000000 : ℚ)) + (U := (-(2317676460388831441057 / 1000000000000000000000 : ℚ))) + (U' := (454912260811168558943 / 1000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (61329165528959 / 625000000000000 : ℚ)) + (q := (7880175484632751 / 80000000000000000 : ℚ)) + (U := (-(2317676460388831441057 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_4 : Uω (aρ 4) (bρ 4) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2135,25 +1955,21 @@ lemma U_167_4 : have hlg : Real.log (287608853384591 / 3200000000000000 : ℝ) ≤ (-(24093046787011313355059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (287608853384591 / 3200000000000000 : ℝ) = - (287608853384591 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (287608853384591 / 200000000000000 : ℚ)) - (U := (3632840424988686644941 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (287608853384591 / 200000000000000 : ℝ) ≤ - (3632840424988686644941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17741445840477 / 200000000000000 : ℝ)) (q := - (287608853384591 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (287608853384591 / 3200000000000000 : ℚ)) + (r' := (287608853384591 / 200000000000000 : ℚ)) + (U := (-(24093046787011313355059 / 10000000000000000000000 : ℚ))) + (U' := (3632840424988686644941 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (17741445840477 / 200000000000000 : ℚ)) + (q := (287608853384591 / 3200000000000000 : ℚ)) + (U := (-(24093046787011313355059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_5 : Uω (aρ 5) (bρ 5) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2161,25 +1977,21 @@ lemma U_167_5 : have hlg : Real.log (1211396065534587 / 16000000000000000 : ℝ) ≤ (-(6452038133767527073457 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1211396065534587 / 16000000000000000 : ℝ) = - (1211396065534587 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1211396065534587 / 1000000000000000 : ℚ)) - (U := (479433669232472926543 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1211396065534587 / 1000000000000000 : ℝ) ≤ - (479433669232472926543 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (72195195962339 / 1000000000000000 : ℝ)) (q := - (1211396065534587 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1211396065534587 / 16000000000000000 : ℚ)) + (r' := (1211396065534587 / 1000000000000000 : ℚ)) + (U := (-(6452038133767527073457 / 2500000000000000000000 : ℚ))) + (U' := (479433669232472926543 / 2500000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (72195195962339 / 1000000000000000 : ℚ)) + (q := (1211396065534587 / 16000000000000000 : ℚ)) + (U := (-(6452038133767527073457 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_6 : Uω (aρ 6) (bρ 6) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2187,25 +1999,21 @@ lemma U_167_6 : have hlg : Real.log (4024659356395267 / 80000000000000000 : ℝ) ≤ (-(29895863580366005101939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4024659356395267 / 80000000000000000 : ℝ) = - (4024659356395267 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4024659356395267 / 2500000000000000 : ℚ)) - (U := (4761495434633994898061 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4024659356395267 / 2500000000000000 : ℝ) ≤ - (4761495434633994898061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (381112091943973 / 10000000000000000 : ℝ)) (q := - (4024659356395267 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4024659356395267 / 80000000000000000 : ℚ)) + (r' := (4024659356395267 / 2500000000000000 : ℚ)) + (U := (-(29895863580366005101939 / 10000000000000000000000 : ℚ))) + (U' := (4761495434633994898061 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1439282636339 / 12800000000000 : ℚ)) + (s := (381112091943973 / 10000000000000000 : ℚ)) + (q := (4024659356395267 / 80000000000000000 : ℚ)) + (U := (-(29895863580366005101939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_167_7 : Uω (aρ 7) (bρ 7) (1439282636339 / 12800000000000 : ℝ) ≤ @@ -2348,25 +2156,21 @@ lemma U_168_1 : have hlg : Real.log (850635030808907 / 8000000000000000 : ℝ) ≤ (-(22412136540051290770829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (850635030808907 / 8000000000000000 : ℝ) = - (850635030808907 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (850635030808907 / 500000000000000 : ℚ)) - (U := (5313750671948709229171 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (850635030808907 / 500000000000000 : ℝ) ≤ - (5313750671948709229171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (212628348818891 / 2000000000000000 : ℝ)) (q := - (850635030808907 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (850635030808907 / 8000000000000000 : ℚ)) + (r' := (850635030808907 / 500000000000000 : ℚ)) + (U := (-(22412136540051290770829 / 10000000000000000000000 : ℚ))) + (U' := (5313750671948709229171 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (212628348818891 / 2000000000000000 : ℚ)) + (q := (850635030808907 / 8000000000000000 : ℚ)) + (U := (-(22412136540051290770829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_2 : Uω (aρ 2) (bρ 2) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2374,25 +2178,21 @@ lemma U_168_2 : have hlg : Real.log (4154621510790221 / 40000000000000000 : ℝ) ≤ (-(22646581213851753936333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4154621510790221 / 40000000000000000 : ℝ) = - (4154621510790221 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4154621510790221 / 2500000000000000 : ℚ)) - (U := (5079305998148246063667 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4154621510790221 / 2500000000000000 : ℝ) ≤ - (5079305998148246063667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (518816967488649 / 5000000000000000 : ℝ)) (q := - (4154621510790221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4154621510790221 / 40000000000000000 : ℚ)) + (r' := (4154621510790221 / 2500000000000000 : ℚ)) + (U := (-(22646581213851753936333 / 10000000000000000000000 : ℚ))) + (U' := (5079305998148246063667 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (518816967488649 / 5000000000000000 : ℚ)) + (q := (4154621510790221 / 40000000000000000 : ℚ)) + (U := (-(22646581213851753936333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_3 : Uω (aρ 3) (bρ 3) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2400,25 +2200,21 @@ lemma U_168_3 : have hlg : Real.log (3954155147436417 / 40000000000000000 : ℝ) ≤ (-(23141124909983015902357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3954155147436417 / 40000000000000000 : ℝ) = - (3954155147436417 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3954155147436417 / 2500000000000000 : ℚ)) - (U := (4584762302016984097643 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3954155147436417 / 2500000000000000 : ℝ) ≤ - (4584762302016984097643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (246199214912599 / 2500000000000000 : ℝ)) (q := - (3954155147436417 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3954155147436417 / 40000000000000000 : ℚ)) + (r' := (3954155147436417 / 2500000000000000 : ℚ)) + (U := (-(23141124909983015902357 / 10000000000000000000000 : ℚ))) + (U' := (4584762302016984097643 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (246199214912599 / 2500000000000000 : ℚ)) + (q := (3954155147436417 / 40000000000000000 : ℚ)) + (U := (-(23141124909983015902357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_4 : Uω (aρ 4) (bρ 4) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2426,25 +2222,21 @@ lemma U_168_4 : have hlg : Real.log (3609308817279277 / 40000000000000000 : ℝ) ≤ (-(12026815812091775261959 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3609308817279277 / 40000000000000000 : ℝ) = - (3609308817279277 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3609308817279277 / 2500000000000000 : ℚ)) - (U := (1836127793908224738041 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3609308817279277 / 2500000000000000 : ℝ) ≤ - (1836127793908224738041 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (445333937818413 / 5000000000000000 : ℝ)) (q := - (3609308817279277 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3609308817279277 / 40000000000000000 : ℚ)) + (r' := (3609308817279277 / 2500000000000000 : ℚ)) + (U := (-(12026815812091775261959 / 5000000000000000000000 : ℚ))) + (U' := (1836127793908224738041 / 5000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (445333937818413 / 5000000000000000 : ℚ)) + (q := (3609308817279277 / 40000000000000000 : ℚ)) + (U := (-(12026815812091775261959 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_5 : Uω (aρ 5) (bρ 5) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2452,25 +2244,21 @@ lemma U_168_5 : have hlg : Real.log (3043183377059021 / 40000000000000000 : ℝ) ≤ (-(12879876610215081971411 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3043183377059021 / 40000000000000000 : ℝ) = - (3043183377059021 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3043183377059021 / 2500000000000000 : ℚ)) - (U := (983066995784918028589 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3043183377059021 / 2500000000000000 : ℝ) ≤ - (983066995784918028589 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (362897537430849 / 5000000000000000 : ℝ)) (q := - (3043183377059021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3043183377059021 / 40000000000000000 : ℚ)) + (r' := (3043183377059021 / 2500000000000000 : ℚ)) + (U := (-(12879876610215081971411 / 5000000000000000000000 : ℚ))) + (U' := (983066995784918028589 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (362897537430849 / 5000000000000000 : ℚ)) + (q := (3043183377059021 / 40000000000000000 : ℚ)) + (U := (-(12879876610215081971411 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_6 : Uω (aρ 6) (bρ 6) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2478,25 +2266,21 @@ lemma U_168_6 : have hlg : Real.log (2030775025954889 / 40000000000000000 : ℝ) ≤ (-(7451154866094100783241 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2030775025954889 / 40000000000000000 : ℝ) = - (2030775025954889 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2030775025954889 / 1250000000000000 : ℚ)) - (U := (1213184887655899216759 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2030775025954889 / 1250000000000000 : ℝ) ≤ - (1213184887655899216759 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12088477326551 / 312500000000000 : ℝ)) (q := - (2030775025954889 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2030775025954889 / 40000000000000000 : ℚ)) + (r' := (2030775025954889 / 1250000000000000 : ℚ)) + (U := (-(7451154866094100783241 / 2500000000000000000000 : ℚ))) + (U' := (1213184887655899216759 / 2500000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3609417763241 / 32000000000000 : ℚ)) + (s := (12088477326551 / 312500000000000 : ℚ)) + (q := (2030775025954889 / 40000000000000000 : ℚ)) + (U := (-(7451154866094100783241 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_168_7 : Uω (aρ 7) (bρ 7) (3609417763241 / 32000000000000 : ℝ) ≤ @@ -2639,25 +2423,21 @@ lemma U_169_1 : have hlg : Real.log (1706876446859697 / 16000000000000000 : ℝ) ≤ (-(22379236602886479923973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1706876446859697 / 16000000000000000 : ℝ) = - (1706876446859697 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1706876446859697 / 1000000000000000 : ℚ)) - (U := (5346650609113520076027 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1706876446859697 / 1000000000000000 : ℝ) ≤ - (5346650609113520076027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13333077928423 / 125000000000000 : ℝ)) (q := - (1706876446859697 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1706876446859697 / 16000000000000000 : ℚ)) + (r' := (1706876446859697 / 1000000000000000 : ℚ)) + (U := (-(22379236602886479923973 / 10000000000000000000000 : ℚ))) + (U' := (5346650609113520076027 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (13333077928423 / 125000000000000 : ℚ)) + (q := (1706876446859697 / 16000000000000000 : ℚ)) + (U := (-(22379236602886479923973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_2 : Uω (aρ 2) (bρ 2) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2665,25 +2445,21 @@ lemma U_169_2 : have hlg : Real.log (8337298450213229 / 80000000000000000 : ℝ) ≤ (-(22612873965720201807563 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8337298450213229 / 80000000000000000 : ℝ) = - (8337298450213229 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8337298450213229 / 5000000000000000 : ℚ)) - (U := (5113013246279798192437 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8337298450213229 / 5000000000000000 : ℝ) ≤ - (5113013246279798192437 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (520572150381263 / 5000000000000000 : ℝ)) (q := - (8337298450213229 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8337298450213229 / 80000000000000000 : ℚ)) + (r' := (8337298450213229 / 5000000000000000 : ℚ)) + (U := (-(22612873965720201807563 / 10000000000000000000000 : ℚ))) + (U' := (5113013246279798192437 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (520572150381263 / 5000000000000000 : ℚ)) + (q := (8337298450213229 / 80000000000000000 : ℚ)) + (U := (-(22612873965720201807563 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_3 : Uω (aρ 3) (bρ 3) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2691,25 +2467,21 @@ lemma U_169_3 : have hlg : Real.log (7936444344477101 / 80000000000000000 : ℝ) ≤ (-(23105612742314276111357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7936444344477101 / 80000000000000000 : ℝ) = - (7936444344477101 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7936444344477101 / 5000000000000000 : ℚ)) - (U := (4620274469685723888643 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7936444344477101 / 5000000000000000 : ℝ) ≤ - (4620274469685723888643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (494163440339247 / 5000000000000000 : ℝ)) (q := - (7936444344477101 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7936444344477101 / 80000000000000000 : ℚ)) + (r' := (7936444344477101 / 5000000000000000 : ℚ)) + (U := (-(23105612742314276111357 / 10000000000000000000000 : ℚ))) + (U' := (4620274469685723888643 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (494163440339247 / 5000000000000000 : ℚ)) + (q := (7936444344477101 / 80000000000000000 : ℚ)) + (U := (-(23105612742314276111357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_4 : Uω (aρ 4) (bρ 4) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2717,25 +2489,21 @@ lemma U_169_4 : have hlg : Real.log (1449402202043753 / 16000000000000000 : ℝ) ≤ (-(24014375242285785827619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1449402202043753 / 16000000000000000 : ℝ) = - (1449402202043753 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1449402202043753 / 1000000000000000 : ℚ)) - (U := (3711511969714214172381 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1449402202043753 / 1000000000000000 : ℝ) ≤ - (3711511969714214172381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89426272817891 / 1000000000000000 : ℝ)) (q := - (1449402202043753 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1449402202043753 / 16000000000000000 : ℚ)) + (r' := (1449402202043753 / 1000000000000000 : ℚ)) + (U := (-(24014375242285785827619 / 10000000000000000000000 : ℚ))) + (U' := (3711511969714214172381 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (89426272817891 / 1000000000000000 : ℚ)) + (q := (1449402202043753 / 16000000000000000 : ℚ)) + (U := (-(24014375242285785827619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_5 : Uω (aρ 5) (bρ 5) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2743,25 +2511,21 @@ lemma U_169_5 : have hlg : Real.log (6115739502064329 / 80000000000000000 : ℝ) ≤ (-(25711609393350256228287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6115739502064329 / 80000000000000000 : ℝ) = - (6115739502064329 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6115739502064329 / 5000000000000000 : ℚ)) - (U := (2014277818649743771713 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6115739502064329 / 5000000000000000 : ℝ) ≤ - (2014277818649743771713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (729634770475301 / 10000000000000000 : ℝ)) (q := - (6115739502064329 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6115739502064329 / 80000000000000000 : ℚ)) + (r' := (6115739502064329 / 5000000000000000 : ℚ)) + (U := (-(25711609393350256228287 / 10000000000000000000000 : ℚ))) + (U' := (2014277818649743771713 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (729634770475301 / 10000000000000000 : ℚ)) + (q := (6115739502064329 / 80000000000000000 : ℚ)) + (U := (-(25711609393350256228287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_6 : Uω (aρ 6) (bρ 6) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2769,24 +2533,21 @@ lemma U_169_6 : have hlg : Real.log (32785860077733 / 640000000000000 : ℝ) ≤ (-(29714708478032058836987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (32785860077733 / 640000000000000 : ℝ) = (32785860077733 / 20000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32785860077733 / 20000000000000 : ℚ)) - (U := (4942650536967941163013 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32785860077733 / 20000000000000 : ℝ) ≤ - (4942650536967941163013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3139987180227 / 80000000000000 : ℝ)) (q := - (32785860077733 / 640000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32785860077733 / 640000000000000 : ℚ)) + (r' := (32785860077733 / 20000000000000 : ℚ)) + (U := (-(29714708478032058836987 / 10000000000000000000000 : ℚ))) + (U' := (4942650536967941163013 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7241257871269 / 64000000000000 : ℚ)) + (s := (3139987180227 / 80000000000000 : ℚ)) + (q := (32785860077733 / 640000000000000 : ℚ)) + (U := (-(29714708478032058836987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_169_7 : Uω (aρ 7) (bρ 7) (7241257871269 / 64000000000000 : ℝ) ≤ @@ -2929,25 +2690,21 @@ lemma U_170_1 : have hlg : Real.log (2140603533586199 / 20000000000000000 : ℝ) ≤ (-(1396652786376097337059 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2140603533586199 / 20000000000000000 : ℝ) = - (2140603533586199 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2140603533586199 / 1250000000000000 : ℚ)) - (U := (336215164373902662941 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2140603533586199 / 1250000000000000 : ℝ) ≤ - (336215164373902662941 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1070150717912449 / 10000000000000000 : ℝ)) (q := - (2140603533586199 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2140603533586199 / 20000000000000000 : ℚ)) + (r' := (2140603533586199 / 1250000000000000 : ℚ)) + (U := (-(1396652786376097337059 / 625000000000000000000 : ℚ))) + (U' := (336215164373902662941 / 625000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (1070150717912449 / 10000000000000000 : ℚ)) + (q := (2140603533586199 / 20000000000000000 : ℚ)) + (U := (-(1396652786376097337059 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_2 : Uω (aρ 2) (bρ 2) (907960027007 / 8000000000000 : ℝ) ≤ @@ -2955,25 +2712,21 @@ lemma U_170_2 : have hlg : Real.log (2091338423556399 / 20000000000000000 : ℝ) ≤ (-(22579280174561325422027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2091338423556399 / 20000000000000000 : ℝ) = - (2091338423556399 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2091338423556399 / 1250000000000000 : ℚ)) - (U := (5146607037438674577973 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2091338423556399 / 1250000000000000 : ℝ) ≤ - (5146607037438674577973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1044654620392649 / 10000000000000000 : ℝ)) (q := - (2091338423556399 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2091338423556399 / 20000000000000000 : ℚ)) + (r' := (2091338423556399 / 1250000000000000 : ℚ)) + (U := (-(22579280174561325422027 / 10000000000000000000000 : ℚ))) + (U' := (5146607037438674577973 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (1044654620392649 / 10000000000000000 : ℚ)) + (q := (2091338423556399 / 20000000000000000 : ℚ)) + (U := (-(22579280174561325422027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_3 : Uω (aρ 3) (bρ 3) (907960027007 / 8000000000000 : ℝ) ≤ @@ -2981,25 +2734,21 @@ lemma U_170_3 : have hlg : Real.log (497786102597929 / 5000000000000000 : ℝ) ≤ (-(4614045436948869884133 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (497786102597929 / 5000000000000000 : ℝ) = - (497786102597929 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (497786102597929 / 312500000000000 : ℚ)) - (U := (931132005451130115867 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (497786102597929 / 312500000000000 : ℝ) ≤ - (931132005451130115867 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (495928356788983 / 5000000000000000 : ℝ)) (q := - (497786102597929 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (497786102597929 / 5000000000000000 : ℚ)) + (r' := (497786102597929 / 312500000000000 : ℚ)) + (U := (-(4614045436948869884133 / 2000000000000000000000 : ℚ))) + (U' := (931132005451130115867 / 2000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (495928356788983 / 5000000000000000 : ℚ)) + (q := (497786102597929 / 5000000000000000 : ℚ)) + (U := (-(4614045436948869884133 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_4 : Uω (aρ 4) (bρ 4) (907960027007 / 8000000000000 : ℝ) ≤ @@ -3007,25 +2756,21 @@ lemma U_170_4 : have hlg : Real.log (181885037418007 / 2000000000000000 : ℝ) ≤ (-(1498454770966725311139 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (181885037418007 / 2000000000000000 : ℝ) = - (181885037418007 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (181885037418007 / 125000000000000 : ℚ)) - (U := (234413179783274688861 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (181885037418007 / 125000000000000 : ℝ) ≤ - (234413179783274688861 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (22446421460783 / 250000000000000 : ℝ)) (q := - (181885037418007 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (181885037418007 / 2000000000000000 : ℚ)) + (r' := (181885037418007 / 125000000000000 : ℚ)) + (U := (-(1498454770966725311139 / 625000000000000000000 : ℚ))) + (U' := (234413179783274688861 / 625000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (22446421460783 / 250000000000000 : ℚ)) + (q := (181885037418007 / 2000000000000000 : ℚ)) + (U := (-(1498454770966725311139 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_5 : Uω (aρ 5) (bρ 5) (907960027007 / 8000000000000 : ℝ) ≤ @@ -3033,25 +2778,21 @@ lemma U_170_5 : have hlg : Real.log (1536274696582797 / 20000000000000000 : ℝ) ≤ (-(12831859074287055078487 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1536274696582797 / 20000000000000000 : ℝ) = - (1536274696582797 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1536274696582797 / 1250000000000000 : ℚ)) - (U := (1031084531712944921513 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1536274696582797 / 1250000000000000 : ℝ) ≤ - (1031084531712944921513 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (733471100169047 / 10000000000000000 : ℝ)) (q := - (1536274696582797 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1536274696582797 / 20000000000000000 : ℚ)) + (r' := (1536274696582797 / 1250000000000000 : ℚ)) + (U := (-(12831859074287055078487 / 5000000000000000000000 : ℚ))) + (U' := (1031084531712944921513 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (733471100169047 / 10000000000000000 : ℚ)) + (q := (1536274696582797 / 20000000000000000 : ℚ)) + (U := (-(12831859074287055078487 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_6 : Uω (aρ 6) (bρ 6) (907960027007 / 8000000000000 : ℝ) ≤ @@ -3059,25 +2800,21 @@ lemma U_170_6 : have hlg : Real.log (516839452818463 / 10000000000000000 : ℝ) ≤ (-(29626080805288577062113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (516839452818463 / 10000000000000000 : ℝ) = - (516839452818463 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (516839452818463 / 312500000000000 : ℚ)) - (U := (5031278209711422937887 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (516839452818463 / 312500000000000 : ℝ) ≤ - (5031278209711422937887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (49764460545397 / 1250000000000000 : ℝ)) (q := - (516839452818463 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (516839452818463 / 10000000000000000 : ℚ)) + (r' := (516839452818463 / 312500000000000 : ℚ)) + (U := (-(29626080805288577062113 / 10000000000000000000000 : ℚ))) + (U' := (5031278209711422937887 / 10000000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (907960027007 / 8000000000000 : ℚ)) + (s := (49764460545397 / 1250000000000000 : ℚ)) + (q := (516839452818463 / 10000000000000000 : ℚ)) + (U := (-(29626080805288577062113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_170_7 : Uω (aρ 7) (bρ 7) (907960027007 / 8000000000000 : ℝ) ≤ @@ -3219,25 +2956,21 @@ lemma U_171_1 : have hlg : Real.log (1718089201696839 / 16000000000000000 : ℝ) ≤ (-(2789219971449951260491 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1718089201696839 / 16000000000000000 : ℝ) = - (1718089201696839 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1718089201696839 / 1000000000000000 : ℚ)) - (U := (676515930050048739509 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1718089201696839 / 1000000000000000 : ℝ) ≤ - (676515930050048739509 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (107365519507433 / 1000000000000000 : ℝ)) (q := - (1718089201696839 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1718089201696839 / 16000000000000000 : ℚ)) + (r' := (1718089201696839 / 1000000000000000 : ℚ)) + (U := (-(2789219971449951260491 / 1250000000000000000000 : ℚ))) + (U' := (676515930050048739509 / 1250000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (107365519507433 / 1000000000000000 : ℚ)) + (q := (1718089201696839 / 16000000000000000 : ℚ)) + (U := (-(2789219971449951260491 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_2 : Uω (aρ 2) (bρ 2) (7286102560843 / 64000000000000 : ℝ) ≤ @@ -3245,25 +2978,21 @@ lemma U_171_2 : have hlg : Real.log (8393408755472431 / 80000000000000000 : ℝ) ≤ (-(11272899538842934213803 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8393408755472431 / 80000000000000000 : ℝ) = - (8393408755472431 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8393408755472431 / 5000000000000000 : ℚ)) - (U := (2590044067157065786197 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8393408755472431 / 5000000000000000 : ℝ) ≤ - (2590044067157065786197 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1048164894331389 / 10000000000000000 : ℝ)) (q := - (8393408755472431 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8393408755472431 / 80000000000000000 : ℚ)) + (r' := (8393408755472431 / 5000000000000000 : ℚ)) + (U := (-(11272899538842934213803 / 5000000000000000000000 : ℚ))) + (U' := (2590044067157065786197 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (1048164894331389 / 10000000000000000 : ℚ)) + (q := (8393408755472431 / 80000000000000000 : ℚ)) + (U := (-(11272899538842934213803 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_3 : Uω (aρ 3) (bρ 3) (7286102560843 / 64000000000000 : ℝ) ≤ @@ -3271,25 +3000,21 @@ lemma U_171_3 : have hlg : Real.log (7992710194147811 / 80000000000000000 : ℝ) ≤ (-(23034967331043341839631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7992710194147811 / 80000000000000000 : ℝ) = - (7992710194147811 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7992710194147811 / 5000000000000000 : ℚ)) - (U := (4690919880956658160369 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7992710194147811 / 5000000000000000 : ℝ) ≤ - (4690919880956658160369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (497693180175117 / 5000000000000000 : ℝ)) (q := - (7992710194147811 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7992710194147811 / 80000000000000000 : ℚ)) + (r' := (7992710194147811 / 5000000000000000 : ℚ)) + (U := (-(23034967331043341839631 / 10000000000000000000000 : ℚ))) + (U' := (4690919880956658160369 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (497693180175117 / 5000000000000000 : ℚ)) + (q := (7992710194147811 / 80000000000000000 : ℚ)) + (U := (-(23034967331043341839631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_4 : Uω (aρ 4) (bρ 4) (7286102560843 / 64000000000000 : ℝ) ≤ @@ -3297,25 +3022,21 @@ lemma U_171_4 : have hlg : Real.log (7303789128620783 / 80000000000000000 : ℝ) ≤ (-(11968166807144784725189 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7303789128620783 / 80000000000000000 : ℝ) = - (7303789128620783 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7303789128620783 / 5000000000000000 : ℚ)) - (U := (1894776798855215274811 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7303789128620783 / 5000000000000000 : ℝ) ≤ - (1894776798855215274811 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (901450275033477 / 10000000000000000 : ℝ)) (q := - (7303789128620783 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7303789128620783 / 80000000000000000 : ℚ)) + (r' := (7303789128620783 / 5000000000000000 : ℚ)) + (U := (-(11968166807144784725189 / 5000000000000000000000 : ℚ))) + (U' := (1894776798855215274811 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (901450275033477 / 10000000000000000 : ℚ)) + (q := (7303789128620783 / 80000000000000000 : ℚ)) + (U := (-(11968166807144784725189 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_5 : Uω (aρ 5) (bρ 5) (7286102560843 / 64000000000000 : ℝ) ≤ @@ -3323,25 +3044,21 @@ lemma U_171_5 : have hlg : Real.log (246977792683227 / 3200000000000000 : ℝ) ≤ (-(25616076633271137021301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (246977792683227 / 3200000000000000 : ℝ) = - (246977792683227 / 200000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (246977792683227 / 200000000000000 : ℚ)) - (U := (2109810578728862978699 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (246977792683227 / 200000000000000 : ℝ) ≤ - (2109810578728862978699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14746082329669 / 200000000000000 : ℝ)) (q := - (246977792683227 / 3200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (246977792683227 / 3200000000000000 : ℚ)) + (r' := (246977792683227 / 200000000000000 : ℚ)) + (U := (-(25616076633271137021301 / 10000000000000000000000 : ℚ))) + (U' := (2109810578728862978699 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (14746082329669 / 200000000000000 : ℚ)) + (q := (246977792683227 / 3200000000000000 : ℚ)) + (U := (-(25616076633271137021301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_6 : Uω (aρ 6) (bρ 6) (7286102560843 / 64000000000000 : ℝ) ≤ @@ -3349,25 +3066,21 @@ lemma U_171_6 : have hlg : Real.log (4171007712090927 / 80000000000000000 : ℝ) ≤ (-(29538689691821717904251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4171007712090927 / 80000000000000000 : ℝ) = - (4171007712090927 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4171007712090927 / 2500000000000000 : ℚ)) - (U := (5118669323178282095749 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4171007712090927 / 2500000000000000 : ℝ) ≤ - (5118669323178282095749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (403685215376013 / 10000000000000000 : ℝ)) (q := - (4171007712090927 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4171007712090927 / 80000000000000000 : ℚ)) + (r' := (4171007712090927 / 2500000000000000 : ℚ)) + (U := (-(29538689691821717904251 / 10000000000000000000000 : ℚ))) + (U' := (5118669323178282095749 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7286102560843 / 64000000000000 : ℚ)) + (s := (403685215376013 / 10000000000000000 : ℚ)) + (q := (4171007712090927 / 80000000000000000 : ℚ)) + (U := (-(29538689691821717904251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_171_7 : Uω (aρ 7) (bρ 7) (7286102560843 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U14.lean b/LeanPool/Zeta5Irrational/Table/U14.lean index fd41a3921b..15daf4432e 100644 --- a/LeanPool/Zeta5Irrational/Table/U14.lean +++ b/LeanPool/Zeta5Irrational/Table/U14.lean @@ -24,25 +24,21 @@ lemma U_172_1 : have hlg : Real.log (4309238928484769 / 40000000000000000 : ℝ) ≤ (-(22281181472692134742863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4309238928484769 / 40000000000000000 : ℝ) = - (4309238928484769 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4309238928484769 / 2500000000000000 : ℚ)) - (U := (5444705739307865257137 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4309238928484769 / 2500000000000000 : ℝ) ≤ - (5444705739307865257137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1077159665822697 / 10000000000000000 : ℝ)) (q := - (4309238928484769 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4309238928484769 / 40000000000000000 : ℚ)) + (r' := (4309238928484769 / 2500000000000000 : ℚ)) + (U := (-(22281181472692134742863 / 10000000000000000000000 : ℚ))) + (U' := (5444705739307865257137 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (1077159665822697 / 10000000000000000 : ℚ)) + (q := (4309238928484769 / 40000000000000000 : ℚ)) + (U := (-(22281181472692134742863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_2 : Uω (aρ 2) (bρ 2) (730852490563 / 6400000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_172_2 : have hlg : Real.log (842146363578383 / 8000000000000000 : ℝ) ≤ (-(11256214960041973685579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (842146363578383 / 8000000000000000 : ℝ) = - (842146363578383 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (842146363578383 / 500000000000000 : ℚ)) - (U := (2606728645958026314421 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (842146363578383 / 500000000000000 : ℝ) ≤ - (2606728645958026314421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105167512303627 / 1000000000000000 : ℝ)) (q := - (842146363578383 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (842146363578383 / 8000000000000000 : ℚ)) + (r' := (842146363578383 / 500000000000000 : ℚ)) + (U := (-(11256214960041973685579 / 5000000000000000000000 : ℚ))) + (U' := (2606728645958026314421 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (105167512303627 / 1000000000000000 : ℚ)) + (q := (842146363578383 / 8000000000000000 : ℚ)) + (U := (-(11256214960041973685579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_3 : Uω (aρ 3) (bρ 3) (730852490563 / 6400000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_172_3 : have hlg : Real.log (4010421005056027 / 40000000000000000 : ℝ) ≤ (-(1149991614237294033779 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4010421005056027 / 40000000000000000 : ℝ) = - (4010421005056027 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4010421005056027 / 2500000000000000 : ℚ)) - (U := (236302746362705966221 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4010421005056027 / 2500000000000000 : ℝ) ≤ - (236302746362705966221 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (499457911484163 / 5000000000000000 : ℝ)) (q := - (4010421005056027 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4010421005056027 / 40000000000000000 : ℚ)) + (r' := (4010421005056027 / 2500000000000000 : ℚ)) + (U := (-(1149991614237294033779 / 500000000000000000000 : ℚ))) + (U' := (236302746362705966221 / 500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (499457911484163 / 5000000000000000 : ℚ)) + (q := (4010421005056027 / 40000000000000000 : ℚ)) + (U := (-(1149991614237294033779 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_4 : Uω (aρ 4) (bρ 4) (730852490563 / 6400000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_172_4 : have hlg : Real.log (3666086969961161 / 40000000000000000 : ℝ) ≤ (-(11948772902721880539821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3666086969961161 / 40000000000000000 : ℝ) = - (3666086969961161 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3666086969961161 / 2500000000000000 : ℚ)) - (U := (1914170703278119460179 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3666086969961161 / 2500000000000000 : ℝ) ≤ - (1914170703278119460179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (905042986485893 / 10000000000000000 : ℝ)) (q := - (3666086969961161 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3666086969961161 / 40000000000000000 : ℚ)) + (r' := (3666086969961161 / 2500000000000000 : ℚ)) + (U := (-(11948772902721880539821 / 5000000000000000000000 : ℚ))) + (U' := (1914170703278119460179 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (905042986485893 / 10000000000000000 : ℚ)) + (q := (3666086969961161 / 40000000000000000 : ℚ)) + (U := (-(11948772902721880539821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_5 : Uω (aρ 5) (bρ 5) (730852490563 / 6400000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_172_5 : have hlg : Real.log (3101888899973749 / 40000000000000000 : ℝ) ≤ (-(199755328482226702363 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3101888899973749 / 40000000000000000 : ℝ) = - (3101888899973749 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3101888899973749 / 2500000000000000 : ℚ)) - (U := (16853165361523297637 / 78125000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3101888899973749 / 2500000000000000 : ℝ) ≤ - (16853165361523297637 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (741133870827187 / 10000000000000000 : ℝ)) (q := - (3101888899973749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3101888899973749 / 40000000000000000 : ℚ)) + (r' := (3101888899973749 / 2500000000000000 : ℚ)) + (U := (-(199755328482226702363 / 78125000000000000000 : ℚ))) + (U' := (16853165361523297637 / 78125000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (741133870827187 / 10000000000000000 : ℚ)) + (q := (3101888899973749 / 40000000000000000 : ℚ)) + (U := (-(199755328482226702363 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_6 : Uω (aρ 6) (bρ 6) (730852490563 / 6400000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_172_6 : have hlg : Real.log (2103558289061037 / 40000000000000000 : ℝ) ≤ (-(1840780699148846481243 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2103558289061037 / 40000000000000000 : ℝ) = - (2103558289061037 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2103558289061037 / 1250000000000000 : ℚ)) - (U := (325304239288653518757 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2103558289061037 / 1250000000000000 : ℝ) ≤ - (325304239288653518757 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (409208940510831 / 10000000000000000 : ℝ)) (q := - (2103558289061037 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2103558289061037 / 40000000000000000 : ℚ)) + (r' := (2103558289061037 / 1250000000000000 : ℚ)) + (U := (-(1840780699148846481243 / 625000000000000000000 : ℚ))) + (U' := (325304239288653518757 / 625000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (730852490563 / 6400000000000 : ℚ)) + (s := (409208940510831 / 10000000000000000 : ℚ)) + (q := (2103558289061037 / 40000000000000000 : ℚ)) + (U := (-(1840780699148846481243 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_172_7 : Uω (aρ 7) (bρ 7) (730852490563 / 6400000000000 : ℝ) ≤ @@ -314,25 +290,21 @@ lemma U_173_1 : have hlg : Real.log (8646509680050409 / 80000000000000000 : ℝ) ≤ (-(22248708993169244456213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8646509680050409 / 80000000000000000 : ℝ) = - (8646509680050409 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8646509680050409 / 5000000000000000 : ℚ)) - (U := (5477178218830755543787 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8646509680050409 / 5000000000000000 : ℝ) ≤ - (5477178218830755543787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (540332065109973 / 5000000000000000 : ℝ)) (q := - (8646509680050409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8646509680050409 / 80000000000000000 : ℚ)) + (r' := (8646509680050409 / 5000000000000000 : ℚ)) + (U := (-(22248708993169244456213 / 10000000000000000000000 : ℚ))) + (U' := (5477178218830755543787 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (540332065109973 / 5000000000000000 : ℚ)) + (q := (8646509680050409 / 80000000000000000 : ℚ)) + (U := (-(22248708993169244456213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_2 : Uω (aρ 2) (bρ 2) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -340,25 +312,21 @@ lemma U_173_2 : have hlg : Real.log (8449518336965521 / 80000000000000000 : ℝ) ≤ (-(22479171954322094534041 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8449518336965521 / 80000000000000000 : ℝ) = - (8449518336965521 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8449518336965521 / 5000000000000000 : ℚ)) - (U := (5246715257677905465959 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8449518336965521 / 5000000000000000 : ℝ) ≤ - (5246715257677905465959 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263796326739681 / 2500000000000000 : ℝ)) (q := - (8449518336965521 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8449518336965521 / 80000000000000000 : ℚ)) + (r' := (8449518336965521 / 5000000000000000 : ℚ)) + (U := (-(22479171954322094534041 / 10000000000000000000000 : ℚ))) + (U' := (5246715257677905465959 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (263796326739681 / 2500000000000000 : ℚ)) + (q := (8449518336965521 / 80000000000000000 : ℚ)) + (U := (-(22479171954322094534041 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_3 : Uω (aρ 3) (bρ 3) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -366,25 +334,21 @@ lemma U_173_3 : have hlg : Real.log (8048973097240157 / 80000000000000000 : ℝ) ≤ (-(22964821159010354163667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8048973097240157 / 80000000000000000 : ℝ) = - (8048973097240157 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8048973097240157 / 5000000000000000 : ℚ)) - (U := (4761066052989645836333 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8048973097240157 / 5000000000000000 : ℝ) ≤ - (4761066052989645836333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1002445103377383 / 10000000000000000 : ℝ)) (q := - (8048973097240157 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8048973097240157 / 80000000000000000 : ℚ)) + (r' := (8048973097240157 / 5000000000000000 : ℚ)) + (U := (-(22964821159010354163667 / 10000000000000000000000 : ℚ))) + (U' := (4761066052989645836333 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (1002445103377383 / 10000000000000000 : ℚ)) + (q := (8048973097240157 / 80000000000000000 : ℚ)) + (U := (-(22964821159010354163667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_4 : Uω (aρ 4) (bρ 4) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -392,25 +356,21 @@ lemma U_173_4 : have hlg : Real.log (7360555964082549 / 80000000000000000 : ℝ) ≤ (-(23858911651480393246513 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7360555964082549 / 80000000000000000 : ℝ) = - (7360555964082549 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7360555964082549 / 5000000000000000 : ℚ)) - (U := (3866975560519606753487 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7360555964082549 / 5000000000000000 : ℝ) ≤ - (3866975560519606753487 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (908635001152981 / 10000000000000000 : ℝ)) (q := - (7360555964082549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7360555964082549 / 80000000000000000 : ℚ)) + (r' := (7360555964082549 / 5000000000000000 : ℚ)) + (U := (-(23858911651480393246513 / 10000000000000000000000 : ℚ))) + (U' := (3866975560519606753487 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (908635001152981 / 10000000000000000 : ℚ)) + (q := (7360555964082549 / 80000000000000000 : ℚ)) + (U := (-(23858911651480393246513 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_5 : Uω (aρ 5) (bρ 5) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -418,25 +378,21 @@ lemma U_173_5 : have hlg : Real.log (6233097936164581 / 80000000000000000 : ℝ) ≤ (-(204172253072514234181 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6233097936164581 / 80000000000000000 : ℝ) = - (6233097936164581 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6233097936164581 / 5000000000000000 : ℚ)) - (U := (17634844623485765819 / 80000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6233097936164581 / 5000000000000000 : ℝ) ≤ - (17634844623485765819 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (744960413508489 / 10000000000000000 : ℝ)) (q := - (6233097936164581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6233097936164581 / 80000000000000000 : ℚ)) + (r' := (6233097936164581 / 5000000000000000 : ℚ)) + (U := (-(204172253072514234181 / 80000000000000000000 : ℚ))) + (U' := (17634844623485765819 / 80000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (744960413508489 / 10000000000000000 : ℚ)) + (q := (6233097936164581 / 80000000000000000 : ℚ)) + (U := (-(204172253072514234181 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_6 : Uω (aρ 6) (bρ 6) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -444,25 +400,21 @@ lemma U_173_6 : have hlg : Real.log (4243049542363997 / 80000000000000000 : ℝ) ≤ (-(5873488781927654282487 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4243049542363997 / 80000000000000000 : ℝ) = - (4243049542363997 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4243049542363997 / 2500000000000000 : ℚ)) - (U := (1057983021072345717513 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4243049542363997 / 2500000000000000 : ℝ) ≤ - (1057983021072345717513 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (414688690198343 / 10000000000000000 : ℝ)) (q := - (4243049542363997 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4243049542363997 / 80000000000000000 : ℚ)) + (r' := (4243049542363997 / 2500000000000000 : ℚ)) + (U := (-(5873488781927654282487 / 2000000000000000000000 : ℚ))) + (U' := (1057983021072345717513 / 2000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7330947250417 / 64000000000000 : ℚ)) + (s := (414688690198343 / 10000000000000000 : ℚ)) + (q := (4243049542363997 / 80000000000000000 : ℚ)) + (U := (-(5873488781927654282487 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_173_7 : Uω (aρ 7) (bρ 7) (7330947250417 / 64000000000000 : ℝ) ≤ @@ -604,25 +556,21 @@ lemma U_174_1 : have hlg : Real.log (216863536949329 / 2000000000000000 : ℝ) ≤ (-(888653665905254274529 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (216863536949329 / 2000000000000000 : ℝ) = - (216863536949329 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (216863536949329 / 125000000000000 : ℚ)) - (U := (220381822574745725471 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (216863536949329 / 125000000000000 : ℝ) ≤ - (220381822574745725471 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216833717665533 / 2000000000000000 : ℝ)) (q := - (216863536949329 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (216863536949329 / 2000000000000000 : ℚ)) + (r' := (216863536949329 / 125000000000000 : ℚ)) + (U := (-(888653665905254274529 / 400000000000000000000 : ℚ))) + (U' := (220381822574745725471 / 400000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (216833717665533 / 2000000000000000 : ℚ)) + (q := (216863536949329 / 2000000000000000 : ℚ)) + (U := (-(888653665905254274529 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_2 : Uω (aρ 2) (bρ 2) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -630,25 +578,21 @@ lemma U_174_2 : have hlg : Real.log (1059696607599907 / 10000000000000000 : ℝ) ≤ (-(22446024440442051456091 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1059696607599907 / 10000000000000000 : ℝ) = - (1059696607599907 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1059696607599907 / 625000000000000 : ℚ)) - (U := (5279862771557948543909 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1059696607599907 / 625000000000000 : ℝ) ≤ - (5279862771557948543909 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1058695446544189 / 10000000000000000 : ℝ)) (q := - (1059696607599907 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1059696607599907 / 10000000000000000 : ℚ)) + (r' := (1059696607599907 / 625000000000000 : ℚ)) + (U := (-(22446024440442051456091 / 10000000000000000000000 : ℚ))) + (U' := (5279862771557948543909 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (1058695446544189 / 10000000000000000 : ℚ)) + (q := (1059696607599907 / 10000000000000000 : ℚ)) + (U := (-(22446024440442051456091 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_3 : Uω (aρ 3) (bρ 3) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -656,25 +600,21 @@ lemma U_174_3 : have hlg : Real.log (2019275865800773 / 20000000000000000 : ℝ) ≤ (-(22929933076480730785293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2019275865800773 / 20000000000000000 : ℝ) = - (2019275865800773 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2019275865800773 / 1250000000000000 : ℚ)) - (U := (4795954135519269214707 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2019275865800773 / 1250000000000000 : ℝ) ≤ - (4795954135519269214707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (251493550873787 / 2500000000000000 : ℝ)) (q := - (2019275865800773 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2019275865800773 / 20000000000000000 : ℚ)) + (r' := (2019275865800773 / 1250000000000000 : ℚ)) + (U := (-(22929933076480730785293 / 10000000000000000000000 : ℚ))) + (U' := (4795954135519269214707 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (251493550873787 / 2500000000000000 : ℚ)) + (q := (2019275865800773 / 20000000000000000 : ℚ)) + (U := (-(22929933076480730785293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_4 : Uω (aρ 4) (bρ 4) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -682,25 +622,21 @@ lemma U_174_4 : have hlg : Real.log (1847233808506427 / 20000000000000000 : ℝ) ≤ (-(4764085982108051921477 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1847233808506427 / 20000000000000000 : ℝ) = - (1847233808506427 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1847233808506427 / 1250000000000000 : ℚ)) - (U := (781091460291948078523 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1847233808506427 / 1250000000000000 : ℝ) ≤ - (781091460291948078523 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (456113163632901 / 5000000000000000 : ℝ)) (q := - (1847233808506427 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1847233808506427 / 20000000000000000 : ℚ)) + (r' := (1847233808506427 / 1250000000000000 : ℚ)) + (U := (-(4764085982108051921477 / 2000000000000000000000 : ℚ))) + (U' := (781091460291948078523 / 2000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (456113163632901 / 5000000000000000 : ℚ)) + (q := (1847233808506427 / 20000000000000000 : ℚ)) + (U := (-(4764085982108051921477 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_5 : Uω (aρ 5) (bρ 5) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -708,25 +644,21 @@ lemma U_174_5 : have hlg : Real.log (782800677835541 / 10000000000000000 : ℝ) ≤ (-(12737311347516656082539 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (782800677835541 / 10000000000000000 : ℝ) = - (782800677835541 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (782800677835541 / 625000000000000 : ℚ)) - (U := (1125632258483343917461 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (782800677835541 / 625000000000000 : ℝ) ≤ - (1125632258483343917461 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (748783793765457 / 10000000000000000 : ℝ)) (q := - (782800677835541 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (782800677835541 / 10000000000000000 : ℚ)) + (r' := (782800677835541 / 625000000000000 : ℚ)) + (U := (-(12737311347516656082539 / 5000000000000000000000 : ℚ))) + (U' := (1125632258483343917461 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (748783793765457 / 10000000000000000 : ℚ)) + (q := (782800677835541 / 10000000000000000 : ℚ)) + (U := (-(12737311347516656082539 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_6 : Uω (aρ 6) (bρ 6) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -734,25 +666,21 @@ lemma U_174_6 : have hlg : Real.log (213940674387349 / 4000000000000000 : ℝ) ≤ (-(29283508847027304206383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (213940674387349 / 4000000000000000 : ℝ) = - (213940674387349 / 125000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (213940674387349 / 125000000000000 : ℚ)) - (U := (5373850167972695793617 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (213940674387349 / 125000000000000 : ℝ) ≤ - (5373850167972695793617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5251577314639 / 125000000000000 : ℝ)) (q := - (213940674387349 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (213940674387349 / 4000000000000000 : ℚ)) + (r' := (213940674387349 / 125000000000000 : ℚ)) + (U := (-(29283508847027304206383 / 10000000000000000000000 : ℚ))) + (U' := (5373850167972695793617 / 10000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1838342398801 / 16000000000000 : ℚ)) + (s := (5251577314639 / 125000000000000 : ℚ)) + (q := (213940674387349 / 4000000000000000 : ℚ)) + (U := (-(29283508847027304206383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_174_7 : Uω (aρ 7) (bρ 7) (1838342398801 / 16000000000000 : ℝ) ≤ @@ -894,25 +822,21 @@ lemma U_175_1 : have hlg : Real.log (4365302499656941 / 40000000000000000 : ℝ) ≤ (-(22151919650023756881351 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4365302499656941 / 40000000000000000 : ℝ) = - (4365302499656941 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4365302499656941 / 2500000000000000 : ℚ)) - (U := (5573967561976243118649 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4365302499656941 / 2500000000000000 : ℝ) ≤ - (5573967561976243118649 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (272794371479227 / 2500000000000000 : ℝ)) (q := - (4365302499656941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4365302499656941 / 40000000000000000 : ℚ)) + (r' := (4365302499656941 / 2500000000000000 : ℚ)) + (U := (-(22151919650023756881351 / 10000000000000000000000 : ℚ))) + (U' := (5573967561976243118649 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (272794371479227 / 2500000000000000 : ℚ)) + (q := (4365302499656941 / 40000000000000000 : ℚ)) + (U := (-(22151919650023756881351 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_2 : Uω (aρ 2) (bρ 2) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -920,25 +844,21 @@ lemma U_175_2 : have hlg : Real.log (4266840691716199 / 40000000000000000 : ℝ) ≤ (-(11190028922637405674731 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4266840691716199 / 40000000000000000 : ℝ) = - (4266840691716199 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4266840691716199 / 2500000000000000 : ℚ)) - (U := (2672914683362594325269 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4266840691716199 / 2500000000000000 : ℝ) ≤ - (2672914683362594325269 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1065715594456537 / 10000000000000000 : ℝ)) (q := - (4266840691716199 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4266840691716199 / 40000000000000000 : ℚ)) + (r' := (4266840691716199 / 2500000000000000 : ℚ)) + (U := (-(11190028922637405674731 / 5000000000000000000000 : ℚ))) + (U' := (2672914683362594325269 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (1065715594456537 / 10000000000000000 : ℚ)) + (q := (4266840691716199 / 40000000000000000 : ℚ)) + (U := (-(11190028922637405674731 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_3 : Uω (aρ 3) (bρ 3) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -946,25 +866,21 @@ lemma U_175_3 : have hlg : Real.log (4066681030890477 / 40000000000000000 : ℝ) ≤ (-(11430261289115545831809 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4066681030890477 / 40000000000000000 : ℝ) = - (4066681030890477 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4066681030890477 / 2500000000000000 : ℚ)) - (U := (2432682316884454168191 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4066681030890477 / 2500000000000000 : ℝ) ≤ - (2432682316884454168191 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253257967598419 / 2500000000000000 : ℝ)) (q := - (4066681030890477 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4066681030890477 / 40000000000000000 : ℚ)) + (r' := (4066681030890477 / 2500000000000000 : ℚ)) + (U := (-(11430261289115545831809 / 5000000000000000000000 : ℚ))) + (U' := (2432682316884454168191 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (253257967598419 / 2500000000000000 : ℚ)) + (q := (4066681030890477 / 40000000000000000 : ℚ)) + (U := (-(11430261289115545831809 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_4 : Uω (aρ 4) (bρ 4) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -972,25 +888,21 @@ lemma U_175_4 : have hlg : Real.log (3722842820177343 / 40000000000000000 : ℝ) ≤ (-(23743918776680516836079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3722842820177343 / 40000000000000000 : ℝ) = - (3722842820177343 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3722842820177343 / 2500000000000000 : ℚ)) - (U := (3981968435319483163921 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3722842820177343 / 2500000000000000 : ℝ) ≤ - (3981968435319483163921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (919406946102109 / 10000000000000000 : ℝ)) (q := - (3722842820177343 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3722842820177343 / 40000000000000000 : ℚ)) + (r' := (3722842820177343 / 2500000000000000 : ℚ)) + (U := (-(23743918776680516836079 / 10000000000000000000000 : ℚ))) + (U' := (3981968435319483163921 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (919406946102109 / 10000000000000000 : ℚ)) + (q := (3722842820177343 / 40000000000000000 : ℚ)) + (U := (-(23743918776680516836079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_5 : Uω (aρ 5) (bρ 5) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -998,25 +910,21 @@ lemma U_175_5 : have hlg : Real.log (3160491606868909 / 40000000000000000 : ℝ) ≤ (-(5076303731562824760583 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3160491606868909 / 40000000000000000 : ℝ) = - (3160491606868909 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3160491606868909 / 2500000000000000 : ℚ)) - (U := (468873710837175239417 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3160491606868909 / 2500000000000000 : ℝ) ≤ - (468873710837175239417 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (189105314695723 / 2500000000000000 : ℝ)) (q := - (3160491606868909 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3160491606868909 / 40000000000000000 : ℚ)) + (r' := (3160491606868909 / 2500000000000000 : ℚ)) + (U := (-(5076303731562824760583 / 2000000000000000000000 : ℚ))) + (U' := (468873710837175239417 / 2000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (189105314695723 / 2500000000000000 : ℚ)) + (q := (3160491606868909 / 40000000000000000 : ℚ)) + (U := (-(5076303731562824760583 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_6 : Uω (aρ 6) (bρ 6) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -1024,25 +932,21 @@ lemma U_175_6 : have hlg : Real.log (2174929933788829 / 40000000000000000 : ℝ) ≤ (-(14559415015712096654269 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2174929933788829 / 40000000000000000 : ℝ) = - (2174929933788829 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2174929933788829 / 1250000000000000 : ℚ)) - (U := (2769264491787903345731 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2174929933788829 / 1250000000000000 : ℝ) ≤ - (2769264491787903345731 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (107720199345713 / 2500000000000000 : ℝ)) (q := - (2174929933788829 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2174929933788829 / 40000000000000000 : ℚ)) + (r' := (2174929933788829 / 1250000000000000 : ℚ)) + (U := (-(14559415015712096654269 / 5000000000000000000000 : ℚ))) + (U' := (2769264491787903345731 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3699107142389 / 32000000000000 : ℚ)) + (s := (107720199345713 / 2500000000000000 : ℚ)) + (q := (2174929933788829 / 40000000000000000 : ℚ)) + (U := (-(14559415015712096654269 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_175_7 : Uω (aρ 7) (bρ 7) (3699107142389 / 32000000000000 : ℝ) ≤ @@ -1185,25 +1089,21 @@ lemma U_176_1 : have hlg : Real.log (2196667105724981 / 20000000000000000 : ℝ) ≤ (-(22087910127931218969373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2196667105724981 / 20000000000000000 : ℝ) = - (2196667105724981 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2196667105724981 / 1250000000000000 : ℚ)) - (U := (5637977084068781030627 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2196667105724981 / 1250000000000000 : ℝ) ≤ - (5637977084068781030627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1098186359067481 / 10000000000000000 : ℝ)) (q := - (2196667105724981 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2196667105724981 / 20000000000000000 : ℚ)) + (r' := (2196667105724981 / 1250000000000000 : ℚ)) + (U := (-(22087910127931218969373 / 10000000000000000000000 : ℚ))) + (U' := (5637977084068781030627 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (1098186359067481 / 10000000000000000 : ℚ)) + (q := (2196667105724981 / 20000000000000000 : ℚ)) + (U := (-(22087910127931218969373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_2 : Uω (aρ 2) (bρ 2) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1211,25 +1111,21 @@ lemma U_176_2 : have hlg : Real.log (536861826092047 / 5000000000000000 : ℝ) ≤ (-(5578631090169752076037 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (536861826092047 / 5000000000000000 : ℝ) = - (536861826092047 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (536861826092047 / 312500000000000 : ℚ)) - (U := (1352840712830247923963 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (536861826092047 / 312500000000000 : ℝ) ≤ - (1352840712830247923963 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (67045973138793 / 625000000000000 : ℝ)) (q := - (536861826092047 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (536861826092047 / 5000000000000000 : ℚ)) + (r' := (536861826092047 / 312500000000000 : ℚ)) + (U := (-(5578631090169752076037 / 2500000000000000000000 : ℚ))) + (U' := (1352840712830247923963 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (67045973138793 / 625000000000000 : ℚ)) + (q := (536861826092047 / 5000000000000000 : ℚ)) + (U := (-(5578631090169752076037 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_3 : Uω (aρ 3) (bρ 3) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1237,25 +1133,21 @@ lemma U_176_3 : have hlg : Real.log (1023702233136753 / 10000000000000000 : ℝ) ≤ (-(22791593955763525787333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1023702233136753 / 10000000000000000 : ℝ) = - (1023702233136753 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1023702233136753 / 625000000000000 : ℚ)) - (U := (4934293256236474212667 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1023702233136753 / 625000000000000 : ℝ) ≤ - (4934293256236474212667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (510044419238003 / 5000000000000000 : ℝ)) (q := - (1023702233136753 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1023702233136753 / 10000000000000000 : ℚ)) + (r' := (1023702233136753 / 625000000000000 : ℚ)) + (U := (-(22791593955763525787333 / 10000000000000000000000 : ℚ))) + (U' := (4934293256236474212667 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (510044419238003 / 5000000000000000 : ℚ)) + (q := (1023702233136753 / 10000000000000000 : ℚ)) + (U := (-(22791593955763525787333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_4 : Uω (aρ 4) (bρ 4) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1263,25 +1155,21 @@ lemma U_176_4 : have hlg : Real.log (234450794126107 / 2500000000000000 : ℝ) ≤ (-(23668002770991622080457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (234450794126107 / 2500000000000000 : ℝ) = - (234450794126107 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (234450794126107 / 156250000000000 : ℚ)) - (U := (4057884441008377919543 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (234450794126107 / 156250000000000 : ℝ) ≤ - (4057884441008377919543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231646226569089 / 2500000000000000 : ℝ)) (q := - (234450794126107 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (234450794126107 / 2500000000000000 : ℚ)) + (r' := (234450794126107 / 156250000000000 : ℚ)) + (U := (-(23668002770991622080457 / 10000000000000000000000 : ℚ))) + (U' := (4057884441008377919543 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (231646226569089 / 2500000000000000 : ℚ)) + (q := (234450794126107 / 2500000000000000 : ℚ)) + (U := (-(23668002770991622080457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_5 : Uω (aρ 5) (bρ 5) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1289,25 +1177,21 @@ lemma U_176_5 : have hlg : Real.log (318975633373579 / 4000000000000000 : ℝ) ≤ (-(6322337309009206611799 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (318975633373579 / 4000000000000000 : ℝ) = - (318975633373579 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (318975633373579 / 250000000000000 : ℚ)) - (U := (609134493990793388201 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (318975633373579 / 250000000000000 : ℝ) ≤ - (609134493990793388201 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152809327894079 / 2000000000000000 : ℝ)) (q := - (318975633373579 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (318975633373579 / 4000000000000000 : ℚ)) + (r' := (318975633373579 / 250000000000000 : ℚ)) + (U := (-(6322337309009206611799 / 2500000000000000000000 : ℚ))) + (U' := (609134493990793388201 / 2500000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (152809327894079 / 2000000000000000 : ℚ)) + (q := (318975633373579 / 4000000000000000 : ℚ)) + (U := (-(6322337309009206611799 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_6 : Uω (aρ 6) (bρ 6) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1315,25 +1199,21 @@ lemma U_176_6 : have hlg : Real.log (552537907396753 / 10000000000000000 : ℝ) ≤ (-(2895818328965296759049 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (552537907396753 / 10000000000000000 : ℝ) = - (552537907396753 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (552537907396753 / 312500000000000 : ℚ)) - (U := (569917572534703240951 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (552537907396753 / 312500000000000 : ℝ) ≤ - (569917572534703240951 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (220742331268003 / 5000000000000000 : ℝ)) (q := - (552537907396753 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (552537907396753 / 10000000000000000 : ℚ)) + (r' := (552537907396753 / 312500000000000 : ℚ)) + (U := (-(2895818328965296759049 / 1000000000000000000000 : ℚ))) + (U' := (569917572534703240951 / 1000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (465191185897 / 4000000000000 : ℚ)) + (s := (220742331268003 / 5000000000000000 : ℚ)) + (q := (552537907396753 / 10000000000000000 : ℚ)) + (U := (-(2895818328965296759049 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_176_7 : Uω (aρ 7) (bρ 7) (465191185897 / 4000000000000 : ℝ) ≤ @@ -1476,25 +1356,21 @@ lemma U_177_1 : have hlg : Real.log (884273175059109 / 8000000000000000 : ℝ) ≤ (-(11012153915808991134077 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (884273175059109 / 8000000000000000 : ℝ) = - (884273175059109 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (884273175059109 / 500000000000000 : ℚ)) - (U := (2850789690191008865923 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (884273175059109 / 500000000000000 : ℝ) ≤ - (2850789690191008865923 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221039041648867 / 2000000000000000 : ℝ)) (q := - (884273175059109 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (884273175059109 / 8000000000000000 : ℚ)) + (r' := (884273175059109 / 500000000000000 : ℚ)) + (U := (-(11012153915808991134077 / 5000000000000000000000 : ℚ))) + (U' := (2850789690191008865923 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (221039041648867 / 2000000000000000 : ℚ)) + (q := (884273175059109 / 8000000000000000 : ℚ)) + (U := (-(11012153915808991134077 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_2 : Uω (aρ 2) (bρ 2) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1502,25 +1378,21 @@ lemma U_177_2 : have hlg : Real.log (4322948188175437 / 40000000000000000 : ℝ) ≤ (-(22249418326153667549627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4322948188175437 / 40000000000000000 : ℝ) = - (4322948188175437 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4322948188175437 / 2500000000000000 : ℚ)) - (U := (5476468885846332450373 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4322948188175437 / 2500000000000000 : ℝ) ≤ - (5476468885846332450373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1079755377194281 / 10000000000000000 : ℝ)) (q := - (4322948188175437 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4322948188175437 / 40000000000000000 : ℚ)) + (r' := (4322948188175437 / 2500000000000000 : ℚ)) + (U := (-(22249418326153667549627 / 10000000000000000000000 : ℚ))) + (U' := (5476468885846332450373 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (1079755377194281 / 10000000000000000 : ℚ)) + (q := (4322948188175437 / 40000000000000000 : ℚ)) + (U := (-(22249418326153667549627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_3 : Uω (aρ 3) (bρ 3) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1528,25 +1400,21 @@ lemma U_177_3 : have hlg : Real.log (824587093075663 / 8000000000000000 : ℝ) ≤ (-(1136157025908839802787 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (824587093075663 / 8000000000000000 : ℝ) = - (824587093075663 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (824587093075663 / 500000000000000 : ℚ)) - (U := (250137334691160197213 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (824587093075663 / 500000000000000 : ℝ) ≤ - (250137334691160197213 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25678628053643 / 250000000000000 : ℝ)) (q := - (824587093075663 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (824587093075663 / 8000000000000000 : ℚ)) + (r' := (824587093075663 / 500000000000000 : ℚ)) + (U := (-(1136157025908839802787 / 500000000000000000000 : ℚ))) + (U' := (250137334691160197213 / 500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (25678628053643 / 250000000000000 : ℚ)) + (q := (824587093075663 / 8000000000000000 : ℚ)) + (U := (-(1136157025908839802787 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_4 : Uω (aρ 4) (bρ 4) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1554,25 +1422,21 @@ lemma U_177_4 : have hlg : Real.log (3779577397159251 / 40000000000000000 : ℝ) ≤ (-(5898168123465075345177 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3779577397159251 / 40000000000000000 : ℝ) = - (3779577397159251 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3779577397159251 / 2500000000000000 : ℚ)) - (U := (1033303679534924654823 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3779577397159251 / 2500000000000000 : ℝ) ≤ - (1033303679534924654823 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (233440067275297 / 2500000000000000 : ℝ)) (q := - (3779577397159251 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3779577397159251 / 40000000000000000 : ℚ)) + (r' := (3779577397159251 / 2500000000000000 : ℚ)) + (U := (-(5898168123465075345177 / 2500000000000000000000 : ℚ))) + (U' := (1033303679534924654823 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (233440067275297 / 2500000000000000 : ℚ)) + (q := (3779577397159251 / 40000000000000000 : ℚ)) + (U := (-(5898168123465075345177 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_5 : Uω (aρ 5) (bρ 5) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1580,25 +1444,21 @@ lemma U_177_5 : have hlg : Real.log (3218997608431433 / 40000000000000000 : ℝ) ≤ (-(25198094437116484192507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3218997608431433 / 40000000000000000 : ℝ) = - (3218997608431433 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3218997608431433 / 2500000000000000 : ℚ)) - (U := (2527792774883515807493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3218997608431433 / 2500000000000000 : ℝ) ≤ - (2527792774883515807493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (771660294072279 / 10000000000000000 : ℝ)) (q := - (3218997608431433 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3218997608431433 / 40000000000000000 : ℚ)) + (r' := (3218997608431433 / 2500000000000000 : ℚ)) + (U := (-(25198094437116484192507 / 10000000000000000000000 : ℚ))) + (U' := (2527792774883515807493 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (771660294072279 / 10000000000000000 : ℚ)) + (q := (3218997608431433 / 40000000000000000 : ℚ)) + (U := (-(25198094437116484192507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_6 : Uω (aρ 6) (bρ 6) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1606,25 +1466,21 @@ lemma U_177_6 : have hlg : Real.log (2245093052986399 / 40000000000000000 : ℝ) ≤ (-(14400662417436316917723 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2245093052986399 / 40000000000000000 : ℝ) = - (2245093052986399 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2245093052986399 / 1250000000000000 : ℚ)) - (U := (2928017090063683082277 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2245093052986399 / 1250000000000000 : ℝ) ≤ - (2928017090063683082277 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (225974195744881 / 5000000000000000 : ℝ)) (q := - (2245093052986399 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2245093052986399 / 40000000000000000 : ℚ)) + (r' := (2245093052986399 / 1250000000000000 : ℚ)) + (U := (-(14400662417436316917723 / 5000000000000000000000 : ℚ))) + (U' := (2928017090063683082277 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3743951831963 / 32000000000000 : ℚ)) + (s := (225974195744881 / 5000000000000000 : ℚ)) + (q := (2245093052986399 / 40000000000000000 : ℚ)) + (U := (-(14400662417436316917723 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_177_7 : Uω (aρ 7) (bρ 7) (3743951831963 / 32000000000000 : ℝ) ≤ @@ -1766,25 +1622,21 @@ lemma U_178_1 : have hlg : Real.log (556174686512519 / 5000000000000000 : ℝ) ≤ (-(21961107610964149289349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (556174686512519 / 5000000000000000 : ℝ) = - (556174686512519 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (556174686512519 / 312500000000000 : ℚ)) - (U := (5764779601035850710651 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (556174686512519 / 312500000000000 : ℝ) ≤ - (5764779601035850710651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1112204033900701 / 10000000000000000 : ℝ)) (q := - (556174686512519 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (556174686512519 / 5000000000000000 : ℚ)) + (r' := (556174686512519 / 312500000000000 : ℚ)) + (U := (-(21961107610964149289349 / 10000000000000000000000 : ℚ))) + (U' := (5764779601035850710651 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (15065496707 / 128000000000 : ℚ)) + (s := (1112204033900701 / 10000000000000000 : ℚ)) + (q := (556174686512519 / 5000000000000000 : ℚ)) + (U := (-(21961107610964149289349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_2 : Uω (aρ 2) (bρ 2) (15065496707 / 128000000000 : ℝ) ≤ @@ -1792,25 +1644,21 @@ lemma U_178_2 : have hlg : Real.log (2175500718287497 / 20000000000000000 : ℝ) ≤ (-(5546183547911107213653 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2175500718287497 / 20000000000000000 : ℝ) = - (2175500718287497 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2175500718287497 / 1250000000000000 : ℚ)) - (U := (1385288255088892786347 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2175500718287497 / 1250000000000000 : ℝ) ≤ - (1385288255088892786347 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (543387509324061 / 5000000000000000 : ℝ)) (q := - (2175500718287497 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2175500718287497 / 20000000000000000 : ℚ)) + (r' := (2175500718287497 / 1250000000000000 : ℚ)) + (U := (-(5546183547911107213653 / 2500000000000000000000 : ℚ))) + (U' := (1385288255088892786347 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (15065496707 / 128000000000 : ℚ)) + (s := (543387509324061 / 5000000000000000 : ℚ)) + (q := (2175500718287497 / 20000000000000000 : ℚ)) + (U := (-(5546183547911107213653 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_3 : Uω (aρ 3) (bρ 3) (15065496707 / 128000000000 : ℝ) ≤ @@ -1818,25 +1666,21 @@ lemma U_178_3 : have hlg : Real.log (1037765164350651 / 10000000000000000 : ℝ) ≤ (-(5663788928473910630479 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1037765164350651 / 10000000000000000 : ℝ) = - (1037765164350651 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1037765164350651 / 625000000000000 : ℚ)) - (U := (1267682874526089369521 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1037765164350651 / 625000000000000 : ℝ) ≤ - (1267682874526089369521 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1034200735411927 / 10000000000000000 : ℝ)) (q := - (1037765164350651 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1037765164350651 / 10000000000000000 : ℚ)) + (r' := (1037765164350651 / 625000000000000 : ℚ)) + (U := (-(5663788928473910630479 / 2500000000000000000000 : ℚ))) + (U' := (1267682874526089369521 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (15065496707 / 128000000000 : ℚ)) + (s := (1034200735411927 / 10000000000000000 : ℚ)) + (q := (1037765164350651 / 10000000000000000 : ℚ)) + (U := (-(5663788928473910630479 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_4 : Uω (aρ 4) (bρ 4) (15065496707 / 128000000000 : ℝ) ≤ @@ -1844,25 +1688,21 @@ lemma U_178_4 : have hlg : Real.log (380793701244309 / 4000000000000000 : ℝ) ≤ (-(23517918771318664380059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (380793701244309 / 4000000000000000 : ℝ) = - (380793701244309 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (380793701244309 / 250000000000000 : ℚ)) - (U := (4207968440681335619941 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (380793701244309 / 250000000000000 : ℝ) ≤ - (4207968440681335619941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (94093309399717 / 1000000000000000 : ℝ)) (q := - (380793701244309 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (380793701244309 / 4000000000000000 : ℚ)) + (r' := (380793701244309 / 250000000000000 : ℚ)) + (U := (-(23517918771318664380059 / 10000000000000000000000 : ℚ))) + (U' := (4207968440681335619941 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (15065496707 / 128000000000 : ℚ)) + (s := (94093309399717 / 1000000000000000 : ℚ)) + (q := (380793701244309 / 4000000000000000 : ℚ)) + (U := (-(23517918771318664380059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_5 : Uω (aρ 5) (bρ 5) (15065496707 / 128000000000 : ℝ) ≤ @@ -1870,25 +1710,21 @@ lemma U_178_5 : have hlg : Real.log (1624108059181271 / 20000000000000000 : ℝ) ≤ (-(6276933735209036880089 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1624108059181271 / 20000000000000000 : ℝ) = - (1624108059181271 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1624108059181271 / 1250000000000000 : ℚ)) - (U := (654538067790963119911 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1624108059181271 / 1250000000000000 : ℝ) ≤ - (654538067790963119911 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (97407820786487 / 1250000000000000 : ℝ)) (q := - (1624108059181271 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1624108059181271 / 20000000000000000 : ℚ)) + (r' := (1624108059181271 / 1250000000000000 : ℚ)) + (U := (-(6276933735209036880089 / 2500000000000000000000 : ℚ))) + (U' := (654538067790963119911 / 2500000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (15065496707 / 128000000000 : ℚ)) + (s := (97407820786487 / 1250000000000000 : ℚ)) + (q := (1624108059181271 / 20000000000000000 : ℚ)) + (U := (-(6276933735209036880089 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_6 : Uω (aρ 6) (bρ 6) (15065496707 / 128000000000 : ℝ) ≤ @@ -1896,25 +1732,21 @@ lemma U_178_6 : have hlg : Real.log (1139886618028413 / 20000000000000000 : ℝ) ≤ (-(572960694532787081867 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (1139886618028413 / 20000000000000000 : ℝ) = - (1139886618028413 / 625000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1139886618028413 / 625000000000000 : ℚ)) - (U := (120186485767212918133 / 200000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1139886618028413 / 625000000000000 : ℝ) ≤ - (120186485767212918133 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231140750139519 / 5000000000000000 : ℝ)) (q := - (1139886618028413 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1139886618028413 / 20000000000000000 : ℚ)) + (r' := (1139886618028413 / 625000000000000 : ℚ)) + (U := (-(572960694532787081867 / 200000000000000000000 : ℚ))) + (U' := (120186485767212918133 / 200000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (15065496707 / 128000000000 : ℚ)) + (s := (231140750139519 / 5000000000000000 : ℚ)) + (q := (1139886618028413 / 20000000000000000 : ℚ)) + (U := (-(572960694532787081867 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_178_7 : Uω (aρ 7) (bρ 7) (15065496707 / 128000000000 : ℝ) ≤ @@ -2057,25 +1889,21 @@ lemma U_179_1 : have hlg : Real.log (895485812549507 / 8000000000000000 : ℝ) ≤ (-(5474576103240136115701 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (895485812549507 / 8000000000000000 : ℝ) = - (895485812549507 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (895485812549507 / 500000000000000 : ℚ)) - (U := (1456895699759863884299 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (895485812549507 / 500000000000000 : ℝ) ≤ - (1456895699759863884299 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (223842567295691 / 2000000000000000 : ℝ)) (q := - (895485812549507 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (895485812549507 / 8000000000000000 : ℚ)) + (r' := (895485812549507 / 500000000000000 : ℚ)) + (U := (-(5474576103240136115701 / 2500000000000000000000 : ℚ))) + (U' := (1456895699759863884299 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (223842567295691 / 2000000000000000 : ℚ)) + (q := (895485812549507 / 8000000000000000 : ℚ)) + (U := (-(5474576103240136115701 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_2 : Uω (aρ 2) (bρ 2) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2083,25 +1911,21 @@ lemma U_179_2 : have hlg : Real.log (4379054360308581 / 40000000000000000 : ℝ) ≤ (-(11060233257341866518873 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4379054360308581 / 40000000000000000 : ℝ) = - (4379054360308581 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4379054360308581 / 2500000000000000 : ℚ)) - (U := (2802710348658133481127 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4379054360308581 / 2500000000000000 : ℝ) ≤ - (2802710348658133481127 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (546897248884489 / 5000000000000000 : ℝ)) (q := - (4379054360308581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4379054360308581 / 40000000000000000 : ℚ)) + (r' := (4379054360308581 / 2500000000000000 : ℚ)) + (U := (-(11060233257341866518873 / 5000000000000000000000 : ℚ))) + (U' := (2802710348658133481127 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (546897248884489 / 5000000000000000 : ℚ)) + (q := (4379054360308581 / 40000000000000000 : ℚ)) + (U := (-(11060233257341866518873 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_3 : Uω (aρ 3) (bρ 3) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2109,25 +1933,21 @@ lemma U_179_3 : have hlg : Real.log (4179184535876051 / 40000000000000000 : ℝ) ≤ (-(2258763312680448441801 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4179184535876051 / 40000000000000000 : ℝ) = - (4179184535876051 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4179184535876051 / 2500000000000000 : ℚ)) - (U := (513825408519551558199 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4179184535876051 / 2500000000000000 : ℝ) ≤ - (513825408519551558199 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1041255691902713 / 10000000000000000 : ℝ)) (q := - (4179184535876051 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4179184535876051 / 40000000000000000 : ℚ)) + (r' := (4179184535876051 / 2500000000000000 : ℚ)) + (U := (-(2258763312680448441801 / 1000000000000000000000 : ℚ))) + (U' := (513825408519551558199 / 1000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (1041255691902713 / 10000000000000000 : ℚ)) + (q := (4179184535876051 / 40000000000000000 : ℚ)) + (U := (-(2258763312680448441801 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_4 : Uω (aρ 4) (bρ 4) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2135,25 +1955,21 @@ lemma U_179_4 : have hlg : Real.log (3836291667072607 / 40000000000000000 : ℝ) ≤ (-(468874652954865998573 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3836291667072607 / 40000000000000000 : ℝ) = - (3836291667072607 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3836291667072607 / 2500000000000000 : ℚ)) - (U := (85643091285134001427 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3836291667072607 / 2500000000000000 : ℝ) ≤ - (85643091285134001427 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (948103438565991 / 10000000000000000 : ℝ)) (q := - (3836291667072607 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3836291667072607 / 40000000000000000 : ℚ)) + (r' := (3836291667072607 / 2500000000000000 : ℚ)) + (U := (-(468874652954865998573 / 200000000000000000000 : ℚ))) + (U' := (85643091285134001427 / 200000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (948103438565991 / 10000000000000000 : ℚ)) + (q := (3836291667072607 / 40000000000000000 : ℚ)) + (U := (-(468874652954865998573 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_5 : Uω (aρ 5) (bρ 5) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2161,25 +1977,21 @@ lemma U_179_5 : have hlg : Real.log (3277412523361897 / 40000000000000000 : ℝ) ≤ (-(2501825206824387380069 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3277412523361897 / 40000000000000000 : ℝ) = - (3277412523361897 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3277412523361897 / 2500000000000000 : ℚ)) - (U := (270763514375612619931 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3277412523361897 / 2500000000000000 : ℝ) ≤ - (270763514375612619931 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (196713446511409 / 2500000000000000 : ℝ)) (q := - (3277412523361897 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3277412523361897 / 40000000000000000 : ℚ)) + (r' := (3277412523361897 / 2500000000000000 : ℚ)) + (U := (-(2501825206824387380069 / 1000000000000000000000 : ℚ))) + (U' := (270763514375612619931 / 1000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (196713446511409 / 2500000000000000 : ℚ)) + (q := (3277412523361897 / 40000000000000000 : ℚ)) + (U := (-(2501825206824387380069 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_6 : Uω (aρ 6) (bρ 6) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2187,25 +1999,21 @@ lemma U_179_6 : have hlg : Real.log (2314209318428351 / 40000000000000000 : ℝ) ≤ (-(14249056853658479258529 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2314209318428351 / 40000000000000000 : ℝ) = - (2314209318428351 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2314209318428351 / 1250000000000000 : ℚ)) - (U := (3079622653841520741471 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2314209318428351 / 1250000000000000 : ℝ) ≤ - (3079622653841520741471 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (472492558718863 / 10000000000000000 : ℝ)) (q := - (2314209318428351 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2314209318428351 / 40000000000000000 : ℚ)) + (r' := (2314209318428351 / 1250000000000000 : ℚ)) + (U := (-(14249056853658479258529 / 5000000000000000000000 : ℚ))) + (U' := (3079622653841520741471 / 5000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3788796521537 / 32000000000000 : ℚ)) + (s := (472492558718863 / 10000000000000000 : ℚ)) + (q := (2314209318428351 / 40000000000000000 : ℚ)) + (U := (-(14249056853658479258529 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_179_7 : Uω (aρ 7) (bρ 7) (3788796521537 / 32000000000000 : ℝ) ≤ @@ -2346,25 +2154,21 @@ lemma U_180_1 : have hlg : Real.log (2252730294049721 / 20000000000000000 : ℝ) ≤ (-(5458973319820460563247 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2252730294049721 / 20000000000000000 : ℝ) = - (2252730294049721 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2252730294049721 / 1250000000000000 : ℚ)) - (U := (1472498483179539436753 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2252730294049721 / 1250000000000000 : ℝ) ≤ - (1472498483179539436753 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1126221616408471 / 10000000000000000 : ℝ)) (q := - (2252730294049721 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2252730294049721 / 20000000000000000 : ℚ)) + (r' := (2252730294049721 / 1250000000000000 : ℚ)) + (U := (-(5458973319820460563247 / 2500000000000000000000 : ℚ))) + (U' := (1472498483179539436753 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (1126221616408471 / 10000000000000000 : ℚ)) + (q := (2252730294049721 / 20000000000000000 : ℚ)) + (U := (-(5458973319820460563247 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_2 : Uω (aρ 2) (bρ 2) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2372,25 +2176,21 @@ lemma U_180_2 : have hlg : Real.log (220355348279351 / 2000000000000000 : ℝ) ≤ (-(11028304978811575276189 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (220355348279351 / 2000000000000000 : ℝ) = - (220355348279351 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (220355348279351 / 125000000000000 : ℚ)) - (U := (2834638627188424723811 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (220355348279351 / 125000000000000 : ℝ) ≤ - (2834638627188424723811 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55040690883113 / 500000000000000 : ℝ)) (q := - (220355348279351 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (220355348279351 / 2000000000000000 : ℚ)) + (r' := (220355348279351 / 125000000000000 : ℚ)) + (U := (-(11028304978811575276189 / 5000000000000000000000 : ℚ))) + (U' := (2834638627188424723811 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (55040690883113 / 500000000000000 : ℚ)) + (q := (220355348279351 / 2000000000000000 : ℚ)) + (U := (-(11028304978811575276189 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_3 : Uω (aρ 3) (bρ 3) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2398,25 +2198,21 @@ lemma U_180_3 : have hlg : Real.log (420730712731861 / 4000000000000000 : ℝ) ≤ (-(11260283236257531228509 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (420730712731861 / 4000000000000000 : ℝ) = - (420730712731861 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (420730712731861 / 250000000000000 : ℚ)) - (U := (2602660369742468771491 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (420730712731861 / 250000000000000 : ℝ) ≤ - (2602660369742468771491 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (209662000975611 / 2000000000000000 : ℝ)) (q := - (420730712731861 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (420730712731861 / 4000000000000000 : ℚ)) + (r' := (420730712731861 / 250000000000000 : ℚ)) + (U := (-(11260283236257531228509 / 5000000000000000000000 : ℚ))) + (U' := (2602660369742468771491 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (209662000975611 / 2000000000000000 : ℚ)) + (q := (420730712731861 / 4000000000000000 : ℚ)) + (U := (-(11260283236257531228509 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_4 : Uω (aρ 4) (bρ 4) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2424,25 +2220,21 @@ lemma U_180_4 : have hlg : Real.log (966160368188257 / 10000000000000000 : ℝ) ≤ (-(23370105378852098455103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (966160368188257 / 10000000000000000 : ℝ) = - (966160368188257 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (966160368188257 / 625000000000000 : ℚ)) - (U := (4355781833147901544897 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (966160368188257 / 625000000000000 : ℝ) ≤ - (4355781833147901544897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (119408919832533 / 1250000000000000 : ℝ)) (q := - (966160368188257 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (966160368188257 / 10000000000000000 : ℚ)) + (r' := (966160368188257 / 625000000000000 : ℚ)) + (U := (-(23370105378852098455103 / 10000000000000000000000 : ℚ))) + (U' := (4355781833147901544897 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (119408919832533 / 1250000000000000 : ℚ)) + (q := (966160368188257 / 10000000000000000 : ℚ)) + (U := (-(23370105378852098455103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_5 : Uω (aρ 5) (bρ 5) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2450,25 +2242,21 @@ lemma U_180_5 : have hlg : Real.log (1653293728550453 / 20000000000000000 : ℝ) ≤ (-(99718511009526859259 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1653293728550453 / 20000000000000000 : ℝ) = - (1653293728550453 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1653293728550453 / 1250000000000000 : ℚ)) - (U := (11185037838473140741 / 40000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1653293728550453 / 1250000000000000 : ℝ) ≤ - (11185037838473140741 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (794434270169203 / 10000000000000000 : ℝ)) (q := - (1653293728550453 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1653293728550453 / 20000000000000000 : ℚ)) + (r' := (1653293728550453 / 1250000000000000 : ℚ)) + (U := (-(99718511009526859259 / 40000000000000000000 : ℚ))) + (U' := (11185037838473140741 / 40000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (794434270169203 / 10000000000000000 : ℚ)) + (q := (1653293728550453 / 20000000000000000 : ℚ)) + (U := (-(99718511009526859259 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_6 : Uω (aρ 6) (bρ 6) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2476,25 +2264,21 @@ lemma U_180_6 : have hlg : Real.log (587104198732817 / 10000000000000000 : ℝ) ≤ (-(7087845139958546029759 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (587104198732817 / 10000000000000000 : ℝ) = - (587104198732817 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (587104198732817 / 312500000000000 : ℚ)) - (U := (1576494613791453970241 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (587104198732817 / 312500000000000 : ℝ) ≤ - (1576494613791453970241 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1885114508689 / 39062500000000 : ℝ)) (q := - (587104198732817 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (587104198732817 / 10000000000000000 : ℚ)) + (r' := (587104198732817 / 312500000000000 : ℚ)) + (U := (-(7087845139958546029759 / 2500000000000000000000 : ℚ))) + (U' := (1576494613791453970241 / 2500000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (952804716581 / 8000000000000 : ℚ)) + (s := (1885114508689 / 39062500000000 : ℚ)) + (q := (587104198732817 / 10000000000000000 : ℚ)) + (U := (-(7087845139958546029759 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_180_7 : Uω (aρ 7) (bρ 7) (952804716581 / 8000000000000 : ℝ) ≤ @@ -2635,25 +2419,21 @@ lemma U_181_1 : have hlg : Real.log (4533492068996301 / 40000000000000000 : ℝ) ≤ (-(21773869343935046491781 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4533492068996301 / 40000000000000000 : ℝ) = - (4533492068996301 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4533492068996301 / 2500000000000000 : ℚ)) - (U := (5952017868064953508219 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4533492068996301 / 2500000000000000 : ℝ) ≤ - (5952017868064953508219 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1133230374110963 / 10000000000000000 : ℝ)) (q := - (4533492068996301 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4533492068996301 / 40000000000000000 : ℚ)) + (r' := (4533492068996301 / 2500000000000000 : ℚ)) + (U := (-(21773869343935046491781 / 10000000000000000000000 : ℚ))) + (U' := (5952017868064953508219 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (1133230374110963 / 10000000000000000 : ℚ)) + (q := (4533492068996301 / 40000000000000000 : ℚ)) + (U := (-(21773869343935046491781 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_2 : Uω (aρ 2) (bρ 2) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2661,25 +2441,21 @@ lemma U_181_2 : have hlg : Real.log (887031851692717 / 8000000000000000 : ℝ) ≤ (-(21993159284954283541103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (887031851692717 / 8000000000000000 : ℝ) = - (887031851692717 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (887031851692717 / 500000000000000 : ℚ)) - (U := (5732727927045716458897 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (887031851692717 / 500000000000000 : ℝ) ≤ - (5732727927045716458897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221566596270921 / 2000000000000000 : ℝ)) (q := - (887031851692717 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (887031851692717 / 8000000000000000 : ℚ)) + (r' := (887031851692717 / 500000000000000 : ℚ)) + (U := (-(21993159284954283541103 / 10000000000000000000000 : ℚ))) + (U' := (5732727927045716458897 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (221566596270921 / 2000000000000000 : ℚ)) + (q := (887031851692717 / 8000000000000000 : ℚ)) + (U := (-(21993159284954283541103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_3 : Uω (aρ 3) (bρ 3) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2687,25 +2463,21 @@ lemma U_181_3 : have hlg : Real.log (847085691507757 / 8000000000000000 : ℝ) ≤ (-(11226974797381275692259 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (847085691507757 / 8000000000000000 : ℝ) = - (847085691507757 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (847085691507757 / 500000000000000 : ℚ)) - (U := (2635968808618724307741 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (847085691507757 / 500000000000000 : ℝ) ≤ - (2635968808618724307741 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (211072737448441 / 2000000000000000 : ℝ)) (q := - (847085691507757 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (847085691507757 / 8000000000000000 : ℚ)) + (r' := (847085691507757 / 500000000000000 : ℚ)) + (U := (-(11226974797381275692259 / 5000000000000000000000 : ℚ))) + (U' := (2635968808618724307741 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (211072737448441 / 2000000000000000 : ℚ)) + (q := (847085691507757 / 8000000000000000 : ℚ)) + (U := (-(11226974797381275692259 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_4 : Uω (aρ 4) (bρ 4) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2713,25 +2485,21 @@ lemma U_181_4 : have hlg : Real.log (3892986537824593 / 40000000000000000 : ℝ) ≤ (-(1164851421249206849263 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3892986537824593 / 40000000000000000 : ℝ) = - (3892986537824593 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3892986537824593 / 2500000000000000 : ℚ)) - (U := (221442939350793150737 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3892986537824593 / 2500000000000000 : ℝ) ≤ - (221442939350793150737 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (962436908450109 / 10000000000000000 : ℝ)) (q := - (3892986537824593 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3892986537824593 / 40000000000000000 : ℚ)) + (r' := (3892986537824593 / 2500000000000000 : ℚ)) + (U := (-(1164851421249206849263 / 500000000000000000000 : ℚ))) + (U' := (221442939350793150737 / 500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (962436908450109 / 10000000000000000 : ℚ)) + (q := (3892986537824593 / 40000000000000000 : ℚ)) + (U := (-(1164851421249206849263 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_5 : Uω (aρ 5) (bρ 5) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2739,25 +2507,21 @@ lemma U_181_5 : have hlg : Real.log (3335741528413867 / 40000000000000000 : ℝ) ≤ (-(24841844510715917490201 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3335741528413867 / 40000000000000000 : ℝ) = - (3335741528413867 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3335741528413867 / 2500000000000000 : ℚ)) - (U := (2884042701284082509799 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3335741528413867 / 2500000000000000 : ℝ) ≤ - (2884042701284082509799 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (401002161539873 / 5000000000000000 : ℝ)) (q := - (3335741528413867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3335741528413867 / 40000000000000000 : ℚ)) + (r' := (3335741528413867 / 2500000000000000 : ℚ)) + (U := (-(24841844510715917490201 / 10000000000000000000000 : ℚ))) + (U' := (2884042701284082509799 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (401002161539873 / 5000000000000000 : ℚ)) + (q := (3335741528413867 / 40000000000000000 : ℚ)) + (U := (-(24841844510715917490201 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_6 : Uω (aρ 6) (bρ 6) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2765,25 +2529,21 @@ lemma U_181_6 : have hlg : Real.log (476481944676323 / 8000000000000000 : ℝ) ≤ (-(28207669885361066139551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (476481944676323 / 8000000000000000 : ℝ) = - (476481944676323 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (476481944676323 / 250000000000000 : ℚ)) - (U := (6449689129638933860449 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (476481944676323 / 250000000000000 : ℝ) ≤ - (6449689129638933860449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24628939785181 / 500000000000000 : ℝ)) (q := - (476481944676323 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (476481944676323 / 8000000000000000 : ℚ)) + (r' := (476481944676323 / 250000000000000 : ℚ)) + (U := (-(28207669885361066139551 / 10000000000000000000000 : ℚ))) + (U' := (6449689129638933860449 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3833641211111 / 32000000000000 : ℚ)) + (s := (24628939785181 / 500000000000000 : ℚ)) + (q := (476481944676323 / 8000000000000000 : ℚ)) + (U := (-(28207669885361066139551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_181_7 : Uω (aρ 7) (bρ 7) (3833641211111 / 32000000000000 : ℝ) ≤ @@ -2926,25 +2686,21 @@ lemma U_182_1 : have hlg : Real.log (2280761753128937 / 20000000000000000 : ℝ) ≤ (-(542805695774513738577 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2280761753128937 / 20000000000000000 : ℝ) = - (2280761753128937 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2280761753128937 / 1250000000000000 : ℚ)) - (U := (150341484525486261423 / 250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2280761753128937 / 1250000000000000 : ℝ) ≤ - (150341484525486261423 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (285059777498953 / 2500000000000000 : ℝ)) (q := - (2280761753128937 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2280761753128937 / 20000000000000000 : ℚ)) + (r' := (2280761753128937 / 1250000000000000 : ℚ)) + (U := (-(542805695774513738577 / 250000000000000000000 : ℚ))) + (U' := (150341484525486261423 / 250000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (285059777498953 / 2500000000000000 : ℚ)) + (q := (2280761753128937 / 20000000000000000 : ℚ)) + (U := (-(542805695774513738577 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_2 : Uω (aρ 2) (bρ 2) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -2952,25 +2708,21 @@ lemma U_182_2 : have hlg : Real.log (557901405604871 / 5000000000000000 : ℝ) ≤ (-(10965054680357433308143 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (557901405604871 / 5000000000000000 : ℝ) = - (557901405604871 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (557901405604871 / 312500000000000 : ℚ)) - (U := (2897888925642566691857 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (557901405604871 / 312500000000000 : ℝ) ≤ - (2897888925642566691857 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1114851991796359 / 10000000000000000 : ℝ)) (q := - (557901405604871 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (557901405604871 / 5000000000000000 : ℚ)) + (r' := (557901405604871 / 312500000000000 : ℚ)) + (U := (-(10965054680357433308143 / 5000000000000000000000 : ℚ))) + (U' := (2897888925642566691857 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (1114851991796359 / 10000000000000000 : ℚ)) + (q := (557901405604871 / 5000000000000000 : ℚ)) + (U := (-(10965054680357433308143 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_3 : Uω (aρ 3) (bρ 3) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -2978,25 +2730,21 @@ lemma U_182_3 : have hlg : Real.log (2131774275828701 / 20000000000000000 : ℝ) ≤ (-(22387776461924809992277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2131774275828701 / 20000000000000000 : ℝ) = - (2131774275828701 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2131774275828701 / 1250000000000000 : ℚ)) - (U := (5338110750075190007723 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2131774275828701 / 1250000000000000 : ℝ) ≤ - (5338110750075190007723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (132802093944447 / 1250000000000000 : ℝ)) (q := - (2131774275828701 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2131774275828701 / 20000000000000000 : ℚ)) + (r' := (2131774275828701 / 1250000000000000 : ℚ)) + (U := (-(22387776461924809992277 / 10000000000000000000000 : ℚ))) + (U' := (5338110750075190007723 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (132802093944447 / 1250000000000000 : ℚ)) + (q := (2131774275828701 / 20000000000000000 : ℚ)) + (U := (-(22387776461924809992277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_4 : Uω (aρ 4) (bρ 4) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -3004,25 +2752,21 @@ lemma U_182_4 : have hlg : Real.log (1960663483694801 / 20000000000000000 : ℝ) ≤ (-(11612246722324450860351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1960663483694801 / 20000000000000000 : ℝ) = - (1960663483694801 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1960663483694801 / 1250000000000000 : ℚ)) - (U := (2250696883675549139649 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1960663483694801 / 1250000000000000 : ℝ) ≤ - (2250696883675549139649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242400035121669 / 2500000000000000 : ℝ)) (q := - (1960663483694801 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1960663483694801 / 20000000000000000 : ℚ)) + (r' := (1960663483694801 / 1250000000000000 : ℚ)) + (U := (-(11612246722324450860351 / 5000000000000000000000 : ℚ))) + (U' := (2250696883675549139649 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (242400035121669 / 2500000000000000 : ℚ)) + (q := (1960663483694801 / 20000000000000000 : ℚ)) + (U := (-(11612246722324450860351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_5 : Uω (aρ 5) (bρ 5) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -3030,25 +2774,21 @@ lemma U_182_5 : have hlg : Real.log (210304707658777 / 2500000000000000 : ℝ) ≤ (-(6188721354787161308899 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (210304707658777 / 2500000000000000 : ℝ) = - (210304707658777 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (210304707658777 / 156250000000000 : ℚ)) - (U := (742750448212838691101 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (210304707658777 / 156250000000000 : ℝ) ≤ - (742750448212838691101 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (809564237397091 / 10000000000000000 : ℝ)) (q := - (210304707658777 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (210304707658777 / 2500000000000000 : ℚ)) + (r' := (210304707658777 / 156250000000000 : ℚ)) + (U := (-(6188721354787161308899 / 2500000000000000000000 : ℚ))) + (U' := (742750448212838691101 / 2500000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (809564237397091 / 10000000000000000 : ℚ)) + (q := (210304707658777 / 2500000000000000 : ℚ)) + (U := (-(6188721354787161308899 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_6 : Uω (aρ 6) (bρ 6) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -3056,25 +2796,21 @@ lemma U_182_6 : have hlg : Real.log (151012556253559 / 2500000000000000 : ℝ) ≤ (-(14033415111008318688351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (151012556253559 / 2500000000000000 : ℝ) = - (151012556253559 / 78125000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (151012556253559 / 78125000000000 : ℚ)) - (U := (3295264396491681311649 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (151012556253559 / 78125000000000 : ℝ) ≤ - (3295264396491681311649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (502467401295347 / 10000000000000000 : ℝ)) (q := - (151012556253559 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (151012556253559 / 2500000000000000 : ℚ)) + (r' := (151012556253559 / 78125000000000 : ℚ)) + (U := (-(14033415111008318688351 / 5000000000000000000000 : ℚ))) + (U' := (3295264396491681311649 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1928031777949 / 16000000000000 : ℚ)) + (s := (502467401295347 / 10000000000000000 : ℚ)) + (q := (151012556253559 / 2500000000000000 : ℚ)) + (U := (-(14033415111008318688351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_182_7 : Uω (aρ 7) (bρ 7) (1928031777949 / 16000000000000 : ℝ) ≤ @@ -3216,25 +2952,21 @@ lemma U_183_1 : have hlg : Real.log (2308793126527319 / 20000000000000000 : ℝ) ≤ (-(431801468111400782417 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2308793126527319 / 20000000000000000 : ℝ) = - (2308793126527319 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2308793126527319 / 1250000000000000 : ℚ)) - (U := (122716276128599217583 / 200000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2308793126527319 / 1250000000000000 : ℝ) ≤ - (122716276128599217583 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1154256517902319 / 10000000000000000 : ℝ)) (q := - (2308793126527319 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2308793126527319 / 20000000000000000 : ℚ)) + (r' := (2308793126527319 / 1250000000000000 : ℚ)) + (U := (-(431801468111400782417 / 200000000000000000000 : ℚ))) + (U' := (122716276128599217583 / 200000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (1154256517902319 / 10000000000000000 : ℚ)) + (q := (2308793126527319 / 20000000000000000 : ℚ)) + (U := (-(431801468111400782417 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_2 : Uω (aρ 2) (bρ 2) (121903382671 / 1000000000000 : ℝ) ≤ @@ -3242,25 +2974,21 @@ lemma U_183_2 : have hlg : Real.log (2259657160477287 / 20000000000000000 : ℝ) ≤ (-(10902595848206565310453 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2259657160477287 / 20000000000000000 : ℝ) = - (2259657160477287 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2259657160477287 / 1250000000000000 : ℚ)) - (U := (2960347757793434689547 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2259657160477287 / 1250000000000000 : ℝ) ≤ - (2960347757793434689547 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1128889564362287 / 10000000000000000 : ℝ)) (q := - (2259657160477287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2259657160477287 / 20000000000000000 : ℚ)) + (r' := (2259657160477287 / 1250000000000000 : ℚ)) + (U := (-(10902595848206565310453 / 5000000000000000000000 : ℚ))) + (U' := (2960347757793434689547 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (1128889564362287 / 10000000000000000 : ℚ)) + (q := (2259657160477287 / 20000000000000000 : ℚ)) + (U := (-(10902595848206565310453 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_3 : Uω (aρ 3) (bρ 3) (121903382671 / 1000000000000 : ℝ) ≤ @@ -3268,25 +2996,21 @@ lemma U_183_3 : have hlg : Real.log (107994628219273 / 1000000000000000 : ℝ) ≤ (-(5564184476913954951537 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (107994628219273 / 1000000000000000 : ℝ) = - (107994628219273 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (107994628219273 / 62500000000000 : ℚ)) - (U := (1367287326086045048463 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (107994628219273 / 62500000000000 : ℝ) ≤ - (1367287326086045048463 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53826053731023 / 500000000000000 : ℝ)) (q := - (107994628219273 / 1000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (107994628219273 / 1000000000000000 : ℚ)) + (r' := (107994628219273 / 62500000000000 : ℚ)) + (U := (-(5564184476913954951537 / 2500000000000000000000 : ℚ))) + (U' := (1367287326086045048463 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (53826053731023 / 500000000000000 : ℚ)) + (q := (107994628219273 / 1000000000000000 : ℚ)) + (U := (-(5564184476913954951537 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_4 : Uω (aρ 4) (bρ 4) (121903382671 / 1000000000000 : ℝ) ≤ @@ -3294,25 +3018,21 @@ lemma U_183_4 : have hlg : Real.log (1988997162470901 / 20000000000000000 : ℝ) ≤ (-(23081016992543017206069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1988997162470901 / 20000000000000000 : ℝ) = - (1988997162470901 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1988997162470901 / 1250000000000000 : ℚ)) - (U := (4644870219456982793931 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1988997162470901 / 1250000000000000 : ℝ) ≤ - (4644870219456982793931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (983919853770901 / 10000000000000000 : ℝ)) (q := - (1988997162470901 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1988997162470901 / 20000000000000000 : ℚ)) + (r' := (1988997162470901 / 1250000000000000 : ℚ)) + (U := (-(23081016992543017206069 / 10000000000000000000000 : ℚ))) + (U' := (4644870219456982793931 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (983919853770901 / 10000000000000000 : ℚ)) + (q := (1988997162470901 / 20000000000000000 : ℚ)) + (U := (-(23081016992543017206069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_5 : Uω (aρ 5) (bρ 5) (121903382671 / 1000000000000 : ℝ) ≤ @@ -3320,25 +3040,21 @@ lemma U_183_5 : have hlg : Real.log (213942769321833 / 2500000000000000 : ℝ) ≤ (-(196666997090944639807 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (213942769321833 / 2500000000000000 : ℝ) = - (213942769321833 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (213942769321833 / 156250000000000 : ℚ)) - (U := (25140100605055360193 / 80000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (213942769321833 / 156250000000000 : ℝ) ≤ - (25140100605055360193 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12885230706401 / 156250000000000 : ℝ)) (q := - (213942769321833 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (213942769321833 / 2500000000000000 : ℚ)) + (r' := (213942769321833 / 156250000000000 : ℚ)) + (U := (-(196666997090944639807 / 80000000000000000000 : ℚ))) + (U' := (25140100605055360193 / 80000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (12885230706401 / 156250000000000 : ℚ)) + (q := (213942769321833 / 2500000000000000 : ℚ)) + (U := (-(196666997090944639807 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_6 : Uω (aρ 6) (bρ 6) (121903382671 / 1000000000000 : ℝ) ≤ @@ -3346,25 +3062,21 @@ lemma U_183_6 : have hlg : Real.log (620805937068547 / 10000000000000000 : ℝ) ≤ (-(27793218382762658487643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (620805937068547 / 10000000000000000 : ℝ) = - (620805937068547 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (620805937068547 / 312500000000000 : ℚ)) - (U := (6864140632237341512357 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (620805937068547 / 312500000000000 : ℝ) ≤ - (6864140632237341512357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260982429956047 / 5000000000000000 : ℝ)) (q := - (620805937068547 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (620805937068547 / 10000000000000000 : ℚ)) + (r' := (620805937068547 / 312500000000000 : ℚ)) + (U := (-(27793218382762658487643 / 10000000000000000000000 : ℚ))) + (U' := (6864140632237341512357 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (121903382671 / 1000000000000 : ℚ)) + (s := (260982429956047 / 5000000000000000 : ℚ)) + (q := (620805937068547 / 10000000000000000 : ℚ)) + (U := (-(27793218382762658487643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_183_7 : Uω (aρ 7) (bρ 7) (121903382671 / 1000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U15.lean b/LeanPool/Zeta5Irrational/Table/U15.lean index 5139d27628..74f3adf382 100644 --- a/LeanPool/Zeta5Irrational/Table/U15.lean +++ b/LeanPool/Zeta5Irrational/Table/U15.lean @@ -24,25 +24,21 @@ lemma U_184_1 : have hlg : Real.log (1168412208664483 / 10000000000000000 : ℝ) ≤ (-(10734696757160727232713 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1168412208664483 / 10000000000000000 : ℝ) = - (1168412208664483 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1168412208664483 / 625000000000000 : ℚ)) - (U := (3128246848839272767287 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1168412208664483 / 625000000000000 : ℝ) ≤ - (3128246848839272767287 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1168273843212091 / 10000000000000000 : ℝ)) (q := - (1168412208664483 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1168412208664483 / 10000000000000000 : ℚ)) + (r' := (1168412208664483 / 625000000000000 : ℚ)) + (U := (-(10734696757160727232713 / 5000000000000000000000 : ℚ))) + (U' := (3128246848839272767287 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (1168273843212091 / 10000000000000000 : ℚ)) + (q := (1168412208664483 / 10000000000000000 : ℚ)) + (U := (-(10734696757160727232713 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_2 : Uω (aρ 2) (bρ 2) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_184_2 : have hlg : Real.log (1143854059566267 / 10000000000000000 : ℝ) ≤ (-(10840908887218247258763 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1143854059566267 / 10000000000000000 : ℝ) = - (1143854059566267 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1143854059566267 / 625000000000000 : ℚ)) - (U := (3022034718781752741237 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1143854059566267 / 625000000000000 : ℝ) ≤ - (3022034718781752741237 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1142926557525659 / 10000000000000000 : ℝ)) (q := - (1143854059566267 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1143854059566267 / 10000000000000000 : ℚ)) + (r' := (1143854059566267 / 625000000000000 : ℚ)) + (U := (-(10840908887218247258763 / 5000000000000000000000 : ℚ))) + (U' := (3022034718781752741237 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (1142926557525659 / 10000000000000000 : ℚ)) + (q := (1143854059566267 / 10000000000000000 : ℚ)) + (U := (-(10840908887218247258763 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_3 : Uω (aρ 3) (bρ 3) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_184_3 : have hlg : Real.log (1094004261679317 / 10000000000000000 : ℝ) ≤ (-(11063702462299722560483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1094004261679317 / 10000000000000000 : ℝ) = - (1094004261679317 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1094004261679317 / 625000000000000 : ℚ)) - (U := (2799241143700277439517 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1094004261679317 / 625000000000000 : ℝ) ≤ - (2799241143700277439517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1090623068101759 / 10000000000000000 : ℝ)) (q := - (1094004261679317 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1094004261679317 / 10000000000000000 : ℚ)) + (r' := (1094004261679317 / 625000000000000 : ℚ)) + (U := (-(11063702462299722560483 / 5000000000000000000000 : ℚ))) + (U' := (2799241143700277439517 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (1090623068101759 / 10000000000000000 : ℚ)) + (q := (1094004261679317 / 10000000000000000 : ℚ)) + (U := (-(11063702462299722560483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_4 : Uω (aρ 4) (bρ 4) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_184_4 : have hlg : Real.log (2017322162972089 / 20000000000000000 : ℝ) ≤ (-(22939613024631683193711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2017322162972089 / 20000000000000000 : ℝ) = - (2017322162972089 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2017322162972089 / 1250000000000000 : ℚ)) - (U := (4786274187368316806289 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2017322162972089 / 1250000000000000 : ℝ) ≤ - (4786274187368316806289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (499115444390107 / 5000000000000000 : ℝ)) (q := - (2017322162972089 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2017322162972089 / 20000000000000000 : ℚ)) + (r' := (2017322162972089 / 1250000000000000 : ℚ)) + (U := (-(22939613024631683193711 / 10000000000000000000000 : ℚ))) + (U' := (4786274187368316806289 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (499115444390107 / 5000000000000000 : ℚ)) + (q := (2017322162972089 / 20000000000000000 : ℚ)) + (U := (-(22939613024631683193711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_5 : Uω (aρ 5) (bρ 5) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_184_5 : have hlg : Real.log (174060933478281 / 2000000000000000 : ℝ) ≤ (-(4882994056373813382959 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (174060933478281 / 2000000000000000 : ℝ) = - (174060933478281 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (174060933478281 / 125000000000000 : ℚ)) - (U := (662183386026186617041 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (174060933478281 / 125000000000000 : ℝ) ≤ - (662183386026186617041 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (167941595985187 / 2000000000000000 : ℝ)) (q := - (174060933478281 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (174060933478281 / 2000000000000000 : ℚ)) + (r' := (174060933478281 / 125000000000000 : ℚ)) + (U := (-(4882994056373813382959 / 2000000000000000000000 : ℚ))) + (U' := (662183386026186617041 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (167941595985187 / 2000000000000000 : ℚ)) + (q := (174060933478281 / 2000000000000000 : ℚ)) + (U := (-(4882994056373813382959 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_6 : Uω (aρ 6) (bρ 6) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -154,23 +134,21 @@ lemma U_184_6 : have hlg : Real.log (3186959537949 / 50000000000000 : ℝ) ≤ (-(13764778325010343518127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (3186959537949 / 50000000000000 : ℝ) = (3186959537949 / 3125000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3186959537949 / 3125000000000 : ℚ)) - (U := (98165280989656481873 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (3186959537949 / 3125000000000 : ℝ) ≤ - (98165280989656481873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21644913418509 / 400000000000000 : ℝ)) (q := - (3186959537949 / 50000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3186959537949 / 50000000000000 : ℚ)) + (r' := (3186959537949 / 3125000000000 : ℚ)) + (U := (-(13764778325010343518127 / 5000000000000000000000 : ℚ))) + (U' := (98165280989656481873 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1972876467523 / 16000000000000 : ℚ)) + (s := (21644913418509 / 400000000000000 : ℚ)) + (q := (3186959537949 / 50000000000000 : ℚ)) + (U := (-(13764778325010343518127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_184_7 : Uω (aρ 7) (bρ 7) (1972876467523 / 16000000000000 : ℝ) ≤ @@ -312,25 +290,21 @@ lemma U_185_1 : have hlg : Real.log (1182427814235847 / 10000000000000000 : ℝ) ≤ (-(4270030594954638318783 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1182427814235847 / 10000000000000000 : ℝ) = - (1182427814235847 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1182427814235847 / 625000000000000 : ℚ)) - (U := (1275146847445361681217 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1182427814235847 / 625000000000000 : ℝ) ≤ - (1275146847445361681217 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36946596526967 / 312500000000000 : ℝ)) (q := - (1182427814235847 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1182427814235847 / 10000000000000000 : ℚ)) + (r' := (1182427814235847 / 625000000000000 : ℚ)) + (U := (-(4270030594954638318783 / 2000000000000000000000 : ℚ))) + (U' := (1275146847445361681217 / 2000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (36946596526967 / 312500000000000 : ℚ)) + (q := (1182427814235847 / 10000000000000000 : ℚ)) + (U := (-(4270030594954638318783 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_2 : Uω (aρ 2) (bρ 2) (199529881231 / 1600000000000 : ℝ) ≤ @@ -338,23 +312,21 @@ lemma U_185_2 : have hlg : Real.log (7236745373357 / 62500000000000 : ℝ) ≤ (-(21559949844423918091557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (7236745373357 / 62500000000000 : ℝ) = (7236745373357 / 3906250000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7236745373357 / 3906250000000 : ℚ)) - (U := (6165937367576081908443 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7236745373357 / 3906250000000 : ℝ) ≤ - (6165937367576081908443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (115696299237549 / 1000000000000000 : ℝ)) (q := - (7236745373357 / 62500000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7236745373357 / 62500000000000 : ℚ)) + (r' := (7236745373357 / 3906250000000 : ℚ)) + (U := (-(21559949844423918091557 / 10000000000000000000000 : ℚ))) + (U' := (6165937367576081908443 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (115696299237549 / 1000000000000000 : ℚ)) + (q := (7236745373357 / 62500000000000 : ℚ)) + (U := (-(21559949844423918091557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_3 : Uω (aρ 3) (bρ 3) (199529881231 / 1600000000000 : ℝ) ≤ @@ -362,25 +334,21 @@ lemma U_185_3 : have hlg : Real.log (277015280245117 / 2500000000000000 : ℝ) ≤ (-(21999733418108408918803 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (277015280245117 / 2500000000000000 : ℝ) = - (277015280245117 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (277015280245117 / 156250000000000 : ℚ)) - (U := (5726153793891591081197 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (277015280245117 / 156250000000000 : ℝ) ≤ - (5726153793891591081197 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (552361410606093 / 5000000000000000 : ℝ)) (q := - (277015280245117 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (277015280245117 / 2500000000000000 : ℚ)) + (r' := (277015280245117 / 156250000000000 : ℚ)) + (U := (-(21999733418108408918803 / 10000000000000000000000 : ℚ))) + (U' := (5726153793891591081197 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (552361410606093 / 5000000000000000 : ℚ)) + (q := (277015280245117 / 2500000000000000 : ℚ)) + (U := (-(21999733418108408918803 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_4 : Uω (aρ 4) (bρ 4) (199529881231 / 1600000000000 : ℝ) ≤ @@ -388,25 +356,21 @@ lemma U_185_4 : have hlg : Real.log (409127770634337 / 4000000000000000 : ℝ) ≤ (-(22800221341664611774923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (409127770634337 / 4000000000000000 : ℝ) = - (409127770634337 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (409127770634337 / 250000000000000 : ℚ)) - (U := (4925665870335388225077 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (409127770634337 / 250000000000000 : ℝ) ≤ - (4925665870335388225077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (202506722697587 / 2000000000000000 : ℝ)) (q := - (409127770634337 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (409127770634337 / 4000000000000000 : ℚ)) + (r' := (409127770634337 / 250000000000000 : ℚ)) + (U := (-(22800221341664611774923 / 10000000000000000000000 : ℚ))) + (U' := (4925665870335388225077 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (202506722697587 / 2000000000000000 : ℚ)) + (q := (409127770634337 / 4000000000000000 : ℚ)) + (U := (-(22800221341664611774923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_5 : Uω (aρ 5) (bρ 5) (199529881231 / 1600000000000 : ℝ) ≤ @@ -414,25 +378,21 @@ lemma U_185_5 : have hlg : Real.log (884820586671631 / 10000000000000000 : ℝ) ≤ (-(24249554734050633766169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (884820586671631 / 10000000000000000 : ℝ) = - (884820586671631 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (884820586671631 / 625000000000000 : ℚ)) - (U := (3476332477949366233831 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (884820586671631 / 625000000000000 : ℝ) ≤ - (3476332477949366233831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53420365812157 / 625000000000000 : ℝ)) (q := - (884820586671631 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (884820586671631 / 10000000000000000 : ℚ)) + (r' := (884820586671631 / 625000000000000 : ℚ)) + (U := (-(24249554734050633766169 / 10000000000000000000000 : ℚ))) + (U' := (3476332477949366233831 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (53420365812157 / 625000000000000 : ℚ)) + (q := (884820586671631 / 10000000000000000 : ℚ)) + (U := (-(24249554734050633766169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_6 : Uω (aρ 6) (bρ 6) (199529881231 / 1600000000000 : ℝ) ≤ @@ -440,25 +400,21 @@ lemma U_185_6 : have hlg : Real.log (653825558776359 / 10000000000000000 : ℝ) ≤ (-(5454999569515305561689 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (653825558776359 / 10000000000000000 : ℝ) = - (653825558776359 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (653825558776359 / 625000000000000 : ℚ)) - (U := (90177872884694438311 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (653825558776359 / 625000000000000 : ℝ) ≤ - (90177872884694438311 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17499255385749 / 312500000000000 : ℝ)) (q := - (653825558776359 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (653825558776359 / 10000000000000000 : ℚ)) + (r' := (653825558776359 / 625000000000000 : ℚ)) + (U := (-(5454999569515305561689 / 2000000000000000000000 : ℚ))) + (U' := (90177872884694438311 / 2000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (199529881231 / 1600000000000 : ℚ)) + (s := (17499255385749 / 312500000000000 : ℚ)) + (q := (653825558776359 / 10000000000000000 : ℚ)) + (U := (-(5454999569515305561689 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_185_7 : Uω (aρ 7) (bρ 7) (199529881231 / 1600000000000 : ℝ) ≤ @@ -600,25 +556,21 @@ lemma U_186_1 : have hlg : Real.log (478577352551123 / 4000000000000000 : ℝ) ≤ (-(2654039731137533813037 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (478577352551123 / 4000000000000000 : ℝ) = - (478577352551123 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (478577352551123 / 250000000000000 : ℚ)) - (U := (811696170362466186963 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (478577352551123 / 250000000000000 : ℝ) ≤ - (811696170362466186963 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (119630825765499 / 1000000000000000 : ℝ)) (q := - (478577352551123 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (478577352551123 / 4000000000000000 : ℚ)) + (r' := (478577352551123 / 250000000000000 : ℚ)) + (U := (-(2654039731137533813037 / 1250000000000000000000 : ℚ))) + (U' := (811696170362466186963 / 1250000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (119630825765499 / 1000000000000000 : ℚ)) + (q := (478577352551123 / 4000000000000000 : ℚ)) + (U := (-(2654039731137533813037 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_2 : Uω (aρ 2) (bρ 2) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -626,25 +578,21 @@ lemma U_186_2 : have hlg : Real.log (292976047697431 / 2500000000000000 : ℝ) ≤ (-(4287910305227927671211 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (292976047697431 / 2500000000000000 : ℝ) = - (292976047697431 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (292976047697431 / 156250000000000 : ℚ)) - (U := (1257267137172072328789 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (292976047697431 / 156250000000000 : ℝ) ≤ - (1257267137172072328789 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1170998888988823 / 10000000000000000 : ℝ)) (q := - (292976047697431 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (292976047697431 / 2500000000000000 : ℚ)) + (r' := (292976047697431 / 156250000000000 : ℚ)) + (U := (-(4287910305227927671211 / 2000000000000000000000 : ℚ))) + (U' := (1257267137172072328789 / 2000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (1170998888988823 / 10000000000000000 : ℚ)) + (q := (292976047697431 / 2500000000000000 : ℚ)) + (U := (-(4287910305227927671211 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_3 : Uω (aρ 3) (bρ 3) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -652,25 +600,21 @@ lemma U_186_3 : have hlg : Real.log (280529225611763 / 2500000000000000 : ℝ) ≤ (-(21873680991519987290401 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (280529225611763 / 2500000000000000 : ℝ) = - (280529225611763 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (280529225611763 / 156250000000000 : ℚ)) - (U := (5852206220480012709599 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (280529225611763 / 156250000000000 : ℝ) ≤ - (5852206220480012709599 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1118820418653479 / 10000000000000000 : ℝ)) (q := - (280529225611763 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (280529225611763 / 2500000000000000 : ℚ)) + (r' := (280529225611763 / 156250000000000 : ℚ)) + (U := (-(21873680991519987290401 / 10000000000000000000000 : ℚ))) + (U' := (5852206220480012709599 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (1118820418653479 / 10000000000000000 : ℚ)) + (q := (280529225611763 / 2500000000000000 : ℚ)) + (U := (-(21873680991519987290401 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_4 : Uω (aρ 4) (bρ 4) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -678,25 +622,21 @@ lemma U_186_4 : have hlg : Real.log (129621723770819 / 1250000000000000 : ℝ) ≤ (-(22662784376969185616087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (129621723770819 / 1250000000000000 : ℝ) = - (129621723770819 / 78125000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (129621723770819 / 78125000000000 : ℚ)) - (U := (5063102835030814383913 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (129621723770819 / 78125000000000 : ℝ) ≤ - (5063102835030814383913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1026828375157479 / 10000000000000000 : ℝ)) (q := - (129621723770819 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (129621723770819 / 1250000000000000 : ℚ)) + (r' := (129621723770819 / 78125000000000 : ℚ)) + (U := (-(22662784376969185616087 / 10000000000000000000000 : ℚ))) + (U' := (5063102835030814383913 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (1026828375157479 / 10000000000000000 : ℚ)) + (q := (129621723770819 / 1250000000000000 : ℚ)) + (U := (-(22662784376969185616087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_5 : Uω (aρ 5) (bρ 5) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -704,24 +644,21 @@ lemma U_186_5 : have hlg : Real.log (71945580042487 / 800000000000000 : ℝ) ≤ (-(4817403452281815741051 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (71945580042487 / 800000000000000 : ℝ) = (71945580042487 / 50000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (71945580042487 / 50000000000000 : ℚ)) - (U := (727773990118184258949 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (71945580042487 / 50000000000000 : ℝ) ≤ - (727773990118184258949 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17394204304431 / 200000000000000 : ℝ)) (q := - (71945580042487 / 800000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (71945580042487 / 800000000000000 : ℚ)) + (r' := (71945580042487 / 50000000000000 : ℚ)) + (U := (-(4817403452281815741051 / 2000000000000000000000 : ℚ))) + (U' := (727773990118184258949 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (17394204304431 / 200000000000000 : ℚ)) + (q := (71945580042487 / 800000000000000 : ℚ)) + (U := (-(4817403452281815741051 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_6 : Uω (aρ 6) (bρ 6) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -729,25 +666,21 @@ lemma U_186_6 : have hlg : Real.log (670121781883347 / 10000000000000000 : ℝ) ≤ (-(27028809110634695454701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (670121781883347 / 10000000000000000 : ℝ) = - (670121781883347 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (670121781883347 / 625000000000000 : ℚ)) - (U := (697078101365304545299 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (670121781883347 / 625000000000000 : ℝ) ≤ - (697078101365304545299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (578554653066069 / 10000000000000000 : ℝ)) (q := - (670121781883347 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (670121781883347 / 10000000000000000 : ℚ)) + (r' := (670121781883347 / 625000000000000 : ℚ)) + (U := (-(27028809110634695454701 / 10000000000000000000000 : ℚ))) + (U' := (697078101365304545299 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2017721157097 / 16000000000000 : ℚ)) + (s := (578554653066069 / 10000000000000000 : ℚ)) + (q := (670121781883347 / 10000000000000000 : ℚ)) + (U := (-(27028809110634695454701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_186_7 : Uω (aρ 7) (bρ 7) (2017721157097 / 16000000000000 : ℝ) ≤ @@ -889,25 +822,21 @@ lemma U_187_1 : have hlg : Real.log (605229455712777 / 5000000000000000 : ℝ) ≤ (-(10557927693038472750489 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (605229455712777 / 5000000000000000 : ℝ) = - (605229455712777 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (605229455712777 / 312500000000000 : ℚ)) - (U := (3305015912961527249511 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (605229455712777 / 312500000000000 : ℝ) ≤ - (3305015912961527249511 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (75645334516163 / 625000000000000 : ℝ)) (q := - (605229455712777 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (605229455712777 / 5000000000000000 : ℚ)) + (r' := (605229455712777 / 312500000000000 : ℚ)) + (U := (-(10557927693038472750489 / 5000000000000000000000 : ℚ))) + (U' := (3305015912961527249511 / 5000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (75645334516163 / 625000000000000 : ℚ)) + (q := (605229455712777 / 5000000000000000 : ℚ)) + (U := (-(10557927693038472750489 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_2 : Uω (aρ 2) (bρ 2) (510035875471 / 4000000000000 : ℝ) ≤ @@ -915,25 +844,21 @@ lemma U_187_2 : have hlg : Real.log (474371544914651 / 4000000000000000 : ℝ) ≤ (-(21320587743862525124249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (474371544914651 / 4000000000000000 : ℝ) = - (474371544914651 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (474371544914651 / 250000000000000 : ℚ)) - (U := (6405299468137474875751 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (474371544914651 / 250000000000000 : ℝ) ≤ - (6405299468137474875751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (237006853298151 / 2000000000000000 : ℝ)) (q := - (474371544914651 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (474371544914651 / 4000000000000000 : ℚ)) + (r' := (474371544914651 / 250000000000000 : ℚ)) + (U := (-(21320587743862525124249 / 10000000000000000000000 : ℚ))) + (U' := (6405299468137474875751 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (237006853298151 / 2000000000000000 : ℚ)) + (q := (474371544914651 / 4000000000000000 : ℚ)) + (U := (-(21320587743862525124249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_3 : Uω (aρ 3) (bρ 3) (510035875471 / 4000000000000 : ℝ) ≤ @@ -941,25 +866,21 @@ lemma U_187_3 : have hlg : Real.log (2272343292631247 / 20000000000000000 : ℝ) ≤ (-(4349841371920999492129 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2272343292631247 / 20000000000000000 : ℝ) = - (2272343292631247 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2272343292631247 / 1250000000000000 : ℚ)) - (U := (1195336070479000507871 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2272343292631247 / 1250000000000000 : ℝ) ≤ - (1195336070479000507871 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1132915940898747 / 10000000000000000 : ℝ)) (q := - (2272343292631247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2272343292631247 / 20000000000000000 : ℚ)) + (r' := (2272343292631247 / 1250000000000000 : ℚ)) + (U := (-(4349841371920999492129 / 2000000000000000000000 : ℚ))) + (U' := (1195336070479000507871 / 2000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (1132915940898747 / 10000000000000000 : ℚ)) + (q := (2272343292631247 / 20000000000000000 : ℚ)) + (U := (-(4349841371920999492129 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_4 : Uω (aρ 4) (bρ 4) (510035875471 / 4000000000000 : ℝ) ≤ @@ -967,25 +888,21 @@ lemma U_187_4 : have hlg : Real.log (1051124336229791 / 10000000000000000 : ℝ) ≤ (-(28159058803363137901 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1051124336229791 / 10000000000000000 : ℝ) = - (1051124336229791 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1051124336229791 / 625000000000000 : ℚ)) - (U := (6498300211636862099 / 12500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1051124336229791 / 625000000000000 : ℝ) ≤ - (6498300211636862099 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (520557750896041 / 5000000000000000 : ℝ)) (q := - (1051124336229791 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1051124336229791 / 10000000000000000 : ℚ)) + (r' := (1051124336229791 / 625000000000000 : ℚ)) + (U := (-(28159058803363137901 / 12500000000000000000 : ℚ))) + (U' := (6498300211636862099 / 12500000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (520557750896041 / 5000000000000000 : ℚ)) + (q := (1051124336229791 / 10000000000000000 : ℚ)) + (U := (-(28159058803363137901 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_5 : Uω (aρ 5) (bρ 5) (510035875471 / 4000000000000 : ℝ) ≤ @@ -993,25 +910,21 @@ lemma U_187_5 : have hlg : Real.log (1827606020754751 / 20000000000000000 : ℝ) ≤ (-(11963626737311393197339 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1827606020754751 / 20000000000000000 : ℝ) = - (1827606020754751 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1827606020754751 / 1250000000000000 : ℚ)) - (U := (1899316868688606802661 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1827606020754751 / 1250000000000000 : ℝ) ≤ - (1899316868688606802661 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (884662769422251 / 10000000000000000 : ℝ)) (q := - (1827606020754751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1827606020754751 / 20000000000000000 : ℚ)) + (r' := (1827606020754751 / 1250000000000000 : ℚ)) + (U := (-(11963626737311393197339 / 5000000000000000000000 : ℚ))) + (U' := (1899316868688606802661 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (884662769422251 / 10000000000000000 : ℚ)) + (q := (1827606020754751 / 20000000000000000 : ℚ)) + (U := (-(11963626737311393197339 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_6 : Uω (aρ 6) (bρ 6) (510035875471 / 4000000000000 : ℝ) ≤ @@ -1019,25 +932,21 @@ lemma U_187_6 : have hlg : Real.log (686293409856847 / 10000000000000000 : ℝ) ≤ (-(13395175617456387926221 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (686293409856847 / 10000000000000000 : ℝ) = - (686293409856847 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (686293409856847 / 625000000000000 : ℚ)) - (U := (467767988543612073779 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (686293409856847 / 625000000000000 : ℝ) ≤ - (467767988543612073779 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (298441971760597 / 5000000000000000 : ℝ)) (q := - (686293409856847 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (686293409856847 / 10000000000000000 : ℚ)) + (r' := (686293409856847 / 625000000000000 : ℚ)) + (U := (-(13395175617456387926221 / 5000000000000000000000 : ℚ))) + (U' := (467767988543612073779 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (510035875471 / 4000000000000 : ℚ)) + (s := (298441971760597 / 5000000000000000 : ℚ)) + (q := (686293409856847 / 10000000000000000 : ℚ)) + (U := (-(13395175617456387926221 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_187_7 : Uω (aρ 7) (bρ 7) (510035875471 / 4000000000000 : ℝ) ≤ @@ -1178,25 +1087,21 @@ lemma U_188_1 : have hlg : Real.log (2476979730553741 / 20000000000000000 : ℝ) ≤ (-(2088692305103148942643 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2476979730553741 / 20000000000000000 : ℝ) = - (2476979730553741 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2476979730553741 / 1250000000000000 : ℚ)) - (U := (683896416096851057357 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2476979730553741 / 1250000000000000 : ℝ) ≤ - (683896416096851057357 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1238359328977491 / 10000000000000000 : ℝ)) (q := - (2476979730553741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2476979730553741 / 20000000000000000 : ℚ)) + (r' := (2476979730553741 / 1250000000000000 : ℚ)) + (U := (-(2088692305103148942643 / 1000000000000000000000 : ℚ))) + (U' := (683896416096851057357 / 1000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (1238359328977491 / 10000000000000000 : ℚ)) + (q := (2476979730553741 / 20000000000000000 : ℚ)) + (U := (-(2088692305103148942643 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_2 : Uω (aρ 2) (bρ 2) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1204,25 +1109,21 @@ lemma U_188_2 : have hlg : Real.log (2427954925298247 / 20000000000000000 : ℝ) ≤ (-(5271707410071795261109 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2427954925298247 / 20000000000000000 : ℝ) = - (2427954925298247 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2427954925298247 / 1250000000000000 : ℚ)) - (U := (1659764392928204738891 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2427954925298247 / 1250000000000000 : ℝ) ≤ - (1659764392928204738891 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1213103536231997 / 10000000000000000 : ℝ)) (q := - (2427954925298247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2427954925298247 / 20000000000000000 : ℚ)) + (r' := (2427954925298247 / 1250000000000000 : ℚ)) + (U := (-(5271707410071795261109 / 2500000000000000000000 : ℚ))) + (U' := (1659764392928204738891 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (1213103536231997 / 10000000000000000 : ℚ)) + (q := (2427954925298247 / 20000000000000000 : ℚ)) + (U := (-(5271707410071795261109 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_3 : Uω (aρ 3) (bρ 3) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1230,25 +1131,21 @@ lemma U_188_3 : have hlg : Real.log (582139086203921 / 5000000000000000 : ℝ) ≤ (-(4300967582928605563113 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (582139086203921 / 5000000000000000 : ℝ) = - (582139086203921 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (582139086203921 / 312500000000000 : ℚ)) - (U := (1244209859471394436887 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (582139086203921 / 312500000000000 : ℝ) ≤ - (1244209859471394436887 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (580550531049717 / 5000000000000000 : ℝ)) (q := - (582139086203921 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (582139086203921 / 5000000000000000 : ℚ)) + (r' := (582139086203921 / 312500000000000 : ℚ)) + (U := (-(4300967582928605563113 / 2000000000000000000000 : ℚ))) + (U' := (1244209859471394436887 / 2000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (580550531049717 / 5000000000000000 : ℚ)) + (q := (582139086203921 / 5000000000000000 : ℚ)) + (U := (-(4300967582928605563113 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_4 : Uω (aρ 4) (bρ 4) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1256,25 +1153,21 @@ lemma U_188_4 : have hlg : Real.log (539707293795511 / 5000000000000000 : ℝ) ≤ (-(22261662463063795315849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (539707293795511 / 5000000000000000 : ℝ) = - (539707293795511 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (539707293795511 / 312500000000000 : ℚ)) - (U := (5464224748936204684151 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (539707293795511 / 312500000000000 : ℝ) ≤ - (5464224748936204684151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (534834036765397 / 5000000000000000 : ℝ)) (q := - (539707293795511 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (539707293795511 / 5000000000000000 : ℚ)) + (r' := (539707293795511 / 312500000000000 : ℚ)) + (U := (-(22261662463063795315849 / 10000000000000000000000 : ℚ))) + (U' := (5464224748936204684151 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (534834036765397 / 5000000000000000 : ℚ)) + (q := (539707293795511 / 5000000000000000 : ℚ)) + (U := (-(22261662463063795315849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_5 : Uω (aρ 5) (bρ 5) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1282,25 +1175,21 @@ lemma U_188_5 : have hlg : Real.log (1885449873843263 / 20000000000000000 : ℝ) ≤ (-(23615658202251705360119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1885449873843263 / 20000000000000000 : ℝ) = - (1885449873843263 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1885449873843263 / 1250000000000000 : ℚ)) - (U := (4110229009748294639881 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1885449873843263 / 1250000000000000 : ℝ) ≤ - (4110229009748294639881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (914478691527013 / 10000000000000000 : ℝ)) (q := - (1885449873843263 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1885449873843263 / 20000000000000000 : ℚ)) + (r' := (1885449873843263 / 1250000000000000 : ℚ)) + (U := (-(23615658202251705360119 / 10000000000000000000000 : ℚ))) + (U' := (4110229009748294639881 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (914478691527013 / 10000000000000000 : ℚ)) + (q := (1885449873843263 / 20000000000000000 : ℚ)) + (U := (-(23615658202251705360119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_6 : Uω (aρ 6) (bρ 6) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1308,25 +1197,21 @@ lemma U_188_6 : have hlg : Real.log (1436612075902289 / 20000000000000000 : ℝ) ≤ (-(329180582000059646687 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1436612075902289 / 20000000000000000 : ℝ) = - (1436612075902289 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1436612075902289 / 1250000000000000 : ℚ)) - (U := (17393008149940353313 / 125000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1436612075902289 / 1250000000000000 : ℝ) ≤ - (17393008149940353313 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (632881268726039 / 10000000000000000 : ℝ)) (q := - (1436612075902289 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1436612075902289 / 20000000000000000 : ℚ)) + (r' := (1436612075902289 / 1250000000000000 : ℚ)) + (U := (-(329180582000059646687 / 125000000000000000000 : ℚ))) + (U' := (17393008149940353313 / 125000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1042494095729 / 8000000000000 : ℚ)) + (s := (632881268726039 / 10000000000000000 : ℚ)) + (q := (1436612075902289 / 20000000000000000 : ℚ)) + (U := (-(329180582000059646687 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_188_7 : Uω (aρ 7) (bρ 7) (1042494095729 / 8000000000000 : ℝ) ≤ @@ -1468,25 +1353,21 @@ lemma U_189_1 : have hlg : Real.log (633260342654493 / 5000000000000000 : ℝ) ≤ (-(20663115692318653602647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (633260342654493 / 5000000000000000 : ℝ) = - (633260342654493 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (633260342654493 / 625000000000000 : ℚ)) - (U := (131299716681346397353 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (633260342654493 / 625000000000000 : ℝ) ≤ - (131299716681346397353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (316598259514493 / 2500000000000000 : ℝ)) (q := - (633260342654493 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (633260342654493 / 5000000000000000 : ℚ)) + (r' := (633260342654493 / 625000000000000 : ℚ)) + (U := (-(20663115692318653602647 / 10000000000000000000000 : ℚ))) + (U' := (131299716681346397353 / 10000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (316598259514493 / 2500000000000000 : ℚ)) + (q := (633260342654493 / 5000000000000000 : ℚ)) + (U := (-(20663115692318653602647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_2 : Uω (aρ 2) (bρ 2) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1494,25 +1375,21 @@ lemma U_189_2 : have hlg : Real.log (1242025128818447 / 10000000000000000 : ℝ) ≤ (-(20858418761046195439279 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1242025128818447 / 10000000000000000 : ℝ) = - (1242025128818447 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1242025128818447 / 625000000000000 : ℚ)) - (U := (6867468450953804560721 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1242025128818447 / 625000000000000 : ℝ) ≤ - (6867468450953804560721 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (620585468793447 / 5000000000000000 : ℝ)) (q := - (1242025128818447 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1242025128818447 / 10000000000000000 : ℚ)) + (r' := (1242025128818447 / 625000000000000 : ℚ)) + (U := (-(20858418761046195439279 / 10000000000000000000000 : ℚ))) + (U' := (6867468450953804560721 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (620585468793447 / 5000000000000000 : ℚ)) + (q := (1242025128818447 / 10000000000000000 : ℚ)) + (U := (-(20858418761046195439279 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_3 : Uω (aρ 3) (bρ 3) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1520,25 +1397,21 @@ lemma U_189_3 : have hlg : Real.log (1192380983595443 / 10000000000000000 : ℝ) ≤ (-(4253265914535006292877 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1192380983595443 / 10000000000000000 : ℝ) = - (1192380983595443 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1192380983595443 / 625000000000000 : ℚ)) - (U := (1291911527864993707123 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1192380983595443 / 625000000000000 : ℝ) ≤ - (1291911527864993707123 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (594639376745443 / 5000000000000000 : ℝ)) (q := - (1192380983595443 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1192380983595443 / 10000000000000000 : ℚ)) + (r' := (1192380983595443 / 625000000000000 : ℚ)) + (U := (-(4253265914535006292877 / 2000000000000000000000 : ℚ))) + (U' := (1291911527864993707123 / 2000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (594639376745443 / 5000000000000000 : ℚ)) + (q := (1192380983595443 / 10000000000000000 : ℚ)) + (U := (-(4253265914535006292877 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_4 : Uω (aρ 4) (bρ 4) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1546,25 +1419,21 @@ lemma U_189_4 : have hlg : Real.log (2215382647996537 / 20000000000000000 : ℝ) ≤ (-(22003071308913592837197 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2215382647996537 / 20000000000000000 : ℝ) = - (2215382647996537 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2215382647996537 / 1250000000000000 : ℚ)) - (U := (5722815903086407162803 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2215382647996537 / 1250000000000000 : ℝ) ≤ - (5722815903086407162803 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1098193615361537 / 10000000000000000 : ℝ)) (q := - (2215382647996537 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2215382647996537 / 20000000000000000 : ℚ)) + (r' := (2215382647996537 / 1250000000000000 : ℚ)) + (U := (-(22003071308913592837197 / 10000000000000000000000 : ℚ))) + (U' := (5722815903086407162803 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (1098193615361537 / 10000000000000000 : ℚ)) + (q := (2215382647996537 / 20000000000000000 : ℚ)) + (U := (-(22003071308913592837197 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_5 : Uω (aρ 5) (bρ 5) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1572,25 +1441,21 @@ lemma U_189_5 : have hlg : Real.log (1943184195125871 / 20000000000000000 : ℝ) ≤ (-(11657021536339170325913 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1943184195125871 / 20000000000000000 : ℝ) = - (1943184195125871 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1943184195125871 / 1250000000000000 : ℚ)) - (U := (2205922069660829674087 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1943184195125871 / 1250000000000000 : ℝ) ≤ - (2205922069660829674087 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (944185081825871 / 10000000000000000 : ℝ)) (q := - (1943184195125871 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1943184195125871 / 20000000000000000 : ℚ)) + (r' := (1943184195125871 / 1250000000000000 : ℚ)) + (U := (-(11657021536339170325913 / 5000000000000000000000 : ℚ))) + (U' := (2205922069660829674087 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (944185081825871 / 10000000000000000 : ℚ)) + (q := (1943184195125871 / 20000000000000000 : ℚ)) + (U := (-(11657021536339170325913 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_6 : Uω (aρ 6) (bρ 6) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1598,25 +1463,21 @@ lemma U_189_6 : have hlg : Real.log (1499874063837843 / 20000000000000000 : ℝ) ≤ (-(25903511253721066404459 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1499874063837843 / 20000000000000000 : ℝ) = - (1499874063837843 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1499874063837843 / 1250000000000000 : ℚ)) - (U := (1822375958278933595541 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1499874063837843 / 1250000000000000 : ℝ) ≤ - (1822375958278933595541 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (668115325677843 / 10000000000000000 : ℝ)) (q := - (1499874063837843 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1499874063837843 / 20000000000000000 : ℚ)) + (r' := (1499874063837843 / 1250000000000000 : ℚ)) + (U := (-(25903511253721066404459 / 10000000000000000000000 : ℚ))) + (U' := (1822375958278933595541 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (266229110129 / 2000000000000 : ℚ)) + (s := (668115325677843 / 10000000000000000 : ℚ)) + (q := (1499874063837843 / 20000000000000000 : ℚ)) + (U := (-(25903511253721066404459 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_189_7 : Uω (aρ 7) (bρ 7) (266229110129 / 2000000000000 : ℝ) ≤ @@ -1759,25 +1620,21 @@ lemma U_190_1 : have hlg : Real.log (2645163915912357 / 20000000000000000 : ℝ) ≤ (-(20229992373945278136929 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2645163915912357 / 20000000000000000 : ℝ) = - (2645163915912357 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2645163915912357 / 2500000000000000 : ℚ)) - (U := (564423035054721863071 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2645163915912357 / 2500000000000000 : ℝ) ≤ - (564423035054721863071 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1322459721384857 / 10000000000000000 : ℝ)) (q := - (2645163915912357 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2645163915912357 / 20000000000000000 : ℚ)) + (r' := (2645163915912357 / 2500000000000000 : ℚ)) + (U := (-(20229992373945278136929 / 10000000000000000000000 : ℚ))) + (U' := (564423035054721863071 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (110976113009 / 800000000000 : ℚ)) + (s := (1322459721384857 / 10000000000000000 : ℚ)) + (q := (2645163915912357 / 20000000000000000 : ℚ)) + (U := (-(20229992373945278136929 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_2 : Uω (aρ 2) (bρ 2) (110976113009 / 800000000000 : ℝ) ≤ @@ -1785,25 +1642,21 @@ lemma U_190_2 : have hlg : Real.log (2596235802222861 / 20000000000000000 : ℝ) ≤ (-(20416696451517995856967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2596235802222861 / 20000000000000000 : ℝ) = - (2596235802222861 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2596235802222861 / 2500000000000000 : ℚ)) - (U := (377718957482004143033 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2596235802222861 / 2500000000000000 : ℝ) ≤ - (377718957482004143033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1297300620205361 / 10000000000000000 : ℝ)) (q := - (2596235802222861 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2596235802222861 / 20000000000000000 : ℚ)) + (r' := (2596235802222861 / 2500000000000000 : ℚ)) + (U := (-(20416696451517995856967 / 10000000000000000000000 : ℚ))) + (U' := (377718957482004143033 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (110976113009 / 800000000000 : ℚ)) + (s := (1297300620205361 / 10000000000000000 : ℚ)) + (q := (2596235802222861 / 20000000000000000 : ℚ)) + (U := (-(20416696451517995856967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_3 : Uω (aρ 3) (bρ 3) (110976113009 / 800000000000 : ℝ) ≤ @@ -1811,25 +1664,21 @@ lemma U_190_3 : have hlg : Real.log (1248576469633047 / 10000000000000000 : ℝ) ≤ (-(2080581013886745405213 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1248576469633047 / 10000000000000000 : ℝ) = - (1248576469633047 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1248576469633047 / 625000000000000 : ℚ)) - (U := (692007707313254594787 / 1000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (1248576469633047 / 625000000000000 : ℝ) ≤ - (692007707313254594787 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (622806931799297 / 5000000000000000 : ℝ)) (q := - (1248576469633047 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1248576469633047 / 10000000000000000 : ℚ)) + (r' := (1248576469633047 / 625000000000000 : ℚ)) + (U := (-(2080581013886745405213 / 1000000000000000000000 : ℚ))) + (U' := (692007707313254594787 / 1000000000000000000000 : ℚ)) + 4 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (110976113009 / 800000000000 : ℚ)) + (s := (622806931799297 / 5000000000000000 : ℚ)) + (q := (1248576469633047 / 10000000000000000 : ℚ)) + (U := (-(2080581013886745405213 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_4 : Uω (aρ 4) (bρ 4) (110976113009 / 800000000000 : ℝ) ≤ @@ -1837,25 +1686,21 @@ lemma U_190_4 : have hlg : Real.log (1164208255837901 / 10000000000000000 : ℝ) ≤ (-(21505438446981235916047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1164208255837901 / 10000000000000000 : ℝ) = - (1164208255837901 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1164208255837901 / 625000000000000 : ℚ)) - (U := (6220448765018764083953 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1164208255837901 / 625000000000000 : ℝ) ≤ - (6220448765018764083953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (577585808536651 / 5000000000000000 : ℝ)) (q := - (1164208255837901 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1164208255837901 / 10000000000000000 : ℚ)) + (r' := (1164208255837901 / 625000000000000 : ℚ)) + (U := (-(21505438446981235916047 / 10000000000000000000000 : ℚ))) + (U' := (6220448765018764083953 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (110976113009 / 800000000000 : ℚ)) + (s := (577585808536651 / 5000000000000000 : ℚ)) + (q := (1164208255837901 / 10000000000000000 : ℚ)) + (U := (-(21505438446981235916047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_5 : Uω (aρ 5) (bρ 5) (110976113009 / 800000000000 : ℝ) ≤ @@ -1863,25 +1708,21 @@ lemma U_190_5 : have hlg : Real.log (2058363123946183 / 20000000000000000 : ℝ) ≤ (-(4547642411201558481751 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2058363123946183 / 20000000000000000 : ℝ) = - (2058363123946183 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2058363123946183 / 1250000000000000 : ℚ)) - (U := (997535031198441518249 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2058363123946183 / 1250000000000000 : ℝ) ≤ - (997535031198441518249 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1003308148678683 / 10000000000000000 : ℝ)) (q := - (2058363123946183 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2058363123946183 / 20000000000000000 : ℚ)) + (r' := (2058363123946183 / 1250000000000000 : ℚ)) + (U := (-(4547642411201558481751 / 2000000000000000000000 : ℚ))) + (U' := (997535031198441518249 / 2000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (110976113009 / 800000000000 : ℚ)) + (s := (1003308148678683 / 10000000000000000 : ℚ)) + (q := (2058363123946183 / 20000000000000000 : ℚ)) + (U := (-(4547642411201558481751 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_6 : Uω (aρ 6) (bρ 6) (110976113009 / 800000000000 : ℝ) ≤ @@ -1889,25 +1730,21 @@ lemma U_190_6 : have hlg : Real.log (406136007713679 / 5000000000000000 : ℝ) ≤ (-(25105050925041415667209 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (406136007713679 / 5000000000000000 : ℝ) = - (406136007713679 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (406136007713679 / 312500000000000 : ℚ)) - (U := (2620836286958584332791 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (406136007713679 / 312500000000000 : ℝ) ≤ - (2620836286958584332791 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46045589420451 / 625000000000000 : ℝ)) (q := - (406136007713679 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (406136007713679 / 5000000000000000 : ℚ)) + (r' := (406136007713679 / 312500000000000 : ℚ)) + (U := (-(25105050925041415667209 / 10000000000000000000000 : ℚ))) + (U' := (2620836286958584332791 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (110976113009 / 800000000000 : ℚ)) + (s := (46045589420451 / 625000000000000 : ℚ)) + (q := (406136007713679 / 5000000000000000 : ℚ)) + (U := (-(25105050925041415667209 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_190_7 : Uω (aρ 7) (bρ 7) (110976113009 / 800000000000 : ℝ) ≤ @@ -2050,25 +1887,21 @@ lemma U_191_1 : have hlg : Real.log (275728558105041 / 2000000000000000 : ℝ) ≤ (-(19814855621105804326481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (275728558105041 / 2000000000000000 : ℝ) = - (275728558105041 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (275728558105041 / 250000000000000 : ℚ)) - (U := (979559787894195673519 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (275728558105041 / 250000000000000 : ℝ) ≤ - (979559787894195673519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (137852552455541 / 1000000000000000 : ℝ)) (q := - (275728558105041 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (275728558105041 / 2000000000000000 : ℚ)) + (r' := (275728558105041 / 250000000000000 : ℚ)) + (U := (-(19814855621105804326481 / 10000000000000000000000 : ℚ))) + (U' := (979559787894195673519 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (72162863729 / 500000000000 : ℚ)) + (s := (137852552455541 / 1000000000000000 : ℚ)) + (q := (275728558105041 / 2000000000000000 : ℚ)) + (U := (-(19814855621105804326481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_2 : Uω (aρ 2) (bρ 2) (72162863729 / 500000000000 : ℝ) ≤ @@ -2076,25 +1909,21 @@ lemma U_191_2 : have hlg : Real.log (2708415227817231 / 20000000000000000 : ℝ) ≤ (-(19993685957203362780097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2708415227817231 / 20000000000000000 : ℝ) = - (2708415227817231 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2708415227817231 / 2500000000000000 : ℚ)) - (U := (800729451796637219903 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2708415227817231 / 2500000000000000 : ℝ) ≤ - (800729451796637219903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1353424183832231 / 10000000000000000 : ℝ)) (q := - (2708415227817231 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2708415227817231 / 20000000000000000 : ℚ)) + (r' := (2708415227817231 / 2500000000000000 : ℚ)) + (U := (-(19993685957203362780097 / 10000000000000000000000 : ℚ))) + (U' := (800729451796637219903 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (72162863729 / 500000000000 : ℚ)) + (s := (1353424183832231 / 10000000000000000 : ℚ)) + (q := (2708415227817231 / 20000000000000000 : ℚ)) + (U := (-(19993685957203362780097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_3 : Uω (aρ 3) (bρ 3) (72162863729 / 500000000000 : ℝ) ≤ @@ -2102,25 +1931,21 @@ lemma U_191_3 : have hlg : Real.log (521903960994751 / 4000000000000000 : ℝ) ≤ (-(10182830255675675289117 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (521903960994751 / 4000000000000000 : ℝ) = - (521903960994751 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (521903960994751 / 500000000000000 : ℚ)) - (U := (214377448824324710883 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (521903960994751 / 500000000000000 : ℝ) ≤ - (214377448824324710883 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260384973467751 / 2000000000000000 : ℝ)) (q := - (521903960994751 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (521903960994751 / 4000000000000000 : ℚ)) + (r' := (521903960994751 / 500000000000000 : ℚ)) + (U := (-(10182830255675675289117 / 5000000000000000000000 : ℚ))) + (U' := (214377448824324710883 / 5000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (72162863729 / 500000000000 : ℚ)) + (s := (260384973467751 / 2000000000000000 : ℚ)) + (q := (521903960994751 / 4000000000000000 : ℚ)) + (U := (-(10182830255675675289117 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_4 : Uω (aρ 4) (bρ 4) (72162863729 / 500000000000 : ℝ) ≤ @@ -2128,25 +1953,21 @@ lemma U_191_4 : have hlg : Real.log (2441364382080019 / 20000000000000000 : ℝ) ≤ (-(2628969020630553055031 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2441364382080019 / 20000000000000000 : ℝ) = - (2441364382080019 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2441364382080019 / 1250000000000000 : ℚ)) - (U := (836766880869446944969 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2441364382080019 / 1250000000000000 : ℝ) ≤ - (836766880869446944969 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1212063625510019 / 10000000000000000 : ℝ)) (q := - (2441364382080019 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2441364382080019 / 20000000000000000 : ℚ)) + (r' := (2441364382080019 / 1250000000000000 : ℚ)) + (U := (-(2628969020630553055031 / 1250000000000000000000 : ℚ))) + (U' := (836766880869446944969 / 1250000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (72162863729 / 500000000000 : ℚ)) + (s := (1212063625510019 / 10000000000000000 : ℚ)) + (q := (2441364382080019 / 20000000000000000 : ℚ)) + (U := (-(2628969020630553055031 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_5 : Uω (aρ 5) (bρ 5) (72162863729 / 500000000000 : ℝ) ≤ @@ -2154,25 +1975,21 @@ lemma U_191_5 : have hlg : Real.log (2173209482836907 / 20000000000000000 : ℝ) ≤ (-(22195271732922818939507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2173209482836907 / 20000000000000000 : ℝ) = - (2173209482836907 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2173209482836907 / 1250000000000000 : ℚ)) - (U := (5530615479077181060493 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2173209482836907 / 1250000000000000 : ℝ) ≤ - (5530615479077181060493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1062098645601907 / 10000000000000000 : ℝ)) (q := - (2173209482836907 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2173209482836907 / 20000000000000000 : ℚ)) + (r' := (2173209482836907 / 1250000000000000 : ℚ)) + (U := (-(22195271732922818939507 / 10000000000000000000000 : ℚ))) + (U' := (5530615479077181060493 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (72162863729 / 500000000000 : ℚ)) + (s := (1062098645601907 / 10000000000000000 : ℚ)) + (q := (2173209482836907 / 20000000000000000 : ℚ)) + (U := (-(22195271732922818939507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_6 : Uω (aρ 6) (bρ 6) (72162863729 / 500000000000 : ℝ) ≤ @@ -2180,25 +1997,21 @@ lemma U_191_6 : have hlg : Real.log (349453517251867 / 4000000000000000 : ℝ) ≤ (-(24376790840821149583193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (349453517251867 / 4000000000000000 : ℝ) = - (349453517251867 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (349453517251867 / 250000000000000 : ℚ)) - (U := (3349096371178850416807 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (349453517251867 / 250000000000000 : ℝ) ≤ - (3349096371178850416807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160679424832867 / 2000000000000000 : ℝ)) (q := - (349453517251867 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (349453517251867 / 4000000000000000 : ℚ)) + (r' := (349453517251867 / 250000000000000 : ℚ)) + (U := (-(24376790840821149583193 / 10000000000000000000000 : ℚ))) + (U' := (3349096371178850416807 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (72162863729 / 500000000000 : ℚ)) + (s := (160679424832867 / 2000000000000000 : ℚ)) + (q := (349453517251867 / 4000000000000000 : ℚ)) + (U := (-(24376790840821149583193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_191_7 : Uω (aρ 7) (bρ 7) (72162863729 / 500000000000 : ℝ) ≤ @@ -2341,25 +2154,21 @@ lemma U_192_1 : have hlg : Real.log (5585552167037221 / 40000000000000000 : ℝ) ≤ (-(787478463849348170387 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5585552167037221 / 40000000000000000 : ℝ) = - (5585552167037221 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5585552167037221 / 5000000000000000 : ℚ)) - (U := (44298152510651829613 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5585552167037221 / 5000000000000000 : ℝ) ≤ - (44298152510651829613 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1396272266001423 / 10000000000000000 : ℝ)) (q := - (5585552167037221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5585552167037221 / 40000000000000000 : ℚ)) + (r' := (5585552167037221 / 5000000000000000 : ℚ)) + (U := (-(787478463849348170387 / 400000000000000000000 : ℚ))) + (U' := (44298152510651829613 / 400000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (1396272266001423 / 10000000000000000 : ℚ)) + (q := (5585552167037221 / 40000000000000000 : ℚ)) + (U := (-(787478463849348170387 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_2 : Uω (aρ 2) (bρ 2) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2367,25 +2176,21 @@ lemma U_192_2 : have hlg : Real.log (5487846051701767 / 40000000000000000 : ℝ) ≤ (-(19863436151075893595487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5487846051701767 / 40000000000000000 : ℝ) = - (5487846051701767 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5487846051701767 / 5000000000000000 : ℚ)) - (U := (930979257924106404513 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5487846051701767 / 5000000000000000 : ℝ) ≤ - (930979257924106404513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85699263802731 / 625000000000000 : ℝ)) (q := - (5487846051701767 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5487846051701767 / 40000000000000000 : ℚ)) + (r' := (5487846051701767 / 5000000000000000 : ℚ)) + (U := (-(19863436151075893595487 / 10000000000000000000000 : ℚ))) + (U' := (930979257924106404513 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (85699263802731 / 625000000000000 : ℚ)) + (q := (5487846051701767 / 40000000000000000 : ℚ)) + (U := (-(19863436151075893595487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_3 : Uω (aρ 3) (bρ 3) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2393,25 +2198,21 @@ lemma U_192_3 : have hlg : Real.log (5290167124837241 / 40000000000000000 : ℝ) ≤ (-(4046059230732191981441 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5290167124837241 / 40000000000000000 : ℝ) = - (5290167124837241 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5290167124837241 / 5000000000000000 : ℚ)) - (U := (112823851067808018559 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5290167124837241 / 5000000000000000 : ℝ) ≤ - (112823851067808018559 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1319744863761433 / 10000000000000000 : ℝ)) (q := - (5290167124837241 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5290167124837241 / 40000000000000000 : ℚ)) + (r' := (5290167124837241 / 5000000000000000 : ℚ)) + (U := (-(4046059230732191981441 / 2000000000000000000000 : ℚ))) + (U' := (112823851067808018559 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (1319744863761433 / 10000000000000000 : ℚ)) + (q := (5290167124837241 / 40000000000000000 : ℚ)) + (U := (-(4046059230732191981441 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_4 : Uω (aρ 4) (bρ 4) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2419,25 +2220,21 @@ lemma U_192_4 : have hlg : Real.log (4954201155424141 / 40000000000000000 : ℝ) ≤ (-(20886435181837476410703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4954201155424141 / 40000000000000000 : ℝ) = - (4954201155424141 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4954201155424141 / 2500000000000000 : ℚ)) - (U := (6839452030162523589297 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4954201155424141 / 2500000000000000 : ℝ) ≤ - (6839452030162523589297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1230056060119883 / 10000000000000000 : ℝ)) (q := - (4954201155424141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4954201155424141 / 40000000000000000 : ℚ)) + (r' := (4954201155424141 / 2500000000000000 : ℚ)) + (U := (-(20886435181837476410703 / 10000000000000000000000 : ℚ))) + (U' := (6839452030162523589297 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (1230056060119883 / 10000000000000000 : ℚ)) + (q := (4954201155424141 / 40000000000000000 : ℚ)) + (U := (-(20886435181837476410703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_5 : Uω (aρ 5) (bρ 5) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2445,25 +2242,21 @@ lemma U_192_5 : have hlg : Real.log (883800825444237 / 8000000000000000 : ℝ) ≤ (-(22029650929542333847147 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (883800825444237 / 8000000000000000 : ℝ) = - (883800825444237 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (883800825444237 / 500000000000000 : ℚ)) - (U := (5696236282457666152853 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (883800825444237 / 500000000000000 : ℝ) ≤ - (5696236282457666152853 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216129493070681 / 2000000000000000 : ℝ)) (q := - (883800825444237 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (883800825444237 / 8000000000000000 : ℚ)) + (r' := (883800825444237 / 500000000000000 : ℚ)) + (U := (-(22029650929542333847147 / 10000000000000000000000 : ℚ))) + (U' := (5696236282457666152853 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (216129493070681 / 2000000000000000 : ℚ)) + (q := (883800825444237 / 8000000000000000 : ℚ)) + (U := (-(22029650929542333847147 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_6 : Uω (aρ 6) (bρ 6) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2471,25 +2264,21 @@ lemma U_192_6 : have hlg : Real.log (3571569920567127 / 40000000000000000 : ℝ) ≤ (-(19326993602285207127 / 8000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3571569920567127 / 40000000000000000 : ℝ) = - (3571569920567127 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3571569920567127 / 2500000000000000 : ℚ)) - (U := (2853716167314792873 / 8000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3571569920567127 / 2500000000000000 : ℝ) ≤ - (2853716167314792873 / 8000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103021342145797 / 1250000000000000 : ℝ)) (q := - (3571569920567127 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3571569920567127 / 40000000000000000 : ℚ)) + (r' := (3571569920567127 / 2500000000000000 : ℚ)) + (U := (-(19326993602285207127 / 8000000000000000000 : ℚ))) + (U' := (2853716167314792873 / 8000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (103021342145797 / 1250000000000000 : ℚ)) + (q := (3571569920567127 / 40000000000000000 : ℚ)) + (U := (-(19326993602285207127 / 8000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_7 : Uω (aρ 7) (bρ 7) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2497,25 +2286,21 @@ lemma U_192_7 : have hlg : Real.log (359521826035421 / 8000000000000000 : ℝ) ≤ (-(969506853701683875103 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (359521826035421 / 8000000000000000 : ℝ) = - (359521826035421 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (359521826035421 / 250000000000000 : ℚ)) - (U := (113535615517066124897 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (359521826035421 / 250000000000000 : ℝ) ≤ - (113535615517066124897 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (32170344546273 / 2000000000000000 : ℝ)) (q := - (359521826035421 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (359521826035421 / 8000000000000000 : ℚ)) + (r' := (359521826035421 / 250000000000000 : ℚ)) + (U := (-(969506853701683875103 / 312500000000000000000 : ℚ))) + (U' := (113535615517066124897 / 312500000000000000000 : ℚ)) + 5 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4675203313927 / 32000000000000 : ℚ)) + (s := (32170344546273 / 2000000000000000 : ℚ)) + (q := (359521826035421 / 8000000000000000 : ℚ)) + (U := (-(969506853701683875103 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_192_8 : Uω (aρ 8) (bρ 8) (4675203313927 / 32000000000000 : ℝ) ≤ @@ -2651,25 +2436,21 @@ lemma U_193_1 : have hlg : Real.log (282826651118107 / 2000000000000000 : ℝ) ≤ (-(19560682890171164556221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (282826651118107 / 2000000000000000 : ℝ) = - (282826651118107 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (282826651118107 / 250000000000000 : ℚ)) - (U := (1233732518828835443779 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (282826651118107 / 250000000000000 : ℝ) ≤ - (1233732518828835443779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (282803786528339 / 2000000000000000 : ℝ)) (q := - (282826651118107 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (282826651118107 / 2000000000000000 : ℚ)) + (r' := (282826651118107 / 250000000000000 : ℚ)) + (U := (-(19560682890171164556221 / 10000000000000000000000 : ℚ))) + (U' := (1233732518828835443779 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (282803786528339 / 2000000000000000 : ℚ)) + (q := (282826651118107 / 2000000000000000 : ℚ)) + (U := (-(19560682890171164556221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_2 : Uω (aρ 2) (bρ 2) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2677,25 +2458,21 @@ lemma U_193_2 : have hlg : Real.log (1389715152769981 / 10000000000000000 : ℝ) ≤ (-(394697258427317257959 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1389715152769981 / 10000000000000000 : ℝ) = - (1389715152769981 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1389715152769981 / 1250000000000000 : ℚ)) - (U := (21191049752682742041 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1389715152769981 / 1250000000000000 : ℝ) ≤ - (21191049752682742041 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1388951739510587 / 10000000000000000 : ℝ)) (q := - (1389715152769981 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1389715152769981 / 10000000000000000 : ℚ)) + (r' := (1389715152769981 / 1250000000000000 : ℚ)) + (U := (-(394697258427317257959 / 200000000000000000000 : ℚ))) + (U' := (21191049752682742041 / 200000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (1388951739510587 / 10000000000000000 : ℚ)) + (q := (1389715152769981 / 10000000000000000 : ℚ)) + (U := (-(394697258427317257959 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_3 : Uω (aρ 3) (bρ 3) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2703,25 +2480,21 @@ lemma U_193_3 : have hlg : Real.log (335080661610237 / 2500000000000000 : ℝ) ≤ (-(2512093407885480065093 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (335080661610237 / 2500000000000000 : ℝ) = - (335080661610237 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (335080661610237 / 312500000000000 : ℚ)) - (U := (87208518239519934907 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (335080661610237 / 312500000000000 : ℝ) ≤ - (87208518239519934907 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1337562833202521 / 10000000000000000 : ℝ)) (q := - (335080661610237 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (335080661610237 / 2500000000000000 : ℚ)) + (r' := (335080661610237 / 312500000000000 : ℚ)) + (U := (-(2512093407885480065093 / 1250000000000000000000 : ℚ))) + (U' := (87208518239519934907 / 1250000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (1337562833202521 / 10000000000000000 : ℚ)) + (q := (335080661610237 / 2500000000000000 : ℚ)) + (U := (-(2512093407885480065093 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_4 : Uω (aρ 4) (bρ 4) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2729,25 +2502,21 @@ lemma U_193_4 : have hlg : Real.log (1256414826444487 / 10000000000000000 : ℝ) ≤ (-(10371614014328306359131 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1256414826444487 / 10000000000000000 : ℝ) = - (1256414826444487 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1256414826444487 / 1250000000000000 : ℚ)) - (U := (25593690171693640869 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1256414826444487 / 1250000000000000 : ℝ) ≤ - (25593690171693640869 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1248041374274599 / 10000000000000000 : ℝ)) (q := - (1256414826444487 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1256414826444487 / 10000000000000000 : ℚ)) + (r' := (1256414826444487 / 1250000000000000 : ℚ)) + (U := (-(10371614014328306359131 / 5000000000000000000000 : ℚ))) + (U' := (25593690171693640869 / 5000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (1248041374274599 / 10000000000000000 : ℚ)) + (q := (1256414826444487 / 10000000000000000 : ℚ)) + (U := (-(10371614014328306359131 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_5 : Uω (aρ 5) (bρ 5) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2755,25 +2524,21 @@ lemma U_193_5 : have hlg : Real.log (1122884031566689 / 10000000000000000 : ℝ) ≤ (-(5466711720418222399723 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1122884031566689 / 10000000000000000 : ℝ) = - (1122884031566689 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1122884031566689 / 625000000000000 : ℚ)) - (U := (1464760082581777600277 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1122884031566689 / 625000000000000 : ℝ) ≤ - (1464760082581777600277 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1099169703854003 / 10000000000000000 : ℝ)) (q := - (1122884031566689 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1122884031566689 / 10000000000000000 : ℚ)) + (r' := (1122884031566689 / 625000000000000 : ℚ)) + (U := (-(5466711720418222399723 / 2500000000000000000000 : ℚ))) + (U' := (1464760082581777600277 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (1099169703854003 / 10000000000000000 : ℚ)) + (q := (1122884031566689 / 10000000000000000 : ℚ)) + (U := (-(5466711720418222399723 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_6 : Uω (aρ 6) (bρ 6) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2781,25 +2546,21 @@ lemma U_193_6 : have hlg : Real.log (456041051278531 / 5000000000000000 : ℝ) ≤ (-(23946103601804326428943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (456041051278531 / 5000000000000000 : ℝ) = - (456041051278531 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (456041051278531 / 312500000000000 : ℚ)) - (U := (3779783610195673571057 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (456041051278531 / 312500000000000 : ℝ) ≤ - (3779783610195673571057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (844806220974749 / 10000000000000000 : ℝ)) (q := - (456041051278531 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (456041051278531 / 5000000000000000 : ℚ)) + (r' := (456041051278531 / 312500000000000 : ℚ)) + (U := (-(23946103601804326428943 / 10000000000000000000000 : ℚ))) + (U' := (3779783610195673571057 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (844806220974749 / 10000000000000000 : ℚ)) + (q := (456041051278531 / 5000000000000000 : ℚ)) + (U := (-(23946103601804326428943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_7 : Uω (aρ 7) (bρ 7) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2807,24 +2568,21 @@ lemma U_193_7 : have hlg : Real.log (39382206101409 / 800000000000000 : ℝ) ≤ (-(752824408466949677751 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (39382206101409 / 800000000000000 : ℝ) = (39382206101409 / 25000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39382206101409 / 25000000000000 : ℚ)) - (U := (113609566908050322249 / 250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (39382206101409 / 25000000000000 : ℝ) ≤ - (113609566908050322249 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4577170983117 / 200000000000000 : ℝ)) (q := - (39382206101409 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39382206101409 / 800000000000000 : ℚ)) + (r' := (39382206101409 / 25000000000000 : ℚ)) + (U := (-(752824408466949677751 / 250000000000000000000 : ℚ))) + (U' := (113609566908050322249 / 250000000000000000000 : ℚ)) + 5 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2365991674599 / 16000000000000 : ℚ)) + (s := (4577170983117 / 200000000000000 : ℚ)) + (q := (39382206101409 / 800000000000000 : ℚ)) + (U := (-(752824408466949677751 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_193_8 : Uω (aρ 8) (bρ 8) (2365991674599 / 16000000000000 : ℝ) ≤ @@ -2962,25 +2720,21 @@ lemma U_194_1 : have hlg : Real.log (5727513733638853 / 40000000000000000 : ℝ) ≤ (-(3887195840299343045543 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5727513733638853 / 40000000000000000 : ℝ) = - (5727513733638853 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5727513733638853 / 5000000000000000 : ℚ)) - (U := (271687241500656954457 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5727513733638853 / 5000000000000000 : ℝ) ≤ - (271687241500656954457 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (178970690907233 / 1250000000000000 : ℝ)) (q := - (5727513733638853 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5727513733638853 / 40000000000000000 : ℚ)) + (r' := (5727513733638853 / 5000000000000000 : ℚ)) + (U := (-(3887195840299343045543 / 2000000000000000000000 : ℚ))) + (U' := (271687241500656954457 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (178970690907233 / 1250000000000000 : ℚ)) + (q := (5727513733638853 / 40000000000000000 : ℚ)) + (U := (-(3887195840299343045543 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_2 : Uω (aρ 2) (bρ 2) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -2988,25 +2742,21 @@ lemma U_194_2 : have hlg : Real.log (1125974834608363 / 8000000000000000 : ℝ) ≤ (-(1960792360803155468861 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1125974834608363 / 8000000000000000 : ℝ) = - (1125974834608363 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1125974834608363 / 1000000000000000 : ℚ)) - (U := (118649180096844531139 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1125974834608363 / 1000000000000000 : ℝ) ≤ - (118649180096844531139 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (281342951893869 / 2000000000000000 : ℝ)) (q := - (1125974834608363 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1125974834608363 / 8000000000000000 : ℚ)) + (r' := (1125974834608363 / 1000000000000000 : ℚ)) + (U := (-(1960792360803155468861 / 1000000000000000000000 : ℚ))) + (U' := (118649180096844531139 / 1000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (281342951893869 / 2000000000000000 : ℚ)) + (q := (1125974834608363 / 8000000000000000 : ℚ)) + (U := (-(1960792360803155468861 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_3 : Uω (aρ 3) (bρ 3) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3014,25 +2764,21 @@ lemma U_194_3 : have hlg : Real.log (5432410152608797 / 40000000000000000 : ℝ) ≤ (-(19964965591887264809447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5432410152608797 / 40000000000000000 : ℝ) = - (5432410152608797 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5432410152608797 / 5000000000000000 : ℚ)) - (U := (829449817112735190553 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5432410152608797 / 5000000000000000 : ℝ) ≤ - (829449817112735190553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (338844713900709 / 2500000000000000 : ℝ)) (q := - (5432410152608797 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5432410152608797 / 40000000000000000 : ℚ)) + (r' := (5432410152608797 / 5000000000000000 : ℚ)) + (U := (-(19964965591887264809447 / 10000000000000000000000 : ℚ))) + (U' := (829449817112735190553 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (338844713900709 / 2500000000000000 : ℚ)) + (q := (5432410152608797 / 40000000000000000 : ℚ)) + (U := (-(19964965591887264809447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_4 : Uω (aρ 4) (bρ 4) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3040,25 +2786,21 @@ lemma U_194_4 : have hlg : Real.log (5097103822148609 / 40000000000000000 : ℝ) ≤ (-(20602069529176842578973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5097103822148609 / 40000000000000000 : ℝ) = - (5097103822148609 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5097103822148609 / 5000000000000000 : ℚ)) - (U := (192345879823157421027 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5097103822148609 / 5000000000000000 : ℝ) ≤ - (192345879823157421027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (633009935718871 / 5000000000000000 : ℝ)) (q := - (5097103822148609 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5097103822148609 / 40000000000000000 : ℚ)) + (r' := (5097103822148609 / 5000000000000000 : ℚ)) + (U := (-(20602069529176842578973 / 10000000000000000000000 : ℚ))) + (U' := (192345879823157421027 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (633009935718871 / 5000000000000000 : ℚ)) + (q := (5097103822148609 / 40000000000000000 : ℚ)) + (U := (-(20602069529176842578973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_5 : Uω (aρ 5) (bρ 5) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3066,25 +2808,21 @@ lemma U_194_5 : have hlg : Real.log (4564017605877021 / 40000000000000000 : ℝ) ≤ (-(21706761635276424051639 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4564017605877021 / 40000000000000000 : ℝ) = - (4564017605877021 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4564017605877021 / 2500000000000000 : ℚ)) - (U := (6019125576723575948361 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4564017605877021 / 2500000000000000 : ℝ) ≤ - (6019125576723575948361 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (279416670659237 / 2500000000000000 : ℝ)) (q := - (4564017605877021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4564017605877021 / 40000000000000000 : ℚ)) + (r' := (4564017605877021 / 2500000000000000 : ℚ)) + (U := (-(21706761635276424051639 / 10000000000000000000000 : ℚ))) + (U' := (6019125576723575948361 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (279416670659237 / 2500000000000000 : ℚ)) + (q := (4564017605877021 / 40000000000000000 : ℚ)) + (U := (-(21706761635276424051639 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_6 : Uω (aρ 6) (bρ 6) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3092,25 +2830,21 @@ lemma U_194_6 : have hlg : Real.log (3724830405755021 / 40000000000000000 : ℝ) ≤ (-(4747716261870926325079 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3724830405755021 / 40000000000000000 : ℝ) = - (3724830405755021 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3724830405755021 / 2500000000000000 : ℚ)) - (U := (797461180529073674921 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3724830405755021 / 2500000000000000 : ℝ) ≤ - (797461180529073674921 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216328364428987 / 2500000000000000 : ℝ)) (q := - (3724830405755021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3724830405755021 / 40000000000000000 : ℚ)) + (r' := (3724830405755021 / 2500000000000000 : ℚ)) + (U := (-(4747716261870926325079 / 2000000000000000000000 : ℚ))) + (U' := (797461180529073674921 / 2000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (216328364428987 / 2500000000000000 : ℚ)) + (q := (3724830405755021 / 40000000000000000 : ℚ)) + (U := (-(4747716261870926325079 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_7 : Uω (aρ 7) (bρ 7) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3118,25 +2852,21 @@ lemma U_194_7 : have hlg : Real.log (2110827096636869 / 40000000000000000 : ℝ) ≤ (-(14708997966031985063453 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (2110827096636869 / 40000000000000000 : ℝ) = - (2110827096636869 / 1250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2110827096636869 / 1250000000000000 : ℚ)) - (U := (2619681541468014936547 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2110827096636869 / 1250000000000000 : ℝ) ≤ - (2619681541468014936547 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35246647989609 / 1250000000000000 : ℝ)) (q := - (2110827096636869 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2110827096636869 / 40000000000000000 : ℚ)) + (r' := (2110827096636869 / 1250000000000000 : ℚ)) + (U := (-(14708997966031985063453 / 5000000000000000000000 : ℚ))) + (U' := (2619681541468014936547 / 5000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4788763384469 / 32000000000000 : ℚ)) + (s := (35246647989609 / 1250000000000000 : ℚ)) + (q := (2110827096636869 / 40000000000000000 : ℚ)) + (U := (-(14708997966031985063453 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_194_8 : Uω (aρ 8) (bρ 8) (4788763384469 / 32000000000000 : ℝ) ≤ @@ -3273,25 +3003,21 @@ lemma U_195_1 : have hlg : Real.log (11526008073845393 / 80000000000000000 : ℝ) ≤ (-(1210887862743762534847 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11526008073845393 / 80000000000000000 : ℝ) = - (11526008073845393 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11526008073845393 / 10000000000000000 : ℚ)) - (U := (88763100318737465153 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11526008073845393 / 10000000000000000 : ℝ) ≤ - (88763100318737465153 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (360159699597173 / 2500000000000000 : ℝ)) (q := - (11526008073845393 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11526008073845393 / 80000000000000000 : ℚ)) + (r' := (11526008073845393 / 10000000000000000 : ℚ)) + (U := (-(1210887862743762534847 / 625000000000000000000 : ℚ))) + (U' := (88763100318737465153 / 625000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (360159699597173 / 2500000000000000 : ℚ)) + (q := (11526008073845393 / 80000000000000000 : ℚ)) + (U := (-(1210887862743762534847 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_2 : Uω (aρ 2) (bρ 2) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3299,25 +3025,21 @@ lemma U_195_2 : have hlg : Real.log (11330761183450273 / 80000000000000000 : ℝ) ≤ (-(977252689052743997793 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11330761183450273 / 80000000000000000 : ℝ) = - (11330761183450273 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11330761183450273 / 10000000000000000 : ℚ)) - (U := (62468081397256002207 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11330761183450273 / 10000000000000000 : ℝ) ≤ - (62468081397256002207 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (176949511037489 / 1250000000000000 : ℝ)) (q := - (11330761183450273 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11330761183450273 / 80000000000000000 : ℚ)) + (r' := (11330761183450273 / 10000000000000000 : ℚ)) + (U := (-(977252689052743997793 / 500000000000000000000 : ℚ))) + (U' := (62468081397256002207 / 500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (176949511037489 / 1250000000000000 : ℚ)) + (q := (11330761183450273 / 80000000000000000 : ℚ)) + (U := (-(977252689052743997793 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_3 : Uω (aρ 3) (bρ 3) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3325,25 +3047,21 @@ lemma U_195_3 : have hlg : Real.log (10935937046850741 / 80000000000000000 : ℝ) ≤ (-(9949861454974666734381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10935937046850741 / 80000000000000000 : ℝ) = - (10935937046850741 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10935937046850741 / 10000000000000000 : ℚ)) - (U := (447346249525333265619 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10935937046850741 / 10000000000000000 : ℝ) ≤ - (447346249525333265619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1364286160500029 / 10000000000000000 : ℝ)) (q := - (10935937046850741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10935937046850741 / 80000000000000000 : ℚ)) + (r' := (10935937046850741 / 10000000000000000 : ℚ)) + (U := (-(9949861454974666734381 / 5000000000000000000000 : ℚ))) + (U' := (447346249525333265619 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (1364286160500029 / 10000000000000000 : ℚ)) + (q := (10935937046850741 / 80000000000000000 : ℚ)) + (U := (-(9949861454974666734381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_4 : Uω (aρ 4) (bρ 4) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3351,25 +3069,21 @@ lemma U_195_4 : have hlg : Real.log (10265642295664161 / 80000000000000000 : ℝ) ≤ (-(20532240139569703071389 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10265642295664161 / 80000000000000000 : ℝ) = - (10265642295664161 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10265642295664161 / 10000000000000000 : ℚ)) - (U := (262175269430296928611 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10265642295664161 / 10000000000000000 : ℝ) ≤ - (262175269430296928611 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19921978965131 / 156250000000000 : ℝ)) (q := - (10265642295664161 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10265642295664161 / 80000000000000000 : ℚ)) + (r' := (10265642295664161 / 10000000000000000 : ℚ)) + (U := (-(20532240139569703071389 / 10000000000000000000000 : ℚ))) + (U' := (262175269430296928611 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (19921978965131 / 156250000000000 : ℚ)) + (q := (10265642295664161 / 80000000000000000 : ℚ)) + (U := (-(20532240139569703071389 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_5 : Uω (aρ 5) (bρ 5) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3377,25 +3091,21 @@ lemma U_195_5 : have hlg : Real.log (9200480356847417 / 80000000000000000 : ℝ) ≤ (-(21627709382413351683267 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9200480356847417 / 80000000000000000 : ℝ) = - (9200480356847417 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9200480356847417 / 5000000000000000 : ℚ)) - (U := (6098177829586648316733 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9200480356847417 / 5000000000000000 : ℝ) ≤ - (6098177829586648316733 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (563453044199599 / 5000000000000000 : ℝ)) (q := - (9200480356847417 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9200480356847417 / 80000000000000000 : ℚ)) + (r' := (9200480356847417 / 5000000000000000 : ℚ)) + (U := (-(21627709382413351683267 / 10000000000000000000000 : ℚ))) + (U' := (6098177829586648316733 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (563453044199599 / 5000000000000000 : ℚ)) + (q := (9200480356847417 / 80000000000000000 : ℚ)) + (U := (-(21627709382413351683267 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_6 : Uω (aρ 6) (bρ 6) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3403,25 +3113,21 @@ lemma U_195_6 : have hlg : Real.log (1505196341988161 / 16000000000000000 : ℝ) ≤ (-(5909163429288754127091 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1505196341988161 / 16000000000000000 : ℝ) = - (1505196341988161 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1505196341988161 / 1000000000000000 : ℚ)) - (U := (1022308373711245872909 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1505196341988161 / 1000000000000000 : ℝ) ≤ - (1022308373711245872909 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (175104360362509 / 2000000000000000 : ℝ)) (q := - (1505196341988161 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1505196341988161 / 16000000000000000 : ℚ)) + (r' := (1505196341988161 / 1000000000000000 : ℚ)) + (U := (-(5909163429288754127091 / 2500000000000000000000 : ℚ))) + (U' := (1022308373711245872909 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (175104360362509 / 2000000000000000 : ℚ)) + (q := (1505196341988161 / 16000000000000000 : ℚ)) + (U := (-(5909163429288754127091 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_7 : Uω (aρ 7) (bρ 7) (9634306804209 / 64000000000000 : ℝ) ≤ @@ -3429,25 +3135,21 @@ lemma U_195_7 : have hlg : Real.log (4351125095812169 / 80000000000000000 : ℝ) ≤ (-(2911592179000382039081 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4351125095812169 / 80000000000000000 : ℝ) = - (4351125095812169 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4351125095812169 / 2500000000000000 : ℚ)) - (U := (554143722499617960919 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4351125095812169 / 2500000000000000 : ℝ) ≤ - (554143722499617960919 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152734514520193 / 5000000000000000 : ℝ)) (q := - (4351125095812169 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4351125095812169 / 80000000000000000 : ℚ)) + (r' := (4351125095812169 / 2500000000000000 : ℚ)) + (U := (-(2911592179000382039081 / 1000000000000000000000 : ℚ))) + (U' := (554143722499617960919 / 1000000000000000000000 : ℚ)) + 5 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9634306804209 / 64000000000000 : ℚ)) + (s := (152734514520193 / 5000000000000000 : ℚ)) + (q := (4351125095812169 / 80000000000000000 : ℚ)) + (U := (-(2911592179000382039081 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_195_8 : Uω (aρ 8) (bρ 8) (9634306804209 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U16.lean b/LeanPool/Zeta5Irrational/Table/U16.lean index b3aacc59ef..64429c94ff 100644 --- a/LeanPool/Zeta5Irrational/Table/U16.lean +++ b/LeanPool/Zeta5Irrational/Table/U16.lean @@ -24,25 +24,21 @@ lemma U_196_1 : have hlg : Real.log (181202947067443 / 1250000000000000 : ℝ) ≤ (-(2414101464838475762107 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (181202947067443 / 1250000000000000 : ℝ) = - (181202947067443 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (181202947067443 / 156250000000000 : ℚ)) - (U := (185200461286524237893 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (181202947067443 / 156250000000000 : ℝ) ≤ - (185200461286524237893 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (724756026247669 / 5000000000000000 : ℝ)) (q := - (181202947067443 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (181202947067443 / 1250000000000000 : ℚ)) + (r' := (181202947067443 / 156250000000000 : ℚ)) + (U := (-(2414101464838475762107 / 1250000000000000000000 : ℚ))) + (U' := (185200461286524237893 / 1250000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (724756026247669 / 5000000000000000 : ℚ)) + (q := (181202947067443 / 1250000000000000 : ℚ)) + (U := (-(2414101464838475762107 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_2 : Uω (aρ 2) (bρ 2) (242277170987 / 1600000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_196_2 : have hlg : Real.log (356305423431271 / 2500000000000000 : ℝ) ≤ (-(19482577160501416685469 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (356305423431271 / 2500000000000000 : ℝ) = - (356305423431271 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (356305423431271 / 312500000000000 : ℚ)) - (U := (1311838248498583314531 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (356305423431271 / 312500000000000 : ℝ) ≤ - (1311838248498583314531 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (712238649688209 / 5000000000000000 : ℝ)) (q := - (356305423431271 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (356305423431271 / 2500000000000000 : ℚ)) + (r' := (356305423431271 / 312500000000000 : ℚ)) + (U := (-(19482577160501416685469 / 10000000000000000000000 : ℚ))) + (U' := (1311838248498583314531 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (712238649688209 / 5000000000000000 : ℚ)) + (q := (356305423431271 / 2500000000000000 : ℚ)) + (U := (-(19482577160501416685469 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_3 : Uω (aρ 3) (bρ 3) (242277170987 / 1600000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_196_3 : have hlg : Real.log (2751762988469771 / 20000000000000000 : ℝ) ≤ (-(4958726199469246675321 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2751762988469771 / 20000000000000000 : ℝ) = - (2751762988469771 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2751762988469771 / 2500000000000000 : ℚ)) - (U := (239877652780753324679 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2751762988469771 / 2500000000000000 : ℝ) ≤ - (239877652780753324679 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1373193006746021 / 10000000000000000 : ℝ)) (q := - (2751762988469771 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2751762988469771 / 20000000000000000 : ℚ)) + (r' := (2751762988469771 / 2500000000000000 : ℚ)) + (U := (-(4958726199469246675321 / 2500000000000000000000 : ℚ))) + (U' := (239877652780753324679 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (1373193006746021 / 10000000000000000 : ℚ)) + (q := (2751762988469771 / 20000000000000000 : ℚ)) + (U := (-(4958726199469246675321 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_4 : Uω (aρ 4) (bρ 4) (242277170987 / 1600000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_196_4 : have hlg : Real.log (1292133819311667 / 10000000000000000 : ℝ) ≤ (-(10231450584493624514443 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1292133819311667 / 10000000000000000 : ℝ) = - (1292133819311667 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1292133819311667 / 1250000000000000 : ℚ)) - (U := (165757120006375485557 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1292133819311667 / 1250000000000000 : ℝ) ≤ - (165757120006375485557 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160498979745573 / 1250000000000000 : ℝ)) (q := - (1292133819311667 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1292133819311667 / 10000000000000000 : ℚ)) + (r' := (1292133819311667 / 1250000000000000 : ℚ)) + (U := (-(10231450584493624514443 / 5000000000000000000000 : ℚ))) + (U' := (165757120006375485557 / 5000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (160498979745573 / 1250000000000000 : ℚ)) + (q := (1292133819311667 / 10000000000000000 : ℚ)) + (U := (-(10231450584493624514443 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_5 : Uω (aρ 5) (bρ 5) (242277170987 / 1600000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_196_5 : have hlg : Real.log (2318225516752991 / 20000000000000000 : ℝ) ≤ (-(2154930242961830379761 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2318225516752991 / 20000000000000000 : ℝ) = - (2318225516752991 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2318225516752991 / 1250000000000000 : ℚ)) - (U := (617658478238169620239 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2318225516752991 / 1250000000000000 : ℝ) ≤ - (617658478238169620239 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1136139635429241 / 10000000000000000 : ℝ)) (q := - (2318225516752991 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2318225516752991 / 20000000000000000 : ℚ)) + (r' := (2318225516752991 / 1250000000000000 : ℚ)) + (U := (-(2154930242961830379761 / 1000000000000000000000 : ℚ))) + (U' := (617658478238169620239 / 1000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (1136139635429241 / 10000000000000000 : ℚ)) + (q := (2318225516752991 / 20000000000000000 : ℚ)) + (U := (-(2154930242961830379761 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_6 : Uω (aρ 6) (bρ 6) (242277170987 / 1600000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_196_6 : have hlg : Real.log (380109372357853 / 4000000000000000 : ℝ) ≤ (-(5883976514400672601683 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (380109372357853 / 4000000000000000 : ℝ) = - (380109372357853 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (380109372357853 / 250000000000000 : ℚ)) - (U := (1047495288599327398317 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (380109372357853 / 250000000000000 : ℝ) ≤ - (1047495288599327398317 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177140271121103 / 2000000000000000 : ℝ)) (q := - (380109372357853 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (380109372357853 / 4000000000000000 : ℚ)) + (r' := (380109372357853 / 250000000000000 : ℚ)) + (U := (-(5883976514400672601683 / 2500000000000000000000 : ℚ))) + (U' := (1047495288599327398317 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (177140271121103 / 2000000000000000 : ℚ)) + (q := (380109372357853 / 4000000000000000 : ℚ)) + (U := (-(5883976514400672601683 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_7 : Uω (aρ 7) (bρ 7) (242277170987 / 1600000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_196_7 : have hlg : Real.log (559353474134973 / 10000000000000000 : ℝ) ≤ (-(28835587643811316305909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (559353474134973 / 10000000000000000 : ℝ) = - (559353474134973 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (559353474134973 / 312500000000000 : ℚ)) - (U := (5821771371188683694091 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (559353474134973 / 312500000000000 : ℝ) ≤ - (5821771371188683694091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (81880705711549 / 2500000000000000 : ℝ)) (q := - (559353474134973 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (559353474134973 / 10000000000000000 : ℚ)) + (r' := (559353474134973 / 312500000000000 : ℚ)) + (U := (-(28835587643811316305909 / 10000000000000000000000 : ℚ))) + (U' := (5821771371188683694091 / 10000000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (242277170987 / 1600000000000 : ℚ)) + (s := (81880705711549 / 2500000000000000 : ℚ)) + (q := (559353474134973 / 10000000000000000 : ℚ)) + (U := (-(28835587643811316305909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_196_8 : Uω (aρ 8) (bρ 8) (242277170987 / 1600000000000 : ℝ) ≤ @@ -335,25 +307,21 @@ lemma U_197_1 : have hlg : Real.log (11667969083933543 / 80000000000000000 : ℝ) ≤ (-(9625896157689089085363 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11667969083933543 / 80000000000000000 : ℝ) = - (11667969083933543 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11667969083933543 / 10000000000000000 : ℚ)) - (U := (771311546810910914637 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11667969083933543 / 10000000000000000 : ℝ) ≤ - (771311546810910914637 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (729192644944271 / 5000000000000000 : ℝ)) (q := - (11667969083933543 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11667969083933543 / 80000000000000000 : ℚ)) + (r' := (11667969083933543 / 10000000000000000 : ℚ)) + (U := (-(9625896157689089085363 / 5000000000000000000000 : ℚ))) + (U' := (771311546810910914637 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (729192644944271 / 5000000000000000 : ℚ)) + (q := (11667969083933543 / 80000000000000000 : ℚ)) + (U := (-(9625896157689089085363 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_2 : Uω (aρ 2) (bρ 2) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -361,25 +329,21 @@ lemma U_197_2 : have hlg : Real.log (11472785453890199 / 80000000000000000 : ℝ) ≤ (-(9710244426699519995267 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11472785453890199 / 80000000000000000 : ℝ) = - (11472785453890199 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11472785453890199 / 10000000000000000 : ℚ)) - (U := (686963277800480004733 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11472785453890199 / 10000000000000000 : ℝ) ≤ - (686963277800480004733 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (716679197443853 / 5000000000000000 : ℝ)) (q := - (11472785453890199 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11472785453890199 / 80000000000000000 : ℚ)) + (r' := (11472785453890199 / 10000000000000000 : ℚ)) + (U := (-(9710244426699519995267 / 5000000000000000000000 : ℚ))) + (U' := (686963277800480004733 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (716679197443853 / 5000000000000000 : ℚ)) + (q := (11472785453890199 / 80000000000000000 : ℚ)) + (U := (-(9710244426699519995267 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_3 : Uω (aρ 3) (bρ 3) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -387,25 +351,21 @@ lemma U_197_3 : have hlg : Real.log (443126602470863 / 3200000000000000 : ℝ) ≤ (-(9885252872164051723893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (443126602470863 / 3200000000000000 : ℝ) = - (443126602470863 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (443126602470863 / 400000000000000 : ℚ)) - (U := (511954832335948276107 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (443126602470863 / 400000000000000 : ℝ) ≤ - (511954832335948276107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27641988064161 / 200000000000000 : ℝ)) (q := - (443126602470863 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (443126602470863 / 3200000000000000 : ℚ)) + (r' := (443126602470863 / 400000000000000 : ℚ)) + (U := (-(9885252872164051723893 / 5000000000000000000000 : ℚ))) + (U' := (511954832335948276107 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (27641988064161 / 200000000000000 : ℚ)) + (q := (443126602470863 / 3200000000000000 : ℚ)) + (U := (-(9885252872164051723893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_4 : Uω (aρ 4) (bρ 4) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -413,25 +373,21 @@ lemma U_197_4 : have hlg : Real.log (10408492554054399 / 80000000000000000 : ℝ) ≤ (-(5098511423100886032829 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10408492554054399 / 80000000000000000 : ℝ) = - (10408492554054399 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10408492554054399 / 10000000000000000 : ℚ)) - (U := (100092429149113967171 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10408492554054399 / 10000000000000000 : ℝ) ≤ - (100092429149113967171 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (323243864335939 / 2500000000000000 : ℝ)) (q := - (10408492554054399 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10408492554054399 / 80000000000000000 : ℚ)) + (r' := (10408492554054399 / 10000000000000000 : ℚ)) + (U := (-(5098511423100886032829 / 2500000000000000000000 : ℚ))) + (U' := (100092429149113967171 / 2500000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (323243864335939 / 2500000000000000 : ℚ)) + (q := (10408492554054399 / 80000000000000000 : ℚ)) + (U := (-(5098511423100886032829 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_5 : Uω (aρ 5) (bρ 5) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -439,25 +395,21 @@ lemma U_197_5 : have hlg : Real.log (1869060181804003 / 16000000000000000 : ℝ) ≤ (-(5367882483107103412791 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1869060181804003 / 16000000000000000 : ℝ) = - (1869060181804003 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1869060181804003 / 1000000000000000 : ℚ)) - (U := (1563589319892896587209 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1869060181804003 / 1000000000000000 : ℝ) ≤ - (1563589319892896587209 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1789636664719 / 15625000000000 : ℝ)) (q := - (1869060181804003 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1869060181804003 / 16000000000000000 : ℚ)) + (r' := (1869060181804003 / 1000000000000000 : ℚ)) + (U := (-(5367882483107103412791 / 2500000000000000000000 : ℚ))) + (U' := (1563589319892896587209 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (1789636664719 / 15625000000000 : ℚ)) + (q := (1869060181804003 / 16000000000000000 : ℚ)) + (U := (-(5367882483107103412791 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_6 : Uω (aρ 6) (bρ 6) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -465,25 +417,21 @@ lemma U_197_6 : have hlg : Real.log (7678281948881963 / 80000000000000000 : ℝ) ≤ (-(5859077040181952131849 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7678281948881963 / 80000000000000000 : ℝ) = - (7678281948881963 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7678281948881963 / 5000000000000000 : ℚ)) - (U := (1072394762818047868151 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7678281948881963 / 5000000000000000 : ℝ) ≤ - (1072394762818047868151 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (895853100525647 / 10000000000000000 : ℝ)) (q := - (7678281948881963 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7678281948881963 / 80000000000000000 : ℚ)) + (r' := (7678281948881963 / 5000000000000000 : ℚ)) + (U := (-(5859077040181952131849 / 2500000000000000000000 : ℚ))) + (U' := (1072394762818047868151 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (895853100525647 / 10000000000000000 : ℚ)) + (q := (7678281948881963 / 80000000000000000 : ℚ)) + (U := (-(5859077040181952131849 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_7 : Uω (aρ 7) (bρ 7) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -491,25 +439,21 @@ lemma U_197_7 : have hlg : Real.log (4593858074959487 / 80000000000000000 : ℝ) ≤ (-(7143266057875241232323 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (4593858074959487 / 80000000000000000 : ℝ) = - (4593858074959487 / 2500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4593858074959487 / 2500000000000000 : ℚ)) - (U := (1521073695874758767677 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4593858074959487 / 2500000000000000 : ℝ) ≤ - (1521073695874758767677 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (87102128201257 / 2500000000000000 : ℝ)) (q := - (4593858074959487 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4593858074959487 / 80000000000000000 : ℚ)) + (r' := (4593858074959487 / 2500000000000000 : ℚ)) + (U := (-(7143266057875241232323 / 2500000000000000000000 : ℚ))) + (U' := (1521073695874758767677 / 2500000000000000000000 : ℚ)) + 5 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9747866874751 / 64000000000000 : ℚ)) + (s := (87102128201257 / 2500000000000000 : ℚ)) + (q := (4593858074959487 / 80000000000000000 : ℚ)) + (U := (-(7143266057875241232323 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_197_8 : Uω (aρ 8) (bρ 8) (9747866874751 / 64000000000000 : ℝ) ≤ @@ -646,25 +590,21 @@ lemma U_198_1 : have hlg : Real.log (5869474744954929 / 40000000000000000 : ℝ) ≤ (-(19191143047661083763181 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5869474744954929 / 40000000000000000 : ℝ) = - (5869474744954929 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5869474744954929 / 5000000000000000 : ℚ)) - (U := (1603272361338916236819 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5869474744954929 / 5000000000000000 : ℝ) ≤ - (1603272361338916236819 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1467258510871527 / 10000000000000000 : ℝ)) (q := - (5869474744954929 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5869474744954929 / 40000000000000000 : ℚ)) + (r' := (5869474744954929 / 5000000000000000 : ℚ)) + (U := (-(19191143047661083763181 / 10000000000000000000000 : ℚ))) + (U' := (1603272361338916236819 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (1467258510871527 / 10000000000000000 : ℚ)) + (q := (5869474744954929 / 40000000000000000 : ℚ)) + (U := (-(19191143047661083763181 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_2 : Uω (aρ 2) (bρ 2) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -672,25 +612,21 @@ lemma U_198_2 : have hlg : Real.log (5771898452129227 / 40000000000000000 : ℝ) ≤ (-(9679392028817212299531 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5771898452129227 / 40000000000000000 : ℝ) = - (5771898452129227 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5771898452129227 / 5000000000000000 : ℚ)) - (U := (717815675682787700469 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5771898452129227 / 5000000000000000 : ℝ) ≤ - (717815675682787700469 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (360559844242169 / 2500000000000000 : ℝ)) (q := - (5771898452129227 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5771898452129227 / 40000000000000000 : ℚ)) + (r' := (5771898452129227 / 5000000000000000 : ℚ)) + (U := (-(9679392028817212299531 / 5000000000000000000000 : ℚ))) + (U' := (717815675682787700469 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (360559844242169 / 2500000000000000 : ℚ)) + (q := (5771898452129227 / 40000000000000000 : ℚ)) + (U := (-(9679392028817212299531 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_3 : Uω (aρ 3) (bρ 3) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -698,25 +634,21 @@ lemma U_198_3 : have hlg : Real.log (5574638202543499 / 40000000000000000 : ℝ) ≤ (-(492663008624633561373 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5574638202543499 / 40000000000000000 : ℝ) = - (5574638202543499 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5574638202543499 / 5000000000000000 : ℚ)) - (U := (27197376600366438627 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5574638202543499 / 5000000000000000 : ℝ) ≤ - (27197376600366438627 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (347751339631453 / 2500000000000000 : ℝ)) (q := - (5574638202543499 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5574638202543499 / 40000000000000000 : ℚ)) + (r' := (5574638202543499 / 5000000000000000 : ℚ)) + (U := (-(492663008624633561373 / 250000000000000000000 : ℚ))) + (U' := (27197376600366438627 / 250000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (347751339631453 / 2500000000000000 : ℚ)) + (q := (5574638202543499 / 40000000000000000 : ℚ)) + (U := (-(492663008624633561373 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_4 : Uω (aρ 4) (bρ 4) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -724,25 +656,21 @@ lemma U_198_4 : have hlg : Real.log (5239954211957913 / 40000000000000000 : ℝ) ≤ (-(20325666932152984631853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5239954211957913 / 40000000000000000 : ℝ) = - (5239954211957913 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5239954211957913 / 5000000000000000 : ℚ)) - (U := (468748476847015368147 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5239954211957913 / 5000000000000000 : ℝ) ≤ - (468748476847015368147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1301957544298019 / 10000000000000000 : ℝ)) (q := - (5239954211957913 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5239954211957913 / 40000000000000000 : ℚ)) + (r' := (5239954211957913 / 5000000000000000 : ℚ)) + (U := (-(20325666932152984631853 / 10000000000000000000000 : ℚ))) + (U' := (468748476847015368147 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (1301957544298019 / 10000000000000000 : ℚ)) + (q := (5239954211957913 / 40000000000000000 : ℚ)) + (U := (-(20325666932152984631853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_5 : Uω (aρ 5) (bρ 5) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -750,25 +678,21 @@ lemma U_198_5 : have hlg : Real.log (4708838715589633 / 40000000000000000 : ℝ) ≤ (-(42788762652914107141 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4708838715589633 / 40000000000000000 : ℝ) = - (4708838715589633 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4708838715589633 / 2500000000000000 : ℚ)) - (U := (12663011771085892859 / 20000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4708838715589633 / 2500000000000000 : ℝ) ≤ - (12663011771085892859 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1154589715448879 / 10000000000000000 : ℝ)) (q := - (4708838715589633 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4708838715589633 / 40000000000000000 : ℚ)) + (r' := (4708838715589633 / 2500000000000000 : ℚ)) + (U := (-(42788762652914107141 / 20000000000000000000 : ℚ))) + (U' := (12663011771085892859 / 20000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (1154589715448879 / 10000000000000000 : ℚ)) + (q := (4708838715589633 / 40000000000000000 : ℚ)) + (U := (-(42788762652914107141 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_6 : Uω (aρ 6) (bρ 6) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -776,25 +700,21 @@ lemma U_198_6 : have hlg : Real.log (3877134477197451 / 40000000000000000 : ℝ) ≤ (-(23337831090964090934793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3877134477197451 / 40000000000000000 : ℝ) = - (3877134477197451 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3877134477197451 / 2500000000000000 : ℚ)) - (U := (4388056121035909065207 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3877134477197451 / 2500000000000000 : ℝ) ≤ - (4388056121035909065207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (226494492848197 / 2500000000000000 : ℝ)) (q := - (3877134477197451 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3877134477197451 / 40000000000000000 : ℚ)) + (r' := (3877134477197451 / 2500000000000000 : ℚ)) + (U := (-(23337831090964090934793 / 10000000000000000000000 : ℚ))) + (U' := (4388056121035909065207 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (226494492848197 / 2500000000000000 : ℚ)) + (q := (3877134477197451 / 40000000000000000 : ℚ)) + (U := (-(23337831090964090934793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_7 : Uω (aρ 7) (bρ 7) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -802,25 +722,21 @@ lemma U_198_7 : have hlg : Real.log (470901099739561 / 8000000000000000 : ℝ) ≤ (-(113301949068643981267 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (470901099739561 / 8000000000000000 : ℝ) = - (470901099739561 / 250000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (470901099739561 / 250000000000000 : ℚ)) - (U := (25327486991356018733 / 40000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (470901099739561 / 250000000000000 : ℝ) ≤ - (25327486991356018733 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73664972580593 / 2000000000000000 : ℝ)) (q := - (470901099739561 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (470901099739561 / 8000000000000000 : ℚ)) + (r' := (470901099739561 / 250000000000000 : ℚ)) + (U := (-(113301949068643981267 / 40000000000000000000 : ℚ))) + (U' := (25327486991356018733 / 40000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4902323455011 / 32000000000000 : ℚ)) + (s := (73664972580593 / 2000000000000000 : ℚ)) + (q := (470901099739561 / 8000000000000000 : ℚ)) + (U := (-(113301949068643981267 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_198_8 : Uω (aρ 8) (bρ 8) (4902323455011 / 32000000000000 : ℝ) ≤ @@ -956,25 +872,21 @@ lemma U_199_1 : have hlg : Real.log (472397193257161 / 3200000000000000 : ℝ) ≤ (-(19130859451563604787399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (472397193257161 / 3200000000000000 : ℝ) = - (472397193257161 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (472397193257161 / 400000000000000 : ℚ)) - (U := (1663555957436395212601 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (472397193257161 / 400000000000000 : ℝ) ≤ - (1663555957436395212601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59045268629609 / 400000000000000 : ℝ)) (q := - (472397193257161 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (472397193257161 / 3200000000000000 : ℚ)) + (r' := (472397193257161 / 400000000000000 : ℚ)) + (U := (-(19130859451563604787399 / 10000000000000000000000 : ℚ))) + (U' := (1663555957436395212601 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (59045268629609 / 400000000000000 : ℚ)) + (q := (472397193257161 / 3200000000000000 : ℚ)) + (U := (-(19130859451563604787399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_2 : Uω (aρ 2) (bρ 2) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -982,25 +894,21 @@ lemma U_199_2 : have hlg : Real.log (11614807909235877 / 80000000000000000 : ℝ) ≤ (-(2412182257464382172739 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11614807909235877 / 80000000000000000 : ℝ) = - (11614807909235877 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11614807909235877 / 10000000000000000 : ℚ)) - (U := (187119668660617827261 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11614807909235877 / 10000000000000000 : ℝ) ≤ - (187119668660617827261 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (725560123850969 / 5000000000000000 : ℝ)) (q := - (11614807909235877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11614807909235877 / 80000000000000000 : ℚ)) + (r' := (11614807909235877 / 10000000000000000 : ℚ)) + (U := (-(2412182257464382172739 / 1250000000000000000000 : ℚ))) + (U' := (187119668660617827261 / 1250000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (725560123850969 / 5000000000000000 : ℚ)) + (q := (11614807909235877 / 80000000000000000 : ℚ)) + (U := (-(2412182257464382172739 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_3 : Uω (aρ 3) (bρ 3) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1008,25 +916,21 @@ lemma U_199_3 : have hlg : Real.log (11220386017503029 / 80000000000000000 : ℝ) ≤ (-(19642943299792789663527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11220386017503029 / 80000000000000000 : ℝ) = - (11220386017503029 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11220386017503029 / 10000000000000000 : ℚ)) - (U := (1151472109207210336473 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11220386017503029 / 10000000000000000 : ℝ) ≤ - (1151472109207210336473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (699955440559363 / 5000000000000000 : ℝ)) (q := - (11220386017503029 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11220386017503029 / 80000000000000000 : ℚ)) + (r' := (11220386017503029 / 10000000000000000 : ℚ)) + (U := (-(19642943299792789663527 / 10000000000000000000000 : ℚ))) + (U' := (1151472109207210336473 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (699955440559363 / 5000000000000000 : ℚ)) + (q := (11220386017503029 / 80000000000000000 : ℚ)) + (U := (-(19642943299792789663527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_4 : Uω (aρ 4) (bρ 4) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1034,25 +938,21 @@ lemma U_199_4 : have hlg : Real.log (10551318290073249 / 80000000000000000 : ℝ) ≤ (-(20257758253733241645161 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10551318290073249 / 80000000000000000 : ℝ) = - (10551318290073249 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10551318290073249 / 10000000000000000 : ℚ)) - (U := (536657155266758354839 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10551318290073249 / 10000000000000000 : ℝ) ≤ - (536657155266758354839 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1310938130326281 / 10000000000000000 : ℝ)) (q := - (10551318290073249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10551318290073249 / 80000000000000000 : ℚ)) + (r' := (10551318290073249 / 10000000000000000 : ℚ)) + (U := (-(20257758253733241645161 / 10000000000000000000000 : ℚ))) + (U' := (536657155266758354839 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (1310938130326281 / 10000000000000000 : ℚ)) + (q := (10551318290073249 / 80000000000000000 : ℚ)) + (U := (-(20257758253733241645161 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_5 : Uω (aρ 5) (bρ 5) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1060,25 +960,21 @@ lemma U_199_5 : have hlg : Real.log (1898006432818281 / 16000000000000000 : ℝ) ≤ (-(5329461579391329115803 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1898006432818281 / 16000000000000000 : ℝ) = - (1898006432818281 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1898006432818281 / 1000000000000000 : ℚ)) - (U := (1602010223608670884197 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1898006432818281 / 1000000000000000 : ℝ) ≤ - (1602010223608670884197 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58190325908291 / 500000000000000 : ℝ)) (q := - (1898006432818281 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1898006432818281 / 16000000000000000 : ℚ)) + (r' := (1898006432818281 / 1000000000000000 : ℚ)) + (U := (-(5329461579391329115803 / 2500000000000000000000 : ℚ))) + (U' := (1602010223608670884197 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (58190325908291 / 500000000000000 : ℚ)) + (q := (1898006432818281 / 16000000000000000 : ℚ)) + (U := (-(5329461579391329115803 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_6 : Uω (aρ 6) (bρ 6) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1086,25 +982,21 @@ lemma U_199_6 : have hlg : Real.log (7830152027979093 / 80000000000000000 : ℝ) ≤ (-(23240447077305945546461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7830152027979093 / 80000000000000000 : ℝ) = - (7830152027979093 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7830152027979093 / 5000000000000000 : ℚ)) - (U := (4485440134694054453539 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7830152027979093 / 5000000000000000 : ℝ) ≤ - (4485440134694054453539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (458038429638871 / 5000000000000000 : ℝ)) (q := - (7830152027979093 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7830152027979093 / 80000000000000000 : ℚ)) + (r' := (7830152027979093 / 5000000000000000 : ℚ)) + (U := (-(23240447077305945546461 / 10000000000000000000000 : ℚ))) + (U' := (4485440134694054453539 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (458038429638871 / 5000000000000000 : ℚ)) + (q := (7830152027979093 / 80000000000000000 : ℚ)) + (U := (-(23240447077305945546461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_7 : Uω (aρ 7) (bρ 7) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1112,25 +1004,21 @@ lemma U_199_7 : have hlg : Real.log (964176930281977 / 16000000000000000 : ℝ) ≤ (-(28090691845157120020427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (964176930281977 / 16000000000000000 : ℝ) = - (964176930281977 / 500000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (964176930281977 / 500000000000000 : ℚ)) - (U := (6566667169842879979573 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (964176930281977 / 500000000000000 : ℝ) ≤ - (6566667169842879979573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4842767448693 / 125000000000000 : ℝ)) (q := - (964176930281977 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (964176930281977 / 16000000000000000 : ℚ)) + (r' := (964176930281977 / 500000000000000 : ℚ)) + (U := (-(28090691845157120020427 / 10000000000000000000000 : ℚ))) + (U' := (6566667169842879979573 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9861426945293 / 64000000000000 : ℚ)) + (s := (4842767448693 / 125000000000000 : ℚ)) + (q := (964176930281977 / 16000000000000000 : ℚ)) + (U := (-(28090691845157120020427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_199_8 : Uω (aρ 8) (bρ 8) (9861426945293 / 64000000000000 : ℝ) ≤ @@ -1268,25 +1156,21 @@ lemma U_200_1 : have hlg : Real.log (148511376370581 / 1000000000000000 : ℝ) ≤ (-(9535468571688656894177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (148511376370581 / 1000000000000000 : ℝ) = - (148511376370581 / 125000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (148511376370581 / 125000000000000 : ℚ)) - (U := (861739132811343105823 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (148511376370581 / 125000000000000 : ℝ) ≤ - (861739132811343105823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (297000980956699 / 2000000000000000 : ℝ)) (q := - (148511376370581 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (148511376370581 / 1000000000000000 : ℚ)) + (r' := (148511376370581 / 125000000000000 : ℚ)) + (U := (-(9535468571688656894177 / 5000000000000000000000 : ℚ))) + (U' := (861739132811343105823 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (297000980956699 / 2000000000000000 : ℚ)) + (q := (148511376370581 / 1000000000000000 : ℚ)) + (U := (-(9535468571688656894177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_2 : Uω (aρ 2) (bρ 2) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1294,25 +1178,21 @@ lemma U_200_2 : have hlg : Real.log (292145461923753 / 2000000000000000 : ℝ) ≤ (-(19236506232599800661231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (292145461923753 / 2000000000000000 : ℝ) = - (292145461923753 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (292145461923753 / 250000000000000 : ℚ)) - (U := (1557909176400199338769 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (292145461923753 / 250000000000000 : ℝ) ≤ - (1557909176400199338769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292000201823881 / 2000000000000000 : ℝ)) (q := - (292145461923753 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (292145461923753 / 2000000000000000 : ℚ)) + (r' := (292145461923753 / 250000000000000 : ℚ)) + (U := (-(19236506232599800661231 / 10000000000000000000000 : ℚ))) + (U' := (1557909176400199338769 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (292000201823881 / 2000000000000000 : ℚ)) + (q := (292145461923753 / 2000000000000000 : ℚ)) + (U := (-(19236506232599800661231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_3 : Uω (aρ 3) (bρ 3) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1320,25 +1200,21 @@ lemma U_200_3 : have hlg : Real.log (1411436741480521 / 10000000000000000 : ℝ) ≤ (-(19579769410281550678357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1411436741480521 / 10000000000000000 : ℝ) = - (1411436741480521 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1411436741480521 / 1250000000000000 : ℚ)) - (U := (1214645998718449321643 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1411436741480521 / 1250000000000000 : ℝ) ≤ - (1214645998718449321643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1408815979192917 / 10000000000000000 : ℝ)) (q := - (1411436741480521 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1411436741480521 / 10000000000000000 : ℚ)) + (r' := (1411436741480521 / 1250000000000000 : ℚ)) + (U := (-(19579769410281550678357 / 10000000000000000000000 : ℚ))) + (U' := (1214645998718449321643 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (1408815979192917 / 10000000000000000 : ℚ)) + (q := (1411436741480521 / 10000000000000000 : ℚ)) + (U := (-(19579769410281550678357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_4 : Uω (aρ 4) (bρ 4) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1346,25 +1222,21 @@ lemma U_200_4 : have hlg : Real.log (2655680568768123 / 20000000000000000 : ℝ) ≤ (-(2019031316175803607789 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2655680568768123 / 20000000000000000 : ℝ) = - (2655680568768123 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2655680568768123 / 2500000000000000 : ℚ)) - (U := (60410224724196392211 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2655680568768123 / 2500000000000000 : ℝ) ≤ - (60410224724196392211 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (659958623032499 / 5000000000000000 : ℝ)) (q := - (2655680568768123 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2655680568768123 / 20000000000000000 : ℚ)) + (r' := (2655680568768123 / 2500000000000000 : ℚ)) + (U := (-(2019031316175803607789 / 1000000000000000000000 : ℚ))) + (U' := (60410224724196392211 / 1000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (659958623032499 / 5000000000000000 : ℚ)) + (q := (2655680568768123 / 20000000000000000 : ℚ)) + (U := (-(2019031316175803607789 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_5 : Uω (aρ 5) (bρ 5) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1372,25 +1244,21 @@ lemma U_200_5 : have hlg : Real.log (1195295702671639 / 10000000000000000 : ℝ) ≤ (-(21241914872470499005599 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1195295702671639 / 10000000000000000 : ℝ) = - (1195295702671639 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1195295702671639 / 625000000000000 : ℚ)) - (U := (6483972339529500994401 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1195295702671639 / 625000000000000 : ℝ) ≤ - (6483972339529500994401 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1173018001975153 / 10000000000000000 : ℝ)) (q := - (1195295702671639 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1195295702671639 / 10000000000000000 : ℚ)) + (r' := (1195295702671639 / 625000000000000 : ℚ)) + (U := (-(21241914872470499005599 / 10000000000000000000000 : ℚ))) + (U' := (6483972339529500994401 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (1173018001975153 / 10000000000000000 : ℚ)) + (q := (1195295702671639 / 10000000000000000 : ℚ)) + (U := (-(21241914872470499005599 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_6 : Uω (aρ 6) (bρ 6) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1398,25 +1266,21 @@ lemma U_200_6 : have hlg : Real.log (395296728475251 / 4000000000000000 : ℝ) ≤ (-(23144129448493782607159 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (395296728475251 / 4000000000000000 : ℝ) = - (395296728475251 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (395296728475251 / 250000000000000 : ℚ)) - (U := (4581757763506217392841 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (395296728475251 / 250000000000000 : ℝ) ≤ - (4581757763506217392841 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (92615061414813 / 1000000000000000 : ℝ)) (q := - (395296728475251 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (395296728475251 / 4000000000000000 : ℚ)) + (r' := (395296728475251 / 250000000000000 : ℚ)) + (U := (-(23144129448493782607159 / 10000000000000000000000 : ℚ))) + (U' := (4581757763506217392841 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (92615061414813 / 1000000000000000 : ℚ)) + (q := (395296728475251 / 4000000000000000 : ℚ)) + (U := (-(23144129448493782607159 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_7 : Uω (aρ 7) (bρ 7) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1424,24 +1288,21 @@ lemma U_200_7 : have hlg : Real.log (77030344441781 / 1250000000000000 : ℝ) ≤ (-(13933497005570068083757 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (77030344441781 / 1250000000000000 : ℝ) = (77030344441781 / 39062500000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77030344441781 / 39062500000000 : ℚ)) - (U := (3395182501929931916243 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (77030344441781 / 39062500000000 : ℝ) ≤ - (3395182501929931916243 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (405813863600371 / 10000000000000000 : ℝ)) (q := - (77030344441781 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77030344441781 / 1250000000000000 : ℚ)) + (r' := (77030344441781 / 39062500000000 : ℚ)) + (U := (-(13933497005570068083757 / 5000000000000000000000 : ℚ))) + (U' := (3395182501929931916243 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2479551745141 / 16000000000000 : ℚ)) + (s := (405813863600371 / 10000000000000000 : ℚ)) + (q := (77030344441781 / 1250000000000000 : ℚ)) + (U := (-(13933497005570068083757 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_200_8 : Uω (aρ 8) (bρ 8) (2479551745141 / 16000000000000 : ℝ) ≤ @@ -1578,25 +1439,21 @@ lemma U_201_1 : have hlg : Real.log (23832800450741223 / 160000000000000000 : ℝ) ≤ (-(3808222024764513750947 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23832800450741223 / 160000000000000000 : ℝ) = - (23832800450741223 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23832800450741223 / 20000000000000000 : ℚ)) - (U := (350661057035486249053 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23832800450741223 / 20000000000000000 : ℝ) ≤ - (350661057035486249053 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1489441493458981 / 10000000000000000 : ℝ)) (q := - (23832800450741223 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23832800450741223 / 160000000000000000 : ℚ)) + (r' := (23832800450741223 / 20000000000000000 : ℚ)) + (U := (-(3808222024764513750947 / 2000000000000000000000 : ℚ))) + (U' := (350661057035486249053 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (1489441493458981 / 10000000000000000 : ℚ)) + (q := (23832800450741223 / 160000000000000000 : ℚ)) + (U := (-(3808222024764513750947 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_2 : Uω (aρ 2) (bρ 2) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1604,25 +1461,21 @@ lemma U_201_2 : have hlg : Real.log (23442647198638999 / 160000000000000000 : ℝ) ≤ (-(19206169210263464948851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23442647198638999 / 160000000000000000 : ℝ) = - (23442647198638999 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23442647198638999 / 20000000000000000 : ℚ)) - (U := (1588246198736535051149 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23442647198638999 / 20000000000000000 : ℝ) ≤ - (1588246198736535051149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1464441349456203 / 10000000000000000 : ℝ)) (q := - (23442647198638999 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23442647198638999 / 160000000000000000 : ℚ)) + (r' := (23442647198638999 / 20000000000000000 : ℚ)) + (U := (-(19206169210263464948851 / 10000000000000000000000 : ℚ))) + (U' := (1588246198736535051149 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (1464441349456203 / 10000000000000000 : ℚ)) + (q := (23442647198638999 / 160000000000000000 : ℚ)) + (U := (-(19206169210263464948851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_3 : Uω (aρ 3) (bρ 3) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1630,25 +1483,21 @@ lemma U_201_3 : have hlg : Real.log (22654094524535327 / 160000000000000000 : ℝ) ≤ (-(9774166025761886195709 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22654094524535327 / 160000000000000000 : ℝ) = - (22654094524535327 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22654094524535327 / 20000000000000000 : ℚ)) - (U := (623041678738113804291 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22654094524535327 / 20000000000000000 : ℝ) ≤ - (623041678738113804291 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (353317092885811 / 2500000000000000 : ℝ)) (q := - (22654094524535327 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22654094524535327 / 160000000000000000 : ℚ)) + (r' := (22654094524535327 / 20000000000000000 : ℚ)) + (U := (-(9774166025761886195709 / 5000000000000000000000 : ℚ))) + (U' := (623041678738113804291 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (353317092885811 / 2500000000000000 : ℚ)) + (q := (22654094524535327 / 160000000000000000 : ℚ)) + (U := (-(9774166025761886195709 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_4 : Uω (aρ 4) (bρ 4) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1656,25 +1505,21 @@ lemma U_201_4 : have hlg : Real.log (21316844199038367 / 160000000000000000 : ℝ) ≤ (-(20156762467954930955953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (21316844199038367 / 160000000000000000 : ℝ) = - (21316844199038367 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21316844199038367 / 20000000000000000 : ℚ)) - (U := (637652941045069044047 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21316844199038367 / 20000000000000000 : ℝ) ≤ - (637652941045069044047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (331101565480281 / 2500000000000000 : ℝ)) (q := - (21316844199038367 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21316844199038367 / 160000000000000000 : ℚ)) + (r' := (21316844199038367 / 20000000000000000 : ℚ)) + (U := (-(20156762467954930955953 / 10000000000000000000000 : ℚ))) + (U' := (637652941045069044047 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (331101565480281 / 2500000000000000 : ℚ)) + (q := (21316844199038367 / 160000000000000000 : ℚ)) + (U := (-(20156762467954930955953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_5 : Uω (aρ 5) (bρ 5) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1682,25 +1527,21 @@ lemma U_201_5 : have hlg : Real.log (19197049055365631 / 160000000000000000 : ℝ) ≤ (-(10602086210028209019321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19197049055365631 / 160000000000000000 : ℝ) = - (19197049055365631 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19197049055365631 / 10000000000000000 : ℚ)) - (U := (3260857395971790980679 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19197049055365631 / 10000000000000000 : ℝ) ≤ - (3260857395971790980679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (147202723537129 / 1250000000000000 : ℝ)) (q := - (19197049055365631 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19197049055365631 / 160000000000000000 : ℚ)) + (r' := (19197049055365631 / 10000000000000000 : ℚ)) + (U := (-(10602086210028209019321 / 5000000000000000000000 : ℚ))) + (U' := (3260857395971790980679 / 5000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (147202723537129 / 1250000000000000 : ℚ)) + (q := (19197049055365631 / 160000000000000000 : ℚ)) + (U := (-(10602086210028209019321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_6 : Uω (aρ 6) (bρ 6) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1708,25 +1549,21 @@ lemma U_201_6 : have hlg : Real.log (3177515664269971 / 32000000000000000 : ℝ) ≤ (-(23096362479439773573517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3177515664269971 / 32000000000000000 : ℝ) = - (3177515664269971 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3177515664269971 / 2000000000000000 : ℚ)) - (U := (4629524732560226426483 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3177515664269971 / 2000000000000000 : ℝ) ≤ - (4629524732560226426483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46558916084253 / 500000000000000 : ℝ)) (q := - (3177515664269971 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3177515664269971 / 32000000000000000 : ℚ)) + (r' := (3177515664269971 / 2000000000000000 : ℚ)) + (U := (-(23096362479439773573517 / 10000000000000000000000 : ℚ))) + (U' := (4629524732560226426483 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (46558916084253 / 500000000000000 : ℚ)) + (q := (3177515664269971 / 32000000000000000 : ℚ)) + (U := (-(23096362479439773573517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_7 : Uω (aρ 7) (bρ 7) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1734,25 +1571,21 @@ lemma U_201_7 : have hlg : Real.log (9967064568070847 / 160000000000000000 : ℝ) ≤ (-(27758876997846690296493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (9967064568070847 / 160000000000000000 : ℝ) = - (9967064568070847 / 5000000000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9967064568070847 / 5000000000000000 : ℚ)) - (U := (6898482017153309703507 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9967064568070847 / 5000000000000000 : ℝ) ≤ - (6898482017153309703507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6480866926331 / 156250000000000 : ℝ)) (q := - (9967064568070847 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9967064568070847 / 160000000000000000 : ℚ)) + (r' := (9967064568070847 / 5000000000000000 : ℚ)) + (U := (-(27758876997846690296493 / 10000000000000000000000 : ℚ))) + (U' := (6898482017153309703507 / 10000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19893193996399 / 128000000000000 : ℚ)) + (s := (6480866926331 / 156250000000000 : ℚ)) + (q := (9967064568070847 / 160000000000000000 : ℚ)) + (U := (-(27758876997846690296493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_201_8 : Uω (aρ 8) (bρ 8) (19893193996399 / 128000000000000 : ℝ) ≤ @@ -1890,25 +1723,21 @@ lemma U_202_1 : have hlg : Real.log (11951890325690203 / 80000000000000000 : ℝ) ≤ (-(19011371817764254291277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11951890325690203 / 80000000000000000 : ℝ) = - (11951890325690203 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11951890325690203 / 10000000000000000 : ℚ)) - (U := (1783043591235745708723 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11951890325690203 / 10000000000000000 : ℝ) ≤ - (1783043591235745708723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (373469519570833 / 2500000000000000 : ℝ)) (q := - (11951890325690203 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11951890325690203 / 80000000000000000 : ℚ)) + (r' := (11951890325690203 / 10000000000000000 : ℚ)) + (U := (-(19011371817764254291277 / 10000000000000000000000 : ℚ))) + (U' := (1783043591235745708723 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (373469519570833 / 2500000000000000 : ℚ)) + (q := (11951890325690203 / 80000000000000000 : ℚ)) + (U := (-(19011371817764254291277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_2 : Uω (aρ 2) (bρ 2) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -1916,25 +1745,21 @@ lemma U_202_2 : have hlg : Real.log (11756828615332171 / 80000000000000000 : ℝ) ≤ (-(19175924033595514993157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11756828615332171 / 80000000000000000 : ℝ) = - (11756828615332171 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11756828615332171 / 10000000000000000 : ℚ)) - (U := (1618491375404485006843 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11756828615332171 / 10000000000000000 : ℝ) ≤ - (1618491375404485006843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (91805103950239 / 625000000000000 : ℝ)) (q := - (11756828615332171 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11756828615332171 / 80000000000000000 : ℚ)) + (r' := (11756828615332171 / 10000000000000000 : ℚ)) + (U := (-(19175924033595514993157 / 10000000000000000000000 : ℚ))) + (U' := (1618491375404485006843 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (91805103950239 / 625000000000000 : ℚ)) + (q := (11756828615332171 / 80000000000000000 : ℚ)) + (U := (-(19175924033595514993157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_3 : Uω (aρ 3) (bρ 3) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -1942,25 +1767,21 @@ lemma U_202_3 : have hlg : Real.log (11362600180108659 / 80000000000000000 : ℝ) ≤ (-(19516993576980804934593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11362600180108659 / 80000000000000000 : ℝ) = - (11362600180108659 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11362600180108659 / 10000000000000000 : ℚ)) - (U := (1277421832019195065407 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11362600180108659 / 10000000000000000 : ℝ) ≤ - (1277421832019195065407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (708860330373973 / 5000000000000000 : ℝ)) (q := - (11362600180108659 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11362600180108659 / 80000000000000000 : ℚ)) + (r' := (11362600180108659 / 10000000000000000 : ℚ)) + (U := (-(19516993576980804934593 / 10000000000000000000000 : ℚ))) + (U' := (1277421832019195065407 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (708860330373973 / 5000000000000000 : ℚ)) + (q := (11362600180108659 / 80000000000000000 : ℚ)) + (U := (-(19516993576980804934593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_4 : Uω (aρ 4) (bρ 4) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -1968,25 +1789,21 @@ lemma U_202_4 : have hlg : Real.log (10694120498127499 / 80000000000000000 : ℝ) ≤ (-(10061662648026687643777 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10694120498127499 / 80000000000000000 : ℝ) = - (10694120498127499 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10694120498127499 / 10000000000000000 : ℚ)) - (U := (335545056473312356223 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10694120498127499 / 10000000000000000 : ℝ) ≤ - (335545056473312356223 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (166111865164707 / 1250000000000000 : ℝ)) (q := - (10694120498127499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10694120498127499 / 80000000000000000 : ℚ)) + (r' := (10694120498127499 / 10000000000000000 : ℚ)) + (U := (-(10061662648026687643777 / 5000000000000000000000 : ℚ))) + (U' := (335545056473312356223 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (166111865164707 / 1250000000000000 : ℚ)) + (q := (10694120498127499 / 80000000000000000 : ℚ)) + (U := (-(10061662648026687643777 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_5 : Uω (aρ 5) (bρ 5) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -1994,25 +1811,21 @@ lemma U_202_5 : have hlg : Real.log (1926935660068307 / 16000000000000000 : ℝ) ≤ (-(2645822151221018910863 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1926935660068307 / 16000000000000000 : ℝ) = - (1926935660068307 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1926935660068307 / 1000000000000000 : ℚ)) - (U := (819913750278981089137 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1926935660068307 / 1000000000000000 : ℝ) ≤ - (819913750278981089137 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (236444858241233 / 2000000000000000 : ℝ)) (q := - (1926935660068307 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1926935660068307 / 16000000000000000 : ℚ)) + (r' := (1926935660068307 / 1000000000000000 : ℚ)) + (U := (-(2645822151221018910863 / 1250000000000000000000 : ℚ))) + (U' := (819913750278981089137 / 1250000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (236444858241233 / 2000000000000000 : ℚ)) + (q := (1926935660068307 / 16000000000000000 : ℚ)) + (U := (-(2645822151221018910863 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_6 : Uω (aρ 6) (bρ 6) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -2020,25 +1833,21 @@ lemma U_202_6 : have hlg : Real.log (7981619824227011 / 80000000000000000 : ℝ) ≤ (-(5762213143197609709187 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7981619824227011 / 80000000000000000 : ℝ) = - (7981619824227011 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7981619824227011 / 5000000000000000 : ℚ)) - (U := (1169258659802390290813 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7981619824227011 / 5000000000000000 : ℝ) ≤ - (1169258659802390290813 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (468100023658767 / 5000000000000000 : ℝ)) (q := - (7981619824227011 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7981619824227011 / 80000000000000000 : ℚ)) + (r' := (7981619824227011 / 5000000000000000 : ℚ)) + (U := (-(5762213143197609709187 / 2500000000000000000000 : ℚ))) + (U' := (1169258659802390290813 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (468100023658767 / 5000000000000000 : ℚ)) + (q := (7981619824227011 / 80000000000000000 : ℚ)) + (U := (-(5762213143197609709187 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_7 : Uω (aρ 7) (bρ 7) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -2046,25 +1855,21 @@ lemma U_202_7 : have hlg : Real.log (5036550062220967 / 80000000000000000 : ℝ) ≤ (-(13826526486999273842053 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5036550062220967 / 80000000000000000 : ℝ) = - (5036550062220967 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5036550062220967 / 5000000000000000 : ℚ)) - (U := (36417119000726157947 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5036550062220967 / 5000000000000000 : ℝ) ≤ - (36417119000726157947 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (423593987576023 / 10000000000000000 : ℝ)) (q := - (5036550062220967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5036550062220967 / 80000000000000000 : ℚ)) + (r' := (5036550062220967 / 5000000000000000 : ℚ)) + (U := (-(13826526486999273842053 / 5000000000000000000000 : ℚ))) + (U' := (36417119000726157947 / 5000000000000000000000 : ℚ)) + 4 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1994997403167 / 12800000000000 : ℚ)) + (s := (423593987576023 / 10000000000000000 : ℚ)) + (q := (5036550062220967 / 80000000000000000 : ℚ)) + (U := (-(13826526486999273842053 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_202_8 : Uω (aρ 8) (bρ 8) (1994997403167 / 12800000000000 : ℝ) ≤ @@ -2202,25 +2007,21 @@ lemma U_203_1 : have hlg : Real.log (4794952164296841 / 32000000000000000 : ℝ) ≤ (-(18981721698975795827751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4794952164296841 / 32000000000000000 : ℝ) = - (4794952164296841 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4794952164296841 / 4000000000000000 : ℚ)) - (U := (1812693710024204172249 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4794952164296841 / 4000000000000000 : ℝ) ≤ - (1812693710024204172249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (37457866482269 / 250000000000000 : ℝ)) (q := - (4794952164296841 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4794952164296841 / 32000000000000000 : ℚ)) + (r' := (4794952164296841 / 4000000000000000 : ℚ)) + (U := (-(18981721698975795827751 / 10000000000000000000000 : ℚ))) + (U' := (1812693710024204172249 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (37457866482269 / 250000000000000 : ℚ)) + (q := (4794952164296841 / 32000000000000000 : ℚ)) + (U := (-(18981721698975795827751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_2 : Uω (aρ 2) (bρ 2) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2228,25 +2029,21 @@ lemma U_203_2 : have hlg : Real.log (23584667051899501 / 160000000000000000 : ℝ) ≤ (-(3829154029520808723151 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23584667051899501 / 160000000000000000 : ℝ) = - (23584667051899501 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23584667051899501 / 20000000000000000 : ℚ)) - (U := (329729052279191276849 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23584667051899501 / 20000000000000000 : ℝ) ≤ - (329729052279191276849 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (92082621912667 / 625000000000000 : ℝ)) (q := - (23584667051899501 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23584667051899501 / 160000000000000000 : ℚ)) + (r' := (23584667051899501 / 20000000000000000 : ℚ)) + (U := (-(3829154029520808723151 / 2000000000000000000000 : ℚ))) + (U' := (329729052279191276849 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (92082621912667 / 625000000000000 : ℚ)) + (q := (23584667051899501 / 160000000000000000 : ℚ)) + (U := (-(3829154029520808723151 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_3 : Uω (aρ 3) (bρ 3) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2254,25 +2051,21 @@ lemma U_203_3 : have hlg : Real.log (22796305378484141 / 160000000000000000 : ℝ) ≤ (-(19485753364276007235131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22796305378484141 / 160000000000000000 : ℝ) = - (22796305378484141 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22796305378484141 / 20000000000000000 : ℚ)) - (U := (1308662044723992764869 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22796305378484141 / 20000000000000000 : ℝ) ≤ - (1308662044723992764869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177771605971969 / 1250000000000000 : ℝ)) (q := - (22796305378484141 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22796305378484141 / 160000000000000000 : ℚ)) + (r' := (22796305378484141 / 20000000000000000 : ℚ)) + (U := (-(19485753364276007235131 / 10000000000000000000000 : ℚ))) + (U' := (1308662044723992764869 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (177771605971969 / 1250000000000000 : ℚ)) + (q := (22796305378484141 / 160000000000000000 : ℚ)) + (U := (-(19485753364276007235131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_4 : Uω (aρ 4) (bρ 4) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2280,25 +2073,21 @@ lemma U_203_4 : have hlg : Real.log (4291926994118857 / 32000000000000000 : ℝ) ≤ (-(4018000174308122372943 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4291926994118857 / 32000000000000000 : ℝ) = - (4291926994118857 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4291926994118857 / 4000000000000000 : ℚ)) - (U := (140882907491877627057 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4291926994118857 / 4000000000000000 : ℝ) ≤ - (140882907491877627057 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33334580696363 / 250000000000000 : ℝ)) (q := - (4291926994118857 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4291926994118857 / 32000000000000000 : ℚ)) + (r' := (4291926994118857 / 4000000000000000 : ℚ)) + (U := (-(4018000174308122372943 / 2000000000000000000000 : ℚ))) + (U' := (140882907491877627057 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (33334580696363 / 250000000000000 : ℚ)) + (q := (4291926994118857 / 32000000000000000 : ℚ)) + (U := (-(4018000174308122372943 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_5 : Uω (aρ 5) (bρ 5) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2306,25 +2095,21 @@ lemma U_203_5 : have hlg : Real.log (19341653998148173 / 160000000000000000 : ℝ) ≤ (-(4225825611375491178981 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19341653998148173 / 160000000000000000 : ℝ) = - (19341653998148173 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19341653998148173 / 10000000000000000 : ℚ)) - (U := (1319351831024508821019 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19341653998148173 / 10000000000000000 : ℝ) ≤ - (1319351831024508821019 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (296706381408439 / 2500000000000000 : ℝ)) (q := - (19341653998148173 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19341653998148173 / 160000000000000000 : ℚ)) + (r' := (19341653998148173 / 10000000000000000 : ℚ)) + (U := (-(4225825611375491178981 / 2000000000000000000000 : ℚ))) + (U' := (1319351831024508821019 / 2000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (296706381408439 / 2500000000000000 : ℚ)) + (q := (19341653998148173 / 160000000000000000 : ℚ)) + (U := (-(4225825611375491178981 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_6 : Uω (aρ 6) (bρ 6) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2332,25 +2117,21 @@ lemma U_203_6 : have hlg : Real.log (16038853886297317 / 160000000000000000 : ℝ) ≤ (-(1437599792363333804987 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16038853886297317 / 160000000000000000 : ℝ) = - (16038853886297317 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16038853886297317 / 10000000000000000 : ℚ)) - (U := (295268158386666195013 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16038853886297317 / 10000000000000000 : ℝ) ≤ - (295268158386666195013 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (941215886792399 / 10000000000000000 : ℝ)) (q := - (16038853886297317 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16038853886297317 / 160000000000000000 : ℚ)) + (r' := (16038853886297317 / 10000000000000000 : ℚ)) + (U := (-(1437599792363333804987 / 625000000000000000000 : ℚ))) + (U' := (295268158386666195013 / 625000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (941215886792399 / 10000000000000000 : ℚ)) + (q := (16038853886297317 / 160000000000000000 : ℚ)) + (U := (-(1437599792363333804987 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_7 : Uω (aρ 7) (bρ 7) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2358,25 +2139,21 @@ lemma U_203_7 : have hlg : Real.log (10178060827909021 / 160000000000000000 : ℝ) ≤ (-(27549393096344733901133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10178060827909021 / 160000000000000000 : ℝ) = - (10178060827909021 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10178060827909021 / 10000000000000000 : ℚ)) - (U := (176494115655266098867 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10178060827909021 / 10000000000000000 : ℝ) ≤ - (176494115655266098867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216139067626931 / 5000000000000000 : ℝ)) (q := - (10178060827909021 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10178060827909021 / 160000000000000000 : ℚ)) + (r' := (10178060827909021 / 10000000000000000 : ℚ)) + (U := (-(27549393096344733901133 / 10000000000000000000000 : ℚ))) + (U' := (176494115655266098867 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20006754066941 / 128000000000000 : ℚ)) + (s := (216139067626931 / 5000000000000000 : ℚ)) + (q := (10178060827909021 / 160000000000000000 : ℚ)) + (U := (-(27549393096344733901133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_203_8 : Uω (aρ 8) (bρ 8) (20006754066941 / 128000000000000 : ℝ) ≤ @@ -2515,25 +2292,21 @@ lemma U_204_1 : have hlg : Real.log (6011435240330763 / 40000000000000000 : ℝ) ≤ (-(18952159245899628942921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6011435240330763 / 40000000000000000 : ℝ) = - (6011435240330763 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6011435240330763 / 5000000000000000 : ℚ)) - (U := (1842256163100371057079 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6011435240330763 / 5000000000000000 : ℝ) ≤ - (1842256163100371057079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1502751236515069 / 10000000000000000 : ℝ)) (q := - (6011435240330763 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6011435240330763 / 40000000000000000 : ℚ)) + (r' := (6011435240330763 / 5000000000000000 : ℚ)) + (U := (-(18952159245899628942921 / 10000000000000000000000 : ℚ))) + (U' := (1842256163100371057079 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (1502751236515069 / 10000000000000000 : ℚ)) + (q := (6011435240330763 / 40000000000000000 : ℚ)) + (U := (-(18952159245899628942921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_2 : Uω (aρ 2) (bρ 2) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2541,25 +2314,21 @@ lemma U_204_2 : have hlg : Real.log (5913919166061143 / 40000000000000000 : ℝ) ≤ (-(2389463375289662657993 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5913919166061143 / 40000000000000000 : ℝ) = - (5913919166061143 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5913919166061143 / 5000000000000000 : ℚ)) - (U := (209838550835337342007 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5913919166061143 / 5000000000000000 : ℝ) ≤ - (209838550835337342007 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1477762211890259 / 10000000000000000 : ℝ)) (q := - (5913919166061143 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5913919166061143 / 40000000000000000 : ℚ)) + (r' := (5913919166061143 / 5000000000000000 : ℚ)) + (U := (-(2389463375289662657993 / 1250000000000000000000 : ℚ))) + (U' := (209838550835337342007 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (1477762211890259 / 10000000000000000 : ℚ)) + (q := (5913919166061143 / 40000000000000000 : ℚ)) + (U := (-(2389463375289662657993 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_3 : Uω (aρ 3) (bρ 3) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2567,25 +2336,21 @@ lemma U_204_3 : have hlg : Real.log (5716852396747183 / 40000000000000000 : ℝ) ≤ (-(19454610796911121675621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5716852396747183 / 40000000000000000 : ℝ) = - (5716852396747183 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5716852396747183 / 5000000000000000 : ℚ)) - (U := (1339804612088878324379 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5716852396747183 / 5000000000000000 : ℝ) ≤ - (1339804612088878324379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1426624933583279 / 10000000000000000 : ℝ)) (q := - (5716852396747183 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5716852396747183 / 40000000000000000 : ℚ)) + (r' := (5716852396747183 / 5000000000000000 : ℚ)) + (U := (-(19454610796911121675621 / 10000000000000000000000 : ℚ))) + (U' := (1339804612088878324379 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (1426624933583279 / 10000000000000000 : ℚ)) + (q := (5716852396747183 / 40000000000000000 : ℚ)) + (U := (-(19454610796911121675621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_4 : Uω (aρ 4) (bρ 4) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2593,25 +2358,21 @@ lemma U_204_4 : have hlg : Real.log (5382756537616719 / 40000000000000000 : ℝ) ≤ (-(20056788427891101095629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5382756537616719 / 40000000000000000 : ℝ) = - (5382756537616719 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5382756537616719 / 5000000000000000 : ℚ)) - (U := (737626981108898904371 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5382756537616719 / 5000000000000000 : ℝ) ≤ - (737626981108898904371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1337871185083047 / 10000000000000000 : ℝ)) (q := - (5382756537616719 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5382756537616719 / 40000000000000000 : ℚ)) + (r' := (5382756537616719 / 5000000000000000 : ℚ)) + (U := (-(20056788427891101095629 / 10000000000000000000000 : ℚ))) + (U' := (737626981108898904371 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (1337871185083047 / 10000000000000000 : ℚ)) + (q := (5382756537616719 / 40000000000000000 : ℚ)) + (U := (-(20056788427891101095629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_5 : Uω (aρ 5) (bρ 5) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2619,25 +2380,21 @@ lemma U_204_5 : have hlg : Real.log (4853485341333163 / 40000000000000000 : ℝ) ≤ (-(4218364758269121785757 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4853485341333163 / 40000000000000000 : ℝ) = - (4853485341333163 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4853485341333163 / 2500000000000000 : ℚ)) - (U := (1326812684130878214243 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4853485341333163 / 2500000000000000 : ℝ) ≤ - (1326812684130878214243 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1191425506276269 / 10000000000000000 : ℝ)) (q := - (4853485341333163 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4853485341333163 / 40000000000000000 : ℚ)) + (r' := (4853485341333163 / 2500000000000000 : ℚ)) + (U := (-(4218364758269121785757 / 2000000000000000000000 : ℚ))) + (U' := (1326812684130878214243 / 2000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (1191425506276269 / 10000000000000000 : ℚ)) + (q := (4853485341333163 / 40000000000000000 : ℚ)) + (U := (-(4218364758269121785757 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_6 : Uω (aρ 6) (bρ 6) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2645,25 +2402,21 @@ lemma U_204_6 : have hlg : Real.log (4028605445931183 / 40000000000000000 : ℝ) ≤ (-(22954591801955800902821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4028605445931183 / 40000000000000000 : ℝ) = - (4028605445931183 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4028605445931183 / 2500000000000000 : ℚ)) - (U := (4771295410044199097179 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4028605445931183 / 2500000000000000 : ℝ) ≤ - (4771295410044199097179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (946225933715279 / 10000000000000000 : ℝ)) (q := - (4028605445931183 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4028605445931183 / 40000000000000000 : ℚ)) + (r' := (4028605445931183 / 2500000000000000 : ℚ)) + (U := (-(22954591801955800902821 / 10000000000000000000000 : ℚ))) + (U' := (4771295410044199097179 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (946225933715279 / 10000000000000000 : ℚ)) + (q := (4028605445931183 / 40000000000000000 : ℚ)) + (U := (-(22954591801955800902821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_7 : Uω (aρ 7) (bρ 7) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2671,25 +2424,21 @@ lemma U_204_7 : have hlg : Real.log (2570502550129551 / 40000000000000000 : ℝ) ≤ (-(68619450712148196321 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2570502550129551 / 40000000000000000 : ℝ) = - (2570502550129551 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2570502550129551 / 2500000000000000 : ℚ)) - (U := (695267317851803679 / 25000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2570502550129551 / 2500000000000000 : ℝ) ≤ - (695267317851803679 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (440835866574463 / 10000000000000000 : ℝ)) (q := - (2570502550129551 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2570502550129551 / 40000000000000000 : ℚ)) + (r' := (2570502550129551 / 2500000000000000 : ℚ)) + (U := (-(68619450712148196321 / 25000000000000000000 : ℚ))) + (U' := (695267317851803679 / 25000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5015883525553 / 32000000000000 : ℚ)) + (s := (440835866574463 / 10000000000000000 : ℚ)) + (q := (2570502550129551 / 40000000000000000 : ℚ)) + (U := (-(68619450712148196321 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_204_8 : Uω (aρ 8) (bρ 8) (5015883525553 / 32000000000000 : ℝ) ≤ @@ -2826,25 +2575,21 @@ lemma U_205_1 : have hlg : Real.log (4823344214232847 / 32000000000000000 : ℝ) ≤ (-(4730670985398022320463 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4823344214232847 / 32000000000000000 : ℝ) = - (4823344214232847 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4823344214232847 / 4000000000000000 : ℚ)) - (U := (467932866851977679537 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4823344214232847 / 4000000000000000 : ℝ) ≤ - (467932866851977679537 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (150718780998967 / 1000000000000000 : ℝ)) (q := - (4823344214232847 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4823344214232847 / 32000000000000000 : ℚ)) + (r' := (4823344214232847 / 4000000000000000 : ℚ)) + (U := (-(4730670985398022320463 / 2500000000000000000000 : ℚ))) + (U' := (467932866851977679537 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (150718780998967 / 1000000000000000 : ℚ)) + (q := (4823344214232847 / 32000000000000000 : ℚ)) + (U := (-(4730670985398022320463 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_2 : Uω (aρ 2) (bρ 2) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2852,25 +2597,21 @@ lemma U_205_2 : have hlg : Real.log (23726686069576899 / 160000000000000000 : ℝ) ≤ (-(9542867026361629120287 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23726686069576899 / 160000000000000000 : ℝ) = - (23726686069576899 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23726686069576899 / 20000000000000000 : ℚ)) - (U := (854340678138370879713 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23726686069576899 / 20000000000000000 : ℝ) ≤ - (854340678138370879713 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1482202447301253 / 10000000000000000 : ℝ)) (q := - (23726686069576899 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23726686069576899 / 160000000000000000 : ℚ)) + (r' := (23726686069576899 / 20000000000000000 : ℚ)) + (U := (-(9542867026361629120287 / 5000000000000000000000 : ℚ))) + (U' := (854340678138370879713 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (1482202447301253 / 10000000000000000 : ℚ)) + (q := (23726686069576899 / 160000000000000000 : ℚ)) + (U := (-(9542867026361629120287 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_3 : Uω (aρ 3) (bρ 3) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2878,25 +2619,21 @@ lemma U_205_3 : have hlg : Real.log (22938512993288603 / 160000000000000000 : ℝ) ≤ (-(3884713052838447392357 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22938512993288603 / 160000000000000000 : ℝ) = - (22938512993288603 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22938512993288603 / 20000000000000000 : ℚ)) - (U := (274170028961552607643 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22938512993288603 / 20000000000000000 : ℝ) ≤ - (274170028961552607643 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89442307444701 / 625000000000000 : ℝ)) (q := - (22938512993288603 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22938512993288603 / 160000000000000000 : ℚ)) + (r' := (22938512993288603 / 20000000000000000 : ℚ)) + (U := (-(3884713052838447392357 / 2000000000000000000000 : ℚ))) + (U' := (274170028961552607643 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (89442307444701 / 625000000000000 : ℚ)) + (q := (22938512993288603 / 160000000000000000 : ℚ)) + (U := (-(3884713052838447392357 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_4 : Uω (aρ 4) (bρ 4) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2904,25 +2641,21 @@ lemma U_205_4 : have hlg : Real.log (4320482912780263 / 32000000000000000 : ℝ) ≤ (-(2502960900806985594063 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4320482912780263 / 32000000000000000 : ℝ) = - (4320482912780263 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4320482912780263 / 4000000000000000 : ℚ)) - (U := (96341025318014405937 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4320482912780263 / 4000000000000000 : ℝ) ≤ - (96341025318014405937 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268471759301361 / 2000000000000000 : ℝ)) (q := - (4320482912780263 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4320482912780263 / 32000000000000000 : ℚ)) + (r' := (4320482912780263 / 4000000000000000 : ℚ)) + (U := (-(2502960900806985594063 / 1250000000000000000000 : ℚ))) + (U' := (96341025318014405937 / 1250000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (268471759301361 / 2000000000000000 : ℚ)) + (q := (4320482912780263 / 32000000000000000 : ℚ)) + (U := (-(2502960900806985594063 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_5 : Uω (aρ 5) (bρ 5) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2930,25 +2663,21 @@ lemma U_205_5 : have hlg : Real.log (19486218817967691 / 160000000000000000 : ℝ) ≤ (-(421093265151500674027 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19486218817967691 / 160000000000000000 : ℝ) = - (19486218817967691 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19486218817967691 / 10000000000000000 : ℚ)) - (U := (133424479088499325973 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19486218817967691 / 10000000000000000 : ℝ) ≤ - (133424479088499325973 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (598012123800051 / 5000000000000000 : ℝ)) (q := - (19486218817967691 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19486218817967691 / 160000000000000000 : ℚ)) + (r' := (19486218817967691 / 10000000000000000 : ℚ)) + (U := (-(421093265151500674027 / 200000000000000000000 : ℚ))) + (U' := (133424479088499325973 / 200000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (598012123800051 / 5000000000000000 : ℚ)) + (q := (19486218817967691 / 160000000000000000 : ℚ)) + (U := (-(421093265151500674027 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_6 : Uω (aρ 6) (bρ 6) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2956,25 +2685,21 @@ lemma U_205_6 : have hlg : Real.log (16189944072949099 / 160000000000000000 : ℝ) ≤ (-(22907835009299187804699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16189944072949099 / 160000000000000000 : ℝ) = - (16189944072949099 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16189944072949099 / 10000000000000000 : ℚ)) - (U := (4818052202700812195301 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16189944072949099 / 10000000000000000 : ℝ) ≤ - (4818052202700812195301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (475615139806389 / 5000000000000000 : ℝ)) (q := - (16189944072949099 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16189944072949099 / 160000000000000000 : ℚ)) + (r' := (16189944072949099 / 10000000000000000 : ℚ)) + (U := (-(22907835009299187804699 / 10000000000000000000000 : ℚ))) + (U' := (4818052202700812195301 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (475615139806389 / 5000000000000000 : ℚ)) + (q := (16189944072949099 / 160000000000000000 : ℚ)) + (U := (-(22907835009299187804699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_7 : Uω (aρ 7) (bρ 7) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -2982,25 +2707,21 @@ lemma U_205_7 : have hlg : Real.log (10385006033903507 / 160000000000000000 : ℝ) ≤ (-(27348107758450982129949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10385006033903507 / 160000000000000000 : ℝ) = - (10385006033903507 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10385006033903507 / 10000000000000000 : ℚ)) - (U := (377779453549017870051 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10385006033903507 / 10000000000000000 : ℝ) ≤ - (377779453549017870051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (449274405492079 / 10000000000000000 : ℝ)) (q := - (10385006033903507 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10385006033903507 / 160000000000000000 : ℚ)) + (r' := (10385006033903507 / 10000000000000000 : ℚ)) + (U := (-(27348107758450982129949 / 10000000000000000000000 : ℚ))) + (U' := (377779453549017870051 / 10000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20120314137483 / 128000000000000 : ℚ)) + (s := (449274405492079 / 10000000000000000 : ℚ)) + (q := (10385006033903507 / 160000000000000000 : ℚ)) + (U := (-(27348107758450982129949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_205_8 : Uω (aρ 8) (bρ 8) (20120314137483 / 128000000000000 : ℝ) ≤ @@ -3137,25 +2858,21 @@ lemma U_206_1 : have hlg : Real.log (12093850575635933 / 80000000000000000 : ℝ) ≤ (-(151146362189353403557 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12093850575635933 / 80000000000000000 : ℝ) = - (12093850575635933 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12093850575635933 / 10000000000000000 : ℚ)) - (U := (15208961082646596443 / 80000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12093850575635933 / 10000000000000000 : ℝ) ≤ - (15208961082646596443 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1511624379747577 / 10000000000000000 : ℝ)) (q := - (12093850575635933 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12093850575635933 / 80000000000000000 : ℚ)) + (r' := (12093850575635933 / 10000000000000000 : ℚ)) + (U := (-(151146362189353403557 / 80000000000000000000 : ℚ))) + (U' := (15208961082646596443 / 80000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (1511624379747577 / 10000000000000000 : ℚ)) + (q := (12093850575635933 / 80000000000000000 : ℚ)) + (U := (-(151146362189353403557 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_2 : Uω (aρ 2) (bρ 2) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3163,25 +2880,21 @@ lemma U_206_2 : have hlg : Real.log (11898847634875677 / 80000000000000000 : ℝ) ≤ (-(1905585075871011538629 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11898847634875677 / 80000000000000000 : ℝ) = - (11898847634875677 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11898847634875677 / 10000000000000000 : ℚ)) - (U := (173856465028988461371 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11898847634875677 / 10000000000000000 : ℝ) ≤ - (173856465028988461371 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1486642657067513 / 10000000000000000 : ℝ)) (q := - (11898847634875677 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11898847634875677 / 80000000000000000 : ℚ)) + (r' := (11898847634875677 / 10000000000000000 : ℚ)) + (U := (-(1905585075871011538629 / 1000000000000000000000 : ℚ))) + (U' := (173856465028988461371 / 1000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (1486642657067513 / 10000000000000000 : ℚ)) + (q := (11898847634875677 / 80000000000000000 : ℚ)) + (U := (-(1905585075871011538629 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_3 : Uω (aρ 3) (bρ 3) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3189,25 +2902,21 @@ lemma U_206_3 : have hlg : Real.log (11504807802423677 / 80000000000000000 : ℝ) ≤ (-(775704646446275497539 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11504807802423677 / 80000000000000000 : ℝ) = - (11504807802423677 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11504807802423677 / 10000000000000000 : ℚ)) - (U := (56071969913724502461 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11504807802423677 / 10000000000000000 : ℝ) ≤ - (56071969913724502461 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1435528805304513 / 10000000000000000 : ℝ)) (q := - (11504807802423677 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11504807802423677 / 80000000000000000 : ℚ)) + (r' := (11504807802423677 / 10000000000000000 : ℚ)) + (U := (-(775704646446275497539 / 400000000000000000000 : ℚ))) + (U' := (56071969913724502461 / 400000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (1435528805304513 / 10000000000000000 : ℚ)) + (q := (11504807802423677 / 80000000000000000 : ℚ)) + (U := (-(775704646446275497539 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_4 : Uω (aρ 4) (bρ 4) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3215,25 +2924,21 @@ lemma U_206_4 : have hlg : Real.log (10836900119275209 / 80000000000000000 : ℝ) ≤ (-(19990696456353944320339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10836900119275209 / 80000000000000000 : ℝ) = - (10836900119275209 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10836900119275209 / 10000000000000000 : ℚ)) - (U := (803718952646055679661 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10836900119275209 / 10000000000000000 : ℝ) ≤ - (803718952646055679661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (336711516395599 / 2500000000000000 : ℝ)) (q := - (10836900119275209 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10836900119275209 / 80000000000000000 : ℚ)) + (r' := (10836900119275209 / 10000000000000000 : ℚ)) + (U := (-(19990696456353944320339 / 10000000000000000000000 : ℚ))) + (U' := (803718952646055679661 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (336711516395599 / 2500000000000000 : ℚ)) + (q := (10836900119275209 / 80000000000000000 : ℚ)) + (U := (-(19990696456353944320339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_5 : Uω (aρ 5) (bρ 5) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3241,25 +2946,21 @@ lemma U_206_5 : have hlg : Real.log (1955848646998037 / 16000000000000000 : ℝ) ≤ (-(21017645314166303358547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1955848646998037 / 16000000000000000 : ℝ) = - (1955848646998037 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1955848646998037 / 1000000000000000 : ℚ)) - (U := (6708241897833696641453 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1955848646998037 / 1000000000000000 : ℝ) ≤ - (6708241897833696641453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (60031088192307 / 500000000000000 : ℝ)) (q := - (1955848646998037 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1955848646998037 / 16000000000000000 : ℚ)) + (r' := (1955848646998037 / 1000000000000000 : ℚ)) + (U := (-(21017645314166303358547 / 10000000000000000000000 : ℚ))) + (U' := (6708241897833696641453 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (60031088192307 / 500000000000000 : ℚ)) + (q := (1955848646998037 / 16000000000000000 : ℚ)) + (U := (-(21017645314166303358547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_6 : Uω (aρ 6) (bρ 6) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3267,25 +2968,21 @@ lemma U_206_6 : have hlg : Real.log (8132710735015393 / 80000000000000000 : ℝ) ≤ (-(11430661709532966677083 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8132710735015393 / 80000000000000000 : ℝ) = - (8132710735015393 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8132710735015393 / 5000000000000000 : ℚ)) - (U := (2432281896467033322917 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8132710735015393 / 5000000000000000 : ℝ) ≤ - (2432281896467033322917 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (478114506996221 / 5000000000000000 : ℝ)) (q := - (8132710735015393 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8132710735015393 / 80000000000000000 : ℚ)) + (r' := (8132710735015393 / 5000000000000000 : ℚ)) + (U := (-(11430661709532966677083 / 5000000000000000000000 : ℚ))) + (U' := (2432281896467033322917 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (478114506996221 / 5000000000000000 : ℚ)) + (q := (8132710735015393 / 80000000000000000 : ℚ)) + (U := (-(11430661709532966677083 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_7 : Uω (aρ 7) (bρ 7) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3293,25 +2990,21 @@ lemma U_206_7 : have hlg : Real.log (5243550540331877 / 80000000000000000 : ℝ) ≤ (-(13625138903623822801247 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5243550540331877 / 80000000000000000 : ℝ) = - (5243550540331877 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5243550540331877 / 5000000000000000 : ℚ)) - (U := (237804702376177198753 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5243550540331877 / 5000000000000000 : ℝ) ≤ - (237804702376177198753 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (457600346081563 / 10000000000000000 : ℝ)) (q := - (5243550540331877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5243550540331877 / 80000000000000000 : ℚ)) + (r' := (5243550540331877 / 5000000000000000 : ℚ)) + (U := (-(13625138903623822801247 / 5000000000000000000000 : ℚ))) + (U' := (237804702376177198753 / 5000000000000000000000 : ℚ)) + 4 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10088547086377 / 64000000000000 : ℚ)) + (s := (457600346081563 / 10000000000000000 : ℚ)) + (q := (5243550540331877 / 80000000000000000 : ℚ)) + (U := (-(13625138903623822801247 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_206_8 : Uω (aρ 8) (bρ 8) (10088547086377 / 64000000000000 : ℝ) ≤ @@ -3448,25 +3141,21 @@ lemma U_207_1 : have hlg : Real.log (24258681201906977 / 160000000000000000 : ℝ) ≤ (-(9431996367126526943871 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24258681201906977 / 160000000000000000 : ℝ) = - (24258681201906977 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24258681201906977 / 20000000000000000 : ℚ)) - (U := (965211337373473056129 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24258681201906977 / 20000000000000000 : ℝ) ≤ - (965211337373473056129 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1516060945821419 / 10000000000000000 : ℝ)) (q := - (24258681201906977 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24258681201906977 / 160000000000000000 : ℚ)) + (r' := (24258681201906977 / 20000000000000000 : ℚ)) + (U := (-(9431996367126526943871 / 5000000000000000000000 : ℚ))) + (U' := (965211337373473056129 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (1516060945821419 / 10000000000000000 : ℚ)) + (q := (24258681201906977 / 160000000000000000 : ℚ)) + (U := (-(9431996367126526943871 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_2 : Uω (aρ 2) (bρ 2) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3474,25 +3163,21 @@ lemma U_207_2 : have hlg : Real.log (23868704266600737 / 160000000000000000 : ℝ) ≤ (-(4756514146251913096419 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23868704266600737 / 160000000000000000 : ℝ) = - (23868704266600737 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23868704266600737 / 20000000000000000 : ℚ)) - (U := (442089705998086903581 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23868704266600737 / 20000000000000000 : ℝ) ≤ - (442089705998086903581 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1491082841418139 / 10000000000000000 : ℝ)) (q := - (23868704266600737 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23868704266600737 / 160000000000000000 : ℚ)) + (r' := (23868704266600737 / 20000000000000000 : ℚ)) + (U := (-(4756514146251913096419 / 2500000000000000000000 : ℚ))) + (U' := (442089705998086903581 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (1491082841418139 / 10000000000000000 : ℚ)) + (q := (23868704266600737 / 160000000000000000 : ℚ)) + (U := (-(4756514146251913096419 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_3 : Uω (aρ 3) (bρ 3) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3500,25 +3185,21 @@ lemma U_207_3 : have hlg : Real.log (23080717429036129 / 160000000000000000 : ℝ) ≤ (-(19361762888502309310361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23080717429036129 / 160000000000000000 : ℝ) = - (23080717429036129 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23080717429036129 / 20000000000000000 : ℚ)) - (U := (1432652520497690689639 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23080717429036129 / 20000000000000000 : ℝ) ≤ - (1432652520497690689639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1439980593072563 / 10000000000000000 : ℝ)) (q := - (23080717429036129 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23080717429036129 / 160000000000000000 : ℚ)) + (r' := (23080717429036129 / 20000000000000000 : ℚ)) + (U := (-(19361762888502309310361 / 10000000000000000000000 : ℚ))) + (U' := (1432652520497690689639 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (1439980593072563 / 10000000000000000 : ℚ)) + (q := (23080717429036129 / 160000000000000000 : ℚ)) + (U := (-(19361762888502309310361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_4 : Uω (aρ 4) (bρ 4) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3526,25 +3207,21 @@ lemma U_207_4 : have hlg : Real.log (173961465613581 / 1280000000000000 : ℝ) ≤ (-(4989453858591348907371 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (173961465613581 / 1280000000000000 : ℝ) = - (173961465613581 / 160000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (173961465613581 / 160000000000000 : ℚ)) - (U := (209149993658651092629 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (173961465613581 / 160000000000000 : ℝ) ≤ - (209149993658651092629 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5405331982881 / 40000000000000 : ℝ)) (q := - (173961465613581 / 1280000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (173961465613581 / 1280000000000000 : ℚ)) + (r' := (173961465613581 / 160000000000000 : ℚ)) + (U := (-(4989453858591348907371 / 2500000000000000000000 : ℚ))) + (U' := (209149993658651092629 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (5405331982881 / 40000000000000 : ℚ)) + (q := (173961465613581 / 1280000000000000 : ℚ)) + (U := (-(4989453858591348907371 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_5 : Uω (aρ 5) (bρ 5) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3552,25 +3229,21 @@ lemma U_207_5 : have hlg : Real.log (19630744433529281 / 160000000000000000 : ℝ) ≤ (-(262259610421003907303 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19630744433529281 / 160000000000000000 : ℝ) = - (19630744433529281 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19630744433529281 / 10000000000000000 : ℚ)) - (U := (84313979728996092697 / 125000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19630744433529281 / 10000000000000000 : ℝ) ≤ - (84313979728996092697 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1205218069034207 / 10000000000000000 : ℝ)) (q := - (19630744433529281 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19630744433529281 / 160000000000000000 : ℚ)) + (r' := (19630744433529281 / 10000000000000000 : ℚ)) + (U := (-(262259610421003907303 / 125000000000000000000 : ℚ))) + (U' := (84313979728996092697 / 125000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (1205218069034207 / 10000000000000000 : ℚ)) + (q := (19630744433529281 / 160000000000000000 : ℚ)) + (U := (-(262259610421003907303 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_6 : Uω (aρ 6) (bρ 6) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3578,25 +3251,21 @@ lemma U_207_6 : have hlg : Real.log (16340854675340329 / 160000000000000000 : ℝ) ≤ (-(22815054204177024956727 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16340854675340329 / 160000000000000000 : ℝ) = - (16340854675340329 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16340854675340329 / 10000000000000000 : ℚ)) - (U := (4910833007822975043273 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16340854675340329 / 10000000000000000 : ℝ) ≤ - (4910833007822975043273 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (240305556100147 / 2500000000000000 : ℝ)) (q := - (16340854675340329 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16340854675340329 / 160000000000000000 : ℚ)) + (r' := (16340854675340329 / 10000000000000000 : ℚ)) + (U := (-(22815054204177024956727 / 10000000000000000000000 : ℚ))) + (U' := (4910833007822975043273 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (240305556100147 / 2500000000000000 : ℚ)) + (q := (16340854675340329 / 160000000000000000 : ℚ)) + (U := (-(22815054204177024956727 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_7 : Uω (aρ 7) (bρ 7) (809354968321 / 5120000000000 : ℝ) ≤ @@ -3604,25 +3273,21 @@ lemma U_207_7 : have hlg : Real.log (10588343642389297 / 160000000000000000 : ℝ) ≤ (-(1086168029808033831629 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10588343642389297 / 160000000000000000 : ℝ) = - (10588343642389297 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10588343642389297 / 10000000000000000 : ℚ)) - (U := (22867458671966168371 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10588343642389297 / 10000000000000000 : ℝ) ≤ - (22867458671966168371 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (465819726041709 / 10000000000000000 : ℝ)) (q := - (10588343642389297 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10588343642389297 / 160000000000000000 : ℚ)) + (r' := (10588343642389297 / 10000000000000000 : ℚ)) + (U := (-(1086168029808033831629 / 400000000000000000000 : ℚ))) + (U' := (22867458671966168371 / 400000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (809354968321 / 5120000000000 : ℚ)) + (s := (465819726041709 / 10000000000000000 : ℚ)) + (q := (10588343642389297 / 160000000000000000 : ℚ)) + (U := (-(1086168029808033831629 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_207_8 : Uω (aρ 8) (bρ 8) (809354968321 / 5120000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U17.lean b/LeanPool/Zeta5Irrational/Table/U17.lean index f5a72d6638..31f325d75f 100644 --- a/LeanPool/Zeta5Irrational/Table/U17.lean +++ b/LeanPool/Zeta5Irrational/Table/U17.lean @@ -24,25 +24,21 @@ lemma U_208_1 : have hlg : Real.log (1520603826457973 / 10000000000000000 : ℝ) ≤ (-(18834775819919365320531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1520603826457973 / 10000000000000000 : ℝ) = - (1520603826457973 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1520603826457973 / 1250000000000000 : ℚ)) - (U := (1959639589080634679469 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1520603826457973 / 1250000000000000 : ℝ) ≤ - (1959639589080634679469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (760248754121723 / 5000000000000000 : ℝ)) (q := - (1520603826457973 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1520603826457973 / 10000000000000000 : ℚ)) + (r' := (1520603826457973 / 1250000000000000 : ℚ)) + (U := (-(18834775819919365320531 / 10000000000000000000000 : ℚ))) + (U' := (1959639589080634679469 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (760248754121723 / 5000000000000000 : ℚ)) + (q := (1520603826457973 / 10000000000000000 : ℚ)) + (U := (-(18834775819919365320531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_2 : Uω (aρ 2) (bρ 2) (634082945103 / 4000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_208_2 : have hlg : Real.log (598492826548401 / 4000000000000000 : ℝ) ≤ (-(18996351001129505770501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (598492826548401 / 4000000000000000 : ℝ) = - (598492826548401 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (598492826548401 / 500000000000000 : ℚ)) - (U := (1798064407870494229499 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (598492826548401 / 500000000000000 : ℝ) ≤ - (1798064407870494229499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (299104600115901 / 2000000000000000 : ℝ)) (q := - (598492826548401 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (598492826548401 / 4000000000000000 : ℚ)) + (r' := (598492826548401 / 500000000000000 : ℚ)) + (U := (-(18996351001129505770501 / 10000000000000000000000 : ℚ))) + (U' := (1798064407870494229499 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (299104600115901 / 2000000000000000 : ℚ)) + (q := (598492826548401 / 4000000000000000 : ℚ)) + (U := (-(18996351001129505770501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_3 : Uω (aρ 3) (bρ 3) (634082945103 / 4000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_208_3 : have hlg : Real.log (2893977309141877 / 20000000000000000 : ℝ) ≤ (-(19331004852514832193709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2893977309141877 / 20000000000000000 : ℝ) = - (2893977309141877 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2893977309141877 / 2500000000000000 : ℚ)) - (U := (1463410556485167806291 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2893977309141877 / 2500000000000000 : ℝ) ≤ - (1463410556485167806291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1444432283329377 / 10000000000000000 : ℝ)) (q := - (2893977309141877 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2893977309141877 / 20000000000000000 : ℚ)) + (r' := (2893977309141877 / 2500000000000000 : ℚ)) + (U := (-(19331004852514832193709 / 10000000000000000000000 : ℚ))) + (U' := (1463410556485167806291 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (1444432283329377 / 10000000000000000 : ℚ)) + (q := (2893977309141877 / 20000000000000000 : ℚ)) + (U := (-(19331004852514832193709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_4 : Uω (aρ 4) (bρ 4) (634082945103 / 4000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_208_4 : have hlg : Real.log (681767608758223 / 5000000000000000 : ℝ) ≤ (-(19925043404826570845423 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (681767608758223 / 5000000000000000 : ℝ) = - (681767608758223 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (681767608758223 / 625000000000000 : ℚ)) - (U := (869372004173429154577 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (681767608758223 / 625000000000000 : ℝ) ≤ - (869372004173429154577 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84738724392837 / 625000000000000 : ℝ)) (q := - (681767608758223 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (681767608758223 / 5000000000000000 : ℚ)) + (r' := (681767608758223 / 625000000000000 : ℚ)) + (U := (-(19925043404826570845423 / 10000000000000000000000 : ℚ))) + (U' := (869372004173429154577 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (84738724392837 / 625000000000000 : ℚ)) + (q := (681767608758223 / 5000000000000000 : ℚ)) + (U := (-(19925043404826570845423 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_5 : Uω (aρ 5) (bρ 5) (634082945103 / 4000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_208_5 : have hlg : Real.log (615718525594977 / 5000000000000000 : ℝ) ≤ (-(2618004087800691493427 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (615718525594977 / 5000000000000000 : ℝ) = - (615718525594977 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (615718525594977 / 312500000000000 : ℚ)) - (U := (847731813699308506573 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (615718525594977 / 312500000000000 : ℝ) ≤ - (847731813699308506573 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (75613323560463 / 625000000000000 : ℝ)) (q := - (615718525594977 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (615718525594977 / 5000000000000000 : ℚ)) + (r' := (615718525594977 / 312500000000000 : ℚ)) + (U := (-(2618004087800691493427 / 1250000000000000000000 : ℚ))) + (U' := (847731813699308506573 / 1250000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (75613323560463 / 625000000000000 : ℚ)) + (q := (615718525594977 / 5000000000000000 : ℚ)) + (U := (-(2618004087800691493427 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_6 : Uω (aρ 6) (bρ 6) (634082945103 / 4000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_208_6 : have hlg : Real.log (102601527337529 / 1000000000000000 : ℝ) ≤ (-(22769024589857949647633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (102601527337529 / 1000000000000000 : ℝ) = - (102601527337529 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (102601527337529 / 62500000000000 : ℚ)) - (U := (4956862622142050352367 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (102601527337529 / 62500000000000 : ℝ) ≤ - (4956862622142050352367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1509703119497 / 15625000000000 : ℝ)) (q := - (102601527337529 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (102601527337529 / 1000000000000000 : ℚ)) + (r' := (102601527337529 / 62500000000000 : ℚ)) + (U := (-(22769024589857949647633 / 10000000000000000000000 : ℚ))) + (U' := (4956862622142050352367 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (1509703119497 / 15625000000000 : ℚ)) + (q := (102601527337529 / 1000000000000000 : ℚ)) + (U := (-(22769024589857949647633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_7 : Uω (aρ 7) (bρ 7) (634082945103 / 4000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_208_7 : have hlg : Real.log (1336097259073869 / 20000000000000000 : ℝ) ≤ (-(27059794013414673404811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1336097259073869 / 20000000000000000 : ℝ) = - (1336097259073869 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1336097259073869 / 1250000000000000 : ℚ)) - (U := (666093198585326595189 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1336097259073869 / 1250000000000000 : ℝ) ≤ - (666093198585326595189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (473938089561369 / 10000000000000000 : ℝ)) (q := - (1336097259073869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1336097259073869 / 20000000000000000 : ℚ)) + (r' := (1336097259073869 / 1250000000000000 : ℚ)) + (U := (-(27059794013414673404811 / 10000000000000000000000 : ℚ))) + (U' := (666093198585326595189 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (634082945103 / 4000000000000 : ℚ)) + (s := (473938089561369 / 10000000000000000 : ℚ)) + (q := (1336097259073869 / 20000000000000000 : ℚ)) + (U := (-(27059794013414673404811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_208_8 : Uω (aρ 8) (bρ 8) (634082945103 / 4000000000000 : ℝ) ≤ @@ -336,25 +308,21 @@ lemma U_209_1 : have hlg : Real.log (4880128243157723 / 32000000000000000 : ℝ) ≤ (-(9402822015822657623339 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4880128243157723 / 32000000000000000 : ℝ) = - (4880128243157723 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4880128243157723 / 4000000000000000 : ℚ)) - (U := (994385688677342376661 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4880128243157723 / 4000000000000000 : ℝ) ≤ - (994385688677342376661 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152493406704553 / 1000000000000000 : ℝ)) (q := - (4880128243157723 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4880128243157723 / 32000000000000000 : ℚ)) + (r' := (4880128243157723 / 4000000000000000 : ℚ)) + (U := (-(9402822015822657623339 / 5000000000000000000000 : ℚ))) + (U' := (994385688677342376661 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (152493406704553 / 1000000000000000 : ℚ)) + (q := (4880128243157723 / 32000000000000000 : ℚ)) + (U := (-(9402822015822657623339 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_2 : Uω (aρ 2) (bρ 2) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -362,25 +330,21 @@ lemma U_209_2 : have hlg : Real.log (24010721657546831 / 160000000000000000 : ℝ) ≤ (-(18966733481316253290297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24010721657546831 / 160000000000000000 : ℝ) = - (24010721657546831 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24010721657546831 / 20000000000000000 : ℚ)) - (U := (1827681927683746709703 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24010721657546831 / 20000000000000000 : ℝ) ≤ - (1827681927683746709703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1499963134775307 / 10000000000000000 : ℝ)) (q := - (24010721657546831 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24010721657546831 / 160000000000000000 : ℚ)) + (r' := (24010721657546831 / 20000000000000000 : ℚ)) + (U := (-(18966733481316253290297 / 10000000000000000000000 : ℚ))) + (U' := (1827681927683746709703 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (1499963134775307 / 10000000000000000 : ℚ)) + (q := (24010721657546831 / 160000000000000000 : ℚ)) + (U := (-(18966733481316253290297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_3 : Uω (aρ 3) (bρ 3) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -388,25 +352,21 @@ lemma U_209_3 : have hlg : Real.log (4644583748866899 / 32000000000000000 : ℝ) ≤ (-(19300341465000340110197 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4644583748866899 / 32000000000000000 : ℝ) = - (4644583748866899 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4644583748866899 / 4000000000000000 : ℚ)) - (U := (1494073943999659889803 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4644583748866899 / 4000000000000000 : ℝ) ≤ - (1494073943999659889803 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (289776775394753 / 2000000000000000 : ℝ)) (q := - (4644583748866899 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4644583748866899 / 32000000000000000 : ℚ)) + (r' := (4644583748866899 / 4000000000000000 : ℚ)) + (U := (-(19300341465000340110197 / 10000000000000000000000 : ℚ))) + (U' := (1494073943999659889803 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (289776775394753 / 2000000000000000 : ℚ)) + (q := (4644583748866899 / 32000000000000000 : ℚ)) + (U := (-(19300341465000340110197 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_4 : Uω (aρ 4) (bρ 4) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -414,25 +374,21 @@ lemma U_209_4 : have hlg : Real.log (21887941100810039 / 160000000000000000 : ℝ) ≤ (-(3978475927905370941629 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (21887941100810039 / 160000000000000000 : ℝ) = - (21887941100810039 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21887941100810039 / 20000000000000000 : ℚ)) - (U := (180407153894629058371 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21887941100810039 / 20000000000000000 : ℝ) ≤ - (180407153894629058371 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21254778946847 / 156250000000000 : ℝ)) (q := - (21887941100810039 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21887941100810039 / 160000000000000000 : ℚ)) + (r' := (21887941100810039 / 20000000000000000 : ℚ)) + (U := (-(3978475927905370941629 / 2000000000000000000000 : ℚ))) + (U' := (180407153894629058371 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (21254778946847 / 156250000000000 : ℚ)) + (q := (21887941100810039 / 160000000000000000 : ℚ)) + (U := (-(3978475927905370941629 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_5 : Uω (aρ 5) (bρ 5) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -440,25 +396,21 @@ lemma U_209_5 : have hlg : Real.log (19775231735235271 / 160000000000000000 : ℝ) ≤ (-(5226858955032555311931 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19775231735235271 / 160000000000000000 : ℝ) = - (19775231735235271 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19775231735235271 / 10000000000000000 : ℚ)) - (U := (1704612847967444688069 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19775231735235271 / 10000000000000000 : ℝ) ≤ - (1704612847967444688069 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (607203550618181 / 5000000000000000 : ℝ)) (q := - (19775231735235271 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19775231735235271 / 160000000000000000 : ℚ)) + (r' := (19775231735235271 / 10000000000000000 : ℚ)) + (U := (-(5226858955032555311931 / 2500000000000000000000 : ℚ))) + (U' := (1704612847967444688069 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (607203550618181 / 5000000000000000 : ℚ)) + (q := (19775231735235271 / 160000000000000000 : ℚ)) + (U := (-(5226858955032555311931 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_6 : Uω (aρ 6) (bρ 6) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -466,25 +418,21 @@ lemma U_209_6 : have hlg : Real.log (16491591236337559 / 160000000000000000 : ℝ) ≤ (-(22723231852291062307257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16491591236337559 / 160000000000000000 : ℝ) = - (16491591236337559 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16491591236337559 / 10000000000000000 : ℚ)) - (U := (5002655359708937692743 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16491591236337559 / 10000000000000000 : ℝ) ≤ - (5002655359708937692743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242798103503537 / 2500000000000000 : ℝ)) (q := - (16491591236337559 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16491591236337559 / 160000000000000000 : ℚ)) + (r' := (16491591236337559 / 10000000000000000 : ℚ)) + (U := (-(22723231852291062307257 / 10000000000000000000000 : ℚ))) + (U' := (5002655359708937692743 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (242798103503537 / 2500000000000000 : ℚ)) + (q := (16491591236337559 / 160000000000000000 : ℚ)) + (U := (-(22723231852291062307257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_7 : Uω (aρ 7) (bρ 7) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -492,25 +440,21 @@ lemma U_209_7 : have hlg : Real.log (10788445209094639 / 160000000000000000 : ℝ) ≤ (-(26966981408494280424653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10788445209094639 / 160000000000000000 : ℝ) = - (10788445209094639 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10788445209094639 / 10000000000000000 : ℚ)) - (U := (758905803505719575347 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10788445209094639 / 10000000000000000 : ℝ) ≤ - (758905803505719575347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (481960541368783 / 10000000000000000 : ℝ)) (q := - (10788445209094639 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10788445209094639 / 160000000000000000 : ℚ)) + (r' := (10788445209094639 / 10000000000000000 : ℚ)) + (U := (-(26966981408494280424653 / 10000000000000000000000 : ℚ))) + (U' := (758905803505719575347 / 10000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20347434278567 / 128000000000000 : ℚ)) + (s := (481960541368783 / 10000000000000000 : ℚ)) + (q := (10788445209094639 / 160000000000000000 : ℚ)) + (U := (-(26966981408494280424653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_209_8 : Uω (aρ 8) (bρ 8) (20347434278567 / 128000000000000 : ℝ) ≤ @@ -648,25 +592,21 @@ lemma U_210_1 : have hlg : Real.log (489432423590843 / 3200000000000000 : ℝ) ≤ (-(18776596874758489166257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (489432423590843 / 3200000000000000 : ℝ) = - (489432423590843 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (489432423590843 / 400000000000000 : ℚ)) - (U := (2017818534241510833743 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (489432423590843 / 400000000000000 : ℝ) ≤ - (2017818534241510833743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61174824890367 / 400000000000000 : ℝ)) (q := - (489432423590843 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (489432423590843 / 3200000000000000 : ℚ)) + (r' := (489432423590843 / 400000000000000 : ℚ)) + (U := (-(18776596874758489166257 / 10000000000000000000000 : ℚ))) + (U' := (2017818534241510833743 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (61174824890367 / 400000000000000 : ℚ)) + (q := (489432423590843 / 3200000000000000 : ℚ)) + (U := (-(18776596874758489166257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_2 : Uω (aρ 2) (bρ 2) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -674,25 +614,21 @@ lemma U_210_2 : have hlg : Real.log (2408173005520151 / 16000000000000000 : ℝ) ≤ (-(9468601752239696732103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2408173005520151 / 16000000000000000 : ℝ) = - (2408173005520151 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2408173005520151 / 2000000000000000 : ℚ)) - (U := (928605952260303267897 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2408173005520151 / 2000000000000000 : ℝ) ≤ - (928605952260303267897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (300880648845319 / 2000000000000000 : ℝ)) (q := - (2408173005520151 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2408173005520151 / 16000000000000000 : ℚ)) + (r' := (2408173005520151 / 2000000000000000 : ℚ)) + (U := (-(9468601752239696732103 / 5000000000000000000000 : ℚ))) + (U' := (928605952260303267897 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (300880648845319 / 2000000000000000 : ℚ)) + (q := (2408173005520151 / 16000000000000000 : ℚ)) + (U := (-(9468601752239696732103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_3 : Uω (aρ 3) (bρ 3) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -700,25 +636,21 @@ lemma U_210_3 : have hlg : Real.log (11647009124868387 / 80000000000000000 : ℝ) ≤ (-(19269772143215850917411 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11647009124868387 / 80000000000000000 : ℝ) = - (11647009124868387 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11647009124868387 / 10000000000000000 : ℚ)) - (U := (1524643265784149082589 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11647009124868387 / 10000000000000000 : ℝ) ≤ - (1524643265784149082589 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1453335374893503 / 10000000000000000 : ℝ)) (q := - (11647009124868387 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11647009124868387 / 80000000000000000 : ℚ)) + (r' := (11647009124868387 / 10000000000000000 : ℚ)) + (U := (-(19269772143215850917411 / 10000000000000000000000 : ℚ))) + (U' := (1524643265784149082589 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (1453335374893503 / 10000000000000000 : ℚ)) + (q := (11647009124868387 / 80000000000000000 : ℚ)) + (U := (-(19269772143215850917411 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_4 : Uω (aρ 4) (bρ 4) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -726,25 +658,21 @@ lemma U_210_4 : have hlg : Real.log (439186321791003 / 3200000000000000 : ℝ) ≤ (-(124123896360046046919 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (439186321791003 / 3200000000000000 : ℝ) = - (439186321791003 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (439186321791003 / 400000000000000 : ℚ)) - (U := (5841199946203953081 / 62500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (439186321791003 / 400000000000000 : ℝ) ≤ - (5841199946203953081 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (54591671437407 / 400000000000000 : ℝ)) (q := - (439186321791003 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (439186321791003 / 3200000000000000 : ℚ)) + (r' := (439186321791003 / 400000000000000 : ℚ)) + (U := (-(124123896360046046919 / 62500000000000000000 : ℚ))) + (U' := (5841199946203953081 / 62500000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (54591671437407 / 400000000000000 : ℚ)) + (q := (439186321791003 / 3200000000000000 : ℚ)) + (U := (-(124123896360046046919 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_5 : Uω (aρ 5) (bρ 5) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -752,25 +680,21 @@ lemma U_210_5 : have hlg : Real.log (1984746128917551 / 16000000000000000 : ℝ) ≤ (-(20870977099919409056433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1984746128917551 / 16000000000000000 : ℝ) = - (1984746128917551 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1984746128917551 / 1000000000000000 : ℚ)) - (U := (6854910112080590943567 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1984746128917551 / 1000000000000000 : ℝ) ≤ - (6854910112080590943567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243799971044669 / 2000000000000000 : ℝ)) (q := - (1984746128917551 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1984746128917551 / 16000000000000000 : ℚ)) + (r' := (1984746128917551 / 1000000000000000 : ℚ)) + (U := (-(20870977099919409056433 / 10000000000000000000000 : ℚ))) + (U' := (6854910112080590943567 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (243799971044669 / 2000000000000000 : ℚ)) + (q := (1984746128917551 / 16000000000000000 : ℚ)) + (U := (-(20870977099919409056433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_6 : Uω (aρ 6) (bρ 6) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -778,25 +702,21 @@ lemma U_210_6 : have hlg : Real.log (8283447959127683 / 80000000000000000 : ℝ) ≤ (-(11338836658656259650589 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8283447959127683 / 80000000000000000 : ℝ) = - (8283447959127683 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8283447959127683 / 5000000000000000 : ℚ)) - (U := (2524106947343740349411 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8283447959127683 / 5000000000000000 : ℝ) ≤ - (2524106947343740349411 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (976169558998327 / 10000000000000000 : ℝ)) (q := - (8283447959127683 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8283447959127683 / 80000000000000000 : ℚ)) + (r' := (8283447959127683 / 5000000000000000 : ℚ)) + (U := (-(11338836658656259650589 / 5000000000000000000000 : ℚ))) + (U' := (2524106947343740349411 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (976169558998327 / 10000000000000000 : ℚ)) + (q := (8283447959127683 / 80000000000000000 : ℚ)) + (U := (-(11338836658656259650589 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_7 : Uω (aρ 7) (bρ 7) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -804,25 +724,21 @@ lemma U_210_7 : have hlg : Real.log (5443691373805147 / 80000000000000000 : ℝ) ≤ (-(13437846207618377346453 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5443691373805147 / 80000000000000000 : ℝ) = - (5443691373805147 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5443691373805147 / 5000000000000000 : ℚ)) - (U := (425097398381622653547 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5443691373805147 / 5000000000000000 : ℝ) ≤ - (425097398381622653547 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (489891793427693 / 10000000000000000 : ℝ)) (q := - (5443691373805147 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5443691373805147 / 80000000000000000 : ℚ)) + (r' := (5443691373805147 / 5000000000000000 : ℚ)) + (U := (-(13437846207618377346453 / 5000000000000000000000 : ℚ))) + (U' := (425097398381622653547 / 5000000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10202107156919 / 64000000000000 : ℚ)) + (s := (489891793427693 / 10000000000000000 : ℚ)) + (q := (5443691373805147 / 80000000000000000 : ℚ)) + (U := (-(13437846207618377346453 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_210_8 : Uω (aρ 8) (bρ 8) (10202107156919 / 64000000000000 : ℝ) ≤ @@ -959,25 +875,21 @@ lemma U_211_1 : have hlg : Real.log (24542601114837277 / 160000000000000000 : ℝ) ≤ (-(9373816929443217670237 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24542601114837277 / 160000000000000000 : ℝ) = - (24542601114837277 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24542601114837277 / 20000000000000000 : ℚ)) - (U := (1023390775056782329763 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24542601114837277 / 20000000000000000 : ℝ) ≤ - (1023390775056782329763 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1533807173915519 / 10000000000000000 : ℝ)) (q := - (24542601114837277 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24542601114837277 / 160000000000000000 : ℚ)) + (r' := (24542601114837277 / 20000000000000000 : ℚ)) + (U := (-(9373816929443217670237 / 5000000000000000000000 : ℚ))) + (U' := (1023390775056782329763 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (1533807173915519 / 10000000000000000 : ℚ)) + (q := (24542601114837277 / 160000000000000000 : ℚ)) + (U := (-(9373816929443217670237 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_2 : Uω (aρ 2) (bρ 2) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -985,25 +897,21 @@ lemma U_211_2 : have hlg : Real.log (24152738256647677 / 160000000000000000 : ℝ) ≤ (-(1890776055414610494797 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24152738256647677 / 160000000000000000 : ℝ) = - (24152738256647677 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24152738256647677 / 20000000000000000 : ℚ)) - (U := (188665485485389505203 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24152738256647677 / 20000000000000000 : ℝ) ≤ - (188665485485389505203 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1508843329151819 / 10000000000000000 : ℝ)) (q := - (24152738256647677 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24152738256647677 / 160000000000000000 : ℚ)) + (r' := (24152738256647677 / 20000000000000000 : ℚ)) + (U := (-(1890776055414610494797 / 1000000000000000000000 : ℚ))) + (U' := (188665485485389505203 / 1000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (1508843329151819 / 10000000000000000 : ℚ)) + (q := (24152738256647677 / 160000000000000000 : ℚ)) + (U := (-(1890776055414610494797 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_3 : Uω (aρ 3) (bρ 3) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1011,25 +919,21 @@ lemma U_211_3 : have hlg : Real.log (23365116996357173 / 160000000000000000 : ℝ) ≤ (-(19239296309802124964013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23365116996357173 / 160000000000000000 : ℝ) = - (23365116996357173 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23365116996357173 / 20000000000000000 : ℚ)) - (U := (1555119099197875035987 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23365116996357173 / 20000000000000000 : ℝ) ≤ - (1555119099197875035987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (728893388982753 / 5000000000000000 : ℝ)) (q := - (23365116996357173 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23365116996357173 / 160000000000000000 : ℚ)) + (r' := (23365116996357173 / 20000000000000000 : ℚ)) + (U := (-(19239296309802124964013 / 10000000000000000000000 : ℚ))) + (U' := (1555119099197875035987 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (728893388982753 / 5000000000000000 : ℚ)) + (q := (23365116996357173 / 160000000000000000 : ℚ)) + (U := (-(19239296309802124964013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_4 : Uω (aρ 4) (bρ 4) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1037,25 +941,21 @@ lemma U_211_4 : have hlg : Real.log (881227538893997 / 6400000000000000 : ℝ) ≤ (-(4956843506365323570481 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (881227538893997 / 6400000000000000 : ℝ) = - (881227538893997 / 800000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (881227538893997 / 800000000000000 : ℚ)) - (U := (241760345884676429519 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (881227538893997 / 800000000000000 : ℝ) ≤ - (241760345884676429519 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (213949592739 / 1562500000000 : ℝ)) (q := - (881227538893997 / 6400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (881227538893997 / 6400000000000000 : ℚ)) + (r' := (881227538893997 / 800000000000000 : ℚ)) + (U := (-(4956843506365323570481 / 2500000000000000000000 : ℚ))) + (U' := (241760345884676429519 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (213949592739 / 1562500000000 : ℚ)) + (q := (881227538893997 / 6400000000000000 : ℚ)) + (U := (-(4956843506365323570481 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_5 : Uω (aρ 5) (bρ 5) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1063,25 +963,21 @@ lemma U_211_5 : have hlg : Real.log (19919681586283741 / 160000000000000000 : ℝ) ≤ (-(10417327733948295803493 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19919681586283741 / 160000000000000000 : ℝ) = - (19919681586283741 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19919681586283741 / 10000000000000000 : ℚ)) - (U := (3445615872051704196507 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19919681586283741 / 10000000000000000 : ℝ) ≤ - (3445615872051704196507 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1223591452106327 / 10000000000000000 : ℝ)) (q := - (19919681586283741 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19919681586283741 / 160000000000000000 : ℚ)) + (r' := (19919681586283741 / 10000000000000000 : ℚ)) + (U := (-(10417327733948295803493 / 5000000000000000000000 : ℚ))) + (U' := (3445615872051704196507 / 5000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (1223591452106327 / 10000000000000000 : ℚ)) + (q := (19919681586283741 / 160000000000000000 : ℚ)) + (U := (-(10417327733948295803493 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_6 : Uω (aρ 6) (bρ 6) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1089,25 +985,21 @@ lemma U_211_6 : have hlg : Real.log (3328431812335569 / 32000000000000000 : ℝ) ≤ (-(5658086589788000643379 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3328431812335569 / 32000000000000000 : ℝ) = - (3328431812335569 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3328431812335569 / 2000000000000000 : ℚ)) - (U := (1273385213211999356621 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3328431812335569 / 2000000000000000 : ℝ) ≤ - (1273385213211999356621 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98114151167059 / 1000000000000000 : ℝ)) (q := - (3328431812335569 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3328431812335569 / 32000000000000000 : ℚ)) + (r' := (3328431812335569 / 2000000000000000 : ℚ)) + (U := (-(5658086589788000643379 / 2500000000000000000000 : ℚ))) + (U' := (1273385213211999356621 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (98114151167059 / 1000000000000000 : ℚ)) + (q := (3328431812335569 / 32000000000000000 : ℚ)) + (U := (-(5658086589788000643379 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_7 : Uω (aρ 7) (bρ 7) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1115,25 +1007,21 @@ lemma U_211_7 : have hlg : Real.log (10985625565955669 / 160000000000000000 : ℝ) ≤ (-(6696465406727953716517 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (10985625565955669 / 160000000000000000 : ℝ) = - (10985625565955669 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10985625565955669 / 10000000000000000 : ℚ)) - (U := (235006396272046283483 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10985625565955669 / 10000000000000000 : ℝ) ≤ - (235006396272046283483 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (248868102732659 / 5000000000000000 : ℝ)) (q := - (10985625565955669 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10985625565955669 / 160000000000000000 : ℚ)) + (r' := (10985625565955669 / 10000000000000000 : ℚ)) + (U := (-(6696465406727953716517 / 2500000000000000000000 : ℚ))) + (U' := (235006396272046283483 / 2500000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20460994349109 / 128000000000000 : ℚ)) + (s := (248868102732659 / 5000000000000000 : ℚ)) + (q := (10985625565955669 / 160000000000000000 : ℚ)) + (U := (-(6696465406727953716517 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_211_8 : Uω (aρ 8) (bρ 8) (20460994349109 / 128000000000000 : ℝ) ≤ @@ -1271,25 +1159,21 @@ lemma U_212_1 : have hlg : Real.log (6153395255480061 / 40000000000000000 : ℝ) ≤ (-(9359377248953476493289 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6153395255480061 / 40000000000000000 : ℝ) = - (6153395255480061 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6153395255480061 / 5000000000000000 : ℚ)) - (U := (1037830455546523506711 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6153395255480061 / 5000000000000000 : ℝ) ≤ - (1037830455546523506711 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1538243722045343 / 10000000000000000 : ℝ)) (q := - (6153395255480061 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6153395255480061 / 40000000000000000 : ℚ)) + (r' := (6153395255480061 / 5000000000000000 : ℚ)) + (U := (-(9359377248953476493289 / 5000000000000000000000 : ℚ))) + (U' := (1037830455546523506711 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (1538243722045343 / 10000000000000000 : ℚ)) + (q := (6153395255480061 / 40000000000000000 : ℚ)) + (U := (-(9359377248953476493289 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_2 : Uω (aρ 2) (bρ 2) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1297,25 +1181,21 @@ lemma U_212_2 : have hlg : Real.log (6055936565903101 / 40000000000000000 : ℝ) ≤ (-(943920205920242897763 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6055936565903101 / 40000000000000000 : ℝ) = - (6055936565903101 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6055936565903101 / 5000000000000000 : ℚ)) - (U := (95800564529757102237 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6055936565903101 / 5000000000000000 : ℝ) ≤ - (95800564529757102237 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1513283389766863 / 10000000000000000 : ℝ)) (q := - (6055936565903101 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6055936565903101 / 40000000000000000 : ℚ)) + (r' := (6055936565903101 / 5000000000000000 : ℚ)) + (U := (-(943920205920242897763 / 500000000000000000000 : ℚ))) + (U' := (95800564529757102237 / 500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (1513283389766863 / 10000000000000000 : ℚ)) + (q := (6055936565903101 / 40000000000000000 : ℚ)) + (U := (-(943920205920242897763 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_3 : Uω (aρ 3) (bρ 3) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1323,25 +1203,21 @@ lemma U_212_3 : have hlg : Real.log (5859053747781357 / 40000000000000000 : ℝ) ≤ (-(19208913392717338753281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5859053747781357 / 40000000000000000 : ℝ) = - (5859053747781357 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5859053747781357 / 5000000000000000 : ℚ)) - (U := (1585502016282661246719 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5859053747781357 / 5000000000000000 : ℝ) ≤ - (1585502016282661246719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1462238087055991 / 10000000000000000 : ℝ)) (q := - (5859053747781357 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5859053747781357 / 40000000000000000 : ℚ)) + (r' := (5859053747781357 / 5000000000000000 : ℚ)) + (U := (-(19208913392717338753281 / 10000000000000000000000 : ℚ))) + (U' := (1585502016282661246719 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (1462238087055991 / 10000000000000000 : ℚ)) + (q := (5859053747781357 / 40000000000000000 : ℚ)) + (U := (-(19208913392717338753281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_4 : Uω (aρ 4) (bρ 4) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1349,25 +1225,21 @@ lemma U_212_4 : have hlg : Real.log (5525514568684023 / 40000000000000000 : ℝ) ≤ (-(791801230265439478831 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5525514568684023 / 40000000000000000 : ℝ) = - (5525514568684023 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5525514568684023 / 5000000000000000 : ℚ)) - (U := (39975386094560521169 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5525514568684023 / 5000000000000000 : ℝ) ≤ - (39975386094560521169 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (343440669643081 / 2500000000000000 : ℝ)) (q := - (5525514568684023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5525514568684023 / 40000000000000000 : ℚ)) + (r' := (5525514568684023 / 5000000000000000 : ℚ)) + (U := (-(791801230265439478831 / 400000000000000000000 : ℚ))) + (U' := (39975386094560521169 / 400000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (343440669643081 / 2500000000000000 : ℚ)) + (q := (5525514568684023 / 40000000000000000 : ℚ)) + (U := (-(791801230265439478831 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_5 : Uω (aρ 5) (bρ 5) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1375,25 +1247,21 @@ lemma U_212_5 : have hlg : Real.log (4997973182595211 / 40000000000000000 : ℝ) ≤ (-(20798469863029981377397 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4997973182595211 / 40000000000000000 : ℝ) = - (4997973182595211 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4997973182595211 / 2500000000000000 : ℚ)) - (U := (6927417348970018622603 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (4997973182595211 / 2500000000000000 : ℝ) ≤ - (6927417348970018622603 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (614090952431459 / 5000000000000000 : ℝ)) (q := - (4997973182595211 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4997973182595211 / 40000000000000000 : ℚ)) + (r' := (4997973182595211 / 2500000000000000 : ℚ)) + (U := (-(20798469863029981377397 / 10000000000000000000000 : ℚ))) + (U' := (6927417348970018622603 / 10000000000000000000000 : ℚ)) + 4 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (614090952431459 / 5000000000000000 : ℚ)) + (q := (4997973182595211 / 40000000000000000 : ℚ)) + (U := (-(20798469863029981377397 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_6 : Uω (aρ 6) (bρ 6) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1401,25 +1269,21 @@ lemma U_212_6 : have hlg : Real.log (4179345323728897 / 40000000000000000 : ℝ) ≤ (-(2823406049901683619027 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4179345323728897 / 40000000000000000 : ℝ) = - (4179345323728897 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4179345323728897 / 2500000000000000 : ℚ)) - (U := (642329851598316380973 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4179345323728897 / 2500000000000000 : ℝ) ≤ - (642329851598316380973 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (986108350569761 / 10000000000000000 : ℝ)) (q := - (4179345323728897 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4179345323728897 / 40000000000000000 : ℚ)) + (r' := (4179345323728897 / 2500000000000000 : ℚ)) + (U := (-(2823406049901683619027 / 1250000000000000000000 : ℚ))) + (U' := (642329851598316380973 / 1250000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (986108350569761 / 10000000000000000 : ℚ)) + (q := (4179345323728897 / 40000000000000000 : ℚ)) + (U := (-(2823406049901683619027 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_7 : Uω (aρ 7) (bρ 7) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1427,25 +1291,21 @@ lemma U_212_7 : have hlg : Real.log (2770801501665571 / 40000000000000000 : ℝ) ≤ (-(26697428239469773735417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2770801501665571 / 40000000000000000 : ℝ) = - (2770801501665571 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2770801501665571 / 2500000000000000 : ℚ)) - (U := (1028458972530226264583 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2770801501665571 / 2500000000000000 : ℝ) ≤ - (1028458972530226264583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252748910149049 / 5000000000000000 : ℝ)) (q := - (2770801501665571 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2770801501665571 / 40000000000000000 : ℚ)) + (r' := (2770801501665571 / 2500000000000000 : ℚ)) + (U := (-(26697428239469773735417 / 10000000000000000000000 : ℚ))) + (U' := (1028458972530226264583 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1025888719219 / 6400000000000 : ℚ)) + (s := (252748910149049 / 5000000000000000 : ℚ)) + (q := (2770801501665571 / 40000000000000000 : ℚ)) + (U := (-(26697428239469773735417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_212_8 : Uω (aρ 8) (bρ 8) (1025888719219 / 6400000000000 : ℝ) ≤ @@ -1581,25 +1441,21 @@ lemma U_213_1 : have hlg : Real.log (24684560901034443 / 160000000000000000 : ℝ) ≤ (-(18689958309899125630867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24684560901034443 / 160000000000000000 : ℝ) = - (24684560901034443 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24684560901034443 / 20000000000000000 : ℚ)) - (U := (2104457099100874369133 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24684560901034443 / 20000000000000000 : ℝ) ≤ - (2104457099100874369133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1542680266679071 / 10000000000000000 : ℝ)) (q := - (24684560901034443 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24684560901034443 / 160000000000000000 : ℚ)) + (r' := (24684560901034443 / 20000000000000000 : ℚ)) + (U := (-(18689958309899125630867 / 10000000000000000000000 : ℚ))) + (U' := (2104457099100874369133 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (1542680266679071 / 10000000000000000 : ℚ)) + (q := (24684560901034443 / 160000000000000000 : ℚ)) + (U := (-(18689958309899125630867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_2 : Uω (aρ 2) (bρ 2) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1607,25 +1463,21 @@ lemma U_213_2 : have hlg : Real.log (24294754077802539 / 160000000000000000 : ℝ) ≤ (-(294517713903934530317 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24294754077802539 / 160000000000000000 : ℝ) = - (24294754077802539 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24294754077802539 / 20000000000000000 : ℚ)) - (U := (30395026861690469683 / 156250000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24294754077802539 / 20000000000000000 : ℝ) ≤ - (30395026861690469683 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1517723426285083 / 10000000000000000 : ℝ)) (q := - (24294754077802539 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24294754077802539 / 160000000000000000 : ℚ)) + (r' := (24294754077802539 / 20000000000000000 : ℚ)) + (U := (-(294517713903934530317 / 156250000000000000000 : ℚ))) + (U' := (30395026861690469683 / 156250000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (1517723426285083 / 10000000000000000 : ℚ)) + (q := (24294754077802539 / 160000000000000000 : ℚ)) + (U := (-(294517713903934530317 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_3 : Uω (aρ 3) (bρ 3) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1633,25 +1485,21 @@ lemma U_213_3 : have hlg : Real.log (23507312240887027 / 160000000000000000 : ℝ) ≤ (-(19178622825171756382173 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23507312240887027 / 160000000000000000 : ℝ) = - (23507312240887027 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23507312240887027 / 20000000000000000 : ℚ)) - (U := (1615792583828243617827 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23507312240887027 / 20000000000000000 : ℝ) ≤ - (1615792583828243617827 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (366672325755161 / 2500000000000000 : ℝ)) (q := - (23507312240887027 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23507312240887027 / 160000000000000000 : ℚ)) + (r' := (23507312240887027 / 20000000000000000 : ℚ)) + (U := (-(19178622825171756382173 / 10000000000000000000000 : ℚ))) + (U' := (1615792583828243617827 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (366672325755161 / 2500000000000000 : ℚ)) + (q := (23507312240887027 / 160000000000000000 : ℚ)) + (U := (-(19178622825171756382173 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_4 : Uω (aρ 4) (bρ 4) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1659,25 +1507,21 @@ lemma U_213_4 : have hlg : Real.log (886937020876051 / 6400000000000000 : ℝ) ≤ (-(988139645586834072963 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (886937020876051 / 6400000000000000 : ℝ) = - (886937020876051 / 800000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (886937020876051 / 800000000000000 : ℚ)) - (U := (51581124863165927037 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (886937020876051 / 800000000000000 : ℝ) ≤ - (51581124863165927037 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55129905768497 / 400000000000000 : ℝ)) (q := - (886937020876051 / 6400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (886937020876051 / 6400000000000000 : ℚ)) + (r' := (886937020876051 / 800000000000000 : ℚ)) + (U := (-(988139645586834072963 / 500000000000000000000 : ℚ))) + (U' := (51581124863165927037 / 500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (55129905768497 / 400000000000000 : ℚ)) + (q := (886937020876051 / 6400000000000000 : ℚ)) + (U := (-(988139645586834072963 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_5 : Uω (aρ 5) (bρ 5) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1685,25 +1529,21 @@ lemma U_213_5 : have hlg : Real.log (4012818964743127 / 32000000000000000 : ℝ) ≤ (-(5190604809880666183443 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4012818964743127 / 32000000000000000 : ℝ) = - (4012818964743127 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4012818964743127 / 4000000000000000 : ℚ)) - (U := (7999042369333816557 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (4012818964743127 / 4000000000000000 : ℝ) ≤ - (7999042369333816557 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61638561313711 / 500000000000000 : ℝ)) (q := - (4012818964743127 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4012818964743127 / 32000000000000000 : ℚ)) + (r' := (4012818964743127 / 4000000000000000 : ℚ)) + (U := (-(5190604809880666183443 / 2500000000000000000000 : ℚ))) + (U' := (7999042369333816557 / 2500000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (61638561313711 / 500000000000000 : ℚ)) + (q := (4012818964743127 / 32000000000000000 : ℚ)) + (U := (-(5190604809880666183443 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_6 : Uω (aρ 6) (bρ 6) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1711,25 +1551,21 @@ lemma U_213_6 : have hlg : Real.log (16792563233044027 / 160000000000000000 : ℝ) ≤ (-(11271188452447671165599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16792563233044027 / 160000000000000000 : ℝ) = - (16792563233044027 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16792563233044027 / 10000000000000000 : ℚ)) - (U := (2591755153552328834401 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16792563233044027 / 10000000000000000 : ℝ) ≤ - (2591755153552328834401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (991070152580269 / 10000000000000000 : ℝ)) (q := - (16792563233044027 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16792563233044027 / 160000000000000000 : ℚ)) + (r' := (16792563233044027 / 10000000000000000 : ℚ)) + (U := (-(11271188452447671165599 / 5000000000000000000000 : ℚ))) + (U' := (2591755153552328834401 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (991070152580269 / 10000000000000000 : ℚ)) + (q := (16792563233044027 / 160000000000000000 : ℚ)) + (U := (-(11271188452447671165599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_7 : Uω (aρ 7) (bρ 7) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1737,25 +1573,21 @@ lemma U_213_7 : have hlg : Real.log (2236030824860287 / 32000000000000000 : ℝ) ≤ (-(2661033560846422827913 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2236030824860287 / 32000000000000000 : ℝ) = - (2236030824860287 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2236030824860287 / 2000000000000000 : ℚ)) - (U := (111555160353577172087 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2236030824860287 / 2000000000000000 : ℝ) ≤ - (111555160353577172087 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102636078949489 / 2000000000000000 : ℝ)) (q := - (2236030824860287 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2236030824860287 / 32000000000000000 : ℚ)) + (r' := (2236030824860287 / 2000000000000000 : ℚ)) + (U := (-(2661033560846422827913 / 1000000000000000000000 : ℚ))) + (U' := (111555160353577172087 / 1000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20574554419651 / 128000000000000 : ℚ)) + (s := (102636078949489 / 2000000000000000 : ℚ)) + (q := (2236030824860287 / 32000000000000000 : ℚ)) + (U := (-(2661033560846422827913 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_213_8 : Uω (aρ 8) (bρ 8) (20574554419651 / 128000000000000 : ℝ) ≤ @@ -1893,25 +1725,21 @@ lemma U_214_1 : have hlg : Real.log (2475554075242049 / 16000000000000000 : ℝ) ≤ (-(18661244817095025294763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2475554075242049 / 16000000000000000 : ℝ) = - (2475554075242049 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2475554075242049 / 2000000000000000 : ℚ)) - (U := (2133170591904974705237 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2475554075242049 / 2000000000000000 : ℝ) ≤ - (2133170591904974705237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (77355840392339 / 500000000000000 : ℝ)) (q := - (2475554075242049 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2475554075242049 / 16000000000000000 : ℚ)) + (r' := (2475554075242049 / 2000000000000000 : ℚ)) + (U := (-(18661244817095025294763 / 10000000000000000000000 : ℚ))) + (U' := (2133170591904974705237 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (77355840392339 / 500000000000000 : ℚ)) + (q := (2475554075242049 / 16000000000000000 : ℚ)) + (U := (-(18661244817095025294763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_2 : Uω (aρ 2) (bρ 2) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -1919,25 +1747,21 @@ lemma U_214_2 : have hlg : Real.log (2436576170090501 / 16000000000000000 : ℝ) ≤ (-(4704987191384496238617 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2436576170090501 / 16000000000000000 : ℝ) = - (2436576170090501 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2436576170090501 / 2000000000000000 : ℚ)) - (U := (493616660865503761383 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2436576170090501 / 2000000000000000 : ℝ) ≤ - (493616660865503761383 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (304432687783469 / 2000000000000000 : ℝ)) (q := - (2436576170090501 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2436576170090501 / 16000000000000000 : ℚ)) + (r' := (2436576170090501 / 2000000000000000 : ℚ)) + (U := (-(4704987191384496238617 / 2500000000000000000000 : ℚ))) + (U' := (493616660865503761383 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (304432687783469 / 2000000000000000 : ℚ)) + (q := (2436576170090501 / 16000000000000000 : ℚ)) + (U := (-(4704987191384496238617 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_3 : Uω (aρ 3) (bρ 3) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -1945,25 +1769,21 @@ lemma U_214_3 : have hlg : Real.log (11789204376202213 / 80000000000000000 : ℝ) ≤ (-(19148424045563445068967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11789204376202213 / 80000000000000000 : ℝ) = - (11789204376202213 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11789204376202213 / 10000000000000000 : ℚ)) - (U := (1645991363436554931033 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11789204376202213 / 10000000000000000 : ℝ) ≤ - (1645991363436554931033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (367785106676193 / 2500000000000000 : ℝ)) (q := - (11789204376202213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11789204376202213 / 80000000000000000 : ℚ)) + (r' := (11789204376202213 / 10000000000000000 : ℚ)) + (U := (-(19148424045563445068967 / 10000000000000000000000 : ℚ))) + (U' := (1645991363436554931033 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (367785106676193 / 2500000000000000 : ℚ)) + (q := (11789204376202213 / 80000000000000000 : ℚ)) + (U := (-(19148424045563445068967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_4 : Uω (aρ 4) (bρ 4) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -1971,25 +1791,21 @@ lemma U_214_4 : have hlg : Real.log (11122395119354733 / 80000000000000000 : ℝ) ≤ (-(1973065979833186243353 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11122395119354733 / 80000000000000000 : ℝ) = - (11122395119354733 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11122395119354733 / 10000000000000000 : ℚ)) - (U := (106375561066813756647 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11122395119354733 / 10000000000000000 : ℝ) ≤ - (106375561066813756647 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (691366146778951 / 5000000000000000 : ℝ)) (q := - (11122395119354733 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11122395119354733 / 80000000000000000 : ℚ)) + (r' := (11122395119354733 / 10000000000000000 : ℚ)) + (U := (-(1973065979833186243353 / 1000000000000000000000 : ℚ))) + (U' := (106375561066813756647 / 1000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (691366146778951 / 5000000000000000 : ℚ)) + (q := (11122395119354733 / 80000000000000000 : ℚ)) + (U := (-(1973065979833186243353 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_5 : Uω (aρ 5) (bρ 5) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -1997,25 +1813,21 @@ lemma U_214_5 : have hlg : Real.log (10068143983497481 / 80000000000000000 : ℝ) ≤ (-(10363251278104916277097 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10068143983497481 / 80000000000000000 : ℝ) = - (10068143983497481 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10068143983497481 / 10000000000000000 : ℚ)) - (U := (33956426395083722903 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10068143983497481 / 10000000000000000 : ℝ) ≤ - (33956426395083722903 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1237359428928589 / 10000000000000000 : ℝ)) (q := - (10068143983497481 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10068143983497481 / 80000000000000000 : ℚ)) + (r' := (10068143983497481 / 10000000000000000 : ℚ)) + (U := (-(10363251278104916277097 / 5000000000000000000000 : ℚ))) + (U' := (33956426395083722903 / 5000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (1237359428928589 / 10000000000000000 : ℚ)) + (q := (10068143983497481 / 80000000000000000 : ℚ)) + (U := (-(10363251278104916277097 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_6 : Uω (aρ 6) (bρ 6) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -2023,25 +1835,21 @@ lemma U_214_6 : have hlg : Real.log (8433852739132409 / 80000000000000000 : ℝ) ≤ (-(703054043389017050231 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8433852739132409 / 80000000000000000 : ℝ) = - (8433852739132409 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8433852739132409 / 5000000000000000 : ℚ)) - (U := (163379931985982949769 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8433852739132409 / 5000000000000000 : ℝ) ≤ - (163379931985982949769 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (996026992977321 / 10000000000000000 : ℝ)) (q := - (8433852739132409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8433852739132409 / 80000000000000000 : ℚ)) + (r' := (8433852739132409 / 5000000000000000 : ℚ)) + (U := (-(703054043389017050231 / 312500000000000000000 : ℚ))) + (U' := (163379931985982949769 / 312500000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (996026992977321 / 10000000000000000 : ℚ)) + (q := (8433852739132409 / 80000000000000000 : ℚ)) + (U := (-(703054043389017050231 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_7 : Uω (aρ 7) (bρ 7) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -2049,25 +1857,21 @@ lemma U_214_7 : have hlg : Real.log (5638248951379653 / 80000000000000000 : ℝ) ≤ (-(13262265429716689337577 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5638248951379653 / 80000000000000000 : ℝ) = - (5638248951379653 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5638248951379653 / 5000000000000000 : ℚ)) - (U := (600678176283310662423 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5638248951379653 / 5000000000000000 : ℝ) ≤ - (600678176283310662423 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (130196856699783 / 2500000000000000 : ℝ)) (q := - (5638248951379653 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5638248951379653 / 80000000000000000 : ℚ)) + (r' := (5638248951379653 / 5000000000000000 : ℚ)) + (U := (-(13262265429716689337577 / 5000000000000000000000 : ℚ))) + (U' := (600678176283310662423 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10315667227461 / 64000000000000 : ℚ)) + (s := (130196856699783 / 2500000000000000 : ℚ)) + (q := (5638248951379653 / 80000000000000000 : ℚ)) + (U := (-(13262265429716689337577 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_214_8 : Uω (aρ 8) (bρ 8) (10315667227461 / 64000000000000 : ℝ) ≤ @@ -2205,25 +2009,21 @@ lemma U_215_1 : have hlg : Real.log (24826520576316249 / 160000000000000000 : ℝ) ≤ (-(18632613545832130859089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24826520576316249 / 160000000000000000 : ℝ) = - (24826520576316249 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24826520576316249 / 20000000000000000 : ℚ)) - (U := (2161801863167869140911 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24826520576316249 / 20000000000000000 : ℝ) ≤ - (2161801863167869140911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1551553345578203 / 10000000000000000 : ℝ)) (q := - (24826520576316249 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24826520576316249 / 160000000000000000 : ℚ)) + (r' := (24826520576316249 / 20000000000000000 : ℚ)) + (U := (-(18632613545832130859089 / 10000000000000000000000 : ℚ))) + (U' := (2161801863167869140911 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (1551553345578203 / 10000000000000000 : ℚ)) + (q := (24826520576316249 / 160000000000000000 : ℚ)) + (U := (-(18632613545832130859089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_2 : Uω (aρ 2) (bρ 2) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2231,25 +2031,21 @@ lemma U_215_2 : have hlg : Real.log (4887353826917421 / 32000000000000000 : ℝ) ≤ (-(18790848846917232790029 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4887353826917421 / 32000000000000000 : ℝ) = - (4887353826917421 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4887353826917421 / 4000000000000000 : ℚ)) - (U := (2003566562082767209971 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4887353826917421 / 4000000000000000 : ℝ) ≤ - (2003566562082767209971 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (76330171393603 / 500000000000000 : ℝ)) (q := - (4887353826917421 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4887353826917421 / 32000000000000000 : ℚ)) + (r' := (4887353826917421 / 4000000000000000 : ℚ)) + (U := (-(18790848846917232790029 / 10000000000000000000000 : ℚ))) + (U' := (2003566562082767209971 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (76330171393603 / 500000000000000 : ℚ)) + (q := (4887353826917421 / 32000000000000000 : ℚ)) + (U := (-(18790848846917232790029 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_3 : Uω (aρ 3) (bρ 3) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2257,25 +2053,21 @@ lemma U_215_3 : have hlg : Real.log (4729900906471677 / 32000000000000000 : ℝ) ≤ (-(19118316497414914090889 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4729900906471677 / 32000000000000000 : ℝ) = - (4729900906471677 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4729900906471677 / 4000000000000000 : ℚ)) - (U := (1676098911585085909111 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4729900906471677 / 4000000000000000 : ℝ) ≤ - (1676098911585085909111 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (147559145894347 / 1000000000000000 : ℝ)) (q := - (4729900906471677 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4729900906471677 / 32000000000000000 : ℚ)) + (r' := (4729900906471677 / 4000000000000000 : ℚ)) + (U := (-(19118316497414914090889 / 10000000000000000000000 : ℚ))) + (U' := (1676098911585085909111 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (147559145894347 / 1000000000000000 : ℚ)) + (q := (4729900906471677 / 32000000000000000 : ℚ)) + (U := (-(19118316497414914090889 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_4 : Uω (aρ 4) (bρ 4) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2283,25 +2075,21 @@ lemma U_215_4 : have hlg : Real.log (22316152449701369 / 160000000000000000 : ℝ) ≤ (-(19698630730860232821229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22316152449701369 / 160000000000000000 : ℝ) = - (22316152449701369 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22316152449701369 / 20000000000000000 : ℚ)) - (U := (1095784678139767178771 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22316152449701369 / 20000000000000000 : ℝ) ≤ - (1095784678139767178771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1387216629676343 / 10000000000000000 : ℝ)) (q := - (22316152449701369 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22316152449701369 / 160000000000000000 : ℚ)) + (r' := (22316152449701369 / 20000000000000000 : ℚ)) + (U := (-(19698630730860232821229 / 10000000000000000000000 : ℚ))) + (U' := (1095784678139767178771 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (1387216629676343 / 10000000000000000 : ℚ)) + (q := (22316152449701369 / 160000000000000000 : ℚ)) + (U := (-(19698630730860232821229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_5 : Uω (aρ 5) (bρ 5) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2309,25 +2097,21 @@ lemma U_215_5 : have hlg : Real.log (20208472259413113 / 160000000000000000 : ℝ) ≤ (-(20690718791954763536791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (20208472259413113 / 160000000000000000 : ℝ) = - (20208472259413113 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20208472259413113 / 20000000000000000 : ℚ)) - (U := (103696617045236463209 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20208472259413113 / 20000000000000000 : ℝ) ≤ - (103696617045236463209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1241946525225311 / 10000000000000000 : ℝ)) (q := - (20208472259413113 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20208472259413113 / 160000000000000000 : ℚ)) + (r' := (20208472259413113 / 20000000000000000 : ℚ)) + (U := (-(20690718791954763536791 / 10000000000000000000000 : ℚ))) + (U' := (103696617045236463209 / 10000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (1241946525225311 / 10000000000000000 : ℚ)) + (q := (20208472259413113 / 160000000000000000 : ℚ)) + (U := (-(20690718791954763536791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_6 : Uω (aρ 6) (bρ 6) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2335,25 +2119,21 @@ lemma U_215_6 : have hlg : Real.log (16942808620254937 / 160000000000000000 : ℝ) ≤ (-(22453303405870982867681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (16942808620254937 / 160000000000000000 : ℝ) = - (16942808620254937 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16942808620254937 / 10000000000000000 : ℚ)) - (U := (5272583806129017132319 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16942808620254937 / 10000000000000000 : ℝ) ≤ - (5272583806129017132319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1000978945470539 / 10000000000000000 : ℝ)) (q := - (16942808620254937 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16942808620254937 / 160000000000000000 : ℚ)) + (r' := (16942808620254937 / 10000000000000000 : ℚ)) + (U := (-(22453303405870982867681 / 10000000000000000000000 : ℚ))) + (U' := (5272583806129017132319 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (1000978945470539 / 10000000000000000 : ℚ)) + (q := (16942808620254937 / 160000000000000000 : ℚ)) + (U := (-(22453303405870982867681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_7 : Uω (aρ 7) (bρ 7) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2361,25 +2141,21 @@ lemma U_215_7 : have hlg : Real.log (11372263446798641 / 160000000000000000 : ℝ) ≤ (-(6609991136014297365741 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (11372263446798641 / 160000000000000000 : ℝ) = - (11372263446798641 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11372263446798641 / 10000000000000000 : ℚ)) - (U := (321480666985702634259 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11372263446798641 / 10000000000000000 : ℝ) ≤ - (321480666985702634259 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (264161089774251 / 5000000000000000 : ℝ)) (q := - (11372263446798641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11372263446798641 / 160000000000000000 : ℚ)) + (r' := (11372263446798641 / 10000000000000000 : ℚ)) + (U := (-(6609991136014297365741 / 2500000000000000000000 : ℚ))) + (U' := (321480666985702634259 / 2500000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20688114490193 / 128000000000000 : ℚ)) + (s := (264161089774251 / 5000000000000000 : ℚ)) + (q := (11372263446798641 / 160000000000000000 : ℚ)) + (U := (-(6609991136014297365741 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_215_8 : Uω (aρ 8) (bρ 8) (20688114490193 / 128000000000000 : ℝ) ≤ @@ -2518,25 +2294,21 @@ lemma U_216_1 : have hlg : Real.log (3112187546619607 / 20000000000000000 : ℝ) ≤ (-(744162561060257032513 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3112187546619607 / 20000000000000000 : ℝ) = - (3112187546619607 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3112187546619607 / 2500000000000000 : ℚ)) - (U := (87614055299742967487 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3112187546619607 / 2500000000000000 : ℝ) ≤ - (87614055299742967487 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (388997469975683 / 2500000000000000 : ℝ)) (q := - (3112187546619607 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3112187546619607 / 20000000000000000 : ℚ)) + (r' := (3112187546619607 / 2500000000000000 : ℚ)) + (U := (-(744162561060257032513 / 400000000000000000000 : ℚ))) + (U' := (87614055299742967487 / 400000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (388997469975683 / 2500000000000000 : ℚ)) + (q := (3112187546619607 / 20000000000000000 : ℚ)) + (U := (-(744162561060257032513 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_2 : Uω (aρ 2) (bρ 2) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2544,25 +2316,21 @@ lemma U_216_2 : have hlg : Real.log (3063472047562097 / 20000000000000000 : ℝ) ≤ (-(18761833439794934696371 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3063472047562097 / 20000000000000000 : ℝ) = - (3063472047562097 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3063472047562097 / 2500000000000000 : ℚ)) - (U := (2032581969205065303629 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3063472047562097 / 2500000000000000 : ℝ) ≤ - (2032581969205065303629 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (765521696677611 / 5000000000000000 : ℝ)) (q := - (3063472047562097 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3063472047562097 / 20000000000000000 : ℚ)) + (r' := (3063472047562097 / 2500000000000000 : ℚ)) + (U := (-(18761833439794934696371 / 10000000000000000000000 : ℚ))) + (U' := (2032581969205065303629 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (765521696677611 / 5000000000000000 : ℚ)) + (q := (3063472047562097 / 20000000000000000 : ℚ)) + (U := (-(18761833439794934696371 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_3 : Uω (aρ 3) (bρ 3) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2570,25 +2338,21 @@ lemma U_216_3 : have hlg : Real.log (1482537474209321 / 10000000000000000 : ℝ) ≤ (-(19088299629310782092179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1482537474209321 / 10000000000000000 : ℝ) = - (1482537474209321 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1482537474209321 / 1250000000000000 : ℚ)) - (U := (1706115779689217907821 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1482537474209321 / 1250000000000000 : ℝ) ≤ - (1706115779689217907821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1480042400561767 / 10000000000000000 : ℝ)) (q := - (1482537474209321 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1482537474209321 / 10000000000000000 : ℚ)) + (r' := (1482537474209321 / 1250000000000000 : ℚ)) + (U := (-(19088299629310782092179 / 10000000000000000000000 : ℚ))) + (U' := (1706115779689217907821 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (1480042400561767 / 10000000000000000 : ℚ)) + (q := (1482537474209321 / 10000000000000000 : ℚ)) + (U := (-(19088299629310782092179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_4 : Uω (aρ 4) (bρ 4) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2596,25 +2360,21 @@ lemma U_216_4 : have hlg : Real.log (2798439022387463 / 20000000000000000 : ℝ) ≤ (-(393334100610784337877 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2798439022387463 / 20000000000000000 : ℝ) = - (2798439022387463 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2798439022387463 / 2500000000000000 : ℚ)) - (U := (22554207569215662123 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2798439022387463 / 2500000000000000 : ℝ) ≤ - (22554207569215662123 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (347925163898897 / 2500000000000000 : ℝ)) (q := - (2798439022387463 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2798439022387463 / 20000000000000000 : ℚ)) + (r' := (2798439022387463 / 2500000000000000 : ℚ)) + (U := (-(393334100610784337877 / 200000000000000000000 : ℚ))) + (U' := (22554207569215662123 / 200000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (347925163898897 / 2500000000000000 : ℚ)) + (q := (2798439022387463 / 20000000000000000 : ℚ)) + (U := (-(393334100610784337877 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_5 : Uω (aρ 5) (bρ 5) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2622,25 +2382,21 @@ lemma U_216_5 : have hlg : Real.log (633770243708767 / 5000000000000000 : ℝ) ≤ (-(20655066935054398764263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (633770243708767 / 5000000000000000 : ℝ) = - (633770243708767 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (633770243708767 / 625000000000000 : ℚ)) - (U := (139348473945601235737 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (633770243708767 / 625000000000000 : ℝ) ≤ - (139348473945601235737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1246532527378193 / 10000000000000000 : ℝ)) (q := - (633770243708767 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (633770243708767 / 5000000000000000 : ℚ)) + (r' := (633770243708767 / 625000000000000 : ℚ)) + (U := (-(20655066935054398764263 / 10000000000000000000000 : ℚ))) + (U' := (139348473945601235737 / 10000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (1246532527378193 / 10000000000000000 : ℚ)) + (q := (633770243708767 / 5000000000000000 : ℚ)) + (U := (-(20655066935054398764263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_6 : Uω (aρ 6) (bρ 6) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2648,25 +2404,21 @@ lemma U_216_6 : have hlg : Real.log (1063617077281511 / 10000000000000000 : ℝ) ≤ (-(22409096555836940562381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1063617077281511 / 10000000000000000 : ℝ) = - (1063617077281511 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1063617077281511 / 625000000000000 : ℚ)) - (U := (5316790656163059437619 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1063617077281511 / 625000000000000 : ℝ) ≤ - (5316790656163059437619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1005926082246147 / 10000000000000000 : ℝ)) (q := - (1063617077281511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1063617077281511 / 10000000000000000 : ℚ)) + (r' := (1063617077281511 / 625000000000000 : ℚ)) + (U := (-(22409096555836940562381 / 10000000000000000000000 : ℚ))) + (U' := (5316790656163059437619 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (1005926082246147 / 10000000000000000 : ℚ)) + (q := (1063617077281511 / 10000000000000000 : ℚ)) + (U := (-(22409096555836940562381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_7 : Uω (aρ 7) (bρ 7) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2674,25 +2426,21 @@ lemma U_216_7 : have hlg : Real.log (1433434393940571 / 20000000000000000 : ℝ) ≤ (-(3294573791959917824413 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1433434393940571 / 20000000000000000 : ℝ) = - (1433434393940571 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1433434393940571 / 1250000000000000 : ℚ)) - (U := (171162109540082175587 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1433434393940571 / 1250000000000000 : ℝ) ≤ - (171162109540082175587 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33486731398981 / 625000000000000 : ℝ)) (q := - (1433434393940571 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1433434393940571 / 20000000000000000 : ℚ)) + (r' := (1433434393940571 / 1250000000000000 : ℚ)) + (U := (-(3294573791959917824413 / 1250000000000000000000 : ℚ))) + (U' := (171162109540082175587 / 1250000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2593111815683 / 16000000000000 : ℚ)) + (s := (33486731398981 / 625000000000000 : ℚ)) + (q := (1433434393940571 / 20000000000000000 : ℚ)) + (U := (-(3294573791959917824413 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_216_8 : Uω (aρ 8) (bρ 8) (2593111815683 / 16000000000000 : ℝ) ≤ @@ -2828,25 +2576,21 @@ lemma U_217_1 : have hlg : Real.log (24968480142574791 / 160000000000000000 : ℝ) ≤ (-(18575595793526144554733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24968480142574791 / 160000000000000000 : ℝ) = - (24968480142574791 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24968480142574791 / 20000000000000000 : ℚ)) - (U := (2218819615473855445267 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24968480142574791 / 20000000000000000 : ℝ) ≤ - (2218819615473855445267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1560426410849427 / 10000000000000000 : ℝ)) (q := - (24968480142574791 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24968480142574791 / 160000000000000000 : ℚ)) + (r' := (24968480142574791 / 20000000000000000 : ℚ)) + (U := (-(18575595793526144554733 / 10000000000000000000000 : ℚ))) + (U' := (2218819615473855445267 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (1560426410849427 / 10000000000000000 : ℚ)) + (q := (24968480142574791 / 160000000000000000 : ℚ)) + (U := (-(18575595793526144554733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_2 : Uω (aρ 2) (bρ 2) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2854,25 +2598,21 @@ lemma U_217_2 : have hlg : Real.log (4915756688052579 / 32000000000000000 : ℝ) ≤ (-(9366451027138736003651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4915756688052579 / 32000000000000000 : ℝ) = - (4915756688052579 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4915756688052579 / 4000000000000000 : ℚ)) - (U := (1030756677361263996349 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4915756688052579 / 4000000000000000 : ℝ) ≤ - (1030756677361263996349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38387083389261 / 250000000000000 : ℝ)) (q := - (4915756688052579 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4915756688052579 / 32000000000000000 : ℚ)) + (r' := (4915756688052579 / 4000000000000000 : ℚ)) + (U := (-(9366451027138736003651 / 5000000000000000000000 : ℚ))) + (U' := (1030756677361263996349 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (38387083389261 / 250000000000000 : ℚ)) + (q := (4915756688052579 / 32000000000000000 : ℚ)) + (U := (-(9366451027138736003651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_3 : Uω (aρ 3) (bρ 3) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2880,25 +2620,21 @@ lemma U_217_3 : have hlg : Real.log (23791693923897639 / 160000000000000000 : ℝ) ≤ (-(19058372894836346185957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23791693923897639 / 160000000000000000 : ℝ) = - (23791693923897639 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23791693923897639 / 20000000000000000 : ℚ)) - (U := (1736042514163653814043 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23791693923897639 / 20000000000000000 : ℝ) ≤ - (1736042514163653814043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1484493252374783 / 10000000000000000 : ℝ)) (q := - (23791693923897639 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23791693923897639 / 160000000000000000 : ℚ)) + (r' := (23791693923897639 / 20000000000000000 : ℚ)) + (U := (-(19058372894836346185957 / 10000000000000000000000 : ℚ))) + (U' := (1736042514163653814043 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (1484493252374783 / 10000000000000000 : ℚ)) + (q := (23791693923897639 / 160000000000000000 : ℚ)) + (U := (-(19058372894836346185957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_4 : Uω (aρ 4) (bρ 4) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2906,25 +2642,21 @@ lemma U_217_4 : have hlg : Real.log (22458869450814343 / 160000000000000000 : ℝ) ≤ (-(490872050631875603417 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22458869450814343 / 160000000000000000 : ℝ) = - (22458869450814343 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22458869450814343 / 20000000000000000 : ℚ)) - (U := (28988334593124396583 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22458869450814343 / 20000000000000000 : ℝ) ≤ - (28988334593124396583 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1396184374304371 / 10000000000000000 : ℝ)) (q := - (22458869450814343 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22458869450814343 / 160000000000000000 : ℚ)) + (r' := (22458869450814343 / 20000000000000000 : ℚ)) + (U := (-(490872050631875603417 / 250000000000000000000 : ℚ))) + (U' := (28988334593124396583 / 250000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (1396184374304371 / 10000000000000000 : ℚ)) + (q := (22458869450814343 / 160000000000000000 : ℚ)) + (U := (-(490872050631875603417 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_5 : Uω (aρ 5) (bρ 5) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2932,25 +2664,21 @@ lemma U_217_5 : have hlg : Real.log (4070562936210387 / 32000000000000000 : ℝ) ≤ (-(20619545985646205896543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4070562936210387 / 32000000000000000 : ℝ) = - (4070562936210387 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4070562936210387 / 4000000000000000 : ℚ)) - (U := (174869423353794103457 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4070562936210387 / 4000000000000000 : ℝ) ≤ - (174869423353794103457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (125111744741907 / 1000000000000000 : ℝ)) (q := - (4070562936210387 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4070562936210387 / 32000000000000000 : ℚ)) + (r' := (4070562936210387 / 4000000000000000 : ℚ)) + (U := (-(20619545985646205896543 / 10000000000000000000000 : ℚ))) + (U' := (174869423353794103457 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (125111744741907 / 1000000000000000 : ℚ)) + (q := (4070562936210387 / 32000000000000000 : ℚ)) + (U := (-(20619545985646205896543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_6 : Uω (aρ 6) (bρ 6) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2958,25 +2686,21 @@ lemma U_217_6 : have hlg : Real.log (17092899892641359 / 160000000000000000 : ℝ) ≤ (-(22365106478660146974889 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17092899892641359 / 160000000000000000 : ℝ) = - (17092899892641359 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17092899892641359 / 10000000000000000 : ℚ)) - (U := (5360780733339853025111 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17092899892641359 / 10000000000000000 : ℝ) ≤ - (5360780733339853025111 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252717118501937 / 2500000000000000 : ℝ)) (q := - (17092899892641359 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17092899892641359 / 160000000000000000 : ℚ)) + (r' := (17092899892641359 / 10000000000000000 : ℚ)) + (U := (-(22365106478660146974889 / 10000000000000000000000 : ℚ))) + (U' := (5360780733339853025111 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (252717118501937 / 2500000000000000 : ℚ)) + (q := (17092899892641359 / 160000000000000000 : ℚ)) + (U := (-(22365106478660146974889 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_7 : Uω (aρ 7) (bρ 7) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -2984,25 +2708,21 @@ lemma U_217_7 : have hlg : Real.log (11562155852785783 / 160000000000000000 : ℝ) ≤ (-(26274364758818529627057 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (11562155852785783 / 160000000000000000 : ℝ) = - (11562155852785783 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11562155852785783 / 10000000000000000 : ℚ)) - (U := (1451522453181470372943 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11562155852785783 / 10000000000000000 : ℝ) ≤ - (1451522453181470372943 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (543186849785801 / 10000000000000000 : ℝ)) (q := - (11562155852785783 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11562155852785783 / 160000000000000000 : ℚ)) + (r' := (11562155852785783 / 10000000000000000 : ℚ)) + (U := (-(26274364758818529627057 / 10000000000000000000000 : ℚ))) + (U' := (1451522453181470372943 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4160334912147 / 25600000000000 : ℚ)) + (s := (543186849785801 / 10000000000000000 : ℚ)) + (q := (11562155852785783 / 160000000000000000 : ℚ)) + (U := (-(26274364758818529627057 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_217_8 : Uω (aρ 8) (bρ 8) (4160334912147 / 25600000000000 : ℝ) ≤ @@ -3139,25 +2859,21 @@ lemma U_218_1 : have hlg : Real.log (12519729942699943 / 80000000000000000 : ℝ) ≤ (-(18547208385266200982007 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12519729942699943 / 80000000000000000 : ℝ) = - (12519729942699943 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12519729942699943 / 10000000000000000 : ℚ)) - (U := (2247207023733799017993 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12519729942699943 / 10000000000000000 : ℝ) ≤ - (2247207023733799017993 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1564862938447017 / 10000000000000000 : ℝ)) (q := - (12519729942699943 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12519729942699943 / 80000000000000000 : ℚ)) + (r' := (12519729942699943 / 10000000000000000 : ℚ)) + (U := (-(18547208385266200982007 / 10000000000000000000000 : ℚ))) + (U' := (2247207023733799017993 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (1564862938447017 / 10000000000000000 : ℚ)) + (q := (12519729942699943 / 80000000000000000 : ℚ)) + (U := (-(18547208385266200982007 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_2 : Uω (aρ 2) (bρ 2) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3165,25 +2881,21 @@ lemma U_218_2 : have hlg : Real.log (12324895157747767 / 80000000000000000 : ℝ) ≤ (-(3740810840944483037073 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12324895157747767 / 80000000000000000 : ℝ) = - (12324895157747767 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12324895157747767 / 10000000000000000 : ℚ)) - (U := (418072240855516962927 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12324895157747767 / 10000000000000000 : ℝ) ≤ - (418072240855516962927 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1539923254718973 / 10000000000000000 : ℝ)) (q := - (12324895157747767 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12324895157747767 / 80000000000000000 : ℚ)) + (r' := (12324895157747767 / 10000000000000000 : ℚ)) + (U := (-(3740810840944483037073 / 2000000000000000000000 : ℚ))) + (U' := (418072240855516962927 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (1539923254718973 / 10000000000000000 : ℚ)) + (q := (12324895157747767 / 80000000000000000 : ℚ)) + (U := (-(3740810840944483037073 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_3 : Uω (aρ 3) (bρ 3) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3191,25 +2903,21 @@ lemma U_218_3 : have hlg : Real.log (11931393774223367 / 80000000000000000 : ℝ) ≤ (-(19028535752517117294929 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11931393774223367 / 80000000000000000 : ℝ) = - (11931393774223367 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11931393774223367 / 10000000000000000 : ℚ)) - (U := (1765879656482882705071 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11931393774223367 / 10000000000000000 : ℝ) ≤ - (1765879656482882705071 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1488944015187873 / 10000000000000000 : ℝ)) (q := - (11931393774223367 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11931393774223367 / 80000000000000000 : ℚ)) + (r' := (11931393774223367 / 10000000000000000 : ℚ)) + (U := (-(19028535752517117294929 / 10000000000000000000000 : ℚ))) + (U' := (1765879656482882705071 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (1488944015187873 / 10000000000000000 : ℚ)) + (q := (11931393774223367 / 80000000000000000 : ℚ)) + (U := (-(19028535752517117294929 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_4 : Uω (aρ 4) (bρ 4) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3217,25 +2925,21 @@ lemma U_218_4 : have hlg : Real.log (11265112144223691 / 80000000000000000 : ℝ) ≤ (-(19603161049574197177753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11265112144223691 / 80000000000000000 : ℝ) = - (11265112144223691 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11265112144223691 / 10000000000000000 : ℚ)) - (U := (1191254359425802822247 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11265112144223691 / 10000000000000000 : ℝ) ≤ - (1191254359425802822247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (700333894376477 / 5000000000000000 : ℝ)) (q := - (11265112144223691 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11265112144223691 / 80000000000000000 : ℚ)) + (r' := (11265112144223691 / 10000000000000000 : ℚ)) + (U := (-(19603161049574197177753 / 10000000000000000000000 : ℚ))) + (U' := (1191254359425802822247 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (700333894376477 / 5000000000000000 : ℚ)) + (q := (11265112144223691 / 80000000000000000 : ℚ)) + (U := (-(19603161049574197177753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_5 : Uω (aρ 5) (bρ 5) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3243,25 +2947,21 @@ lemma U_218_5 : have hlg : Real.log (10212486500676799 / 80000000000000000 : ℝ) ≤ (-(4116830991103902289863 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10212486500676799 / 80000000000000000 : ℝ) = - (10212486500676799 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10212486500676799 / 10000000000000000 : ℚ)) - (U := (42052090696097710137 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10212486500676799 / 10000000000000000 : ℝ) ≤ - (42052090696097710137 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1255701297201231 / 10000000000000000 : ℝ)) (q := - (10212486500676799 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10212486500676799 / 80000000000000000 : ℚ)) + (r' := (10212486500676799 / 10000000000000000 : ℚ)) + (U := (-(4116830991103902289863 / 2000000000000000000000 : ℚ))) + (U' := (42052090696097710137 / 2000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (1255701297201231 / 10000000000000000 : ℚ)) + (q := (10212486500676799 / 80000000000000000 : ℚ)) + (U := (-(4116830991103902289863 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_6 : Uω (aρ 6) (bρ 6) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3269,25 +2969,21 @@ lemma U_218_6 : have hlg : Real.log (8583944571374899 / 80000000000000000 : ℝ) ≤ (-(2790166356911144784423 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8583944571374899 / 80000000000000000 : ℝ) = - (8583944571374899 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8583944571374899 / 5000000000000000 : ℚ)) - (U := (675569544588855215577 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8583944571374899 / 5000000000000000 : ℝ) ≤ - (675569544588855215577 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253951547503939 / 2500000000000000 : ℝ)) (q := - (8583944571374899 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8583944571374899 / 80000000000000000 : ℚ)) + (r' := (8583944571374899 / 5000000000000000 : ℚ)) + (U := (-(2790166356911144784423 / 1250000000000000000000 : ℚ))) + (U' := (675569544588855215577 / 1250000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (253951547503939 / 2500000000000000 : ℚ)) + (q := (8583944571374899 / 80000000000000000 : ℚ)) + (U := (-(2790166356911144784423 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_7 : Uω (aρ 7) (bρ 7) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3295,25 +2991,21 @@ lemma U_218_7 : have hlg : Real.log (5828163480531791 / 80000000000000000 : ℝ) ≤ (-(2619324694814019901359 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (5828163480531791 / 80000000000000000 : ℝ) = - (5828163480531791 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5828163480531791 / 5000000000000000 : ℚ)) - (U := (153264026385980098641 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5828163480531791 / 5000000000000000 : ℝ) ≤ - (153264026385980098641 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (550522298064979 / 10000000000000000 : ℝ)) (q := - (5828163480531791 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5828163480531791 / 80000000000000000 : ℚ)) + (r' := (5828163480531791 / 5000000000000000 : ℚ)) + (U := (-(2619324694814019901359 / 1000000000000000000000 : ℚ))) + (U' := (153264026385980098641 / 1000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10429227298003 / 64000000000000 : ℚ)) + (s := (550522298064979 / 10000000000000000 : ℚ)) + (q := (5828163480531791 / 80000000000000000 : ℚ)) + (U := (-(2619324694814019901359 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_218_8 : Uω (aρ 8) (bρ 8) (10429227298003 / 64000000000000 : ℝ) ≤ @@ -3451,25 +3143,21 @@ lemma U_219_1 : have hlg : Real.log (25110439601659373 / 160000000000000000 : ℝ) ≤ (-(4629725336005811571373 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25110439601659373 / 160000000000000000 : ℝ) = - (25110439601659373 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25110439601659373 / 20000000000000000 : ℚ)) - (U := (568878516244188428627 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25110439601659373 / 20000000000000000 : ℝ) ≤ - (568878516244188428627 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (784649731361953 / 5000000000000000 : ℝ)) (q := - (25110439601659373 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25110439601659373 / 160000000000000000 : ℚ)) + (r' := (25110439601659373 / 20000000000000000 : ℚ)) + (U := (-(4629725336005811571373 / 2500000000000000000000 : ℚ))) + (U' := (568878516244188428627 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (784649731361953 / 5000000000000000 : ℚ)) + (q := (25110439601659373 / 160000000000000000 : ℚ)) + (U := (-(4629725336005811571373 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_2 : Uω (aρ 2) (bρ 2) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3477,25 +3165,21 @@ lemma U_219_2 : have hlg : Real.log (24720797007786261 / 160000000000000000 : ℝ) ≤ (-(2334411176211178011403 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24720797007786261 / 160000000000000000 : ℝ) = - (24720797007786261 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24720797007786261 / 20000000000000000 : ℚ)) - (U := (264890749913821988597 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24720797007786261 / 20000000000000000 : ℝ) ≤ - (264890749913821988597 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1544363150999767 / 10000000000000000 : ℝ)) (q := - (24720797007786261 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24720797007786261 / 160000000000000000 : ℚ)) + (r' := (24720797007786261 / 20000000000000000 : ℚ)) + (U := (-(2334411176211178011403 / 1250000000000000000000 : ℚ))) + (U' := (264890749913821988597 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (1544363150999767 / 10000000000000000 : ℚ)) + (q := (24720797007786261 / 160000000000000000 : ℚ)) + (U := (-(2334411176211178011403 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_3 : Uω (aρ 3) (bρ 3) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3503,25 +3187,21 @@ lemma U_219_3 : have hlg : Real.log (23933880467362333 / 160000000000000000 : ℝ) ≤ (-(18998787665759244029903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23933880467362333 / 160000000000000000 : ℝ) = - (23933880467362333 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23933880467362333 / 20000000000000000 : ℚ)) - (U := (1795627743240755970097 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23933880467362333 / 20000000000000000 : ℝ) ≤ - (1795627743240755970097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (186674336224597 / 1250000000000000 : ℝ)) (q := - (23933880467362333 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23933880467362333 / 160000000000000000 : ℚ)) + (r' := (23933880467362333 / 20000000000000000 : ℚ)) + (U := (-(18998787665759244029903 / 10000000000000000000000 : ℚ))) + (U' := (1795627743240755970097 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (186674336224597 / 1250000000000000 : ℚ)) + (q := (23933880467362333 / 160000000000000000 : ℚ)) + (U := (-(18998787665759244029903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_4 : Uω (aρ 4) (bρ 4) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3529,25 +3209,21 @@ lemma U_219_4 : have hlg : Real.log (4520315343059617 / 32000000000000000 : ℝ) ≤ (-(19571541444456643283281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4520315343059617 / 32000000000000000 : ℝ) = - (4520315343059617 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4520315343059617 / 4000000000000000 : ℚ)) - (U := (1222873964543356716719 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4520315343059617 / 4000000000000000 : ℝ) ≤ - (1222873964543356716719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (281030180370749 / 2000000000000000 : ℝ)) (q := - (4520315343059617 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4520315343059617 / 32000000000000000 : ℚ)) + (r' := (4520315343059617 / 4000000000000000 : ℚ)) + (U := (-(19571541444456643283281 / 10000000000000000000000 : ℚ))) + (U' := (1222873964543356716719 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (281030180370749 / 2000000000000000 : ℚ)) + (q := (4520315343059617 / 32000000000000000 : ℚ)) + (U := (-(19571541444456643283281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_5 : Uω (aρ 5) (bρ 5) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3555,25 +3231,21 @@ lemma U_219_5 : have hlg : Real.log (4099424570602057 / 32000000000000000 : ℝ) ≤ (-(821955714717225692007 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4099424570602057 / 32000000000000000 : ℝ) = - (4099424570602057 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4099424570602057 / 4000000000000000 : ℚ)) - (U := (9820901642774307993 / 400000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4099424570602057 / 4000000000000000 : ℝ) ≤ - (9820901642774307993 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (126028408840277 / 1000000000000000 : ℝ)) (q := - (4099424570602057 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4099424570602057 / 32000000000000000 : ℚ)) + (r' := (4099424570602057 / 4000000000000000 : ℚ)) + (U := (-(821955714717225692007 / 400000000000000000000 : ℚ))) + (U' := (9820901642774307993 / 400000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (126028408840277 / 1000000000000000 : ℚ)) + (q := (4099424570602057 / 32000000000000000 : ℚ)) + (U := (-(821955714717225692007 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_6 : Uω (aρ 6) (bρ 6) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3581,25 +3253,21 @@ lemma U_219_6 : have hlg : Real.log (3448568305934473 / 32000000000000000 : ℝ) ≤ (-(44555534812667741173 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3448568305934473 / 32000000000000000 : ℝ) = - (3448568305934473 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3448568305934473 / 2000000000000000 : ℚ)) - (U := (10896239611332258827 / 20000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3448568305934473 / 2000000000000000 : ℝ) ≤ - (10896239611332258827 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102073929812553 / 1000000000000000 : ℝ)) (q := - (3448568305934473 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3448568305934473 / 32000000000000000 : ℚ)) + (r' := (3448568305934473 / 2000000000000000 : ℚ)) + (U := (-(44555534812667741173 / 20000000000000000000 : ℚ))) + (U' := (10896239611332258827 / 20000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (102073929812553 / 1000000000000000 : ℚ)) + (q := (3448568305934473 / 32000000000000000 : ℚ)) + (U := (-(44555534812667741173 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_7 : Uω (aρ 7) (bρ 7) (20915234631277 / 128000000000000 : ℝ) ≤ @@ -3607,25 +3275,21 @@ lemma U_219_7 : have hlg : Real.log (11750008581007197 / 160000000000000000 : ℝ) ≤ (-(13056599216528297659903 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (11750008581007197 / 160000000000000000 : ℝ) = - (11750008581007197 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11750008581007197 / 10000000000000000 : ℚ)) - (U := (806344389471702340097 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11750008581007197 / 10000000000000000 : ℝ) ≤ - (806344389471702340097 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (34862285018899 / 625000000000000 : ℝ)) (q := - (11750008581007197 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11750008581007197 / 160000000000000000 : ℚ)) + (r' := (11750008581007197 / 10000000000000000 : ℚ)) + (U := (-(13056599216528297659903 / 5000000000000000000000 : ℚ))) + (U' := (806344389471702340097 / 5000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20915234631277 / 128000000000000 : ℚ)) + (s := (34862285018899 / 625000000000000 : ℚ)) + (q := (11750008581007197 / 160000000000000000 : ℚ)) + (U := (-(13056599216528297659903 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_219_8 : Uω (aρ 8) (bρ 8) (20915234631277 / 128000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U18.lean b/LeanPool/Zeta5Irrational/Table/U18.lean index 41942104ed..2c0ee0d968 100644 --- a/LeanPool/Zeta5Irrational/Table/U18.lean +++ b/LeanPool/Zeta5Irrational/Table/U18.lean @@ -24,25 +24,21 @@ lemma U_220_1 : have hlg : Real.log (6295354822894483 / 40000000000000000 : ℝ) ≤ (-(18490674215971361238241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6295354822894483 / 40000000000000000 : ℝ) = - (6295354822894483 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6295354822894483 / 5000000000000000 : ℚ)) - (U := (2303741193028638761759 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6295354822894483 / 5000000000000000 : ℝ) ≤ - (2303741193028638761759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1573735983708179 / 10000000000000000 : ℝ)) (q := - (6295354822894483 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6295354822894483 / 40000000000000000 : ℚ)) + (r' := (6295354822894483 / 5000000000000000 : ℚ)) + (U := (-(18490674215971361238241 / 10000000000000000000000 : ℚ))) + (U' := (2303741193028638761759 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (1573735983708179 / 10000000000000000 : ℚ)) + (q := (6295354822894483 / 40000000000000000 : ℚ)) + (U := (-(18490674215971361238241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_2 : Uω (aρ 2) (bρ 2) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_220_2 : have hlg : Real.log (6197950879677093 / 40000000000000000 : ℝ) ≤ (-(2330825898986484937893 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6197950879677093 / 40000000000000000 : ℝ) = - (6197950879677093 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6197950879677093 / 5000000000000000 : ℚ)) - (U := (268476027138515062107 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6197950879677093 / 5000000000000000 : ℝ) ≤ - (268476027138515062107 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (387200756152371 / 2500000000000000 : ℝ)) (q := - (6197950879677093 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6197950879677093 / 40000000000000000 : ℚ)) + (r' := (6197950879677093 / 5000000000000000 : ℚ)) + (U := (-(2330825898986484937893 / 1250000000000000000000 : ℚ))) + (U' := (268476027138515062107 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (387200756152371 / 2500000000000000 : ℚ)) + (q := (6197950879677093 / 40000000000000000 : ℚ)) + (U := (-(2330825898986484937893 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_3 : Uω (aρ 3) (bρ 3) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_220_3 : have hlg : Real.log (6001243171733643 / 40000000000000000 : ℝ) ≤ (-(9484564051395421285797 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6001243171733643 / 40000000000000000 : ℝ) = - (6001243171733643 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6001243171733643 / 5000000000000000 : ℚ)) - (U := (912643653104578714203 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6001243171733643 / 5000000000000000 : ℝ) ≤ - (912643653104578714203 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1497845276987759 / 10000000000000000 : ℝ)) (q := - (6001243171733643 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6001243171733643 / 40000000000000000 : ℚ)) + (r' := (6001243171733643 / 5000000000000000 : ℚ)) + (U := (-(9484564051395421285797 / 5000000000000000000000 : ℚ))) + (U' := (912643653104578714203 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (1497845276987759 / 10000000000000000 : ℚ)) + (q := (6001243171733643 / 40000000000000000 : ℚ)) + (U := (-(9484564051395421285797 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_4 : Uω (aρ 4) (bρ 4) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_220_4 : have hlg : Real.log (5668231688591941 / 40000000000000000 : ℝ) ≤ (-(9770011278685046203197 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5668231688591941 / 40000000000000000 : ℝ) = - (5668231688591941 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5668231688591941 / 5000000000000000 : ℚ)) - (U := (627196425814953796803 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5668231688591941 / 5000000000000000 : ℝ) ≤ - (627196425814953796803 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (352408429120477 / 2500000000000000 : ℝ)) (q := - (5668231688591941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5668231688591941 / 40000000000000000 : ℚ)) + (r' := (5668231688591941 / 5000000000000000 : ℚ)) + (U := (-(9770011278685046203197 / 5000000000000000000000 : ℚ))) + (U' := (627196425814953796803 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (352408429120477 / 2500000000000000 : ℚ)) + (q := (5668231688591941 / 40000000000000000 : ℚ)) + (U := (-(9770011278685046203197 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_5 : Uω (aρ 5) (bρ 5) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_220_5 : have hlg : Real.log (5142316082017839 / 40000000000000000 : ℝ) ≤ (-(20513758757421810226879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5142316082017839 / 40000000000000000 : ℝ) = - (5142316082017839 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5142316082017839 / 5000000000000000 : ℚ)) - (U := (280656651578189773121 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5142316082017839 / 5000000000000000 : ℝ) ≤ - (280656651578189773121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1264865832529857 / 10000000000000000 : ℝ)) (q := - (5142316082017839 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5142316082017839 / 40000000000000000 : ℚ)) + (r' := (5142316082017839 / 5000000000000000 : ℚ)) + (U := (-(20513758757421810226879 / 10000000000000000000000 : ℚ))) + (U' := (280656651578189773121 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (1264865832529857 / 10000000000000000 : ℚ)) + (q := (5142316082017839 / 40000000000000000 : ℚ)) + (U := (-(20513758757421810226879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_6 : Uω (aρ 6) (bρ 6) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_220_6 : have hlg : Real.log (4329439396326663 / 40000000000000000 : ℝ) ≤ (-(22234413891121944816083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4329439396326663 / 40000000000000000 : ℝ) = - (4329439396326663 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4329439396326663 / 2500000000000000 : ℚ)) - (U := (5491473320878055183917 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4329439396326663 / 2500000000000000 : ℝ) ≤ - (5491473320878055183917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1025667864824269 / 10000000000000000 : ℝ)) (q := - (4329439396326663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4329439396326663 / 40000000000000000 : ℚ)) + (r' := (4329439396326663 / 2500000000000000 : ℚ)) + (U := (-(22234413891121944816083 / 10000000000000000000000 : ℚ))) + (U' := (5491473320878055183917 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (1025667864824269 / 10000000000000000 : ℚ)) + (q := (4329439396326663 / 40000000000000000 : ℚ)) + (U := (-(22234413891121944816083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_7 : Uω (aρ 7) (bρ 7) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_220_7 : have hlg : Real.log (592160980922423 / 8000000000000000 : ℝ) ≤ (-(26034182944698725387439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (592160980922423 / 8000000000000000 : ℝ) = - (592160980922423 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (592160980922423 / 500000000000000 : ℚ)) - (U := (1691704267301274612561 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (592160980922423 / 500000000000000 : ℝ) ≤ - (1691704267301274612561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (113002399945399 / 2000000000000000 : ℝ)) (q := - (592160980922423 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (592160980922423 / 8000000000000000 : ℚ)) + (r' := (592160980922423 / 500000000000000 : ℚ)) + (U := (-(26034182944698725387439 / 10000000000000000000000 : ℚ))) + (U' := (1691704267301274612561 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5243003666637 / 32000000000000 : ℚ)) + (s := (113002399945399 / 2000000000000000 : ℚ)) + (q := (592160980922423 / 8000000000000000 : ℚ)) + (U := (-(26034182944698725387439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_220_8 : Uω (aρ 8) (bρ 8) (5243003666637 / 32000000000000 : ℝ) ≤ @@ -336,25 +308,21 @@ lemma U_221_1 : have hlg : Real.log (5050479791075543 / 32000000000000000 : ℝ) ≤ (-(4615631637779595417191 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5050479791075543 / 32000000000000000 : ℝ) = - (5050479791075543 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5050479791075543 / 4000000000000000 : ℚ)) - (U := (582972214470404582809 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5050479791075543 / 4000000000000000 : ℝ) ≤ - (582972214470404582809 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (315634500285521 / 2000000000000000 : ℝ)) (q := - (5050479791075543 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5050479791075543 / 32000000000000000 : ℚ)) + (r' := (5050479791075543 / 4000000000000000 : ℚ)) + (U := (-(4615631637779595417191 / 2500000000000000000000 : ℚ))) + (U' := (582972214470404582809 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (315634500285521 / 2000000000000000 : ℚ)) + (q := (5050479791075543 / 32000000000000000 : ℚ)) + (U := (-(4615631637779595417191 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_2 : Uω (aρ 2) (bρ 2) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -362,25 +330,21 @@ lemma U_221_2 : have hlg : Real.log (24862809849817163 / 160000000000000000 : ℝ) ≤ (-(465450176953729785337 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24862809849817163 / 160000000000000000 : ℝ) = - (24862809849817163 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24862809849817163 / 20000000000000000 : ℚ)) - (U := (54410208271270214663 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24862809849817163 / 20000000000000000 : ℝ) ≤ - (54410208271270214663 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (194155359467817 / 1250000000000000 : ℝ)) (q := - (24862809849817163 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24862809849817163 / 160000000000000000 : ℚ)) + (r' := (24862809849817163 / 20000000000000000 : ℚ)) + (U := (-(465450176953729785337 / 250000000000000000000 : ℚ))) + (U' := (54410208271270214663 / 250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (194155359467817 / 1250000000000000 : ℚ)) + (q := (24862809849817163 / 160000000000000000 : ℚ)) + (U := (-(465450176953729785337 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_3 : Uω (aρ 3) (bρ 3) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -388,25 +352,21 @@ lemma U_221_3 : have hlg : Real.log (24076064213378907 / 160000000000000000 : ℝ) ≤ (-(591861141768881967909 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24076064213378907 / 160000000000000000 : ℝ) = - (24076064213378907 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24076064213378907 / 20000000000000000 : ℚ)) - (U := (57964339762368032091 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24076064213378907 / 20000000000000000 : ℝ) ≤ - (57964339762368032091 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (751147888768877 / 5000000000000000 : ℝ)) (q := - (24076064213378907 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24076064213378907 / 160000000000000000 : ℚ)) + (r' := (24076064213378907 / 20000000000000000 : ℚ)) + (U := (-(591861141768881967909 / 312500000000000000000 : ℚ))) + (U' := (57964339762368032091 / 312500000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (751147888768877 / 5000000000000000 : ℚ)) + (q := (24076064213378907 / 160000000000000000 : ℚ)) + (U := (-(591861141768881967909 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_4 : Uω (aρ 4) (bρ 4) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -414,25 +374,21 @@ lemma U_221_4 : have hlg : Real.log (4548854885672911 / 32000000000000000 : ℝ) ≤ (-(9754301871052985929913 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4548854885672911 / 32000000000000000 : ℝ) = - (4548854885672911 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4548854885672911 / 4000000000000000 : ℚ)) - (U := (642905833447014070087 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4548854885672911 / 4000000000000000 : ℝ) ≤ - (642905833447014070087 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35352905886899 / 250000000000000 : ℝ)) (q := - (4548854885672911 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4548854885672911 / 32000000000000000 : ℚ)) + (r' := (4548854885672911 / 4000000000000000 : ℚ)) + (U := (-(9754301871052985929913 / 5000000000000000000000 : ℚ))) + (U' := (642905833447014070087 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (35352905886899 / 250000000000000 : ℚ)) + (q := (4548854885672911 / 32000000000000000 : ℚ)) + (U := (-(9754301871052985929913 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_5 : Uω (aρ 5) (bρ 5) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -440,25 +396,21 @@ lemma U_221_5 : have hlg : Real.log (20641397517236387 / 160000000000000000 : ℝ) ≤ (-(10239375834821808422919 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (20641397517236387 / 160000000000000000 : ℝ) = - (20641397517236387 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20641397517236387 / 20000000000000000 : ℚ)) - (U := (157831869678191577081 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20641397517236387 / 20000000000000000 : ℝ) ≤ - (157831869678191577081 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1269446540919939 / 10000000000000000 : ℝ)) (q := - (20641397517236387 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20641397517236387 / 160000000000000000 : ℚ)) + (r' := (20641397517236387 / 20000000000000000 : ℚ)) + (U := (-(10239375834821808422919 / 5000000000000000000000 : ℚ))) + (U' := (157831869678191577081 / 5000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (1269446540919939 / 10000000000000000 : ℚ)) + (q := (20641397517236387 / 160000000000000000 : ℚ)) + (U := (-(10239375834821808422919 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_6 : Uω (aρ 6) (bρ 6) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -466,25 +418,21 @@ lemma U_221_6 : have hlg : Real.log (17392637830890523 / 160000000000000000 : ℝ) ≤ (-(887650724271362820473 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17392637830890523 / 160000000000000000 : ℝ) = - (17392637830890523 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17392637830890523 / 10000000000000000 : ℚ)) - (U := (221384764208637179527 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17392637830890523 / 10000000000000000 : ℝ) ≤ - (221384764208637179527 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (515295977633353 / 5000000000000000 : ℝ)) (q := - (17392637830890523 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17392637830890523 / 160000000000000000 : ℚ)) + (r' := (17392637830890523 / 10000000000000000 : ℚ)) + (U := (-(887650724271362820473 / 400000000000000000000 : ℚ))) + (U' := (221384764208637179527 / 400000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (515295977633353 / 5000000000000000 : ℚ)) + (q := (17392637830890523 / 160000000000000000 : ℚ)) + (U := (-(887650724271362820473 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_7 : Uω (aρ 7) (bρ 7) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -492,25 +440,21 @@ lemma U_221_7 : have hlg : Real.log (2387195575291783 / 32000000000000000 : ℝ) ≤ (-(12978083121240946271847 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2387195575291783 / 32000000000000000 : ℝ) = - (2387195575291783 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2387195575291783 / 2000000000000000 : ℚ)) - (U := (884860484759053728153 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2387195575291783 / 2000000000000000 : ℝ) ≤ - (884860484759053728153 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114434168344551 / 2000000000000000 : ℝ)) (q := - (2387195575291783 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2387195575291783 / 32000000000000000 : ℚ)) + (r' := (2387195575291783 / 2000000000000000 : ℚ)) + (U := (-(12978083121240946271847 / 5000000000000000000000 : ℚ))) + (U' := (884860484759053728153 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21028794701819 / 128000000000000 : ℚ)) + (s := (114434168344551 / 2000000000000000 : ℚ)) + (q := (2387195575291783 / 32000000000000000 : ℚ)) + (U := (-(12978083121240946271847 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_221_8 : Uω (aρ 8) (bρ 8) (21028794701819 / 128000000000000 : ℝ) ≤ @@ -648,25 +592,21 @@ lemma U_222_1 : have hlg : Real.log (12661689296639181 / 80000000000000000 : ℝ) ≤ (-(1843445790326284033331 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12661689296639181 / 80000000000000000 : ℝ) = - (12661689296639181 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12661689296639181 / 10000000000000000 : ℚ)) - (U := (235995750573715966669 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12661689296639181 / 10000000000000000 : ℝ) ≤ - (235995750573715966669 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1582609015909639 / 10000000000000000 : ℝ)) (q := - (12661689296639181 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12661689296639181 / 80000000000000000 : ℚ)) + (r' := (12661689296639181 / 10000000000000000 : ℚ)) + (U := (-(1843445790326284033331 / 1000000000000000000000 : ℚ))) + (U' := (235995750573715966669 / 1000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (1582609015909639 / 10000000000000000 : ℚ)) + (q := (12661689296639181 / 80000000000000000 : ℚ)) + (U := (-(1843445790326284033331 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_2 : Uω (aρ 2) (bρ 2) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -674,25 +614,21 @@ lemma U_222_2 : have hlg : Real.log (12466908001325097 / 80000000000000000 : ℝ) ≤ (-(18589488599339791797713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12466908001325097 / 80000000000000000 : ℝ) = - (12466908001325097 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12466908001325097 / 10000000000000000 : ℚ)) - (U := (2204926809660208202287 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12466908001325097 / 10000000000000000 : ℝ) ≤ - (2204926809660208202287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (778841352295559 / 5000000000000000 : ℝ)) (q := - (12466908001325097 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12466908001325097 / 80000000000000000 : ℚ)) + (r' := (12466908001325097 / 10000000000000000 : ℚ)) + (U := (-(18589488599339791797713 / 10000000000000000000000 : ℚ))) + (U' := (2204926809660208202287 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (778841352295559 / 5000000000000000 : ℚ)) + (q := (12466908001325097 / 80000000000000000 : ℚ)) + (U := (-(18589488599339791797713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_3 : Uω (aρ 3) (bρ 3) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -700,24 +636,21 @@ lemma U_222_3 : have hlg : Real.log (96588620211349 / 640000000000000 : ℝ) ≤ (-(1891007244489895609963 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (96588620211349 / 640000000000000 : ℝ) = (96588620211349 / 80000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96588620211349 / 80000000000000 : ℚ)) - (U := (188434296410104390037 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (96588620211349 / 80000000000000 : ℝ) ≤ - (188434296410104390037 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3013492384429 / 20000000000000 : ℝ)) (q := - (96588620211349 / 640000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96588620211349 / 640000000000000 : ℚ)) + (r' := (96588620211349 / 80000000000000 : ℚ)) + (U := (-(1891007244489895609963 / 1000000000000000000000 : ℚ))) + (U' := (188434296410104390037 / 1000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (3013492384429 / 20000000000000 : ℚ)) + (q := (96588620211349 / 640000000000000 : ℚ)) + (U := (-(1891007244489895609963 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_4 : Uω (aρ 4) (bρ 4) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -725,25 +658,21 @@ lemma U_222_4 : have hlg : Real.log (11407809879854049 / 80000000000000000 : ℝ) ≤ (-(19477284358716666822331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11407809879854049 / 80000000000000000 : ℝ) = - (11407809879854049 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11407809879854049 / 10000000000000000 : ℚ)) - (U := (1317131050283333177669 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11407809879854049 / 10000000000000000 : ℝ) ≤ - (1317131050283333177669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (354649615409589 / 2500000000000000 : ℝ)) (q := - (11407809879854049 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11407809879854049 / 80000000000000000 : ℚ)) + (r' := (11407809879854049 / 10000000000000000 : ℚ)) + (U := (-(19477284358716666822331 / 10000000000000000000000 : ℚ))) + (U' := (1317131050283333177669 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (354649615409589 / 2500000000000000 : ℚ)) + (q := (11407809879854049 / 80000000000000000 : ℚ)) + (U := (-(19477284358716666822331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_5 : Uω (aρ 5) (bρ 5) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -751,25 +680,21 @@ lemma U_222_5 : have hlg : Real.log (10356761254940081 / 80000000000000000 : ℝ) ≤ (-(20443870661181125243673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10356761254940081 / 80000000000000000 : ℝ) = - (10356761254940081 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10356761254940081 / 10000000000000000 : ℚ)) - (U := (350544747818874756327 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10356761254940081 / 10000000000000000 : ℝ) ≤ - (350544747818874756327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (39813319523277 / 312500000000000 : ℝ)) (q := - (10356761254940081 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10356761254940081 / 80000000000000000 : ℚ)) + (r' := (10356761254940081 / 10000000000000000 : ℚ)) + (U := (-(20443870661181125243673 / 10000000000000000000000 : ℚ))) + (U' := (350544747818874756327 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (39813319523277 / 312500000000000 : ℚ)) + (q := (10356761254940081 / 80000000000000000 : ℚ)) + (U := (-(20443870661181125243673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_6 : Uω (aρ 6) (bρ 6) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -777,25 +702,21 @@ lemma U_222_6 : have hlg : Real.log (8733741388639249 / 80000000000000000 : ℝ) ≤ (-(11074163943683477485381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8733741388639249 / 80000000000000000 : ℝ) = - (8733741388639249 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8733741388639249 / 5000000000000000 : ℚ)) - (U := (2788779662316522514619 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8733741388639249 / 5000000000000000 : ℝ) ≤ - (2788779662316522514619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (129438954163707 / 1250000000000000 : ℝ)) (q := - (8733741388639249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8733741388639249 / 80000000000000000 : ℚ)) + (r' := (8733741388639249 / 5000000000000000 : ℚ)) + (U := (-(11074163943683477485381 / 5000000000000000000000 : ℚ))) + (U' := (2788779662316522514619 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (129438954163707 / 1250000000000000 : ℚ)) + (q := (8733741388639249 / 80000000000000000 : ℚ)) + (U := (-(11074163943683477485381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_7 : Uω (aρ 7) (bρ 7) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -803,25 +724,21 @@ lemma U_222_7 : have hlg : Real.log (6014150070893521 / 80000000000000000 : ℝ) ≤ (-(12939557978942782377787 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6014150070893521 / 80000000000000000 : ℝ) = - (6014150070893521 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6014150070893521 / 5000000000000000 : ℚ)) - (U := (923385627057217622213 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6014150070893521 / 5000000000000000 : ℝ) ≤ - (923385627057217622213 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (72409398079153 / 1250000000000000 : ℝ)) (q := - (6014150070893521 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6014150070893521 / 80000000000000000 : ℚ)) + (r' := (6014150070893521 / 5000000000000000 : ℚ)) + (U := (-(12939557978942782377787 / 5000000000000000000000 : ℚ))) + (U' := (923385627057217622213 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2108557473709 / 12800000000000 : ℚ)) + (s := (72409398079153 / 1250000000000000 : ℚ)) + (q := (6014150070893521 / 80000000000000000 : ℚ)) + (U := (-(12939557978942782377787 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_222_8 : Uω (aρ 8) (bρ 8) (2108557473709 / 12800000000000 : ℝ) ≤ @@ -958,25 +875,21 @@ lemma U_223_1 : have hlg : Real.log (25394358205497089 / 160000000000000000 : ℝ) ≤ (-(1840646782995148303141 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25394358205497089 / 160000000000000000 : ℝ) = - (25394358205497089 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25394358205497089 / 20000000000000000 : ℚ)) - (U := (238794757904851696859 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25394358205497089 / 20000000000000000 : ℝ) ≤ - (238794757904851696859 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1587045527181433 / 10000000000000000 : ℝ)) (q := - (25394358205497089 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25394358205497089 / 160000000000000000 : ℚ)) + (r' := (25394358205497089 / 20000000000000000 : ℚ)) + (U := (-(1840646782995148303141 / 1000000000000000000000 : ℚ))) + (U' := (238794757904851696859 / 1000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (1587045527181433 / 10000000000000000 : ℚ)) + (q := (25394358205497089 / 160000000000000000 : ℚ)) + (U := (-(1840646782995148303141 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_2 : Uω (aρ 2) (bρ 2) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -984,25 +897,21 @@ lemma U_223_2 : have hlg : Real.log (5000964395745509 / 32000000000000000 : ℝ) ≤ (-(4640262822588700036873 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5000964395745509 / 32000000000000000 : ℝ) = - (5000964395745509 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5000964395745509 / 4000000000000000 : ℚ)) - (U := (558341029661299963127 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5000964395745509 / 4000000000000000 : ℝ) ≤ - (558341029661299963127 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (39053062783631 / 250000000000000 : ℝ)) (q := - (5000964395745509 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5000964395745509 / 32000000000000000 : ℚ)) + (r' := (5000964395745509 / 4000000000000000 : ℚ)) + (U := (-(4640262822588700036873 / 2500000000000000000000 : ℚ))) + (U' := (558341029661299963127 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (39053062783631 / 250000000000000 : ℚ)) + (q := (5000964395745509 / 32000000000000000 : ℚ)) + (U := (-(4640262822588700036873 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_3 : Uω (aρ 3) (bρ 3) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1010,25 +919,21 @@ lemma U_223_3 : have hlg : Real.log (24218245211379041 / 160000000000000000 : ℝ) ≤ (-(18880675310025809271703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24218245211379041 / 160000000000000000 : ℝ) = - (24218245211379041 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24218245211379041 / 20000000000000000 : ℚ)) - (U := (1913740098974190728297 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24218245211379041 / 20000000000000000 : ℝ) ≤ - (1913740098974190728297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1511196521776677 / 10000000000000000 : ℝ)) (q := - (24218245211379041 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24218245211379041 / 160000000000000000 : ℚ)) + (r' := (24218245211379041 / 20000000000000000 : ℚ)) + (U := (-(18880675310025809271703 / 10000000000000000000000 : ℚ))) + (U' := (1913740098974190728297 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (1511196521776677 / 10000000000000000 : ℚ)) + (q := (24218245211379041 / 160000000000000000 : ℚ)) + (U := (-(18880675310025809271703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_4 : Uω (aρ 4) (bρ 4) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1036,25 +941,21 @@ lemma U_223_4 : have hlg : Real.log (22886962770534089 / 160000000000000000 : ℝ) ≤ (-(19446063773434154064433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22886962770534089 / 160000000000000000 : ℝ) = - (22886962770534089 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22886962770534089 / 20000000000000000 : ℚ)) - (U := (1348351635565845935567 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22886962770534089 / 20000000000000000 : ℝ) ≤ - (1348351635565845935567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (711540198868029 / 5000000000000000 : ℝ)) (q := - (22886962770534089 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22886962770534089 / 160000000000000000 : ℚ)) + (r' := (22886962770534089 / 20000000000000000 : ℚ)) + (U := (-(19446063773434154064433 / 10000000000000000000000 : ℚ))) + (U' := (1348351635565845935567 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (711540198868029 / 5000000000000000 : ℚ)) + (q := (22886962770534089 / 160000000000000000 : ℚ)) + (U := (-(19446063773434154064433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_5 : Uω (aρ 5) (bρ 5) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1062,25 +963,21 @@ lemma U_223_5 : have hlg : Real.log (20785639394077129 / 160000000000000000 : ℝ) ≤ (-(20409114799383380511043 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (20785639394077129 / 160000000000000000 : ℝ) = - (20785639394077129 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20785639394077129 / 20000000000000000 : ℚ)) - (U := (385300609616619488957 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20785639394077129 / 20000000000000000 : ℝ) ≤ - (385300609616619488957 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (639302447506969 / 5000000000000000 : ℝ)) (q := - (20785639394077129 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20785639394077129 / 160000000000000000 : ℚ)) + (r' := (20785639394077129 / 20000000000000000 : ℚ)) + (U := (-(20409114799383380511043 / 10000000000000000000000 : ℚ))) + (U' := (385300609616619488957 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (639302447506969 / 5000000000000000 : ℚ)) + (q := (20785639394077129 / 160000000000000000 : ℚ)) + (U := (-(20409114799383380511043 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_6 : Uω (aρ 6) (bρ 6) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1088,25 +985,21 @@ lemma U_223_6 : have hlg : Real.log (17542292925209281 / 160000000000000000 : ℝ) ≤ (-(4421118220594607150783 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17542292925209281 / 160000000000000000 : ℝ) = - (17542292925209281 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17542292925209281 / 10000000000000000 : ℚ)) - (U := (1124059221805392849217 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17542292925209281 / 10000000000000000 : ℝ) ≤ - (1124059221805392849217 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1040426961545457 / 10000000000000000 : ℝ)) (q := - (17542292925209281 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17542292925209281 / 160000000000000000 : ℚ)) + (r' := (17542292925209281 / 10000000000000000 : ℚ)) + (U := (-(4421118220594607150783 / 2000000000000000000000 : ℚ))) + (U' := (1124059221805392849217 / 2000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (1040426961545457 / 10000000000000000 : ℚ)) + (q := (17542292925209281 / 160000000000000000 : ℚ)) + (U := (-(4421118220594607150783 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_7 : Uω (aρ 7) (bρ 7) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1114,25 +1007,21 @@ lemma U_223_7 : have hlg : Real.log (12120202262824801 / 160000000000000000 : ℝ) ≤ (-(25803001453402450152699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (12120202262824801 / 160000000000000000 : ℝ) = - (12120202262824801 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12120202262824801 / 10000000000000000 : ℚ)) - (U := (1922885758597549847301 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12120202262824801 / 10000000000000000 : ℝ) ≤ - (1922885758597549847301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (586327009507397 / 10000000000000000 : ℝ)) (q := - (12120202262824801 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12120202262824801 / 160000000000000000 : ℚ)) + (r' := (12120202262824801 / 10000000000000000 : ℚ)) + (U := (-(25803001453402450152699 / 10000000000000000000000 : ℚ))) + (U' := (1922885758597549847301 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21142354772361 / 128000000000000 : ℚ)) + (s := (586327009507397 / 10000000000000000 : ℚ)) + (q := (12120202262824801 / 160000000000000000 : ℚ)) + (U := (-(25803001453402450152699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_223_8 : Uω (aρ 8) (bρ 8) (21142354772361 / 128000000000000 : ℝ) ≤ @@ -1270,25 +1159,21 @@ lemma U_224_1 : have hlg : Real.log (1591583612015541 / 10000000000000000 : ℝ) ≤ (-(4594638973109356257451 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1591583612015541 / 10000000000000000 : ℝ) = - (1591583612015541 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1591583612015541 / 1250000000000000 : ℚ)) - (U := (603964879140643742549 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1591583612015541 / 1250000000000000 : ℝ) ≤ - (603964879140643742549 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (198935254408729 / 1250000000000000 : ℝ)) (q := - (1591583612015541 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1591583612015541 / 10000000000000000 : ℚ)) + (r' := (1591583612015541 / 1250000000000000 : ℚ)) + (U := (-(4594638973109356257451 / 2500000000000000000000 : ℚ))) + (U' := (603964879140643742549 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (198935254408729 / 1250000000000000 : ℚ)) + (q := (1591583612015541 / 10000000000000000 : ℚ)) + (U := (-(4594638973109356257451 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_2 : Uω (aρ 2) (bρ 2) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1296,25 +1181,21 @@ lemma U_224_2 : have hlg : Real.log (1567239236222003 / 10000000000000000 : ℝ) ≤ (-(2316586836256544584097 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1567239236222003 / 10000000000000000 : ℝ) = - (1567239236222003 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1567239236222003 / 1250000000000000 : ℚ)) - (U := (282715089868455415903 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1567239236222003 / 1250000000000000 : ℝ) ≤ - (282715089868455415903 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (391640574048189 / 2500000000000000 : ℝ)) (q := - (1567239236222003 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1567239236222003 / 10000000000000000 : ℚ)) + (r' := (1567239236222003 / 1250000000000000 : ℚ)) + (U := (-(2316586836256544584097 / 1250000000000000000000 : ℚ))) + (U' := (282715089868455415903 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (391640574048189 / 2500000000000000 : ℚ)) + (q := (1567239236222003 / 10000000000000000 : ℚ)) + (U := (-(2316586836256544584097 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_3 : Uω (aρ 3) (bρ 3) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1322,25 +1203,21 @@ lemma U_224_3 : have hlg : Real.log (303616683687529 / 2000000000000000 : ℝ) ≤ (-(2356420577366438601497 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (303616683687529 / 2000000000000000 : ℝ) = - (303616683687529 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (303616683687529 / 250000000000000 : ℚ)) - (U := (242881348758561398503 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (303616683687529 / 250000000000000 : ℝ) ≤ - (242881348758561398503 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (37891169174351 / 250000000000000 : ℝ)) (q := - (303616683687529 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (303616683687529 / 2000000000000000 : ℚ)) + (r' := (303616683687529 / 250000000000000 : ℚ)) + (U := (-(2356420577366438601497 / 1250000000000000000000 : ℚ))) + (U' := (242881348758561398503 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (37891169174351 / 250000000000000 : ℚ)) + (q := (303616683687529 / 2000000000000000 : ℚ)) + (U := (-(2356420577366438601497 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_4 : Uω (aρ 4) (bρ 4) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1348,25 +1225,21 @@ lemma U_224_4 : have hlg : Real.log (2869787935337357 / 20000000000000000 : ℝ) ≤ (-(3882988271717983275987 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2869787935337357 / 20000000000000000 : ℝ) = - (2869787935337357 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2869787935337357 / 2500000000000000 : ℚ)) - (U := (275894810082016724013 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2869787935337357 / 2500000000000000 : ℝ) ≤ - (275894810082016724013 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1427562046501107 / 10000000000000000 : ℝ)) (q := - (2869787935337357 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2869787935337357 / 20000000000000000 : ℚ)) + (r' := (2869787935337357 / 2500000000000000 : ℚ)) + (U := (-(3882988271717983275987 / 2000000000000000000000 : ℚ))) + (U' := (275894810082016724013 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (1427562046501107 / 10000000000000000 : ℚ)) + (q := (2869787935337357 / 20000000000000000 : ℚ)) + (U := (-(3882988271717983275987 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_5 : Uω (aρ 5) (bρ 5) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1374,25 +1247,21 @@ lemma U_224_5 : have hlg : Real.log (521443706415633 / 4000000000000000 : ℝ) ≤ (-(1018724158109815143011 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (521443706415633 / 4000000000000000 : ℝ) = - (521443706415633 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (521443706415633 / 500000000000000 : ℚ)) - (U := (20996612340184856989 / 500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (521443706415633 / 500000000000000 : ℝ) ≤ - (20996612340184856989 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256636512515383 / 2000000000000000 : ℝ)) (q := - (521443706415633 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (521443706415633 / 4000000000000000 : ℚ)) + (r' := (521443706415633 / 500000000000000 : ℚ)) + (U := (-(1018724158109815143011 / 500000000000000000000 : ℚ))) + (U' := (20996612340184856989 / 500000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (256636512515383 / 2000000000000000 : ℚ)) + (q := (521443706415633 / 4000000000000000 : ℚ)) + (U := (-(1018724158109815143011 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_6 : Uω (aρ 6) (bρ 6) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1400,23 +1269,21 @@ lemma U_224_6 : have hlg : Real.log (5505333989239 / 50000000000000 : ℝ) ≤ (-(882522226357036714549 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (5505333989239 / 50000000000000 : ℝ) = (5505333989239 / 3125000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5505333989239 / 3125000000000 : ℚ)) - (U := (226513262122963285451 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (5505333989239 / 3125000000000 : ℝ) ≤ - (226513262122963285451 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (20906760026687 / 200000000000000 : ℝ)) (q := - (5505333989239 / 50000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5505333989239 / 50000000000000 : ℚ)) + (r' := (5505333989239 / 3125000000000 : ℚ)) + (U := (-(882522226357036714549 / 400000000000000000000 : ℚ))) + (U' := (226513262122963285451 / 400000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (20906760026687 / 200000000000000 : ℚ)) + (q := (5505333989239 / 50000000000000 : ℚ)) + (U := (-(882522226357036714549 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_7 : Uω (aρ 7) (bρ 7) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1424,25 +1291,21 @@ lemma U_224_7 : have hlg : Real.log (305292480502351 / 4000000000000000 : ℝ) ≤ (-(643194842372322635267 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (305292480502351 / 4000000000000000 : ℝ) = - (305292480502351 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (305292480502351 / 250000000000000 : ℚ)) - (U := (49952337927677364733 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (305292480502351 / 250000000000000 : ℝ) ≤ - (49952337927677364733 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (118665637782101 / 2000000000000000 : ℝ)) (q := - (305292480502351 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (305292480502351 / 4000000000000000 : ℚ)) + (r' := (305292480502351 / 250000000000000 : ℚ)) + (U := (-(643194842372322635267 / 250000000000000000000 : ℚ))) + (U' := (49952337927677364733 / 250000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1324945925477 / 8000000000000 : ℚ)) + (s := (118665637782101 / 2000000000000000 : ℚ)) + (q := (305292480502351 / 4000000000000000 : ℚ)) + (U := (-(643194842372322635267 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_224_8 : Uω (aρ 8) (bρ 8) (1324945925477 / 8000000000000 : ℝ) ≤ @@ -1578,25 +1441,21 @@ lemma U_225_1 : have hlg : Real.log (12803648445098779 / 80000000000000000 : ℝ) ≤ (-(4580741172024563874411 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12803648445098779 / 80000000000000000 : ℝ) = - (12803648445098779 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12803648445098779 / 10000000000000000 : ℚ)) - (U := (617862680225436125589 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12803648445098779 / 10000000000000000 : ℝ) ≤ - (617862680225436125589 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1600355042002351 / 10000000000000000 : ℝ)) (q := - (12803648445098779 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12803648445098779 / 80000000000000000 : ℚ)) + (r' := (12803648445098779 / 10000000000000000 : ℚ)) + (U := (-(4580741172024563874411 / 2500000000000000000000 : ℚ))) + (U' := (617862680225436125589 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (1600355042002351 / 10000000000000000 : ℚ)) + (q := (12803648445098779 / 80000000000000000 : ℚ)) + (U := (-(4580741172024563874411 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_2 : Uω (aρ 2) (bρ 2) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1604,25 +1463,21 @@ lemma U_225_2 : have hlg : Real.log (2521783886136911 / 16000000000000000 : ℝ) ≤ (-(9238110895246623312471 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2521783886136911 / 16000000000000000 : ℝ) = - (2521783886136911 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2521783886136911 / 2000000000000000 : ℚ)) - (U := (1159096809253376687529 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2521783886136911 / 2000000000000000 : ℝ) ≤ - (1159096809253376687529 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (315088360181759 / 2000000000000000 : ℝ)) (q := - (2521783886136911 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2521783886136911 / 16000000000000000 : ℚ)) + (r' := (2521783886136911 / 2000000000000000 : ℚ)) + (U := (-(9238110895246623312471 / 5000000000000000000000 : ℚ))) + (U' := (1159096809253376687529 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (315088360181759 / 2000000000000000 : ℚ)) + (q := (2521783886136911 / 16000000000000000 : ℚ)) + (U := (-(9238110895246623312471 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_3 : Uω (aρ 3) (bρ 3) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1630,25 +1485,21 @@ lemma U_225_3 : have hlg : Real.log (12215755830567379 / 80000000000000000 : ℝ) ≤ (-(939650026926023325251 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12215755830567379 / 80000000000000000 : ℝ) = - (12215755830567379 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12215755830567379 / 10000000000000000 : ℚ)) - (U := (100070743523976674749 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12215755830567379 / 10000000000000000 : ℝ) ≤ - (100070743523976674749 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1524547007229501 / 10000000000000000 : ℝ)) (q := - (12215755830567379 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12215755830567379 / 80000000000000000 : ℚ)) + (r' := (12215755830567379 / 10000000000000000 : ℚ)) + (U := (-(939650026926023325251 / 500000000000000000000 : ℚ))) + (U' := (100070743523976674749 / 500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (1524547007229501 / 10000000000000000 : ℚ)) + (q := (12215755830567379 / 80000000000000000 : ℚ)) + (U := (-(939650026926023325251 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_4 : Uω (aρ 4) (bρ 4) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1656,25 +1507,21 @@ lemma U_225_4 : have hlg : Real.log (2310097809709927 / 16000000000000000 : ℝ) ≤ (-(9676494279784326839573 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2310097809709927 / 16000000000000000 : ℝ) = - (2310097809709927 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2310097809709927 / 2000000000000000 : ℚ)) - (U := (720713424715673160427 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2310097809709927 / 2000000000000000 : ℝ) ≤ - (720713424715673160427 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (287304898558013 / 2000000000000000 : ℝ)) (q := - (2310097809709927 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2310097809709927 / 16000000000000000 : ℚ)) + (r' := (2310097809709927 / 2000000000000000 : ℚ)) + (U := (-(9676494279784326839573 / 5000000000000000000000 : ℚ))) + (U' := (720713424715673160427 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (287304898558013 / 2000000000000000 : ℚ)) + (q := (2310097809709927 / 16000000000000000 : ℚ)) + (U := (-(9676494279784326839573 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_5 : Uω (aρ 5) (bρ 5) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1682,25 +1529,21 @@ lemma U_225_5 : have hlg : Real.log (10500971128862519 / 80000000000000000 : ℝ) ≤ (-(20305588925442651515513 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10500971128862519 / 80000000000000000 : ℝ) = - (10500971128862519 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10500971128862519 / 10000000000000000 : ℚ)) - (U := (488826483557348484487 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10500971128862519 / 10000000000000000 : ℝ) ≤ - (488826483557348484487 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (646167466101643 / 5000000000000000 : ℝ)) (q := - (10500971128862519 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10500971128862519 / 80000000000000000 : ℚ)) + (r' := (10500971128862519 / 10000000000000000 : ℚ)) + (U := (-(20305588925442651515513 / 10000000000000000000000 : ℚ))) + (U' := (488826483557348484487 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (646167466101643 / 5000000000000000 : ℚ)) + (q := (10500971128862519 / 80000000000000000 : ℚ)) + (U := (-(20305588925442651515513 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_6 : Uω (aρ 6) (bρ 6) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1708,25 +1551,21 @@ lemma U_225_6 : have hlg : Real.log (1776651943929107 / 16000000000000000 : ℝ) ≤ (-(5494645146109420751617 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1776651943929107 / 16000000000000000 : ℝ) = - (1776651943929107 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1776651943929107 / 1000000000000000 : ℚ)) - (U := (1436826656890579248383 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1776651943929107 / 1000000000000000 : ℝ) ≤ - (1436826656890579248383 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3297335796997 / 31250000000000 : ℝ)) (q := - (1776651943929107 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1776651943929107 / 16000000000000000 : ℚ)) + (r' := (1776651943929107 / 1000000000000000 : ℚ)) + (U := (-(5494645146109420751617 / 2500000000000000000000 : ℚ))) + (U' := (1436826656890579248383 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (3297335796997 / 31250000000000 : ℚ)) + (q := (1776651943929107 / 16000000000000000 : ℚ)) + (U := (-(5494645146109420751617 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_7 : Uω (aρ 7) (bρ 7) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1734,25 +1573,21 @@ lemma U_225_7 : have hlg : Real.log (6196766801680643 / 80000000000000000 : ℝ) ≤ (-(12789994806014067070709 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6196766801680643 / 80000000000000000 : ℝ) = - (6196766801680643 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6196766801680643 / 5000000000000000 : ℚ)) - (U := (1072948799985932929291 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6196766801680643 / 5000000000000000 : ℝ) ≤ - (1072948799985932929291 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (607185606307817 / 10000000000000000 : ℝ)) (q := - (6196766801680643 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6196766801680643 / 80000000000000000 : ℚ)) + (r' := (6196766801680643 / 5000000000000000 : ℚ)) + (U := (-(12789994806014067070709 / 5000000000000000000000 : ℚ))) + (U' := (1072948799985932929291 / 5000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10656347439087 / 64000000000000 : ℚ)) + (s := (607185606307817 / 10000000000000000 : ℚ)) + (q := (6196766801680643 / 80000000000000000 : ℚ)) + (U := (-(12789994806014067070709 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_225_8 : Uω (aρ 8) (bρ 8) (10656347439087 / 64000000000000 : ℝ) ≤ @@ -1889,25 +1724,21 @@ lemma U_226_1 : have hlg : Real.log (257492558887961 / 1600000000000000 : ℝ) ≤ (-(71358128331416751623 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (257492558887961 / 1600000000000000 : ℝ) = - (257492558887961 / 200000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (257492558887961 / 200000000000000 : ℚ)) - (U := (9870056859989498377 / 39062500000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (257492558887961 / 200000000000000 : ℝ) ≤ - (9870056859989498377 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (64369121452643 / 400000000000000 : ℝ)) (q := - (257492558887961 / 1600000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (257492558887961 / 1600000000000000 : ℚ)) + (r' := (257492558887961 / 200000000000000 : ℚ)) + (U := (-(71358128331416751623 / 39062500000000000000 : ℚ))) + (U' := (9870056859989498377 / 39062500000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (64369121452643 / 400000000000000 : ℚ)) + (q := (257492558887961 / 1600000000000000 : ℚ)) + (U := (-(71358128331416751623 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_2 : Uω (aρ 2) (bρ 2) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -1915,25 +1746,21 @@ lemma U_226_2 : have hlg : Real.log (1267992462989421 / 8000000000000000 : ℝ) ≤ (-(18420066289172837522877 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1267992462989421 / 8000000000000000 : ℝ) = - (1267992462989421 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1267992462989421 / 1000000000000000 : ℚ)) - (U := (2374349119827162477123 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1267992462989421 / 1000000000000000 : ℝ) ≤ - (2374349119827162477123 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (316864244040023 / 2000000000000000 : ℝ)) (q := - (1267992462989421 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1267992462989421 / 8000000000000000 : ℚ)) + (r' := (1267992462989421 / 1000000000000000 : ℚ)) + (U := (-(18420066289172837522877 / 10000000000000000000000 : ℚ))) + (U' := (2374349119827162477123 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (316864244040023 / 2000000000000000 : ℚ)) + (q := (1267992462989421 / 8000000000000000 : ℚ)) + (U := (-(18420066289172837522877 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_3 : Uω (aρ 3) (bρ 3) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -1941,25 +1768,21 @@ lemma U_226_3 : have hlg : Real.log (1228684299891513 / 8000000000000000 : ℝ) ≤ (-(18734976189111055348777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1228684299891513 / 8000000000000000 : ℝ) = - (1228684299891513 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1228684299891513 / 1000000000000000 : ℚ)) - (U := (2059439219888944651223 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1228684299891513 / 1000000000000000 : ℝ) ≤ - (2059439219888944651223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (306689383761069 / 2000000000000000 : ℝ)) (q := - (1228684299891513 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1228684299891513 / 8000000000000000 : ℚ)) + (r' := (1228684299891513 / 1000000000000000 : ℚ)) + (U := (-(18734976189111055348777 / 10000000000000000000000 : ℚ))) + (U' := (2059439219888944651223 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (306689383761069 / 2000000000000000 : ℚ)) + (q := (1228684299891513 / 8000000000000000 : ℚ)) + (U := (-(18734976189111055348777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_4 : Uω (aρ 4) (bρ 4) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -1967,25 +1790,21 @@ lemma U_226_4 : have hlg : Real.log (5810910943084333 / 40000000000000000 : ℝ) ≤ (-(19291421059334564470881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5810910943084333 / 40000000000000000 : ℝ) = - (5810910943084333 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5810910943084333 / 5000000000000000 : ℚ)) - (U := (1502994349665435529119 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5810910943084333 / 5000000000000000 : ℝ) ≤ - (1502994349665435529119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1445485821683729 / 10000000000000000 : ℝ)) (q := - (5810910943084333 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5810910943084333 / 40000000000000000 : ℚ)) + (r' := (5810910943084333 / 5000000000000000 : ℚ)) + (U := (-(19291421059334564470881 / 10000000000000000000000 : ℚ))) + (U' := (1502994349665435529119 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (1445485821683729 / 10000000000000000 : ℚ)) + (q := (5810910943084333 / 40000000000000000 : ℚ)) + (U := (-(19291421059334564470881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_5 : Uω (aρ 5) (bρ 5) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -1993,25 +1812,21 @@ lemma U_226_5 : have hlg : Real.log (5286526295727557 / 40000000000000000 : ℝ) ≤ (-(10118590390140244503249 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5286526295727557 / 40000000000000000 : ℝ) = - (5286526295727557 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5286526295727557 / 5000000000000000 : ℚ)) - (U := (278617314359755496751 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5286526295727557 / 5000000000000000 : ℝ) ≤ - (278617314359755496751 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1301483417340341 / 10000000000000000 : ℝ)) (q := - (5286526295727557 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5286526295727557 / 40000000000000000 : ℚ)) + (r' := (5286526295727557 / 5000000000000000 : ℚ)) + (U := (-(10118590390140244503249 / 5000000000000000000000 : ℚ))) + (U' := (278617314359755496751 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (1301483417340341 / 10000000000000000 : ℚ)) + (q := (5286526295727557 / 40000000000000000 : ℚ)) + (U := (-(10118590390140244503249 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_6 : Uω (aρ 6) (bρ 6) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -2019,25 +1834,21 @@ lemma U_226_6 : have hlg : Real.log (4478959634428699 / 40000000000000000 : ℝ) ≤ (-(175159092645873246921 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4478959634428699 / 40000000000000000 : ℝ) = - (4478959634428699 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4478959634428699 / 2500000000000000 : ℚ)) - (U := (46648005050126753079 / 80000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4478959634428699 / 2500000000000000 : ℝ) ≤ - (46648005050126753079 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4159923679027 / 39062500000000 : ℝ)) (q := - (4478959634428699 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4478959634428699 / 40000000000000000 : ℚ)) + (r' := (4478959634428699 / 2500000000000000 : ℚ)) + (U := (-(175159092645873246921 / 80000000000000000000 : ℚ))) + (U' := (46648005050126753079 / 80000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (4159923679027 / 39062500000000 : ℚ)) + (q := (4478959634428699 / 40000000000000000 : ℚ)) + (U := (-(175159092645873246921 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_7 : Uω (aρ 7) (bρ 7) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -2045,25 +1856,21 @@ lemma U_226_7 : have hlg : Real.log (3143477015809841 / 40000000000000000 : ℝ) ≤ (-(25435499359157548817667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3143477015809841 / 40000000000000000 : ℝ) = - (3143477015809841 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3143477015809841 / 2500000000000000 : ℚ)) - (U := (2290387852842451182333 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3143477015809841 / 2500000000000000 : ℝ) ≤ - (2290387852842451182333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (620860533281483 / 10000000000000000 : ℝ)) (q := - (3143477015809841 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3143477015809841 / 40000000000000000 : ℚ)) + (r' := (3143477015809841 / 2500000000000000 : ℚ)) + (U := (-(25435499359157548817667 / 10000000000000000000000 : ℚ))) + (U' := (2290387852842451182333 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5356563737179 / 32000000000000 : ℚ)) + (s := (620860533281483 / 10000000000000000 : ℚ)) + (q := (3143477015809841 / 40000000000000000 : ℚ)) + (U := (-(25435499359157548817667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_226_8 : Uω (aρ 8) (bρ 8) (5356563737179 / 32000000000000 : ℝ) ≤ @@ -2199,25 +2006,21 @@ lemma U_227_1 : have hlg : Real.log (12945607394839337 / 80000000000000000 : ℝ) ≤ (-(9106350502993110805211 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12945607394839337 / 80000000000000000 : ℝ) = - (12945607394839337 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12945607394839337 / 10000000000000000 : ℚ)) - (U := (1290857201506889194789 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12945607394839337 / 10000000000000000 : ℝ) ≤ - (1290857201506889194789 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1618101018415303 / 10000000000000000 : ℝ)) (q := - (12945607394839337 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12945607394839337 / 80000000000000000 : ℚ)) + (r' := (12945607394839337 / 10000000000000000 : ℚ)) + (U := (-(9106350502993110805211 / 5000000000000000000000 : ℚ))) + (U' := (1290857201506889194789 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (1618101018415303 / 10000000000000000 : ℚ)) + (q := (12945607394839337 / 80000000000000000 : ℚ)) + (U := (-(9106350502993110805211 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_2 : Uω (aρ 2) (bρ 2) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2225,25 +2028,21 @@ lemma U_227_2 : have hlg : Real.log (12750929493118181 / 80000000000000000 : ℝ) ≤ (-(18364224635257561809589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12750929493118181 / 80000000000000000 : ℝ) = - (12750929493118181 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12750929493118181 / 10000000000000000 : ℚ)) - (U := (2430190773742438190411 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12750929493118181 / 10000000000000000 : ℝ) ≤ - (2430190773742438190411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (796600277747507 / 5000000000000000 : ℝ)) (q := - (12750929493118181 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12750929493118181 / 80000000000000000 : ℚ)) + (r' := (12750929493118181 / 10000000000000000 : ℚ)) + (U := (-(18364224635257561809589 / 10000000000000000000000 : ℚ))) + (U' := (2430190773742438190411 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (796600277747507 / 5000000000000000 : ℚ)) + (q := (12750929493118181 / 80000000000000000 : ℚ)) + (U := (-(18364224635257561809589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_3 : Uω (aρ 3) (bρ 3) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2251,25 +2050,21 @@ lemma U_227_3 : have hlg : Real.log (2471585775060729 / 16000000000000000 : ℝ) ≤ (-(4669321906570947279869 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2471585775060729 / 16000000000000000 : ℝ) = - (2471585775060729 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2471585775060729 / 2000000000000000 : ℚ)) - (U := (529281945679052720131 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2471585775060729 / 2000000000000000 : ℝ) ≤ - (529281945679052720131 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (77117325369569 / 500000000000000 : ℝ)) (q := - (2471585775060729 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2471585775060729 / 16000000000000000 : ℚ)) + (r' := (2471585775060729 / 2000000000000000 : ℚ)) + (U := (-(4669321906570947279869 / 2500000000000000000000 : ℚ))) + (U' := (529281945679052720131 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (77117325369569 / 500000000000000 : ℚ)) + (q := (2471585775060729 / 16000000000000000 : ℚ)) + (U := (-(4669321906570947279869 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_4 : Uω (aρ 4) (bρ 4) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2277,25 +2072,21 @@ lemma U_227_4 : have hlg : Real.log (11693150336822277 / 80000000000000000 : ℝ) ≤ (-(9615117024126235910581 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11693150336822277 / 80000000000000000 : ℝ) = - (11693150336822277 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11693150336822277 / 10000000000000000 : ℚ)) - (U := (782090680373764089419 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11693150336822277 / 10000000000000000 : ℝ) ≤ - (782090680373764089419 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (727223026918019 / 5000000000000000 : ℝ)) (q := - (11693150336822277 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11693150336822277 / 80000000000000000 : ℚ)) + (r' := (11693150336822277 / 10000000000000000 : ℚ)) + (U := (-(9615117024126235910581 / 5000000000000000000000 : ℚ))) + (U' := (782090680373764089419 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (727223026918019 / 5000000000000000 : ℚ)) + (q := (11693150336822277 / 80000000000000000 : ℚ)) + (U := (-(9615117024126235910581 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_5 : Uω (aρ 5) (bρ 5) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2303,25 +2094,21 @@ lemma U_227_5 : have hlg : Real.log (10645118841465981 / 80000000000000000 : ℝ) ≤ (-(20169251715464789785997 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10645118841465981 / 80000000000000000 : ℝ) = - (10645118841465981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10645118841465981 / 10000000000000000 : ℚ)) - (U := (625163693535210214003 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10645118841465981 / 10000000000000000 : ℝ) ≤ - (625163693535210214003 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (327657024832991 / 2500000000000000 : ℝ)) (q := - (10645118841465981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10645118841465981 / 80000000000000000 : ℚ)) + (r' := (10645118841465981 / 10000000000000000 : ℚ)) + (U := (-(20169251715464789785997 / 10000000000000000000000 : ℚ))) + (U' := (625163693535210214003 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (327657024832991 / 2500000000000000 : ℚ)) + (q := (10645118841465981 / 80000000000000000 : ℚ)) + (U := (-(20169251715464789785997 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_6 : Uω (aρ 6) (bρ 6) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2329,25 +2116,21 @@ lemma U_227_6 : have hlg : Real.log (1806502965764577 / 16000000000000000 : ℝ) ≤ (-(10905979039386153311897 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1806502965764577 / 16000000000000000 : ℝ) = - (1806502965764577 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1806502965764577 / 1000000000000000 : ℚ)) - (U := (2956964566613846688103 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1806502965764577 / 1000000000000000 : ℝ) ≤ - (2956964566613846688103 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (107471747131119 / 1000000000000000 : ℝ)) (q := - (1806502965764577 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1806502965764577 / 16000000000000000 : ℚ)) + (r' := (1806502965764577 / 1000000000000000 : ℚ)) + (U := (-(10905979039386153311897 / 5000000000000000000000 : ℚ))) + (U' := (2956964566613846688103 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (107471747131119 / 1000000000000000 : ℚ)) + (q := (1806502965764577 / 16000000000000000 : ℚ)) + (U := (-(10905979039386153311897 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_7 : Uω (aρ 7) (bρ 7) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2355,25 +2138,21 @@ lemma U_227_7 : have hlg : Real.log (6376458507399157 / 80000000000000000 : ℝ) ≤ (-(25294137832826385335031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6376458507399157 / 80000000000000000 : ℝ) = - (6376458507399157 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6376458507399157 / 5000000000000000 : ℚ)) - (U := (2431749379173614664969 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6376458507399157 / 5000000000000000 : ℝ) ≤ - (2431749379173614664969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (317182385857629 / 5000000000000000 : ℝ)) (q := - (6376458507399157 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6376458507399157 / 80000000000000000 : ℚ)) + (r' := (6376458507399157 / 5000000000000000 : ℚ)) + (U := (-(25294137832826385335031 / 10000000000000000000000 : ℚ))) + (U' := (2431749379173614664969 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10769907509629 / 64000000000000 : ℚ)) + (s := (317182385857629 / 5000000000000000 : ℚ)) + (q := (6376458507399157 / 80000000000000000 : ℚ)) + (U := (-(25294137832826385335031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_227_8 : Uω (aρ 8) (bρ 8) (10769907509629 / 64000000000000 : ℝ) ≤ @@ -2510,25 +2289,21 @@ lemma U_228_1 : have hlg : Real.log (1627073349652751 / 10000000000000000 : ℝ) ≤ (-(9079010911160674591103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1627073349652751 / 10000000000000000 : ℝ) = - (1627073349652751 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1627073349652751 / 1250000000000000 : ℚ)) - (U := (1318196793339325408897 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1627073349652751 / 1250000000000000 : ℝ) ≤ - (1318196793339325408897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1626973988499877 / 10000000000000000 : ℝ)) (q := - (1627073349652751 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1627073349652751 / 10000000000000000 : ℚ)) + (r' := (1627073349652751 / 1250000000000000 : ℚ)) + (U := (-(9079010911160674591103 / 5000000000000000000000 : ℚ))) + (U' := (1318196793339325408897 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (108266875449 / 640000000000 : ℚ)) + (s := (1626973988499877 / 10000000000000000 : ℚ)) + (q := (1627073349652751 / 10000000000000000 : ℚ)) + (U := (-(9079010911160674591103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_2 : Uω (aρ 2) (bρ 2) (108266875449 / 640000000000 : ℝ) ≤ @@ -2536,25 +2311,21 @@ lemma U_228_2 : have hlg : Real.log (1602741753242869 / 10000000000000000 : ℝ) ≤ (-(18308693337218033383591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1602741753242869 / 10000000000000000 : ℝ) = - (1602741753242869 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1602741753242869 / 1250000000000000 : ℚ)) - (U := (2485722071781966616409 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1602741753242869 / 1250000000000000 : ℝ) ≤ - (2485722071781966616409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1602079808190113 / 10000000000000000 : ℝ)) (q := - (1602741753242869 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1602741753242869 / 10000000000000000 : ℚ)) + (r' := (1602741753242869 / 1250000000000000 : ℚ)) + (U := (-(18308693337218033383591 / 10000000000000000000000 : ℚ))) + (U' := (2485722071781966616409 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (108266875449 / 640000000000 : ℚ)) + (s := (1602079808190113 / 10000000000000000 : ℚ)) + (q := (1602741753242869 / 10000000000000000 : ℚ)) + (U := (-(18308693337218033383591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_3 : Uω (aρ 3) (bρ 3) (108266875449 / 640000000000 : ℝ) ≤ @@ -2562,25 +2333,21 @@ lemma U_228_3 : have hlg : Real.log (776813342623067 / 5000000000000000 : ℝ) ≤ (-(18619930974125314054273 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (776813342623067 / 5000000000000000 : ℝ) = - (776813342623067 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (776813342623067 / 625000000000000 : ℚ)) - (U := (2174484434874685945727 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (776813342623067 / 625000000000000 : ℝ) ≤ - (2174484434874685945727 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1551245778546643 / 10000000000000000 : ℝ)) (q := - (776813342623067 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (776813342623067 / 5000000000000000 : ℚ)) + (r' := (776813342623067 / 625000000000000 : ℚ)) + (U := (-(18619930974125314054273 / 10000000000000000000000 : ℚ))) + (U' := (2174484434874685945727 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (108266875449 / 640000000000 : ℚ)) + (s := (1551245778546643 / 10000000000000000 : ℚ)) + (q := (776813342623067 / 5000000000000000 : ℚ)) + (U := (-(18619930974125314054273 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_4 : Uω (aρ 4) (bρ 4) (108266875449 / 640000000000 : ℝ) ≤ @@ -2588,25 +2355,21 @@ lemma U_228_4 : have hlg : Real.log (1470559310136607 / 10000000000000000 : ℝ) ≤ (-(766776912281108700213 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1470559310136607 / 10000000000000000 : ℝ) = - (1470559310136607 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1470559310136607 / 1250000000000000 : ℚ)) - (U := (64999704078891299787 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1470559310136607 / 1250000000000000 : ℝ) ≤ - (64999704078891299787 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1463405209392589 / 10000000000000000 : ℝ)) (q := - (1470559310136607 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1470559310136607 / 10000000000000000 : ℚ)) + (r' := (1470559310136607 / 1250000000000000 : ℚ)) + (U := (-(766776912281108700213 / 400000000000000000000 : ℚ))) + (U' := (64999704078891299787 / 400000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (108266875449 / 640000000000 : ℚ)) + (s := (1463405209392589 / 10000000000000000 : ℚ)) + (q := (1470559310136607 / 10000000000000000 : ℚ)) + (U := (-(766776912281108700213 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_5 : Uω (aρ 5) (bρ 5) (108266875449 / 640000000000 : ℝ) ≤ @@ -2614,25 +2377,21 @@ lemma U_228_5 : have hlg : Real.log (2679292548779787 / 20000000000000000 : ℝ) ≤ (-(502544871858661952131 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2679292548779787 / 20000000000000000 : ℝ) = - (2679292548779787 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2679292548779787 / 2500000000000000 : ℚ)) - (U := (17315513366338047869 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2679292548779787 / 2500000000000000 : ℝ) ≤ - (17315513366338047869 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (659884528617081 / 5000000000000000 : ℝ)) (q := - (2679292548779787 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2679292548779787 / 20000000000000000 : ℚ)) + (r' := (2679292548779787 / 2500000000000000 : ℚ)) + (U := (-(502544871858661952131 / 250000000000000000000 : ℚ))) + (U' := (17315513366338047869 / 250000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (108266875449 / 640000000000 : ℚ)) + (s := (659884528617081 / 5000000000000000 : ℚ)) + (q := (2679292548779787 / 20000000000000000 : ℚ)) + (U := (-(502544871858661952131 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_6 : Uω (aρ 6) (bρ 6) (108266875449 / 640000000000 : ℝ) ≤ @@ -2640,25 +2399,21 @@ lemma U_228_6 : have hlg : Real.log (455352406510399 / 4000000000000000 : ℝ) ≤ (-(679055625029343955549 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (455352406510399 / 4000000000000000 : ℝ) = - (455352406510399 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (455352406510399 / 250000000000000 : ℚ)) - (U := (187378350345656044451 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (455352406510399 / 250000000000000 : ℝ) ≤ - (187378350345656044451 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (108447891614637 / 1000000000000000 : ℝ)) (q := - (455352406510399 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (455352406510399 / 4000000000000000 : ℚ)) + (r' := (455352406510399 / 250000000000000 : ℚ)) + (U := (-(679055625029343955549 / 312500000000000000000 : ℚ))) + (U' := (187378350345656044451 / 312500000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (108266875449 / 640000000000 : ℚ)) + (s := (108447891614637 / 1000000000000000 : ℚ)) + (q := (455352406510399 / 4000000000000000 : ℚ)) + (U := (-(679055625029343955549 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_7 : Uω (aρ 7) (bρ 7) (108266875449 / 640000000000 : ℝ) ≤ @@ -2666,25 +2421,21 @@ lemma U_228_7 : have hlg : Real.log (808165366760121 / 10000000000000000 : ℝ) ≤ (-(25155736715238488212441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (808165366760121 / 10000000000000000 : ℝ) = - (808165366760121 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (808165366760121 / 625000000000000 : ℚ)) - (U := (2570150496761511787559 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (808165366760121 / 625000000000000 : ℝ) ≤ - (2570150496761511787559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (647708997874617 / 10000000000000000 : ℝ)) (q := - (808165366760121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (808165366760121 / 10000000000000000 : ℚ)) + (r' := (808165366760121 / 625000000000000 : ℚ)) + (U := (-(25155736715238488212441 / 10000000000000000000000 : ℚ))) + (U' := (2570150496761511787559 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (108266875449 / 640000000000 : ℚ)) + (s := (647708997874617 / 10000000000000000 : ℚ)) + (q := (808165366760121 / 10000000000000000 : ℚ)) + (U := (-(25155736715238488212441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_228_8 : Uω (aρ 8) (bρ 8) (108266875449 / 640000000000 : ℝ) ≤ @@ -2819,25 +2570,21 @@ lemma U_229_1 : have hlg : Real.log (13087566152328083 / 80000000000000000 : ℝ) ≤ (-(3620728006182036485219 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13087566152328083 / 80000000000000000 : ℝ) = - (13087566152328083 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13087566152328083 / 10000000000000000 : ℚ)) - (U := (538155075617963514781 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13087566152328083 / 10000000000000000 : ℝ) ≤ - (538155075617963514781 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (817923473382651 / 5000000000000000 : ℝ)) (q := - (13087566152328083 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13087566152328083 / 80000000000000000 : ℚ)) + (r' := (13087566152328083 / 10000000000000000 : ℚ)) + (U := (-(3620728006182036485219 / 2000000000000000000000 : ℚ))) + (U' := (538155075617963514781 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (817923473382651 / 5000000000000000 : ℚ)) + (q := (13087566152328083 / 80000000000000000 : ℚ)) + (U := (-(3620728006182036485219 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_2 : Uω (aρ 2) (bρ 2) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2845,25 +2592,21 @@ lemma U_229_2 : have hlg : Real.log (12892938233831779 / 80000000000000000 : ℝ) ≤ (-(18253468961514672487477 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12892938233831779 / 80000000000000000 : ℝ) = - (12892938233831779 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12892938233831779 / 10000000000000000 : ℚ)) - (U := (2540946447485327512523 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12892938233831779 / 10000000000000000 : ℝ) ≤ - (2540946447485327512523 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (805479489825613 / 5000000000000000 : ℝ)) (q := - (12892938233831779 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12892938233831779 / 80000000000000000 : ℚ)) + (r' := (12892938233831779 / 10000000000000000 : ℚ)) + (U := (-(18253468961514672487477 / 10000000000000000000000 : ℚ))) + (U' := (2540946447485327512523 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (805479489825613 / 5000000000000000 : ℚ)) + (q := (12892938233831779 / 80000000000000000 : ℚ)) + (U := (-(18253468961514672487477 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_3 : Uω (aρ 3) (bρ 3) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2871,25 +2614,21 @@ lemma U_229_3 : have hlg : Real.log (12500096840639403 / 80000000000000000 : ℝ) ≤ (-(9281451211823238992419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12500096840639403 / 80000000000000000 : ℝ) = - (12500096840639403 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12500096840639403 / 10000000000000000 : ℚ)) - (U := (1115756492676761007581 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12500096840639403 / 10000000000000000 : ℝ) ≤ - (1115756492676761007581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (390036184425783 / 2500000000000000 : ℝ)) (q := - (12500096840639403 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12500096840639403 / 80000000000000000 : ℚ)) + (r' := (12500096840639403 / 10000000000000000 : ℚ)) + (U := (-(9281451211823238992419 / 5000000000000000000000 : ℚ))) + (U' := (1115756492676761007581 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (390036184425783 / 2500000000000000 : ℚ)) + (q := (12500096840639403 / 80000000000000000 : ℚ)) + (U := (-(9281451211823238992419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_4 : Uω (aρ 4) (bρ 4) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2897,25 +2636,21 @@ lemma U_229_4 : have hlg : Real.log (11835794397591891 / 80000000000000000 : ℝ) ≤ (-(19108982704437711202299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11835794397591891 / 80000000000000000 : ℝ) = - (11835794397591891 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11835794397591891 / 10000000000000000 : ℚ)) - (U := (1685432704562288797701 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11835794397591891 / 10000000000000000 : ℝ) ≤ - (1685432704562288797701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (736181654003127 / 5000000000000000 : ℝ)) (q := - (11835794397591891 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11835794397591891 / 80000000000000000 : ℚ)) + (r' := (11835794397591891 / 10000000000000000 : ℚ)) + (U := (-(19108982704437711202299 / 10000000000000000000000 : ℚ))) + (U' := (1685432704562288797701 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (736181654003127 / 5000000000000000 : ℚ)) + (q := (11835794397591891 / 80000000000000000 : ℚ)) + (U := (-(19108982704437711202299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_5 : Uω (aρ 5) (bρ 5) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2923,25 +2658,21 @@ lemma U_229_5 : have hlg : Real.log (10789206959810951 / 80000000000000000 : ℝ) ≤ (-(5008700887564128370101 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10789206959810951 / 80000000000000000 : ℝ) = - (10789206959810951 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10789206959810951 / 10000000000000000 : ℚ)) - (U := (189902964685871629899 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10789206959810951 / 10000000000000000 : ℝ) ≤ - (189902964685871629899 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1328906367896019 / 10000000000000000 : ℝ)) (q := - (10789206959810951 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10789206959810951 / 80000000000000000 : ℚ)) + (r' := (10789206959810951 / 10000000000000000 : ℚ)) + (U := (-(5008700887564128370101 / 2500000000000000000000 : ℚ))) + (U' := (189902964685871629899 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (1328906367896019 / 10000000000000000 : ℚ)) + (q := (10789206959810951 / 80000000000000000 : ℚ)) + (U := (-(5008700887564128370101 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_6 : Uω (aρ 6) (bρ 6) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2949,25 +2680,21 @@ lemma U_229_6 : have hlg : Real.log (9181520839215787 / 80000000000000000 : ℝ) ≤ (-(21648337739633651589547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9181520839215787 / 80000000000000000 : ℝ) = - (9181520839215787 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9181520839215787 / 5000000000000000 : ℚ)) - (U := (6077549472366348410453 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9181520839215787 / 5000000000000000 : ℝ) ≤ - (6077549472366348410453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (273556303221807 / 2500000000000000 : ℝ)) (q := - (9181520839215787 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9181520839215787 / 80000000000000000 : ℚ)) + (r' := (9181520839215787 / 5000000000000000 : ℚ)) + (U := (-(21648337739633651589547 / 10000000000000000000000 : ℚ))) + (U' := (6077549472366348410453 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (273556303221807 / 2500000000000000 : ℚ)) + (q := (9181520839215787 / 80000000000000000 : ℚ)) + (U := (-(21648337739633651589547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_7 : Uω (aρ 7) (bρ 7) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -2975,25 +2702,21 @@ lemma U_229_7 : have hlg : Real.log (1310717216291271 / 16000000000000000 : ℝ) ≤ (-(12510071202273143955923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1310717216291271 / 16000000000000000 : ℝ) = - (1310717216291271 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1310717216291271 / 1000000000000000 : ℚ)) - (U := (1352872403726856044077 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1310717216291271 / 1000000000000000 : ℝ) ≤ - (1352872403726856044077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (66090290420737 / 1000000000000000 : ℝ)) (q := - (1310717216291271 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1310717216291271 / 16000000000000000 : ℚ)) + (r' := (1310717216291271 / 1000000000000000 : ℚ)) + (U := (-(12510071202273143955923 / 5000000000000000000000 : ℚ))) + (U' := (1352872403726856044077 / 5000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10883467580171 / 64000000000000 : ℚ)) + (s := (66090290420737 / 1000000000000000 : ℚ)) + (q := (1310717216291271 / 16000000000000000 : ℚ)) + (U := (-(12510071202273143955923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_229_8 : Uω (aρ 8) (bρ 8) (10883467580171 / 64000000000000 : ℝ) ≤ @@ -3130,25 +2853,21 @@ lemma U_230_1 : have hlg : Real.log (1315854546092271 / 8000000000000000 : ℝ) ≤ (-(18049552413909734351791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1315854546092271 / 8000000000000000 : ℝ) = - (1315854546092271 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1315854546092271 / 1000000000000000 : ℚ)) - (U := (2744862995090265648209 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1315854546092271 / 1000000000000000 : ℝ) ≤ - (2744862995090265648209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (328943978680573 / 2000000000000000 : ℝ)) (q := - (1315854546092271 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1315854546092271 / 8000000000000000 : ℚ)) + (r' := (1315854546092271 / 1000000000000000 : ℚ)) + (U := (-(18049552413909734351791 / 10000000000000000000000 : ℚ))) + (U' := (2744862995090265648209 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (328943978680573 / 2000000000000000 : ℚ)) + (q := (1315854546092271 / 8000000000000000 : ℚ)) + (U := (-(18049552413909734351791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_2 : Uω (aρ 2) (bρ 2) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3156,25 +2875,21 @@ lemma U_230_2 : have hlg : Real.log (6481971061064049 / 40000000000000000 : ℝ) ≤ (-(727941925252781587649 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6481971061064049 / 40000000000000000 : ℝ) = - (6481971061064049 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6481971061064049 / 5000000000000000 : ℚ)) - (U := (103834691107218412351 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6481971061064049 / 5000000000000000 : ℝ) ≤ - (103834691107218412351 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404959517803553 / 2500000000000000 : ℝ)) (q := - (6481971061064049 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6481971061064049 / 40000000000000000 : ℚ)) + (r' := (6481971061064049 / 5000000000000000 : ℚ)) + (U := (-(727941925252781587649 / 400000000000000000000 : ℚ))) + (U' := (103834691107218412351 / 400000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (404959517803553 / 2500000000000000 : ℚ)) + (q := (6481971061064049 / 40000000000000000 : ℚ)) + (U := (-(727941925252781587649 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_3 : Uω (aρ 3) (bρ 3) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3182,25 +2897,21 @@ lemma U_230_3 : have hlg : Real.log (1257117897254897 / 8000000000000000 : ℝ) ≤ (-(9253099115622933870931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1257117897254897 / 8000000000000000 : ℝ) = - (1257117897254897 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1257117897254897 / 1000000000000000 : ℚ)) - (U := (1144108588877066129069 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1257117897254897 / 1000000000000000 : ℝ) ≤ - (1144108588877066129069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156904339016943 / 1000000000000000 : ℝ)) (q := - (1257117897254897 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1257117897254897 / 8000000000000000 : ℚ)) + (r' := (1257117897254897 / 1000000000000000 : ℚ)) + (U := (-(9253099115622933870931 / 5000000000000000000000 : ℚ))) + (U' := (1144108588877066129069 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (156904339016943 / 1000000000000000 : ℚ)) + (q := (1257117897254897 / 8000000000000000 : ℚ)) + (U := (-(9253099115622933870931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_4 : Uω (aρ 4) (bρ 4) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3208,25 +2919,21 @@ lemma U_230_4 : have hlg : Real.log (5953555081510063 / 40000000000000000 : ℝ) ≤ (-(952445459756741781521 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5953555081510063 / 40000000000000000 : ℝ) = - (5953555081510063 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5953555081510063 / 5000000000000000 : ℚ)) - (U := (87275310693258218479 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5953555081510063 / 5000000000000000 : ℝ) ≤ - (87275310693258218479 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1481320368852219 / 10000000000000000 : ℝ)) (q := - (5953555081510063 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5953555081510063 / 40000000000000000 : ℚ)) + (r' := (5953555081510063 / 5000000000000000 : ℚ)) + (U := (-(952445459756741781521 / 500000000000000000000 : ℚ))) + (U' := (87275310693258218479 / 500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (1481320368852219 / 10000000000000000 : ℚ)) + (q := (5953555081510063 / 40000000000000000 : ℚ)) + (U := (-(952445459756741781521 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_5 : Uω (aρ 5) (bρ 5) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3234,25 +2941,21 @@ lemma U_230_5 : have hlg : Real.log (5430614717210019 / 40000000000000000 : ℝ) ≤ (-(19968271182064297647983 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5430614717210019 / 40000000000000000 : ℝ) = - (5430614717210019 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5430614717210019 / 5000000000000000 : ℚ)) - (U := (826144226935702352017 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5430614717210019 / 5000000000000000 : ℝ) ≤ - (826144226935702352017 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1338040106037197 / 10000000000000000 : ℝ)) (q := - (5430614717210019 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5430614717210019 / 40000000000000000 : ℚ)) + (r' := (5430614717210019 / 5000000000000000 : ℚ)) + (U := (-(19968271182064297647983 / 10000000000000000000000 : ℚ))) + (U' := (826144226935702352017 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (1338040106037197 / 10000000000000000 : ℚ)) + (q := (5430614717210019 / 40000000000000000 : ℚ)) + (U := (-(19968271182064297647983 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_6 : Uω (aρ 6) (bρ 6) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3260,25 +2963,21 @@ lemma U_230_6 : have hlg : Real.log (4627967280334191 / 40000000000000000 : ℝ) ≤ (-(10783808568520747034887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4627967280334191 / 40000000000000000 : ℝ) = - (4627967280334191 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4627967280334191 / 2500000000000000 : ℚ)) - (U := (3079135037479252965113 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4627967280334191 / 2500000000000000 : ℝ) ≤ - (3079135037479252965113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1103956762739283 / 10000000000000000 : ℝ)) (q := - (4627967280334191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4627967280334191 / 40000000000000000 : ℚ)) + (r' := (4627967280334191 / 2500000000000000 : ℚ)) + (U := (-(10783808568520747034887 / 5000000000000000000000 : ℚ))) + (U' := (3079135037479252965113 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (1103956762739283 / 10000000000000000 : ℚ)) + (q := (4627967280334191 / 40000000000000000 : ℚ)) + (U := (-(10783808568520747034887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_7 : Uω (aρ 7) (bρ 7) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3286,25 +2985,21 @@ lemma U_230_7 : have hlg : Real.log (3320641631589271 / 40000000000000000 : ℝ) ≤ (-(6221803565729163471369 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3320641631589271 / 40000000000000000 : ℝ) = - (3320641631589271 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3320641631589271 / 2500000000000000 : ℚ)) - (U := (709668237270836528631 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3320641631589271 / 2500000000000000 : ℝ) ≤ - (709668237270836528631 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (673955319126823 / 10000000000000000 : ℝ)) (q := - (3320641631589271 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3320641631589271 / 40000000000000000 : ℚ)) + (r' := (3320641631589271 / 2500000000000000 : ℚ)) + (U := (-(6221803565729163471369 / 2500000000000000000000 : ℚ))) + (U' := (709668237270836528631 / 2500000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5470123807721 / 32000000000000 : ℚ)) + (s := (673955319126823 / 10000000000000000 : ℚ)) + (q := (3320641631589271 / 40000000000000000 : ℚ)) + (U := (-(6221803565729163471369 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_230_8 : Uω (aρ 8) (bρ 8) (5470123807721 / 32000000000000 : ℝ) ≤ @@ -3441,25 +3136,21 @@ lemma U_231_1 : have hlg : Real.log (2645904944750921 / 16000000000000000 : ℝ) ≤ (-(17995755805428837382471 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2645904944750921 / 16000000000000000 : ℝ) = - (2645904944750921 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2645904944750921 / 2000000000000000 : ℚ)) - (U := (2798659603571162617529 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2645904944750921 / 2000000000000000 : ℝ) ≤ - (2798659603571162617529 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (330718565719949 / 2000000000000000 : ℝ)) (q := - (2645904944750921 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2645904944750921 / 16000000000000000 : ℚ)) + (r' := (2645904944750921 / 2000000000000000 : ℚ)) + (U := (-(17995755805428837382471 / 10000000000000000000000 : ℚ))) + (U' := (2798659603571162617529 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (330718565719949 / 2000000000000000 : ℚ)) + (q := (2645904944750921 / 16000000000000000 : ℚ)) + (U := (-(17995755805428837382471 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_2 : Uω (aρ 2) (bρ 2) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3467,25 +3158,21 @@ lemma U_231_2 : have hlg : Real.log (13034945696058761 / 80000000000000000 : ℝ) ≤ (-(4535981881318316691607 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13034945696058761 / 80000000000000000 : ℝ) = - (13034945696058761 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13034945696058761 / 10000000000000000 : ℚ)) - (U := (662621970931683308393 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13034945696058761 / 10000000000000000 : ℝ) ≤ - (662621970931683308393 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203589635523223 / 1250000000000000 : ℝ)) (q := - (13034945696058761 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13034945696058761 / 80000000000000000 : ℚ)) + (r' := (13034945696058761 / 10000000000000000 : ℚ)) + (U := (-(4535981881318316691607 / 2500000000000000000000 : ℚ))) + (U' := (662621970931683308393 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (203589635523223 / 1250000000000000 : ℚ)) + (q := (13034945696058761 / 80000000000000000 : ℚ)) + (U := (-(4535981881318316691607 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_3 : Uω (aρ 3) (bρ 3) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3493,25 +3180,21 @@ lemma U_231_3 : have hlg : Real.log (12642259898452369 / 80000000000000000 : ℝ) ≤ (-(2306226839652172024137 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12642259898452369 / 80000000000000000 : ℝ) = - (12642259898452369 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12642259898452369 / 10000000000000000 : ℚ)) - (U := (293075086472827975863 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12642259898452369 / 10000000000000000 : ℝ) ≤ - (293075086472827975863 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (788970870567093 / 5000000000000000 : ℝ)) (q := - (12642259898452369 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12642259898452369 / 80000000000000000 : ℚ)) + (r' := (12642259898452369 / 10000000000000000 : ℚ)) + (U := (-(2306226839652172024137 / 1250000000000000000000 : ℚ))) + (U' := (293075086472827975863 / 1250000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (788970870567093 / 5000000000000000 : ℚ)) + (q := (12642259898452369 / 80000000000000000 : ℚ)) + (U := (-(2306226839652172024137 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_4 : Uω (aρ 4) (bρ 4) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3519,25 +3202,21 @@ lemma U_231_4 : have hlg : Real.log (11978421852225553 / 80000000000000000 : ℝ) ≤ (-(18989197817517969399161 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11978421852225553 / 80000000000000000 : ℝ) = - (11978421852225553 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11978421852225553 / 10000000000000000 : ℚ)) - (U := (1805217591482030600839 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11978421852225553 / 10000000000000000 : ℝ) ≤ - (1805217591482030600839 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (745138205321241 / 5000000000000000 : ℝ)) (q := - (11978421852225553 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11978421852225553 / 80000000000000000 : ℚ)) + (r' := (11978421852225553 / 10000000000000000 : ℚ)) + (U := (-(18989197817517969399161 / 10000000000000000000000 : ℚ))) + (U' := (1805217591482030600839 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (745138205321241 / 5000000000000000 : ℚ)) + (q := (11978421852225553 / 80000000000000000 : ℚ)) + (U := (-(18989197817517969399161 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_5 : Uω (aρ 5) (bρ 5) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3545,25 +3224,21 @@ lemma U_231_5 : have hlg : Real.log (10933237909604261 / 80000000000000000 : ℝ) ≤ (-(19902191349902427008359 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10933237909604261 / 80000000000000000 : ℝ) = - (10933237909604261 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10933237909604261 / 10000000000000000 : ℚ)) - (U := (892224059097572991641 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10933237909604261 / 10000000000000000 : ℝ) ≤ - (892224059097572991641 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1347170344322159 / 10000000000000000 : ℝ)) (q := - (10933237909604261 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10933237909604261 / 80000000000000000 : ℚ)) + (r' := (10933237909604261 / 10000000000000000 : ℚ)) + (U := (-(19902191349902427008359 / 10000000000000000000000 : ℚ))) + (U' := (892224059097572991641 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (1347170344322159 / 10000000000000000 : ℚ)) + (q := (10933237909604261 / 80000000000000000 : ℚ)) + (U := (-(19902191349902427008359 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_6 : Uω (aρ 6) (bρ 6) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3571,25 +3246,21 @@ lemma U_231_6 : have hlg : Real.log (9330290840908217 / 80000000000000000 : ℝ) ≤ (-(10743802233008661327371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9330290840908217 / 80000000000000000 : ℝ) = - (9330290840908217 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9330290840908217 / 5000000000000000 : ℚ)) - (U := (3119141372991338672629 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9330290840908217 / 5000000000000000 : ℝ) ≤ - (3119141372991338672629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (278418488072037 / 2500000000000000 : ℝ)) (q := - (9330290840908217 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9330290840908217 / 80000000000000000 : ℚ)) + (r' := (9330290840908217 / 5000000000000000 : ℚ)) + (U := (-(10743802233008661327371 / 5000000000000000000000 : ℚ))) + (U' := (3119141372991338672629 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (278418488072037 / 2500000000000000 : ℚ)) + (q := (9330290840908217 / 80000000000000000 : ℚ)) + (U := (-(10743802233008661327371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_7 : Uω (aρ 7) (bρ 7) (10997027650713 / 64000000000000 : ℝ) ≤ @@ -3597,25 +3268,21 @@ lemma U_231_7 : have hlg : Real.log (1345689348787241 / 16000000000000000 : ℝ) ≤ (-(12378411562319641158947 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1345689348787241 / 16000000000000000 : ℝ) = - (1345689348787241 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1345689348787241 / 1000000000000000 : ℚ)) - (U := (1484532043680358841053 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1345689348787241 / 1000000000000000 : ℝ) ≤ - (1484532043680358841053 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (137374861761029 / 2000000000000000 : ℝ)) (q := - (1345689348787241 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1345689348787241 / 16000000000000000 : ℚ)) + (r' := (1345689348787241 / 1000000000000000 : ℚ)) + (U := (-(12378411562319641158947 / 5000000000000000000000 : ℚ))) + (U' := (1484532043680358841053 / 5000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10997027650713 / 64000000000000 : ℚ)) + (s := (137374861761029 / 2000000000000000 : ℚ)) + (q := (1345689348787241 / 16000000000000000 : ℚ)) + (U := (-(12378411562319641158947 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_231_8 : Uω (aρ 8) (bρ 8) (10997027650713 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U19.lean b/LeanPool/Zeta5Irrational/Table/U19.lean index f37b17f479..ae146365a7 100644 --- a/LeanPool/Zeta5Irrational/Table/U19.lean +++ b/LeanPool/Zeta5Irrational/Table/U19.lean @@ -24,25 +24,21 @@ lemma U_232_1 : have hlg : Real.log (415640748173641 / 2500000000000000 : ℝ) ≤ (-(1121390443150977258413 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (415640748173641 / 2500000000000000 : ℝ) = - (415640748173641 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (415640748173641 / 312500000000000 : ℚ)) - (U := (178260519911522741587 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (415640748173641 / 312500000000000 : ℝ) ≤ - (178260519911522741587 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207808219067391 / 1250000000000000 : ℝ)) (q := - (415640748173641 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (415640748173641 / 2500000000000000 : ℚ)) + (r' := (415640748173641 / 312500000000000 : ℚ)) + (U := (-(1121390443150977258413 / 625000000000000000000 : ℚ))) + (U' := (178260519911522741587 / 625000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (207808219067391 / 1250000000000000 : ℚ)) + (q := (415640748173641 / 2500000000000000 : ℚ)) + (U := (-(1121390443150977258413 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_2 : Uω (aρ 2) (bρ 2) (345431490187 / 2000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_232_2 : have hlg : Real.log (3276487240184307 / 20000000000000000 : ℝ) ≤ (-(113060024226724001509 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3276487240184307 / 20000000000000000 : ℝ) = - (3276487240184307 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3276487240184307 / 2500000000000000 : ℚ)) - (U := (16905072079525998491 / 62500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3276487240184307 / 2500000000000000 : ℝ) ≤ - (16905072079525998491 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1637596019844307 / 10000000000000000 : ℝ)) (q := - (3276487240184307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3276487240184307 / 20000000000000000 : ℚ)) + (r' := (3276487240184307 / 2500000000000000 : ℚ)) + (U := (-(113060024226724001509 / 62500000000000000000 : ℚ))) + (U' := (16905072079525998491 / 62500000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (1637596019844307 / 10000000000000000 : ℚ)) + (q := (3276487240184307 / 20000000000000000 : ℚ)) + (U := (-(113060024226724001509 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_3 : Uω (aρ 3) (bρ 3) (345431490187 / 2000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_232_3 : have hlg : Real.log (3178334909659493 / 20000000000000000 : ℝ) ≤ (-(3678749652860036091943 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3178334909659493 / 20000000000000000 : ℝ) = - (3178334909659493 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3178334909659493 / 2500000000000000 : ℚ)) - (U := (480133428939963908057 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3178334909659493 / 2500000000000000 : ℝ) ≤ - (480133428939963908057 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1586839795669493 / 10000000000000000 : ℝ)) (q := - (3178334909659493 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3178334909659493 / 20000000000000000 : ℚ)) + (r' := (3178334909659493 / 2500000000000000 : ℚ)) + (U := (-(3678749652860036091943 / 2000000000000000000000 : ℚ))) + (U' := (480133428939963908057 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (1586839795669493 / 10000000000000000 : ℚ)) + (q := (3178334909659493 / 20000000000000000 : ℚ)) + (U := (-(3678749652860036091943 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_4 : Uω (aρ 4) (bρ 4) (345431490187 / 2000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_232_4 : have hlg : Real.log (3012432384564809 / 20000000000000000 : ℝ) ≤ (-(18929844191670132660891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3012432384564809 / 20000000000000000 : ℝ) = - (3012432384564809 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3012432384564809 / 2500000000000000 : ℚ)) - (U := (1864571217329867339109 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3012432384564809 / 2500000000000000 : ℝ) ≤ - (1864571217329867339109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1499231451639809 / 10000000000000000 : ℝ)) (q := - (3012432384564809 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3012432384564809 / 20000000000000000 : ℚ)) + (r' := (3012432384564809 / 2500000000000000 : ℚ)) + (U := (-(18929844191670132660891 / 10000000000000000000000 : ℚ))) + (U' := (1864571217329867339109 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (1499231451639809 / 10000000000000000 : ℚ)) + (q := (3012432384564809 / 20000000000000000 : ℚ)) + (U := (-(18929844191670132660891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_5 : Uω (aρ 5) (bρ 5) (345431490187 / 2000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_232_5 : have hlg : Real.log (2751308167021261 / 20000000000000000 : ℝ) ≤ (-(4959139442762577320171 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2751308167021261 / 20000000000000000 : ℝ) = - (2751308167021261 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2751308167021261 / 2500000000000000 : ℚ)) - (U := (239464409487422679829 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2751308167021261 / 2500000000000000 : ℝ) ≤ - (239464409487422679829 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1356297153431261 / 10000000000000000 : ℝ)) (q := - (2751308167021261 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2751308167021261 / 20000000000000000 : ℚ)) + (r' := (2751308167021261 / 2500000000000000 : ℚ)) + (U := (-(4959139442762577320171 / 2500000000000000000000 : ℚ))) + (U' := (239464409487422679829 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (1356297153431261 / 10000000000000000 : ℚ)) + (q := (2751308167021261 / 20000000000000000 : ℚ)) + (U := (-(4959139442762577320171 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_6 : Uω (aρ 6) (bρ 6) (345431490187 / 2000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_232_6 : have hlg : Real.log (587786948158219 / 5000000000000000 : ℝ) ≤ (-(5352071603001420085127 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (587786948158219 / 5000000000000000 : ℝ) = - (587786948158219 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (587786948158219 / 312500000000000 : ℚ)) - (U := (1579400199998579914873 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (587786948158219 / 312500000000000 : ℝ) ≤ - (1579400199998579914873 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (280844288545719 / 2500000000000000 : ℝ)) (q := - (587786948158219 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (587786948158219 / 5000000000000000 : ℚ)) + (r' := (587786948158219 / 312500000000000 : ℚ)) + (U := (-(5352071603001420085127 / 2500000000000000000000 : ℚ))) + (U' := (1579400199998579914873 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (280844288545719 / 2500000000000000 : ℚ)) + (q := (587786948158219 / 5000000000000000 : ℚ)) + (U := (-(5352071603001420085127 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_7 : Uω (aρ 7) (bρ 7) (345431490187 / 2000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_232_7 : have hlg : Real.log (212972065231627 / 2500000000000000 : ℝ) ≤ (-(1539303126159486415141 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (212972065231627 / 2500000000000000 : ℝ) = - (212972065231627 / 156250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (212972065231627 / 156250000000000 : ℚ)) - (U := (193564824590513584859 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (212972065231627 / 156250000000000 : ℝ) ≤ - (193564824590513584859 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (87458408020377 / 1250000000000000 : ℝ)) (q := - (212972065231627 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (212972065231627 / 2500000000000000 : ℚ)) + (r' := (212972065231627 / 156250000000000 : ℚ)) + (U := (-(1539303126159486415141 / 625000000000000000000 : ℚ))) + (U' := (193564824590513584859 / 625000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (345431490187 / 2000000000000 : ℚ)) + (s := (87458408020377 / 1250000000000000 : ℚ)) + (q := (212972065231627 / 2500000000000000 : ℚ)) + (U := (-(1539303126159486415141 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_232_8 : Uω (aρ 8) (bρ 8) (345431490187 / 2000000000000 : ℝ) ≤ @@ -334,25 +306,21 @@ lemma U_233_1 : have hlg : Real.log (6721231122461949 / 40000000000000000 : ℝ) ≤ (-(17836081128313023247777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6721231122461949 / 40000000000000000 : ℝ) = - (6721231122461949 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6721231122461949 / 5000000000000000 : ℚ)) - (U := (2958334280686976752223 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6721231122461949 / 5000000000000000 : ℝ) ≤ - (2958334280686976752223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1680211567358787 / 10000000000000000 : ℝ)) (q := - (6721231122461949 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6721231122461949 / 40000000000000000 : ℚ)) + (r' := (6721231122461949 / 5000000000000000 : ℚ)) + (U := (-(17836081128313023247777 / 10000000000000000000000 : ℚ))) + (U' := (2958334280686976752223 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (1680211567358787 / 10000000000000000 : ℚ)) + (q := (6721231122461949 / 40000000000000000 : ℚ)) + (U := (-(17836081128313023247777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_2 : Uω (aρ 2) (bρ 2) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -360,25 +328,21 @@ lemma U_233_2 : have hlg : Real.log (6623977291121299 / 40000000000000000 : ℝ) ≤ (-(17981834645297691005227 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6623977291121299 / 40000000000000000 : ℝ) = - (6623977291121299 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6623977291121299 / 5000000000000000 : ℚ)) - (U := (2812580763702308994773 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6623977291121299 / 5000000000000000 : ℝ) ≤ - (2812580763702308994773 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (827676832099231 / 5000000000000000 : ℝ)) (q := - (6623977291121299 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6623977291121299 / 40000000000000000 : ℚ)) + (r' := (6623977291121299 / 5000000000000000 : ℚ)) + (U := (-(17981834645297691005227 / 10000000000000000000000 : ℚ))) + (U' := (2812580763702308994773 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (827676832099231 / 5000000000000000 : ℚ)) + (q := (6623977291121299 / 40000000000000000 : ℚ)) + (U := (-(17981834645297691005227 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_3 : Uω (aρ 3) (bρ 3) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -386,25 +350,21 @@ lemma U_233_3 : have hlg : Real.log (6427747820377973 / 40000000000000000 : ℝ) ≤ (-(3656510475313698243173 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6427747820377973 / 40000000000000000 : ℝ) = - (6427747820377973 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6427747820377973 / 5000000000000000 : ℚ)) - (U := (502372606486301756827 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6427747820377973 / 5000000000000000 : ℝ) ≤ - (502372606486301756827 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1604635035176799 / 10000000000000000 : ℝ)) (q := - (6427747820377973 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6427747820377973 / 40000000000000000 : ℚ)) + (r' := (6427747820377973 / 5000000000000000 : ℚ)) + (U := (-(3656510475313698243173 / 2000000000000000000000 : ℚ))) + (U' := (502372606486301756827 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (1604635035176799 / 10000000000000000 : ℚ)) + (q := (6427747820377973 / 40000000000000000 : ℚ)) + (U := (-(3656510475313698243173 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_4 : Uω (aρ 4) (bρ 4) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -412,25 +372,21 @@ lemma U_233_4 : have hlg : Real.log (6096166592176123 / 40000000000000000 : ℝ) ≤ (-(2351524134012850285883 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6096166592176123 / 40000000000000000 : ℝ) = - (6096166592176123 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6096166592176123 / 5000000000000000 : ℚ)) - (U := (247777792112149714117 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6096166592176123 / 5000000000000000 : ℝ) ≤ - (247777792112149714117 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (758569301070437 / 5000000000000000 : ℝ)) (q := - (6096166592176123 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6096166592176123 / 40000000000000000 : ℚ)) + (r' := (6096166592176123 / 5000000000000000 : ℚ)) + (U := (-(2351524134012850285883 / 1250000000000000000000 : ℚ))) + (U' := (247777792112149714117 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (758569301070437 / 5000000000000000 : ℚ)) + (q := (6096166592176123 / 40000000000000000 : ℚ)) + (U := (-(2351524134012850285883 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_5 : Uω (aρ 5) (bρ 5) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -438,25 +394,21 @@ lemma U_233_5 : have hlg : Real.log (5574591063881861 / 40000000000000000 : ℝ) ≤ (-(9853302452241801719929 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5574591063881861 / 40000000000000000 : ℝ) = - (5574591063881861 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5574591063881861 / 5000000000000000 : ℚ)) - (U := (543905252258198280071 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5574591063881861 / 5000000000000000 : ℝ) ≤ - (543905252258198280071 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1374540757328743 / 10000000000000000 : ℝ)) (q := - (5574591063881861 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5574591063881861 / 40000000000000000 : ℚ)) + (r' := (5574591063881861 / 5000000000000000 : ℚ)) + (U := (-(9853302452241801719929 / 5000000000000000000000 : ℚ))) + (U' := (543905252258198280071 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (1374540757328743 / 10000000000000000 : ℚ)) + (q := (5574591063881861 / 40000000000000000 : ℚ)) + (U := (-(9853302452241801719929 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_6 : Uω (aρ 6) (bρ 6) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -464,25 +416,21 @@ lemma U_233_6 : have hlg : Real.log (4776514838449023 / 40000000000000000 : ℝ) ≤ (-(425033657159668721931 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4776514838449023 / 40000000000000000 : ℝ) = - (4776514838449023 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4776514838449023 / 2500000000000000 : ℚ)) - (U := (129484087080331278069 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4776514838449023 / 2500000000000000 : ℝ) ≤ - (129484087080331278069 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (285685754938081 / 2500000000000000 : ℝ)) (q := - (4776514838449023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4776514838449023 / 40000000000000000 : ℚ)) + (r' := (4776514838449023 / 2500000000000000 : ℚ)) + (U := (-(425033657159668721931 / 200000000000000000000 : ℚ))) + (U' := (129484087080331278069 / 200000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (285685754938081 / 2500000000000000 : ℚ)) + (q := (4776514838449023 / 40000000000000000 : ℚ)) + (U := (-(425033657159668721931 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_7 : Uω (aρ 7) (bρ 7) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -490,25 +438,21 @@ lemma U_233_7 : have hlg : Real.log (139740377295619 / 1600000000000000 : ℝ) ≤ (-(24379726540844704730177 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (139740377295619 / 1600000000000000 : ℝ) = - (139740377295619 / 100000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (139740377295619 / 100000000000000 : ℚ)) - (U := (3346160671155295269823 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (139740377295619 / 100000000000000 : ℝ) ≤ - (3346160671155295269823 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14498033949661 / 200000000000000 : ℝ)) (q := - (139740377295619 / 1600000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (139740377295619 / 1600000000000000 : ℚ)) + (r' := (139740377295619 / 100000000000000 : ℚ)) + (U := (-(24379726540844704730177 / 10000000000000000000000 : ℚ))) + (U' := (3346160671155295269823 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5583683878263 / 32000000000000 : ℚ)) + (s := (14498033949661 / 200000000000000 : ℚ)) + (q := (139740377295619 / 1600000000000000 : ℚ)) + (U := (-(24379726540844704730177 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_233_8 : Uω (aρ 8) (bρ 8) (5583683878263 / 32000000000000 : ℝ) ≤ @@ -646,25 +590,21 @@ lemma U_234_1 : have hlg : Real.log (212256568384107 / 1250000000000000 : ℝ) ≤ (-(4432757645883601178647 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (212256568384107 / 1250000000000000 : ℝ) = - (212256568384107 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (212256568384107 / 156250000000000 : ℚ)) - (U := (765846206366398821353 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (212256568384107 / 156250000000000 : ℝ) ≤ - (765846206366398821353 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1697957339251337 / 10000000000000000 : ℝ)) (q := - (212256568384107 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (212256568384107 / 1250000000000000 : ℚ)) + (r' := (212256568384107 / 156250000000000 : ℚ)) + (U := (-(4432757645883601178647 / 2500000000000000000000 : ℚ))) + (U' := (765846206366398821353 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (1697957339251337 / 10000000000000000 : ℚ)) + (q := (212256568384107 / 1250000000000000 : ℚ)) + (U := (-(4432757645883601178647 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_2 : Uω (aρ 2) (bρ 2) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -672,25 +612,21 @@ lemma U_234_2 : have hlg : Real.log (836872439087349 / 5000000000000000 : ℝ) ≤ (-(17875215342854461799939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (836872439087349 / 5000000000000000 : ℝ) = - (836872439087349 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (836872439087349 / 625000000000000 : ℚ)) - (U := (2919200066145538200061 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (836872439087349 / 625000000000000 : ℝ) ≤ - (2919200066145538200061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1673111013965021 / 10000000000000000 : ℝ)) (q := - (836872439087349 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (836872439087349 / 5000000000000000 : ℚ)) + (r' := (836872439087349 / 625000000000000 : ℚ)) + (U := (-(17875215342854461799939 / 10000000000000000000000 : ℚ))) + (U' := (2919200066145538200061 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (1673111013965021 / 10000000000000000 : ℚ)) + (q := (836872439087349 / 5000000000000000 : ℚ)) + (U := (-(17875215342854461799939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_3 : Uω (aρ 3) (bρ 3) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -698,25 +634,21 @@ lemma U_234_3 : have hlg : Real.log (3249411783092489 / 20000000000000000 : ℝ) ≤ (-(9086291413154191049523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3249411783092489 / 20000000000000000 : ℝ) = - (3249411783092489 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3249411783092489 / 2500000000000000 : ℚ)) - (U := (1310916291345808950477 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3249411783092489 / 2500000000000000 : ℝ) ≤ - (1310916291345808950477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (811214573529057 / 5000000000000000 : ℝ)) (q := - (3249411783092489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3249411783092489 / 20000000000000000 : ℚ)) + (r' := (3249411783092489 / 2500000000000000 : ℚ)) + (U := (-(9086291413154191049523 / 5000000000000000000000 : ℚ))) + (U' := (1310916291345808950477 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (811214573529057 / 5000000000000000 : ℚ)) + (q := (3249411783092489 / 20000000000000000 : ℚ)) + (U := (-(9086291413154191049523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_4 : Uω (aρ 4) (bρ 4) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -724,25 +656,21 @@ lemma U_234_4 : have hlg : Real.log (3083730412941973 / 20000000000000000 : ℝ) ≤ (-(4673980589084799832807 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3083730412941973 / 20000000000000000 : ℝ) = - (3083730412941973 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3083730412941973 / 2500000000000000 : ℚ)) - (U := (524623263165200167193 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3083730412941973 / 2500000000000000 : ℝ) ≤ - (524623263165200167193 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (767520978986299 / 5000000000000000 : ℝ)) (q := - (3083730412941973 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3083730412941973 / 20000000000000000 : ℚ)) + (r' := (3083730412941973 / 2500000000000000 : ℚ)) + (U := (-(4673980589084799832807 / 2500000000000000000000 : ℚ))) + (U' := (524623263165200167193 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (767520978986299 / 5000000000000000 : ℚ)) + (q := (3083730412941973 / 20000000000000000 : ℚ)) + (U := (-(4673980589084799832807 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_5 : Uω (aρ 5) (bρ 5) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -750,25 +678,21 @@ lemma U_234_5 : have hlg : Real.log (352908747705531 / 2500000000000000 : ℝ) ≤ (-(19578364916448394077517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (352908747705531 / 2500000000000000 : ℝ) = - (352908747705531 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (352908747705531 / 312500000000000 : ℚ)) - (U := (1216050492551605922483 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (352908747705531 / 312500000000000 : ℝ) ≤ - (1216050492551605922483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1392771446009873 / 10000000000000000 : ℝ)) (q := - (352908747705531 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (352908747705531 / 2500000000000000 : ℚ)) + (r' := (352908747705531 / 312500000000000 : ℚ)) + (U := (-(19578364916448394077517 / 10000000000000000000000 : ℚ))) + (U' := (1216050492551605922483 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (1392771446009873 / 10000000000000000 : ℚ)) + (q := (352908747705531 / 2500000000000000 : ℚ)) + (U := (-(19578364916448394077517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_6 : Uω (aρ 6) (bρ 6) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -776,25 +700,21 @@ lemma U_234_6 : have hlg : Real.log (2425315245992213 / 20000000000000000 : ℝ) ≤ (-(21097707582265118210857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2425315245992213 / 20000000000000000 : ℝ) = - (2425315245992213 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2425315245992213 / 1250000000000000 : ℚ)) - (U := (6628179629734881789143 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2425315245992213 / 1250000000000000 : ℝ) ≤ - (6628179629734881789143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (581028542748919 / 5000000000000000 : ℝ)) (q := - (2425315245992213 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2425315245992213 / 20000000000000000 : ℚ)) + (r' := (2425315245992213 / 1250000000000000 : ℚ)) + (U := (-(21097707582265118210857 / 10000000000000000000000 : ℚ))) + (U' := (6628179629734881789143 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (581028542748919 / 5000000000000000 : ℚ)) + (q := (2425315245992213 / 20000000000000000 : ℚ)) + (U := (-(21097707582265118210857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_7 : Uω (aρ 7) (bρ 7) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -802,25 +722,21 @@ lemma U_234_7 : have hlg : Real.log (1789303618169693 / 20000000000000000 : ℝ) ≤ (-(24139057684859532006813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1789303618169693 / 20000000000000000 : ℝ) = - (1789303618169693 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1789303618169693 / 1250000000000000 : ℚ)) - (U := (3586829527140467993187 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1789303618169693 / 1250000000000000 : ℝ) ≤ - (3586829527140467993187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (374853419217659 / 5000000000000000 : ℝ)) (q := - (1789303618169693 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1789303618169693 / 20000000000000000 : ℚ)) + (r' := (1789303618169693 / 1250000000000000 : ℚ)) + (U := (-(24139057684859532006813 / 10000000000000000000000 : ℚ))) + (U' := (3586829527140467993187 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2820231956767 / 16000000000000 : ℚ)) + (s := (374853419217659 / 5000000000000000 : ℚ)) + (q := (1789303618169693 / 20000000000000000 : ℚ)) + (U := (-(24139057684859532006813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_234_8 : Uω (aρ 8) (bρ 8) (2820231956767 / 16000000000000 : ℝ) ≤ @@ -957,25 +873,21 @@ lemma U_235_1 : have hlg : Real.log (6863189170930689 / 40000000000000000 : ℝ) ≤ (-(17627072259042377358077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6863189170930689 / 40000000000000000 : ℝ) = - (6863189170930689 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6863189170930689 / 5000000000000000 : ℚ)) - (U := (3167343149957622641923 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6863189170930689 / 5000000000000000 : ℝ) ≤ - (3167343149957622641923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (857851534774391 / 5000000000000000 : ℝ)) (q := - (6863189170930689 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6863189170930689 / 40000000000000000 : ℚ)) + (r' := (6863189170930689 / 5000000000000000 : ℚ)) + (U := (-(17627072259042377358077 / 10000000000000000000000 : ℚ))) + (U' := (3167343149957622641923 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (857851534774391 / 5000000000000000 : ℚ)) + (q := (6863189170930689 / 40000000000000000 : ℚ)) + (U := (-(17627072259042377358077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_2 : Uω (aρ 2) (bρ 2) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -983,25 +895,21 @@ lemma U_235_2 : have hlg : Real.log (6765981163663493 / 40000000000000000 : ℝ) ≤ (-(17769721669487918798127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6765981163663493 / 40000000000000000 : ℝ) = - (6765981163663493 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6765981163663493 / 5000000000000000 : ℚ)) - (U := (3024693739512081201873 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6765981163663493 / 5000000000000000 : ℝ) ≤ - (3024693739512081201873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (52839627450787 / 312500000000000 : ℝ)) (q := - (6765981163663493 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6765981163663493 / 40000000000000000 : ℚ)) + (r' := (6765981163663493 / 5000000000000000 : ℚ)) + (U := (-(17769721669487918798127 / 10000000000000000000000 : ℚ))) + (U' := (3024693739512081201873 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (52839627450787 / 312500000000000 : ℚ)) + (q := (6765981163663493 / 40000000000000000 : ℚ)) + (U := (-(17769721669487918798127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_3 : Uω (aρ 3) (bρ 3) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1009,25 +917,21 @@ lemma U_235_3 : have hlg : Real.log (6569897130138973 / 40000000000000000 : ℝ) ≤ (-(18063812784732552797297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6569897130138973 / 40000000000000000 : ℝ) = - (6569897130138973 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6569897130138973 / 5000000000000000 : ℚ)) - (U := (2730602624267447202703 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6569897130138973 / 5000000000000000 : ℝ) ≤ - (2730602624267447202703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410055542003231 / 2500000000000000 : ℝ)) (q := - (6569897130138973 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6569897130138973 / 40000000000000000 : ℚ)) + (r' := (6569897130138973 / 5000000000000000 : ℚ)) + (U := (-(18063812784732552797297 / 10000000000000000000000 : ℚ))) + (U' := (2730602624267447202703 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (410055542003231 / 2500000000000000 : ℚ)) + (q := (6569897130138973 / 40000000000000000 : ℚ)) + (U := (-(18063812784732552797297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_4 : Uω (aρ 4) (bρ 4) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1035,25 +939,21 @@ lemma U_235_4 : have hlg : Real.log (6238747732738101 / 40000000000000000 : ℝ) ≤ (-(18580999749485371987611 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6238747732738101 / 40000000000000000 : ℝ) = - (6238747732738101 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6238747732738101 / 5000000000000000 : ℚ)) - (U := (2213415659514628012389 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6238747732738101 / 5000000000000000 : ℝ) ≤ - (2213415659514628012389 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (97058853148593 / 625000000000000 : ℝ)) (q := - (6238747732738101 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6238747732738101 / 40000000000000000 : ℚ)) + (r' := (6238747732738101 / 5000000000000000 : ℚ)) + (U := (-(18580999749485371987611 / 10000000000000000000000 : ℚ))) + (U' := (2213415659514628012389 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (97058853148593 / 625000000000000 : ℚ)) + (q := (6238747732738101 / 40000000000000000 : ℚ)) + (U := (-(18580999749485371987611 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_5 : Uω (aρ 5) (bρ 5) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1061,25 +961,21 @@ lemma U_235_5 : have hlg : Real.log (5718464033488703 / 40000000000000000 : ℝ) ≤ (-(19451792096157150090147 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5718464033488703 / 40000000000000000 : ℝ) = - (5718464033488703 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5718464033488703 / 5000000000000000 : ℚ)) - (U := (1342623312842849909853 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5718464033488703 / 5000000000000000 : ℝ) ≤ - (1342623312842849909853 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1410989720087789 / 10000000000000000 : ℝ)) (q := - (5718464033488703 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5718464033488703 / 40000000000000000 : ℚ)) + (r' := (5718464033488703 / 5000000000000000 : ℚ)) + (U := (-(19451792096157150090147 / 10000000000000000000000 : ℚ))) + (U' := (1342623312842849909853 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (1410989720087789 / 10000000000000000 : ℚ)) + (q := (5718464033488703 / 40000000000000000 : ℚ)) + (U := (-(19451792096157150090147 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_6 : Uω (aρ 6) (bρ 6) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1087,25 +983,21 @@ lemma U_235_6 : have hlg : Real.log (4924647627296189 / 40000000000000000 : ℝ) ≤ (-(20946267287668847085137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4924647627296189 / 40000000000000000 : ℝ) = - (4924647627296189 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4924647627296189 / 2500000000000000 : ℚ)) - (U := (6779619924331152914863 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4924647627296189 / 2500000000000000 : ℝ) ≤ - (6779619924331152914863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (295330473032883 / 2500000000000000 : ℝ)) (q := - (4924647627296189 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4924647627296189 / 40000000000000000 : ℚ)) + (r' := (4924647627296189 / 2500000000000000 : ℚ)) + (U := (-(20946267287668847085137 / 10000000000000000000000 : ℚ))) + (U' := (6779619924331152914863 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (295330473032883 / 2500000000000000 : ℚ)) + (q := (4924647627296189 / 40000000000000000 : ℚ)) + (U := (-(20946267287668847085137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_7 : Uω (aρ 7) (bρ 7) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1113,25 +1005,21 @@ lemma U_235_7 : have hlg : Real.log (3662928992268993 / 40000000000000000 : ℝ) ≤ (-(23906163545953218465999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3662928992268993 / 40000000000000000 : ℝ) = - (3662928992268993 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3662928992268993 / 2500000000000000 : ℚ)) - (U := (3819723666046781534001 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3662928992268993 / 2500000000000000 : ℝ) ≤ - (3819723666046781534001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (387061977688967 / 5000000000000000 : ℝ)) (q := - (3662928992268993 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3662928992268993 / 40000000000000000 : ℚ)) + (r' := (3662928992268993 / 2500000000000000 : ℚ)) + (U := (-(23906163545953218465999 / 10000000000000000000000 : ℚ))) + (U' := (3819723666046781534001 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1139448789761 / 6400000000000 : ℚ)) + (s := (387061977688967 / 5000000000000000 : ℚ)) + (q := (3662928992268993 / 40000000000000000 : ℚ)) + (U := (-(23906163545953218465999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_235_8 : Uω (aρ 8) (bρ 8) (1139448789761 / 6400000000000 : ℝ) ≤ @@ -1269,25 +1157,21 @@ lemma U_236_1 : have hlg : Real.log (3467084036467329 / 20000000000000000 : ℝ) ≤ (-(3504836734814087840143 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3467084036467329 / 20000000000000000 : ℝ) = - (3467084036467329 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3467084036467329 / 2500000000000000 : ℚ)) - (U := (654046346985912159857 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3467084036467329 / 2500000000000000 : ℝ) ≤ - (654046346985912159857 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1733448759528579 / 10000000000000000 : ℝ)) (q := - (3467084036467329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3467084036467329 / 20000000000000000 : ℚ)) + (r' := (3467084036467329 / 2500000000000000 : ℚ)) + (U := (-(3504836734814087840143 / 2000000000000000000000 : ℚ))) + (U' := (654046346985912159857 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (1733448759528579 / 10000000000000000 : ℚ)) + (q := (3467084036467329 / 20000000000000000 : ℚ)) + (U := (-(3504836734814087840143 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_2 : Uω (aρ 2) (bρ 2) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1295,25 +1179,21 @@ lemma U_236_2 : have hlg : Real.log (341849113090293 / 2000000000000000 : ℝ) ≤ (-(8832665044234793364127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (341849113090293 / 2000000000000000 : ℝ) = - (341849113090293 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (341849113090293 / 250000000000000 : ℚ)) - (U := (1564542660265206635873 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (341849113090293 / 250000000000000 : ℝ) ≤ - (1564542660265206635873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85431243323709 / 500000000000000 : ℝ)) (q := - (341849113090293 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (341849113090293 / 2000000000000000 : ℚ)) + (r' := (341849113090293 / 250000000000000 : ℚ)) + (U := (-(8832665044234793364127 / 5000000000000000000000 : ℚ))) + (U' := (1564542660265206635873 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (85431243323709 / 500000000000000 : ℚ)) + (q := (341849113090293 / 2000000000000000 : ℚ)) + (U := (-(8832665044234793364127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_3 : Uω (aρ 3) (bρ 3) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1321,25 +1201,21 @@ lemma U_236_3 : have hlg : Real.log (3320484291241897 / 20000000000000000 : ℝ) ≤ (-(561131759258713630229 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3320484291241897 / 20000000000000000 : ℝ) = - (3320484291241897 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3320484291241897 / 2500000000000000 : ℚ)) - (U := (88693722272536369771 / 312500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3320484291241897 / 2500000000000000 : ℝ) ≤ - (88693722272536369771 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1658014133163147 / 10000000000000000 : ℝ)) (q := - (3320484291241897 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3320484291241897 / 20000000000000000 : ℚ)) + (r' := (3320484291241897 / 2500000000000000 : ℚ)) + (U := (-(561131759258713630229 / 312500000000000000000 : ℚ))) + (U' := (88693722272536369771 / 312500000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (1658014133163147 / 10000000000000000 : ℚ)) + (q := (3320484291241897 / 20000000000000000 : ℚ)) + (U := (-(561131759258713630229 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_4 : Uω (aρ 4) (bρ 4) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1347,25 +1223,21 @@ lemma U_236_4 : have hlg : Real.log (3155013781603513 / 20000000000000000 : ℝ) ≤ (-(18467394086119095410203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3155013781603513 / 20000000000000000 : ℝ) = - (3155013781603513 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3155013781603513 / 2500000000000000 : ℚ)) - (U := (2327021322880904589797 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3155013781603513 / 2500000000000000 : ℝ) ≤ - (2327021322880904589797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1570837804589763 / 10000000000000000 : ℝ)) (q := - (3155013781603513 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3155013781603513 / 20000000000000000 : ℚ)) + (r' := (3155013781603513 / 2500000000000000 : ℚ)) + (U := (-(18467394086119095410203 / 10000000000000000000000 : ℚ))) + (U' := (2327021322880904589797 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (1570837804589763 / 10000000000000000 : ℚ)) + (q := (3155013781603513 / 20000000000000000 : ℚ)) + (U := (-(18467394086119095410203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_5 : Uω (aρ 5) (bρ 5) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1373,25 +1245,21 @@ lemma U_236_5 : have hlg : Real.log (289518211199629 / 2000000000000000 : ℝ) ≤ (-(19326842580294766154441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (289518211199629 / 2000000000000000 : ℝ) = - (289518211199629 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (289518211199629 / 250000000000000 : ℚ)) - (U := (1467572828705233845559 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (289518211199629 / 250000000000000 : ℝ) ≤ - (1467572828705233845559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (71459802715877 / 500000000000000 : ℝ)) (q := - (289518211199629 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (289518211199629 / 2000000000000000 : ℚ)) + (r' := (289518211199629 / 250000000000000 : ℚ)) + (U := (-(19326842580294766154441 / 10000000000000000000000 : ℚ))) + (U' := (1467572828705233845559 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (71459802715877 / 500000000000000 : ℚ)) + (q := (289518211199629 / 2000000000000000 : ℚ)) + (U := (-(19326842580294766154441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_6 : Uω (aρ 6) (bρ 6) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1399,25 +1267,21 @@ lemma U_236_6 : have hlg : Real.log (624821373386481 / 5000000000000000 : ℝ) ≤ (-(4159454768142052679751 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (624821373386481 / 5000000000000000 : ℝ) = - (624821373386481 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (624821373386481 / 312500000000000 : ℚ)) - (U := (1385722674257947320249 / 2000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (624821373386481 / 312500000000000 : ℝ) ≤ - (1385722674257947320249 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (600269905503587 / 5000000000000000 : ℝ)) (q := - (624821373386481 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (624821373386481 / 5000000000000000 : ℚ)) + (r' := (624821373386481 / 312500000000000 : ℚ)) + (U := (-(4159454768142052679751 / 2000000000000000000000 : ℚ))) + (U' := (1385722674257947320249 / 2000000000000000000000 : ℚ)) + 4 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (600269905503587 / 5000000000000000 : ℚ)) + (q := (624821373386481 / 5000000000000000 : ℚ)) + (U := (-(4159454768142052679751 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_7 : Uω (aρ 7) (bρ 7) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1425,24 +1289,21 @@ lemma U_236_7 : have hlg : Real.log (58539780019197 / 625000000000000 : ℝ) ≤ (-(23680451252261213551871 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (58539780019197 / 625000000000000 : ℝ) = (58539780019197 / 39062500000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58539780019197 / 39062500000000 : ℚ)) - (U := (4045435959738786448129 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58539780019197 / 39062500000000 : ℝ) ≤ - (4045435959738786448129 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (399094329417777 / 5000000000000000 : ℝ)) (q := - (58539780019197 / 625000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58539780019197 / 625000000000000 : ℚ)) + (r' := (58539780019197 / 39062500000000 : ℚ)) + (U := (-(23680451252261213551871 / 10000000000000000000000 : ℚ))) + (U' := (4045435959738786448129 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1438505996019 / 8000000000000 : ℚ)) + (s := (399094329417777 / 5000000000000000 : ℚ)) + (q := (58539780019197 / 625000000000000 : ℚ)) + (U := (-(23680451252261213551871 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_236_8 : Uω (aρ 8) (bρ 8) (1438505996019 / 8000000000000 : ℝ) ≤ @@ -1579,25 +1440,21 @@ lemma U_237_1 : have hlg : Real.log (1769031411185933 / 10000000000000000 : ℝ) ≤ (-(216519115091196781593 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1769031411185933 / 10000000000000000 : ℝ) = - (1769031411185933 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1769031411185933 / 1250000000000000 : ℚ)) - (U := (43411077521303218407 / 125000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1769031411185933 / 1250000000000000 : ℝ) ≤ - (43411077521303218407 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1768940023388741 / 10000000000000000 : ℝ)) (q := - (1769031411185933 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1769031411185933 / 10000000000000000 : ℚ)) + (r' := (1769031411185933 / 1250000000000000 : ℚ)) + (U := (-(216519115091196781593 / 125000000000000000000 : ℚ))) + (U' := (43411077521303218407 / 125000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (1768940023388741 / 10000000000000000 : ℚ)) + (q := (1769031411185933 / 10000000000000000 : ℚ)) + (U := (-(216519115091196781593 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_2 : Uω (aρ 2) (bρ 2) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1605,25 +1462,21 @@ lemma U_237_2 : have hlg : Real.log (1744745716790423 / 10000000000000000 : ℝ) ≤ (-(545617583817240004993 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1744745716790423 / 10000000000000000 : ℝ) = - (1744745716790423 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1744745716790423 / 1250000000000000 : ℚ)) - (U := (104207897714009995007 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1744745716790423 / 1250000000000000 : ℝ) ≤ - (104207897714009995007 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1744137647107721 / 10000000000000000 : ℝ)) (q := - (1744745716790423 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1744745716790423 / 10000000000000000 : ℚ)) + (r' := (1744745716790423 / 1250000000000000 : ℚ)) + (U := (-(545617583817240004993 / 312500000000000000000 : ℚ))) + (U' := (104207897714009995007 / 312500000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (1744137647107721 / 10000000000000000 : ℚ)) + (q := (1744745716790423 / 10000000000000000 : ℚ)) + (U := (-(545617583817240004993 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_3 : Uω (aρ 3) (bρ 3) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1631,25 +1484,21 @@ lemma U_237_3 : have hlg : Real.log (847888177317829 / 5000000000000000 : ℝ) ≤ (-(17744444299101173343339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (847888177317829 / 5000000000000000 : ℝ) = - (847888177317829 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (847888177317829 / 625000000000000 : ℚ)) - (U := (3049971109898826656661 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (847888177317829 / 625000000000000 : ℝ) ≤ - (3049971109898826656661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1693595029148191 / 10000000000000000 : ℝ)) (q := - (847888177317829 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (847888177317829 / 5000000000000000 : ℚ)) + (r' := (847888177317829 / 625000000000000 : ℚ)) + (U := (-(17744444299101173343339 / 10000000000000000000000 : ℚ))) + (U' := (3049971109898826656661 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (1693595029148191 / 10000000000000000 : ℚ)) + (q := (847888177317829 / 5000000000000000 : ℚ)) + (U := (-(17744444299101173343339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_4 : Uω (aρ 4) (bρ 4) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1657,25 +1506,21 @@ lemma U_237_4 : have hlg : Real.log (3226283470414801 / 20000000000000000 : ℝ) ≤ (-(18244014263751742130657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3226283470414801 / 20000000000000000 : ℝ) = - (3226283470414801 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3226283470414801 / 2500000000000000 : ℚ)) - (U := (2550401145248257869343 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3226283470414801 / 2500000000000000 : ℝ) ≤ - (2550401145248257869343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (401654992839169 / 2500000000000000 : ℝ)) (q := - (3226283470414801 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3226283470414801 / 20000000000000000 : ℚ)) + (r' := (3226283470414801 / 2500000000000000 : ℚ)) + (U := (-(18244014263751742130657 / 10000000000000000000000 : ℚ))) + (U' := (2550401145248257869343 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (401654992839169 / 2500000000000000 : ℚ)) + (q := (3226283470414801 / 20000000000000000 : ℚ)) + (U := (-(18244014263751742130657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_5 : Uω (aρ 5) (bρ 5) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1683,25 +1528,21 @@ lemma U_237_5 : have hlg : Real.log (2967048262560857 / 20000000000000000 : ℝ) ≤ (-(9540823325732590924141 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2967048262560857 / 20000000000000000 : ℝ) = - (2967048262560857 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2967048262560857 / 2500000000000000 : ℚ)) - (U := (856384378767409075859 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2967048262560857 / 2500000000000000 : ℝ) ≤ - (856384378767409075859 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (366393670709433 / 2500000000000000 : ℝ)) (q := - (2967048262560857 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2967048262560857 / 20000000000000000 : ℚ)) + (r' := (2967048262560857 / 2500000000000000 : ℚ)) + (U := (-(9540823325732590924141 / 5000000000000000000000 : ℚ))) + (U' := (856384378767409075859 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (366393670709433 / 2500000000000000 : ℚ)) + (q := (2967048262560857 / 20000000000000000 : ℚ)) + (U := (-(9540823325732590924141 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_6 : Uω (aρ 6) (bρ 6) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1709,25 +1550,21 @@ lemma U_237_6 : have hlg : Real.log (2573076913092093 / 20000000000000000 : ℝ) ≤ (-(20506298475419563252639 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2573076913092093 / 20000000000000000 : ℝ) = - (2573076913092093 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2573076913092093 / 2500000000000000 : ℚ)) - (U := (288116933580436747361 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2573076913092093 / 2500000000000000 : ℝ) ≤ - (288116933580436747361 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154855463563621 / 1250000000000000 : ℝ)) (q := - (2573076913092093 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2573076913092093 / 20000000000000000 : ℚ)) + (r' := (2573076913092093 / 2500000000000000 : ℚ)) + (U := (-(20506298475419563252639 / 10000000000000000000000 : ℚ))) + (U' := (288116933580436747361 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (154855463563621 / 1250000000000000 : ℚ)) + (q := (2573076913092093 / 20000000000000000 : ℚ)) + (U := (-(20506298475419563252639 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_7 : Uω (aρ 7) (bρ 7) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1735,25 +1572,21 @@ lemma U_237_7 : have hlg : Real.log (1955952598996313 / 20000000000000000 : ℝ) ≤ (-(2906068668546487972029 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1955952598996313 / 20000000000000000 : ℝ) = - (1955952598996313 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1955952598996313 / 1250000000000000 : ℚ)) - (U := (559667232953512027971 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1955952598996313 / 1250000000000000 : ℝ) ≤ - (559667232953512027971 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (211345193793297 / 2500000000000000 : ℝ)) (q := - (1955952598996313 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1955952598996313 / 20000000000000000 : ℚ)) + (r' := (1955952598996313 / 1250000000000000 : ℚ)) + (U := (-(2906068668546487972029 / 1250000000000000000000 : ℚ))) + (U' := (559667232953512027971 / 1250000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2933792027309 / 16000000000000 : ℚ)) + (s := (211345193793297 / 2500000000000000 : ℚ)) + (q := (1955952598996313 / 20000000000000000 : ℚ)) + (U := (-(2906068668546487972029 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_237_8 : Uω (aρ 8) (bρ 8) (2933792027309 / 16000000000000 : ℝ) ≤ @@ -1890,25 +1723,21 @@ lemma U_238_1 : have hlg : Real.log (3609041461089001 / 20000000000000000 : ℝ) ≤ (-(17122900589309473870993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3609041461089001 / 20000000000000000 : ℝ) = - (3609041461089001 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3609041461089001 / 2500000000000000 : ℚ)) - (U := (3671514819690526129007 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3609041461089001 / 2500000000000000 : ℝ) ≤ - (3671514819690526129007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1804431140061501 / 10000000000000000 : ℝ)) (q := - (3609041461089001 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3609041461089001 / 20000000000000000 : ℚ)) + (r' := (3609041461089001 / 2500000000000000 : ℚ)) + (U := (-(17122900589309473870993 / 10000000000000000000000 : ℚ))) + (U' := (3671514819690526129007 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (149528603129 / 800000000000 : ℚ)) + (s := (1804431140061501 / 10000000000000000 : ℚ)) + (q := (3609041461089001 / 20000000000000000 : ℚ)) + (U := (-(17122900589309473870993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_2 : Uω (aρ 2) (bρ 2) (149528603129 / 800000000000 : ℝ) ≤ @@ -1916,25 +1745,21 @@ lemma U_238_2 : have hlg : Real.log (712098145710151 / 4000000000000000 : ℝ) ≤ (-(8629169461557259480653 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (712098145710151 / 4000000000000000 : ℝ) = - (712098145710151 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (712098145710151 / 500000000000000 : ℚ)) - (U := (1768038242942740519347 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (712098145710151 / 500000000000000 : ℝ) ≤ - (1768038242942740519347 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (355929884006651 / 2000000000000000 : ℝ)) (q := - (712098145710151 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (712098145710151 / 4000000000000000 : ℚ)) + (r' := (712098145710151 / 500000000000000 : ℚ)) + (U := (-(8629169461557259480653 / 5000000000000000000000 : ℚ))) + (U' := (1768038242942740519347 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (149528603129 / 800000000000 : ℚ)) + (s := (355929884006651 / 2000000000000000 : ℚ)) + (q := (712098145710151 / 4000000000000000 : ℚ)) + (U := (-(8629169461557259480653 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_3 : Uω (aρ 3) (bρ 3) (149528603129 / 800000000000 : ℝ) ≤ @@ -1942,25 +1767,21 @@ lemma U_238_3 : have hlg : Real.log (3462617289665989 / 20000000000000000 : ℝ) ≤ (-(3507415055125305177593 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3462617289665989 / 20000000000000000 : ℝ) = - (3462617289665989 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3462617289665989 / 2500000000000000 : ℚ)) - (U := (651468026674694822407 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3462617289665989 / 2500000000000000 : ℝ) ≤ - (651468026674694822407 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1729172087498489 / 10000000000000000 : ℝ)) (q := - (3462617289665989 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3462617289665989 / 20000000000000000 : ℚ)) + (r' := (3462617289665989 / 2500000000000000 : ℚ)) + (U := (-(3507415055125305177593 / 2000000000000000000000 : ℚ))) + (U' := (651468026674694822407 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (149528603129 / 800000000000 : ℚ)) + (s := (1729172087498489 / 10000000000000000 : ℚ)) + (q := (3462617289665989 / 20000000000000000 : ℚ)) + (U := (-(3507415055125305177593 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_4 : Uω (aρ 4) (bρ 4) (149528603129 / 800000000000 : ℝ) ≤ @@ -1968,24 +1789,21 @@ lemma U_238_4 : have hlg : Real.log (103048136671579 / 625000000000000 : ℝ) ≤ (-(3605110847146402910907 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (103048136671579 / 625000000000000 : ℝ) = (103048136671579 / 78125000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (103048136671579 / 78125000000000 : ℚ)) - (U := (553772234653597089093 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (103048136671579 / 78125000000000 : ℝ) ≤ - (553772234653597089093 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410597338097007 / 2500000000000000 : ℝ)) (q := - (103048136671579 / 625000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (103048136671579 / 625000000000000 : ℚ)) + (r' := (103048136671579 / 78125000000000 : ℚ)) + (U := (-(3605110847146402910907 / 2000000000000000000000 : ℚ))) + (U' := (553772234653597089093 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (149528603129 / 800000000000 : ℚ)) + (s := (410597338097007 / 2500000000000000 : ℚ)) + (q := (103048136671579 / 625000000000000 : ℚ)) + (U := (-(3605110847146402910907 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_5 : Uω (aρ 5) (bρ 5) (149528603129 / 800000000000 : ℝ) ≤ @@ -1993,25 +1811,21 @@ lemma U_238_5 : have hlg : Real.log (1519435887224519 / 10000000000000000 : ℝ) ≤ (-(9421229765333016833399 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1519435887224519 / 10000000000000000 : ℝ) = - (1519435887224519 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1519435887224519 / 1250000000000000 : ℚ)) - (U := (975977939166983166601 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1519435887224519 / 1250000000000000 : ℝ) ≤ - (975977939166983166601 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (750955336340769 / 5000000000000000 : ℝ)) (q := - (1519435887224519 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1519435887224519 / 10000000000000000 : ℚ)) + (r' := (1519435887224519 / 1250000000000000 : ℚ)) + (U := (-(9421229765333016833399 / 5000000000000000000000 : ℚ))) + (U' := (975977939166983166601 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (149528603129 / 800000000000 : ℚ)) + (s := (750955336340769 / 5000000000000000 : ℚ)) + (q := (1519435887224519 / 10000000000000000 : ℚ)) + (U := (-(9421229765333016833399 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_6 : Uω (aρ 6) (bρ 6) (149528603129 / 800000000000 : ℝ) ≤ @@ -2019,25 +1833,21 @@ lemma U_238_6 : have hlg : Real.log (1323352798439857 / 10000000000000000 : ℝ) ≤ (-(20224165771428923170819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1323352798439857 / 10000000000000000 : ℝ) = - (1323352798439857 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1323352798439857 / 1250000000000000 : ℚ)) - (U := (570249637571076829181 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1323352798439857 / 1250000000000000 : ℝ) ≤ - (570249637571076829181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (638492435126107 / 5000000000000000 : ℝ)) (q := - (1323352798439857 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1323352798439857 / 10000000000000000 : ℚ)) + (r' := (1323352798439857 / 1250000000000000 : ℚ)) + (U := (-(20224165771428923170819 / 10000000000000000000000 : ℚ))) + (U' := (570249637571076829181 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (149528603129 / 800000000000 : ℚ)) + (s := (638492435126107 / 5000000000000000 : ℚ)) + (q := (1323352798439857 / 10000000000000000 : ℚ)) + (U := (-(20224165771428923170819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_7 : Uω (aρ 7) (bρ 7) (149528603129 / 800000000000 : ℝ) ≤ @@ -2045,25 +1855,21 @@ lemma U_238_7 : have hlg : Real.log (2037547373500423 / 20000000000000000 : ℝ) ≤ (-(22839854558538710203403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2037547373500423 / 20000000000000000 : ℝ) = - (2037547373500423 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2037547373500423 / 1250000000000000 : ℚ)) - (U := (4886032653461289796597 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2037547373500423 / 1250000000000000 : ℝ) ≤ - (4886032653461289796597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (891488027632923 / 10000000000000000 : ℝ)) (q := - (2037547373500423 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2037547373500423 / 20000000000000000 : ℚ)) + (r' := (2037547373500423 / 1250000000000000 : ℚ)) + (U := (-(22839854558538710203403 / 10000000000000000000000 : ℚ))) + (U' := (4886032653461289796597 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (149528603129 / 800000000000 : ℚ)) + (s := (891488027632923 / 10000000000000000 : ℚ)) + (q := (2037547373500423 / 20000000000000000 : ℚ)) + (U := (-(22839854558538710203403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_238_8 : Uω (aρ 8) (bρ 8) (149528603129 / 800000000000 : ℝ) ≤ @@ -2201,25 +2007,21 @@ lemma U_239_1 : have hlg : Real.log (736003992227247 / 4000000000000000 : ℝ) ≤ (-(423203524096555888311 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (736003992227247 / 4000000000000000 : ℝ) = - (736003992227247 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (736003992227247 / 500000000000000 : ℚ)) - (U := (96656861128444111689 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (736003992227247 / 500000000000000 : ℝ) ≤ - (96656861128444111689 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45998052951609 / 250000000000000 : ℝ)) (q := - (736003992227247 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (736003992227247 / 4000000000000000 : ℚ)) + (r' := (736003992227247 / 500000000000000 : ℚ)) + (U := (-(423203524096555888311 / 250000000000000000000 : ℚ))) + (U' := (96656861128444111689 / 250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (45998052951609 / 250000000000000 : ℚ)) + (q := (736003992227247 / 4000000000000000 : ℚ)) + (U := (-(423203524096555888311 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_2 : Uω (aρ 2) (bρ 2) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2227,25 +2029,21 @@ lemma U_239_2 : have hlg : Real.log (1815744537478511 / 10000000000000000 : ℝ) ≤ (-(17060894951251626070951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1815744537478511 / 10000000000000000 : ℝ) = - (1815744537478511 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1815744537478511 / 1250000000000000 : ℚ)) - (U := (3733520457748373929049 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1815744537478511 / 1250000000000000 : ℝ) ≤ - (3733520457748373929049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1815160244395147 / 10000000000000000 : ℝ)) (q := - (1815744537478511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1815744537478511 / 10000000000000000 : ℚ)) + (r' := (1815744537478511 / 1250000000000000 : ℚ)) + (U := (-(17060894951251626070951 / 10000000000000000000000 : ℚ))) + (U' := (3733520457748373929049 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (1815160244395147 / 10000000000000000 : ℚ)) + (q := (1815744537478511 / 10000000000000000 : ℚ)) + (U := (-(17060894951251626070951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_3 : Uω (aρ 3) (bρ 3) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2253,25 +2051,21 @@ lemma U_239_3 : have hlg : Real.log (3533678264524699 / 20000000000000000 : ℝ) ≤ (-(3466785886107343843369 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3533678264524699 / 20000000000000000 : ℝ) = - (3533678264524699 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3533678264524699 / 2500000000000000 : ℚ)) - (U := (692097195692656156631 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3533678264524699 / 2500000000000000 : ℝ) ≤ - (692097195692656156631 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (220593192539103 / 1250000000000000 : ℝ)) (q := - (3533678264524699 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3533678264524699 / 20000000000000000 : ℚ)) + (r' := (3533678264524699 / 2500000000000000 : ℚ)) + (U := (-(3466785886107343843369 / 2000000000000000000000 : ℚ))) + (U' := (692097195692656156631 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (220593192539103 / 1250000000000000 : ℚ)) + (q := (3533678264524699 / 20000000000000000 : ℚ)) + (U := (-(3466785886107343843369 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_4 : Uω (aρ 4) (bρ 4) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2279,25 +2073,21 @@ lemma U_239_4 : have hlg : Real.log (1684392654203751 / 10000000000000000 : ℝ) ≤ (-(17811800359939854210869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1684392654203751 / 10000000000000000 : ℝ) = - (1684392654203751 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1684392654203751 / 1250000000000000 : ℚ)) - (U := (2982615049060145789131 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1684392654203751 / 1250000000000000 : ℝ) ≤ - (2982615049060145789131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1678146765260627 / 10000000000000000 : ℝ)) (q := - (1684392654203751 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1684392654203751 / 10000000000000000 : ℚ)) + (r' := (1684392654203751 / 1250000000000000 : ℚ)) + (U := (-(17811800359939854210869 / 10000000000000000000000 : ℚ))) + (U' := (2982615049060145789131 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (1678146765260627 / 10000000000000000 : ℚ)) + (q := (1684392654203751 / 10000000000000000 : ℚ)) + (U := (-(17811800359939854210869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_5 : Uω (aρ 5) (bρ 5) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2305,25 +2095,21 @@ lemma U_239_5 : have hlg : Real.log (3110655669334747 / 20000000000000000 : ℝ) ≤ (-(9304493713255353838983 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3110655669334747 / 20000000000000000 : ℝ) = - (3110655669334747 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3110655669334747 / 2500000000000000 : ℚ)) - (U := (1092713991244646161017 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3110655669334747 / 2500000000000000 : ℝ) ≤ - (1092713991244646161017 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (192275880690359 / 1250000000000000 : ℝ)) (q := - (3110655669334747 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3110655669334747 / 20000000000000000 : ℚ)) + (r' := (3110655669334747 / 2500000000000000 : ℚ)) + (U := (-(9304493713255353838983 / 5000000000000000000000 : ℚ))) + (U' := (1092713991244646161017 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (192275880690359 / 1250000000000000 : ℚ)) + (q := (3110655669334747 / 20000000000000000 : ℚ)) + (U := (-(9304493713255353838983 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_6 : Uω (aρ 6) (bρ 6) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2331,25 +2117,21 @@ lemma U_239_6 : have hlg : Real.log (2720185705526393 / 20000000000000000 : ℝ) ≤ (-(19950321207062330984031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2720185705526393 / 20000000000000000 : ℝ) = - (2720185705526393 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2720185705526393 / 2500000000000000 : ℚ)) - (U := (844094201937669015969 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2720185705526393 / 2500000000000000 : ℝ) ≤ - (844094201937669015969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (657488728427259 / 5000000000000000 : ℝ)) (q := - (2720185705526393 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2720185705526393 / 20000000000000000 : ℚ)) + (r' := (2720185705526393 / 2500000000000000 : ℚ)) + (U := (-(19950321207062330984031 / 10000000000000000000000 : ℚ))) + (U' := (844094201937669015969 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (657488728427259 / 5000000000000000 : ℚ)) + (q := (2720185705526393 / 20000000000000000 : ℚ)) + (U := (-(19950321207062330984031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_7 : Uω (aρ 7) (bρ 7) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2357,24 +2139,21 @@ lemma U_239_7 : have hlg : Real.log (84728700154133 / 800000000000000 : ℝ) ≤ (-(22451573375701112560891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (84728700154133 / 800000000000000 : ℝ) = (84728700154133 / 50000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84728700154133 / 50000000000000 : ℚ)) - (U := (5274313836298887439109 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (84728700154133 / 50000000000000 : ℝ) ≤ - (5274313836298887439109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18733412718829 / 200000000000000 : ℝ)) (q := - (84728700154133 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84728700154133 / 800000000000000 : ℚ)) + (r' := (84728700154133 / 50000000000000 : ℚ)) + (U := (-(22451573375701112560891 / 10000000000000000000000 : ℚ))) + (U' := (5274313836298887439109 / 10000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3047352097851 / 16000000000000 : ℚ)) + (s := (18733412718829 / 200000000000000 : ℚ)) + (q := (84728700154133 / 800000000000000 : ℚ)) + (U := (-(22451573375701112560891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_239_8 : Uω (aρ 8) (bρ 8) (3047352097851 / 16000000000000 : ℝ) ≤ @@ -2511,25 +2290,21 @@ lemma U_240_1 : have hlg : Real.log (3750998330386281 / 20000000000000000 : ℝ) ≤ (-(3347420493572264953999 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3750998330386281 / 20000000000000000 : ℝ) = - (3750998330386281 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3750998330386281 / 2500000000000000 : ℚ)) - (U := (811462588227735046001 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3750998330386281 / 2500000000000000 : ℝ) ≤ - (811462588227735046001 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1875412965270031 / 10000000000000000 : ℝ)) (q := - (3750998330386281 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3750998330386281 / 20000000000000000 : ℚ)) + (r' := (3750998330386281 / 2500000000000000 : ℚ)) + (U := (-(3347420493572264953999 / 2000000000000000000000 : ℚ))) + (U' := (811462588227735046001 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (1875412965270031 / 10000000000000000 : ℚ)) + (q := (3750998330386281 / 20000000000000000 : ℚ)) + (U := (-(3347420493572264953999 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_2 : Uω (aρ 2) (bρ 2) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2537,25 +2312,21 @@ lemma U_240_2 : have hlg : Real.log (3702486527403017 / 20000000000000000 : ℝ) ≤ (-(4216819111011872001949 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3702486527403017 / 20000000000000000 : ℝ) = - (3702486527403017 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3702486527403017 / 2500000000000000 : ℚ)) - (U := (981784741238127998051 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3702486527403017 / 2500000000000000 : ℝ) ≤ - (981784741238127998051 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1850670174796767 / 10000000000000000 : ℝ)) (q := - (3702486527403017 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3702486527403017 / 20000000000000000 : ℚ)) + (r' := (3702486527403017 / 2500000000000000 : ℚ)) + (U := (-(4216819111011872001949 / 2500000000000000000000 : ℚ))) + (U' := (981784741238127998051 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (1850670174796767 / 10000000000000000 : ℚ)) + (q := (3702486527403017 / 20000000000000000 : ℚ)) + (U := (-(4216819111011872001949 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_3 : Uω (aρ 3) (bρ 3) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2563,25 +2334,21 @@ lemma U_240_3 : have hlg : Real.log (144189433903157 / 800000000000000 : ℝ) ≤ (-(3426967557250234145729 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (144189433903157 / 800000000000000 : ℝ) = - (144189433903157 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (144189433903157 / 100000000000000 : ℚ)) - (U := (731915524549765854271 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (144189433903157 / 100000000000000 : ℝ) ≤ - (731915524549765854271 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (72012624052907 / 400000000000000 : ℝ)) (q := - (144189433903157 / 800000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (144189433903157 / 800000000000000 : ℚ)) + (r' := (144189433903157 / 100000000000000 : ℚ)) + (U := (-(3426967557250234145729 / 2000000000000000000000 : ℚ))) + (U' := (731915524549765854271 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (72012624052907 / 400000000000000 : ℚ)) + (q := (144189433903157 / 800000000000000 : ℚ)) + (U := (-(3426967557250234145729 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_4 : Uω (aρ 4) (bρ 4) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2589,25 +2356,21 @@ lemma U_240_4 : have hlg : Real.log (430002378031337 / 2500000000000000 : ℝ) ≤ (-(1100159544436690800209 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (430002378031337 / 2500000000000000 : ℝ) = - (430002378031337 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (430002378031337 / 312500000000000 : ℚ)) - (U := (199491418625809199791 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (430002378031337 / 312500000000000 : ℝ) ≤ - (199491418625809199791 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (856946479529723 / 5000000000000000 : ℝ)) (q := - (430002378031337 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (430002378031337 / 2500000000000000 : ℚ)) + (r' := (430002378031337 / 312500000000000 : ℚ)) + (U := (-(1100159544436690800209 / 625000000000000000000 : ℚ))) + (U' := (199491418625809199791 / 625000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (856946479529723 / 5000000000000000 : ℚ)) + (q := (430002378031337 / 2500000000000000 : ℚ)) + (U := (-(1100159544436690800209 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_5 : Uω (aρ 5) (bρ 5) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2615,25 +2378,21 @@ lemma U_240_5 : have hlg : Real.log (3182402687107411 / 20000000000000000 : ℝ) ≤ (-(18380957992918669968001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3182402687107411 / 20000000000000000 : ℝ) = - (3182402687107411 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3182402687107411 / 2500000000000000 : ℚ)) - (U := (2413457416081330031999 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3182402687107411 / 2500000000000000 : ℝ) ≤ - (2413457416081330031999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1574466541251161 / 10000000000000000 : ℝ)) (q := - (3182402687107411 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3182402687107411 / 20000000000000000 : ℚ)) + (r' := (3182402687107411 / 2500000000000000 : ℚ)) + (U := (-(18380957992918669968001 / 10000000000000000000000 : ℚ))) + (U' := (2413457416081330031999 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (1574466541251161 / 10000000000000000 : ℚ)) + (q := (3182402687107411 / 20000000000000000 : ℚ)) + (U := (-(18380957992918669968001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_6 : Uω (aρ 6) (bρ 6) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2641,25 +2400,21 @@ lemma U_240_6 : have hlg : Real.log (1396764878355009 / 10000000000000000 : ℝ) ≤ (-(3936852661578481560173 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1396764878355009 / 10000000000000000 : ℝ) = - (1396764878355009 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1396764878355009 / 1250000000000000 : ℚ)) - (U := (222030420221518439827 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1396764878355009 / 1250000000000000 : ℝ) ≤ - (222030420221518439827 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (169104248249221 / 1250000000000000 : ℝ)) (q := - (1396764878355009 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1396764878355009 / 10000000000000000 : ℚ)) + (r' := (1396764878355009 / 1250000000000000 : ℚ)) + (U := (-(3936852661578481560173 / 2000000000000000000000 : ℚ))) + (U' := (222030420221518439827 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (169104248249221 / 1250000000000000 : ℚ)) + (q := (1396764878355009 / 10000000000000000 : ℚ)) + (U := (-(3936852661578481560173 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_7 : Uω (aρ 7) (bρ 7) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2667,25 +2422,21 @@ lemma U_240_7 : have hlg : Real.log (2198090751996057 / 20000000000000000 : ℝ) ≤ (-(5520357822357195670947 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2198090751996057 / 20000000000000000 : ℝ) = - (2198090751996057 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2198090751996057 / 1250000000000000 : ℚ)) - (U := (1411113980642804329053 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2198090751996057 / 1250000000000000 : ℝ) ≤ - (1411113980642804329053 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (981056362039807 / 10000000000000000 : ℝ)) (q := - (2198090751996057 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2198090751996057 / 20000000000000000 : ℚ)) + (r' := (2198090751996057 / 1250000000000000 : ℚ)) + (U := (-(5520357822357195670947 / 2500000000000000000000 : ℚ))) + (U' := (1411113980642804329053 / 2500000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1552066066561 / 8000000000000 : ℚ)) + (s := (981056362039807 / 10000000000000000 : ℚ)) + (q := (2198090751996057 / 20000000000000000 : ℚ)) + (U := (-(5520357822357195670947 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_240_8 : Uω (aρ 8) (bρ 8) (1552066066561 / 8000000000000 : ℝ) ≤ @@ -2822,25 +2573,21 @@ lemma U_241_1 : have hlg : Real.log (3892954705114493 / 20000000000000000 : ℝ) ≤ (-(8182819195849925653851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3892954705114493 / 20000000000000000 : ℝ) = - (3892954705114493 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3892954705114493 / 2500000000000000 : ℚ)) - (U := (2214388508650074346149 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3892954705114493 / 2500000000000000 : ℝ) ≤ - (2214388508650074346149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1946394295909493 / 10000000000000000 : ℝ)) (q := - (3892954705114493 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3892954705114493 / 20000000000000000 : ℚ)) + (r' := (3892954705114493 / 2500000000000000 : ℚ)) + (U := (-(8182819195849925653851 / 5000000000000000000000 : ℚ))) + (U' := (2214388508650074346149 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (1946394295909493 / 10000000000000000 : ℚ)) + (q := (3892954705114493 / 20000000000000000 : ℚ)) + (U := (-(8182819195849925653851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_2 : Uω (aρ 2) (bρ 2) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2848,25 +2595,21 @@ lemma U_241_2 : have hlg : Real.log (768895789728329 / 4000000000000000 : ℝ) ≤ (-(16490941930067749877633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (768895789728329 / 4000000000000000 : ℝ) = - (768895789728329 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (768895789728329 / 500000000000000 : ℚ)) - (U := (4303473478932250122367 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (768895789728329 / 500000000000000 : ℝ) ≤ - (4303473478932250122367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (384337510389329 / 2000000000000000 : ℝ)) (q := - (768895789728329 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (768895789728329 / 4000000000000000 : ℚ)) + (r' := (768895789728329 / 500000000000000 : ℚ)) + (U := (-(16490941930067749877633 / 10000000000000000000000 : ℚ))) + (U' := (4303473478932250122367 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (384337510389329 / 2000000000000000 : ℚ)) + (q := (768895789728329 / 4000000000000000 : ℚ)) + (U := (-(16490941930067749877633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_3 : Uω (aρ 3) (bρ 3) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2874,25 +2617,21 @@ lemma U_241_3 : have hlg : Real.log (1873420805930339 / 10000000000000000 : ℝ) ≤ (-(3349638049019418963313 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1873420805930339 / 10000000000000000 : ℝ) = - (1873420805930339 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1873420805930339 / 1250000000000000 : ℚ)) - (U := (809245032780581036687 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1873420805930339 / 1250000000000000 : ℝ) ≤ - (809245032780581036687 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (935723160757839 / 5000000000000000 : ℝ)) (q := - (1873420805930339 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1873420805930339 / 10000000000000000 : ℚ)) + (r' := (1873420805930339 / 1250000000000000 : ℚ)) + (U := (-(3349638049019418963313 / 2000000000000000000000 : ℚ))) + (U' := (809245032780581036687 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (935723160757839 / 5000000000000000 : ℚ)) + (q := (1873420805930339 / 10000000000000000 : ℚ)) + (U := (-(3349638049019418963313 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_4 : Uω (aρ 4) (bρ 4) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2900,25 +2639,21 @@ lemma U_241_4 : have hlg : Real.log (3582455494032877 / 20000000000000000 : ℝ) ≤ (-(8598419076450674071003 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3582455494032877 / 20000000000000000 : ℝ) = - (3582455494032877 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3582455494032877 / 2500000000000000 : ℚ)) - (U := (1798788628049325928997 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3582455494032877 / 2500000000000000 : ℝ) ≤ - (1798788628049325928997 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1785354384752877 / 10000000000000000 : ℝ)) (q := - (3582455494032877 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3582455494032877 / 20000000000000000 : ℚ)) + (r' := (3582455494032877 / 2500000000000000 : ℚ)) + (U := (-(8598419076450674071003 / 5000000000000000000000 : ℚ))) + (U' := (1798788628049325928997 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (1785354384752877 / 10000000000000000 : ℚ)) + (q := (3582455494032877 / 20000000000000000 : ℚ)) + (U := (-(8598419076450674071003 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_5 : Uω (aρ 5) (bρ 5) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2926,25 +2661,21 @@ lemma U_241_5 : have hlg : Real.log (3325795831955751 / 20000000000000000 : ℝ) ≤ (-(17940232793488732042317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3325795831955751 / 20000000000000000 : ℝ) = - (3325795831955751 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3325795831955751 / 2500000000000000 : ℚ)) - (U := (2854182615511267957683 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3325795831955751 / 2500000000000000 : ℝ) ≤ - (2854182615511267957683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1646884642010751 / 10000000000000000 : ℝ)) (q := - (3325795831955751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3325795831955751 / 20000000000000000 : ℚ)) + (r' := (3325795831955751 / 2500000000000000 : ℚ)) + (U := (-(17940232793488732042317 / 10000000000000000000000 : ℚ))) + (U' := (2854182615511267957683 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (1646884642010751 / 10000000000000000 : ℚ)) + (q := (3325795831955751 / 20000000000000000 : ℚ)) + (U := (-(17940232793488732042317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_6 : Uω (aρ 6) (bρ 6) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2952,25 +2683,21 @@ lemma U_241_6 : have hlg : Real.log (1469926462911759 / 10000000000000000 : ℝ) ≤ (-(19173727179049642941211 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1469926462911759 / 10000000000000000 : ℝ) = - (1469926462911759 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1469926462911759 / 1250000000000000 : ℚ)) - (U := (1620688229950357058789 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1469926462911759 / 1250000000000000 : ℝ) ≤ - (1620688229950357058789 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (714091055509259 / 5000000000000000 : ℝ)) (q := - (1469926462911759 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1469926462911759 / 10000000000000000 : ℚ)) + (r' := (1469926462911759 / 1250000000000000 : ℚ)) + (U := (-(19173727179049642941211 / 10000000000000000000000 : ℚ))) + (U' := (1620688229950357058789 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (714091055509259 / 5000000000000000 : ℚ)) + (q := (1469926462911759 / 10000000000000000 : ℚ)) + (U := (-(19173727179049642941211 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_7 : Uω (aρ 7) (bρ 7) (201105762729 / 1000000000000 : ℝ) ≤ @@ -2978,25 +2705,21 @@ lemma U_241_7 : have hlg : Real.log (588960592762359 / 5000000000000000 : ℝ) ≤ (-(21388339142901952282833 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (588960592762359 / 5000000000000000 : ℝ) = - (588960592762359 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (588960592762359 / 312500000000000 : ℚ)) - (U := (6337548069098047717167 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (588960592762359 / 312500000000000 : ℝ) ≤ - (6337548069098047717167 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (266958234251109 / 2500000000000000 : ℝ)) (q := - (588960592762359 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (588960592762359 / 5000000000000000 : ℚ)) + (r' := (588960592762359 / 312500000000000 : ℚ)) + (U := (-(21388339142901952282833 / 10000000000000000000000 : ℚ))) + (U' := (6337548069098047717167 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (201105762729 / 1000000000000 : ℚ)) + (s := (266958234251109 / 2500000000000000 : ℚ)) + (q := (588960592762359 / 5000000000000000 : ℚ)) + (U := (-(21388339142901952282833 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_241_8 : Uω (aρ 8) (bρ 8) (201105762729 / 1000000000000 : ℝ) ≤ @@ -3133,25 +2856,21 @@ lemma U_242_1 : have hlg : Real.log (3935606651718043 / 20000000000000000 : ℝ) ≤ (-(16256672346253327359079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3935606651718043 / 20000000000000000 : ℝ) = - (3935606651718043 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3935606651718043 / 2500000000000000 : ℚ)) - (U := (4537743062746672640921 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3935606651718043 / 2500000000000000 : ℝ) ≤ - (4537743062746672640921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (491930292333417 / 2500000000000000 : ℝ)) (q := - (3935606651718043 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3935606651718043 / 20000000000000000 : ℚ)) + (r' := (3935606651718043 / 2500000000000000 : ℚ)) + (U := (-(16256672346253327359079 / 10000000000000000000000 : ℚ))) + (U' := (4537743062746672640921 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (491930292333417 / 2500000000000000 : ℚ)) + (q := (3935606651718043 / 20000000000000000 : ℚ)) + (U := (-(16256672346253327359079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_2 : Uω (aρ 2) (bρ 2) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3159,25 +2878,21 @@ lemma U_242_2 : have hlg : Real.log (3887141209948259 / 20000000000000000 : ℝ) ≤ (-(16380582927889856239697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3887141209948259 / 20000000000000000 : ℝ) = - (3887141209948259 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3887141209948259 / 2500000000000000 : ℚ)) - (U := (4413832481110143760303 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3887141209948259 / 2500000000000000 : ℝ) ≤ - (4413832481110143760303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (485756185018471 / 2500000000000000 : ℝ)) (q := - (3887141209948259 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3887141209948259 / 20000000000000000 : ℚ)) + (r' := (3887141209948259 / 2500000000000000 : ℚ)) + (U := (-(16380582927889856239697 / 10000000000000000000000 : ℚ))) + (U' := (4413832481110143760303 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (485756185018471 / 2500000000000000 : ℚ)) + (q := (3887141209948259 / 20000000000000000 : ℚ)) + (U := (-(16380582927889856239697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_3 : Uω (aρ 3) (bρ 3) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3185,25 +2900,21 @@ lemma U_242_3 : have hlg : Real.log (757907249819311 / 4000000000000000 : ℝ) ≤ (-(8317443114412870681471 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (757907249819311 / 4000000000000000 : ℝ) = - (757907249819311 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (757907249819311 / 500000000000000 : ℚ)) - (U := (2079764590087129318529 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (757907249819311 / 500000000000000 : ℝ) ≤ - (2079764590087129318529 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (94640794278609 / 500000000000000 : ℝ)) (q := - (757907249819311 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (757907249819311 / 4000000000000000 : ℚ)) + (r' := (757907249819311 / 500000000000000 : ℚ)) + (U := (-(8317443114412870681471 / 5000000000000000000000 : ℚ))) + (U' := (2079764590087129318529 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (94640794278609 / 500000000000000 : ℚ)) + (q := (757907249819311 / 4000000000000000 : ℚ)) + (U := (-(8317443114412870681471 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_4 : Uω (aρ 4) (bρ 4) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3211,25 +2922,21 @@ lemma U_242_4 : have hlg : Real.log (3625244287093789 / 20000000000000000 : ℝ) ≤ (-(17078105971949760117981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3625244287093789 / 20000000000000000 : ℝ) = - (3625244287093789 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3625244287093789 / 2500000000000000 : ℚ)) - (U := (3716309437050239882019 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3625244287093789 / 2500000000000000 : ℝ) ≤ - (3716309437050239882019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (903409052317207 / 5000000000000000 : ℝ)) (q := - (3625244287093789 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3625244287093789 / 20000000000000000 : ℚ)) + (r' := (3625244287093789 / 2500000000000000 : ℚ)) + (U := (-(17078105971949760117981 / 10000000000000000000000 : ℚ))) + (U' := (3716309437050239882019 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (903409052317207 / 5000000000000000 : ℚ)) + (q := (3625244287093789 / 20000000000000000 : ℚ)) + (U := (-(17078105971949760117981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_5 : Uω (aρ 5) (bρ 5) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3237,25 +2944,21 @@ lemma U_242_5 : have hlg : Real.log (673771066028203 / 4000000000000000 : ℝ) ≤ (-(17811592507555697950333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (673771066028203 / 4000000000000000 : ℝ) = - (673771066028203 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (673771066028203 / 500000000000000 : ℚ)) - (U := (2982822901444302049667 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (673771066028203 / 500000000000000 : ℝ) ≤ - (2982822901444302049667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5214434584427 / 31250000000000 : ℝ)) (q := - (673771066028203 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (673771066028203 / 4000000000000000 : ℚ)) + (r' := (673771066028203 / 500000000000000 : ℚ)) + (U := (-(17811592507555697950333 / 10000000000000000000000 : ℚ))) + (U' := (2982822901444302049667 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (5214434584427 / 31250000000000 : ℚ)) + (q := (673771066028203 / 4000000000000000 : ℚ)) + (U := (-(17811592507555697950333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_6 : Uω (aρ 6) (bρ 6) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3263,25 +2966,21 @@ lemma U_242_6 : have hlg : Real.log (596746166723221 / 4000000000000000 : ℝ) ≤ (-(9512788988564780394523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (596746166723221 / 4000000000000000 : ℝ) = - (596746166723221 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (596746166723221 / 500000000000000 : ℚ)) - (U := (884418715935219605477 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (596746166723221 / 500000000000000 : ℝ) ≤ - (884418715935219605477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (145073494563173 / 1000000000000000 : ℝ)) (q := - (596746166723221 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (596746166723221 / 4000000000000000 : ℚ)) + (r' := (596746166723221 / 500000000000000 : ℚ)) + (U := (-(9512788988564780394523 / 5000000000000000000000 : ℚ))) + (U' := (884418715935219605477 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (145073494563173 / 1000000000000000 : ℚ)) + (q := (596746166723221 / 4000000000000000 : ℚ)) + (U := (-(9512788988564780394523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_7 : Uω (aρ 7) (bρ 7) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3289,25 +2988,21 @@ lemma U_242_7 : have hlg : Real.log (480558989182049 / 4000000000000000 : ℝ) ≤ (-(21190996519392976753163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (480558989182049 / 4000000000000000 : ℝ) = - (480558989182049 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (480558989182049 / 250000000000000 : ℚ)) - (U := (6534890692607023246837 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (480558989182049 / 250000000000000 : ℝ) ≤ - (6534890692607023246837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109346043868587 / 1000000000000000 : ℝ)) (q := - (480558989182049 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (480558989182049 / 4000000000000000 : ℚ)) + (r' := (480558989182049 / 250000000000000 : ℚ)) + (U := (-(21190996519392976753163 / 10000000000000000000000 : ℚ))) + (U' := (6534890692607023246837 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (109346043868587 / 1000000000000000 : ℚ)) + (q := (480558989182049 / 4000000000000000 : ℚ)) + (U := (-(21190996519392976753163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_8 : Uω (aρ 8) (bρ 8) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3315,25 +3010,21 @@ lemma U_242_8 : have hlg : Real.log (616934229595149 / 10000000000000000 : ℝ) ≤ (-(13927889747717311336039 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 5 - (show - (616934229595149 / 10000000000000000 : ℝ) = - (616934229595149 / 312500000000000 : ℝ) / 2 ^ 5 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (616934229595149 / 312500000000000 : ℚ)) - (U := (3400789759782688663961 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (616934229595149 / 312500000000000 : ℝ) ≤ - (3400789759782688663961 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (208075603305923 / 10000000000000000 : ℝ)) (q := - (616934229595149 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (616934229595149 / 10000000000000000 : ℚ)) + (r' := (616934229595149 / 312500000000000 : ℚ)) + (U := (-(13927889747717311336039 / 5000000000000000000000 : ℚ))) + (U' := (3400789759782688663961 / 5000000000000000000000 : ℚ)) + 5 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3251812320751 / 16000000000000 : ℚ)) + (s := (208075603305923 / 10000000000000000 : ℚ)) + (q := (616934229595149 / 10000000000000000 : ℚ)) + (U := (-(13927889747717311336039 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_242_9 : Uω (aρ 9) (bρ 9) (3251812320751 / 16000000000000 : ℝ) ≤ @@ -3466,25 +3157,21 @@ lemma U_243_1 : have hlg : Real.log (3978258559718229 / 20000000000000000 : ℝ) ≤ (-(16148880970392734533323 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3978258559718229 / 20000000000000000 : ℝ) = - (3978258559718229 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3978258559718229 / 2500000000000000 : ℚ)) - (U := (4645534438607265466677 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3978258559718229 / 2500000000000000 : ℝ) ≤ - (4645534438607265466677 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1989048004154479 / 10000000000000000 : ℝ)) (q := - (3978258559718229 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3978258559718229 / 20000000000000000 : ℚ)) + (r' := (3978258559718229 / 2500000000000000 : ℚ)) + (U := (-(16148880970392734533323 / 10000000000000000000000 : ℚ))) + (U' := (4645534438607265466677 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1989048004154479 / 10000000000000000 : ℚ)) + (q := (3978258559718229 / 20000000000000000 : ℚ)) + (U := (-(16148880970392734533323 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_2 : Uω (aρ 2) (bρ 2) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3492,25 +3179,21 @@ lemma U_243_2 : have hlg : Real.log (3929803208140881 / 20000000000000000 : ℝ) ≤ (-(16271429224111498996607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3929803208140881 / 20000000000000000 : ℝ) = - (3929803208140881 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3929803208140881 / 2500000000000000 : ℚ)) - (U := (4522986184888501003393 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3929803208140881 / 2500000000000000 : ℝ) ≤ - (4522986184888501003393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1964361665087131 / 10000000000000000 : ℝ)) (q := - (3929803208140881 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3929803208140881 / 20000000000000000 : ℚ)) + (r' := (3929803208140881 / 2500000000000000 : ℚ)) + (U := (-(16271429224111498996607 / 10000000000000000000000 : ℚ))) + (U' := (4522986184888501003393 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1964361665087131 / 10000000000000000 : ℚ)) + (q := (3929803208140881 / 20000000000000000 : ℚ)) + (U := (-(16271429224111498996607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_3 : Uω (aρ 3) (bρ 3) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3518,25 +3201,21 @@ lemma U_243_3 : have hlg : Real.log (3832229893992659 / 20000000000000000 : ℝ) ≤ (-(16522854212519461836571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3832229893992659 / 20000000000000000 : ℝ) = - (3832229893992659 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3832229893992659 / 2500000000000000 : ℚ)) - (U := (4271561196480538163429 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3832229893992659 / 2500000000000000 : ℝ) ≤ - (4271561196480538163429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1914184457288909 / 10000000000000000 : ℝ)) (q := - (3832229893992659 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3832229893992659 / 20000000000000000 : ℚ)) + (r' := (3832229893992659 / 2500000000000000 : ℚ)) + (U := (-(16522854212519461836571 / 10000000000000000000000 : ℚ))) + (U' := (4271561196480538163429 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1914184457288909 / 10000000000000000 : ℚ)) + (q := (3832229893992659 / 20000000000000000 : ℚ)) + (U := (-(16522854212519461836571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_4 : Uω (aρ 4) (bρ 4) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3544,25 +3223,21 @@ lemma U_243_4 : have hlg : Real.log (3668029835288273 / 20000000000000000 : ℝ) ≤ (-(16960775844740112262383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3668029835288273 / 20000000000000000 : ℝ) = - (3668029835288273 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3668029835288273 / 2500000000000000 : ℚ)) - (U := (3833639564259887737617 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3668029835288273 / 2500000000000000 : ℝ) ≤ - (3833639564259887737617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1828278579649523 / 10000000000000000 : ℝ)) (q := - (3668029835288273 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3668029835288273 / 20000000000000000 : ℚ)) + (r' := (3668029835288273 / 2500000000000000 : ℚ)) + (U := (-(16960775844740112262383 / 10000000000000000000000 : ℚ))) + (U' := (3833639564259887737617 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1828278579649523 / 10000000000000000 : ℚ)) + (q := (3668029835288273 / 20000000000000000 : ℚ)) + (U := (-(16960775844740112262383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_5 : Uω (aρ 5) (bρ 5) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3570,25 +3245,21 @@ lemma U_243_5 : have hlg : Real.log (3411904400602917 / 20000000000000000 : ℝ) ≤ (-(8842308310589361790873 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3411904400602917 / 20000000000000000 : ℝ) = - (3411904400602917 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3411904400602917 / 2500000000000000 : ℚ)) - (U := (1554899393910638209127 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3411904400602917 / 2500000000000000 : ℝ) ≤ - (1554899393910638209127 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1690343064299167 / 10000000000000000 : ℝ)) (q := - (3411904400602917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3411904400602917 / 20000000000000000 : ℚ)) + (r' := (3411904400602917 / 2500000000000000 : ℚ)) + (U := (-(8842308310589361790873 / 5000000000000000000000 : ℚ))) + (U' := (1554899393910638209127 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1690343064299167 / 10000000000000000 : ℚ)) + (q := (3411904400602917 / 20000000000000000 : ℚ)) + (U := (-(8842308310589361790873 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_6 : Uω (aρ 6) (bρ 6) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3596,25 +3267,21 @@ lemma U_243_6 : have hlg : Real.log (3027572175387957 / 20000000000000000 : ℝ) ≤ (-(3775942473366500779873 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3027572175387957 / 20000000000000000 : ℝ) = - (3027572175387957 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3027572175387957 / 2500000000000000 : ℚ)) - (U := (382940608433499220127 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3027572175387957 / 2500000000000000 : ℝ) ≤ - (382940608433499220127 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1473251214224207 / 10000000000000000 : ℝ)) (q := - (3027572175387957 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3027572175387957 / 20000000000000000 : ℚ)) + (r' := (3027572175387957 / 2500000000000000 : ℚ)) + (U := (-(3775942473366500779873 / 2000000000000000000000 : ℚ))) + (U' := (382940608433499220127 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (1473251214224207 / 10000000000000000 : ℚ)) + (q := (3027572175387957 / 20000000000000000 : ℚ)) + (U := (-(3775942473366500779873 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_7 : Uω (aρ 7) (bρ 7) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3622,25 +3289,21 @@ lemma U_243_7 : have hlg : Real.log (489913398610729 / 4000000000000000 : ℝ) ≤ (-(20998210011066161697331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (489913398610729 / 4000000000000000 : ℝ) = - (489913398610729 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (489913398610729 / 250000000000000 : ℚ)) - (U := (6727677200933838302669 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (489913398610729 / 250000000000000 : ℝ) ≤ - (6727677200933838302669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (223781482529979 / 2000000000000000 : ℝ)) (q := - (489913398610729 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (489913398610729 / 4000000000000000 : ℚ)) + (r' := (489913398610729 / 250000000000000 : ℚ)) + (U := (-(20998210011066161697331 / 10000000000000000000000 : ℚ))) + (U' := (6727677200933838302669 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (223781482529979 / 2000000000000000 : ℚ)) + (q := (489913398610729 / 4000000000000000 : ℚ)) + (U := (-(20998210011066161697331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_8 : Uω (aρ 8) (bρ 8) (1642966218919 / 8000000000000 : ℝ) ≤ @@ -3648,25 +3311,21 @@ lemma U_243_8 : have hlg : Real.log (671461323264299 / 10000000000000000 : ℝ) ≤ (-(270088395415343064811 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (671461323264299 / 10000000000000000 : ℝ) = - (671461323264299 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (671461323264299 / 625000000000000 : ℚ)) - (U := (7170476704656935189 / 100000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (671461323264299 / 625000000000000 : ℝ) ≤ - (7170476704656935189 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18487794841553 / 625000000000000 : ℝ)) (q := - (671461323264299 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (671461323264299 / 10000000000000000 : ℚ)) + (r' := (671461323264299 / 625000000000000 : ℚ)) + (U := (-(270088395415343064811 / 100000000000000000000 : ℚ))) + (U' := (7170476704656935189 / 100000000000000000000 : ℚ)) + 4 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1642966218919 / 8000000000000 : ℚ)) + (s := (18487794841553 / 625000000000000 : ℚ)) + (q := (671461323264299 / 10000000000000000 : ℚ)) + (U := (-(270088395415343064811 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_243_9 : Uω (aρ 9) (bρ 9) (1642966218919 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U20.lean b/LeanPool/Zeta5Irrational/Table/U20.lean index 71cadad142..2730ce2315 100644 --- a/LeanPool/Zeta5Irrational/Table/U20.lean +++ b/LeanPool/Zeta5Irrational/Table/U20.lean @@ -24,25 +24,21 @@ lemma U_244_1 : have hlg : Real.log (4020910430343609 / 20000000000000000 : ℝ) ≤ (-(80211196028750566739 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4020910430343609 / 20000000000000000 : ℝ) = - (4020910430343609 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4020910430343609 / 2500000000000000 : ℚ)) - (U := (23760881016249433261 / 50000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4020910430343609 / 2500000000000000 : ℝ) ≤ - (23760881016249433261 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (502593700400121 / 2500000000000000 : ℝ)) (q := - (4020910430343609 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4020910430343609 / 20000000000000000 : ℚ)) + (r' := (4020910430343609 / 2500000000000000 : ℚ)) + (U := (-(80211196028750566739 / 50000000000000000000 : ℚ))) + (U' := (23760881016249433261 / 50000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (132802102197 / 640000000000 : ℚ)) + (s := (502593700400121 / 2500000000000000 : ℚ)) + (q := (4020910430343609 / 20000000000000000 : ℚ)) + (U := (-(80211196028750566739 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_2 : Uω (aρ 2) (bρ 2) (132802102197 / 640000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_244_2 : have hlg : Real.log (397246495170123 / 2000000000000000 : ℝ) ≤ (-(1010215922572068434639 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (397246495170123 / 2000000000000000 : ℝ) = - (397246495170123 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (397246495170123 / 250000000000000 : ℚ)) - (U := (289435040490431565361 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (397246495170123 / 250000000000000 : ℝ) ≤ - (289435040490431565361 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397139667093621 / 2000000000000000 : ℝ)) (q := - (397246495170123 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (397246495170123 / 2000000000000000 : ℚ)) + (r' := (397246495170123 / 250000000000000 : ℚ)) + (U := (-(1010215922572068434639 / 625000000000000000000 : ℚ))) + (U' := (289435040490431565361 / 625000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (132802102197 / 640000000000 : ℚ)) + (s := (397139667093621 / 2000000000000000 : ℚ)) + (q := (397246495170123 / 2000000000000000 : ℚ)) + (U := (-(1010215922572068434639 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_3 : Uω (aρ 3) (bρ 3) (132802102197 / 640000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_244_3 : have hlg : Real.log (968730644853851 / 5000000000000000 : ℝ) ≤ (-(8206032948370699617277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (968730644853851 / 5000000000000000 : ℝ) = - (968730644853851 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (968730644853851 / 625000000000000 : ℚ)) - (U := (2191174756129300382723 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (968730644853851 / 625000000000000 : ℝ) ≤ - (2191174756129300382723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1935552069532279 / 10000000000000000 : ℝ)) (q := - (968730644853851 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (968730644853851 / 5000000000000000 : ℚ)) + (r' := (968730644853851 / 625000000000000 : ℚ)) + (U := (-(8206032948370699617277 / 5000000000000000000000 : ℚ))) + (U' := (2191174756129300382723 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (132802102197 / 640000000000 : ℚ)) + (s := (1935552069532279 / 10000000000000000 : ℚ)) + (q := (968730644853851 / 5000000000000000 : ℚ)) + (U := (-(8206032948370699617277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_4 : Uω (aρ 4) (bρ 4) (132802102197 / 640000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_244_4 : have hlg : Real.log (1855406125778153 / 10000000000000000 : ℝ) ≤ (-(8422407421941390401861 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1855406125778153 / 10000000000000000 : ℝ) = - (1855406125778153 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1855406125778153 / 1250000000000000 : ℚ)) - (U := (1974800282558609598139 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1855406125778153 / 1250000000000000 : ℝ) ≤ - (1974800282558609598139 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1849735922738181 / 10000000000000000 : ℝ)) (q := - (1855406125778153 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1855406125778153 / 10000000000000000 : ℚ)) + (r' := (1855406125778153 / 1250000000000000 : ℚ)) + (U := (-(8422407421941390401861 / 5000000000000000000000 : ℚ))) + (U' := (1974800282558609598139 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (132802102197 / 640000000000 : ℚ)) + (s := (1849735922738181 / 10000000000000000 : ℚ)) + (q := (1855406125778153 / 10000000000000000 : ℚ)) + (U := (-(8422407421941390401861 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_5 : Uω (aρ 5) (bρ 5) (132802102197 / 640000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_244_5 : have hlg : Real.log (863735860072067 / 5000000000000000 : ℝ) ≤ (-(877963093041325964747 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (863735860072067 / 5000000000000000 : ℝ) = - (863735860072067 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (863735860072067 / 625000000000000 : ℚ)) - (U := (161757677408674035253 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (863735860072067 / 625000000000000 : ℝ) ≤ - (161757677408674035253 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1712057030805143 / 10000000000000000 : ℝ)) (q := - (863735860072067 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (863735860072067 / 5000000000000000 : ℚ)) + (r' := (863735860072067 / 625000000000000 : ℚ)) + (U := (-(877963093041325964747 / 500000000000000000000 : ℚ))) + (U' := (161757677408674035253 / 500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (132802102197 / 640000000000 : ℚ)) + (s := (1712057030805143 / 10000000000000000 : ℚ)) + (q := (863735860072067 / 5000000000000000 : ℚ)) + (U := (-(877963093041325964747 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_6 : Uω (aρ 6) (bρ 6) (132802102197 / 640000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_244_6 : have hlg : Real.log (1535689301249357 / 10000000000000000 : ℝ) ≤ (-(4684014389455247979343 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1535689301249357 / 10000000000000000 : ℝ) = - (1535689301249357 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1535689301249357 / 1250000000000000 : ℚ)) - (U := (514589462794752020657 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1535689301249357 / 1250000000000000 : ℝ) ≤ - (514589462794752020657 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1495732568155589 / 10000000000000000 : ℝ)) (q := - (1535689301249357 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1535689301249357 / 10000000000000000 : ℚ)) + (r' := (1535689301249357 / 1250000000000000 : ℚ)) + (U := (-(4684014389455247979343 / 2500000000000000000000 : ℚ))) + (U' := (514589462794752020657 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (132802102197 / 640000000000 : ℚ)) + (s := (1495732568155589 / 10000000000000000 : ℚ)) + (q := (1535689301249357 / 10000000000000000 : ℚ)) + (U := (-(4684014389455247979343 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_7 : Uω (aρ 7) (bρ 7) (132802102197 / 640000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_244_7 : have hlg : Real.log (124808527874231 / 1000000000000000 : ℝ) ≤ (-(20809744920160066222079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (124808527874231 / 1000000000000000 : ℝ) = - (124808527874231 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (124808527874231 / 62500000000000 : ℚ)) - (U := (6916142291839933777921 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (124808527874231 / 62500000000000 : ℝ) ≤ - (6916142291839933777921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228837180780299 / 2000000000000000 : ℝ)) (q := - (124808527874231 / 1000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (124808527874231 / 1000000000000000 : ℚ)) + (r' := (124808527874231 / 62500000000000 : ℚ)) + (U := (-(20809744920160066222079 / 10000000000000000000000 : ℚ))) + (U' := (6916142291839933777921 / 10000000000000000000000 : ℚ)) + 4 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (132802102197 / 640000000000 : ℚ)) + (s := (228837180780299 / 2000000000000000 : ℚ)) + (q := (124808527874231 / 1000000000000000 : ℚ)) + (U := (-(20809744920160066222079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_8 : Uω (aρ 8) (bρ 8) (132802102197 / 640000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_244_8 : have hlg : Real.log (1432606320755581 / 20000000000000000 : ℝ) ≤ (-(26362368852389073231951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1432606320755581 / 20000000000000000 : ℝ) = - (1432606320755581 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1432606320755581 / 1250000000000000 : ℚ)) - (U := (1363518359610926768049 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1432606320755581 / 1250000000000000 : ℝ) ≤ - (1363518359610926768049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45520414814057 / 1250000000000000 : ℝ)) (q := - (1432606320755581 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1432606320755581 / 20000000000000000 : ℚ)) + (r' := (1432606320755581 / 1250000000000000 : ℚ)) + (U := (-(26362368852389073231951 / 10000000000000000000000 : ℚ))) + (U' := (1363518359610926768049 / 10000000000000000000000 : ℚ)) + 4 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (132802102197 / 640000000000 : ℚ)) + (s := (45520414814057 / 1250000000000000 : ℚ)) + (q := (1432606320755581 / 20000000000000000 : ℚ)) + (U := (-(26362368852389073231951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_244_9 : Uω (aρ 9) (bρ 9) (132802102197 / 640000000000 : ℝ) ≤ @@ -355,25 +323,21 @@ lemma U_245_1 : have hlg : Real.log (8084472704020983 / 40000000000000000 : ℝ) ≤ (-(15989341814769083441683 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8084472704020983 / 40000000000000000 : ℝ) = - (8084472704020983 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8084472704020983 / 5000000000000000 : ℚ)) - (U := (4805073594230916558317 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8084472704020983 / 5000000000000000 : ℝ) ≤ - (4805073594230916558317 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2021038186677679 / 10000000000000000 : ℝ)) (q := - (8084472704020983 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8084472704020983 / 40000000000000000 : ℚ)) + (r' := (8084472704020983 / 5000000000000000 : ℚ)) + (U := (-(15989341814769083441683 / 10000000000000000000000 : ℚ))) + (U' := (4805073594230916558317 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (2021038186677679 / 10000000000000000 : ℚ)) + (q := (8084472704020983 / 40000000000000000 : ℚ)) + (U := (-(15989341814769083441683 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_2 : Uω (aρ 2) (bρ 2) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -381,25 +345,21 @@ lemma U_245_2 : have hlg : Real.log (7987591461091323 / 40000000000000000 : ℝ) ≤ (-(251717216120021689271 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7987591461091323 / 40000000000000000 : ℝ) = - (7987591461091323 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7987591461091323 / 5000000000000000 : ℚ)) - (U := (73195524645603310729 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7987591461091323 / 5000000000000000 : ℝ) ≤ - (73195524645603310729 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1996366577722849 / 10000000000000000 : ℝ)) (q := - (7987591461091323 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7987591461091323 / 40000000000000000 : ℚ)) + (r' := (7987591461091323 / 5000000000000000 : ℚ)) + (U := (-(251717216120021689271 / 156250000000000000000 : ℚ))) + (U' := (73195524645603310729 / 156250000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (1996366577722849 / 10000000000000000 : ℚ)) + (q := (7987591461091323 / 40000000000000000 : ℚ)) + (U := (-(251717216120021689271 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_3 : Uω (aρ 3) (bρ 3) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -407,25 +367,21 @@ lemma U_245_3 : have hlg : Real.log (1558507428879981 / 8000000000000000 : ℝ) ≤ (-(16357129540002021346027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1558507428879981 / 8000000000000000 : ℝ) = - (1558507428879981 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1558507428879981 / 1000000000000000 : ℚ)) - (U := (4437285868997978653973 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1558507428879981 / 1000000000000000 : ℝ) ≤ - (4437285868997978653973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (97311776286357 / 500000000000000 : ℝ)) (q := - (1558507428879981 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1558507428879981 / 8000000000000000 : ℚ)) + (r' := (1558507428879981 / 1000000000000000 : ℚ)) + (U := (-(16357129540002021346027 / 10000000000000000000000 : ℚ))) + (U' := (4437285868997978653973 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (97311776286357 / 500000000000000 : ℚ)) + (q := (1558507428879981 / 8000000000000000 : ℚ)) + (U := (-(16357129540002021346027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_4 : Uω (aρ 4) (bρ 4) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -433,25 +389,21 @@ lemma U_245_4 : have hlg : Real.log (1492880927632989 / 8000000000000000 : ℝ) ≤ (-(839366889642839072517 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1492880927632989 / 8000000000000000 : ℝ) = - (1492880927632989 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1492880927632989 / 1000000000000000 : ℚ)) - (U := (200353880807160927483 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1492880927632989 / 1000000000000000 : ℝ) ≤ - (200353880807160927483 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (93023172683733 / 500000000000000 : ℝ)) (q := - (1492880927632989 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1492880927632989 / 8000000000000000 : ℚ)) + (r' := (1492880927632989 / 1000000000000000 : ℚ)) + (U := (-(839366889642839072517 / 500000000000000000000 : ℚ))) + (U' := (200353880807160927483 / 500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (93023172683733 / 500000000000000 : ℚ)) + (q := (1492880927632989 / 8000000000000000 : ℚ)) + (U := (-(839366889642839072517 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_5 : Uω (aρ 5) (bρ 5) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -459,25 +411,21 @@ lemma U_245_5 : have hlg : Real.log (6952918634228077 / 40000000000000000 : ℝ) ≤ (-(8748589672698357586477 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6952918634228077 / 40000000000000000 : ℝ) = - (6952918634228077 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6952918634228077 / 5000000000000000 : ℚ)) - (U := (1648618031801642413523 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6952918634228077 / 5000000000000000 : ℝ) ≤ - (1648618031801642413523 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (861455185520613 / 5000000000000000 : ℝ)) (q := - (6952918634228077 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6952918634228077 / 40000000000000000 : ℚ)) + (r' := (6952918634228077 / 5000000000000000 : ℚ)) + (U := (-(8748589672698357586477 / 5000000000000000000000 : ℚ))) + (U' := (1648618031801642413523 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (861455185520613 / 5000000000000000 : ℚ)) + (q := (6952918634228077 / 40000000000000000 : ℚ)) + (U := (-(8748589672698357586477 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_6 : Uω (aρ 6) (bρ 6) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -485,25 +433,21 @@ lemma U_245_6 : have hlg : Real.log (6186538422931207 / 40000000000000000 : ℝ) ≤ (-(18665037439110731528699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6186538422931207 / 40000000000000000 : ℝ) = - (6186538422931207 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6186538422931207 / 5000000000000000 : ℚ)) - (U := (2129377969889268471301 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6186538422931207 / 5000000000000000 : ℝ) ≤ - (2129377969889268471301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1506960640532791 / 10000000000000000 : ℝ)) (q := - (6186538422931207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6186538422931207 / 40000000000000000 : ℚ)) + (r' := (6186538422931207 / 5000000000000000 : ℚ)) + (U := (-(18665037439110731528699 / 10000000000000000000000 : ℚ))) + (U' := (2129377969889268471301 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (1506960640532791 / 10000000000000000 : ℚ)) + (q := (6186538422931207 / 40000000000000000 : ℚ)) + (U := (-(18665037439110731528699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_7 : Uω (aρ 7) (bρ 7) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -511,25 +455,21 @@ lemma U_245_7 : have hlg : Real.log (5038825226518599 / 40000000000000000 : ℝ) ≤ (-(129481655524811388393 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5038825226518599 / 40000000000000000 : ℝ) = - (5038825226518599 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5038825226518599 / 5000000000000000 : ℚ)) - (U := (483440781438611607 / 62500000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5038825226518599 / 5000000000000000 : ℝ) ≤ - (483440781438611607 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1156765423086487 / 10000000000000000 : ℝ)) (q := - (5038825226518599 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5038825226518599 / 40000000000000000 : ℚ)) + (r' := (5038825226518599 / 5000000000000000 : ℚ)) + (U := (-(129481655524811388393 / 62500000000000000000 : ℚ))) + (U' := (483440781438611607 / 62500000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (1156765423086487 / 10000000000000000 : ℚ)) + (q := (5038825226518599 / 40000000000000000 : ℚ)) + (U := (-(129481655524811388393 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_8 : Uω (aρ 8) (bρ 8) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -537,25 +477,21 @@ lemma U_245_8 : have hlg : Real.log (117876576485053 / 1600000000000000 : ℝ) ≤ (-(26081207921134859408713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (117876576485053 / 1600000000000000 : ℝ) = - (117876576485053 / 100000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (117876576485053 / 100000000000000 : ℚ)) - (U := (1644679290865140591287 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (117876576485053 / 100000000000000 : ℝ) ≤ - (1644679290865140591287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7887033344607 / 200000000000000 : ℝ)) (q := - (117876576485053 / 1600000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (117876576485053 / 1600000000000000 : ℚ)) + (r' := (117876576485053 / 100000000000000 : ℚ)) + (U := (-(26081207921134859408713 / 10000000000000000000000 : ℚ))) + (U' := (1644679290865140591287 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6674225226937 / 32000000000000 : ℚ)) + (s := (7887033344607 / 200000000000000 : ℚ)) + (q := (117876576485053 / 1600000000000000 : ℚ)) + (U := (-(26081207921134859408713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_245_9 : Uω (aρ 9) (bρ 9) (6674225226937 / 32000000000000 : ℝ) ≤ @@ -686,25 +622,21 @@ lemma U_246_1 : have hlg : Real.log (812712452954231 / 4000000000000000 : ℝ) ≤ (-(1992090348424161097649 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (812712452954231 / 4000000000000000 : ℝ) = - (812712452954231 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (812712452954231 / 500000000000000 : ℚ)) - (U := (607211577700838902351 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (812712452954231 / 500000000000000 : ℝ) ≤ - (607211577700838902351 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (406340312569731 / 2000000000000000 : ℝ)) (q := - (812712452954231 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (812712452954231 / 4000000000000000 : ℚ)) + (r' := (812712452954231 / 500000000000000 : ℚ)) + (U := (-(1992090348424161097649 / 1250000000000000000000 : ℚ))) + (U' := (607211577700838902351 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (406340312569731 / 2000000000000000 : ℚ)) + (q := (812712452954231 / 4000000000000000 : ℚ)) + (U := (-(1992090348424161097649 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_2 : Uω (aρ 2) (bρ 2) (838543168003 / 4000000000000 : ℝ) ≤ @@ -712,25 +644,21 @@ lemma U_246_2 : have hlg : Real.log (4015126448750247 / 20000000000000000 : ℝ) ≤ (-(8028317158933071913149 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4015126448750247 / 20000000000000000 : ℝ) = - (4015126448750247 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4015126448750247 / 2500000000000000 : ℚ)) - (U := (2368890545566928086851 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4015126448750247 / 2500000000000000 : ℝ) ≤ - (2368890545566928086851 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2007034759337747 / 10000000000000000 : ℝ)) (q := - (4015126448750247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4015126448750247 / 20000000000000000 : ℚ)) + (r' := (4015126448750247 / 2500000000000000 : ℚ)) + (U := (-(8028317158933071913149 / 5000000000000000000000 : ℚ))) + (U' := (2368890545566928086851 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (2007034759337747 / 10000000000000000 : ℚ)) + (q := (4015126448750247 / 20000000000000000 : ℚ)) + (U := (-(8028317158933071913149 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_3 : Uω (aρ 3) (bρ 3) (838543168003 / 4000000000000 : ℝ) ≤ @@ -738,25 +666,21 @@ lemma U_246_3 : have hlg : Real.log (3917614336794283 / 20000000000000000 : ℝ) ≤ (-(4075623479472093816281 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3917614336794283 / 20000000000000000 : ℝ) = - (3917614336794283 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3917614336794283 / 2500000000000000 : ℚ)) - (U := (1122980372777906183719 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3917614336794283 / 2500000000000000 : ℝ) ≤ - (1122980372777906183719 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1956918753731783 / 10000000000000000 : ℝ)) (q := - (3917614336794283 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3917614336794283 / 20000000000000000 : ℚ)) + (r' := (3917614336794283 / 2500000000000000 : ℚ)) + (U := (-(4075623479472093816281 / 2500000000000000000000 : ℚ))) + (U' := (1122980372777906183719 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (1956918753731783 / 10000000000000000 : ℚ)) + (q := (3917614336794283 / 20000000000000000 : ℚ)) + (U := (-(4075623479472093816281 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_4 : Uω (aρ 4) (bρ 4) (838543168003 / 4000000000000 : ℝ) ≤ @@ -764,25 +688,21 @@ lemma U_246_4 : have hlg : Real.log (938397910910331 / 5000000000000000 : ℝ) ≤ (-(16730191195247513018179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (938397910910331 / 5000000000000000 : ℝ) = - (938397910910331 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (938397910910331 / 625000000000000 : ℚ)) - (U := (4064224213752486981821 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (938397910910331 / 625000000000000 : ℝ) ≤ - (4064224213752486981821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (116949390102739 / 625000000000000 : ℝ)) (q := - (938397910910331 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (938397910910331 / 5000000000000000 : ℚ)) + (r' := (938397910910331 / 625000000000000 : ℚ)) + (U := (-(16730191195247513018179 / 10000000000000000000000 : ℚ))) + (U' := (4064224213752486981821 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (116949390102739 / 625000000000000 : ℚ)) + (q := (938397910910331 / 5000000000000000 : ℚ)) + (U := (-(16730191195247513018179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_5 : Uω (aρ 5) (bρ 5) (838543168003 / 4000000000000 : ℝ) ≤ @@ -790,25 +710,21 @@ lemma U_246_5 : have hlg : Real.log (1748986413039669 / 10000000000000000 : ℝ) ≤ (-(8717743323121730710593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1748986413039669 / 10000000000000000 : ℝ) = - (1748986413039669 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1748986413039669 / 1250000000000000 : ℚ)) - (U := (1679464381378269289407 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1748986413039669 / 1250000000000000 : ℝ) ≤ - (1679464381378269289407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (866880671708419 / 5000000000000000 : ℝ)) (q := - (1748986413039669 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1748986413039669 / 10000000000000000 : ℚ)) + (r' := (1748986413039669 / 1250000000000000 : ℚ)) + (U := (-(8717743323121730710593 / 5000000000000000000000 : ℚ))) + (U' := (1679464381378269289407 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (866880671708419 / 5000000000000000 : ℚ)) + (q := (1748986413039669 / 10000000000000000 : ℚ)) + (U := (-(8717743323121730710593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_6 : Uω (aρ 6) (bρ 6) (838543168003 / 4000000000000 : ℝ) ≤ @@ -816,25 +732,21 @@ lemma U_246_6 : have hlg : Real.log (3115151666007471 / 20000000000000000 : ℝ) ≤ (-(18594544327930489474517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3115151666007471 / 20000000000000000 : ℝ) = - (3115151666007471 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3115151666007471 / 2500000000000000 : ℚ)) - (U := (2199871081069510525483 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3115151666007471 / 2500000000000000 : ℝ) ≤ - (2199871081069510525483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1518180558484971 / 10000000000000000 : ℝ)) (q := - (3115151666007471 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3115151666007471 / 20000000000000000 : ℚ)) + (r' := (3115151666007471 / 2500000000000000 : ℚ)) + (U := (-(18594544327930489474517 / 10000000000000000000000 : ℚ))) + (U' := (2199871081069510525483 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (1518180558484971 / 10000000000000000 : ℚ)) + (q := (3115151666007471 / 20000000000000000 : ℚ)) + (U := (-(18594544327930489474517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_7 : Uω (aρ 7) (bρ 7) (838543168003 / 4000000000000 : ℝ) ≤ @@ -842,25 +754,21 @@ lemma U_246_7 : have hlg : Real.log (2542616566211877 / 20000000000000000 : ℝ) ≤ (-(825015431120082058003 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2542616566211877 / 20000000000000000 : ℝ) = - (2542616566211877 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2542616566211877 / 2500000000000000 : ℚ)) - (U := (6761185239917941997 / 400000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2542616566211877 / 2500000000000000 : ℝ) ≤ - (6761185239917941997 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1169306839449377 / 10000000000000000 : ℝ)) (q := - (2542616566211877 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2542616566211877 / 20000000000000000 : ℚ)) + (r' := (2542616566211877 / 2500000000000000 : ℚ)) + (U := (-(825015431120082058003 / 400000000000000000000 : ℚ))) + (U' := (6761185239917941997 / 400000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (1169306839449377 / 10000000000000000 : ℚ)) + (q := (2542616566211877 / 20000000000000000 : ℚ)) + (U := (-(825015431120082058003 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_8 : Uω (aρ 8) (bρ 8) (838543168003 / 4000000000000 : ℝ) ≤ @@ -868,25 +776,21 @@ lemma U_246_8 : have hlg : Real.log (756212533019953 / 10000000000000000 : ℝ) ≤ (-(3227522382415953287113 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (756212533019953 / 10000000000000000 : ℝ) = - (756212533019953 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (756212533019953 / 625000000000000 : ℚ)) - (U := (238213519084046712887 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (756212533019953 / 625000000000000 : ℝ) ≤ - (238213519084046712887 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (211328495308703 / 5000000000000000 : ℝ)) (q := - (756212533019953 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (756212533019953 / 10000000000000000 : ℚ)) + (r' := (756212533019953 / 625000000000000 : ℚ)) + (U := (-(3227522382415953287113 / 1250000000000000000000 : ℚ))) + (U' := (238213519084046712887 / 1250000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (838543168003 / 4000000000000 : ℚ)) + (s := (211328495308703 / 5000000000000000 : ℚ)) + (q := (756212533019953 / 10000000000000000 : ℚ)) + (U := (-(3227522382415953287113 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_246_9 : Uω (aρ 9) (bρ 9) (838543168003 / 4000000000000 : ℝ) ≤ @@ -1018,25 +922,21 @@ lemma U_247_1 : have hlg : Real.log (8169776337530201 / 40000000000000000 : ℝ) ≤ (-(15884379209042150851217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8169776337530201 / 40000000000000000 : ℝ) = - (8169776337530201 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8169776337530201 / 5000000000000000 : ℚ)) - (U := (4910036199957849148783 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8169776337530201 / 5000000000000000 : ℝ) ≤ - (4910036199957849148783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2042364930252913 / 10000000000000000 : ℝ)) (q := - (8169776337530201 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8169776337530201 / 40000000000000000 : ℚ)) + (r' := (8169776337530201 / 5000000000000000 : ℚ)) + (U := (-(15884379209042150851217 / 10000000000000000000000 : ℚ))) + (U' := (4910036199957849148783 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (2042364930252913 / 10000000000000000 : ℚ)) + (q := (8169776337530201 / 40000000000000000 : ℚ)) + (U := (-(15884379209042150851217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_2 : Uω (aρ 2) (bρ 2) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1044,25 +944,21 @@ lemma U_247_2 : have hlg : Real.log (8072914214553699 / 40000000000000000 : ℝ) ≤ (-(16003649191942420646063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8072914214553699 / 40000000000000000 : ℝ) = - (8072914214553699 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8072914214553699 / 5000000000000000 : ℚ)) - (U := (4790766217057579353937 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8072914214553699 / 5000000000000000 : ℝ) ≤ - (4790766217057579353937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1008851440637331 / 5000000000000000 : ℝ)) (q := - (8072914214553699 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8072914214553699 / 40000000000000000 : ℚ)) + (r' := (8072914214553699 / 5000000000000000 : ℚ)) + (U := (-(16003649191942420646063 / 10000000000000000000000 : ℚ))) + (U' := (4790766217057579353937 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (1008851440637331 / 5000000000000000 : ℚ)) + (q := (8072914214553699 / 40000000000000000 : ℚ)) + (U := (-(16003649191942420646063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_3 : Uω (aρ 3) (bρ 3) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1070,25 +966,21 @@ lemma U_247_3 : have hlg : Real.log (7877919753830639 / 40000000000000000 : ℝ) ≤ (-(8124077874733012623601 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7877919753830639 / 40000000000000000 : ℝ) = - (7877919753830639 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7877919753830639 / 5000000000000000 : ℚ)) - (U := (2273129829766987376399 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7877919753830639 / 5000000000000000 : ℝ) ≤ - (2273129829766987376399 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (491900439315783 / 2500000000000000 : ℝ)) (q := - (7877919753830639 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7877919753830639 / 40000000000000000 : ℚ)) + (r' := (7877919753830639 / 5000000000000000 : ℚ)) + (U := (-(8124077874733012623601 / 5000000000000000000000 : ℚ))) + (U' := (2273129829766987376399 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (491900439315783 / 2500000000000000 : ℚ)) + (q := (7877919753830639 / 40000000000000000 : ℚ)) + (U := (-(8124077874733012623601 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_4 : Uω (aρ 4) (bρ 4) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1096,25 +988,21 @@ lemma U_247_4 : have hlg : Real.log (7549960475874883 / 40000000000000000 : ℝ) ≤ (-(16673371250703288171891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7549960475874883 / 40000000000000000 : ℝ) = - (7549960475874883 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7549960475874883 / 5000000000000000 : ℚ)) - (U := (4121044158296711828109 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7549960475874883 / 5000000000000000 : ℝ) ≤ - (4121044158296711828109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (940958149675127 / 5000000000000000 : ℝ)) (q := - (7549960475874883 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7549960475874883 / 40000000000000000 : ℚ)) + (r' := (7549960475874883 / 5000000000000000 : ℚ)) + (U := (-(16673371250703288171891 / 10000000000000000000000 : ℚ))) + (U' := (4121044158296711828109 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (940958149675127 / 5000000000000000 : ℚ)) + (q := (7549960475874883 / 40000000000000000 : ℚ)) + (U := (-(16673371250703288171891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_5 : Uω (aρ 5) (bρ 5) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1122,25 +1010,21 @@ lemma U_247_5 : have hlg : Real.log (7038968022732803 / 40000000000000000 : ℝ) ≤ (-(43435447039729323767 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7038968022732803 / 40000000000000000 : ℝ) = - (7038968022732803 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7038968022732803 / 5000000000000000 : ℚ)) - (U := (8550591482770676233 / 25000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7038968022732803 / 5000000000000000 : ℝ) ≤ - (8550591482770676233 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (872304996057107 / 5000000000000000 : ℝ)) (q := - (7038968022732803 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7038968022732803 / 40000000000000000 : ℚ)) + (r' := (7038968022732803 / 5000000000000000 : ℚ)) + (U := (-(43435447039729323767 / 25000000000000000000 : ℚ))) + (U' := (8550591482770676233 / 25000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (872304996057107 / 5000000000000000 : ℚ)) + (q := (7038968022732803 / 40000000000000000 : ℚ)) + (U := (-(43435447039729323767 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_6 : Uω (aρ 6) (bρ 6) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1148,25 +1032,21 @@ lemma U_247_6 : have hlg : Real.log (6274052291183249 / 40000000000000000 : ℝ) ≤ (-(4631142522539577805907 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6274052291183249 / 40000000000000000 : ℝ) = - (6274052291183249 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6274052291183249 / 5000000000000000 : ℚ)) - (U := (567461329710422194093 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6274052291183249 / 5000000000000000 : ℝ) ≤ - (567461329710422194093 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1529392501479437 / 10000000000000000 : ℝ)) (q := - (6274052291183249 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6274052291183249 / 40000000000000000 : ℚ)) + (r' := (6274052291183249 / 5000000000000000 : ℚ)) + (U := (-(4631142522539577805907 / 2500000000000000000000 : ℚ))) + (U' := (567461329710422194093 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (1529392501479437 / 10000000000000000 : ℚ)) + (q := (6274052291183249 / 40000000000000000 : ℚ)) + (U := (-(4631142522539577805907 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_7 : Uω (aρ 7) (bρ 7) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1174,25 +1054,21 @@ lemma U_247_7 : have hlg : Real.log (5131567258775443 / 40000000000000000 : ℝ) ≤ (-(20534683322764266391341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5131567258775443 / 40000000000000000 : ℝ) = - (5131567258775443 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5131567258775443 / 5000000000000000 : ℚ)) - (U := (259732086235733608659 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5131567258775443 / 5000000000000000 : ℝ) ≤ - (259732086235733608659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (590905683017767 / 5000000000000000 : ℝ)) (q := - (5131567258775443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5131567258775443 / 40000000000000000 : ℚ)) + (r' := (5131567258775443 / 5000000000000000 : ℚ)) + (U := (-(20534683322764266391341 / 10000000000000000000000 : ℚ))) + (U' := (259732086235733608659 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (590905683017767 / 5000000000000000 : ℚ)) + (q := (5131567258775443 / 40000000000000000 : ℚ)) + (U := (-(20534683322764266391341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_8 : Uω (aρ 8) (bρ 8) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1200,25 +1076,21 @@ lemma U_247_8 : have hlg : Real.log (3099731638180319 / 40000000000000000 : ℝ) ≤ (-(25575639136592379083153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3099731638180319 / 40000000000000000 : ℝ) = - (3099731638180319 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3099731638180319 / 2500000000000000 : ℚ)) - (U := (2150248075407620916847 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3099731638180319 / 2500000000000000 : ℝ) ≤ - (2150248075407620916847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (112358801769493 / 2500000000000000 : ℝ)) (q := - (3099731638180319 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3099731638180319 / 40000000000000000 : ℚ)) + (r' := (3099731638180319 / 2500000000000000 : ℚ)) + (U := (-(25575639136592379083153 / 10000000000000000000000 : ℚ))) + (U' := (2150248075407620916847 / 10000000000000000000000 : ℚ)) + 4 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6742465461111 / 32000000000000 : ℚ)) + (s := (112358801769493 / 2500000000000000 : ℚ)) + (q := (3099731638180319 / 40000000000000000 : ℚ)) + (U := (-(25575639136592379083153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_247_9 : Uω (aρ 9) (bρ 9) (6742465461111 / 32000000000000 : ℝ) ≤ @@ -1350,25 +1222,21 @@ lemma U_248_1 : have hlg : Real.log (4106214064128931 / 20000000000000000 : ℝ) ≤ (-(15832308210675581165643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4106214064128931 / 20000000000000000 : ℝ) = - (4106214064128931 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4106214064128931 / 2500000000000000 : ℚ)) - (U := (4962107198324418834357 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4106214064128931 / 2500000000000000 : ℝ) ≤ - (4962107198324418834357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128314268064191 / 625000000000000 : ℝ)) (q := - (4106214064128931 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4106214064128931 / 20000000000000000 : ℚ)) + (r' := (4106214064128931 / 2500000000000000 : ℚ)) + (U := (-(15832308210675581165643 / 10000000000000000000000 : ℚ))) + (U' := (4962107198324418834357 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (128314268064191 / 625000000000000 : ℚ)) + (q := (4106214064128931 / 20000000000000000 : ℚ)) + (U := (-(15832308210675581165643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_2 : Uω (aρ 2) (bρ 2) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1376,25 +1244,21 @@ lemma U_248_2 : have hlg : Real.log (253611731691693 / 1250000000000000 : ℝ) ≤ (-(7975471737047489165407 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (253611731691693 / 1250000000000000 : ℝ) = - (253611731691693 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (253611731691693 / 156250000000000 : ℚ)) - (U := (2421735967452510834593 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (253611731691693 / 156250000000000 : ℝ) ≤ - (2421735967452510834593 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2028370944475213 / 10000000000000000 : ℝ)) (q := - (253611731691693 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (253611731691693 / 1250000000000000 : ℚ)) + (r' := (253611731691693 / 156250000000000 : ℚ)) + (U := (-(7975471737047489165407 / 5000000000000000000000 : ℚ))) + (U' := (2421735967452510834593 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (2028370944475213 / 10000000000000000 : ℚ)) + (q := (253611731691693 / 1250000000000000 : ℚ)) + (U := (-(7975471737047489165407 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_3 : Uω (aρ 3) (bρ 3) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1402,25 +1266,21 @@ lemma U_248_3 : have hlg : Real.log (3960305196199621 / 20000000000000000 : ℝ) ≤ (-(3238822361460214488721 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3960305196199621 / 20000000000000000 : ℝ) = - (3960305196199621 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3960305196199621 / 2500000000000000 : ℚ)) - (U := (920060720339785511279 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3960305196199621 / 2500000000000000 : ℝ) ≤ - (920060720339785511279 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (989142269978873 / 5000000000000000 : ℝ)) (q := - (3960305196199621 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3960305196199621 / 20000000000000000 : ℚ)) + (r' := (3960305196199621 / 2500000000000000 : ℚ)) + (U := (-(3238822361460214488721 / 2000000000000000000000 : ℚ))) + (U' := (920060720339785511279 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (989142269978873 / 5000000000000000 : ℚ)) + (q := (3960305196199621 / 20000000000000000 : ℚ)) + (U := (-(3238822361460214488721 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_4 : Uω (aρ 4) (bρ 4) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1428,25 +1288,21 @@ lemma U_248_4 : have hlg : Real.log (3796368114386551 / 20000000000000000 : ℝ) ≤ (-(3323374844885987262029 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3796368114386551 / 20000000000000000 : ℝ) = - (3796368114386551 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3796368114386551 / 2500000000000000 : ℚ)) - (U := (835508236914012737971 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3796368114386551 / 2500000000000000 : ℝ) ≤ - (835508236914012737971 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (473160409802419 / 2500000000000000 : ℝ)) (q := - (3796368114386551 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3796368114386551 / 20000000000000000 : ℚ)) + (r' := (3796368114386551 / 2500000000000000 : ℚ)) + (U := (-(3323374844885987262029 / 2000000000000000000000 : ℚ))) + (U' := (835508236914012737971 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (473160409802419 / 2500000000000000 : ℚ)) + (q := (3796368114386551 / 20000000000000000 : ℚ)) + (U := (-(3323374844885987262029 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_5 : Uω (aρ 5) (bρ 5) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1454,25 +1310,21 @@ lemma U_248_5 : have hlg : Real.log (3540992916055939 / 20000000000000000 : ℝ) ≤ (-(3462650200390808338077 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3540992916055939 / 20000000000000000 : ℝ) = - (3540992916055939 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3540992916055939 / 2500000000000000 : ℚ)) - (U := (696232881409191661923 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3540992916055939 / 2500000000000000 : ℝ) ≤ - (696232881409191661923 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109716022513379 / 625000000000000 : ℝ)) (q := - (3540992916055939 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3540992916055939 / 20000000000000000 : ℚ)) + (r' := (3540992916055939 / 2500000000000000 : ℚ)) + (U := (-(3462650200390808338077 / 2000000000000000000000 : ℚ))) + (U' := (696232881409191661923 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (109716022513379 / 625000000000000 : ℚ)) + (q := (3540992916055939 / 20000000000000000 : ℚ)) + (U := (-(3462650200390808338077 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_6 : Uω (aρ 6) (bρ 6) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1480,25 +1332,21 @@ lemma U_248_6 : have hlg : Real.log (631778564867047 / 4000000000000000 : ℝ) ≤ (-(18455106786157723315289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (631778564867047 / 4000000000000000 : ℝ) = - (631778564867047 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (631778564867047 / 500000000000000 : ℚ)) - (U := (2339308622842276684711 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (631778564867047 / 500000000000000 : ℝ) ≤ - (2339308622842276684711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19257458045417 / 125000000000000 : ℝ)) (q := - (631778564867047 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (631778564867047 / 4000000000000000 : ℚ)) + (r' := (631778564867047 / 500000000000000 : ℚ)) + (U := (-(18455106786157723315289 / 10000000000000000000000 : ℚ))) + (U' := (2339308622842276684711 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (19257458045417 / 125000000000000 : ℚ)) + (q := (631778564867047 / 4000000000000000 : ℚ)) + (U := (-(18455106786157723315289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_7 : Uω (aρ 7) (bρ 7) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1506,25 +1354,21 @@ lemma U_248_7 : have hlg : Real.log (1294457480766791 / 10000000000000000 : ℝ) ≤ (-(20444934186107947075261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1294457480766791 / 10000000000000000 : ℝ) = - (1294457480766791 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1294457480766791 / 1250000000000000 : ℚ)) - (U := (349481222892052924739 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1294457480766791 / 1250000000000000 : ℝ) ≤ - (349481222892052924739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1194280161591707 / 10000000000000000 : ℝ)) (q := - (1294457480766791 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1294457480766791 / 10000000000000000 : ℚ)) + (r' := (1294457480766791 / 1250000000000000 : ℚ)) + (U := (-(20444934186107947075261 / 10000000000000000000000 : ℚ))) + (U' := (349481222892052924739 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (1194280161591707 / 10000000000000000 : ℚ)) + (q := (1294457480766791 / 10000000000000000 : ℚ)) + (U := (-(20444934186107947075261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_8 : Uω (aρ 8) (bρ 8) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1532,25 +1376,21 @@ lemma U_248_8 : have hlg : Real.log (396509459602709 / 5000000000000000 : ℝ) ≤ (-(792029153694985536973 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (396509459602709 / 5000000000000000 : ℝ) = - (396509459602709 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (396509459602709 / 312500000000000 : ℚ)) - (U := (74404821680014463027 / 312500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (396509459602709 / 312500000000000 : ℝ) ≤ - (74404821680014463027 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (474944689808961 / 10000000000000000 : ℝ)) (q := - (396509459602709 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (396509459602709 / 5000000000000000 : ℚ)) + (r' := (396509459602709 / 312500000000000 : ℚ)) + (U := (-(792029153694985536973 / 312500000000000000000 : ℚ))) + (U' := (74404821680014463027 / 312500000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3388292789099 / 16000000000000 : ℚ)) + (s := (474944689808961 / 10000000000000000 : ℚ)) + (q := (396509459602709 / 5000000000000000 : ℚ)) + (U := (-(792029153694985536973 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_248_9 : Uω (aρ 9) (bρ 9) (3388292789099 / 16000000000000 : ℝ) ≤ @@ -1683,25 +1523,21 @@ lemma U_249_1 : have hlg : Real.log (8255079901992847 / 40000000000000000 : ℝ) ≤ (-(7890253483925033164729 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8255079901992847 / 40000000000000000 : ℝ) = - (8255079901992847 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8255079901992847 / 5000000000000000 : ℚ)) - (U := (2506954220574966835271 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8255079901992847 / 5000000000000000 : ℝ) ≤ - (2506954220574966835271 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2063691639304861 / 10000000000000000 : ℝ)) (q := - (8255079901992847 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8255079901992847 / 40000000000000000 : ℚ)) + (r' := (8255079901992847 / 5000000000000000 : ℚ)) + (U := (-(7890253483925033164729 / 5000000000000000000000 : ℚ))) + (U' := (2506954220574966835271 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (2063691639304861 / 10000000000000000 : ℚ)) + (q := (8255079901992847 / 40000000000000000 : ℚ)) + (U := (-(7890253483925033164729 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_2 : Uω (aρ 2) (bρ 2) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1709,25 +1545,21 @@ lemma U_249_2 : have hlg : Real.log (8158236498085747 / 40000000000000000 : ℝ) ≤ (-(3179702846290115685933 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8158236498085747 / 40000000000000000 : ℝ) = - (8158236498085747 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8158236498085747 / 5000000000000000 : ℚ)) - (U := (979180235509884314067 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8158236498085747 / 5000000000000000 : ℝ) ≤ - (979180235509884314067 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2039038949861311 / 10000000000000000 : ℝ)) (q := - (8158236498085747 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8158236498085747 / 40000000000000000 : ℚ)) + (r' := (8158236498085747 / 5000000000000000 : ℚ)) + (U := (-(3179702846290115685933 / 2000000000000000000000 : ℚ))) + (U' := (979180235509884314067 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (2039038949861311 / 10000000000000000 : ℚ)) + (q := (8158236498085747 / 40000000000000000 : ℚ)) + (U := (-(3179702846290115685933 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_3 : Uω (aρ 3) (bρ 3) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1735,25 +1567,21 @@ lemma U_249_3 : have hlg : Real.log (1592660119282217 / 8000000000000000 : ℝ) ≤ (-(3228071783260219938387 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1592660119282217 / 8000000000000000 : ℝ) = - (1592660119282217 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1592660119282217 / 1000000000000000 : ℚ)) - (U := (930811298539780061613 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1592660119282217 / 1000000000000000 : ℝ) ≤ - (930811298539780061613 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99448355268699 / 500000000000000 : ℝ)) (q := - (1592660119282217 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1592660119282217 / 8000000000000000 : ℚ)) + (r' := (1592660119282217 / 1000000000000000 : ℚ)) + (U := (-(3228071783260219938387 / 2000000000000000000000 : ℚ))) + (U' := (930811298539780061613 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (99448355268699 / 500000000000000 : ℚ)) + (q := (1592660119282217 / 8000000000000000 : ℚ)) + (U := (-(3228071783260219938387 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_4 : Uω (aρ 4) (bρ 4) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1761,25 +1589,21 @@ lemma U_249_4 : have hlg : Real.log (7635510570247419 / 40000000000000000 : ℝ) ≤ (-(16560696445683286189297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7635510570247419 / 40000000000000000 : ℝ) = - (7635510570247419 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7635510570247419 / 5000000000000000 : ℚ)) - (U := (4233718963316713810703 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7635510570247419 / 5000000000000000 : ℝ) ≤ - (4233718963316713810703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1903366273357147 / 10000000000000000 : ℝ)) (q := - (7635510570247419 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7635510570247419 / 40000000000000000 : ℚ)) + (r' := (7635510570247419 / 5000000000000000 : ℚ)) + (U := (-(16560696445683286189297 / 10000000000000000000000 : ℚ))) + (U' := (4233718963316713810703 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (1903366273357147 / 10000000000000000 : ℚ)) + (q := (7635510570247419 / 40000000000000000 : ℚ)) + (U := (-(16560696445683286189297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_5 : Uω (aρ 5) (bρ 5) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1787,25 +1611,21 @@ lemma U_249_5 : have hlg : Real.log (1424999832864611 / 8000000000000000 : ℝ) ≤ (-(1725269844467385308997 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1424999832864611 / 8000000000000000 : ℝ) = - (1424999832864611 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1424999832864611 / 1000000000000000 : ℚ)) - (U := (354171696432614691003 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1424999832864611 / 1000000000000000 : ℝ) ≤ - (354171696432614691003 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (353260097945993 / 2000000000000000 : ℝ)) (q := - (1424999832864611 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1424999832864611 / 8000000000000000 : ℚ)) + (r' := (1424999832864611 / 1000000000000000 : ℚ)) + (U := (-(1725269844467385308997 / 1000000000000000000000 : ℚ))) + (U' := (354171696432614691003 / 1000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (353260097945993 / 2000000000000000 : ℚ)) + (q := (1424999832864611 / 8000000000000000 : ℚ)) + (U := (-(1725269844467385308997 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_6 : Uω (aρ 6) (bρ 6) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1813,25 +1633,21 @@ lemma U_249_6 : have hlg : Real.log (1272300748482987 / 8000000000000000 : ℝ) ≤ (-(735445866576952836003 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1272300748482987 / 8000000000000000 : ℝ) = - (1272300748482987 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1272300748482987 / 1000000000000000 : ℚ)) - (U := (96330749783047163997 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1272300748482987 / 1000000000000000 : ℝ) ≤ - (96330749783047163997 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (310358630783181 / 2000000000000000 : ℝ)) (q := - (1272300748482987 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1272300748482987 / 8000000000000000 : ℚ)) + (r' := (1272300748482987 / 1000000000000000 : ℚ)) + (U := (-(735445866576952836003 / 400000000000000000000 : ℚ))) + (U' := (96330749783047163997 / 400000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (310358630783181 / 2000000000000000 : ℚ)) + (q := (1272300748482987 / 8000000000000000 : ℚ)) + (U := (-(735445866576952836003 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_7 : Uω (aρ 7) (bρ 7) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1839,25 +1655,21 @@ lemma U_249_7 : have hlg : Real.log (5224023340519699 / 40000000000000000 : ℝ) ≤ (-(10178057967148668099869 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5224023340519699 / 40000000000000000 : ℝ) = - (5224023340519699 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5224023340519699 / 5000000000000000 : ℚ)) - (U := (219149737351331900131 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5224023340519699 / 5000000000000000 : ℝ) ≤ - (219149737351331900131 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1206714333728287 / 10000000000000000 : ℝ)) (q := - (5224023340519699 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5224023340519699 / 40000000000000000 : ℚ)) + (r' := (5224023340519699 / 5000000000000000 : ℚ)) + (U := (-(10178057967148668099869 / 5000000000000000000000 : ℚ))) + (U' := (219149737351331900131 / 5000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (1206714333728287 / 10000000000000000 : ℚ)) + (q := (5224023340519699 / 40000000000000000 : ℚ)) + (U := (-(10178057967148668099869 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_8 : Uω (aρ 8) (bρ 8) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -1865,25 +1677,21 @@ lemma U_249_8 : have hlg : Real.log (3242271182885199 / 40000000000000000 : ℝ) ≤ (-(201008430917706393269 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3242271182885199 / 40000000000000000 : ℝ) = - (3242271182885199 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3242271182885199 / 2500000000000000 : ℚ)) - (U := (20798666778293606731 / 80000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3242271182885199 / 2500000000000000 : ℝ) ≤ - (20798666778293606731 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (499379906251037 / 10000000000000000 : ℝ)) (q := - (3242271182885199 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3242271182885199 / 40000000000000000 : ℚ)) + (r' := (3242271182885199 / 2500000000000000 : ℚ)) + (U := (-(201008430917706393269 / 80000000000000000000 : ℚ))) + (U' := (20798666778293606731 / 80000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1362141139057 / 6400000000000 : ℚ)) + (s := (499379906251037 / 10000000000000000 : ℚ)) + (q := (3242271182885199 / 40000000000000000 : ℚ)) + (U := (-(201008430917706393269 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_249_9 : Uω (aρ 9) (bρ 9) (1362141139057 / 6400000000000 : ℝ) ≤ @@ -2014,25 +1822,21 @@ lemma U_250_1 : have hlg : Real.log (259304114343663 / 1250000000000000 : ℝ) ≤ (-(15728972699799062262617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (259304114343663 / 1250000000000000 : ℝ) = - (259304114343663 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (259304114343663 / 156250000000000 : ℚ)) - (U := (5065442709200937737383 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (259304114343663 / 156250000000000 : ℝ) ≤ - (5065442709200937737383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1037177490608679 / 5000000000000000 : ℝ)) (q := - (259304114343663 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (259304114343663 / 1250000000000000 : ℚ)) + (r' := (259304114343663 / 156250000000000 : ℚ)) + (U := (-(15728972699799062262617 / 10000000000000000000000 : ℚ))) + (U' := (5065442709200937737383 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (1037177490608679 / 5000000000000000 : ℚ)) + (q := (259304114343663 / 1250000000000000 : ℚ)) + (U := (-(15728972699799062262617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_2 : Uω (aρ 2) (bρ 2) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2040,25 +1844,21 @@ lemma U_250_2 : have hlg : Real.log (1025112183526729 / 5000000000000000 : ℝ) ≤ (-(7923179288548330911731 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1025112183526729 / 5000000000000000 : ℝ) = - (1025112183526729 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1025112183526729 / 625000000000000 : ℚ)) - (U := (2474028415951669088269 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1025112183526729 / 625000000000000 : ℝ) ≤ - (2474028415951669088269 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1024853449167833 / 5000000000000000 : ℝ)) (q := - (1025112183526729 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1025112183526729 / 5000000000000000 : ℚ)) + (r' := (1025112183526729 / 625000000000000 : ℚ)) + (U := (-(7923179288548330911731 / 5000000000000000000000 : ℚ))) + (U' := (2474028415951669088269 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (1024853449167833 / 5000000000000000 : ℚ)) + (q := (1025112183526729 / 5000000000000000 : ℚ)) + (U := (-(7923179288548330911731 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_3 : Uω (aρ 3) (bρ 3) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2066,25 +1866,21 @@ lemma U_250_3 : have hlg : Real.log (400299518641533 / 2000000000000000 : ℝ) ≤ (-(1608689395258738273783 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (400299518641533 / 2000000000000000 : ℝ) = - (400299518641533 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (400299518641533 / 250000000000000 : ℚ)) - (U := (470752145641261726217 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (400299518641533 / 250000000000000 : ℝ) ≤ - (470752145641261726217 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12497809106213 / 62500000000000 : ℝ)) (q := - (400299518641533 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (400299518641533 / 2000000000000000 : ℚ)) + (r' := (400299518641533 / 250000000000000 : ℚ)) + (U := (-(1608689395258738273783 / 1000000000000000000000 : ℚ))) + (U' := (470752145641261726217 / 1000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (12497809106213 / 62500000000000 : ℚ)) + (q := (400299518641533 / 2000000000000000 : ℚ)) + (U := (-(1608689395258738273783 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_4 : Uω (aρ 4) (bρ 4) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2092,25 +1888,21 @@ lemma U_250_4 : have hlg : Real.log (239946360125701 / 1250000000000000 : ℝ) ≤ (-(16504834306304953880329 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (239946360125701 / 1250000000000000 : ℝ) = - (239946360125701 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (239946360125701 / 156250000000000 : ℚ)) - (U := (4289581102695046119671 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (239946360125701 / 156250000000000 : ℝ) ≤ - (4289581102695046119671 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (957045106827483 / 5000000000000000 : ℝ)) (q := - (239946360125701 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (239946360125701 / 1250000000000000 : ℚ)) + (r' := (239946360125701 / 156250000000000 : ℚ)) + (U := (-(16504834306304953880329 / 10000000000000000000000 : ℚ))) + (U' := (4289581102695046119671 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (957045106827483 / 5000000000000000 : ℚ)) + (q := (239946360125701 / 1250000000000000 : ℚ)) + (U := (-(16504834306304953880329 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_5 : Uω (aρ 5) (bρ 5) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2118,25 +1910,21 @@ lemma U_250_5 : have hlg : Real.log (3584004050662709 / 20000000000000000 : ℝ) ≤ (-(17192516474548806354561 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3584004050662709 / 20000000000000000 : ℝ) = - (3584004050662709 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3584004050662709 / 2500000000000000 : ℚ)) - (U := (3601898934451193645439 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3584004050662709 / 2500000000000000 : ℝ) ≤ - (3601898934451193645439 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1777142421641459 / 10000000000000000 : ℝ)) (q := - (3584004050662709 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3584004050662709 / 20000000000000000 : ℚ)) + (r' := (3584004050662709 / 2500000000000000 : ℚ)) + (U := (-(17192516474548806354561 / 10000000000000000000000 : ℚ))) + (U' := (3601898934451193645439 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (1777142421641459 / 10000000000000000 : ℚ)) + (q := (3584004050662709 / 20000000000000000 : ℚ)) + (U := (-(17192516474548806354561 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_6 : Uω (aρ 6) (bρ 6) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2144,25 +1932,21 @@ lemma U_250_6 : have hlg : Real.log (3202603450222341 / 20000000000000000 : ℝ) ≤ (-(9158841077746681639 / 5000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3202603450222341 / 20000000000000000 : ℝ) = - (3202603450222341 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3202603450222341 / 2500000000000000 : ℚ)) - (U := (1238366626753318361 / 5000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3202603450222341 / 2500000000000000 : ℝ) ≤ - (1238366626753318361 / 5000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1562982196341091 / 10000000000000000 : ℝ)) (q := - (3202603450222341 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3202603450222341 / 20000000000000000 : ℚ)) + (r' := (3202603450222341 / 2500000000000000 : ℚ)) + (U := (-(9158841077746681639 / 5000000000000000000 : ℚ))) + (U' := (1238366626753318361 / 5000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (1562982196341091 / 10000000000000000 : ℚ)) + (q := (3202603450222341 / 20000000000000000 : ℚ)) + (U := (-(9158841077746681639 / 5000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_7 : Uω (aρ 7) (bρ 7) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2170,24 +1954,21 @@ lemma U_250_7 : have hlg : Real.log (32938435187193 / 250000000000000 : ℝ) ≤ (-(4053641396807687271301 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (32938435187193 / 250000000000000 : ℝ) = (32938435187193 / 31250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32938435187193 / 31250000000000 : ℚ)) - (U := (105241684992312728699 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (32938435187193 / 31250000000000 : ℝ) ≤ - (105241684992312728699 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121911494185419 / 1000000000000000 : ℝ)) (q := - (32938435187193 / 250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32938435187193 / 250000000000000 : ℚ)) + (r' := (32938435187193 / 31250000000000 : ℚ)) + (U := (-(4053641396807687271301 / 2000000000000000000000 : ℚ))) + (U' := (105241684992312728699 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (121911494185419 / 1000000000000000 : ℚ)) + (q := (32938435187193 / 250000000000000 : ℚ)) + (U := (-(4053641396807687271301 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_8 : Uω (aρ 8) (bρ 8) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2195,24 +1976,21 @@ lemma U_250_8 : have hlg : Real.log (12932107065137 / 156250000000000 : ℝ) ≤ (-(24917441486620581692963 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (12932107065137 / 156250000000000 : ℝ) = (12932107065137 / 9765625000000 : ℝ) / 2 ^ 4 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12932107065137 / 9765625000000 : ℚ)) - (U := (2808445725379418307037 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12932107065137 / 9765625000000 : ℝ) ≤ - (2808445725379418307037 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (261445741278143 / 5000000000000000 : ℝ)) (q := - (12932107065137 / 156250000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12932107065137 / 156250000000000 : ℚ)) + (r' := (12932107065137 / 9765625000000 : ℚ)) + (U := (-(24917441486620581692963 / 10000000000000000000000 : ℚ))) + (U' := (2808445725379418307037 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1711206453093 / 8000000000000 : ℚ)) + (s := (261445741278143 / 5000000000000000 : ℚ)) + (q := (12932107065137 / 156250000000000 : ℚ)) + (U := (-(24917441486620581692963 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_250_9 : Uω (aρ 9) (bρ 9) (1711206453093 / 8000000000000 : ℝ) ≤ @@ -2344,25 +2122,21 @@ lemma U_251_1 : have hlg : Real.log (16638115062611679 / 80000000000000000 : ℝ) ≤ (-(15703304824046411768787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16638115062611679 / 80000000000000000 : ℝ) = - (16638115062611679 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16638115062611679 / 10000000000000000 : ℚ)) - (U := (5091110584953588231213 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16638115062611679 / 10000000000000000 : ℝ) ≤ - (5091110584953588231213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1039843324538413 / 5000000000000000 : ℝ)) (q := - (16638115062611679 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16638115062611679 / 80000000000000000 : ℚ)) + (r' := (16638115062611679 / 10000000000000000 : ℚ)) + (U := (-(15703304824046411768787 / 10000000000000000000000 : ℚ))) + (U' := (5091110584953588231213 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (1039843324538413 / 5000000000000000 : ℚ)) + (q := (16638115062611679 / 80000000000000000 : ℚ)) + (U := (-(15703304824046411768787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_2 : Uω (aρ 2) (bρ 2) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2370,25 +2144,21 @@ lemma U_251_2 : have hlg : Real.log (16444455822296023 / 80000000000000000 : ℝ) ≤ (-(15820382455700095831141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16444455822296023 / 80000000000000000 : ℝ) = - (16444455822296023 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16444455822296023 / 10000000000000000 : ℚ)) - (U := (4974032953299904168859 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16444455822296023 / 10000000000000000 : ℝ) ≤ - (4974032953299904168859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256880106438489 / 1250000000000000 : ℝ)) (q := - (16444455822296023 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16444455822296023 / 80000000000000000 : ℚ)) + (r' := (16444455822296023 / 10000000000000000 : ℚ)) + (U := (-(15820382455700095831141 / 10000000000000000000000 : ℚ))) + (U' := (4974032953299904168859 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (256880106438489 / 1250000000000000 : ℚ)) + (q := (16444455822296023 / 80000000000000000 : ℚ)) + (U := (-(15820382455700095831141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_3 : Uω (aρ 3) (bρ 3) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2396,25 +2166,21 @@ lemma U_251_3 : have hlg : Real.log (3210934041131651 / 16000000000000000 : ℝ) ≤ (-(8030134240491908589773 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3210934041131651 / 16000000000000000 : ℝ) = - (3210934041131651 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3210934041131651 / 2000000000000000 : ℚ)) - (U := (2367073464008091410227 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3210934041131651 / 2000000000000000 : ℝ) ≤ - (2367073464008091410227 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (200499055369847 / 1000000000000000 : ℝ)) (q := - (3210934041131651 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3210934041131651 / 16000000000000000 : ℚ)) + (r' := (3210934041131651 / 2000000000000000 : ℚ)) + (U := (-(8030134240491908589773 / 5000000000000000000000 : ℚ))) + (U' := (2367073464008091410227 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (200499055369847 / 1000000000000000 : ℚ)) + (q := (3210934041131651 / 16000000000000000 : ℚ)) + (U := (-(8030134240491908589773 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_4 : Uω (aρ 4) (bρ 4) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2422,25 +2188,21 @@ lemma U_251_4 : have hlg : Real.log (15399338975582483 / 80000000000000000 : ℝ) ≤ (-(1029813780661990088497 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15399338975582483 / 80000000000000000 : ℝ) = - (15399338975582483 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15399338975582483 / 10000000000000000 : ℚ)) - (U := (269837182400509911503 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15399338975582483 / 10000000000000000 : ℝ) ≤ - (269837182400509911503 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1919451927244527 / 10000000000000000 : ℝ)) (q := - (15399338975582483 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15399338975582483 / 80000000000000000 : ℚ)) + (r' := (15399338975582483 / 10000000000000000 : ℚ)) + (U := (-(1029813780661990088497 / 625000000000000000000 : ℚ))) + (U' := (269837182400509911503 / 625000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (1919451927244527 / 10000000000000000 : ℚ)) + (q := (15399338975582483 / 80000000000000000 : ℚ)) + (U := (-(1029813780661990088497 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_5 : Uω (aρ 5) (bρ 5) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2448,25 +2210,21 @@ lemma U_251_5 : have hlg : Real.log (14379021893371507 / 80000000000000000 : ℝ) ≤ (-(17162563024561307747881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14379021893371507 / 80000000000000000 : ℝ) = - (14379021893371507 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14379021893371507 / 10000000000000000 : ℚ)) - (U := (3631852384438692252119 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14379021893371507 / 10000000000000000 : ℝ) ≤ - (3631852384438692252119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1782562576026783 / 10000000000000000 : ℝ)) (q := - (14379021893371507 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14379021893371507 / 80000000000000000 : ℚ)) + (r' := (14379021893371507 / 10000000000000000 : ℚ)) + (U := (-(17162563024561307747881 / 10000000000000000000000 : ℚ))) + (U' := (3631852384438692252119 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (1782562576026783 / 10000000000000000 : ℚ)) + (q := (14379021893371507 / 80000000000000000 : ℚ)) + (U := (-(17162563024561307747881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_6 : Uω (aρ 6) (bρ 6) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2474,25 +2232,21 @@ lemma U_251_6 : have hlg : Real.log (12854105956912811 / 80000000000000000 : ℝ) ≤ (-(18283633438707248311039 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12854105956912811 / 80000000000000000 : ℝ) = - (12854105956912811 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12854105956912811 / 10000000000000000 : ℚ)) - (U := (2510781970292751688961 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12854105956912811 / 10000000000000000 : ℝ) ≤ - (2510781970292751688961 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1568573967052109 / 10000000000000000 : ℝ)) (q := - (12854105956912811 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12854105956912811 / 80000000000000000 : ℚ)) + (r' := (12854105956912811 / 10000000000000000 : ℚ)) + (U := (-(18283633438707248311039 / 10000000000000000000000 : ℚ))) + (U' := (2510781970292751688961 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (1568573967052109 / 10000000000000000 : ℚ)) + (q := (12854105956912811 / 80000000000000000 : ℚ)) + (U := (-(18283633438707248311039 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_7 : Uω (aρ 7) (bρ 7) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2500,25 +2254,21 @@ lemma U_251_7 : have hlg : Real.log (10586376477557943 / 80000000000000000 : ℝ) ≤ (-(4044917394737842997651 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10586376477557943 / 80000000000000000 : ℝ) = - (10586376477557943 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10586376477557943 / 10000000000000000 : ℚ)) - (U := (113965687062157002349 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10586376477557943 / 10000000000000000 : ℝ) ≤ - (113965687062157002349 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (76581436123337 / 625000000000000 : ℝ)) (q := - (10586376477557943 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10586376477557943 / 80000000000000000 : ℚ)) + (r' := (10586376477557943 / 10000000000000000 : ℚ)) + (U := (-(4044917394737842997651 / 2000000000000000000000 : ℚ))) + (U' := (113965687062157002349 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (76581436123337 / 625000000000000 : ℚ)) + (q := (10586376477557943 / 80000000000000000 : ℚ)) + (U := (-(4044917394737842997651 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_8 : Uω (aρ 8) (bρ 8) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2526,25 +2276,21 @@ lemma U_251_8 : have hlg : Real.log (6688354741662559 / 80000000000000000 : ℝ) ≤ (-(24816587177418204207001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6688354741662559 / 80000000000000000 : ℝ) = - (6688354741662559 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6688354741662559 / 5000000000000000 : ℚ)) - (U := (2909300034581795792999 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6688354741662559 / 5000000000000000 : ℝ) ≤ - (2909300034581795792999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (267169597669773 / 5000000000000000 : ℝ)) (q := - (6688354741662559 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6688354741662559 / 80000000000000000 : ℚ)) + (r' := (6688354741662559 / 5000000000000000 : ℚ)) + (U := (-(24816587177418204207001 / 10000000000000000000000 : ℚ))) + (U' := (2909300034581795792999 / 10000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (13723771741831 / 64000000000000 : ℚ)) + (s := (267169597669773 / 5000000000000000 : ℚ)) + (q := (6688354741662559 / 80000000000000000 : ℚ)) + (U := (-(24816587177418204207001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_251_9 : Uω (aρ 9) (bρ 9) (13723771741831 / 64000000000000 : ℝ) ≤ @@ -2677,25 +2423,21 @@ lemma U_252_1 : have hlg : Real.log (8340383399527659 / 40000000000000000 : ℝ) ≤ (-(7838851334268503496127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8340383399527659 / 40000000000000000 : ℝ) = - (8340383399527659 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8340383399527659 / 5000000000000000 : ℚ)) - (U := (2558356370231496503873 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8340383399527659 / 5000000000000000 : ℝ) ≤ - (2558356370231496503873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (521254578723223 / 2500000000000000 : ℝ)) (q := - (8340383399527659 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8340383399527659 / 40000000000000000 : ℚ)) + (r' := (8340383399527659 / 5000000000000000 : ℚ)) + (U := (-(7838851334268503496127 / 5000000000000000000000 : ℚ))) + (U' := (2558356370231496503873 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (521254578723223 / 2500000000000000 : ℚ)) + (q := (8340383399527659 / 40000000000000000 : ℚ)) + (U := (-(7838851334268503496127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_2 : Uω (aρ 2) (bρ 2) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2703,25 +2445,21 @@ lemma U_252_2 : have hlg : Real.log (8243558326286459 / 40000000000000000 : ℝ) ≤ (-(3158894733825103070931 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8243558326286459 / 40000000000000000 : ℝ) = - (8243558326286459 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8243558326286459 / 5000000000000000 : ℚ)) - (U := (999988347974896929069 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8243558326286459 / 5000000000000000 : ℝ) ≤ - (999988347974896929069 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (515093697695573 / 2500000000000000 : ℝ)) (q := - (8243558326286459 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8243558326286459 / 40000000000000000 : ℚ)) + (r' := (8243558326286459 / 5000000000000000 : ℚ)) + (U := (-(3158894733825103070931 / 2000000000000000000000 : ℚ))) + (U' := (999988347974896929069 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (515093697695573 / 2500000000000000 : ℚ)) + (q := (8243558326286459 / 40000000000000000 : ℚ)) + (U := (-(3158894733825103070931 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_3 : Uω (aρ 3) (bρ 3) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2729,25 +2467,21 @@ lemma U_252_3 : have hlg : Real.log (8048679728474291 / 40000000000000000 : ℝ) ≤ (-(8016856921198687784309 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8048679728474291 / 40000000000000000 : ℝ) = - (8048679728474291 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8048679728474291 / 5000000000000000 : ℚ)) - (U := (2380350783301312215691 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8048679728474291 / 5000000000000000 : ℝ) ≤ - (2380350783301312215691 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62822862444569 / 312500000000000 : ℝ)) (q := - (8048679728474291 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8048679728474291 / 40000000000000000 : ℚ)) + (r' := (8048679728474291 / 5000000000000000 : ℚ)) + (U := (-(8016856921198687784309 / 5000000000000000000000 : ℚ))) + (U' := (2380350783301312215691 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (62822862444569 / 312500000000000 : ℚ)) + (q := (8048679728474291 / 40000000000000000 : ℚ)) + (U := (-(8016856921198687784309 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_4 : Uω (aρ 4) (bρ 4) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2755,25 +2489,21 @@ lemma U_252_4 : have hlg : Real.log (7721055113292499 / 40000000000000000 : ℝ) ≤ (-(8224642129649983668167 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7721055113292499 / 40000000000000000 : ℝ) = - (7721055113292499 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7721055113292499 / 5000000000000000 : ℚ)) - (U := (2172565574850016331833 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7721055113292499 / 5000000000000000 : ℝ) ≤ - (2172565574850016331833 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (240601683962539 / 1250000000000000 : ℝ)) (q := - (7721055113292499 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7721055113292499 / 40000000000000000 : ℚ)) + (r' := (7721055113292499 / 5000000000000000 : ℚ)) + (U := (-(8224642129649983668167 / 5000000000000000000000 : ℚ))) + (U' := (2172565574850016331833 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (240601683962539 / 1250000000000000 : ℚ)) + (q := (7721055113292499 / 40000000000000000 : ℚ)) + (U := (-(8224642129649983668167 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_5 : Uω (aρ 5) (bρ 5) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2781,25 +2511,21 @@ lemma U_252_5 : have hlg : Real.log (7211012723073717 / 40000000000000000 : ℝ) ≤ (-(3426540102006141285593 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7211012723073717 / 40000000000000000 : ℝ) = - (7211012723073717 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7211012723073717 / 5000000000000000 : ℚ)) - (U := (732342979793858714407 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7211012723073717 / 5000000000000000 : ℝ) ≤ - (732342979793858714407 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1787982195925921 / 10000000000000000 : ℝ)) (q := - (7211012723073717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7211012723073717 / 40000000000000000 : ℚ)) + (r' := (7211012723073717 / 5000000000000000 : ℚ)) + (U := (-(3426540102006141285593 / 2000000000000000000000 : ℚ))) + (U' := (732342979793858714407 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (1787982195925921 / 10000000000000000 : ℚ)) + (q := (7211012723073717 / 40000000000000000 : ℚ)) + (U := (-(3426540102006141285593 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_6 : Uω (aρ 6) (bρ 6) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2807,25 +2533,21 @@ lemma U_252_6 : have hlg : Real.log (6448895441245641 / 40000000000000000 : ℝ) ≤ (-(18249705866105557760711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6448895441245641 / 40000000000000000 : ℝ) = - (6448895441245641 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6448895441245641 / 5000000000000000 : ℚ)) - (U := (2544709542894442239289 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6448895441245641 / 5000000000000000 : ℝ) ≤ - (2544709542894442239289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1574163930151883 / 10000000000000000 : ℝ)) (q := - (6448895441245641 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6448895441245641 / 40000000000000000 : ℚ)) + (r' := (6448895441245641 / 5000000000000000 : ℚ)) + (U := (-(18249705866105557760711 / 10000000000000000000000 : ℚ))) + (U' := (2544709542894442239289 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (1574163930151883 / 10000000000000000 : ℚ)) + (q := (6448895441245641 / 40000000000000000 : ℚ)) + (U := (-(18249705866105557760711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_7 : Uω (aρ 7) (bρ 7) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2833,25 +2555,21 @@ lemma U_252_7 : have hlg : Real.log (5316210819229457 / 40000000000000000 : ℝ) ≤ (-(20181186557770656385763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5316210819229457 / 40000000000000000 : ℝ) = - (5316210819229457 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5316210819229457 / 5000000000000000 : ℚ)) - (U := (613228851229343614237 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5316210819229457 / 5000000000000000 : ℝ) ≤ - (613228851229343614237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1231482999903791 / 10000000000000000 : ℝ)) (q := - (5316210819229457 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5316210819229457 / 40000000000000000 : ℚ)) + (r' := (5316210819229457 / 5000000000000000 : ℚ)) + (U := (-(20181186557770656385763 / 10000000000000000000000 : ℚ))) + (U' := (613228851229343614237 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (1231482999903791 / 10000000000000000 : ℚ)) + (q := (5316210819229457 / 40000000000000000 : ℚ)) + (U := (-(20181186557770656385763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_8 : Uω (aρ 8) (bρ 8) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -2859,25 +2577,21 @@ lemma U_252_8 : have hlg : Real.log (675471839149047 / 8000000000000000 : ℝ) ≤ (-(6179463379973671333507 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (675471839149047 / 8000000000000000 : ℝ) = - (675471839149047 / 500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (675471839149047 / 500000000000000 : ℚ)) - (U := (752008423026328666493 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (675471839149047 / 500000000000000 : ℝ) ≤ - (752008423026328666493 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6819985493771 / 125000000000000 : ℝ)) (q := - (675471839149047 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (675471839149047 / 8000000000000000 : ℚ)) + (r' := (675471839149047 / 500000000000000 : ℚ)) + (U := (-(6179463379973671333507 / 2500000000000000000000 : ℚ))) + (U' := (752008423026328666493 / 2500000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6878945929459 / 32000000000000 : ℚ)) + (s := (6819985493771 / 125000000000000 : ℚ)) + (q := (675471839149047 / 8000000000000000 : ℚ)) + (U := (-(6179463379973671333507 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_252_9 : Uω (aρ 9) (bρ 9) (6878945929459 / 32000000000000 : ℝ) ≤ @@ -3009,25 +2723,21 @@ lemma U_253_1 : have hlg : Real.log (16723418527387889 / 80000000000000000 : ℝ) ≤ (-(31304331795127864129 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16723418527387889 / 80000000000000000 : ℝ) = - (16723418527387889 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16723418527387889 / 10000000000000000 : ℚ)) - (U := (10284499022872135871 / 20000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16723418527387889 / 10000000000000000 : ℝ) ≤ - (10284499022872135871 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2090349978681191 / 10000000000000000 : ℝ)) (q := - (16723418527387889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16723418527387889 / 80000000000000000 : ℚ)) + (r' := (16723418527387889 / 10000000000000000 : ℚ)) + (U := (-(31304331795127864129 / 20000000000000000000 : ℚ))) + (U' := (10284499022872135871 / 20000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (2090349978681191 / 10000000000000000 : ℚ)) + (q := (16723418527387889 / 80000000000000000 : ℚ)) + (U := (-(31304331795127864129 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_2 : Uω (aρ 2) (bρ 2) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3035,25 +2745,21 @@ lemma U_253_2 : have hlg : Real.log (16529777427688981 / 80000000000000000 : ℝ) ≤ (-(3153726373802742696967 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16529777427688981 / 80000000000000000 : ℝ) = - (16529777427688981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16529777427688981 / 10000000000000000 : ℚ)) - (U := (1005156707997257303033 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16529777427688981 / 10000000000000000 : ℝ) ≤ - (1005156707997257303033 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (64553397383327 / 312500000000000 : ℝ)) (q := - (16529777427688981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16529777427688981 / 80000000000000000 : ℚ)) + (r' := (16529777427688981 / 10000000000000000 : ℚ)) + (U := (-(3153726373802742696967 / 2000000000000000000000 : ℚ))) + (U' := (1005156707997257303033 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (64553397383327 / 312500000000000 : ℚ)) + (q := (16529777427688981 / 80000000000000000 : ℚ)) + (U := (-(3153726373802742696967 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_3 : Uω (aρ 3) (bρ 3) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3061,25 +2767,21 @@ lemma U_253_3 : have hlg : Real.log (16140048501191369 / 80000000000000000 : ℝ) ≤ (-(16007229660263138625569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16140048501191369 / 80000000000000000 : ℝ) = - (16140048501191369 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16140048501191369 / 10000000000000000 : ℚ)) - (U := (4787185748736861374431 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16140048501191369 / 10000000000000000 : ℝ) ≤ - (4787185748736861374431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2015672590992061 / 10000000000000000 : ℝ)) (q := - (16140048501191369 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16140048501191369 / 80000000000000000 : ℚ)) + (r' := (16140048501191369 / 10000000000000000 : ℚ)) + (U := (-(16007229660263138625569 / 10000000000000000000000 : ℚ))) + (U' := (4787185748736861374431 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (2015672590992061 / 10000000000000000 : ℚ)) + (q := (16140048501191369 / 80000000000000000 : ℚ)) + (U := (-(16007229660263138625569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_4 : Uω (aρ 4) (bρ 4) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3087,25 +2789,21 @@ lemma U_253_4 : have hlg : Real.log (3096976161338029 / 16000000000000000 : ℝ) ≤ (-(4105406294596253327 / 2500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3096976161338029 / 16000000000000000 : ℝ) = - (3096976161338029 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3096976161338029 / 2000000000000000 : ℚ)) - (U := (1093197557653746673 / 2500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3096976161338029 / 2000000000000000 : ℝ) ≤ - (1093197557653746673 / 2500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (386034969686351 / 2000000000000000 : ℝ)) (q := - (3096976161338029 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3096976161338029 / 16000000000000000 : ℚ)) + (r' := (3096976161338029 / 2000000000000000 : ℚ)) + (U := (-(4105406294596253327 / 2500000000000000000 : ℚ))) + (U' := (1093197557653746673 / 2500000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (386034969686351 / 2000000000000000 : ℚ)) + (q := (3096976161338029 / 16000000000000000 : ℚ)) + (U := (-(4105406294596253327 / 2500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_5 : Uω (aρ 5) (bρ 5) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3113,25 +2811,21 @@ lemma U_253_5 : have hlg : Real.log (14465026880361081 / 80000000000000000 : ℝ) ≤ (-(4275732092910269981083 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14465026880361081 / 80000000000000000 : ℝ) = - (14465026880361081 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14465026880361081 / 10000000000000000 : ℚ)) - (U := (922871759339730018917 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14465026880361081 / 10000000000000000 : ℝ) ≤ - (922871759339730018917 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1793401286184489 / 10000000000000000 : ℝ)) (q := - (14465026880361081 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14465026880361081 / 80000000000000000 : ℚ)) + (r' := (14465026880361081 / 10000000000000000 : ℚ)) + (U := (-(4275732092910269981083 / 2500000000000000000000 : ℚ))) + (U' := (922871759339730018917 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (1793401286184489 / 10000000000000000 : ℚ)) + (q := (14465026880361081 / 80000000000000000 : ℚ)) + (U := (-(4275732092910269981083 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_6 : Uω (aρ 6) (bρ 6) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3139,25 +2833,21 @@ lemma U_253_6 : have hlg : Real.log (12941468654379713 / 80000000000000000 : ℝ) ≤ (-(9107949270071717081159 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12941468654379713 / 80000000000000000 : ℝ) = - (12941468654379713 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12941468654379713 / 10000000000000000 : ℚ)) - (U := (1289258434428282918841 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12941468654379713 / 10000000000000000 : ℝ) ≤ - (1289258434428282918841 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1579752104829147 / 10000000000000000 : ℝ)) (q := - (12941468654379713 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12941468654379713 / 80000000000000000 : ℚ)) + (r' := (12941468654379713 / 10000000000000000 : ℚ)) + (U := (-(9107949270071717081159 / 5000000000000000000000 : ℚ))) + (U' := (1289258434428282918841 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (1579752104829147 / 10000000000000000 : ℚ)) + (q := (12941468654379713 / 80000000000000000 : ℚ)) + (U := (-(9107949270071717081159 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_7 : Uω (aρ 7) (bρ 7) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3165,25 +2855,21 @@ lemma U_253_7 : have hlg : Real.log (10678435222814689 / 80000000000000000 : ℝ) ≤ (-(2013800325814052412029 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10678435222814689 / 80000000000000000 : ℝ) = - (10678435222814689 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10678435222814689 / 10000000000000000 : ℚ)) - (U := (65641215085947587971 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10678435222814689 / 10000000000000000 : ℝ) ≤ - (65641215085947587971 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1237655127697891 / 10000000000000000 : ℝ)) (q := - (10678435222814689 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10678435222814689 / 80000000000000000 : ℚ)) + (r' := (10678435222814689 / 10000000000000000 : ℚ)) + (U := (-(2013800325814052412029 / 1000000000000000000000 : ℚ))) + (U' := (65641215085947587971 / 1000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (1237655127697891 / 10000000000000000 : ℚ)) + (q := (10678435222814689 / 80000000000000000 : ℚ)) + (U := (-(2013800325814052412029 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_8 : Uω (aρ 8) (bρ 8) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3191,25 +2877,21 @@ lemma U_253_8 : have hlg : Real.log (6820375414613733 / 80000000000000000 : ℝ) ≤ (-(24621121171626664245687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6820375414613733 / 80000000000000000 : ℝ) = - (6820375414613733 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6820375414613733 / 5000000000000000 : ℚ)) - (U := (3104766040373335754313 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6820375414613733 / 5000000000000000 : ℝ) ≤ - (3104766040373335754313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (139170456746913 / 2500000000000000 : ℝ)) (q := - (6820375414613733 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6820375414613733 / 80000000000000000 : ℚ)) + (r' := (6820375414613733 / 5000000000000000 : ℚ)) + (U := (-(24621121171626664245687 / 10000000000000000000000 : ℚ))) + (U' := (3104766040373335754313 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2758402395201 / 12800000000000 : ℚ)) + (s := (139170456746913 / 2500000000000000 : ℚ)) + (q := (6820375414613733 / 80000000000000000 : ℚ)) + (U := (-(24621121171626664245687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_253_9 : Uω (aρ 9) (bρ 9) (2758402395201 / 12800000000000 : ℝ) ≤ @@ -3340,25 +3022,21 @@ lemma U_254_1 : have hlg : Real.log (167660702476713 / 800000000000000 : ℝ) ≤ (-(15626694177986153223101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (167660702476713 / 800000000000000 : ℝ) = - (167660702476713 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (167660702476713 / 100000000000000 : ℚ)) - (U := (5167721231013846776899 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (167660702476713 / 100000000000000 : ℝ) ≤ - (5167721231013846776899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5239204101143 / 25000000000000 : ℝ)) (q := - (167660702476713 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (167660702476713 / 800000000000000 : ℚ)) + (r' := (167660702476713 / 100000000000000 : ℚ)) + (U := (-(15626694177986153223101 / 10000000000000000000000 : ℚ))) + (U' := (5167721231013846776899 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (5239204101143 / 25000000000000 : ℚ)) + (q := (167660702476713 / 800000000000000 : ℚ)) + (U := (-(15626694177986153223101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_2 : Uω (aρ 2) (bρ 2) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3366,25 +3044,21 @@ lemma U_254_2 : have hlg : Real.log (1035777384254401 / 5000000000000000 : ℝ) ≤ (-(15742856709703212177573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1035777384254401 / 5000000000000000 : ℝ) = - (1035777384254401 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1035777384254401 / 625000000000000 : ℚ)) - (U := (5051558699296787822427 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1035777384254401 / 625000000000000 : ℝ) ≤ - (5051558699296787822427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2071042628066979 / 10000000000000000 : ℝ)) (q := - (1035777384254401 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1035777384254401 / 5000000000000000 : ℚ)) + (r' := (1035777384254401 / 625000000000000 : ℚ)) + (U := (-(15742856709703212177573 / 10000000000000000000000 : ℚ))) + (U' := (5051558699296787822427 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (2071042628066979 / 10000000000000000 : ℚ)) + (q := (1035777384254401 / 5000000000000000 : ℚ)) + (U := (-(15742856709703212177573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_3 : Uω (aρ 3) (bρ 3) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3392,25 +3066,21 @@ lemma U_254_3 : have hlg : Real.log (404568433500703 / 2000000000000000 : ℝ) ≤ (-(1997601945127060592757 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (404568433500703 / 2000000000000000 : ℝ) = - (404568433500703 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (404568433500703 / 250000000000000 : ℚ)) - (U := (601699980997939407243 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (404568433500703 / 250000000000000 : ℝ) ≤ - (601699980997939407243 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404202706481281 / 2000000000000000 : ℝ)) (q := - (404568433500703 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (404568433500703 / 2000000000000000 : ℚ)) + (r' := (404568433500703 / 250000000000000 : ℚ)) + (U := (-(1997601945127060592757 / 1250000000000000000000 : ℚ))) + (U' := (601699980997939407243 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (404202706481281 / 2000000000000000 : ℚ)) + (q := (404568433500703 / 2000000000000000 : ℚ)) + (U := (-(1997601945127060592757 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_4 : Uω (aρ 4) (bρ 4) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3418,24 +3088,21 @@ lemma U_254_4 : have hlg : Real.log (30327442815377 / 156250000000000 : ℝ) ≤ (-(4098510704363691246301 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (30327442815377 / 156250000000000 : ℝ) = (30327442815377 / 19531250000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30327442815377 / 19531250000000 : ℚ)) - (U := (1100093147886308753699 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (30327442815377 / 19531250000000 : ℝ) ≤ - (1100093147886308753699 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1935536058832631 / 10000000000000000 : ℝ)) (q := - (30327442815377 / 156250000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30327442815377 / 156250000000000 : ℚ)) + (r' := (30327442815377 / 19531250000000 : ℚ)) + (U := (-(4098510704363691246301 / 2500000000000000000000 : ℚ))) + (U' := (1100093147886308753699 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (1935536058832631 / 10000000000000000 : ℚ)) + (q := (30327442815377 / 156250000000000 : ℚ)) + (U := (-(4098510704363691246301 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_5 : Uω (aρ 5) (bρ 5) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3443,25 +3110,21 @@ lemma U_254_5 : have hlg : Real.log (1813503276894933 / 10000000000000000 : ℝ) ≤ (-(4268311513824813753719 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1813503276894933 / 10000000000000000 : ℝ) = - (1813503276894933 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1813503276894933 / 1250000000000000 : ℚ)) - (U := (930292338425186246281 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1813503276894933 / 1250000000000000 : ℝ) ≤ - (930292338425186246281 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1798819851589241 / 10000000000000000 : ℝ)) (q := - (1813503276894933 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1813503276894933 / 10000000000000000 : ℚ)) + (r' := (1813503276894933 / 1250000000000000 : ℚ)) + (U := (-(4268311513824813753719 / 2500000000000000000000 : ℚ))) + (U' := (930292338425186246281 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (1798819851589241 / 10000000000000000 : ℚ)) + (q := (1813503276894933 / 10000000000000000 : ℚ)) + (U := (-(4268311513824813753719 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_6 : Uω (aρ 6) (bρ 6) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3469,25 +3132,21 @@ lemma U_254_6 : have hlg : Real.log (1623142418528303 / 10000000000000000 : ℝ) ≤ (-(1818221057360102248173 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1623142418528303 / 10000000000000000 : ℝ) = - (1623142418528303 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1623142418528303 / 1250000000000000 : ℚ)) - (U := (261220483539897751827 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1623142418528303 / 1250000000000000 : ℝ) ≤ - (261220483539897751827 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1585338509995981 / 10000000000000000 : ℝ)) (q := - (1623142418528303 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1623142418528303 / 10000000000000000 : ℚ)) + (r' := (1623142418528303 / 1250000000000000 : ℚ)) + (U := (-(1818221057360102248173 / 1000000000000000000000 : ℚ))) + (U' := (261220483539897751827 / 1000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (1585338509995981 / 10000000000000000 : ℚ)) + (q := (1623142418528303 / 10000000000000000 : ℚ)) + (U := (-(1818221057360102248173 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_7 : Uω (aρ 7) (bρ 7) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3495,25 +3154,21 @@ lemma U_254_7 : have hlg : Real.log (1340552212587031 / 10000000000000000 : ℝ) ≤ (-(10047517320976467956059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1340552212587031 / 10000000000000000 : ℝ) = - (1340552212587031 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1340552212587031 / 1250000000000000 : ℚ)) - (U := (349690383523532043941 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1340552212587031 / 1250000000000000 : ℝ) ≤ - (349690383523532043941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1243819478873437 / 10000000000000000 : ℝ)) (q := - (1340552212587031 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1340552212587031 / 10000000000000000 : ℚ)) + (r' := (1340552212587031 / 1250000000000000 : ℚ)) + (U := (-(10047517320976467956059 / 5000000000000000000000 : ℚ))) + (U' := (349690383523532043941 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (1243819478873437 / 10000000000000000 : ℚ)) + (q := (1340552212587031 / 10000000000000000 : ℚ)) + (U := (-(10047517320976467956059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_8 : Uω (aρ 8) (bρ 8) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3521,23 +3176,21 @@ lemma U_254_8 : have hlg : Real.log (1680997852639 / 19531250000000 : ℝ) ≤ (-(3065785211127408859203 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (1680997852639 / 19531250000000 : ℝ) = (1680997852639 / 1220703125000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1680997852639 / 1220703125000 : ℚ)) - (U := (399950690372591140797 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1680997852639 / 1220703125000 : ℝ) ≤ - (399950690372591140797 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (567598506141711 / 10000000000000000 : ℝ)) (q := - (1680997852639 / 19531250000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1680997852639 / 19531250000000 : ℚ)) + (r' := (1680997852639 / 1220703125000 : ℚ)) + (U := (-(3065785211127408859203 / 1250000000000000000000 : ℚ))) + (U' := (399950690372591140797 / 1250000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3456533023273 / 16000000000000 : ℚ)) + (s := (567598506141711 / 10000000000000000 : ℚ)) + (q := (1680997852639 / 19531250000000 : ℚ)) + (U := (-(3065785211127408859203 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_254_9 : Uω (aρ 9) (bρ 9) (3456533023273 / 16000000000000 : ℝ) ≤ @@ -3670,25 +3323,21 @@ lemma U_255_1 : have hlg : Real.log (16808721959966827 / 80000000000000000 : ℝ) ≤ (-(3900321794800609828613 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16808721959966827 / 80000000000000000 : ℝ) = - (16808721959966827 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16808721959966827 / 10000000000000000 : ℚ)) - (U := (1298282057449390171387 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16808721959966827 / 10000000000000000 : ℝ) ≤ - (1298282057449390171387 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1050506650118119 / 5000000000000000 : ℝ)) (q := - (16808721959966827 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16808721959966827 / 80000000000000000 : ℚ)) + (r' := (16808721959966827 / 10000000000000000 : ℚ)) + (U := (-(3900321794800609828613 / 2500000000000000000000 : ℚ))) + (U' := (1298282057449390171387 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (1050506650118119 / 5000000000000000 : ℚ)) + (q := (16808721959966827 / 80000000000000000 : ℚ)) + (U := (-(3900321794800609828613 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_2 : Uω (aρ 2) (bρ 2) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3696,25 +3345,21 @@ lemma U_255_2 : have hlg : Real.log (3323019762827807 / 16000000000000000 : ℝ) ≤ (-(15717147848202477416551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3323019762827807 / 16000000000000000 : ℝ) = - (3323019762827807 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3323019762827807 / 2000000000000000 : ℚ)) - (U := (5077267560797522583449 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3323019762827807 / 2000000000000000 : ℝ) ≤ - (5077267560797522583449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207637652628929 / 1000000000000000 : ℝ)) (q := - (3323019762827807 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3323019762827807 / 16000000000000000 : ℚ)) + (r' := (3323019762827807 / 2000000000000000 : ℚ)) + (U := (-(15717147848202477416551 / 10000000000000000000000 : ℚ))) + (U' := (5077267560797522583449 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (207637652628929 / 1000000000000000 : ℚ)) + (q := (3323019762827807 / 16000000000000000 : ℚ)) + (U := (-(15717147848202477416551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_3 : Uω (aρ 3) (bρ 3) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3722,25 +3367,21 @@ lemma U_255_3 : have hlg : Real.log (3245085195016607 / 16000000000000000 : ℝ) ≤ (-(15954471174061227251973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3245085195016607 / 16000000000000000 : ℝ) = - (3245085195016607 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3245085195016607 / 2000000000000000 : ℚ)) - (U := (4839944234938772748027 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3245085195016607 / 2000000000000000 : ℝ) ≤ - (4839944234938772748027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (202635442287529 / 1000000000000000 : ℝ)) (q := - (3245085195016607 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3245085195016607 / 16000000000000000 : ℚ)) + (r' := (3245085195016607 / 2000000000000000 : ℚ)) + (U := (-(15954471174061227251973 / 10000000000000000000000 : ℚ))) + (U' := (4839944234938772748027 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (202635442287529 / 1000000000000000 : ℚ)) + (q := (3245085195016607 / 16000000000000000 : ℚ)) + (U := (-(15954471174061227251973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_4 : Uω (aρ 4) (bρ 4) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3748,25 +3389,21 @@ lemma U_255_4 : have hlg : Real.log (3114083995289391 / 16000000000000000 : ℝ) ≤ (-(255727136714500718647 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3114083995289391 / 16000000000000000 : ℝ) = - (3114083995289391 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3114083995289391 / 2000000000000000 : ℚ)) - (U := (69185604051124281353 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3114083995289391 / 2000000000000000 : ℝ) ≤ - (69185604051124281353 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (194089710428127 / 1000000000000000 : ℝ)) (q := - (3114083995289391 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3114083995289391 / 16000000000000000 : ℚ)) + (r' := (3114083995289391 / 2000000000000000 : ℚ)) + (U := (-(255727136714500718647 / 156250000000000000000 : ℚ))) + (U' := (69185604051124281353 / 156250000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (194089710428127 / 1000000000000000 : ℚ)) + (q := (3114083995289391 / 16000000000000000 : ℚ)) + (U := (-(255727136714500718647 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_5 : Uω (aρ 5) (bρ 5) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3774,25 +3411,21 @@ lemma U_255_5 : have hlg : Real.log (14551023469457759 / 80000000000000000 : ℝ) ≤ (-(17043653012069059339703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14551023469457759 / 80000000000000000 : ℝ) = - (14551023469457759 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14551023469457759 / 10000000000000000 : ℚ)) - (U := (3750762396930940660297 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14551023469457759 / 10000000000000000 : ℝ) ≤ - (3750762396930940660297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1804237896868971 / 10000000000000000 : ℝ)) (q := - (14551023469457759 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14551023469457759 / 80000000000000000 : ℚ)) + (r' := (14551023469457759 / 10000000000000000 : ℚ)) + (U := (-(17043653012069059339703 / 10000000000000000000000 : ℚ))) + (U' := (3750762396930940660297 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (1804237896868971 / 10000000000000000 : ℚ)) + (q := (14551023469457759 / 80000000000000000 : ℚ)) + (U := (-(17043653012069059339703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_6 : Uω (aρ 6) (bρ 6) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3800,25 +3433,21 @@ lemma U_255_6 : have hlg : Real.log (2605760607718687 / 16000000000000000 : ℝ) ≤ (-(18148641089420613638953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2605760607718687 / 16000000000000000 : ℝ) = - (2605760607718687 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2605760607718687 / 2000000000000000 : ℚ)) - (U := (2645774319579386361047 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2605760607718687 / 2000000000000000 : ℝ) ≤ - (2645774319579386361047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (159092316429289 / 1000000000000000 : ℝ)) (q := - (2605760607718687 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2605760607718687 / 16000000000000000 : ℚ)) + (r' := (2605760607718687 / 2000000000000000 : ℚ)) + (U := (-(18148641089420613638953 / 10000000000000000000000 : ℚ))) + (U' := (2645774319579386361047 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (159092316429289 / 1000000000000000 : ℚ)) + (q := (2605760607718687 / 16000000000000000 : ℚ)) + (U := (-(18148641089420613638953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_7 : Uω (aρ 7) (bρ 7) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3826,25 +3455,21 @@ lemma U_255_7 : have hlg : Real.log (10770369532315343 / 80000000000000000 : ℝ) ≤ (-(5013069580125437245247 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10770369532315343 / 80000000000000000 : ℝ) = - (10770369532315343 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10770369532315343 / 10000000000000000 : ℚ)) - (U := (185534272124562754753 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10770369532315343 / 10000000000000000 : ℝ) ≤ - (185534272124562754753 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1249976168483367 / 10000000000000000 : ℝ)) (q := - (10770369532315343 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10770369532315343 / 80000000000000000 : ℚ)) + (r' := (10770369532315343 / 10000000000000000 : ℚ)) + (U := (-(5013069580125437245247 / 2500000000000000000000 : ℚ))) + (U' := (185534272124562754753 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (1249976168483367 / 10000000000000000 : ℚ)) + (q := (10770369532315343 / 80000000000000000 : ℚ)) + (U := (-(5013069580125437245247 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_8 : Uω (aρ 8) (bρ 8) (13860252210179 / 64000000000000 : ℝ) ≤ @@ -3852,25 +3477,21 @@ lemma U_255_8 : have hlg : Real.log (6949731430595183 / 80000000000000000 : ℝ) ≤ (-(6108309044709731099283 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (6949731430595183 / 80000000000000000 : ℝ) = - (6949731430595183 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6949731430595183 / 5000000000000000 : ℚ)) - (U := (823162758290268900717 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6949731430595183 / 5000000000000000 : ℝ) ≤ - (823162758290268900717 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (578358294393327 / 10000000000000000 : ℝ)) (q := - (6949731430595183 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6949731430595183 / 80000000000000000 : ℚ)) + (r' := (6949731430595183 / 5000000000000000 : ℚ)) + (U := (-(6108309044709731099283 / 2500000000000000000000 : ℚ))) + (U' := (823162758290268900717 / 2500000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (13860252210179 / 64000000000000 : ℚ)) + (s := (578358294393327 / 10000000000000000 : ℚ)) + (q := (6949731430595183 / 80000000000000000 : ℚ)) + (U := (-(6108309044709731099283 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_255_9 : Uω (aρ 9) (bρ 9) (13860252210179 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U21.lean b/LeanPool/Zeta5Irrational/Table/U21.lean index 811a22a491..4b1a572fa3 100644 --- a/LeanPool/Zeta5Irrational/Table/U21.lean +++ b/LeanPool/Zeta5Irrational/Table/U21.lean @@ -24,25 +24,21 @@ lemma U_256_1 : have hlg : Real.log (8425686832167563 / 40000000000000000 : ℝ) ≤ (-(15575944573125605674177 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8425686832167563 / 40000000000000000 : ℝ) = - (8425686832167563 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8425686832167563 / 5000000000000000 : ℚ)) - (U := (5218470835874394325823 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8425686832167563 / 5000000000000000 : ℝ) ≤ - (5218470835874394325823 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2106344958033469 / 10000000000000000 : ℝ)) (q := - (8425686832167563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8425686832167563 / 40000000000000000 : ℚ)) + (r' := (8425686832167563 / 5000000000000000 : ℚ)) + (U := (-(15575944573125605674177 / 10000000000000000000000 : ℚ))) + (U' := (5218470835874394325823 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (2106344958033469 / 10000000000000000 : ℚ)) + (q := (8425686832167563 / 40000000000000000 : ℚ)) + (U := (-(15575944573125605674177 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_2 : Uω (aρ 2) (bρ 2) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_256_2 : have hlg : Real.log (8328879713156163 / 40000000000000000 : ℝ) ≤ (-(245179764752538628203 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8328879713156163 / 40000000000000000 : ℝ) = - (8328879713156163 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8328879713156163 / 5000000000000000 : ℚ)) - (U := (79732976013086371797 / 156250000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8328879713156163 / 5000000000000000 : ℝ) ≤ - (79732976013086371797 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2081710411037769 / 10000000000000000 : ℝ)) (q := - (8328879713156163 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8328879713156163 / 40000000000000000 : ℚ)) + (r' := (8328879713156163 / 5000000000000000 : ℚ)) + (U := (-(245179764752538628203 / 156250000000000000000 : ℚ))) + (U' := (79732976013086371797 / 156250000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (2081710411037769 / 10000000000000000 : ℚ)) + (q := (8328879713156163 / 40000000000000000 : ℚ)) + (U := (-(245179764752538628203 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_3 : Uω (aρ 3) (bρ 3) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_256_3 : have hlg : Real.log (8134057203981601 / 40000000000000000 : ℝ) ≤ (-(995512258233638353213 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8134057203981601 / 40000000000000000 : ℝ) = - (8134057203981601 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8134057203981601 / 5000000000000000 : ℚ)) - (U := (304138704828861646787 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8134057203981601 / 5000000000000000 : ℝ) ≤ - (304138704828861646787 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253961907850061 / 1250000000000000 : ℝ)) (q := - (8134057203981601 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8134057203981601 / 40000000000000000 : ℚ)) + (r' := (8134057203981601 / 5000000000000000 : ℚ)) + (U := (-(995512258233638353213 / 625000000000000000000 : ℚ))) + (U' := (304138704828861646787 / 625000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (253961907850061 / 1250000000000000 : ℚ)) + (q := (8134057203981601 / 40000000000000000 : ℚ)) + (U := (-(995512258233638353213 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_4 : Uω (aρ 4) (bρ 4) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_256_4 : have hlg : Real.log (7806594288532177 / 40000000000000000 : ℝ) ≤ (-(8169553275997104438517 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7806594288532177 / 40000000000000000 : ℝ) = - (7806594288532177 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7806594288532177 / 5000000000000000 : ℚ)) - (U := (2227654428502895561483 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7806594288532177 / 5000000000000000 : ℝ) ≤ - (2227654428502895561483 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243282248267597 / 1250000000000000 : ℝ)) (q := - (7806594288532177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7806594288532177 / 40000000000000000 : ℚ)) + (r' := (7806594288532177 / 5000000000000000 : ℚ)) + (U := (-(8169553275997104438517 / 5000000000000000000000 : ℚ))) + (U' := (2227654428502895561483 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (243282248267597 / 1250000000000000 : ℚ)) + (q := (7806594288532177 / 40000000000000000 : ℚ)) + (U := (-(8169553275997104438517 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_5 : Uω (aρ 5) (bρ 5) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_256_5 : have hlg : Real.log (1459401866194279 / 8000000000000000 : ℝ) ≤ (-(136113189584853233173 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1459401866194279 / 8000000000000000 : ℝ) = - (1459401866194279 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1459401866194279 / 1000000000000000 : ℚ)) - (U := (30242133687146766827 / 80000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1459401866194279 / 1000000000000000 : ℝ) ≤ - (30242133687146766827 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (361931085339077 / 2000000000000000 : ℝ)) (q := - (1459401866194279 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1459401866194279 / 8000000000000000 : ℚ)) + (r' := (1459401866194279 / 1000000000000000 : ℚ)) + (U := (-(136113189584853233173 / 80000000000000000000 : ℚ))) + (U' := (30242133687146766827 / 80000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (361931085339077 / 2000000000000000 : ℚ)) + (q := (1459401866194279 / 8000000000000000 : ℚ)) + (U := (-(136113189584853233173 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_6 : Uω (aρ 6) (bρ 6) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_256_6 : have hlg : Real.log (6536229899488127 / 40000000000000000 : ℝ) ≤ (-(18115189220547125073919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6536229899488127 / 40000000000000000 : ℝ) = - (6536229899488127 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6536229899488127 / 5000000000000000 : ℚ)) - (U := (2679226188452874926081 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6536229899488127 / 5000000000000000 : ℝ) ≤ - (2679226188452874926081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1596506086093751 / 10000000000000000 : ℝ)) (q := - (6536229899488127 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6536229899488127 / 40000000000000000 : ℚ)) + (r' := (6536229899488127 / 5000000000000000 : ℚ)) + (U := (-(18115189220547125073919 / 10000000000000000000000 : ℚ))) + (U' := (2679226188452874926081 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (1596506086093751 / 10000000000000000 : ℚ)) + (q := (6536229899488127 / 40000000000000000 : ℚ)) + (U := (-(18115189220547125073919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_7 : Uω (aρ 7) (bρ 7) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_256_7 : have hlg : Real.log (1081629116829469 / 8000000000000000 : ℝ) ≤ (-(10004865974050945407887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1081629116829469 / 8000000000000000 : ℝ) = - (1081629116829469 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1081629116829469 / 1000000000000000 : ℚ)) - (U := (392341730449054592113 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1081629116829469 / 1000000000000000 : ℝ) ≤ - (392341730449054592113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1962695795599 / 15625000000000 : ℝ)) (q := - (1081629116829469 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1081629116829469 / 8000000000000000 : ℚ)) + (r' := (1081629116829469 / 1000000000000000 : ℚ)) + (U := (-(10004865974050945407887 / 5000000000000000000000 : ℚ))) + (U' := (392341730449054592113 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (1962695795599 / 15625000000000 : ℚ)) + (q := (1081629116829469 / 8000000000000000 : ℚ)) + (U := (-(10004865974050945407887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_8 : Uω (aρ 8) (bρ 8) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_256_8 : have hlg : Real.log (3506751243989351 / 40000000000000000 : ℝ) ≤ (-(24341894157151895026913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3506751243989351 / 40000000000000000 : ℝ) = - (3506751243989351 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3506751243989351 / 2500000000000000 : ℚ)) - (U := (3383993054848104973087 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3506751243989351 / 2500000000000000 : ℝ) ≤ - (3383993054848104973087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (588969790444363 / 10000000000000000 : ℝ)) (q := - (3506751243989351 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3506751243989351 / 40000000000000000 : ℚ)) + (r' := (3506751243989351 / 2500000000000000 : ℚ)) + (U := (-(24341894157151895026913 / 10000000000000000000000 : ℚ))) + (U' := (3383993054848104973087 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6947186163633 / 32000000000000 : ℚ)) + (s := (588969790444363 / 10000000000000000 : ℚ)) + (q := (3506751243989351 / 40000000000000000 : ℚ)) + (U := (-(24341894157151895026913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_256_9 : Uω (aρ 9) (bρ 9) (6947186163633 / 32000000000000 : ℝ) ≤ @@ -356,25 +324,21 @@ lemma U_257_1 : have hlg : Real.log (16894025360836249 / 80000000000000000 : ℝ) ≤ (-(15550666034157081233191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16894025360836249 / 80000000000000000 : ℝ) = - (16894025360836249 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16894025360836249 / 10000000000000000 : ℚ)) - (U := (5243749374842918766809 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16894025360836249 / 10000000000000000 : ℝ) ≤ - (5243749374842918766809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1055838306931953 / 5000000000000000 : ℝ)) (q := - (16894025360836249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16894025360836249 / 80000000000000000 : ℚ)) + (r' := (16894025360836249 / 10000000000000000 : ℚ)) + (U := (-(15550666034157081233191 / 10000000000000000000000 : ℚ))) + (U' := (5243749374842918766809 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (1055838306931953 / 5000000000000000 : ℚ)) + (q := (16894025360836249 / 80000000000000000 : ℚ)) + (U := (-(15550666034157081233191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_2 : Uω (aρ 2) (bρ 2) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -382,25 +346,21 @@ lemma U_257_2 : have hlg : Real.log (16700419985003521 / 80000000000000000 : ℝ) ≤ (-(7832963829924780234651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16700419985003521 / 80000000000000000 : ℝ) = - (16700419985003521 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16700419985003521 / 10000000000000000 : ℚ)) - (U := (2564243874575219765349 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16700419985003521 / 10000000000000000 : ℝ) ≤ - (2564243874575219765349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (521761070603931 / 2500000000000000 : ℝ)) (q := - (16700419985003521 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16700419985003521 / 80000000000000000 : ℚ)) + (r' := (16700419985003521 / 10000000000000000 : ℚ)) + (U := (-(7832963829924780234651 / 5000000000000000000000 : ℚ))) + (U' := (2564243874575219765349 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (521761070603931 / 2500000000000000 : ℚ)) + (q := (16700419985003521 / 80000000000000000 : ℚ)) + (U := (-(7832963829924780234651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_3 : Uω (aρ 3) (bρ 3) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -408,25 +368,21 @@ lemma U_257_3 : have hlg : Real.log (16310802640258853 / 80000000000000000 : ℝ) ≤ (-(15901990069294298442933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16310802640258853 / 80000000000000000 : ℝ) = - (16310802640258853 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16310802640258853 / 10000000000000000 : ℚ)) - (U := (4892425339705701557067 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16310802640258853 / 10000000000000000 : ℝ) ≤ - (4892425339705701557067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2037036052579557 / 10000000000000000 : ℝ)) (q := - (16310802640258853 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16310802640258853 / 80000000000000000 : ℚ)) + (r' := (16310802640258853 / 10000000000000000 : ℚ)) + (U := (-(15901990069294298442933 / 10000000000000000000000 : ℚ))) + (U' := (4892425339705701557067 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (2037036052579557 / 10000000000000000 : ℚ)) + (q := (16310802640258853 / 80000000000000000 : ℚ)) + (U := (-(15901990069294298442933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_4 : Uω (aρ 4) (bρ 4) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -434,25 +390,21 @@ lemma U_257_4 : have hlg : Real.log (15655956528717557 / 80000000000000000 : ℝ) ≤ (-(16311751804573218956949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15655956528717557 / 80000000000000000 : ℝ) = - (15655956528717557 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15655956528717557 / 10000000000000000 : ℚ)) - (U := (4482663604426781043051 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15655956528717557 / 10000000000000000 : ℝ) ≤ - (4482663604426781043051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1951618705759233 / 10000000000000000 : ℝ)) (q := - (15655956528717557 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15655956528717557 / 80000000000000000 : ℚ)) + (r' := (15655956528717557 / 10000000000000000 : ℚ)) + (U := (-(16311751804573218956949 / 10000000000000000000000 : ℚ))) + (U' := (4482663604426781043051 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (1951618705759233 / 10000000000000000 : ℚ)) + (q := (15655956528717557 / 80000000000000000 : ℚ)) + (U := (-(16311751804573218956949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_5 : Uω (aρ 5) (bρ 5) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -460,25 +412,21 @@ lemma U_257_5 : have hlg : Real.log (585480472443061 / 3200000000000000 : ℝ) ≤ (-(16984732574596841281701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (585480472443061 / 3200000000000000 : ℝ) = - (585480472443061 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (585480472443061 / 400000000000000 : ℚ)) - (U := (3809682834403158718299 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (585480472443061 / 400000000000000 : ℝ) ≤ - (3809682834403158718299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (72602897827359 / 400000000000000 : ℝ)) (q := - (585480472443061 / 3200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (585480472443061 / 3200000000000000 : ℚ)) + (r' := (585480472443061 / 400000000000000 : ℚ)) + (U := (-(16984732574596841281701 / 10000000000000000000000 : ℚ))) + (U' := (3809682834403158718299 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (72602897827359 / 400000000000000 : ℚ)) + (q := (585480472443061 / 3200000000000000 : ℚ)) + (U := (-(16984732574596841281701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_6 : Uω (aρ 6) (bρ 6) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -486,25 +434,21 @@ lemma U_257_6 : have hlg : Real.log (13116109701823297 / 80000000000000000 : ℝ) ≤ (-(18081854109771723636757 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13116109701823297 / 80000000000000000 : ℝ) = - (13116109701823297 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13116109701823297 / 10000000000000000 : ℚ)) - (U := (2712561299228276363243 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13116109701823297 / 10000000000000000 : ℝ) ≤ - (2712561299228276363243 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (400521823377667 / 2500000000000000 : ℝ)) (q := - (13116109701823297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13116109701823297 / 80000000000000000 : ℚ)) + (r' := (13116109701823297 / 10000000000000000 : ℚ)) + (U := (-(18081854109771723636757 / 10000000000000000000000 : ℚ))) + (U' := (2712561299228276363243 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (400521823377667 / 2500000000000000 : ℚ)) + (q := (13116109701823297 / 80000000000000000 : ℚ)) + (U := (-(18081854109771723636757 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_7 : Uω (aρ 7) (bρ 7) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -512,25 +456,21 @@ lemma U_257_7 : have hlg : Real.log (10862183049928981 / 80000000000000000 : ℝ) ≤ (-(19967393221007081062849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10862183049928981 / 80000000000000000 : ℝ) = - (10862183049928981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10862183049928981 / 10000000000000000 : ℚ)) - (U := (827022187992918937151 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10862183049928981 / 10000000000000000 : ℝ) ≤ - (827022187992918937151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1262267011297089 / 10000000000000000 : ℝ)) (q := - (10862183049928981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10862183049928981 / 80000000000000000 : ℚ)) + (r' := (10862183049928981 / 10000000000000000 : ℚ)) + (U := (-(19967393221007081062849 / 10000000000000000000000 : ℚ))) + (U' := (827022187992918937151 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (1262267011297089 / 10000000000000000 : ℚ)) + (q := (10862183049928981 / 80000000000000000 : ℚ)) + (U := (-(19967393221007081062849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_8 : Uω (aρ 8) (bρ 8) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -538,25 +478,21 @@ lemma U_257_8 : have hlg : Real.log (7076711878164501 / 80000000000000000 : ℝ) ≤ (-(4850434515589518544511 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7076711878164501 / 80000000000000000 : ℝ) = - (7076711878164501 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7076711878164501 / 5000000000000000 : ℚ)) - (U := (694742926810481455489 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7076711878164501 / 5000000000000000 : ℝ) ≤ - (694742926810481455489 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (599440869695969 / 10000000000000000 : ℝ)) (q := - (7076711878164501 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7076711878164501 / 80000000000000000 : ℚ)) + (r' := (7076711878164501 / 5000000000000000 : ℚ)) + (U := (-(4850434515589518544511 / 2000000000000000000000 : ℚ))) + (U' := (694742926810481455489 / 2000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (13928492444353 / 64000000000000 : ℚ)) + (s := (599440869695969 / 10000000000000000 : ℚ)) + (q := (7076711878164501 / 80000000000000000 : ℚ)) + (U := (-(4850434515589518544511 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_257_9 : Uω (aρ 9) (bρ 9) (13928492444353 / 64000000000000 : ℝ) ≤ @@ -689,25 +625,21 @@ lemma U_258_1 : have hlg : Real.log (4234169262382407 / 20000000000000000 : ℝ) ≤ (-(1552545123916181522009 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4234169262382407 / 20000000000000000 : ℝ) = - (4234169262382407 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4234169262382407 / 2500000000000000 : ℚ)) - (U := (526896416983818477991 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4234169262382407 / 2500000000000000 : ℝ) ≤ - (526896416983818477991 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2117008267742407 / 10000000000000000 : ℝ)) (q := - (4234169262382407 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4234169262382407 / 20000000000000000 : ℚ)) + (r' := (4234169262382407 / 2500000000000000 : ℚ)) + (U := (-(1552545123916181522009 / 1000000000000000000000 : ℚ))) + (U' := (526896416983818477991 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (87266328509 / 400000000000 : ℚ)) + (s := (2117008267742407 / 10000000000000000 : ℚ)) + (q := (4234169262382407 / 20000000000000000 : ℚ)) + (U := (-(1552545123916181522009 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_2 : Uω (aρ 2) (bρ 2) (87266328509 / 400000000000 : ℝ) ≤ @@ -715,25 +647,21 @@ lemma U_258_2 : have hlg : Real.log (837154024531081 / 4000000000000000 : ℝ) ≤ (-(15640415660118783464449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (837154024531081 / 4000000000000000 : ℝ) = - (837154024531081 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (837154024531081 / 500000000000000 : ℚ)) - (U := (5153999748881216535551 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (837154024531081 / 500000000000000 : ℝ) ≤ - (5153999748881216535551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (418475628105081 / 2000000000000000 : ℝ)) (q := - (837154024531081 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (837154024531081 / 4000000000000000 : ℚ)) + (r' := (837154024531081 / 500000000000000 : ℚ)) + (U := (-(15640415660118783464449 / 10000000000000000000000 : ℚ))) + (U' := (5153999748881216535551 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (87266328509 / 400000000000 : ℚ)) + (s := (418475628105081 / 2000000000000000 : ℚ)) + (q := (837154024531081 / 4000000000000000 : ℚ)) + (U := (-(15640415660118783464449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_3 : Uω (aρ 3) (bρ 3) (87266328509 / 400000000000 : ℝ) ≤ @@ -741,25 +669,21 @@ lemma U_258_3 : have hlg : Real.log (4088372668385891 / 20000000000000000 : ℝ) ≤ (-(15875852624851757203039 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4088372668385891 / 20000000000000000 : ℝ) = - (4088372668385891 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4088372668385891 / 2500000000000000 : ℚ)) - (U := (4918562784148242796961 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4088372668385891 / 2500000000000000 : ℝ) ≤ - (4918562784148242796961 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2042376792605891 / 10000000000000000 : ℝ)) (q := - (4088372668385891 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4088372668385891 / 20000000000000000 : ℚ)) + (r' := (4088372668385891 / 2500000000000000 : ℚ)) + (U := (-(15875852624851757203039 / 10000000000000000000000 : ℚ))) + (U' := (4918562784148242796961 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (87266328509 / 400000000000 : ℚ)) + (s := (2042376792605891 / 10000000000000000 : ℚ)) + (q := (4088372668385891 / 20000000000000000 : ℚ)) + (U := (-(15875852624851757203039 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_4 : Uω (aρ 4) (bρ 4) (87266328509 / 400000000000 : ℝ) ≤ @@ -767,25 +691,21 @@ lemma U_258_4 : have hlg : Real.log (3924680959184913 / 20000000000000000 : ℝ) ≤ (-(16284472091276283593661 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3924680959184913 / 20000000000000000 : ℝ) = - (3924680959184913 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3924680959184913 / 2500000000000000 : ℚ)) - (U := (4509943317723716406339 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3924680959184913 / 2500000000000000 : ℝ) ≤ - (4509943317723716406339 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1956979264469913 / 10000000000000000 : ℝ)) (q := - (3924680959184913 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3924680959184913 / 20000000000000000 : ℚ)) + (r' := (3924680959184913 / 2500000000000000 : ℚ)) + (U := (-(16284472091276283593661 / 10000000000000000000000 : ℚ))) + (U' := (4509943317723716406339 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (87266328509 / 400000000000 : ℚ)) + (s := (1956979264469913 / 10000000000000000 : ℚ)) + (q := (3924680959184913 / 20000000000000000 : ℚ)) + (U := (-(16284472091276283593661 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_5 : Uω (aρ 5) (bρ 5) (87266328509 / 400000000000 : ℝ) ≤ @@ -793,25 +713,21 @@ lemma U_258_5 : have hlg : Real.log (1835000366887433 / 10000000000000000 : ℝ) ≤ (-(1695540410769040563281 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1835000366887433 / 10000000000000000 : ℝ) = - (1835000366887433 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1835000366887433 / 1250000000000000 : ℚ)) - (U := (383901130130959436719 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1835000366887433 / 1250000000000000 : ℝ) ≤ - (383901130130959436719 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (910244479197433 / 5000000000000000 : ℝ)) (q := - (1835000366887433 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1835000366887433 / 10000000000000000 : ℚ)) + (r' := (1835000366887433 / 1250000000000000 : ℚ)) + (U := (-(1695540410769040563281 / 1000000000000000000000 : ℚ))) + (U' := (383901130130959436719 / 1000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (87266328509 / 400000000000 : ℚ)) + (s := (910244479197433 / 5000000000000000 : ℚ)) + (q := (1835000366887433 / 10000000000000000 : ℚ)) + (U := (-(1695540410769040563281 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_6 : Uω (aρ 6) (bρ 6) (87266328509 / 400000000000 : ℝ) ≤ @@ -819,25 +735,21 @@ lemma U_258_6 : have hlg : Real.log (1644969102319353 / 10000000000000000 : ℝ) ≤ (-(18048634909578610900489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1644969102319353 / 10000000000000000 : ℝ) = - (1644969102319353 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1644969102319353 / 1250000000000000 : ℚ)) - (U := (2745780499421389099511 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1644969102319353 / 1250000000000000 : ℝ) ≤ - (2745780499421389099511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (803833402199353 / 5000000000000000 : ℝ)) (q := - (1644969102319353 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1644969102319353 / 10000000000000000 : ℚ)) + (r' := (1644969102319353 / 1250000000000000 : ℚ)) + (U := (-(18048634909578610900489 / 10000000000000000000000 : ℚ))) + (U' := (2745780499421389099511 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (87266328509 / 400000000000 : ℚ)) + (s := (803833402199353 / 5000000000000000 : ℚ)) + (q := (1644969102319353 / 10000000000000000 : ℚ)) + (U := (-(18048634909578610900489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_7 : Uω (aρ 7) (bρ 7) (87266328509 / 400000000000 : ℝ) ≤ @@ -845,25 +757,21 @@ lemma U_258_7 : have hlg : Real.log (272701140235927 / 2000000000000000 : ℝ) ≤ (-(19925259876362511462543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (272701140235927 / 2000000000000000 : ℝ) = - (272701140235927 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (272701140235927 / 250000000000000 : ℚ)) - (U := (869155532637488537457 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (272701140235927 / 250000000000000 : ℝ) ≤ - (869155532637488537457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (126840138287927 / 1000000000000000 : ℝ)) (q := - (272701140235927 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (272701140235927 / 2000000000000000 : ℚ)) + (r' := (272701140235927 / 250000000000000 : ℚ)) + (U := (-(19925259876362511462543 / 10000000000000000000000 : ℚ))) + (U' := (869155532637488537457 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (87266328509 / 400000000000 : ℚ)) + (s := (126840138287927 / 1000000000000000 : ℚ)) + (q := (272701140235927 / 2000000000000000 : ℚ)) + (U := (-(19925259876362511462543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_8 : Uω (aρ 8) (bρ 8) (87266328509 / 400000000000 : ℝ) ≤ @@ -871,25 +779,21 @@ lemma U_258_8 : have hlg : Real.log (1784847134014071 / 20000000000000000 : ℝ) ≤ (-(2416399500157657047719 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1784847134014071 / 20000000000000000 : ℝ) = - (1784847134014071 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1784847134014071 / 1250000000000000 : ℚ)) - (U := (356189221042342952281 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1784847134014071 / 1250000000000000 : ℝ) ≤ - (356189221042342952281 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (609778765874071 / 10000000000000000 : ℝ)) (q := - (1784847134014071 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1784847134014071 / 20000000000000000 : ℚ)) + (r' := (1784847134014071 / 1250000000000000 : ℚ)) + (U := (-(2416399500157657047719 / 1000000000000000000000 : ℚ))) + (U' := (356189221042342952281 / 1000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (87266328509 / 400000000000 : ℚ)) + (s := (609778765874071 / 10000000000000000 : ℚ)) + (q := (1784847134014071 / 20000000000000000 : ℚ)) + (U := (-(2416399500157657047719 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_258_9 : Uω (aρ 9) (bρ 9) (87266328509 / 400000000000 : ℝ) ≤ @@ -1021,25 +925,21 @@ lemma U_259_1 : have hlg : Real.log (16979328730474111 / 80000000000000000 : ℝ) ≤ (-(15500299867443468815179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16979328730474111 / 80000000000000000 : ℝ) = - (16979328730474111 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16979328730474111 / 10000000000000000 : ℚ)) - (U := (5294115541556531184821 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16979328730474111 / 10000000000000000 : ℝ) ≤ - (5294115541556531184821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (530584979920921 / 2500000000000000 : ℝ)) (q := - (16979328730474111 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16979328730474111 / 80000000000000000 : ℚ)) + (r' := (16979328730474111 / 10000000000000000 : ℚ)) + (U := (-(15500299867443468815179 / 10000000000000000000000 : ℚ))) + (U' := (5294115541556531184821 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (530584979920921 / 2500000000000000 : ℚ)) + (q := (16979328730474111 / 80000000000000000 : ℚ)) + (U := (-(15500299867443468815179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_2 : Uω (aρ 2) (bρ 2) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1047,25 +947,21 @@ lemma U_259_2 : have hlg : Real.log (671429637742859 / 3200000000000000 : ℝ) ≤ (-(15614968612387440695619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (671429637742859 / 3200000000000000 : ℝ) = - (671429637742859 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (671429637742859 / 400000000000000 : ℚ)) - (U := (5179446796612559304381 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (671429637742859 / 400000000000000 : ℝ) ≤ - (5179446796612559304381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83908479418721 / 400000000000000 : ℝ)) (q := - (671429637742859 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (671429637742859 / 3200000000000000 : ℚ)) + (r' := (671429637742859 / 400000000000000 : ℚ)) + (U := (-(15614968612387440695619 / 10000000000000000000000 : ℚ))) + (U' := (5179446796612559304381 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (83908479418721 / 400000000000000 : ℚ)) + (q := (671429637742859 / 3200000000000000 : ℚ)) + (U := (-(15614968612387440695619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_3 : Uω (aρ 3) (bρ 3) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1073,25 +969,21 @@ lemma U_259_3 : have hlg : Real.log (16396178509374483 / 80000000000000000 : ℝ) ≤ (-(15849783439378083627973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16396178509374483 / 80000000000000000 : ℝ) = - (16396178509374483 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16396178509374483 / 10000000000000000 : ℚ)) - (U := (4944631969621916372027 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16396178509374483 / 10000000000000000 : ℝ) ≤ - (4944631969621916372027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2047717483268777 / 10000000000000000 : ℝ)) (q := - (16396178509374483 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16396178509374483 / 80000000000000000 : ℚ)) + (r' := (16396178509374483 / 10000000000000000 : ℚ)) + (U := (-(15849783439378083627973 / 10000000000000000000000 : ℚ))) + (U' := (4944631969621916372027 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (2047717483268777 / 10000000000000000 : ℚ)) + (q := (16396178509374483 / 80000000000000000 : ℚ)) + (U := (-(15849783439378083627973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_4 : Uω (aρ 4) (bρ 4) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1099,25 +991,21 @@ lemma U_259_4 : have hlg : Real.log (3148298101281059 / 16000000000000000 : ℝ) ≤ (-(16257266999367032878831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3148298101281059 / 16000000000000000 : ℝ) = - (3148298101281059 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3148298101281059 / 2000000000000000 : ℚ)) - (U := (4537148409632967121169 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3148298101281059 / 2000000000000000 : ℝ) ≤ - (4537148409632967121169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (49058491589787 / 250000000000000 : ℝ)) (q := - (3148298101281059 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3148298101281059 / 16000000000000000 : ℚ)) + (r' := (3148298101281059 / 2000000000000000 : ℚ)) + (U := (-(16257266999367032878831 / 10000000000000000000000 : ℚ))) + (U' := (4537148409632967121169 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (49058491589787 / 250000000000000 : ℚ)) + (q := (3148298101281059 / 16000000000000000 : ℚ)) + (U := (-(16257266999367032878831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_5 : Uω (aρ 5) (bρ 5) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1125,25 +1013,21 @@ lemma U_259_5 : have hlg : Real.log (14722992052033959 / 80000000000000000 : ℝ) ≤ (-(4231540692110611749079 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14722992052033959 / 80000000000000000 : ℝ) = - (14722992052033959 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14722992052033959 / 10000000000000000 : ℚ)) - (U := (967063160139388250921 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14722992052033959 / 10000000000000000 : ℝ) ≤ - (967063160139388250921 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (912952484666823 / 5000000000000000 : ℝ)) (q := - (14722992052033959 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14722992052033959 / 80000000000000000 : ℚ)) + (r' := (14722992052033959 / 10000000000000000 : ℚ)) + (U := (-(4231540692110611749079 / 2500000000000000000000 : ℚ))) + (U' := (967063160139388250921 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (912952484666823 / 5000000000000000 : ℚ)) + (q := (14722992052033959 / 80000000000000000 : ℚ)) + (U := (-(4231540692110611749079 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_6 : Uω (aρ 6) (bρ 6) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1151,25 +1035,21 @@ lemma U_259_6 : have hlg : Real.log (13203389219581499 / 80000000000000000 : ℝ) ≤ (-(9007765390997410364347 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13203389219581499 / 80000000000000000 : ℝ) = - (13203389219581499 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13203389219581499 / 10000000000000000 : ℚ)) - (U := (1389442313502589635653 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13203389219581499 / 10000000000000000 : ℝ) ≤ - (1389442313502589635653 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1613244636360531 / 10000000000000000 : ℝ)) (q := - (13203389219581499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13203389219581499 / 80000000000000000 : ℚ)) + (r' := (13203389219581499 / 10000000000000000 : ℚ)) + (U := (-(9007765390997410364347 / 5000000000000000000000 : ℚ))) + (U' := (1389442313502589635653 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (1613244636360531 / 10000000000000000 : ℚ)) + (q := (13203389219581499 / 80000000000000000 : ℚ)) + (U := (-(9007765390997410364347 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_7 : Uω (aρ 7) (bρ 7) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1177,25 +1057,21 @@ lemma U_259_7 : have hlg : Real.log (10953879270205719 / 80000000000000000 : ℝ) ≤ (-(9941664845595572648541 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10953879270205719 / 80000000000000000 : ℝ) = - (10953879270205719 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10953879270205719 / 10000000000000000 : ℚ)) - (U := (455542858904427351459 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10953879270205719 / 10000000000000000 : ℝ) ≤ - (455542858904427351459 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (637264264888293 / 5000000000000000 : ℝ)) (q := - (10953879270205719 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10953879270205719 / 80000000000000000 : ℚ)) + (r' := (10953879270205719 / 10000000000000000 : ℚ)) + (U := (-(9941664845595572648541 / 5000000000000000000000 : ℚ))) + (U' := (455542858904427351459 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (637264264888293 / 5000000000000000 : ℚ)) + (q := (10953879270205719 / 80000000000000000 : ℚ)) + (U := (-(9941664845595572648541 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_8 : Uω (aρ 8) (bρ 8) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1203,25 +1079,21 @@ lemma U_259_8 : have hlg : Real.log (7201559110597499 / 80000000000000000 : ℝ) ≤ (-(1203864543957815277543 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7201559110597499 / 80000000000000000 : ℝ) = - (7201559110597499 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7201559110597499 / 5000000000000000 : ℚ)) - (U := (182429816642184722457 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7201559110597499 / 5000000000000000 : ℝ) ≤ - (182429816642184722457 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (619990141214531 / 10000000000000000 : ℝ)) (q := - (7201559110597499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7201559110597499 / 80000000000000000 : ℚ)) + (r' := (7201559110597499 / 5000000000000000 : ℚ)) + (U := (-(1203864543957815277543 / 500000000000000000000 : ℚ))) + (U' := (182429816642184722457 / 500000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (13996732678527 / 64000000000000 : ℚ)) + (s := (619990141214531 / 10000000000000000 : ℚ)) + (q := (7201559110597499 / 80000000000000000 : ℚ)) + (U := (-(1203864543957815277543 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_259_9 : Uω (aρ 9) (bρ 9) (13996732678527 / 64000000000000 : ℝ) ≤ @@ -1354,25 +1226,21 @@ lemma U_260_1 : have hlg : Real.log (340439608074559 / 1600000000000000 : ℝ) ≤ (-(154752116007199462903 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (340439608074559 / 1600000000000000 : ℝ) = - (340439608074559 / 200000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (340439608074559 / 200000000000000 : ℚ)) - (U := (53192038082800537097 / 100000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (340439608074559 / 200000000000000 : ℝ) ≤ - (53192038082800537097 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21276715697023 / 100000000000000 : ℝ)) (q := - (340439608074559 / 1600000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (340439608074559 / 1600000000000000 : ℚ)) + (r' := (340439608074559 / 200000000000000 : ℚ)) + (U := (-(154752116007199462903 / 100000000000000000000 : ℚ))) + (U' := (53192038082800537097 / 100000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (21276715697023 / 100000000000000 : ℚ)) + (q := (340439608074559 / 1600000000000000 : ℚ)) + (U := (-(154752116007199462903 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_2 : Uω (aρ 2) (bρ 2) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1380,25 +1248,21 @@ lemma U_260_2 : have hlg : Real.log (8414200672126911 / 40000000000000000 : ℝ) ≤ (-(1948698273326129675261 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8414200672126911 / 40000000000000000 : ℝ) = - (8414200672126911 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8414200672126911 / 5000000000000000 : ℚ)) - (U := (650603652798870324739 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8414200672126911 / 5000000000000000 : ℝ) ≤ - (650603652798870324739 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (262880727167971 / 1250000000000000 : ℝ)) (q := - (8414200672126911 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8414200672126911 / 40000000000000000 : ℚ)) + (r' := (8414200672126911 / 5000000000000000 : ℚ)) + (U := (-(1948698273326129675261 / 1250000000000000000000 : ℚ))) + (U' := (650603652798870324739 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (262880727167971 / 1250000000000000 : ℚ)) + (q := (8414200672126911 / 40000000000000000 : ℚ)) + (U := (-(1948698273326129675261 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_3 : Uω (aρ 3) (bρ 3) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1406,25 +1270,21 @@ lemma U_260_3 : have hlg : Real.log (8219433074646267 / 40000000000000000 : ℝ) ≤ (-(3955945539164048809487 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8219433074646267 / 40000000000000000 : ℝ) = - (8219433074646267 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8219433074646267 / 5000000000000000 : ℚ)) - (U := (1242658313085951190513 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8219433074646267 / 5000000000000000 : ℝ) ≤ - (1242658313085951190513 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1026529062476723 / 5000000000000000 : ℝ)) (q := - (8219433074646267 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8219433074646267 / 40000000000000000 : ℚ)) + (r' := (8219433074646267 / 5000000000000000 : ℚ)) + (U := (-(3955945539164048809487 / 2500000000000000000000 : ℚ))) + (U' := (1242658313085951190513 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (1026529062476723 / 5000000000000000 : ℚ)) + (q := (8219433074646267 / 40000000000000000 : ℚ)) + (U := (-(3955945539164048809487 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_4 : Uω (aρ 4) (bρ 4) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1432,25 +1292,21 @@ lemma U_260_4 : have hlg : Real.log (7892128271465753 / 40000000000000000 : ℝ) ≤ (-(1623013611952324522931 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7892128271465753 / 40000000000000000 : ℝ) = - (7892128271465753 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7892128271465753 / 5000000000000000 : ℚ)) - (U := (456427928947675477069 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7892128271465753 / 5000000000000000 : ℝ) ≤ - (456427928947675477069 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1967699904428189 / 10000000000000000 : ℝ)) (q := - (7892128271465753 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7892128271465753 / 40000000000000000 : ℚ)) + (r' := (7892128271465753 / 5000000000000000 : ℚ)) + (U := (-(1623013611952324522931 / 1000000000000000000000 : ℚ))) + (U' := (456427928947675477069 / 1000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (1967699904428189 / 10000000000000000 : ℚ)) + (q := (7892128271465753 / 40000000000000000 : ℚ)) + (U := (-(1623013611952324522931 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_5 : Uω (aρ 5) (bρ 5) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1458,25 +1314,21 @@ lemma U_260_5 : have hlg : Real.log (7382989589843757 / 40000000000000000 : ℝ) ≤ (-(16897008032751650925741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7382989589843757 / 40000000000000000 : ℝ) = - (7382989589843757 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7382989589843757 / 5000000000000000 : ℚ)) - (U := (3897407376248349074259 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7382989589843757 / 5000000000000000 : ℝ) ≤ - (3897407376248349074259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1831320482952191 / 10000000000000000 : ℝ)) (q := - (7382989589843757 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7382989589843757 / 40000000000000000 : ℚ)) + (r' := (7382989589843757 / 5000000000000000 : ℚ)) + (U := (-(16897008032751650925741 / 10000000000000000000000 : ℚ))) + (U' := (3897407376248349074259 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (1831320482952191 / 10000000000000000 : ℚ)) + (q := (7382989589843757 / 40000000000000000 : ℚ)) + (U := (-(16897008032751650925741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_6 : Uω (aρ 6) (bρ 6) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1484,25 +1336,21 @@ lemma U_260_6 : have hlg : Real.log (6623509487161253 / 40000000000000000 : ℝ) ≤ (-(17982540898443015669829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6623509487161253 / 40000000000000000 : ℝ) = - (6623509487161253 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6623509487161253 / 5000000000000000 : ℚ)) - (U := (2811874510556984330171 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6623509487161253 / 5000000000000000 : ℝ) ≤ - (2811874510556984330171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1618820806750939 / 10000000000000000 : ℝ)) (q := - (6623509487161253 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6623509487161253 / 40000000000000000 : ℚ)) + (r' := (6623509487161253 / 5000000000000000 : ℚ)) + (U := (-(17982540898443015669829 / 10000000000000000000000 : ℚ))) + (U' := (2811874510556984330171 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (1618820806750939 / 10000000000000000 : ℚ)) + (q := (6623509487161253 / 40000000000000000 : ℚ)) + (U := (-(17982540898443015669829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_7 : Uω (aρ 7) (bρ 7) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1510,25 +1358,21 @@ lemma U_260_7 : have hlg : Real.log (5499842223512557 / 40000000000000000 : ℝ) ≤ (-(19841600481412250417977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5499842223512557 / 40000000000000000 : ℝ) = - (5499842223512557 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5499842223512557 / 5000000000000000 : ℚ)) - (U := (952814927587749582023 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5499842223512557 / 5000000000000000 : ℝ) ≤ - (952814927587749582023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1280648555686591 / 10000000000000000 : ℝ)) (q := - (5499842223512557 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5499842223512557 / 40000000000000000 : ℚ)) + (r' := (5499842223512557 / 5000000000000000 : ℚ)) + (U := (-(19841600481412250417977 / 10000000000000000000000 : ℚ))) + (U' := (952814927587749582023 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (1280648555686591 / 10000000000000000 : ℚ)) + (q := (5499842223512557 / 40000000000000000 : ℚ)) + (U := (-(19841600481412250417977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_8 : Uω (aρ 8) (bρ 8) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1536,25 +1380,21 @@ lemma U_260_8 : have hlg : Real.log (3631624103671967 / 40000000000000000 : ℝ) ≤ (-(959679797350474912757 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3631624103671967 / 40000000000000000 : ℝ) = - (3631624103671967 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3631624103671967 / 2500000000000000 : ℚ)) - (U := (149355691129525087243 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3631624103671967 / 2500000000000000 : ℝ) ≤ - (149355691129525087243 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (78760143388287 / 1250000000000000 : ℝ)) (q := - (3631624103671967 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3631624103671967 / 40000000000000000 : ℚ)) + (r' := (3631624103671967 / 2500000000000000 : ℚ)) + (U := (-(959679797350474912757 / 400000000000000000000 : ℚ))) + (U' := (149355691129525087243 / 400000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7015426397807 / 32000000000000 : ℚ)) + (s := (78760143388287 / 1250000000000000 : ℚ)) + (q := (3631624103671967 / 40000000000000000 : ℚ)) + (U := (-(959679797350474912757 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_260_9 : Uω (aρ 9) (bρ 9) (7015426397807 / 32000000000000 : ℝ) ≤ @@ -1686,25 +1526,21 @@ lemma U_261_1 : have hlg : Real.log (17064632069348817 / 80000000000000000 : ℝ) ≤ (-(7725093061549607964581 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17064632069348817 / 80000000000000000 : ℝ) = - (17064632069348817 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17064632069348817 / 10000000000000000 : ℚ)) - (U := (2672114642950392035419 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17064632069348817 / 10000000000000000 : ℝ) ≤ - (2672114642950392035419 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2133003217812673 / 10000000000000000 : ℝ)) (q := - (17064632069348817 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17064632069348817 / 80000000000000000 : ℚ)) + (r' := (17064632069348817 / 10000000000000000 : ℚ)) + (U := (-(7725093061549607964581 / 5000000000000000000000 : ℚ))) + (U' := (2672114642950392035419 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (2133003217812673 / 10000000000000000 : ℚ)) + (q := (17064632069348817 / 80000000000000000 : ℚ)) + (U := (-(7725093061549607964581 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_2 : Uω (aρ 2) (bρ 2) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1712,25 +1548,21 @@ lemma U_261_2 : have hlg : Real.log (3374212338613069 / 16000000000000000 : ℝ) ≤ (-(622570722209901726493 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3374212338613069 / 16000000000000000 : ℝ) = - (3374212338613069 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3374212338613069 / 2000000000000000 : ℚ)) - (U := (209205894150098273507 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3374212338613069 / 2000000000000000 : ℝ) ≤ - (209205894150098273507 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421675927250361 / 2000000000000000 : ℝ)) (q := - (3374212338613069 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3374212338613069 / 16000000000000000 : ℚ)) + (r' := (3374212338613069 / 2000000000000000 : ℚ)) + (U := (-(622570722209901726493 / 400000000000000000000 : ℚ))) + (U' := (209205894150098273507 / 400000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (421675927250361 / 2000000000000000 : ℚ)) + (q := (3374212338613069 / 16000000000000000 : ℚ)) + (U := (-(622570722209901726493 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_3 : Uω (aρ 3) (bρ 3) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1738,25 +1570,21 @@ lemma U_261_3 : have hlg : Real.log (16481553594822649 / 80000000000000000 : ℝ) ≤ (-(157978484232550097711 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16481553594822649 / 80000000000000000 : ℝ) = - (16481553594822649 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16481553594822649 / 10000000000000000 : ℚ)) - (U := (49965669857449902289 / 100000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16481553594822649 / 10000000000000000 : ℝ) ≤ - (49965669857449902289 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2058398718041131 / 10000000000000000 : ℝ)) (q := - (16481553594822649 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16481553594822649 / 80000000000000000 : ℚ)) + (r' := (16481553594822649 / 10000000000000000 : ℚ)) + (U := (-(157978484232550097711 / 100000000000000000000 : ℚ))) + (U' := (49965669857449902289 / 100000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (2058398718041131 / 10000000000000000 : ℚ)) + (q := (16481553594822649 / 80000000000000000 : ℚ)) + (U := (-(157978484232550097711 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_4 : Uω (aρ 4) (bρ 4) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1764,25 +1592,21 @@ lemma U_261_4 : have hlg : Real.log (15827021951478469 / 80000000000000000 : ℝ) ≤ (-(506346220181221679599 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15827021951478469 / 80000000000000000 : ℝ) = - (15827021951478469 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15827021951478469 / 10000000000000000 : ℚ)) - (U := (143479261350028320401 / 312500000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15827021951478469 / 10000000000000000 : ℝ) ≤ - (143479261350028320401 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (986529994135043 / 5000000000000000 : ℝ)) (q := - (15827021951478469 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15827021951478469 / 80000000000000000 : ℚ)) + (r' := (15827021951478469 / 10000000000000000 : ℚ)) + (U := (-(506346220181221679599 / 312500000000000000000 : ℚ))) + (U' := (143479261350028320401 / 312500000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (986529994135043 / 5000000000000000 : ℚ)) + (q := (15827021951478469 / 80000000000000000 : ℚ)) + (U := (-(506346220181221679599 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_5 : Uω (aρ 5) (bρ 5) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1790,25 +1614,21 @@ lemma U_261_5 : have hlg : Real.log (14808964335655981 / 80000000000000000 : ℝ) ≤ (-(16867939381300538389631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14808964335655981 / 80000000000000000 : ℝ) = - (14808964335655981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14808964335655981 / 10000000000000000 : ℚ)) - (U := (3926476027699461610369 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14808964335655981 / 10000000000000000 : ℝ) ≤ - (3926476027699461610369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (229591937956183 / 1250000000000000 : ℝ)) (q := - (14808964335655981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14808964335655981 / 80000000000000000 : ℚ)) + (r' := (14808964335655981 / 10000000000000000 : ℚ)) + (U := (-(16867939381300538389631 / 10000000000000000000000 : ℚ))) + (U' := (3926476027699461610369 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (229591937956183 / 1250000000000000 : ℚ)) + (q := (14808964335655981 / 80000000000000000 : ℚ)) + (U := (-(16867939381300538389631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_6 : Uω (aρ 6) (bρ 6) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1816,25 +1636,21 @@ lemma U_261_6 : have hlg : Real.log (13290642151223293 / 80000000000000000 : ℝ) ≤ (-(17949664439597163688407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13290642151223293 / 80000000000000000 : ℝ) = - (13290642151223293 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13290642151223293 / 10000000000000000 : ℚ)) - (U := (2844750969402836311593 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13290642151223293 / 10000000000000000 : ℝ) ≤ - (2844750969402836311593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (406098833170323 / 2500000000000000 : ℝ)) (q := - (13290642151223293 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13290642151223293 / 80000000000000000 : ℚ)) + (r' := (13290642151223293 / 10000000000000000 : ℚ)) + (U := (-(17949664439597163688407 / 10000000000000000000000 : ℚ))) + (U' := (2844750969402836311593 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (406098833170323 / 2500000000000000 : ℚ)) + (q := (13290642151223293 / 80000000000000000 : ℚ)) + (U := (-(17949664439597163688407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_7 : Uω (aρ 7) (bρ 7) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1842,25 +1658,21 @@ lemma U_261_7 : have hlg : Real.log (2209092309263349 / 16000000000000000 : ℝ) ≤ (-(4950017525222746901699 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2209092309263349 / 16000000000000000 : ℝ) = - (2209092309263349 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2209092309263349 / 2000000000000000 : ℚ)) - (U := (248586327027253098301 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2209092309263349 / 2000000000000000 : ℝ) ≤ - (248586327027253098301 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (257352312442931 / 2000000000000000 : ℝ)) (q := - (2209092309263349 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2209092309263349 / 16000000000000000 : ℚ)) + (r' := (2209092309263349 / 2000000000000000 : ℚ)) + (U := (-(4950017525222746901699 / 2500000000000000000000 : ℚ))) + (U' := (248586327027253098301 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (257352312442931 / 2000000000000000 : ℚ)) + (q := (2209092309263349 / 16000000000000000 : ℚ)) + (U := (-(4950017525222746901699 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_8 : Uω (aρ 8) (bρ 8) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -1868,25 +1680,21 @@ lemma U_261_8 : have hlg : Real.log (7324478599017021 / 80000000000000000 : ℝ) ≤ (-(23908046622860256109079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7324478599017021 / 80000000000000000 : ℝ) = - (7324478599017021 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7324478599017021 / 5000000000000000 : ℚ)) - (U := (3817840589139743890921 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7324478599017021 / 5000000000000000 : ℝ) ≤ - (3817840589139743890921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160014369182431 / 2500000000000000 : ℝ)) (q := - (7324478599017021 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7324478599017021 / 80000000000000000 : ℚ)) + (r' := (7324478599017021 / 5000000000000000 : ℚ)) + (U := (-(23908046622860256109079 / 10000000000000000000000 : ℚ))) + (U' := (3817840589139743890921 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14064972912701 / 64000000000000 : ℚ)) + (s := (160014369182431 / 2500000000000000 : ℚ)) + (q := (7324478599017021 / 80000000000000000 : ℚ)) + (U := (-(23908046622860256109079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_261_9 : Uω (aρ 9) (bρ 9) (14064972912701 / 64000000000000 : ℝ) ≤ @@ -2017,25 +1825,21 @@ lemma U_262_1 : have hlg : Real.log (4276820931848451 / 20000000000000000 : ℝ) ≤ (-(15425223121055442148307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4276820931848451 / 20000000000000000 : ℝ) = - (4276820931848451 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4276820931848451 / 2500000000000000 : ℚ)) - (U := (5369192287944557851693 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4276820931848451 / 2500000000000000 : ℝ) ≤ - (5369192287944557851693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (534583716007269 / 2500000000000000 : ℝ)) (q := - (4276820931848451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4276820931848451 / 20000000000000000 : ℚ)) + (r' := (4276820931848451 / 2500000000000000 : ℚ)) + (U := (-(15425223121055442148307 / 10000000000000000000000 : ℚ))) + (U' := (5369192287944557851693 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (534583716007269 / 2500000000000000 : ℚ)) + (q := (4276820931848451 / 20000000000000000 : ℚ)) + (U := (-(15425223121055442148307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_2 : Uω (aρ 2) (bρ 2) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2043,25 +1847,21 @@ lemma U_262_2 : have hlg : Real.log (4228430497599681 / 20000000000000000 : ℝ) ≤ (-(31078027786503970657 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4228430497599681 / 20000000000000000 : ℝ) = - (4228430497599681 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4228430497599681 / 2500000000000000 : ℚ)) - (U := (10510803031496029343 / 20000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4228430497599681 / 2500000000000000 : ℝ) ≤ - (10510803031496029343 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1056856721145153 / 5000000000000000 : ℝ)) (q := - (4228430497599681 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4228430497599681 / 20000000000000000 : ℚ)) + (r' := (4228430497599681 / 2500000000000000 : ℚ)) + (U := (-(31078027786503970657 / 20000000000000000000 : ℚ))) + (U' := (10510803031496029343 / 20000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (1056856721145153 / 5000000000000000 : ℚ)) + (q := (4228430497599681 / 20000000000000000 : ℚ)) + (U := (-(31078027786503970657 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_3 : Uω (aρ 3) (bρ 3) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2069,25 +1869,21 @@ lemma U_262_3 : have hlg : Real.log (516382526483561 / 2500000000000000 : ℝ) ≤ (-(15771981888500432529827 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (516382526483561 / 2500000000000000 : ℝ) = - (516382526483561 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (516382526483561 / 312500000000000 : ℚ)) - (U := (5022433520499567470173 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (516382526483561 / 312500000000000 : ℝ) ≤ - (5022433520499567470173 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2063739262909113 / 10000000000000000 : ℝ)) (q := - (516382526483561 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (516382526483561 / 2500000000000000 : ℚ)) + (r' := (516382526483561 / 312500000000000 : ℚ)) + (U := (-(15771981888500432529827 / 10000000000000000000000 : ℚ))) + (U' := (5022433520499567470173 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (2063739262909113 / 10000000000000000 : ℚ)) + (q := (516382526483561 / 2500000000000000 : ℚ)) + (U := (-(15771981888500432529827 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_4 : Uω (aρ 4) (bρ 4) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2095,25 +1891,21 @@ lemma U_262_4 : have hlg : Real.log (991861671071893 / 5000000000000000 : ℝ) ≤ (-(16176095375587935077251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (991861671071893 / 5000000000000000 : ℝ) = - (991861671071893 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (991861671071893 / 625000000000000 : ℚ)) - (U := (4618320033412064922749 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (991861671071893 / 625000000000000 : ℝ) ≤ - (4618320033412064922749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1978419916393197 / 10000000000000000 : ℝ)) (q := - (991861671071893 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (991861671071893 / 5000000000000000 : ℚ)) + (r' := (991861671071893 / 625000000000000 : ℚ)) + (U := (-(16176095375587935077251 / 10000000000000000000000 : ℚ))) + (U' := (4618320033412064922749 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (1978419916393197 / 10000000000000000 : ℚ)) + (q := (991861671071893 / 5000000000000000 : ℚ)) + (U := (-(16176095375587935077251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_5 : Uω (aρ 5) (bρ 5) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2121,25 +1913,21 @@ lemma U_262_5 : have hlg : Real.log (928246721082921 / 5000000000000000 : ℝ) ≤ (-(3367791259899323997961 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (928246721082921 / 5000000000000000 : ℝ) = - (928246721082921 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (928246721082921 / 625000000000000 : ℚ)) - (U := (791091821900676002039 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (928246721082921 / 625000000000000 : ℝ) ≤ - (791091821900676002039 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1842150035772309 / 10000000000000000 : ℝ)) (q := - (928246721082921 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (928246721082921 / 5000000000000000 : ℚ)) + (r' := (928246721082921 / 625000000000000 : ℚ)) + (U := (-(3367791259899323997961 / 2000000000000000000000 : ℚ))) + (U' := (791091821900676002039 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (1842150035772309 / 10000000000000000 : ℚ)) + (q := (928246721082921 / 5000000000000000 : ℚ)) + (U := (-(3367791259899323997961 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_6 : Uω (aρ 6) (bρ 6) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2147,25 +1935,21 @@ lemma U_262_6 : have hlg : Real.log (833391176110807 / 5000000000000000 : ℝ) ≤ (-(17916900595241057764019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (833391176110807 / 5000000000000000 : ℝ) = - (833391176110807 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (833391176110807 / 625000000000000 : ℚ)) - (U := (2877514813758942235981 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (833391176110807 / 625000000000000 : ℝ) ≤ - (2877514813758942235981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1629968231023853 / 10000000000000000 : ℝ)) (q := - (833391176110807 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (833391176110807 / 5000000000000000 : ℚ)) + (r' := (833391176110807 / 625000000000000 : ℚ)) + (U := (-(17916900595241057764019 / 10000000000000000000000 : ℚ))) + (U' := (2877514813758942235981 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (1629968231023853 / 10000000000000000 : ℚ)) + (q := (833391176110807 / 5000000000000000 : ℚ)) + (U := (-(17916900595241057764019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_7 : Uω (aρ 7) (bρ 7) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2173,25 +1957,21 @@ lemma U_262_7 : have hlg : Real.log (1386401370794209 / 10000000000000000 : ℝ) ≤ (-(9879368220258900866009 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1386401370794209 / 10000000000000000 : ℝ) = - (1386401370794209 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1386401370794209 / 1250000000000000 : ℚ)) - (U := (517839484241099133991 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1386401370794209 / 1250000000000000 : ℝ) ≤ - (517839484241099133991 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1292867648929043 / 10000000000000000 : ℝ)) (q := - (1386401370794209 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1386401370794209 / 10000000000000000 : ℚ)) + (r' := (1386401370794209 / 1250000000000000 : ℚ)) + (U := (-(9879368220258900866009 / 5000000000000000000000 : ℚ))) + (U' := (517839484241099133991 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (1292867648929043 / 10000000000000000 : ℚ)) + (q := (1386401370794209 / 10000000000000000 : ℚ)) + (U := (-(9879368220258900866009 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_8 : Uω (aρ 8) (bρ 8) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2199,25 +1979,21 @@ lemma U_262_8 : have hlg : Real.log (1846317852262463 / 20000000000000000 : ℝ) ≤ (-(11912694834656871134041 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1846317852262463 / 20000000000000000 : ℝ) = - (1846317852262463 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1846317852262463 / 1250000000000000 : ℚ)) - (U := (1950248771343128865959 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1846317852262463 / 1250000000000000 : ℝ) ≤ - (1950248771343128865959 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40620275683943 / 625000000000000 : ℝ)) (q := - (1846317852262463 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1846317852262463 / 20000000000000000 : ℚ)) + (r' := (1846317852262463 / 1250000000000000 : ℚ)) + (U := (-(11912694834656871134041 / 5000000000000000000000 : ℚ))) + (U' := (1950248771343128865959 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3524773257447 / 16000000000000 : ℚ)) + (s := (40620275683943 / 625000000000000 : ℚ)) + (q := (1846317852262463 / 20000000000000000 : ℚ)) + (U := (-(11912694834656871134041 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_262_9 : Uω (aρ 9) (bρ 9) (3524773257447 / 16000000000000 : ℝ) ≤ @@ -2349,25 +2125,21 @@ lemma U_263_1 : have hlg : Real.log (17149935377919439 / 80000000000000000 : ℝ) ≤ (-(15400322283405405486297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17149935377919439 / 80000000000000000 : ℝ) = - (17149935377919439 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17149935377919439 / 10000000000000000 : ℚ)) - (U := (5394093125594594513703 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17149935377919439 / 10000000000000000 : ℝ) ≤ - (5394093125594594513703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2143666508365641 / 10000000000000000 : ℝ)) (q := - (17149935377919439 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17149935377919439 / 80000000000000000 : ℚ)) + (r' := (17149935377919439 / 10000000000000000 : ℚ)) + (U := (-(15400322283405405486297 / 10000000000000000000000 : ℚ))) + (U' := (5394093125594594513703 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4522628207 / 20480000000 : ℚ)) + (s := (2143666508365641 / 10000000000000000 : ℚ)) + (q := (17149935377919439 / 80000000000000000 : ℚ)) + (U := (-(15400322283405405486297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_2 : Uω (aρ 2) (bρ 2) (4522628207 / 20480000000 : ℝ) ≤ @@ -2375,25 +2147,21 @@ lemma U_263_2 : have hlg : Real.log (16956382236642683 / 80000000000000000 : ℝ) ≤ (-(7756911689015681382531 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16956382236642683 / 80000000000000000 : ℝ) = - (16956382236642683 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16956382236642683 / 10000000000000000 : ℚ)) - (U := (2640296015484318617469 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16956382236642683 / 10000000000000000 : ℝ) ≤ - (2640296015484318617469 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (529761808889113 / 2500000000000000 : ℝ)) (q := - (16956382236642683 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16956382236642683 / 80000000000000000 : ℚ)) + (r' := (16956382236642683 / 10000000000000000 : ℚ)) + (U := (-(7756911689015681382531 / 5000000000000000000000 : ℚ))) + (U' := (2640296015484318617469 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4522628207 / 20480000000 : ℚ)) + (s := (529761808889113 / 2500000000000000 : ℚ)) + (q := (16956382236642683 / 80000000000000000 : ℚ)) + (U := (-(7756911689015681382531 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_3 : Uω (aρ 3) (bρ 3) (4522628207 / 20480000000 : ℝ) ≤ @@ -2401,25 +2169,21 @@ lemma U_263_3 : have hlg : Real.log (16566927908739967 / 80000000000000000 : ℝ) ≤ (-(7873091102223352406081 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16566927908739967 / 80000000000000000 : ℝ) = - (16566927908739967 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16566927908739967 / 10000000000000000 : ℚ)) - (U := (2524116602276647593919 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16566927908739967 / 10000000000000000 : ℝ) ≤ - (2524116602276647593919 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2069079759930773 / 10000000000000000 : ℝ)) (q := - (16566927908739967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16566927908739967 / 80000000000000000 : ℚ)) + (r' := (16566927908739967 / 10000000000000000 : ℚ)) + (U := (-(7873091102223352406081 / 5000000000000000000000 : ℚ))) + (U' := (2524116602276647593919 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4522628207 / 20480000000 : ℚ)) + (s := (2069079759930773 / 10000000000000000 : ℚ)) + (q := (16566927908739967 / 80000000000000000 : ℚ)) + (U := (-(7873091102223352406081 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_4 : Uω (aρ 4) (bρ 4) (4522628207 / 20480000000 : ℝ) ≤ @@ -2427,25 +2191,21 @@ lemma U_263_4 : have hlg : Real.log (15912550904995751 / 80000000000000000 : ℝ) ≤ (-(16149184709585599162011 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15912550904995751 / 80000000000000000 : ℝ) = - (15912550904995751 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15912550904995751 / 10000000000000000 : ℚ)) - (U := (4645230699414400837989 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15912550904995751 / 10000000000000000 : ℝ) ≤ - (4645230699414400837989 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1983779690059719 / 10000000000000000 : ℝ)) (q := - (15912550904995751 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15912550904995751 / 80000000000000000 : ℚ)) + (r' := (15912550904995751 / 10000000000000000 : ℚ)) + (U := (-(16149184709585599162011 / 10000000000000000000000 : ℚ))) + (U' := (4645230699414400837989 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4522628207 / 20480000000 : ℚ)) + (s := (1983779690059719 / 10000000000000000 : ℚ)) + (q := (15912550904995751 / 80000000000000000 : ℚ)) + (U := (-(16149184709585599162011 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_5 : Uω (aρ 5) (bρ 5) (4522628207 / 20480000000 : ℝ) ≤ @@ -2453,25 +2213,21 @@ lemma U_263_5 : have hlg : Real.log (14894928801881763 / 80000000000000000 : ℝ) ≤ (-(16810058277414486902431 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14894928801881763 / 80000000000000000 : ℝ) = - (14894928801881763 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14894928801881763 / 10000000000000000 : ℚ)) - (U := (3984357131585513097569 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14894928801881763 / 10000000000000000 : ℝ) ≤ - (3984357131585513097569 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (923782041808111 / 5000000000000000 : ℝ)) (q := - (14894928801881763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14894928801881763 / 80000000000000000 : ℚ)) + (r' := (14894928801881763 / 10000000000000000 : ℚ)) + (U := (-(16810058277414486902431 / 10000000000000000000000 : ℚ))) + (U' := (3984357131585513097569 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4522628207 / 20480000000 : ℚ)) + (s := (923782041808111 / 5000000000000000 : ℚ)) + (q := (14894928801881763 / 80000000000000000 : ℚ)) + (U := (-(16810058277414486902431 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_6 : Uω (aρ 6) (bρ 6) (4522628207 / 20480000000 : ℝ) ≤ @@ -2479,25 +2235,21 @@ lemma U_263_6 : have hlg : Real.log (13377869040521019 / 80000000000000000 : ℝ) ≤ (-(1788424856412957003267 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13377869040521019 / 80000000000000000 : ℝ) = - (13377869040521019 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13377869040521019 / 10000000000000000 : ℚ)) - (U := (291016684487042996733 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13377869040521019 / 10000000000000000 : ℝ) ≤ - (291016684487042996733 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (408884879604009 / 2500000000000000 : ℝ)) (q := - (13377869040521019 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13377869040521019 / 80000000000000000 : ℚ)) + (r' := (13377869040521019 / 10000000000000000 : ℚ)) + (U := (-(1788424856412957003267 / 1000000000000000000000 : ℚ))) + (U' := (291016684487042996733 / 1000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4522628207 / 20480000000 : ℚ)) + (s := (408884879604009 / 2500000000000000 : ℚ)) + (q := (13377869040521019 / 80000000000000000 : ℚ)) + (U := (-(1788424856412957003267 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_7 : Uω (aρ 7) (bρ 7) (4522628207 / 20480000000 : ℝ) ≤ @@ -2505,25 +2257,21 @@ lemma U_263_7 : have hlg : Real.log (2227386619494727 / 16000000000000000 : ℝ) ≤ (-(19717597427316517697399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2227386619494727 / 16000000000000000 : ℝ) = - (2227386619494727 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2227386619494727 / 2000000000000000 : ℚ)) - (U := (1076817981683482302601 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2227386619494727 / 2000000000000000 : ℝ) ≤ - (1076817981683482302601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (129896691341419 / 1000000000000000 : ℝ)) (q := - (2227386619494727 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2227386619494727 / 16000000000000000 : ℚ)) + (r' := (2227386619494727 / 2000000000000000 : ℚ)) + (U := (-(19717597427316517697399 / 10000000000000000000000 : ℚ))) + (U' := (1076817981683482302601 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4522628207 / 20480000000 : ℚ)) + (s := (129896691341419 / 1000000000000000 : ℚ)) + (q := (2227386619494727 / 16000000000000000 : ℚ)) + (U := (-(19717597427316517697399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_8 : Uω (aρ 8) (bρ 8) (4522628207 / 20480000000 : ℝ) ≤ @@ -2531,25 +2279,21 @@ lemma U_263_8 : have hlg : Real.log (7445646272237019 / 80000000000000000 : ℝ) ≤ (-(237439716505508975011 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7445646272237019 / 80000000000000000 : ℝ) = - (7445646272237019 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7445646272237019 / 5000000000000000 : ℚ)) - (U := (39819155614491024989 / 100000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7445646272237019 / 5000000000000000 : ℝ) ≤ - (39819155614491024989 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (164921714611259 / 2500000000000000 : ℝ)) (q := - (7445646272237019 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7445646272237019 / 80000000000000000 : ℚ)) + (r' := (7445646272237019 / 5000000000000000 : ℚ)) + (U := (-(237439716505508975011 / 100000000000000000000 : ℚ))) + (U' := (39819155614491024989 / 100000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4522628207 / 20480000000 : ℚ)) + (s := (164921714611259 / 2500000000000000 : ℚ)) + (q := (7445646272237019 / 80000000000000000 : ℚ)) + (U := (-(237439716505508975011 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_263_9 : Uω (aρ 9) (bρ 9) (4522628207 / 20480000000 : ℝ) ≤ @@ -2682,25 +2426,21 @@ lemma U_264_1 : have hlg : Real.log (1719258702098169 / 8000000000000000 : ℝ) ≤ (-(7687741650642611239753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1719258702098169 / 8000000000000000 : ℝ) = - (1719258702098169 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1719258702098169 / 1000000000000000 : ℚ)) - (U := (2709466053857388760247 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1719258702098169 / 1000000000000000 : ℝ) ≤ - (2709466053857388760247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53724953770909 / 250000000000000 : ℝ)) (q := - (1719258702098169 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1719258702098169 / 8000000000000000 : ℚ)) + (r' := (1719258702098169 / 1000000000000000 : ℚ)) + (U := (-(7687741650642611239753 / 5000000000000000000000 : ℚ))) + (U' := (2709466053857388760247 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (53724953770909 / 250000000000000 : ℚ)) + (q := (1719258702098169 / 8000000000000000 : ℚ)) + (U := (-(7687741650642611239753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_2 : Uω (aρ 2) (bρ 2) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2708,25 +2448,21 @@ lemma U_264_2 : have hlg : Real.log (8499521216091017 / 40000000000000000 : ℝ) ≤ (-(1936087023678734676367 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8499521216091017 / 40000000000000000 : ℝ) = - (8499521216091017 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8499521216091017 / 5000000000000000 : ℚ)) - (U := (663214902446265323633 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8499521216091017 / 5000000000000000 : ℝ) ≤ - (663214902446265323633 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1062190508073223 / 5000000000000000 : ℝ)) (q := - (8499521216091017 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8499521216091017 / 40000000000000000 : ℚ)) + (r' := (8499521216091017 / 5000000000000000 : ℚ)) + (U := (-(1936087023678734676367 / 1250000000000000000000 : ℚ))) + (U' := (663214902446265323633 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (1062190508073223 / 5000000000000000 : ℚ)) + (q := (8499521216091017 / 40000000000000000 : ℚ)) + (U := (-(1936087023678734676367 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_3 : Uω (aρ 3) (bρ 3) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2734,25 +2470,21 @@ lemma U_264_3 : have hlg : Real.log (8304807390049419 / 40000000000000000 : ℝ) ≤ (-(15720449025848114804897 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8304807390049419 / 40000000000000000 : ℝ) = - (8304807390049419 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8304807390049419 / 5000000000000000 : ℚ)) - (U := (5073966383151885195103 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8304807390049419 / 5000000000000000 : ℝ) ≤ - (5073966383151885195103 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2074420209475647 / 10000000000000000 : ℝ)) (q := - (8304807390049419 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8304807390049419 / 40000000000000000 : ℚ)) + (r' := (8304807390049419 / 5000000000000000 : ℚ)) + (U := (-(15720449025848114804897 / 10000000000000000000000 : ℚ))) + (U' := (5073966383151885195103 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (2074420209475647 / 10000000000000000 : ℚ)) + (q := (8304807390049419 / 40000000000000000 : ℚ)) + (U := (-(15720449025848114804897 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_4 : Uω (aρ 4) (bρ 4) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2760,25 +2492,21 @@ lemma U_264_4 : have hlg : Real.log (7977657230004551 / 40000000000000000 : ℝ) ≤ (-(8061173325877085877879 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7977657230004551 / 40000000000000000 : ℝ) = - (7977657230004551 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7977657230004551 / 5000000000000000 : ℚ)) - (U := (2336034378622914122121 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7977657230004551 / 5000000000000000 : ℝ) ≤ - (2336034378622914122121 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1989139310518213 / 10000000000000000 : ℝ)) (q := - (7977657230004551 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7977657230004551 / 40000000000000000 : ℚ)) + (r' := (7977657230004551 / 5000000000000000 : ℚ)) + (U := (-(8061173325877085877879 / 5000000000000000000000 : ℚ))) + (U' := (2336034378622914122121 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (1989139310518213 / 10000000000000000 : ℚ)) + (q := (7977657230004551 / 40000000000000000 : ℚ)) + (U := (-(8061173325877085877879 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_5 : Uω (aρ 5) (bρ 5) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2786,25 +2514,21 @@ lemma U_264_5 : have hlg : Real.log (7468954073150357 / 40000000000000000 : ℝ) ≤ (-(16781244809738776207101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7468954073150357 / 40000000000000000 : ℝ) = - (7468954073150357 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7468954073150357 / 5000000000000000 : ℚ)) - (U := (4013170599261223792899 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7468954073150357 / 5000000000000000 : ℝ) ≤ - (4013170599261223792899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (463244412856529 / 2500000000000000 : ℝ)) (q := - (7468954073150357 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7468954073150357 / 40000000000000000 : ℚ)) + (r' := (7468954073150357 / 5000000000000000 : ℚ)) + (U := (-(16781244809738776207101 / 10000000000000000000000 : ℚ))) + (U' := (4013170599261223792899 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (463244412856529 / 2500000000000000 : ℚ)) + (q := (7468954073150357 / 40000000000000000 : ℚ)) + (U := (-(16781244809738776207101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_6 : Uω (aρ 6) (bρ 6) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2812,25 +2536,21 @@ lemma U_264_6 : have hlg : Real.log (6710736442547223 / 40000000000000000 : ℝ) ≤ (-(446292688846316203507 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6710736442547223 / 40000000000000000 : ℝ) = - (6710736442547223 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6710736442547223 / 5000000000000000 : ℚ)) - (U := (73567696378683796493 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6710736442547223 / 5000000000000000 : ℝ) ≤ - (73567696378683796493 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1641109211264549 / 10000000000000000 : ℝ)) (q := - (6710736442547223 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6710736442547223 / 40000000000000000 : ℚ)) + (r' := (6710736442547223 / 5000000000000000 : ℚ)) + (U := (-(446292688846316203507 / 250000000000000000000 : ℚ))) + (U' := (73567696378683796493 / 250000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (1641109211264549 / 10000000000000000 : ℚ)) + (q := (6710736442547223 / 40000000000000000 : ℚ)) + (U := (-(446292688846316203507 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_7 : Uω (aρ 7) (bρ 7) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2838,25 +2558,21 @@ lemma U_264_7 : have hlg : Real.log (5591314161142619 / 40000000000000000 : ℝ) ≤ (-(19676651023580034608527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5591314161142619 / 40000000000000000 : ℝ) = - (5591314161142619 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5591314161142619 / 5000000000000000 : ℚ)) - (U := (1117764385419965391473 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5591314161142619 / 5000000000000000 : ℝ) ≤ - (1117764385419965391473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1305059451322247 / 10000000000000000 : ℝ)) (q := - (5591314161142619 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5591314161142619 / 40000000000000000 : ℚ)) + (r' := (5591314161142619 / 5000000000000000 : ℚ)) + (U := (-(19676651023580034608527 / 10000000000000000000000 : ℚ))) + (U' := (1117764385419965391473 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (1305059451322247 / 10000000000000000 : ℚ)) + (q := (5591314161142619 / 40000000000000000 : ℚ)) + (U := (-(19676651023580034608527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_8 : Uω (aρ 8) (bρ 8) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -2864,25 +2580,21 @@ lemma U_264_8 : have hlg : Real.log (3752810737940087 / 40000000000000000 : ℝ) ≤ (-(11831871818659477479103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3752810737940087 / 40000000000000000 : ℝ) = - (3752810737940087 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3752810737940087 / 2500000000000000 : ℚ)) - (U := (2031071787340522520897 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3752810737940087 / 2500000000000000 : ℝ) ≤ - (2031071787340522520897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (669349391060981 / 10000000000000000 : ℝ)) (q := - (3752810737940087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3752810737940087 / 40000000000000000 : ℚ)) + (r' := (3752810737940087 / 2500000000000000 : ℚ)) + (U := (-(11831871818659477479103 / 5000000000000000000000 : ℚ))) + (U' := (2031071787340522520897 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7083666631981 / 32000000000000 : ℚ)) + (s := (669349391060981 / 10000000000000000 : ℚ)) + (q := (3752810737940087 / 40000000000000000 : ℚ)) + (U := (-(11831871818659477479103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_264_9 : Uω (aρ 9) (bρ 9) (7083666631981 / 32000000000000 : ℝ) ≤ @@ -3014,25 +2726,21 @@ lemma U_265_1 : have hlg : Real.log (17235238656635969 / 80000000000000000 : ℝ) ≤ (-(76753529340636769929 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17235238656635969 / 80000000000000000 : ℝ) = - (17235238656635969 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17235238656635969 / 10000000000000000 : ℚ)) - (U := (27218547704363230071 / 50000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17235238656635969 / 10000000000000000 : ℝ) ≤ - (27218547704363230071 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1077164895727543 / 5000000000000000 : ℝ)) (q := - (17235238656635969 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17235238656635969 / 80000000000000000 : ℚ)) + (r' := (17235238656635969 / 10000000000000000 : ℚ)) + (U := (-(76753529340636769929 / 50000000000000000000 : ℚ))) + (U' := (27218547704363230071 / 50000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (1077164895727543 / 5000000000000000 : ℚ)) + (q := (17235238656635969 / 80000000000000000 : ℚ)) + (U := (-(76753529340636769929 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_2 : Uω (aρ 2) (bρ 2) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3040,25 +2748,21 @@ lemma U_265_2 : have hlg : Real.log (3408340515479549 / 16000000000000000 : ℝ) ≤ (-(3092726401940492489023 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3408340515479549 / 16000000000000000 : ℝ) = - (3408340515479549 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3408340515479549 / 2000000000000000 : ℚ)) - (U := (1066156679859507510977 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3408340515479549 / 2000000000000000 : ℝ) ≤ - (1066156679859507510977 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (212971478415553 / 1000000000000000 : ℝ)) (q := - (3408340515479549 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3408340515479549 / 16000000000000000 : ℚ)) + (r' := (3408340515479549 / 2000000000000000 : ℚ)) + (U := (-(3092726401940492489023 / 2000000000000000000000 : ℚ))) + (U' := (1066156679859507510977 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (212971478415553 / 1000000000000000 : ℚ)) + (q := (3408340515479549 / 16000000000000000 : ℚ)) + (U := (-(3092726401940492489023 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_3 : Uω (aρ 3) (bρ 3) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3066,25 +2770,21 @@ lemma U_265_3 : have hlg : Real.log (3330460292602701 / 16000000000000000 : ℝ) ≤ (-(15694782010131099692527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3330460292602701 / 16000000000000000 : ℝ) = - (3330460292602701 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3330460292602701 / 2000000000000000 : ℚ)) - (U := (5099633398868900307473 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3330460292602701 / 2000000000000000 : ℝ) ≤ - (5099633398868900307473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207976061190947 / 1000000000000000 : ℝ)) (q := - (3330460292602701 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3330460292602701 / 16000000000000000 : ℚ)) + (r' := (3330460292602701 / 2000000000000000 : ℚ)) + (U := (-(15694782010131099692527 / 10000000000000000000000 : ℚ))) + (U' := (5099633398868900307473 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (207976061190947 / 1000000000000000 : ℚ)) + (q := (3330460292602701 / 16000000000000000 : ℚ)) + (U := (-(15694782010131099692527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_4 : Uω (aρ 4) (bρ 4) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3092,25 +2792,21 @@ lemma U_265_4 : have hlg : Real.log (15998077407130749 / 80000000000000000 : ℝ) ≤ (-(4023895202321576679941 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15998077407130749 / 80000000000000000 : ℝ) = - (15998077407130749 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15998077407130749 / 10000000000000000 : ℚ)) - (U := (1174708649928423320059 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15998077407130749 / 10000000000000000 : ℝ) ≤ - (1174708649928423320059 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1994498779003781 / 10000000000000000 : ℝ)) (q := - (15998077407130749 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15998077407130749 / 80000000000000000 : ℚ)) + (r' := (15998077407130749 / 10000000000000000 : ℚ)) + (U := (-(4023895202321576679941 / 2500000000000000000000 : ℚ))) + (U' := (1174708649928423320059 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (1994498779003781 / 10000000000000000 : ℚ)) + (q := (15998077407130749 / 80000000000000000 : ℚ)) + (U := (-(4023895202321576679941 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_5 : Uω (aρ 5) (bρ 5) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3118,25 +2814,21 @@ lemma U_265_5 : have hlg : Real.log (14980885587363893 / 80000000000000000 : ℝ) ≤ (-(16752515395708029767003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14980885587363893 / 80000000000000000 : ℝ) = - (14980885587363893 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14980885587363893 / 10000000000000000 : ℚ)) - (U := (4041900013291970232997 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14980885587363893 / 10000000000000000 : ℝ) ≤ - (4041900013291970232997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1858390743397067 / 10000000000000000 : ℝ)) (q := - (14980885587363893 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14980885587363893 / 80000000000000000 : ℚ)) + (r' := (14980885587363893 / 10000000000000000 : ℚ)) + (U := (-(16752515395708029767003 / 10000000000000000000000 : ℚ))) + (U' := (4041900013291970232997 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (1858390743397067 / 10000000000000000 : ℚ)) + (q := (14980885587363893 / 80000000000000000 : ℚ)) + (U := (-(16752515395708029767003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_6 : Uω (aρ 6) (bρ 6) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3144,25 +2836,21 @@ lemma U_265_6 : have hlg : Real.log (13465070416213477 / 80000000000000000 : ℝ) ≤ (-(17819276780701897823461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13465070416213477 / 80000000000000000 : ℝ) = - (13465070416213477 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13465070416213477 / 10000000000000000 : ℚ)) - (U := (2975138628298102176539 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13465070416213477 / 10000000000000000 : ℝ) ≤ - (2975138628298102176539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1646677325749463 / 10000000000000000 : ℝ)) (q := - (13465070416213477 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13465070416213477 / 80000000000000000 : ℚ)) + (r' := (13465070416213477 / 10000000000000000 : ℚ)) + (U := (-(17819276780701897823461 / 10000000000000000000000 : ℚ))) + (U' := (2975138628298102176539 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (1646677325749463 / 10000000000000000 : ℚ)) + (q := (13465070416213477 / 80000000000000000 : ℚ)) + (U := (-(17819276780701897823461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_7 : Uω (aρ 7) (bρ 7) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3170,25 +2858,21 @@ lemma U_265_7 : have hlg : Real.log (11228297015867517 / 80000000000000000 : ℝ) ≤ (-(4908973806508137317557 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11228297015867517 / 80000000000000000 : ℝ) = - (11228297015867517 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11228297015867517 / 10000000000000000 : ℚ)) - (U := (289630045741862682443 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11228297015867517 / 10000000000000000 : ℝ) ≤ - (289630045741862682443 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1311145356422973 / 10000000000000000 : ℝ)) (q := - (11228297015867517 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11228297015867517 / 80000000000000000 : ℚ)) + (r' := (11228297015867517 / 10000000000000000 : ℚ)) + (U := (-(4908973806508137317557 / 2500000000000000000000 : ℚ))) + (U' := (289630045741862682443 / 2500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (1311145356422973 / 10000000000000000 : ℚ)) + (q := (11228297015867517 / 80000000000000000 : ℚ)) + (U := (-(4908973806508137317557 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_8 : Uω (aρ 8) (bρ 8) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3196,25 +2880,21 @@ lemma U_265_8 : have hlg : Real.log (7565214084243297 / 80000000000000000 : ℝ) ≤ (-(5896164968722676067157 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7565214084243297 / 80000000000000000 : ℝ) = - (7565214084243297 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7565214084243297 / 5000000000000000 : ℚ)) - (U := (1035306834277323932843 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7565214084243297 / 5000000000000000 : ℝ) ≤ - (1035306834277323932843 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (339458137428459 / 5000000000000000 : ℝ)) (q := - (7565214084243297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7565214084243297 / 80000000000000000 : ℚ)) + (r' := (7565214084243297 / 5000000000000000 : ℚ)) + (U := (-(5896164968722676067157 / 2500000000000000000000 : ℚ))) + (U' := (1035306834277323932843 / 2500000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14201453381049 / 64000000000000 : ℚ)) + (s := (339458137428459 / 5000000000000000 : ℚ)) + (q := (7565214084243297 / 80000000000000000 : ℚ)) + (U := (-(5896164968722676067157 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_265_9 : Uω (aρ 9) (bρ 9) (14201453381049 / 64000000000000 : ℝ) ≤ @@ -3346,25 +3026,21 @@ lemma U_266_1 : have hlg : Real.log (863894514246857 / 4000000000000000 : ℝ) ≤ (-(3831497419909473840719 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (863894514246857 / 4000000000000000 : ℝ) = - (863894514246857 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (863894514246857 / 500000000000000 : ℚ)) - (U := (1367106432340526159281 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (863894514246857 / 500000000000000 : ℝ) ≤ - (1367106432340526159281 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (431932286047107 / 2000000000000000 : ℝ)) (q := - (863894514246857 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (863894514246857 / 4000000000000000 : ℚ)) + (r' := (863894514246857 / 500000000000000 : ℚ)) + (U := (-(3831497419909473840719 / 2500000000000000000000 : ℚ))) + (U' := (1367106432340526159281 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (431932286047107 / 2000000000000000 : ℚ)) + (q := (863894514246857 / 4000000000000000 : ℚ)) + (U := (-(3831497419909473840719 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_2 : Uω (aρ 2) (bρ 2) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3372,25 +3048,21 @@ lemma U_266_2 : have hlg : Real.log (4271090668166743 / 20000000000000000 : ℝ) ≤ (-(15438630523490637756799 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4271090668166743 / 20000000000000000 : ℝ) = - (4271090668166743 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4271090668166743 / 2500000000000000 : ℚ)) - (U := (5355784885509362243201 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4271090668166743 / 2500000000000000 : ℝ) ≤ - (5355784885509362243201 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2135048539677993 / 10000000000000000 : ℝ)) (q := - (4271090668166743 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4271090668166743 / 20000000000000000 : ℚ)) + (r' := (4271090668166743 / 2500000000000000 : ℚ)) + (U := (-(15438630523490637756799 / 10000000000000000000000 : ℚ))) + (U' := (5355784885509362243201 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (2135048539677993 / 10000000000000000 : ℚ)) + (q := (4271090668166743 / 20000000000000000 : ℚ)) + (U := (-(15438630523490637756799 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_3 : Uω (aρ 3) (bρ 3) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3398,25 +3070,21 @@ lemma U_266_3 : have hlg : Real.log (4173746989732977 / 20000000000000000 : ℝ) ≤ (-(313383616347333776729 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4173746989732977 / 20000000000000000 : ℝ) = - (4173746989732977 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4173746989732977 / 2500000000000000 : ℚ)) - (U := (102504691832666223271 / 200000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4173746989732977 / 2500000000000000 : ℝ) ≤ - (102504691832666223271 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2085100967594227 / 10000000000000000 : ℝ)) (q := - (4173746989732977 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4173746989732977 / 20000000000000000 : ℚ)) + (r' := (4173746989732977 / 2500000000000000 : ℚ)) + (U := (-(313383616347333776729 / 200000000000000000000 : ℚ))) + (U' := (102504691832666223271 / 200000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (2085100967594227 / 10000000000000000 : ℚ)) + (q := (4173746989732977 / 20000000000000000 : ℚ)) + (U := (-(313383616347333776729 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_4 : Uω (aρ 4) (bρ 4) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3424,23 +3092,21 @@ lemma U_266_4 : have hlg : Real.log (1002552484453 / 5000000000000 : ℝ) ≤ (-(16068886792570002071263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show (1002552484453 / 5000000000000 : ℝ) = (1002552484453 / 625000000000 : ℝ) / 2 ^ 3 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1002552484453 / 625000000000 : ℚ)) - (U := (4725528616429997928737 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1002552484453 / 625000000000 : ℝ) ≤ - (4725528616429997928737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7999432386953 / 40000000000000 : ℝ)) (q := - (1002552484453 / 5000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1002552484453 / 5000000000000 : ℚ)) + (r' := (1002552484453 / 625000000000 : ℚ)) + (U := (-(16068886792570002071263 / 10000000000000000000000 : ℚ))) + (U' := (4725528616429997928737 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (7999432386953 / 40000000000000 : ℚ)) + (q := (1002552484453 / 5000000000000 : ℚ)) + (U := (-(16068886792570002071263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_5 : Uω (aρ 5) (bρ 5) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3448,25 +3114,21 @@ lemma U_266_5 : have hlg : Real.log (1877982642706899 / 10000000000000000 : ℝ) ≤ (-(1045241846191213256377 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1877982642706899 / 10000000000000000 : ℝ) = - (1877982642706899 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1877982642706899 / 1250000000000000 : ℚ)) - (U := (254409116871286743623 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1877982642706899 / 1250000000000000 : ℝ) ≤ - (254409116871286743623 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (232975420459381 / 1250000000000000 : ℝ)) (q := - (1877982642706899 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1877982642706899 / 10000000000000000 : ℚ)) + (r' := (1877982642706899 / 1250000000000000 : ℚ)) + (U := (-(1045241846191213256377 / 625000000000000000000 : ℚ))) + (U' := (254409116871286743623 / 625000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (232975420459381 / 1250000000000000 : ℚ)) + (q := (1877982642706899 / 10000000000000000 : ℚ)) + (U := (-(1045241846191213256377 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_6 : Uω (aρ 6) (bρ 6) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3474,25 +3136,21 @@ lemma U_266_6 : have hlg : Real.log (422145678053367 / 2500000000000000 : ℝ) ≤ (-(4446738867384939903639 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (422145678053367 / 2500000000000000 : ℝ) = - (422145678053367 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (422145678053367 / 312500000000000 : ℚ)) - (U := (751864984865060096361 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (422145678053367 / 312500000000000 : ℝ) ≤ - (751864984865060096361 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (826121938914093 / 5000000000000000 : ℝ)) (q := - (422145678053367 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (422145678053367 / 2500000000000000 : ℚ)) + (r' := (422145678053367 / 312500000000000 : ℚ)) + (U := (-(4446738867384939903639 / 2500000000000000000000 : ℚ))) + (U' := (751864984865060096361 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (826121938914093 / 5000000000000000 : ℚ)) + (q := (422145678053367 / 2500000000000000 : ℚ)) + (U := (-(4446738867384939903639 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_7 : Uω (aρ 7) (bρ 7) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3500,25 +3158,21 @@ lemma U_266_7 : have hlg : Real.log (2818484886490769 / 20000000000000000 : ℝ) ≤ (-(19595328065017379469913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2818484886490769 / 20000000000000000 : ℝ) = - (2818484886490769 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2818484886490769 / 2500000000000000 : ℚ)) - (U := (1199087343982620530087 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2818484886490769 / 2500000000000000 : ℝ) ≤ - (1199087343982620530087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1317224720652019 / 10000000000000000 : ℝ)) (q := - (2818484886490769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2818484886490769 / 20000000000000000 : ℚ)) + (r' := (2818484886490769 / 2500000000000000 : ℚ)) + (U := (-(19595328065017379469913 / 10000000000000000000000 : ℚ))) + (U' := (1199087343982620530087 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (1317224720652019 / 10000000000000000 : ℚ)) + (q := (2818484886490769 / 20000000000000000 : ℚ)) + (U := (-(19595328065017379469913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_8 : Uω (aρ 8) (bρ 8) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3526,25 +3180,21 @@ lemma U_266_8 : have hlg : Real.log (381222002433227 / 4000000000000000 : ℝ) ≤ (-(2938334687597392326683 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (381222002433227 / 4000000000000000 : ℝ) = - (381222002433227 / 250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (381222002433227 / 250000000000000 : ℚ)) - (U := (527401213902607673317 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (381222002433227 / 250000000000000 : ℝ) ≤ - (527401213902607673317 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (137678299533477 / 2000000000000000 : ℝ)) (q := - (381222002433227 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (381222002433227 / 4000000000000000 : ℚ)) + (r' := (381222002433227 / 250000000000000 : ℚ)) + (U := (-(2938334687597392326683 / 1250000000000000000000 : ℚ))) + (U' := (527401213902607673317 / 1250000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1779446687267 / 8000000000000 : ℚ)) + (s := (137678299533477 / 2000000000000000 : ℚ)) + (q := (381222002433227 / 4000000000000000 : ℚ)) + (U := (-(2938334687597392326683 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_266_9 : Uω (aρ 9) (bρ 9) (1779446687267 / 8000000000000 : ℝ) ≤ @@ -3675,25 +3325,21 @@ lemma U_267_1 : have hlg : Real.log (17320541905939527 / 80000000000000000 : ℝ) ≤ (-(3060266886754829329249 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17320541905939527 / 80000000000000000 : ℝ) = - (17320541905939527 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17320541905939527 / 10000000000000000 : ℚ)) - (U := (1098616195045170670751 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17320541905939527 / 10000000000000000 : ℝ) ≤ - (1098616195045170670751 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (270624133398911 / 1250000000000000 : ℝ)) (q := - (17320541905939527 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17320541905939527 / 80000000000000000 : ℚ)) + (r' := (17320541905939527 / 10000000000000000 : ℚ)) + (U := (-(3060266886754829329249 / 2000000000000000000000 : ℚ))) + (U' := (1098616195045170670751 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (270624133398911 / 1250000000000000 : ℚ)) + (q := (17320541905939527 / 80000000000000000 : ℚ)) + (U := (-(3060266886754829329249 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_2 : Uω (aρ 2) (bρ 2) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3701,25 +3347,21 @@ lemma U_267_2 : have hlg : Real.log (17127022718363107 / 80000000000000000 : ℝ) ≤ (-(15413691417798657404249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17127022718363107 / 80000000000000000 : ℝ) = - (17127022718363107 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17127022718363107 / 10000000000000000 : ℚ)) - (U := (5380723991201342595751 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17127022718363107 / 10000000000000000 : ℝ) ≤ - (5380723991201342595751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2140382282807183 / 10000000000000000 : ℝ)) (q := - (17127022718363107 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17127022718363107 / 80000000000000000 : ℚ)) + (r' := (17127022718363107 / 10000000000000000 : ℚ)) + (U := (-(15413691417798657404249 / 10000000000000000000000 : ℚ))) + (U' := (5380723991201342595751 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (2140382282807183 / 10000000000000000 : ℚ)) + (q := (17127022718363107 / 80000000000000000 : ℚ)) + (U := (-(15413691417798657404249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_3 : Uω (aρ 3) (bρ 3) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3727,25 +3369,21 @@ lemma U_267_3 : have hlg : Real.log (16737674269287179 / 80000000000000000 : ℝ) ≤ (-(1955455638780413424699 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16737674269287179 / 80000000000000000 : ℝ) = - (16737674269287179 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16737674269287179 / 10000000000000000 : ℚ)) - (U := (643846287344586575301 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16737674269287179 / 10000000000000000 : ℝ) ≤ - (643846287344586575301 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2090441276888201 / 10000000000000000 : ℝ)) (q := - (16737674269287179 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16737674269287179 / 80000000000000000 : ℚ)) + (r' := (16737674269287179 / 10000000000000000 : ℚ)) + (U := (-(1955455638780413424699 / 1250000000000000000000 : ℚ))) + (U' := (643846287344586575301 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (2090441276888201 / 10000000000000000 : ℚ)) + (q := (16737674269287179 / 80000000000000000 : ℚ)) + (U := (-(1955455638780413424699 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_4 : Uω (aρ 4) (bρ 4) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3753,25 +3391,21 @@ lemma U_267_4 : have hlg : Real.log (16083601497195783 / 80000000000000000 : ℝ) ≤ (-(8021132107576929851351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16083601497195783 / 80000000000000000 : ℝ) = - (16083601497195783 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16083601497195783 / 10000000000000000 : ℚ)) - (U := (2376075596923070148649 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16083601497195783 / 10000000000000000 : ℝ) ≤ - (2376075596923070148649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (125326079058147 / 625000000000000 : ℝ)) (q := - (16083601497195783 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16083601497195783 / 80000000000000000 : ℚ)) + (r' := (16083601497195783 / 10000000000000000 : ℚ)) + (U := (-(8021132107576929851351 / 5000000000000000000000 : ℚ))) + (U' := (2376075596923070148649 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (125326079058147 / 625000000000000 : ℚ)) + (q := (16083601497195783 / 80000000000000000 : ℚ)) + (U := (-(8021132107576929851351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_5 : Uω (aρ 5) (bρ 5) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3779,25 +3413,21 @@ lemma U_267_5 : have hlg : Real.log (15066834825564987 / 80000000000000000 : ℝ) ≤ (-(16695306747974266726253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15066834825564987 / 80000000000000000 : ℝ) = - (15066834825564987 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15066834825564987 / 10000000000000000 : ℚ)) - (U := (4099108661025733273747 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15066834825564987 / 10000000000000000 : ℝ) ≤ - (4099108661025733273747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1869215516357653 / 10000000000000000 : ℝ)) (q := - (15066834825564987 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15066834825564987 / 80000000000000000 : ℚ)) + (r' := (15066834825564987 / 10000000000000000 : ℚ)) + (U := (-(16695306747974266726253 / 10000000000000000000000 : ℚ))) + (U' := (4099108661025733273747 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (1869215516357653 / 10000000000000000 : ℚ)) + (q := (15066834825564987 / 80000000000000000 : ℚ)) + (U := (-(16695306747974266726253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_6 : Uω (aρ 6) (bρ 6) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3805,25 +3435,21 @@ lemma U_267_6 : have hlg : Real.log (13552246792531779 / 80000000000000000 : ℝ) ≤ (-(17754742853671198578557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13552246792531779 / 80000000000000000 : ℝ) = - (13552246792531779 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13552246792531779 / 10000000000000000 : ℚ)) - (U := (3039672555328801421443 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13552246792531779 / 10000000000000000 : ℝ) ≤ - (3039672555328801421443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1657808883239351 / 10000000000000000 : ℝ)) (q := - (13552246792531779 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13552246792531779 / 80000000000000000 : ℚ)) + (r' := (13552246792531779 / 10000000000000000 : ℚ)) + (U := (-(17754742853671198578557 / 10000000000000000000000 : ℚ))) + (U' := (3039672555328801421443 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (1657808883239351 / 10000000000000000 : ℚ)) + (q := (13552246792531779 / 80000000000000000 : ℚ)) + (U := (-(17754742853671198578557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_7 : Uω (aρ 7) (bρ 7) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3831,25 +3457,21 @@ lemma U_267_7 : have hlg : Real.log (11319556273165103 / 80000000000000000 : ℝ) ≤ (-(9777473801854687953071 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11319556273165103 / 80000000000000000 : ℝ) = - (11319556273165103 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11319556273165103 / 10000000000000000 : ℚ)) - (U := (619733902645312046929 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11319556273165103 / 10000000000000000 : ℝ) ≤ - (619733902645312046929 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661648817078841 / 5000000000000000 : ℝ)) (q := - (11319556273165103 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11319556273165103 / 80000000000000000 : ℚ)) + (r' := (11319556273165103 / 10000000000000000 : ℚ)) + (U := (-(9777473801854687953071 / 5000000000000000000000 : ℚ))) + (U' := (619733902645312046929 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (661648817078841 / 5000000000000000 : ℚ)) + (q := (11319556273165103 / 80000000000000000 : ℚ)) + (U := (-(9777473801854687953071 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_8 : Uω (aρ 8) (bρ 8) (14269693615223 / 64000000000000 : ℝ) ≤ @@ -3857,25 +3479,21 @@ lemma U_267_8 : have hlg : Real.log (7683314305291443 / 80000000000000000 : ℝ) ≤ (-(11714878146986777122497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7683314305291443 / 80000000000000000 : ℝ) = - (7683314305291443 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7683314305291443 / 5000000000000000 : ℚ)) - (U := (2148065459013222877503 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7683314305291443 / 5000000000000000 : ℝ) ≤ - (2148065459013222877503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (697778793529267 / 10000000000000000 : ℝ)) (q := - (7683314305291443 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7683314305291443 / 80000000000000000 : ℚ)) + (r' := (7683314305291443 / 5000000000000000 : ℚ)) + (U := (-(11714878146986777122497 / 5000000000000000000000 : ℚ))) + (U' := (2148065459013222877503 / 5000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14269693615223 / 64000000000000 : ℚ)) + (s := (697778793529267 / 10000000000000000 : ℚ)) + (q := (7683314305291443 / 80000000000000000 : ℚ)) + (U := (-(11714878146986777122497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_267_9 : Uω (aρ 9) (bρ 9) (14269693615223 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U22.lean b/LeanPool/Zeta5Irrational/Table/U22.lean index f790a2a7b2..920c96c9d1 100644 --- a/LeanPool/Zeta5Irrational/Table/U22.lean +++ b/LeanPool/Zeta5Irrational/Table/U22.lean @@ -24,25 +24,21 @@ lemma U_268_1 : have hlg : Real.log (8681596759848461 / 40000000000000000 : ℝ) ≤ (-(7638369915361229297179 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8681596759848461 / 40000000000000000 : ℝ) = - (8681596759848461 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8681596759848461 / 5000000000000000 : ℚ)) - (U := (2758837789138770702821 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8681596759848461 / 5000000000000000 : ℝ) ≤ - (2758837789138770702821 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2170324702335793 / 10000000000000000 : ℝ)) (q := - (8681596759848461 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8681596759848461 / 40000000000000000 : ℚ)) + (r' := (8681596759848461 / 5000000000000000 : ℚ)) + (U := (-(7638369915361229297179 / 5000000000000000000000 : ℚ))) + (U' := (2758837789138770702821 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (2170324702335793 / 10000000000000000 : ℚ)) + (q := (8681596759848461 / 40000000000000000 : ℚ)) + (U := (-(7638369915361229297179 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_2 : Uω (aρ 2) (bρ 2) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_268_2 : have hlg : Real.log (1716968271485583 / 8000000000000000 : ℝ) ≤ (-(7694407190984975856153 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1716968271485583 / 8000000000000000 : ℝ) = - (1716968271485583 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1716968271485583 / 1000000000000000 : ℚ)) - (U := (2702800513515024143847 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1716968271485583 / 1000000000000000 : ℝ) ≤ - (2702800513515024143847 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6705362542611 / 31250000000000 : ℝ)) (q := - (1716968271485583 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1716968271485583 / 8000000000000000 : ℚ)) + (r' := (1716968271485583 / 1000000000000000 : ℚ)) + (U := (-(7694407190984975856153 / 5000000000000000000000 : ℚ))) + (U' := (2702800513515024143847 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (6705362542611 / 31250000000000 : ℚ)) + (q := (1716968271485583 / 8000000000000000 : ℚ)) + (U := (-(7694407190984975856153 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_3 : Uω (aρ 3) (bρ 3) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_268_3 : have hlg : Real.log (8390180197748917 / 40000000000000000 : ℝ) ≤ (-(3123634910807985488307 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8390180197748917 / 40000000000000000 : ℝ) = - (8390180197748917 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8390180197748917 / 5000000000000000 : ℚ)) - (U := (1035248170992014511693 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8390180197748917 / 5000000000000000 : ℝ) ≤ - (1035248170992014511693 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2095781540146021 / 10000000000000000 : ℝ)) (q := - (8390180197748917 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8390180197748917 / 40000000000000000 : ℚ)) + (r' := (8390180197748917 / 5000000000000000 : ℚ)) + (U := (-(3123634910807985488307 / 2000000000000000000000 : ℚ))) + (U' := (1035248170992014511693 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (2095781540146021 / 10000000000000000 : ℚ)) + (q := (8390180197748917 / 40000000000000000 : ℚ)) + (U := (-(3123634910807985488307 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_4 : Uω (aρ 4) (bρ 4) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_268_4 : have hlg : Real.log (8063181324878669 / 40000000000000000 : ℝ) ≤ (-(16015712693712828402873 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8063181324878669 / 40000000000000000 : ℝ) = - (8063181324878669 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8063181324878669 / 5000000000000000 : ℚ)) - (U := (4778702715287171597127 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8063181324878669 / 5000000000000000 : ℝ) ≤ - (4778702715287171597127 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2010576284775897 / 10000000000000000 : ℝ)) (q := - (8063181324878669 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8063181324878669 / 40000000000000000 : ℚ)) + (r' := (8063181324878669 / 5000000000000000 : ℚ)) + (U := (-(16015712693712828402873 / 10000000000000000000000 : ℚ))) + (U' := (4778702715287171597127 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (2010576284775897 / 10000000000000000 : ℚ)) + (q := (8063181324878669 / 40000000000000000 : ℚ)) + (U := (-(16015712693712828402873 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_5 : Uω (aρ 5) (bρ 5) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_268_5 : have hlg : Real.log (7554903327646481 / 40000000000000000 : ℝ) ≤ (-(16666826535024517328497 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7554903327646481 / 40000000000000000 : ℝ) = - (7554903327646481 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7554903327646481 / 5000000000000000 : ℚ)) - (U := (4127588873975482671503 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7554903327646481 / 5000000000000000 : ℝ) ≤ - (4127588873975482671503 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1874627205494803 / 10000000000000000 : ℝ)) (q := - (7554903327646481 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7554903327646481 / 40000000000000000 : ℚ)) + (r' := (7554903327646481 / 5000000000000000 : ℚ)) + (U := (-(16666826535024517328497 / 10000000000000000000000 : ℚ))) + (U' := (4127588873975482671503 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (1874627205494803 / 10000000000000000 : ℚ)) + (q := (7554903327646481 / 40000000000000000 : ℚ)) + (U := (-(16666826535024517328497 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_6 : Uω (aρ 6) (bρ 6) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -154,24 +134,21 @@ lemma U_268_6 : have hlg : Real.log (54383303051121 / 320000000000000 : ℝ) ≤ (-(8861319087358917193727 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (54383303051121 / 320000000000000 : ℝ) = (54383303051121 / 40000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54383303051121 / 40000000000000 : ℚ)) - (U := (1535888617141082806273 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54383303051121 / 40000000000000 : ℝ) ≤ - (1535888617141082806273 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13306978860053 / 80000000000000 : ℝ)) (q := - (54383303051121 / 320000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54383303051121 / 320000000000000 : ℚ)) + (r' := (54383303051121 / 40000000000000 : ℚ)) + (U := (-(8861319087358917193727 / 5000000000000000000000 : ℚ))) + (U' := (1535888617141082806273 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (13306978860053 / 80000000000000 : ℚ)) + (q := (54383303051121 / 320000000000000 : ℚ)) + (U := (-(8861319087358917193727 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_7 : Uω (aρ 7) (bρ 7) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -179,25 +156,21 @@ lemma U_268_7 : have hlg : Real.log (5682573775549233 / 40000000000000000 : ℝ) ≤ (-(1951475193735104412929 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5682573775549233 / 40000000000000000 : ℝ) = - (5682573775549233 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5682573775549233 / 5000000000000000 : ℚ)) - (U := (127966347164895587071 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5682573775549233 / 5000000000000000 : ℝ) ≤ - (127966347164895587071 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1329364185346179 / 10000000000000000 : ℝ)) (q := - (5682573775549233 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5682573775549233 / 40000000000000000 : ℚ)) + (r' := (5682573775549233 / 5000000000000000 : ℚ)) + (U := (-(1951475193735104412929 / 1000000000000000000000 : ℚ))) + (U' := (127966347164895587071 / 1000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (1329364185346179 / 10000000000000000 : ℚ)) + (q := (5682573775549233 / 40000000000000000 : ℚ)) + (U := (-(1951475193735104412929 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_8 : Uω (aρ 8) (bρ 8) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -205,25 +178,21 @@ lemma U_268_8 : have hlg : Real.log (3870925431047819 / 40000000000000000 : ℝ) ≤ (-(23353858451496383736881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3870925431047819 / 40000000000000000 : ℝ) = - (3870925431047819 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3870925431047819 / 2500000000000000 : ℚ)) - (U := (4372028760503616263119 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3870925431047819 / 2500000000000000 : ℝ) ≤ - (4372028760503616263119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44192604027217 / 625000000000000 : ℝ)) (q := - (3870925431047819 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3870925431047819 / 40000000000000000 : ℚ)) + (r' := (3870925431047819 / 2500000000000000 : ℚ)) + (U := (-(23353858451496383736881 / 10000000000000000000000 : ℚ))) + (U' := (4372028760503616263119 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1430381373231 / 6400000000000 : ℚ)) + (s := (44192604027217 / 625000000000000 : ℚ)) + (q := (3870925431047819 / 40000000000000000 : ℚ)) + (U := (-(23353858451496383736881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_268_9 : Uω (aρ 9) (bρ 9) (1430381373231 / 6400000000000 : ℝ) ≤ @@ -355,25 +324,21 @@ lemma U_269_1 : have hlg : Real.log (17405845126262593 / 80000000000000000 : ℝ) ≤ (-(7626102786438175269679 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17405845126262593 / 80000000000000000 : ℝ) = - (17405845126262593 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17405845126262593 / 10000000000000000 : ℚ)) - (U := (2771104918061824730321 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17405845126262593 / 10000000000000000 : ℝ) ≤ - (2771104918061824730321 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2175656335682367 / 10000000000000000 : ℝ)) (q := - (17405845126262593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17405845126262593 / 80000000000000000 : ℚ)) + (r' := (17405845126262593 / 10000000000000000 : ℚ)) + (U := (-(7626102786438175269679 / 5000000000000000000000 : ℚ))) + (U' := (2771104918061824730321 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (2175656335682367 / 10000000000000000 : ℚ)) + (q := (17405845126262593 / 80000000000000000 : ℚ)) + (U := (-(7626102786438175269679 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_2 : Uω (aρ 2) (bρ 2) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -381,25 +346,21 @@ lemma U_269_2 : have hlg : Real.log (17212342662511157 / 80000000000000000 : ℝ) ≤ (-(7681999553831932135529 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17212342662511157 / 80000000000000000 : ℝ) = - (17212342662511157 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17212342662511157 / 10000000000000000 : ℚ)) - (U := (2715208150668067864471 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17212342662511157 / 10000000000000000 : ℝ) ≤ - (2715208150668067864471 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (537762433063627 / 2500000000000000 : ℝ)) (q := - (17212342662511157 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17212342662511157 / 80000000000000000 : ℚ)) + (r' := (17212342662511157 / 10000000000000000 : ℚ)) + (U := (-(7681999553831932135529 / 5000000000000000000000 : ℚ))) + (U' := (2715208150668067864471 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (537762433063627 / 2500000000000000 : ℚ)) + (q := (17212342662511157 / 80000000000000000 : ℚ)) + (U := (-(7681999553831932135529 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_3 : Uω (aρ 3) (bρ 3) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -407,25 +368,21 @@ lemma U_269_3 : have hlg : Real.log (16823046338967949 / 80000000000000000 : ℝ) ≤ (-(7796384408299785382657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16823046338967949 / 80000000000000000 : ℝ) = - (16823046338967949 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16823046338967949 / 10000000000000000 : ℚ)) - (U := (2600823296200214617343 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16823046338967949 / 10000000000000000 : ℝ) ≤ - (2600823296200214617343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1050560878859353 / 5000000000000000 : ℝ)) (q := - (16823046338967949 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16823046338967949 / 80000000000000000 : ℚ)) + (r' := (16823046338967949 / 10000000000000000 : ℚ)) + (U := (-(7796384408299785382657 / 5000000000000000000000 : ℚ))) + (U' := (2600823296200214617343 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (1050560878859353 / 5000000000000000 : ℚ)) + (q := (16823046338967949 / 80000000000000000 : ℚ)) + (U := (-(7796384408299785382657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_4 : Uω (aρ 4) (bρ 4) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -433,25 +390,21 @@ lemma U_269_4 : have hlg : Real.log (16169123213664917 / 80000000000000000 : ℝ) ≤ (-(7994615924007200057329 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16169123213664917 / 80000000000000000 : ℝ) = - (16169123213664917 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16169123213664917 / 10000000000000000 : ℚ)) - (U := (2402591780492799942671 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16169123213664917 / 10000000000000000 : ℝ) ≤ - (2402591780492799942671 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (503983789364487 / 2500000000000000 : ℝ)) (q := - (16169123213664917 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16169123213664917 / 80000000000000000 : ℚ)) + (r' := (16169123213664917 / 10000000000000000 : ℚ)) + (U := (-(7994615924007200057329 / 5000000000000000000000 : ℚ))) + (U' := (2402591780492799942671 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (503983789364487 / 2500000000000000 : ℚ)) + (q := (16169123213664917 / 80000000000000000 : ℚ)) + (U := (-(7994615924007200057329 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_5 : Uω (aρ 5) (bρ 5) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -459,25 +412,21 @@ lemma U_269_5 : have hlg : Real.log (15152776646850901 / 80000000000000000 : ℝ) ≤ (-(16638428417119872482403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15152776646850901 / 80000000000000000 : ℝ) = - (15152776646850901 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15152776646850901 / 10000000000000000 : ℚ)) - (U := (4155986991880127517597 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15152776646850901 / 10000000000000000 : ℝ) ≤ - (4155986991880127517597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (470009608772361 / 2500000000000000 : ℝ)) (q := - (15152776646850901 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15152776646850901 / 80000000000000000 : ℚ)) + (r' := (15152776646850901 / 10000000000000000 : ℚ)) + (U := (-(16638428417119872482403 / 10000000000000000000000 : ℚ))) + (U' := (4155986991880127517597 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (470009608772361 / 2500000000000000 : ℚ)) + (q := (15152776646850901 / 80000000000000000 : ℚ)) + (U := (-(16638428417119872482403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_6 : Uω (aρ 6) (bρ 6) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -485,25 +434,21 @@ lemma U_269_6 : have hlg : Real.log (13639398669702877 / 80000000000000000 : ℝ) ≤ (-(3538128136498892697533 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13639398669702877 / 80000000000000000 : ℝ) = - (13639398669702877 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13639398669702877 / 10000000000000000 : ℚ)) - (U := (620754945301107302467 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13639398669702877 / 10000000000000000 : ℝ) ≤ - (620754945301107302467 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (834467157971219 / 5000000000000000 : ℝ)) (q := - (13639398669702877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13639398669702877 / 80000000000000000 : ℚ)) + (r' := (13639398669702877 / 10000000000000000 : ℚ)) + (U := (-(3538128136498892697533 / 2000000000000000000000 : ℚ))) + (U' := (620754945301107302467 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (834467157971219 / 5000000000000000 : ℚ)) + (q := (13639398669702877 / 80000000000000000 : ℚ)) + (U := (-(3538128136498892697533 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_7 : Uω (aρ 7) (bρ 7) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -511,24 +456,21 @@ lemma U_269_7 : have hlg : Real.log (91285709812761 / 640000000000000 : ℝ) ≤ (-(4868684798127873941503 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (91285709812761 / 640000000000000 : ℝ) = (91285709812761 / 80000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (91285709812761 / 80000000000000 : ℚ)) - (U := (329919054122126058497 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (91285709812761 / 80000000000000 : ℝ) ≤ - (329919054122126058497 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2670848921851 / 20000000000000 : ℝ)) (q := - (91285709812761 / 640000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (91285709812761 / 640000000000000 : ℚ)) + (r' := (91285709812761 / 80000000000000 : ℚ)) + (U := (-(4868684798127873941503 / 2500000000000000000000 : ℚ))) + (U' := (329919054122126058497 / 2500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (2670848921851 / 20000000000000 : ℚ)) + (q := (91285709812761 / 640000000000000 : ℚ)) + (U := (-(4868684798127873941503 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_8 : Uω (aρ 8) (bρ 8) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -536,25 +478,21 @@ lemma U_269_8 : have hlg : Real.log (1560012575313533 / 16000000000000000 : ℝ) ≤ (-(23278948388726262110201 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1560012575313533 / 16000000000000000 : ℝ) = - (1560012575313533 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1560012575313533 / 1000000000000000 : ℚ)) - (U := (4446938823273737889799 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1560012575313533 / 1000000000000000 : ℝ) ≤ - (4446938823273737889799 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (143260679951727 / 2000000000000000 : ℝ)) (q := - (1560012575313533 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1560012575313533 / 16000000000000000 : ℚ)) + (r' := (1560012575313533 / 1000000000000000 : ℚ)) + (U := (-(23278948388726262110201 / 10000000000000000000000 : ℚ))) + (U' := (4446938823273737889799 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14337933849397 / 64000000000000 : ℚ)) + (s := (143260679951727 / 2000000000000000 : ℚ)) + (q := (1560012575313533 / 16000000000000000 : ℚ)) + (U := (-(23278948388726262110201 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_269_9 : Uω (aρ 9) (bρ 9) (14337933849397 / 64000000000000 : ℝ) ≤ @@ -686,25 +624,21 @@ lemma U_270_1 : have hlg : Real.log (2181062090711159 / 10000000000000000 : ℝ) ≤ (-(15227731364814907513837 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2181062090711159 / 10000000000000000 : ℝ) = - (2181062090711159 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2181062090711159 / 1250000000000000 : ℚ)) - (U := (5566684044185092486163 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2181062090711159 / 1250000000000000 : ℝ) ≤ - (5566684044185092486163 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2180987967244193 / 10000000000000000 : ℝ)) (q := - (2181062090711159 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2181062090711159 / 10000000000000000 : ℚ)) + (r' := (2181062090711159 / 1250000000000000 : ℚ)) + (U := (-(15227731364814907513837 / 10000000000000000000000 : ℚ))) + (U' := (5566684044185092486163 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (2180987967244193 / 10000000000000000 : ℚ)) + (q := (2181062090711159 / 10000000000000000 : ℚ)) + (U := (-(15227731364814907513837 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_2 : Uω (aρ 2) (bρ 2) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -712,25 +646,21 @@ lemma U_270_2 : have hlg : Real.log (431375064042287 / 2000000000000000 : ℝ) ≤ (-(7669622644416340882011 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (431375064042287 / 2000000000000000 : ℝ) = - (431375064042287 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (431375064042287 / 250000000000000 : ℚ)) - (U := (2727585060083659117989 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (431375064042287 / 250000000000000 : ℝ) ≤ - (2727585060083659117989 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (431276687750949 / 2000000000000000 : ℝ)) (q := - (431375064042287 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (431375064042287 / 2000000000000000 : ℚ)) + (r' := (431375064042287 / 250000000000000 : ℚ)) + (U := (-(7669622644416340882011 / 5000000000000000000000 : ℚ))) + (U' := (2727585060083659117989 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (431276687750949 / 2000000000000000 : ℚ)) + (q := (431375064042287 / 2000000000000000 : ℚ)) + (U := (-(7669622644416340882011 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_3 : Uω (aρ 3) (bρ 3) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -738,25 +668,21 @@ lemma U_270_3 : have hlg : Real.log (4216433025271839 / 20000000000000000 : ℝ) ≤ (-(15567427568303136711517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4216433025271839 / 20000000000000000 : ℝ) = - (4216433025271839 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4216433025271839 / 2500000000000000 : ℚ)) - (U := (5226987840696863288483 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4216433025271839 / 2500000000000000 : ℝ) ≤ - (5226987840696863288483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1053230964976857 / 5000000000000000 : ℝ)) (q := - (4216433025271839 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4216433025271839 / 20000000000000000 : ℚ)) + (r' := (4216433025271839 / 2500000000000000 : ℚ)) + (U := (-(15567427568303136711517 / 10000000000000000000000 : ℚ))) + (U' := (5226987840696863288483 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (1053230964976857 / 5000000000000000 : ℚ)) + (q := (4216433025271839 / 20000000000000000 : ℚ)) + (U := (-(15567427568303136711517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_4 : Uω (aρ 4) (bρ 4) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -764,25 +690,21 @@ lemma U_270_4 : have hlg : Real.log (4052970798400113 / 20000000000000000 : ℝ) ≤ (-(7981410650442638429787 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4052970798400113 / 20000000000000000 : ℝ) = - (4052970798400113 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4052970798400113 / 2500000000000000 : ℚ)) - (U := (2415797054057361570213 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4052970798400113 / 2500000000000000 : ℝ) ≤ - (2415797054057361570213 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (505323471036747 / 2500000000000000 : ℝ)) (q := - (4052970798400113 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4052970798400113 / 20000000000000000 : ℚ)) + (r' := (4052970798400113 / 2500000000000000 : ℚ)) + (U := (-(7981410650442638429787 / 5000000000000000000000 : ℚ))) + (U' := (2415797054057361570213 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (505323471036747 / 2500000000000000 : ℚ)) + (q := (4052970798400113 / 20000000000000000 : ℚ)) + (U := (-(7981410650442638429787 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_5 : Uω (aρ 5) (bρ 5) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -790,25 +712,21 @@ lemma U_270_5 : have hlg : Real.log (759787240803271 / 4000000000000000 : ℝ) ≤ (-(16610111915455838225121 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (759787240803271 / 4000000000000000 : ℝ) = - (759787240803271 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (759787240803271 / 500000000000000 : ℚ)) - (U := (4184303493544161774879 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (759787240803271 / 500000000000000 : ℝ) ≤ - (4184303493544161774879 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188544920909823 / 1000000000000000 : ℝ)) (q := - (759787240803271 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (759787240803271 / 4000000000000000 : ℚ)) + (r' := (759787240803271 / 500000000000000 : ℚ)) + (U := (-(16610111915455838225121 / 10000000000000000000000 : ℚ))) + (U' := (4184303493544161774879 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (188544920909823 / 1000000000000000 : ℚ)) + (q := (759787240803271 / 4000000000000000 : ℚ)) + (U := (-(16610111915455838225121 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_6 : Uω (aρ 6) (bρ 6) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -816,25 +734,21 @@ lemma U_270_6 : have hlg : Real.log (855185348357439 / 5000000000000000 : ℝ) ≤ (-(17658749634887927061711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (855185348357439 / 5000000000000000 : ℝ) = - (855185348357439 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (855185348357439 / 625000000000000 : ℚ)) - (U := (3135665774112072938289 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (855185348357439 / 625000000000000 : ℝ) ≤ - (3135665774112072938289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1674494773651631 / 10000000000000000 : ℝ)) (q := - (855185348357439 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (855185348357439 / 5000000000000000 : ℚ)) + (r' := (855185348357439 / 625000000000000 : ℚ)) + (U := (-(17658749634887927061711 / 10000000000000000000000 : ℚ))) + (U' := (3135665774112072938289 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (1674494773651631 / 10000000000000000 : ℚ)) + (q := (855185348357439 / 5000000000000000 : ℚ)) + (U := (-(17658749634887927061711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_7 : Uω (aρ 7) (bρ 7) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -842,25 +756,21 @@ lemma U_270_7 : have hlg : Real.log (2864063784966021 / 20000000000000000 : ℝ) ≤ (-(9717453763183694041361 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2864063784966021 / 20000000000000000 : ℝ) = - (2864063784966021 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2864063784966021 / 2500000000000000 : ℚ)) - (U := (679753941316305958639 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2864063784966021 / 2500000000000000 : ℝ) ≤ - (679753941316305958639 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (167684818243487 / 1250000000000000 : ℝ)) (q := - (2864063784966021 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2864063784966021 / 20000000000000000 : ℚ)) + (r' := (2864063784966021 / 2500000000000000 : ℚ)) + (U := (-(9717453763183694041361 / 5000000000000000000000 : ℚ))) + (U' := (679753941316305958639 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (167684818243487 / 1250000000000000 : ℚ)) + (q := (2864063784966021 / 20000000000000000 : ℚ)) + (U := (-(9717453763183694041361 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_8 : Uω (aρ 8) (bρ 8) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -868,25 +778,21 @@ lemma U_270_8 : have hlg : Real.log (491122670330093 / 5000000000000000 : ℝ) ≤ (-(5801248140116723696391 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (491122670330093 / 5000000000000000 : ℝ) = - (491122670330093 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (491122670330093 / 312500000000000 : ℚ)) - (U := (1130223662883276303609 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (491122670330093 / 312500000000000 : ℝ) ≤ - (1130223662883276303609 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (725447093642247 / 10000000000000000 : ℝ)) (q := - (491122670330093 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (491122670330093 / 5000000000000000 : ℚ)) + (r' := (491122670330093 / 312500000000000 : ℚ)) + (U := (-(5801248140116723696391 / 2500000000000000000000 : ℚ))) + (U' := (1130223662883276303609 / 2500000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3593013491621 / 16000000000000 : ℚ)) + (s := (725447093642247 / 10000000000000000 : ℚ)) + (q := (491122670330093 / 5000000000000000 : ℚ)) + (U := (-(5801248140116723696391 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_270_9 : Uω (aρ 9) (bρ 9) (3593013491621 / 16000000000000 : ℝ) ≤ @@ -1019,25 +925,21 @@ lemma U_271_1 : have hlg : Real.log (3498229663605839 / 16000000000000000 : ℝ) ≤ (-(7601658456640705685281 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3498229663605839 / 16000000000000000 : ℝ) = - (3498229663605839 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3498229663605839 / 2000000000000000 : ℚ)) - (U := (2795549247859294314719 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3498229663605839 / 2000000000000000 : ℝ) ≤ - (2795549247859294314719 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (218631959703433 / 1000000000000000 : ℝ)) (q := - (3498229663605839 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3498229663605839 / 16000000000000000 : ℚ)) + (r' := (3498229663605839 / 2000000000000000 : ℚ)) + (U := (-(7601658456640705685281 / 5000000000000000000000 : ℚ))) + (U' := (2795549247859294314719 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (218631959703433 / 1000000000000000 : ℚ)) + (q := (3498229663605839 / 16000000000000000 : ℚ)) + (U := (-(7601658456640705685281 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_2 : Uω (aρ 2) (bρ 2) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1045,25 +947,21 @@ lemma U_271_2 : have hlg : Real.log (17297662412755607 / 80000000000000000 : ℝ) ≤ (-(15314552621698947647151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17297662412755607 / 80000000000000000 : ℝ) = - (17297662412755607 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17297662412755607 / 10000000000000000 : ℚ)) - (U := (5479862787301052352849 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17297662412755607 / 10000000000000000 : ℝ) ≤ - (5479862787301052352849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2161717133225933 / 10000000000000000 : ℝ)) (q := - (17297662412755607 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17297662412755607 / 80000000000000000 : ℚ)) + (r' := (17297662412755607 / 10000000000000000 : ℚ)) + (U := (-(15314552621698947647151 / 10000000000000000000000 : ℚ))) + (U' := (5479862787301052352849 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (2161717133225933 / 10000000000000000 : ℚ)) + (q := (17297662412755607 / 80000000000000000 : ℚ)) + (U := (-(15314552621698947647151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_3 : Uω (aρ 3) (bρ 3) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1071,25 +969,21 @@ lemma U_271_3 : have hlg : Real.log (3381683536646363 / 16000000000000000 : ℝ) ≤ (-(7771075241021788038101 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3381683536646363 / 16000000000000000 : ℝ) = - (3381683536646363 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3381683536646363 / 2000000000000000 : ℚ)) - (U := (2626132463478211961899 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3381683536646363 / 2000000000000000 : ℝ) ≤ - (2626132463478211961899 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (422360411438997 / 2000000000000000 : ℝ)) (q := - (3381683536646363 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3381683536646363 / 16000000000000000 : ℚ)) + (r' := (3381683536646363 / 2000000000000000 : ℚ)) + (U := (-(7771075241021788038101 / 5000000000000000000000 : ℚ))) + (U' := (2626132463478211961899 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (422360411438997 / 2000000000000000 : ℚ)) + (q := (3381683536646363 / 16000000000000000 : ℚ)) + (U := (-(7771075241021788038101 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_4 : Uω (aρ 4) (bρ 4) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1097,25 +991,21 @@ lemma U_271_4 : have hlg : Real.log (3250928518839247 / 16000000000000000 : ℝ) ≤ (-(15936480678178473697243 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3250928518839247 / 16000000000000000 : ℝ) = - (3250928518839247 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3250928518839247 / 2000000000000000 : ℚ)) - (U := (4857934730821526302757 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3250928518839247 / 2000000000000000 : ℝ) ≤ - (4857934730821526302757 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (202665246600109 / 1000000000000000 : ℝ)) (q := - (3250928518839247 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3250928518839247 / 16000000000000000 : ℚ)) + (r' := (3250928518839247 / 2000000000000000 : ℚ)) + (U := (-(15936480678178473697243 / 10000000000000000000000 : ℚ))) + (U' := (4857934730821526302757 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (202665246600109 / 1000000000000000 : ℚ)) + (q := (3250928518839247 / 16000000000000000 : ℚ)) + (U := (-(15936480678178473697243 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_5 : Uω (aρ 5) (bρ 5) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1123,25 +1013,21 @@ lemma U_271_5 : have hlg : Real.log (15238711178580651 / 80000000000000000 : ℝ) ≤ (-(103636728471640727917 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15238711178580651 / 80000000000000000 : ℝ) = - (15238711178580651 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15238711178580651 / 10000000000000000 : ℚ)) - (U := (26328367834609272083 / 62500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15238711178580651 / 10000000000000000 : ℝ) ≤ - (26328367834609272083 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (945429765716097 / 5000000000000000 : ℝ)) (q := - (15238711178580651 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15238711178580651 / 80000000000000000 : ℚ)) + (r' := (15238711178580651 / 10000000000000000 : ℚ)) + (U := (-(103636728471640727917 / 62500000000000000000 : ℚ))) + (U' := (26328367834609272083 / 62500000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (945429765716097 / 5000000000000000 : ℚ)) + (q := (15238711178580651 / 80000000000000000 : ℚ)) + (U := (-(103636728471640727917 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_6 : Uω (aρ 6) (bρ 6) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1149,25 +1035,21 @@ lemma U_271_6 : have hlg : Real.log (13726526534431967 / 80000000000000000 : ℝ) ≤ (-(17626964297738276232173 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13726526534431967 / 80000000000000000 : ℝ) = - (13726526534431967 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13726526534431967 / 10000000000000000 : ℚ)) - (U := (3167451111261723767827 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13726526534431967 / 10000000000000000 : ℝ) ≤ - (3167451111261723767827 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1680053745535023 / 10000000000000000 : ℝ)) (q := - (13726526534431967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13726526534431967 / 80000000000000000 : ℚ)) + (r' := (13726526534431967 / 10000000000000000 : ℚ)) + (U := (-(17626964297738276232173 / 10000000000000000000000 : ℚ))) + (U' := (3167451111261723767827 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (1680053745535023 / 10000000000000000 : ℚ)) + (q := (13726526534431967 / 80000000000000000 : ℚ)) + (U := (-(17626964297738276232173 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_7 : Uω (aρ 7) (bρ 7) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1175,25 +1057,21 @@ lemma U_271_7 : have hlg : Real.log (11501772124656023 / 80000000000000000 : ℝ) ≤ (-(9697627563002555907191 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11501772124656023 / 80000000000000000 : ℝ) = - (11501772124656023 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11501772124656023 / 10000000000000000 : ℚ)) - (U := (699580141497444092809 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11501772124656023 / 10000000000000000 : ℝ) ≤ - (699580141497444092809 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1347526523851037 / 10000000000000000 : ℝ)) (q := - (11501772124656023 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11501772124656023 / 80000000000000000 : ℚ)) + (r' := (11501772124656023 / 10000000000000000 : ℚ)) + (U := (-(9697627563002555907191 / 5000000000000000000000 : ℚ))) + (U' := (699580141497444092809 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (1347526523851037 / 10000000000000000 : ℚ)) + (q := (11501772124656023 / 80000000000000000 : ℚ)) + (U := (-(9697627563002555907191 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_8 : Uω (aρ 8) (bρ 8) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1201,25 +1079,21 @@ lemma U_271_8 : have hlg : Real.log (7915562066343051 / 80000000000000000 : ℝ) ≤ (-(23131959300184916443993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7915562066343051 / 80000000000000000 : ℝ) = - (7915562066343051 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7915562066343051 / 5000000000000000 : ℚ)) - (U := (4593927911815083556007 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7915562066343051 / 5000000000000000 : ℝ) ≤ - (4593927911815083556007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (367257830306397 / 5000000000000000 : ℝ)) (q := - (7915562066343051 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7915562066343051 / 80000000000000000 : ℚ)) + (r' := (7915562066343051 / 5000000000000000 : ℚ)) + (U := (-(23131959300184916443993 / 10000000000000000000000 : ℚ))) + (U' := (4593927911815083556007 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14406174083571 / 64000000000000 : ℚ)) + (s := (367257830306397 / 5000000000000000 : ℚ)) + (q := (7915562066343051 / 80000000000000000 : ℚ)) + (U := (-(23131959300184916443993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_271_9 : Uω (aρ 9) (bρ 9) (14406174083571 / 64000000000000 : ℝ) ≤ @@ -1350,25 +1224,21 @@ lemma U_272_1 : have hlg : Real.log (8766899951667041 / 40000000000000000 : ℝ) ≤ (-(15178961927162266424097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8766899951667041 / 40000000000000000 : ℝ) = - (8766899951667041 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8766899951667041 / 5000000000000000 : ℚ)) - (U := (5615453481837733575903 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8766899951667041 / 5000000000000000 : ℝ) ≤ - (5615453481837733575903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (547912806266427 / 2500000000000000 : ℝ)) (q := - (8766899951667041 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8766899951667041 / 40000000000000000 : ℚ)) + (r' := (8766899951667041 / 5000000000000000 : ℚ)) + (U := (-(15178961927162266424097 / 10000000000000000000000 : ℚ))) + (U' := (5615453481837733575903 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (547912806266427 / 2500000000000000 : ℚ)) + (q := (8766899951667041 / 40000000000000000 : ℚ)) + (U := (-(15178961927162266424097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_2 : Uω (aρ 2) (bρ 2) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1376,25 +1246,21 @@ lemma U_272_2 : have hlg : Real.log (8670161108029413 / 40000000000000000 : ℝ) ≤ (-(1528992080473304163929 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8670161108029413 / 40000000000000000 : ℝ) = - (8670161108029413 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8670161108029413 / 5000000000000000 : ℚ)) - (U := (550449460426695836071 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8670161108029413 / 5000000000000000 : ℝ) ≤ - (550449460426695836071 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1083525407878447 / 5000000000000000 : ℝ)) (q := - (8670161108029413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8670161108029413 / 40000000000000000 : ℚ)) + (r' := (8670161108029413 / 5000000000000000 : ℚ)) + (U := (-(1528992080473304163929 / 1000000000000000000000 : ℚ))) + (U' := (550449460426695836071 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (1083525407878447 / 5000000000000000 : ℚ)) + (q := (8670161108029413 / 40000000000000000 : ℚ)) + (U := (-(1528992080473304163929 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_3 : Uω (aρ 3) (bρ 3) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1402,25 +1268,21 @@ lemma U_272_3 : have hlg : Real.log (1695110308676319 / 8000000000000000 : ℝ) ≤ (-(3879234308300097326093 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1695110308676319 / 8000000000000000 : ℝ) = - (1695110308676319 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1695110308676319 / 1000000000000000 : ℚ)) - (U := (1319369543949902673907 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1695110308676319 / 1000000000000000 : ℝ) ≤ - (1319369543949902673907 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (423428427956597 / 2000000000000000 : ℝ)) (q := - (1695110308676319 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1695110308676319 / 8000000000000000 : ℚ)) + (r' := (1695110308676319 / 1000000000000000 : ℚ)) + (U := (-(3879234308300097326093 / 2500000000000000000000 : ℚ))) + (U' := (1319369543949902673907 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (423428427956597 / 2000000000000000 : ℚ)) + (q := (1695110308676319 / 8000000000000000 : ℚ)) + (U := (-(3879234308300097326093 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_4 : Uω (aρ 4) (bρ 4) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1428,25 +1290,21 @@ lemma U_272_4 : have hlg : Real.log (8148700710017781 / 40000000000000000 : ℝ) ≤ (-(15910209608740880248149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8148700710017781 / 40000000000000000 : ℝ) = - (8148700710017781 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8148700710017781 / 5000000000000000 : ℚ)) - (U := (4884205800259119751851 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8148700710017781 / 5000000000000000 : ℝ) ≤ - (4884205800259119751851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1016005452083039 / 5000000000000000 : ℝ)) (q := - (8148700710017781 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8148700710017781 / 40000000000000000 : ℚ)) + (r' := (8148700710017781 / 5000000000000000 : ℚ)) + (U := (-(15910209608740880248149 / 10000000000000000000000 : ℚ))) + (U' := (4884205800259119751851 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (1016005452083039 / 5000000000000000 : ℚ)) + (q := (8148700710017781 / 40000000000000000 : ℚ)) + (U := (-(15910209608740880248149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_5 : Uω (aρ 5) (bρ 5) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1454,25 +1312,21 @@ lemma U_272_5 : have hlg : Real.log (7640837874930451 / 40000000000000000 : ℝ) ≤ (-(16553721866754159805869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7640837874930451 / 40000000000000000 : ℝ) = - (7640837874930451 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7640837874930451 / 5000000000000000 : ℚ)) - (U := (4240693542245840194131 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7640837874930451 / 5000000000000000 : ℝ) ≤ - (4240693542245840194131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1896269405957413 / 10000000000000000 : ℝ)) (q := - (7640837874930451 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7640837874930451 / 40000000000000000 : ℚ)) + (r' := (7640837874930451 / 5000000000000000 : ℚ)) + (U := (-(16553721866754159805869 / 10000000000000000000000 : ℚ))) + (U' := (4240693542245840194131 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (1896269405957413 / 10000000000000000 : ℚ)) + (q := (7640837874930451 / 40000000000000000 : ℚ)) + (U := (-(16553721866754159805869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_6 : Uω (aρ 6) (bρ 6) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1480,25 +1334,21 @@ lemma U_272_6 : have hlg : Real.log (6885040805321457 / 40000000000000000 : ℝ) ≤ (-(54985262327256662747 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6885040805321457 / 40000000000000000 : ℝ) = - (6885040805321457 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6885040805321457 / 5000000000000000 : ℚ)) - (U := (9997285825868337253 / 31250000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6885040805321457 / 5000000000000000 : ℝ) ≤ - (9997285825868337253 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421402811573229 / 2500000000000000 : ℝ)) (q := - (6885040805321457 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6885040805321457 / 40000000000000000 : ℚ)) + (r' := (6885040805321457 / 5000000000000000 : ℚ)) + (U := (-(54985262327256662747 / 31250000000000000000 : ℚ))) + (U' := (9997285825868337253 / 31250000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (421402811573229 / 2500000000000000 : ℚ)) + (q := (6885040805321457 / 40000000000000000 : ℚ)) + (U := (-(54985262327256662747 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_7 : Uω (aρ 7) (bρ 7) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1506,25 +1356,21 @@ lemma U_272_7 : have hlg : Real.log (5773632504211469 / 40000000000000000 : ℝ) ≤ (-(19355780207743348837579 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5773632504211469 / 40000000000000000 : ℝ) = - (5773632504211469 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5773632504211469 / 5000000000000000 : ℚ)) - (U := (1438635201256651162421 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5773632504211469 / 5000000000000000 : ℝ) ≤ - (1438635201256651162421 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (676784238248961 / 5000000000000000 : ℝ)) (q := - (5773632504211469 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5773632504211469 / 40000000000000000 : ℚ)) + (r' := (5773632504211469 / 5000000000000000 : ℚ)) + (U := (-(19355780207743348837579 / 10000000000000000000000 : ℚ))) + (U' := (1438635201256651162421 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (676784238248961 / 5000000000000000 : ℚ)) + (q := (5773632504211469 / 40000000000000000 : ℚ)) + (U := (-(19355780207743348837579 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_8 : Uω (aρ 8) (bρ 8) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1532,25 +1378,21 @@ lemma U_272_8 : have hlg : Real.log (3986435947795567 / 40000000000000000 : ℝ) ≤ (-(23059818675209941582027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3986435947795567 / 40000000000000000 : ℝ) = - (3986435947795567 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3986435947795567 / 2500000000000000 : ℚ)) - (U := (4666068536790058417973 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3986435947795567 / 2500000000000000 : ℝ) ≤ - (4666068536790058417973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (743511849629971 / 10000000000000000 : ℝ)) (q := - (3986435947795567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3986435947795567 / 40000000000000000 : ℚ)) + (r' := (3986435947795567 / 2500000000000000 : ℚ)) + (U := (-(23059818675209941582027 / 10000000000000000000000 : ℚ))) + (U' := (4666068536790058417973 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7220147100329 / 32000000000000 : ℚ)) + (s := (743511849629971 / 10000000000000000 : ℚ)) + (q := (3986435947795567 / 40000000000000000 : ℚ)) + (U := (-(23059818675209941582027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_272_9 : Uω (aρ 9) (bρ 9) (7220147100329 / 32000000000000 : ℝ) ≤ @@ -1682,25 +1524,21 @@ lemma U_273_1 : have hlg : Real.log (3515290296331029 / 16000000000000000 : ℝ) ≤ (-(15154666117466165170289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3515290296331029 / 16000000000000000 : ℝ) = - (3515290296331029 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3515290296331029 / 2000000000000000 : ℚ)) - (U := (5639749291533834829711 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3515290296331029 / 2000000000000000 : ℝ) ≤ - (5639749291533834829711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (219698285135113 / 1000000000000000 : ℝ)) (q := - (3515290296331029 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3515290296331029 / 16000000000000000 : ℚ)) + (r' := (3515290296331029 / 2000000000000000 : ℚ)) + (U := (-(15154666117466165170289 / 10000000000000000000000 : ℚ))) + (U' := (5639749291533834829711 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (219698285135113 / 1000000000000000 : ℚ)) + (q := (3515290296331029 / 16000000000000000 : ℚ)) + (U := (-(15154666117466165170289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_2 : Uω (aρ 2) (bρ 2) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1708,25 +1546,21 @@ lemma U_273_2 : have hlg : Real.log (695319278878117 / 3200000000000000 : ℝ) ≤ (-(3816337384657765063509 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (695319278878117 / 3200000000000000 : ℝ) = - (695319278878117 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (695319278878117 / 400000000000000 : ℚ)) - (U := (1382266467592234936491 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (695319278878117 / 400000000000000 : ℝ) ≤ - (1382266467592234936491 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86895379457423 / 400000000000000 : ℝ)) (q := - (695319278878117 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (695319278878117 / 3200000000000000 : ℚ)) + (r' := (695319278878117 / 400000000000000 : ℚ)) + (U := (-(3816337384657765063509 / 2500000000000000000000 : ℚ))) + (U' := (1382266467592234936491 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (86895379457423 / 400000000000000 : ℚ)) + (q := (695319278878117 / 3200000000000000 : ℚ)) + (U := (-(3816337384657765063509 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_3 : Uω (aρ 3) (bρ 3) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1734,25 +1568,21 @@ lemma U_273_3 : have hlg : Real.log (16993788313029637 / 80000000000000000 : ℝ) ≤ (-(7745893749807219680829 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16993788313029637 / 80000000000000000 : ℝ) = - (16993788313029637 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16993788313029637 / 10000000000000000 : ℚ)) - (U := (2651313954692780319171 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16993788313029637 / 10000000000000000 : ℝ) ≤ - (2651313954692780319171 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2122482178054753 / 10000000000000000 : ℝ)) (q := - (16993788313029637 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16993788313029637 / 80000000000000000 : ℚ)) + (r' := (16993788313029637 / 10000000000000000 : ℚ)) + (U := (-(7745893749807219680829 / 5000000000000000000000 : ℚ))) + (U' := (2651313954692780319171 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (2122482178054753 / 10000000000000000 : ℚ)) + (q := (16993788313029637 / 80000000000000000 : ℚ)) + (U := (-(7745893749807219680829 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_4 : Uω (aρ 4) (bρ 4) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1760,25 +1590,21 @@ lemma U_273_4 : have hlg : Real.log (16340159675653393 / 80000000000000000 : ℝ) ≤ (-(15884007724381241620549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16340159675653393 / 80000000000000000 : ℝ) = - (16340159675653393 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16340159675653393 / 10000000000000000 : ℚ)) - (U := (4910407684618758379451 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16340159675653393 / 10000000000000000 : ℝ) ≤ - (4910407684618758379451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (509342299943923 / 2500000000000000 : ℝ)) (q := - (16340159675653393 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16340159675653393 / 80000000000000000 : ℚ)) + (r' := (16340159675653393 / 10000000000000000 : ℚ)) + (U := (-(15884007724381241620549 / 10000000000000000000000 : ℚ))) + (U' := (4910407684618758379451 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (509342299943923 / 2500000000000000 : ℚ)) + (q := (16340159675653393 / 80000000000000000 : ℚ)) + (U := (-(15884007724381241620549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_5 : Uω (aρ 5) (bρ 5) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1786,25 +1612,21 @@ lemma U_273_5 : have hlg : Real.log (15324638545193217 / 80000000000000000 : ℝ) ≤ (-(4131411845769879803169 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15324638545193217 / 80000000000000000 : ℝ) = - (15324638545193217 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15324638545193217 / 10000000000000000 : ℚ)) - (U := (1067192006480120196831 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15324638545193217 / 10000000000000000 : ℝ) ≤ - (1067192006480120196831 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59427463640489 / 312500000000000 : ℝ)) (q := - (15324638545193217 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15324638545193217 / 80000000000000000 : ℚ)) + (r' := (15324638545193217 / 10000000000000000 : ℚ)) + (U := (-(4131411845769879803169 / 2500000000000000000000 : ℚ))) + (U' := (1067192006480120196831 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (59427463640489 / 312500000000000 : ℚ)) + (q := (15324638545193217 / 80000000000000000 : ℚ)) + (U := (-(4131411845769879803169 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_6 : Uω (aρ 6) (bρ 6) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1812,25 +1634,21 @@ lemma U_273_6 : have hlg : Real.log (13813630860364677 / 80000000000000000 : ℝ) ≤ (-(4390926964309566989123 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13813630860364677 / 80000000000000000 : ℝ) = - (13813630860364677 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13813630860364677 / 10000000000000000 : ℚ)) - (U := (807676887940433010877 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13813630860364677 / 10000000000000000 : ℝ) ≤ - (807676887940433010877 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1691167290428513 / 10000000000000000 : ℝ)) (q := - (13813630860364677 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13813630860364677 / 80000000000000000 : ℚ)) + (r' := (13813630860364677 / 10000000000000000 : ℚ)) + (U := (-(4390926964309566989123 / 2500000000000000000000 : ℚ))) + (U' := (807676887940433010877 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (1691167290428513 / 10000000000000000 : ℚ)) + (q := (13813630860364677 / 80000000000000000 : ℚ)) + (U := (-(4390926964309566989123 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_7 : Uω (aρ 7) (bρ 7) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1838,25 +1656,21 @@ lemma U_273_7 : have hlg : Real.log (11592734112472793 / 80000000000000000 : ℝ) ≤ (-(9658240508237714690711 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11592734112472793 / 80000000000000000 : ℝ) = - (11592734112472793 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11592734112472793 / 10000000000000000 : ℚ)) - (U := (738967196262285309289 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11592734112472793 / 10000000000000000 : ℝ) ≤ - (738967196262285309289 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (679802242107771 / 5000000000000000 : ℝ)) (q := - (11592734112472793 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11592734112472793 / 80000000000000000 : ℚ)) + (r' := (11592734112472793 / 10000000000000000 : ℚ)) + (U := (-(9658240508237714690711 / 5000000000000000000000 : ℚ))) + (U' := (738967196262285309289 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (679802242107771 / 5000000000000000 : ℚ)) + (q := (11592734112472793 / 80000000000000000 : ℚ)) + (U := (-(9658240508237714690711 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_8 : Uω (aρ 8) (bρ 8) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -1864,25 +1678,21 @@ lemma U_273_8 : have hlg : Real.log (8029902597296329 / 80000000000000000 : ℝ) ≤ (-(22988542356000148652769 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8029902597296329 / 80000000000000000 : ℝ) = - (8029902597296329 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8029902597296329 / 5000000000000000 : ℚ)) - (U := (4737344855999851347231 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8029902597296329 / 5000000000000000 : ℝ) ≤ - (4737344855999851347231 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (376219128380713 / 5000000000000000 : ℝ)) (q := - (8029902597296329 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8029902597296329 / 80000000000000000 : ℚ)) + (r' := (8029902597296329 / 5000000000000000 : ℚ)) + (U := (-(22988542356000148652769 / 10000000000000000000000 : ℚ))) + (U' := (4737344855999851347231 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2894882863549 / 12800000000000 : ℚ)) + (s := (376219128380713 / 5000000000000000 : ℚ)) + (q := (8029902597296329 / 80000000000000000 : ℚ)) + (U := (-(22988542356000148652769 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_273_9 : Uω (aρ 9) (bρ 9) (2894882863549 / 12800000000000 : ℝ) ≤ @@ -2015,25 +1825,21 @@ lemma U_274_1 : have hlg : Real.log (2202387881630389 / 10000000000000000 : ℝ) ≤ (-(15130429197303497441467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2202387881630389 / 10000000000000000 : ℝ) = - (2202387881630389 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2202387881630389 / 1250000000000000 : ℚ)) - (U := (5663986211696502558533 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2202387881630389 / 1250000000000000 : ℝ) ≤ - (5663986211696502558533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1101157237951639 / 5000000000000000 : ℝ)) (q := - (2202387881630389 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2202387881630389 / 10000000000000000 : ℚ)) + (r' := (2202387881630389 / 1250000000000000 : ℚ)) + (U := (-(15130429197303497441467 / 10000000000000000000000 : ℚ))) + (U' := (5663986211696502558533 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (1101157237951639 / 5000000000000000 : ℚ)) + (q := (2202387881630389 / 10000000000000000 : ℚ)) + (U := (-(15130429197303497441467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_2 : Uω (aρ 2) (bρ 2) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2041,25 +1847,21 @@ lemma U_274_2 : have hlg : Real.log (2178205210098281 / 10000000000000000 : ℝ) ≤ (-(15240838526292947970749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2178205210098281 / 10000000000000000 : ℝ) = - (2178205210098281 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2178205210098281 / 1250000000000000 : ℚ)) - (U := (5553576882707052029251 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2178205210098281 / 1250000000000000 : ℝ) ≤ - (5553576882707052029251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1088859072674531 / 5000000000000000 : ℝ)) (q := - (2178205210098281 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2178205210098281 / 10000000000000000 : ℚ)) + (r' := (2178205210098281 / 1250000000000000 : ℚ)) + (U := (-(15240838526292947970749 / 10000000000000000000000 : ℚ))) + (U' := (5553576882707052029251 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (1088859072674531 / 5000000000000000 : ℚ)) + (q := (2178205210098281 / 10000000000000000 : ℚ)) + (U := (-(15240838526292947970749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_3 : Uω (aρ 3) (bρ 3) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2067,24 +1869,21 @@ lemma U_274_3 : have hlg : Real.log (26619489630259 / 125000000000000 : ℝ) ≤ (-(3866675240390775093581 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (26619489630259 / 125000000000000 : ℝ) = (26619489630259 / 15625000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26619489630259 / 15625000000000 : ℚ)) - (U := (1331928611859224906419 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (26619489630259 / 15625000000000 : ℝ) ≤ - (1331928611859224906419 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (106391108617197 / 500000000000000 : ℝ)) (q := - (26619489630259 / 125000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26619489630259 / 125000000000000 : ℚ)) + (r' := (26619489630259 / 15625000000000 : ℚ)) + (U := (-(3866675240390775093581 / 2500000000000000000000 : ℚ))) + (U' := (1331928611859224906419 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (106391108617197 / 500000000000000 : ℚ)) + (q := (26619489630259 / 125000000000000 : ℚ)) + (U := (-(3866675240390775093581 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_4 : Uω (aρ 4) (bρ 4) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2092,25 +1891,21 @@ lemma U_274_4 : have hlg : Real.log (4095729341384249 / 20000000000000000 : ℝ) ≤ (-(15857874659838571656279 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4095729341384249 / 20000000000000000 : ℝ) = - (4095729341384249 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4095729341384249 / 2500000000000000 : ℚ)) - (U := (4936540749161428343721 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4095729341384249 / 2500000000000000 : ℝ) ≤ - (4936540749161428343721 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2042727353951749 / 10000000000000000 : ℝ)) (q := - (4095729341384249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4095729341384249 / 20000000000000000 : ℚ)) + (r' := (4095729341384249 / 2500000000000000 : ℚ)) + (U := (-(15857874659838571656279 / 10000000000000000000000 : ℚ))) + (U' := (4936540749161428343721 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (2042727353951749 / 10000000000000000 : ℚ)) + (q := (4095729341384249 / 20000000000000000 : ℚ)) + (U := (-(15857874659838571656279 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_5 : Uω (aρ 5) (bρ 5) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2118,25 +1913,21 @@ lemma U_274_5 : have hlg : Real.log (960474973730623 / 5000000000000000 : ℝ) ≤ (-(6444395563387845643 / 3906250000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (960474973730623 / 5000000000000000 : ℝ) = - (960474973730623 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (960474973730623 / 625000000000000 : ℚ)) - (U := (1678422955752779357 / 3906250000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (960474973730623 / 625000000000000 : ℝ) ≤ - (1678422955752779357 / 3906250000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59596494588281 / 312500000000000 : ℝ)) (q := - (960474973730623 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (960474973730623 / 5000000000000000 : ℚ)) + (r' := (960474973730623 / 625000000000000 : ℚ)) + (U := (-(6444395563387845643 / 3906250000000000000 : ℚ))) + (U' := (1678422955752779357 / 3906250000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (59596494588281 / 312500000000000 : ℚ)) + (q := (960474973730623 / 5000000000000000 : ℚ)) + (U := (-(6444395563387845643 / 3906250000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_6 : Uω (aρ 6) (bρ 6) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2144,25 +1935,21 @@ lemma U_274_6 : have hlg : Real.log (3464293585208773 / 20000000000000000 : ℝ) ≤ (-(17532235324295299403419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3464293585208773 / 20000000000000000 : ℝ) = - (3464293585208773 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3464293585208773 / 2500000000000000 : ℚ)) - (U := (3262180084704700596581 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3464293585208773 / 2500000000000000 : ℝ) ≤ - (3262180084704700596581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1696721892251273 / 10000000000000000 : ℝ)) (q := - (3464293585208773 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3464293585208773 / 20000000000000000 : ℚ)) + (r' := (3464293585208773 / 2500000000000000 : ℚ)) + (U := (-(17532235324295299403419 / 10000000000000000000000 : ℚ))) + (U' := (3262180084704700596581 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (1696721892251273 / 10000000000000000 : ℚ)) + (q := (3464293585208773 / 20000000000000000 : ℚ)) + (U := (-(17532235324295299403419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_7 : Uω (aρ 7) (bρ 7) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2170,25 +1957,21 @@ lemma U_274_7 : have hlg : Real.log (2909544938029893 / 20000000000000000 : ℝ) ≤ (-(4819338956257651832129 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2909544938029893 / 20000000000000000 : ℝ) = - (2909544938029893 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2909544938029893 / 2500000000000000 : ℚ)) - (U := (379264895992348167871 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2909544938029893 / 2500000000000000 : ℝ) ≤ - (379264895992348167871 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1365634625832393 / 10000000000000000 : ℝ)) (q := - (2909544938029893 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2909544938029893 / 20000000000000000 : ℚ)) + (r' := (2909544938029893 / 2500000000000000 : ℚ)) + (U := (-(4819338956257651832129 / 2500000000000000000000 : ℚ))) + (U' := (379264895992348167871 / 2500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (1365634625832393 / 10000000000000000 : ℚ)) + (q := (2909544938029893 / 20000000000000000 : ℚ)) + (U := (-(4819338956257651832129 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_8 : Uω (aρ 8) (bρ 8) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2196,25 +1979,21 @@ lemma U_274_8 : have hlg : Real.log (2021665997500307 / 20000000000000000 : ℝ) ≤ (-(11459051748918678550413 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2021665997500307 / 20000000000000000 : ℝ) = - (2021665997500307 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2021665997500307 / 1250000000000000 : ℚ)) - (U := (2403891857081321449587 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2021665997500307 / 1250000000000000 : ℝ) ≤ - (2403891857081321449587 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (761297336642807 / 10000000000000000 : ℝ)) (q := - (2021665997500307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2021665997500307 / 20000000000000000 : ℚ)) + (r' := (2021665997500307 / 1250000000000000 : ℚ)) + (U := (-(11459051748918678550413 / 5000000000000000000000 : ℚ))) + (U' := (2403891857081321449587 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (906783402177 / 4000000000000 : ℚ)) + (s := (761297336642807 / 10000000000000000 : ℚ)) + (q := (2021665997500307 / 20000000000000000 : ℚ)) + (U := (-(11459051748918678550413 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_274_9 : Uω (aρ 9) (bρ 9) (906783402177 / 4000000000000 : ℝ) ≤ @@ -2346,25 +2125,21 @@ lemma U_275_1 : have hlg : Real.log (17661754617548211 / 80000000000000000 : ℝ) ≤ (-(15106250881866031193979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17661754617548211 / 80000000000000000 : ℝ) = - (17661754617548211 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17661754617548211 / 10000000000000000 : ℚ)) - (U := (5688164527133968806021 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17661754617548211 / 10000000000000000 : ℝ) ≤ - (5688164527133968806021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2207646098734709 / 10000000000000000 : ℝ)) (q := - (17661754617548211 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17661754617548211 / 80000000000000000 : ℚ)) + (r' := (17661754617548211 / 10000000000000000 : ℚ)) + (U := (-(15106250881866031193979 / 10000000000000000000000 : ℚ))) + (U' := (5688164527133968806021 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (2207646098734709 / 10000000000000000 : ℚ)) + (q := (17661754617548211 / 80000000000000000 : ℚ)) + (U := (-(15106250881866031193979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_2 : Uω (aρ 2) (bρ 2) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2372,25 +2147,21 @@ lemma U_275_2 : have hlg : Real.log (17468301342903727 / 80000000000000000 : ℝ) ≤ (-(15216387472800909762541 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17468301342903727 / 80000000000000000 : ℝ) = - (17468301342903727 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17468301342903727 / 10000000000000000 : ℚ)) - (U := (5578027936199090237459 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17468301342903727 / 10000000000000000 : ℝ) ≤ - (5578027936199090237459 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (545762948145897 / 2500000000000000 : ℝ)) (q := - (17468301342903727 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17468301342903727 / 80000000000000000 : ℚ)) + (r' := (17468301342903727 / 10000000000000000 : ℚ)) + (U := (-(15216387472800909762541 / 10000000000000000000000 : ℚ))) + (U' := (5578027936199090237459 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (545762948145897 / 2500000000000000 : ℚ)) + (q := (17468301342903727 / 80000000000000000 : ℚ)) + (U := (-(15216387472800909762541 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_3 : Uω (aρ 3) (bρ 3) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2398,25 +2169,21 @@ lemma U_275_3 : have hlg : Real.log (17079158239092787 / 80000000000000000 : ℝ) ≤ (-(15441677301735706487299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17079158239092787 / 80000000000000000 : ℝ) = - (17079158239092787 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17079158239092787 / 10000000000000000 : ℚ)) - (U := (5352738107264293512701 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17079158239092787 / 10000000000000000 : ℝ) ≤ - (5352738107264293512701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2133162122980853 / 10000000000000000 : ℝ)) (q := - (17079158239092787 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17079158239092787 / 80000000000000000 : ℚ)) + (r' := (17079158239092787 / 10000000000000000 : ℚ)) + (U := (-(15441677301735706487299 / 10000000000000000000000 : ℚ))) + (U' := (5352738107264293512701 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (2133162122980853 / 10000000000000000 : ℚ)) + (q := (17079158239092787 / 80000000000000000 : ℚ)) + (U := (-(15441677301735706487299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_4 : Uω (aρ 4) (bρ 4) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2424,25 +2191,21 @@ lemma U_275_4 : have hlg : Real.log (16425674494126547 / 80000000000000000 : ℝ) ≤ (-(633272402110040347591 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16425674494126547 / 80000000000000000 : ℝ) = - (16425674494126547 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16425674494126547 / 10000000000000000 : ℚ)) - (U := (198504214249959652409 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16425674494126547 / 10000000000000000 : ℝ) ≤ - (198504214249959652409 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2048085367804293 / 10000000000000000 : ℝ)) (q := - (16425674494126547 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16425674494126547 / 80000000000000000 : ℚ)) + (r' := (16425674494126547 / 10000000000000000 : ℚ)) + (U := (-(633272402110040347591 / 400000000000000000000 : ℚ))) + (U' := (198504214249959652409 / 400000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (2048085367804293 / 10000000000000000 : ℚ)) + (q := (16425674494126547 / 80000000000000000 : ℚ)) + (U := (-(633272402110040347591 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_5 : Uω (aρ 5) (bρ 5) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2450,25 +2213,21 @@ lemma U_275_5 : have hlg : Real.log (15410558868291319 / 80000000000000000 : ℝ) ≤ (-(8234868593102955975117 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15410558868291319 / 80000000000000000 : ℝ) = - (15410558868291319 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15410558868291319 / 10000000000000000 : ℚ)) - (U := (2162339111397044024883 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15410558868291319 / 10000000000000000 : ℝ) ≤ - (2162339111397044024883 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (956248190340243 / 5000000000000000 : ℝ)) (q := - (15410558868291319 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15410558868291319 / 80000000000000000 : ℚ)) + (r' := (15410558868291319 / 10000000000000000 : ℚ)) + (U := (-(8234868593102955975117 / 5000000000000000000000 : ℚ))) + (U' := (2162339111397044024883 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (956248190340243 / 5000000000000000 : ℚ)) + (q := (15410558868291319 / 80000000000000000 : ℚ)) + (U := (-(8234868593102955975117 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_6 : Uω (aρ 6) (bρ 6) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2476,25 +2235,21 @@ lemma U_275_6 : have hlg : Real.log (13900712108530163 / 80000000000000000 : ℝ) ≤ (-(17500865642401456087003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13900712108530163 / 80000000000000000 : ℝ) = - (13900712108530163 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13900712108530163 / 10000000000000000 : ℚ)) - (U := (3293549766598543912997 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13900712108530163 / 10000000000000000 : ℝ) ≤ - (3293549766598543912997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1702275065880197 / 10000000000000000 : ℝ)) (q := - (13900712108530163 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13900712108530163 / 80000000000000000 : ℚ)) + (r' := (13900712108530163 / 10000000000000000 : ℚ)) + (U := (-(17500865642401456087003 / 10000000000000000000000 : ℚ))) + (U' := (3293549766598543912997 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (1702275065880197 / 10000000000000000 : ℚ)) + (q := (13900712108530163 / 80000000000000000 : ℚ)) + (U := (-(17500865642401456087003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_7 : Uω (aρ 7) (bρ 7) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2502,25 +2257,21 @@ lemma U_275_7 : have hlg : Real.log (11683602236828703 / 80000000000000000 : ℝ) ≤ (-(384768058671075131277 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11683602236828703 / 80000000000000000 : ℝ) = - (11683602236828703 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11683602236828703 / 10000000000000000 : ℚ)) - (U := (31120249508924868723 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11683602236828703 / 10000000000000000 : ℝ) ≤ - (31120249508924868723 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85728686169677 / 625000000000000 : ℝ)) (q := - (11683602236828703 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11683602236828703 / 80000000000000000 : ℚ)) + (r' := (11683602236828703 / 10000000000000000 : ℚ)) + (U := (-(384768058671075131277 / 200000000000000000000 : ℚ))) + (U' := (31120249508924868723 / 200000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (85728686169677 / 625000000000000 : ℚ)) + (q := (11683602236828703 / 80000000000000000 : ℚ)) + (U := (-(384768058671075131277 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_8 : Uω (aρ 8) (bρ 8) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2528,25 +2279,21 @@ lemma U_275_8 : have hlg : Real.log (8143165368057791 / 80000000000000000 : ℝ) ≤ (-(22848476633536171818119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8143165368057791 / 80000000000000000 : ℝ) = - (8143165368057791 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8143165368057791 / 5000000000000000 : ℚ)) - (U := (4877410578463828181881 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8143165368057791 / 5000000000000000 : ℝ) ≤ - (4877410578463828181881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (96261426607763 / 1250000000000000 : ℝ)) (q := - (8143165368057791 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8143165368057791 / 80000000000000000 : ℚ)) + (r' := (8143165368057791 / 5000000000000000 : ℚ)) + (U := (-(22848476633536171818119 / 10000000000000000000000 : ℚ))) + (U' := (4877410578463828181881 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (14542654551919 / 64000000000000 : ℚ)) + (s := (96261426607763 / 1250000000000000 : ℚ)) + (q := (8143165368057791 / 80000000000000000 : ℚ)) + (U := (-(22848476633536171818119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_275_9 : Uω (aρ 9) (bρ 9) (14542654551919 / 64000000000000 : ℝ) ≤ @@ -2678,25 +2425,21 @@ lemma U_276_1 : have hlg : Real.log (8852203087610097 / 40000000000000000 : ℝ) ≤ (-(1508213088840681581873 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8852203087610097 / 40000000000000000 : ℝ) = - (8852203087610097 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8852203087610097 / 5000000000000000 : ℚ)) - (U := (571228452059318418127 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8852203087610097 / 5000000000000000 : ℝ) ≤ - (571228452059318418127 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2212977719857861 / 10000000000000000 : ℝ)) (q := - (8852203087610097 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8852203087610097 / 40000000000000000 : ℚ)) + (r' := (8852203087610097 / 5000000000000000 : ℚ)) + (U := (-(1508213088840681581873 / 1000000000000000000000 : ℚ))) + (U' := (571228452059318418127 / 1000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (2212977719857861 / 10000000000000000 : ℚ)) + (q := (8852203087610097 / 40000000000000000 : ℚ)) + (U := (-(1508213088840681581873 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_2 : Uω (aρ 2) (bρ 2) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2704,25 +2447,21 @@ lemma U_276_2 : have hlg : Real.log (8755480479323473 / 40000000000000000 : ℝ) ≤ (-(15191996085398068846649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8755480479323473 / 40000000000000000 : ℝ) = - (8755480479323473 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8755480479323473 / 5000000000000000 : ℚ)) - (U := (5602419323601931153351 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8755480479323473 / 5000000000000000 : ℝ) ≤ - (5602419323601931153351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2188385428224549 / 10000000000000000 : ℝ)) (q := - (8755480479323473 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8755480479323473 / 40000000000000000 : ℚ)) + (r' := (8755480479323473 / 5000000000000000 : ℚ)) + (U := (-(15191996085398068846649 / 10000000000000000000000 : ℚ))) + (U' := (5602419323601931153351 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (2188385428224549 / 10000000000000000 : ℚ)) + (q := (8755480479323473 / 40000000000000000 : ℚ)) + (U := (-(15191996085398068846649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_3 : Uω (aρ 3) (bρ 3) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2730,25 +2469,21 @@ lemma U_276_3 : have hlg : Real.log (8560921470759373 / 40000000000000000 : ℝ) ≤ (-(3854179051302327034767 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8560921470759373 / 40000000000000000 : ℝ) = - (8560921470759373 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8560921470759373 / 5000000000000000 : ℚ)) - (U := (1344424800947672965233 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8560921470759373 / 5000000000000000 : ℝ) ≤ - (1344424800947672965233 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2138502030292499 / 10000000000000000 : ℝ)) (q := - (8560921470759373 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8560921470759373 / 40000000000000000 : ℚ)) + (r' := (8560921470759373 / 5000000000000000 : ℚ)) + (U := (-(3854179051302327034767 / 2500000000000000000000 : ℚ))) + (U' := (1344424800947672965233 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (2138502030292499 / 10000000000000000 : ℚ)) + (q := (8560921470759373 / 40000000000000000 : ℚ)) + (U := (-(3854179051302327034767 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_4 : Uω (aρ 4) (bρ 4) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2756,25 +2491,21 @@ lemma U_276_4 : have hlg : Real.log (1646843106581577 / 8000000000000000 : ℝ) ≤ (-(1975726692953131972251 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1646843106581577 / 8000000000000000 : ℝ) = - (1646843106581577 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1646843106581577 / 1000000000000000 : ℚ)) - (U := (623575233171868027749 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1646843106581577 / 1000000000000000 : ℝ) ≤ - (623575233171868027749 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410688648486351 / 2000000000000000 : ℝ)) (q := - (1646843106581577 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1646843106581577 / 8000000000000000 : ℚ)) + (r' := (1646843106581577 / 1000000000000000 : ℚ)) + (U := (-(1975726692953131972251 / 1250000000000000000000 : ℚ))) + (U' := (623575233171868027749 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (410688648486351 / 2000000000000000 : ℚ)) + (q := (1646843106581577 / 8000000000000000 : ℚ)) + (U := (-(1975726692953131972251 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_5 : Uω (aρ 5) (bρ 5) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2782,25 +2513,21 @@ lemma U_276_5 : have hlg : Real.log (7726758212883863 / 40000000000000000 : ℝ) ≤ (-(328838011214802240827 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7726758212883863 / 40000000000000000 : ℝ) = - (7726758212883863 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7726758212883863 / 5000000000000000 : ℚ)) - (U := (87050296965197759173 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7726758212883863 / 5000000000000000 : ℝ) ≤ - (87050296965197759173 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239738062719343 / 1250000000000000 : ℝ)) (q := - (7726758212883863 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7726758212883863 / 40000000000000000 : ℚ)) + (r' := (7726758212883863 / 5000000000000000 : ℚ)) + (U := (-(328838011214802240827 / 200000000000000000000 : ℚ))) + (U' := (87050296965197759173 / 200000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (239738062719343 / 1250000000000000 : ℚ)) + (q := (7726758212883863 / 40000000000000000 : ℚ)) + (U := (-(328838011214802240827 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_6 : Uω (aρ 6) (bρ 6) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2808,25 +2535,21 @@ lemma U_276_6 : have hlg : Real.log (6972122109588451 / 40000000000000000 : ℝ) ≤ (-(17469598115456413670451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6972122109588451 / 40000000000000000 : ℝ) = - (6972122109588451 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6972122109588451 / 5000000000000000 : ℚ)) - (U := (3324817293543586329549 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6972122109588451 / 5000000000000000 : ℝ) ≤ - (3324817293543586329549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (853913412623519 / 5000000000000000 : ℝ)) (q := - (6972122109588451 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6972122109588451 / 40000000000000000 : ℚ)) + (r' := (6972122109588451 / 5000000000000000 : ℚ)) + (U := (-(17469598115456413670451 / 10000000000000000000000 : ℚ))) + (U' := (3324817293543586329549 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (853913412623519 / 5000000000000000 : ℚ)) + (q := (6972122109588451 / 40000000000000000 : ℚ)) + (U := (-(17469598115456413670451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_7 : Uω (aρ 7) (bρ 7) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2834,25 +2557,21 @@ lemma U_276_7 : have hlg : Real.log (5864500935179073 / 40000000000000000 : ℝ) ≤ (-(3839924133780546951883 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5864500935179073 / 40000000000000000 : ℝ) = - (5864500935179073 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5864500935179073 / 5000000000000000 : ℚ)) - (U := (318958948019453048117 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5864500935179073 / 5000000000000000 : ℝ) ≤ - (318958948019453048117 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1377677618802349 / 10000000000000000 : ℝ)) (q := - (5864500935179073 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5864500935179073 / 40000000000000000 : ℚ)) + (r' := (5864500935179073 / 5000000000000000 : ℚ)) + (U := (-(3839924133780546951883 / 2000000000000000000000 : ℚ))) + (U' := (318958948019453048117 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (1377677618802349 / 10000000000000000 : ℚ)) + (q := (5864500935179073 / 40000000000000000 : ℚ)) + (U := (-(3839924133780546951883 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_8 : Uω (aρ 8) (bρ 8) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -2860,25 +2579,21 @@ lemma U_276_8 : have hlg : Real.log (4099707769672261 / 40000000000000000 : ℝ) ≤ (-(2277963757593818057009 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4099707769672261 / 40000000000000000 : ℝ) = - (4099707769672261 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4099707769672261 / 2500000000000000 : ℚ)) - (U := (494624963606181942991 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4099707769672261 / 2500000000000000 : ℝ) ≤ - (494624963606181942991 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (778822687388943 / 10000000000000000 : ℝ)) (q := - (4099707769672261 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4099707769672261 / 40000000000000000 : ℚ)) + (r' := (4099707769672261 / 2500000000000000 : ℚ)) + (U := (-(2277963757593818057009 / 1000000000000000000000 : ℚ))) + (U' := (494624963606181942991 / 1000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7288387334503 / 32000000000000 : ℚ)) + (s := (778822687388943 / 10000000000000000 : ℚ)) + (q := (4099707769672261 / 40000000000000000 : ℚ)) + (U := (-(2277963757593818057009 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_276_9 : Uω (aρ 9) (bρ 9) (7288387334503 / 32000000000000 : ℝ) ≤ @@ -3009,24 +2724,21 @@ lemma U_277_1 : have hlg : Real.log (88948546351307 / 400000000000000 : ℝ) ≤ (-(15034064746622953868251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (88948546351307 / 400000000000000 : ℝ) = (88948546351307 / 50000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (88948546351307 / 50000000000000 : ℚ)) - (U := (5760350662377046131749 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (88948546351307 / 50000000000000 : ℝ) ≤ - (5760350662377046131749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (88945638281139 / 400000000000000 : ℝ)) (q := - (88948546351307 / 400000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (88948546351307 / 400000000000000 : ℚ)) + (r' := (88948546351307 / 50000000000000 : ℚ)) + (U := (-(15034064746622953868251 / 10000000000000000000000 : ℚ))) + (U' := (5760350662377046131749 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (88945638281139 / 400000000000000 : ℚ)) + (q := (88948546351307 / 400000000000000 : ℚ)) + (U := (-(15034064746622953868251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_2 : Uω (aρ 2) (bρ 2) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3034,24 +2746,21 @@ lemma U_277_2 : have hlg : Real.log (27494187581813 / 125000000000000 : ℝ) ≤ (-(3028678229702195023461 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (27494187581813 / 125000000000000 : ℝ) = (27494187581813 / 15625000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27494187581813 / 15625000000000 : ℚ)) - (U := (1130204852097804976539 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (27494187581813 / 15625000000000 : ℝ) ≤ - (1130204852097804976539 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (439810533012641 / 2000000000000000 : ℝ)) (q := - (27494187581813 / 125000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27494187581813 / 125000000000000 : ℚ)) + (r' := (27494187581813 / 15625000000000 : ℚ)) + (U := (-(3028678229702195023461 / 2000000000000000000000 : ℚ))) + (U' := (1130204852097804976539 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (439810533012641 / 2000000000000000 : ℚ)) + (q := (27494187581813 / 125000000000000 : ℚ)) + (U := (-(3028678229702195023461 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_3 : Uω (aρ 3) (bρ 3) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3059,24 +2768,21 @@ lemma U_277_3 : have hlg : Real.log (34414423663269 / 160000000000000 : ℝ) ≤ (-(384174511354075211361 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34414423663269 / 160000000000000 : ℝ) = (34414423663269 / 20000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34414423663269 / 20000000000000 : ℚ)) - (U := (135685873870924788639 / 250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34414423663269 / 20000000000000 : ℝ) ≤ - (135685873870924788639 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8596726864927 / 40000000000000 : ℝ)) (q := - (34414423663269 / 160000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34414423663269 / 160000000000000 : ℚ)) + (r' := (34414423663269 / 20000000000000 : ℚ)) + (U := (-(384174511354075211361 / 250000000000000000000 : ℚ))) + (U' := (135685873870924788639 / 250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (8596726864927 / 40000000000000 : ℚ)) + (q := (34414423663269 / 160000000000000 : ℚ)) + (U := (-(384174511354075211361 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_4 : Uω (aρ 4) (bρ 4) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3084,25 +2790,21 @@ lemma U_277_4 : have hlg : Real.log (4138485638959871 / 20000000000000000 : ℝ) ≤ (-(7877011697722102677853 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4138485638959871 / 20000000000000000 : ℝ) = - (4138485638959871 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4138485638959871 / 2500000000000000 : ℚ)) - (U := (2520196006777897322147 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4138485638959871 / 2500000000000000 : ℝ) ≤ - (2520196006777897322147 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (516039644586999 / 2500000000000000 : ℝ)) (q := - (4138485638959871 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4138485638959871 / 20000000000000000 : ℚ)) + (r' := (4138485638959871 / 2500000000000000 : ℚ)) + (U := (-(7877011697722102677853 / 5000000000000000000000 : ℚ))) + (U' := (2520196006777897322147 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (516039644586999 / 2500000000000000 : ℚ)) + (q := (4138485638959871 / 20000000000000000 : ℚ)) + (U := (-(7877011697722102677853 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_5 : Uω (aρ 5) (bρ 5) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3110,25 +2812,21 @@ lemma U_277_5 : have hlg : Real.log (3884856601398333 / 20000000000000000 : ℝ) ≤ (-(4096615501181864826651 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3884856601398333 / 20000000000000000 : ℝ) = - (3884856601398333 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3884856601398333 / 2500000000000000 : ℚ)) - (U := (1101988351068135173349 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3884856601398333 / 2500000000000000 : ℝ) ≤ - (1101988351068135173349 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (964359730060729 / 5000000000000000 : ℝ)) (q := - (3884856601398333 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3884856601398333 / 20000000000000000 : ℚ)) + (r' := (3884856601398333 / 2500000000000000 : ℚ)) + (U := (-(4096615501181864826651 / 2500000000000000000000 : ℚ))) + (U' := (1101988351068135173349 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (964359730060729 / 5000000000000000 : ℚ)) + (q := (3884856601398333 / 20000000000000000 : ℚ)) + (U := (-(4096615501181864826651 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_6 : Uω (aρ 6) (bρ 6) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3136,25 +2834,21 @@ lemma U_277_6 : have hlg : Real.log (701564584428197 / 4000000000000000 : ℝ) ≤ (-(870368338916667326583 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (701564584428197 / 4000000000000000 : ℝ) = - (701564584428197 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (701564584428197 / 500000000000000 : ℚ)) - (U := (169352431533332673417 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (701564584428197 / 500000000000000 : ℝ) ≤ - (169352431533332673417 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (171892615600411 / 1000000000000000 : ℝ)) (q := - (701564584428197 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (701564584428197 / 4000000000000000 : ℚ)) + (r' := (701564584428197 / 500000000000000 : ℚ)) + (U := (-(870368338916667326583 / 500000000000000000000 : ℚ))) + (U' := (169352431533332673417 / 500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (171892615600411 / 1000000000000000 : ℚ)) + (q := (701564584428197 / 4000000000000000 : ℚ)) + (U := (-(870368338916667326583 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_7 : Uω (aρ 7) (bρ 7) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3162,25 +2856,21 @@ lemma U_277_7 : have hlg : Real.log (2954933442797441 / 20000000000000000 : ℝ) ≤ (-(9561280728788798957347 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2954933442797441 / 20000000000000000 : ℝ) = - (2954933442797441 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2954933442797441 / 2500000000000000 : ℚ)) - (U := (835926975711201042653 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2954933442797441 / 2500000000000000 : ℝ) ≤ - (835926975711201042653 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (694849028710283 / 5000000000000000 : ℝ)) (q := - (2954933442797441 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2954933442797441 / 20000000000000000 : ℚ)) + (r' := (2954933442797441 / 2500000000000000 : ℚ)) + (U := (-(9561280728788798957347 / 5000000000000000000000 : ℚ))) + (U' := (835926975711201042653 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (694849028710283 / 5000000000000000 : ℚ)) + (q := (2954933442797441 / 20000000000000000 : ℚ)) + (U := (-(9561280728788798957347 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_8 : Uω (aρ 8) (bρ 8) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3188,25 +2878,21 @@ lemma U_277_8 : have hlg : Real.log (1038899407952763 / 10000000000000000 : ℝ) ≤ (-(11322116003695119553231 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1038899407952763 / 10000000000000000 : ℝ) = - (1038899407952763 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1038899407952763 / 625000000000000 : ℚ)) - (U := (2540827602304880446769 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1038899407952763 / 625000000000000 : ℝ) ≤ - (2540827602304880446769 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (796105081868651 / 10000000000000000 : ℝ)) (q := - (1038899407952763 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1038899407952763 / 10000000000000000 : ℚ)) + (r' := (1038899407952763 / 625000000000000 : ℚ)) + (U := (-(11322116003695119553231 / 5000000000000000000000 : ℚ))) + (U' := (2540827602304880446769 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (732250745159 / 3200000000000 : ℚ)) + (s := (796105081868651 / 10000000000000000 : ℚ)) + (q := (1038899407952763 / 10000000000000000 : ℚ)) + (U := (-(11322116003695119553231 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_277_9 : Uω (aρ 9) (bρ 9) (732250745159 / 3200000000000 : ℝ) ≤ @@ -3339,25 +3025,21 @@ lemma U_278_1 : have hlg : Real.log (8937506169277629 / 40000000000000000 : ℝ) ≤ (-(14986228550453869444753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8937506169277629 / 40000000000000000 : ℝ) = - (8937506169277629 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8937506169277629 / 5000000000000000 : ℚ)) - (U := (5808186858546130555247 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8937506169277629 / 5000000000000000 : ℝ) ≤ - (5808186858546130555247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (558576046878063 / 2500000000000000 : ℝ)) (q := - (8937506169277629 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8937506169277629 / 40000000000000000 : ℚ)) + (r' := (8937506169277629 / 5000000000000000 : ℚ)) + (U := (-(14986228550453869444753 / 10000000000000000000000 : ℚ))) + (U' := (5808186858546130555247 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (558576046878063 / 2500000000000000 : ℚ)) + (q := (8937506169277629 / 40000000000000000 : ℚ)) + (U := (-(14986228550453869444753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_2 : Uω (aρ 2) (bρ 2) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3365,25 +3047,21 @@ lemma U_278_2 : have hlg : Real.log (8840799482296617 / 40000000000000000 : ℝ) ≤ (-(7547510708000491888651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8840799482296617 / 40000000000000000 : ℝ) = - (8840799482296617 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8840799482296617 / 5000000000000000 : ℚ)) - (U := (2849696996499508111349 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8840799482296617 / 5000000000000000 : ℝ) ≤ - (2849696996499508111349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1104859928265873 / 5000000000000000 : ℝ)) (q := - (8840799482296617 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8840799482296617 / 40000000000000000 : ℚ)) + (r' := (8840799482296617 / 5000000000000000 : ℚ)) + (U := (-(7547510708000491888651 / 5000000000000000000000 : ℚ))) + (U' := (2849696996499508111349 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (1104859928265873 / 5000000000000000 : ℚ)) + (q := (8840799482296617 / 40000000000000000 : ℚ)) + (U := (-(7547510708000491888651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_3 : Uω (aρ 3) (bρ 3) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3391,25 +3069,21 @@ lemma U_278_3 : have hlg : Real.log (8646290021959631 / 40000000000000000 : ℝ) ≤ (-(7658745617946492467501 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8646290021959631 / 40000000000000000 : ℝ) = - (8646290021959631 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8646290021959631 / 5000000000000000 : ℚ)) - (U := (2738462086553507532499 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8646290021959631 / 5000000000000000 : ℝ) ≤ - (2738462086553507532499 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2159861232713253 / 10000000000000000 : ℝ)) (q := - (8646290021959631 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8646290021959631 / 40000000000000000 : ℚ)) + (r' := (8646290021959631 / 5000000000000000 : ℚ)) + (U := (-(7658745617946492467501 / 5000000000000000000000 : ℚ))) + (U' := (2738462086553507532499 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (2159861232713253 / 10000000000000000 : ℚ)) + (q := (8646290021959631 / 40000000000000000 : ℚ)) + (U := (-(7658745617946492467501 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_4 : Uω (aρ 4) (bρ 4) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3417,25 +3091,21 @@ lemma U_278_4 : have hlg : Real.log (1663945186985161 / 8000000000000000 : ℝ) ≤ (-(3140500279114518294383 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1663945186985161 / 8000000000000000 : ℝ) = - (1663945186985161 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1663945186985161 / 1000000000000000 : ℚ)) - (U := (1018382802685481705617 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1663945186985161 / 1000000000000000 : ℝ) ≤ - (1018382802685481705617 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103743668513067 / 500000000000000 : ℝ)) (q := - (1663945186985161 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1663945186985161 / 8000000000000000 : ℚ)) + (r' := (1663945186985161 / 1000000000000000 : ℚ)) + (U := (-(3140500279114518294383 / 2000000000000000000000 : ℚ))) + (U' := (1018382802685481705617 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (103743668513067 / 500000000000000 : ℚ)) + (q := (1663945186985161 / 8000000000000000 : ℚ)) + (U := (-(3140500279114518294383 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_5 : Uω (aρ 5) (bρ 5) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3443,25 +3113,21 @@ lemma U_278_5 : have hlg : Real.log (1562532963402677 / 8000000000000000 : ℝ) ≤ (-(16331333419163968740737 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1562532963402677 / 8000000000000000 : ℝ) = - (1562532963402677 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1562532963402677 / 1000000000000000 : ℚ)) - (U := (4463081989836031259263 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1562532963402677 / 1000000000000000 : ℝ) ≤ - (4463081989836031259263 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (193953273064013 / 1000000000000000 : ℝ)) (q := - (1562532963402677 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1562532963402677 / 8000000000000000 : ℚ)) + (r' := (1562532963402677 / 1000000000000000 : ℚ)) + (U := (-(16331333419163968740737 / 10000000000000000000000 : ℚ))) + (U' := (4463081989836031259263 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (193953273064013 / 1000000000000000 : ℚ)) + (q := (1562532963402677 / 8000000000000000 : ℚ)) + (U := (-(16331333419163968740737 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_6 : Uω (aρ 6) (bρ 6) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3469,25 +3135,21 @@ lemma U_278_6 : have hlg : Real.log (7059158590152613 / 40000000000000000 : ℝ) ≤ (-(17345535887965030851513 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7059158590152613 / 40000000000000000 : ℝ) = - (7059158590152613 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7059158590152613 / 5000000000000000 : ℚ)) - (U := (3448879521034969148487 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7059158590152613 / 5000000000000000 : ℝ) ≤ - (3448879521034969148487 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (108126249521859 / 625000000000000 : ℝ)) (q := - (7059158590152613 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7059158590152613 / 40000000000000000 : ℚ)) + (r' := (7059158590152613 / 5000000000000000 : ℚ)) + (U := (-(17345535887965030851513 / 10000000000000000000000 : ℚ))) + (U' := (3448879521034969148487 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (108126249521859 / 625000000000000 : ℚ)) + (q := (7059158590152613 / 40000000000000000 : ℚ)) + (U := (-(17345535887965030851513 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_7 : Uω (aρ 7) (bρ 7) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3495,25 +3157,21 @@ lemma U_278_7 : have hlg : Real.log (5955188887814863 / 40000000000000000 : ℝ) ≤ (-(761846612733371790459 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5955188887814863 / 40000000000000000 : ℝ) = - (5955188887814863 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5955188887814863 / 5000000000000000 : ℚ)) - (U := (69930003626628209541 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5955188887814863 / 5000000000000000 : ℝ) ≤ - (69930003626628209541 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1401696521940869 / 10000000000000000 : ℝ)) (q := - (5955188887814863 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5955188887814863 / 40000000000000000 : ℚ)) + (r' := (5955188887814863 / 5000000000000000 : ℚ)) + (U := (-(761846612733371790459 / 400000000000000000000 : ℚ))) + (U' := (69930003626628209541 / 400000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (1401696521940869 / 10000000000000000 : ℚ)) + (q := (5955188887814863 / 40000000000000000 : ℚ)) + (U := (-(761846612733371790459 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_8 : Uω (aρ 8) (bρ 8) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3521,25 +3179,21 @@ lemma U_278_8 : have hlg : Real.log (4211032563555623 / 40000000000000000 : ℝ) ≤ (-(4502343141899525609949 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4211032563555623 / 40000000000000000 : ℝ) = - (4211032563555623 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4211032563555623 / 2500000000000000 : ℚ)) - (U := (1042834300500474390051 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4211032563555623 / 2500000000000000 : ℝ) ≤ - (1042834300500474390051 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (813160011151249 / 10000000000000000 : ℝ)) (q := - (4211032563555623 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4211032563555623 / 40000000000000000 : ℚ)) + (r' := (4211032563555623 / 2500000000000000 : ℚ)) + (U := (-(4502343141899525609949 / 2000000000000000000000 : ℚ))) + (U' := (1042834300500474390051 / 2000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7356627568677 / 32000000000000 : ℚ)) + (s := (813160011151249 / 10000000000000000 : ℚ)) + (q := (4211032563555623 / 40000000000000000 : ℚ)) + (U := (-(4502343141899525609949 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_278_9 : Uω (aρ 9) (bρ 9) (7356627568677 / 32000000000000 : ℝ) ≤ @@ -3672,25 +3326,21 @@ lemma U_279_1 : have hlg : Real.log (179603153804829 / 800000000000000 : ℝ) ≤ (-(746931005506826067739 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (179603153804829 / 800000000000000 : ℝ) = - (179603153804829 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (179603153804829 / 100000000000000 : ℚ)) - (U := (292789764943173932261 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (179603153804829 / 100000000000000 : ℝ) ≤ - (292789764943173932261 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89798696456179 / 400000000000000 : ℝ)) (q := - (179603153804829 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (179603153804829 / 800000000000000 : ℚ)) + (r' := (179603153804829 / 100000000000000 : ℚ)) + (U := (-(746931005506826067739 / 500000000000000000000 : ℚ))) + (U' := (292789764943173932261 / 500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (89798696456179 / 400000000000000 : ℚ)) + (q := (179603153804829 / 800000000000000 : ℚ)) + (U := (-(746931005506826067739 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_2 : Uω (aρ 2) (bρ 2) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3698,25 +3348,21 @@ lemma U_279_2 : have hlg : Real.log (4441729424490323 / 20000000000000000 : ℝ) ≤ (-(150468846214901381899 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4441729424490323 / 20000000000000000 : ℝ) = - (4441729424490323 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4441729424490323 / 2500000000000000 : ℚ)) - (U := (57475307875098618101 / 100000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4441729424490323 / 2500000000000000 : ℝ) ≤ - (57475307875098618101 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2220387003284073 / 10000000000000000 : ℝ)) (q := - (4441729424490323 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4441729424490323 / 20000000000000000 : ℚ)) + (r' := (4441729424490323 / 2500000000000000 : ℚ)) + (U := (-(150468846214901381899 / 100000000000000000000 : ℚ))) + (U' := (57475307875098618101 / 100000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (2220387003284073 / 10000000000000000 : ℚ)) + (q := (4441729424490323 / 20000000000000000 : ℚ)) + (U := (-(150468846214901381899 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_3 : Uω (aρ 3) (bρ 3) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3724,25 +3370,21 @@ lemma U_279_3 : have hlg : Real.log (4344486897094561 / 20000000000000000 : ℝ) ≤ (-(7634123057285258519997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4344486897094561 / 20000000000000000 : ℝ) = - (4344486897094561 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4344486897094561 / 2500000000000000 : ℚ)) - (U := (2763084647214741480003 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4344486897094561 / 2500000000000000 : ℝ) ≤ - (2763084647214741480003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2170540582238311 / 10000000000000000 : ℝ)) (q := - (4344486897094561 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4344486897094561 / 20000000000000000 : ℚ)) + (r' := (4344486897094561 / 2500000000000000 : ℚ)) + (U := (-(7634123057285258519997 / 5000000000000000000000 : ℚ))) + (U' := (2763084647214741480003 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (2170540582238311 / 10000000000000000 : ℚ)) + (q := (4344486897094561 / 20000000000000000 : ℚ)) + (U := (-(7634123057285258519997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_4 : Uω (aρ 4) (bρ 4) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3750,25 +3392,21 @@ lemma U_279_4 : have hlg : Real.log (4181239760347549 / 20000000000000000 : ℝ) ≤ (-(3130248953656063937241 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4181239760347549 / 20000000000000000 : ℝ) = - (4181239760347549 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4181239760347549 / 2500000000000000 : ℚ)) - (U := (1028634128143936062759 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4181239760347549 / 2500000000000000 : ℝ) ≤ - (1028634128143936062759 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2085587626556299 / 10000000000000000 : ℝ)) (q := - (4181239760347549 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4181239760347549 / 20000000000000000 : ℚ)) + (r' := (4181239760347549 / 2500000000000000 : ℚ)) + (U := (-(3130248953656063937241 / 2000000000000000000000 : ℚ))) + (U' := (1028634128143936062759 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (2085587626556299 / 10000000000000000 : ℚ)) + (q := (4181239760347549 / 20000000000000000 : ℚ)) + (U := (-(3130248953656063937241 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_5 : Uω (aρ 5) (bρ 5) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3776,25 +3414,21 @@ lemma U_279_5 : have hlg : Real.log (785561311168151 / 4000000000000000 : ℝ) ≤ (-(16276511309893494333811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (785561311168151 / 4000000000000000 : ℝ) = - (785561311168151 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (785561311168151 / 500000000000000 : ℚ)) - (U := (4517904099106505666189 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (785561311168151 / 500000000000000 : ℝ) ≤ - (4517904099106505666189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (390068868276901 / 2000000000000000 : ℝ)) (q := - (785561311168151 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (785561311168151 / 4000000000000000 : ℚ)) + (r' := (785561311168151 / 500000000000000 : ℚ)) + (U := (-(16276511309893494333811 / 10000000000000000000000 : ℚ))) + (U' := (4517904099106505666189 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (390068868276901 / 2000000000000000 : ℚ)) + (q := (785561311168151 / 4000000000000000 : ℚ)) + (U := (-(16276511309893494333811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_6 : Uω (aρ 6) (bρ 6) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3802,25 +3436,21 @@ lemma U_279_6 : have hlg : Real.log (1775665139313283 / 10000000000000000 : ℝ) ≤ (-(17284100131055428922333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1775665139313283 / 10000000000000000 : ℝ) = - (1775665139313283 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1775665139313283 / 1250000000000000 : ℚ)) - (U := (3510315277944571077667 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1775665139313283 / 1250000000000000 : ℝ) ≤ - (3510315277944571077667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (435277109827579 / 2500000000000000 : ℝ)) (q := - (1775665139313283 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1775665139313283 / 10000000000000000 : ℚ)) + (r' := (1775665139313283 / 1250000000000000 : ℚ)) + (U := (-(17284100131055428922333 / 10000000000000000000000 : ℚ))) + (U' := (3510315277944571077667 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (435277109827579 / 2500000000000000 : ℚ)) + (q := (1775665139313283 / 10000000000000000 : ℚ)) + (U := (-(17284100131055428922333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_7 : Uω (aρ 7) (bρ 7) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3828,25 +3458,21 @@ lemma U_279_7 : have hlg : Real.log (600046806086179 / 4000000000000000 : ℝ) ≤ (-(9485209885025233626713 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (600046806086179 / 4000000000000000 : ℝ) = - (600046806086179 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (600046806086179 / 500000000000000 : ℚ)) - (U := (911997819474766373287 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (600046806086179 / 500000000000000 : ℝ) ≤ - (911997819474766373287 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (282734714374929 / 2000000000000000 : ℝ)) (q := - (600046806086179 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (600046806086179 / 4000000000000000 : ℚ)) + (r' := (600046806086179 / 500000000000000 : ℚ)) + (U := (-(9485209885025233626713 / 5000000000000000000000 : ℚ))) + (U' := (911997819474766373287 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (282734714374929 / 2000000000000000 : ℚ)) + (q := (600046806086179 / 4000000000000000 : ℚ)) + (U := (-(9485209885025233626713 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_8 : Uω (aρ 8) (bρ 8) (1847686921441 / 8000000000000 : ℝ) ≤ @@ -3854,25 +3480,21 @@ lemma U_279_8 : have hlg : Real.log (1066510152242077 / 10000000000000000 : ℝ) ≤ (-(11190966569279896228593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1066510152242077 / 10000000000000000 : ℝ) = - (1066510152242077 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1066510152242077 / 625000000000000 : ℚ)) - (U := (2671977036720103771407 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1066510152242077 / 625000000000000 : ℝ) ≤ - (2671977036720103771407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12968773394811 / 156250000000000 : ℝ)) (q := - (1066510152242077 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1066510152242077 / 10000000000000000 : ℚ)) + (r' := (1066510152242077 / 625000000000000 : ℚ)) + (U := (-(11190966569279896228593 / 5000000000000000000000 : ℚ))) + (U' := (2671977036720103771407 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1847686921441 / 8000000000000 : ℚ)) + (s := (12968773394811 / 156250000000000 : ℚ)) + (q := (1066510152242077 / 10000000000000000 : ℚ)) + (U := (-(11190966569279896228593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_279_9 : Uω (aρ 9) (bρ 9) (1847686921441 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U23.lean b/LeanPool/Zeta5Irrational/Table/U23.lean index 0c5865839e..28c3865c8e 100644 --- a/LeanPool/Zeta5Irrational/Table/U23.lean +++ b/LeanPool/Zeta5Irrational/Table/U23.lean @@ -24,25 +24,21 @@ lemma U_280_1 : have hlg : Real.log (9022809198209127 / 40000000000000000 : ℝ) ≤ (-(595649490681648873547 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9022809198209127 / 40000000000000000 : ℝ) = - (9022809198209127 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9022809198209127 / 5000000000000000 : ℚ)) - (U := (236127125678351126453 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9022809198209127 / 5000000000000000 : ℝ) ≤ - (236127125678351126453 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1127815314399313 / 5000000000000000 : ℝ)) (q := - (9022809198209127 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9022809198209127 / 40000000000000000 : ℚ)) + (r' := (9022809198209127 / 5000000000000000 : ℚ)) + (U := (-(595649490681648873547 / 400000000000000000000 : ℚ))) + (U' := (236127125678351126453 / 400000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (1127815314399313 / 5000000000000000 : ℚ)) + (q := (9022809198209127 / 40000000000000000 : ℚ)) + (U := (-(595649490681648873547 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_2 : Uω (aρ 2) (bρ 2) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_280_2 : have hlg : Real.log (1785223625503007 / 8000000000000000 : ℝ) ≤ (-(14998978531214893129037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1785223625503007 / 8000000000000000 : ℝ) = - (1785223625503007 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1785223625503007 / 1000000000000000 : ℚ)) - (U := (5795436877785106870963 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1785223625503007 / 1000000000000000 : ℝ) ≤ - (5795436877785106870963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (111552705298079 / 500000000000000 : ℝ)) (q := - (1785223625503007 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1785223625503007 / 8000000000000000 : ℚ)) + (r' := (1785223625503007 / 1000000000000000 : ℚ)) + (U := (-(14998978531214893129037 / 10000000000000000000000 : ℚ))) + (U' := (5795436877785106870963 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (111552705298079 / 500000000000000 : ℚ)) + (q := (1785223625503007 / 8000000000000000 : ℚ)) + (U := (-(14998978531214893129037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_3 : Uω (aρ 3) (bρ 3) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_280_3 : have hlg : Real.log (8731657237410283 / 40000000000000000 : ℝ) ≤ (-(3804810672586354525097 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8731657237410283 / 40000000000000000 : ℝ) = - (8731657237410283 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8731657237410283 / 5000000000000000 : ℚ)) - (U := (1393793179663645474903 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8731657237410283 / 5000000000000000 : ℝ) ≤ - (1393793179663645474903 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (545304941814801 / 2500000000000000 : ℝ)) (q := - (8731657237410283 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8731657237410283 / 40000000000000000 : ℚ)) + (r' := (8731657237410283 / 5000000000000000 : ℚ)) + (U := (-(3804810672586354525097 / 2500000000000000000000 : ℚ))) + (U' := (1393793179663645474903 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (545304941814801 / 2500000000000000 : ℚ)) + (q := (8731657237410283 / 40000000000000000 : ℚ)) + (U := (-(3804810672586354525097 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_4 : Uω (aρ 4) (bρ 4) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_280_4 : have hlg : Real.log (8405232051652987 / 40000000000000000 : ℝ) ≤ (-(15600250780916396574767 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8405232051652987 / 40000000000000000 : ℝ) = - (8405232051652987 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8405232051652987 / 5000000000000000 : ℚ)) - (U := (5194164628083603425233 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8405232051652987 / 5000000000000000 : ℝ) ≤ - (5194164628083603425233 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (524075338861389 / 2500000000000000 : ℝ)) (q := - (8405232051652987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8405232051652987 / 40000000000000000 : ℚ)) + (r' := (8405232051652987 / 5000000000000000 : ℚ)) + (U := (-(15600250780916396574767 / 10000000000000000000000 : ℚ))) + (U' := (5194164628083603425233 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (524075338861389 / 2500000000000000 : ℚ)) + (q := (8405232051652987 / 40000000000000000 : ℚ)) + (U := (-(15600250780916396574767 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_5 : Uω (aρ 5) (bρ 5) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_280_5 : have hlg : Real.log (7898558141701877 / 40000000000000000 : ℝ) ≤ (-(16221992242274015104961 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7898558141701877 / 40000000000000000 : ℝ) = - (7898558141701877 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7898558141701877 / 5000000000000000 : ℚ)) - (U := (4572423166725984895039 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7898558141701877 / 5000000000000000 : ℝ) ≤ - (4572423166725984895039 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1961154319805001 / 10000000000000000 : ℝ)) (q := - (7898558141701877 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7898558141701877 / 40000000000000000 : ℚ)) + (r' := (7898558141701877 / 5000000000000000 : ℚ)) + (U := (-(16221992242274015104961 / 10000000000000000000000 : ℚ))) + (U' := (4572423166725984895039 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (1961154319805001 / 10000000000000000 : ℚ)) + (q := (7898558141701877 / 40000000000000000 : ℚ)) + (U := (-(16221992242274015104961 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_6 : Uω (aρ 6) (bρ 6) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_280_6 : have hlg : Real.log (7146151950218381 / 40000000000000000 : ℝ) ≤ (-(17223054302843945077151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7146151950218381 / 40000000000000000 : ℝ) = - (7146151950218381 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7146151950218381 / 5000000000000000 : ℚ)) - (U := (3571361106156054922849 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7146151950218381 / 5000000000000000 : ℝ) ≤ - (3571361106156054922849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1752191599203253 / 10000000000000000 : ℝ)) (q := - (7146151950218381 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7146151950218381 / 40000000000000000 : ℚ)) + (r' := (7146151950218381 / 5000000000000000 : ℚ)) + (U := (-(17223054302843945077151 / 10000000000000000000000 : ℚ))) + (U' := (3571361106156054922849 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (1752191599203253 / 10000000000000000 : ℚ)) + (q := (7146151950218381 / 40000000000000000 : ℚ)) + (U := (-(17223054302843945077151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_7 : Uω (aρ 7) (bρ 7) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_280_7 : have hlg : Real.log (6045705484189657 / 40000000000000000 : ℝ) ≤ (-(3779062541338344784579 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6045705484189657 / 40000000000000000 : ℝ) = - (6045705484189657 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6045705484189657 / 5000000000000000 : ℚ)) - (U := (379820540461655215421 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6045705484189657 / 5000000000000000 : ℝ) ≤ - (379820540461655215421 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1425629746948891 / 10000000000000000 : ℝ)) (q := - (6045705484189657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6045705484189657 / 40000000000000000 : ℚ)) + (r' := (6045705484189657 / 5000000000000000 : ℚ)) + (U := (-(3779062541338344784579 / 2000000000000000000000 : ℚ))) + (U' := (379820540461655215421 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (1425629746948891 / 10000000000000000 : ℚ)) + (q := (6045705484189657 / 40000000000000000 : ℚ)) + (U := (-(3779062541338344784579 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_8 : Uω (aρ 8) (bρ 8) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_280_8 : have hlg : Real.log (4320647243227353 / 40000000000000000 : ℝ) ≤ (-(11127371186098035850237 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4320647243227353 / 40000000000000000 : ℝ) = - (4320647243227353 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4320647243227353 / 2500000000000000 : ℚ)) - (U := (2735572419901964149763 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4320647243227353 / 2500000000000000 : ℝ) ≤ - (2735572419901964149763 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (846642277807739 / 10000000000000000 : ℝ)) (q := - (4320647243227353 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4320647243227353 / 40000000000000000 : ℚ)) + (r' := (4320647243227353 / 2500000000000000 : ℚ)) + (U := (-(11127371186098035850237 / 5000000000000000000000 : ℚ))) + (U' := (2735572419901964149763 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7424867802851 / 32000000000000 : ℚ)) + (s := (846642277807739 / 10000000000000000 : ℚ)) + (q := (4320647243227353 / 40000000000000000 : ℚ)) + (U := (-(11127371186098035850237 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_280_9 : Uω (aρ 9) (bρ 9) (7424867802851 / 32000000000000 : ℝ) ≤ @@ -356,25 +324,21 @@ lemma U_281_1 : have hlg : Real.log (2266365173341027 / 10000000000000000 : ℝ) ≤ (-(14844077893084188706087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2266365173341027 / 10000000000000000 : ℝ) = - (2266365173341027 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2266365173341027 / 1250000000000000 : ℚ)) - (U := (5950337515915811293913 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2266365173341027 / 1250000000000000 : ℝ) ≤ - (5950337515915811293913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2266293839786429 / 10000000000000000 : ℝ)) (q := - (2266365173341027 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2266365173341027 / 10000000000000000 : ℚ)) + (r' := (2266365173341027 / 1250000000000000 : ℚ)) + (U := (-(14844077893084188706087 / 10000000000000000000000 : ℚ))) + (U' := (5950337515915811293913 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (2266293839786429 / 10000000000000000 : ℚ)) + (q := (2266365173341027 / 10000000000000000 : ℚ)) + (U := (-(14844077893084188706087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_2 : Uω (aρ 2) (bρ 2) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -382,25 +346,21 @@ lemma U_281_2 : have hlg : Real.log (179375546383163 / 800000000000000 : ℝ) ≤ (-(7475650471701528025081 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (179375546383163 / 800000000000000 : ℝ) = - (179375546383163 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (179375546383163 / 100000000000000 : ℚ)) - (U := (2921557232798471974919 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (179375546383163 / 100000000000000 : ℝ) ≤ - (2921557232798471974919 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44834423303869 / 200000000000000 : ℝ)) (q := - (179375546383163 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (179375546383163 / 800000000000000 : ℚ)) + (r' := (179375546383163 / 100000000000000 : ℚ)) + (U := (-(7475650471701528025081 / 5000000000000000000000 : ℚ))) + (U' := (2921557232798471974919 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (44834423303869 / 200000000000000 : ℚ)) + (q := (179375546383163 / 800000000000000 : ℚ)) + (U := (-(7475650471701528025081 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_3 : Uω (aρ 3) (bρ 3) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -408,25 +368,21 @@ lemma U_281_3 : have hlg : Real.log (2193585089108003 / 10000000000000000 : ℝ) ≤ (-(15170478598639876278171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2193585089108003 / 10000000000000000 : ℝ) = - (2193585089108003 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2193585089108003 / 1250000000000000 : ℚ)) - (U := (5623936810360123721829 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2193585089108003 / 1250000000000000 : ℝ) ≤ - (5623936810360123721829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2191898790180381 / 10000000000000000 : ℝ)) (q := - (2193585089108003 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2193585089108003 / 10000000000000000 : ℚ)) + (r' := (2193585089108003 / 1250000000000000 : ℚ)) + (U := (-(15170478598639876278171 / 10000000000000000000000 : ℚ))) + (U' := (5623936810360123721829 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (2191898790180381 / 10000000000000000 : ℚ)) + (q := (2193585089108003 / 10000000000000000 : ℚ)) + (U := (-(15170478598639876278171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_4 : Uω (aρ 4) (bρ 4) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -434,25 +390,21 @@ lemma U_281_4 : have hlg : Real.log (4223991771944979 / 20000000000000000 : ℝ) ≤ (-(3109903348603568808439 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4223991771944979 / 20000000000000000 : ℝ) = - (4223991771944979 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4223991771944979 / 2500000000000000 : ℚ)) - (U := (1048979733196431191561 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4223991771944979 / 2500000000000000 : ℝ) ≤ - (1048979733196431191561 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1053507282487177 / 5000000000000000 : ℝ)) (q := - (4223991771944979 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4223991771944979 / 20000000000000000 : ℚ)) + (r' := (4223991771944979 / 2500000000000000 : ℚ)) + (U := (-(3109903348603568808439 / 2000000000000000000000 : ℚ))) + (U' := (1048979733196431191561 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (1053507282487177 / 5000000000000000 : ℚ)) + (q := (4223991771944979 / 20000000000000000 : ℚ)) + (U := (-(3109903348603568808439 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_5 : Uω (aρ 5) (bρ 5) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -460,25 +412,21 @@ lemma U_281_5 : have hlg : Real.log (1985374990190821 / 10000000000000000 : ℝ) ≤ (-(16167772839817462190979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1985374990190821 / 10000000000000000 : ℝ) = - (1985374990190821 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1985374990190821 / 1250000000000000 : ℚ)) - (U := (4626642569182537809021 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1985374990190821 / 1250000000000000 : ℝ) ≤ - (4626642569182537809021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1971962692746017 / 10000000000000000 : ℝ)) (q := - (1985374990190821 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1985374990190821 / 10000000000000000 : ℚ)) + (r' := (1985374990190821 / 1250000000000000 : ℚ)) + (U := (-(16167772839817462190979 / 10000000000000000000000 : ℚ))) + (U' := (4626642569182537809021 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (1971962692746017 / 10000000000000000 : ℚ)) + (q := (1985374990190821 / 10000000000000000 : ℚ)) + (U := (-(16167772839817462190979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_6 : Uω (aρ 6) (bρ 6) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -486,25 +434,21 @@ lemma U_281_6 : have hlg : Real.log (1797408242110467 / 10000000000000000 : ℝ) ≤ (-(858119665204360662129 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1797408242110467 / 10000000000000000 : ℝ) = - (1797408242110467 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1797408242110467 / 1250000000000000 : ℚ)) - (U := (181601105245639337871 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1797408242110467 / 1250000000000000 : ℝ) ≤ - (181601105245639337871 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1763269571725309 / 10000000000000000 : ℝ)) (q := - (1797408242110467 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1797408242110467 / 10000000000000000 : ℚ)) + (r' := (1797408242110467 / 1250000000000000 : ℚ)) + (U := (-(858119665204360662129 / 500000000000000000000 : ℚ))) + (U' := (181601105245639337871 / 500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (1763269571725309 / 10000000000000000 : ℚ)) + (q := (1797408242110467 / 10000000000000000 : ℚ)) + (U := (-(858119665204360662129 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_7 : Uω (aρ 7) (bρ 7) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -512,25 +456,21 @@ lemma U_281_7 : have hlg : Real.log (304545109974543 / 2000000000000000 : ℝ) ≤ (-(3764166476338037308167 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (304545109974543 / 2000000000000000 : ℝ) = - (304545109974543 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (304545109974543 / 250000000000000 : ℚ)) - (U := (394716605461962691833 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (304545109974543 / 250000000000000 : ℝ) ≤ - (394716605461962691833 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (287513113601961 / 2000000000000000 : ℝ)) (q := - (304545109974543 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (304545109974543 / 2000000000000000 : ℚ)) + (r' := (304545109974543 / 250000000000000 : ℚ)) + (U := (-(3764166476338037308167 / 2000000000000000000000 : ℚ))) + (U' := (394716605461962691833 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (287513113601961 / 2000000000000000 : ℚ)) + (q := (304545109974543 / 2000000000000000 : ℚ)) + (U := (-(3764166476338037308167 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_8 : Uω (aρ 8) (bρ 8) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -538,25 +478,21 @@ lemma U_281_8 : have hlg : Real.log (1093718921142253 / 10000000000000000 : ℝ) ≤ (-(885200539449577683937 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1093718921142253 / 10000000000000000 : ℝ) = - (1093718921142253 / 625000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1093718921142253 / 625000000000000 : ℚ)) - (U := (223834949030422316063 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1093718921142253 / 625000000000000 : ℝ) ≤ - (223834949030422316063 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (863093961888881 / 10000000000000000 : ℝ)) (q := - (1093718921142253 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1093718921142253 / 10000000000000000 : ℚ)) + (r' := (1093718921142253 / 625000000000000 : ℚ)) + (U := (-(885200539449577683937 / 400000000000000000000 : ℚ))) + (U' := (223834949030422316063 / 400000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3729493959969 / 16000000000000 : ℚ)) + (s := (863093961888881 / 10000000000000000 : ℚ)) + (q := (1093718921142253 / 10000000000000000 : ℚ)) + (U := (-(885200539449577683937 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_281_9 : Uω (aρ 9) (bρ 9) (3729493959969 / 16000000000000 : ℝ) ≤ @@ -689,25 +625,21 @@ lemma U_282_1 : have hlg : Real.log (9108112175886401 / 40000000000000000 : ℝ) ≤ (-(1849642486269237145517 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9108112175886401 / 40000000000000000 : ℝ) = - (9108112175886401 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9108112175886401 / 5000000000000000 : ℚ)) - (U := (749659439855762854483 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9108112175886401 / 5000000000000000 : ℝ) ≤ - (749659439855762854483 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (71154907639309 / 312500000000000 : ℝ)) (q := - (9108112175886401 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9108112175886401 / 40000000000000000 : ℚ)) + (r' := (9108112175886401 / 5000000000000000 : ℚ)) + (U := (-(1849642486269237145517 / 1250000000000000000000 : ℚ))) + (U' := (749659439855762854483 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (71154907639309 / 312500000000000 : ℚ)) + (q := (9108112175886401 / 40000000000000000 : ℚ)) + (U := (-(1849642486269237145517 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_2 : Uω (aρ 2) (bρ 2) (299724321481 / 1280000000000 : ℝ) ≤ @@ -715,25 +647,21 @@ lemma U_282_2 : have hlg : Real.log (9011436425144511 / 40000000000000000 : ℝ) ≤ (-(14903849687665541604669 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9011436425144511 / 40000000000000000 : ℝ) = - (9011436425144511 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9011436425144511 / 5000000000000000 : ℚ)) - (U := (5890565721334458395331 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9011436425144511 / 5000000000000000 : ℝ) ≤ - (5890565721334458395331 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2252388181596943 / 10000000000000000 : ℝ)) (q := - (9011436425144511 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9011436425144511 / 40000000000000000 : ℚ)) + (r' := (9011436425144511 / 5000000000000000 : ℚ)) + (U := (-(14903849687665541604669 / 10000000000000000000000 : ℚ))) + (U' := (5890565721334458395331 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (2252388181596943 / 10000000000000000 : ℚ)) + (q := (9011436425144511 / 40000000000000000 : ℚ)) + (U := (-(14903849687665541604669 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_3 : Uω (aρ 3) (bρ 3) (299724321481 / 1280000000000 : ℝ) ≤ @@ -741,24 +669,21 @@ lemma U_282_3 : have hlg : Real.log (70536185247759 / 320000000000000 : ℝ) ≤ (-(3024390301891908800277 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (70536185247759 / 320000000000000 : ℝ) = (70536185247759 / 40000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70536185247759 / 40000000000000 : ℚ)) - (U := (1134492779908091199723 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70536185247759 / 40000000000000 : ℝ) ≤ - (1134492779908091199723 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17620621226877 / 80000000000000 : ℝ)) (q := - (70536185247759 / 320000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70536185247759 / 320000000000000 : ℚ)) + (r' := (70536185247759 / 40000000000000 : ℚ)) + (U := (-(3024390301891908800277 / 2000000000000000000000 : ℚ))) + (U' := (1134492779908091199723 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (17620621226877 / 80000000000000 : ℚ)) + (q := (70536185247759 / 320000000000000 : ℚ)) + (U := (-(3024390301891908800277 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_4 : Uω (aρ 4) (bρ 4) (299724321481 / 1280000000000 : ℝ) ≤ @@ -766,25 +691,21 @@ lemma U_282_4 : have hlg : Real.log (8490734013170131 / 40000000000000000 : ℝ) ≤ (-(193738000068022755659 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8490734013170131 / 40000000000000000 : ℝ) = - (8490734013170131 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8490734013170131 / 5000000000000000 : ℚ)) - (U := (66192192544477244341 / 125000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8490734013170131 / 5000000000000000 : ℝ) ≤ - (66192192544477244341 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2117727263024753 / 10000000000000000 : ℝ)) (q := - (8490734013170131 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8490734013170131 / 40000000000000000 : ℚ)) + (r' := (8490734013170131 / 5000000000000000 : ℚ)) + (U := (-(193738000068022755659 / 125000000000000000000 : ℚ))) + (U' := (66192192544477244341 / 125000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (2117727263024753 / 10000000000000000 : ℚ)) + (q := (8490734013170131 / 40000000000000000 : ℚ)) + (U := (-(193738000068022755659 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_5 : Uω (aρ 5) (bρ 5) (299724321481 / 1280000000000 : ℝ) ≤ @@ -792,25 +713,21 @@ lemma U_282_5 : have hlg : Real.log (7984438621375987 / 40000000000000000 : ℝ) ≤ (-(402846244571714183917 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7984438621375987 / 40000000000000000 : ℝ) = - (7984438621375987 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7984438621375987 / 5000000000000000 : ℚ)) - (U := (117014140653285816083 / 250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7984438621375987 / 5000000000000000 : ℝ) ≤ - (117014140653285816083 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1982769486462681 / 10000000000000000 : ℝ)) (q := - (7984438621375987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7984438621375987 / 40000000000000000 : ℚ)) + (r' := (7984438621375987 / 5000000000000000 : ℚ)) + (U := (-(402846244571714183917 / 250000000000000000000 : ℚ))) + (U' := (117014140653285816083 / 250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (1982769486462681 / 10000000000000000 : ℚ)) + (q := (7984438621375987 / 40000000000000000 : ℚ)) + (U := (-(402846244571714183917 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_6 : Uω (aρ 6) (bρ 6) (299724321481 / 1280000000000 : ℝ) ≤ @@ -818,25 +735,21 @@ lemma U_282_6 : have hlg : Real.log (7233103806245339 / 40000000000000000 : ℝ) ≤ (-(17102112138147452632809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7233103806245339 / 40000000000000000 : ℝ) = - (7233103806245339 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7233103806245339 / 5000000000000000 : ℚ)) - (U := (3692303270852547367191 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7233103806245339 / 5000000000000000 : ℝ) ≤ - (3692303270852547367191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1774342454037357 / 10000000000000000 : ℝ)) (q := - (7233103806245339 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7233103806245339 / 40000000000000000 : ℚ)) + (r' := (7233103806245339 / 5000000000000000 : ℚ)) + (U := (-(17102112138147452632809 / 10000000000000000000000 : ℚ))) + (U' := (3692303270852547367191 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (1774342454037357 / 10000000000000000 : ℚ)) + (q := (7233103806245339 / 40000000000000000 : ℚ)) + (U := (-(17102112138147452632809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_7 : Uω (aρ 7) (bρ 7) (299724321481 / 1280000000000 : ℝ) ≤ @@ -844,25 +757,21 @@ lemma U_282_7 : have hlg : Real.log (1227211842480363 / 8000000000000000 : ℝ) ≤ (-(1171685462072131543447 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1227211842480363 / 8000000000000000 : ℝ) = - (1227211842480363 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1227211842480363 / 1000000000000000 : ℚ)) - (U := (127965500990368456553 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1227211842480363 / 1000000000000000 : ℝ) ≤ - (127965500990368456553 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (289896307575119 / 2000000000000000 : ℝ)) (q := - (1227211842480363 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1227211842480363 / 8000000000000000 : ℚ)) + (r' := (1227211842480363 / 1000000000000000 : ℚ)) + (U := (-(1171685462072131543447 / 625000000000000000000 : ℚ))) + (U' := (127965500990368456553 / 625000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (289896307575119 / 2000000000000000 : ℚ)) + (q := (1227211842480363 / 8000000000000000 : ℚ)) + (U := (-(1171685462072131543447 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_8 : Uω (aρ 8) (bρ 8) (299724321481 / 1280000000000 : ℝ) ≤ @@ -870,25 +779,21 @@ lemma U_282_8 : have hlg : Real.log (4428747159444107 / 40000000000000000 : ℝ) ≤ (-(11003813586334001811501 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4428747159444107 / 40000000000000000 : ℝ) = - (4428747159444107 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4428747159444107 / 2500000000000000 : ℚ)) - (U := (2859130019665998188499 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4428747159444107 / 2500000000000000 : ℝ) ≤ - (2859130019665998188499 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (879367162736741 / 10000000000000000 : ℝ)) (q := - (4428747159444107 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4428747159444107 / 40000000000000000 : ℚ)) + (r' := (4428747159444107 / 2500000000000000 : ℚ)) + (U := (-(11003813586334001811501 / 5000000000000000000000 : ℚ))) + (U' := (2859130019665998188499 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (299724321481 / 1280000000000 : ℚ)) + (s := (879367162736741 / 10000000000000000 : ℚ)) + (q := (4428747159444107 / 40000000000000000 : ℚ)) + (U := (-(11003813586334001811501 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_282_9 : Uω (aρ 9) (bρ 9) (299724321481 / 1280000000000 : ℝ) ≤ @@ -1018,25 +923,21 @@ lemma U_283_1 : have hlg : Real.log (4575381822976329 / 20000000000000000 : ℝ) ≤ (-(14750421189550824741283 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4575381822976329 / 20000000000000000 : ℝ) = - (4575381822976329 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4575381822976329 / 2500000000000000 : ℚ)) - (U := (6043994219449175258717 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4575381822976329 / 2500000000000000 : ℝ) ≤ - (6043994219449175258717 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2287620242901329 / 10000000000000000 : ℝ)) (q := - (4575381822976329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4575381822976329 / 20000000000000000 : ℚ)) + (r' := (4575381822976329 / 2500000000000000 : ℚ)) + (U := (-(14750421189550824741283 / 10000000000000000000000 : ℚ))) + (U' := (6043994219449175258717 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (29403234977 / 125000000000 : ℚ)) + (s := (2287620242901329 / 10000000000000000 : ℚ)) + (q := (4575381822976329 / 20000000000000000 : ℚ)) + (U := (-(14750421189550824741283 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_2 : Uω (aρ 2) (bρ 2) (29403234977 / 125000000000 : ℝ) ≤ @@ -1044,25 +945,21 @@ lemma U_283_2 : have hlg : Real.log (4527047723342681 / 20000000000000000 : ℝ) ≤ (-(7428311312201253933377 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4527047723342681 / 20000000000000000 : ℝ) = - (4527047723342681 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4527047723342681 / 2500000000000000 : ℚ)) - (U := (2968896392298746066623 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4527047723342681 / 2500000000000000 : ℝ) ≤ - (2968896392298746066623 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2263055155777681 / 10000000000000000 : ℝ)) (q := - (4527047723342681 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4527047723342681 / 20000000000000000 : ℚ)) + (r' := (4527047723342681 / 2500000000000000 : ℚ)) + (U := (-(7428311312201253933377 / 5000000000000000000000 : ℚ))) + (U' := (2968896392298746066623 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (29403234977 / 125000000000 : ℚ)) + (s := (2263055155777681 / 10000000000000000 : ℚ)) + (q := (4527047723342681 / 20000000000000000 : ℚ)) + (U := (-(7428311312201253933377 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_3 : Uω (aρ 3) (bρ 3) (29403234977 / 125000000000 : ℝ) ≤ @@ -1070,25 +967,21 @@ lemma U_283_3 : have hlg : Real.log (4429852820324179 / 20000000000000000 : ℝ) ≤ (-(7536829563360700704481 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4429852820324179 / 20000000000000000 : ℝ) = - (4429852820324179 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4429852820324179 / 2500000000000000 : ℚ)) - (U := (2860378141139299295519 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4429852820324179 / 2500000000000000 : ℝ) ≤ - (2860378141139299295519 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2213256359109179 / 10000000000000000 : ℝ)) (q := - (4429852820324179 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4429852820324179 / 20000000000000000 : ℚ)) + (r' := (4429852820324179 / 2500000000000000 : ℚ)) + (U := (-(7536829563360700704481 / 5000000000000000000000 : ℚ))) + (U' := (2860378141139299295519 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (29403234977 / 125000000000 : ℚ)) + (s := (2213256359109179 / 10000000000000000 : ℚ)) + (q := (4429852820324179 / 20000000000000000 : ℚ)) + (U := (-(7536829563360700704481 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_4 : Uω (aρ 4) (bρ 4) (29403234977 / 125000000000 : ℝ) ≤ @@ -1096,25 +989,21 @@ lemma U_283_4 : have hlg : Real.log (2133370868734877 / 10000000000000000 : ℝ) ≤ (-(1931102244940006175991 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2133370868734877 / 10000000000000000 : ℝ) = - (2133370868734877 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2133370868734877 / 1250000000000000 : ℚ)) - (U := (668199681184993824009 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2133370868734877 / 1250000000000000 : ℝ) ≤ - (668199681184993824009 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1064219728659877 / 5000000000000000 : ℝ)) (q := - (2133370868734877 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2133370868734877 / 10000000000000000 : ℚ)) + (r' := (2133370868734877 / 1250000000000000 : ℚ)) + (U := (-(1931102244940006175991 / 1250000000000000000000 : ℚ))) + (U' := (668199681184993824009 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (29403234977 / 125000000000 : ℚ)) + (s := (1064219728659877 / 5000000000000000 : ℚ)) + (q := (2133370868734877 / 10000000000000000 : ℚ)) + (U := (-(1931102244940006175991 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_5 : Uω (aρ 5) (bρ 5) (29403234977 / 125000000000 : ℝ) ≤ @@ -1122,25 +1011,21 @@ lemma U_283_5 : have hlg : Real.log (4013687087452027 / 20000000000000000 : ℝ) ≤ (-(16060219807321465949653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4013687087452027 / 20000000000000000 : ℝ) = - (4013687087452027 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4013687087452027 / 2500000000000000 : ℚ)) - (U := (4734195601678534050347 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4013687087452027 / 2500000000000000 : ℝ) ≤ - (4734195601678534050347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1993574726637027 / 10000000000000000 : ℝ)) (q := - (4013687087452027 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4013687087452027 / 20000000000000000 : ℚ)) + (r' := (4013687087452027 / 2500000000000000 : ℚ)) + (U := (-(16060219807321465949653 / 10000000000000000000000 : ℚ))) + (U' := (4734195601678534050347 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (29403234977 / 125000000000 : ℚ)) + (s := (1993574726637027 / 10000000000000000 : ℚ)) + (q := (4013687087452027 / 20000000000000000 : ℚ)) + (U := (-(16060219807321465949653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_6 : Uω (aρ 6) (bρ 6) (29403234977 / 125000000000 : ℝ) ≤ @@ -1148,25 +1033,21 @@ lemma U_283_6 : have hlg : Real.log (454785290815107 / 2500000000000000 : ℝ) ≤ (-(8521102954091416726939 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (454785290815107 / 2500000000000000 : ℝ) = - (454785290815107 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (454785290815107 / 312500000000000 : ℚ)) - (U := (1876104750408583273061 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (454785290815107 / 312500000000000 : ℝ) ≤ - (1876104750408583273061 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55794073151433 / 312500000000000 : ℝ)) (q := - (454785290815107 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (454785290815107 / 2500000000000000 : ℚ)) + (r' := (454785290815107 / 312500000000000 : ℚ)) + (U := (-(8521102954091416726939 / 5000000000000000000000 : ℚ))) + (U' := (1876104750408583273061 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (29403234977 / 125000000000 : ℚ)) + (s := (55794073151433 / 312500000000000 : ℚ)) + (q := (454785290815107 / 2500000000000000 : ℚ)) + (U := (-(8521102954091416726939 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_7 : Uω (aρ 7) (bρ 7) (29403234977 / 125000000000 : ℝ) ≤ @@ -1174,23 +1055,21 @@ lemma U_283_7 : have hlg : Real.log (12072612293191 / 78125000000000 : ℝ) ≤ (-(18673706669854913901521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show (12072612293191 / 78125000000000 : ℝ) = (12072612293191 / 9765625000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12072612293191 / 9765625000000 : ℚ)) - (U := (2120708739145086098479 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12072612293191 / 9765625000000 : ℝ) ≤ - (2120708739145086098479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (182672267767737 / 1250000000000000 : ℝ)) (q := - (12072612293191 / 78125000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12072612293191 / 78125000000000 : ℚ)) + (r' := (12072612293191 / 9765625000000 : ℚ)) + (U := (-(18673706669854913901521 / 10000000000000000000000 : ℚ))) + (U' := (2120708739145086098479 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (29403234977 / 125000000000 : ℚ)) + (s := (182672267767737 / 1250000000000000 : ℚ)) + (q := (12072612293191 / 78125000000000 : ℚ)) + (U := (-(18673706669854913901521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_8 : Uω (aρ 8) (bρ 8) (29403234977 / 125000000000 : ℝ) ≤ @@ -1198,25 +1077,21 @@ lemma U_283_8 : have hlg : Real.log (2241140564584159 / 20000000000000000 : ℝ) ≤ (-(21887473556177965593987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2241140564584159 / 20000000000000000 : ℝ) = - (2241140564584159 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2241140564584159 / 1250000000000000 : ℚ)) - (U := (5838413655822034406013 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2241140564584159 / 1250000000000000 : ℝ) ≤ - (5838413655822034406013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (895471611009159 / 10000000000000000 : ℝ)) (q := - (2241140564584159 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2241140564584159 / 20000000000000000 : ℚ)) + (r' := (2241140564584159 / 1250000000000000 : ℚ)) + (U := (-(21887473556177965593987 / 10000000000000000000000 : ℚ))) + (U' := (5838413655822034406013 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (29403234977 / 125000000000 : ℚ)) + (s := (895471611009159 / 10000000000000000 : ℚ)) + (q := (2241140564584159 / 20000000000000000 : ℚ)) + (U := (-(21887473556177965593987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_283_9 : Uω (aρ 9) (bρ 9) (29403234977 / 125000000000 : ℝ) ≤ @@ -1349,25 +1224,21 @@ lemma U_284_1 : have hlg : Real.log (1838683020747251 / 8000000000000000 : ℝ) ≤ (-(2940783950288045734059 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1838683020747251 / 8000000000000000 : ℝ) = - (1838683020747251 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1838683020747251 / 1000000000000000 : ℚ)) - (U := (1218099131511954265941 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1838683020747251 / 1000000000000000 : ℝ) ≤ - (1218099131511954265941 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28728542940043 / 125000000000000 : ℝ)) (q := - (1838683020747251 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1838683020747251 / 8000000000000000 : ℚ)) + (r' := (1838683020747251 / 1000000000000000 : ℚ)) + (U := (-(2940783950288045734059 / 2000000000000000000000 : ℚ))) + (U' := (1218099131511954265941 / 2000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (28728542940043 / 125000000000000 : ℚ)) + (q := (1838683020747251 / 8000000000000000 : ℚ)) + (U := (-(2940783950288045734059 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_2 : Uω (aρ 2) (bρ 2) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1375,25 +1246,21 @@ lemma U_284_2 : have hlg : Real.log (9096754384969207 / 40000000000000000 : ℝ) ≤ (-(7404808822111749557067 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9096754384969207 / 40000000000000000 : ℝ) = - (9096754384969207 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9096754384969207 / 5000000000000000 : ℚ)) - (U := (2992398882388250442933 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9096754384969207 / 5000000000000000 : ℝ) ≤ - (2992398882388250442933 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (568430522082479 / 2500000000000000 : ℝ)) (q := - (9096754384969207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9096754384969207 / 40000000000000000 : ℚ)) + (r' := (9096754384969207 / 5000000000000000 : ℚ)) + (U := (-(7404808822111749557067 / 5000000000000000000000 : ℚ))) + (U' := (2992398882388250442933 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (568430522082479 / 2500000000000000 : ℚ)) + (q := (9096754384969207 / 40000000000000000 : ℚ)) + (U := (-(7404808822111749557067 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_3 : Uω (aρ 3) (bρ 3) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1401,25 +1268,21 @@ lemma U_284_3 : have hlg : Real.log (8902387815003059 / 40000000000000000 : ℝ) ≤ (-(15025599187597887615541 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8902387815003059 / 40000000000000000 : ℝ) = - (8902387815003059 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8902387815003059 / 5000000000000000 : ℚ)) - (U := (5768816221402112384459 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8902387815003059 / 5000000000000000 : ℝ) ≤ - (5768816221402112384459 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1111967454848421 / 5000000000000000 : ℝ)) (q := - (8902387815003059 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8902387815003059 / 40000000000000000 : ℚ)) + (r' := (8902387815003059 / 5000000000000000 : ℚ)) + (U := (-(15025599187597887615541 / 10000000000000000000000 : ℚ))) + (U' := (5768816221402112384459 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (1111967454848421 / 5000000000000000 : ℚ)) + (q := (8902387815003059 / 40000000000000000 : ℚ)) + (U := (-(15025599187597887615541 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_4 : Uω (aρ 4) (bρ 4) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1427,25 +1290,21 @@ lemma U_284_4 : have hlg : Real.log (8576231944333977 / 40000000000000000 : ℝ) ≤ (-(15398848036234854074413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8576231944333977 / 40000000000000000 : ℝ) = - (8576231944333977 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8576231944333977 / 5000000000000000 : ℚ)) - (U := (5395567372765145925587 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8576231944333977 / 5000000000000000 : ℝ) ≤ - (5395567372765145925587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2139151155427301 / 10000000000000000 : ℝ)) (q := - (8576231944333977 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8576231944333977 / 40000000000000000 : ℚ)) + (r' := (8576231944333977 / 5000000000000000 : ℚ)) + (U := (-(15398848036234854074413 / 10000000000000000000000 : ℚ))) + (U' := (5395567372765145925587 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (2139151155427301 / 10000000000000000 : ℚ)) + (q := (8576231944333977 / 40000000000000000 : ℚ)) + (U := (-(15398848036234854074413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_5 : Uω (aρ 5) (bρ 5) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1453,25 +1312,21 @@ lemma U_284_5 : have hlg : Real.log (8070306671596673 / 40000000000000000 : ℝ) ≤ (-(3201375940674537947543 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8070306671596673 / 40000000000000000 : ℝ) = - (8070306671596673 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8070306671596673 / 5000000000000000 : ℚ)) - (U := (957507141125462052457 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8070306671596673 / 5000000000000000 : ℝ) ≤ - (957507141125462052457 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2004378438393649 / 10000000000000000 : ℝ)) (q := - (8070306671596673 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8070306671596673 / 40000000000000000 : ℚ)) + (r' := (8070306671596673 / 5000000000000000 : ℚ)) + (U := (-(3201375940674537947543 / 2000000000000000000000 : ℚ))) + (U' := (957507141125462052457 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (2004378438393649 / 10000000000000000 : ℚ)) + (q := (8070306671596673 / 40000000000000000 : ℚ)) + (U := (-(3201375940674537947543 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_6 : Uω (aρ 6) (bρ 6) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1479,25 +1334,21 @@ lemma U_284_6 : have hlg : Real.log (7320015693491687 / 40000000000000000 : ℝ) ≤ (-(16982669814435490042889 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7320015693491687 / 40000000000000000 : ℝ) = - (7320015693491687 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7320015693491687 / 5000000000000000 : ℚ)) - (U := (3811745594564509957111 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7320015693491687 / 5000000000000000 : ℝ) ≤ - (3811745594564509957111 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (449118331120289 / 2500000000000000 : ℝ)) (q := - (7320015693491687 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7320015693491687 / 40000000000000000 : ℚ)) + (r' := (7320015693491687 / 5000000000000000 : ℚ)) + (U := (-(16982669814435490042889 / 10000000000000000000000 : ℚ))) + (U' := (3811745594564509957111 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (449118331120289 / 2500000000000000 : ℚ)) + (q := (7320015693491687 / 40000000000000000 : ℚ)) + (U := (-(16982669814435490042889 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_7 : Uω (aρ 7) (bρ 7) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1505,25 +1356,21 @@ lemma U_284_7 : have hlg : Real.log (6226257982895227 / 40000000000000000 : ℝ) ≤ (-(18601039457942155663267 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6226257982895227 / 40000000000000000 : ℝ) = - (6226257982895227 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6226257982895227 / 5000000000000000 : ℚ)) - (U := (2193375951057844336733 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6226257982895227 / 5000000000000000 : ℝ) ≤ - (2193375951057844336733 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (736627924971463 / 5000000000000000 : ℝ)) (q := - (6226257982895227 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6226257982895227 / 40000000000000000 : ℚ)) + (r' := (6226257982895227 / 5000000000000000 : ℚ)) + (U := (-(18601039457942155663267 / 10000000000000000000000 : ℚ))) + (U' := (2193375951057844336733 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (736627924971463 / 5000000000000000 : ℚ)) + (q := (6226257982895227 / 40000000000000000 : ℚ)) + (U := (-(18601039457942155663267 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_8 : Uω (aρ 8) (bρ 8) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1531,24 +1378,21 @@ lemma U_284_8 : have hlg : Real.log (36283963877359 / 320000000000000 : ℝ) ≤ (-(5442362793886692937687 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (36283963877359 / 320000000000000 : ℝ) = (36283963877359 / 20000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36283963877359 / 20000000000000 : ℚ)) - (U := (1489109009113307062313 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36283963877359 / 20000000000000 : ℝ) ≤ - (1489109009113307062313 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3645665008681 / 40000000000000 : ℝ)) (q := - (36283963877359 / 320000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36283963877359 / 320000000000000 : ℚ)) + (r' := (36283963877359 / 20000000000000 : ℚ)) + (U := (-(5442362793886692937687 / 2500000000000000000000 : ℚ))) + (U' := (1489109009113307062313 / 2500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7561348271199 / 32000000000000 : ℚ)) + (s := (3645665008681 / 40000000000000 : ℚ)) + (q := (36283963877359 / 320000000000000 : ℚ)) + (U := (-(5442362793886692937687 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_284_9 : Uω (aρ 9) (bρ 9) (7561348271199 / 32000000000000 : ℝ) ≤ @@ -1680,25 +1524,21 @@ lemma U_285_1 : have hlg : Real.log (4618033274703681 / 20000000000000000 : ℝ) ≤ (-(3664408391079400055809 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4618033274703681 / 20000000000000000 : ℝ) = - (4618033274703681 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4618033274703681 / 2500000000000000 : ℚ)) - (U := (1534195461170599944191 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4618033274703681 / 2500000000000000 : ℝ) ≤ - (1534195461170599944191 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1154473310724653 / 5000000000000000 : ℝ)) (q := - (4618033274703681 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4618033274703681 / 20000000000000000 : ℚ)) + (r' := (4618033274703681 / 2500000000000000 : ℚ)) + (U := (-(3664408391079400055809 / 2500000000000000000000 : ℚ))) + (U' := (1534195461170599944191 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (1154473310724653 / 5000000000000000 : ℚ)) + (q := (4618033274703681 / 20000000000000000 : ℚ)) + (U := (-(3664408391079400055809 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_2 : Uω (aρ 2) (bρ 2) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1706,25 +1546,21 @@ lemma U_285_2 : have hlg : Real.log (571213327572647 / 2500000000000000 : ℝ) ≤ (-(461338520855661178501 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (571213327572647 / 2500000000000000 : ℝ) = - (571213327572647 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (571213327572647 / 312500000000000 : ℚ)) - (U := (188486960675588821499 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (571213327572647 / 312500000000000 : ℝ) ≤ - (188486960675588821499 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2284388979836801 / 10000000000000000 : ℝ)) (q := - (571213327572647 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (571213327572647 / 2500000000000000 : ℚ)) + (r' := (571213327572647 / 312500000000000 : ℚ)) + (U := (-(461338520855661178501 / 312500000000000000000 : ℚ))) + (U' := (188486960675588821499 / 312500000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (2284388979836801 / 10000000000000000 : ℚ)) + (q := (571213327572647 / 2500000000000000 : ℚ)) + (U := (-(461338520855661178501 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_3 : Uω (aρ 3) (bρ 3) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1732,25 +1568,21 @@ lemma U_285_3 : have hlg : Real.log (894506968348281 / 4000000000000000 : ℝ) ≤ (-(14977769461876843290263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (894506968348281 / 4000000000000000 : ℝ) = - (894506968348281 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (894506968348281 / 500000000000000 : ℚ)) - (U := (5816645947123156709737 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (894506968348281 / 500000000000000 : ℝ) ≤ - (5816645947123156709737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (223461330734703 / 1000000000000000 : ℝ)) (q := - (894506968348281 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (894506968348281 / 4000000000000000 : ℚ)) + (r' := (894506968348281 / 500000000000000 : ℚ)) + (U := (-(14977769461876843290263 / 10000000000000000000000 : ℚ))) + (U' := (5816645947123156709737 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (223461330734703 / 1000000000000000 : ℚ)) + (q := (894506968348281 / 4000000000000000 : ℚ)) + (U := (-(14977769461876843290263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_4 : Uω (aρ 4) (bρ 4) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1758,25 +1590,21 @@ lemma U_285_4 : have hlg : Real.log (2154744859046769 / 10000000000000000 : ℝ) ≤ (-(7674563852708070316761 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2154744859046769 / 10000000000000000 : ℝ) = - (2154744859046769 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2154744859046769 / 1250000000000000 : ℚ)) - (U := (2722643851791929683239 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2154744859046769 / 1250000000000000 : ℝ) ≤ - (2722643851791929683239 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2149862364764163 / 10000000000000000 : ℝ)) (q := - (2154744859046769 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2154744859046769 / 10000000000000000 : ℚ)) + (r' := (2154744859046769 / 1250000000000000 : ℚ)) + (U := (-(7674563852708070316761 / 5000000000000000000000 : ℚ))) + (U' := (2722643851791929683239 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (2149862364764163 / 10000000000000000 : ℚ)) + (q := (2154744859046769 / 10000000000000000 : ℚ)) + (U := (-(7674563852708070316761 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_5 : Uω (aρ 5) (bρ 5) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1784,25 +1612,21 @@ lemma U_285_5 : have hlg : Real.log (1014154520077303 / 5000000000000000 : ℝ) ≤ (-(3190765262861868759431 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1014154520077303 / 5000000000000000 : ℝ) = - (1014154520077303 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1014154520077303 / 625000000000000 : ℚ)) - (U := (968117818938131240569 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1014154520077303 / 625000000000000 : ℝ) ≤ - (968117818938131240569 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2015180646314837 / 10000000000000000 : ℝ)) (q := - (1014154520077303 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1014154520077303 / 5000000000000000 : ℚ)) + (r' := (1014154520077303 / 625000000000000 : ℚ)) + (U := (-(3190765262861868759431 / 2000000000000000000000 : ℚ))) + (U' := (968117818938131240569 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (2015180646314837 / 10000000000000000 : ℚ)) + (q := (1014154520077303 / 5000000000000000 : ℚ)) + (U := (-(3190765262861868759431 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_6 : Uω (aρ 6) (bρ 6) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1810,25 +1634,21 @@ lemma U_285_6 : have hlg : Real.log (3681728553827143 / 20000000000000000 : ℝ) ≤ (-(8461749575806555752881 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3681728553827143 / 20000000000000000 : ℝ) = - (3681728553827143 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3681728553827143 / 2500000000000000 : ℚ)) - (U := (1935458128693444247119 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3681728553827143 / 2500000000000000 : ℝ) ≤ - (1935458128693444247119 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56485359217899 / 312500000000000 : ℝ)) (q := - (3681728553827143 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3681728553827143 / 20000000000000000 : ℚ)) + (r' := (3681728553827143 / 2500000000000000 : ℚ)) + (U := (-(8461749575806555752881 / 5000000000000000000000 : ℚ))) + (U' := (1935458128693444247119 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (56485359217899 / 312500000000000 : ℚ)) + (q := (3681728553827143 / 20000000000000000 : ℚ)) + (U := (-(8461749575806555752881 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_7 : Uω (aρ 7) (bρ 7) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1836,25 +1656,21 @@ lemma U_285_7 : have hlg : Real.log (627130158553129 / 4000000000000000 : ℝ) ≤ (-(18528955308340390514393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (627130158553129 / 4000000000000000 : ℝ) = - (627130158553129 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (627130158553129 / 500000000000000 : ℚ)) - (U := (2265460100659609485607 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (627130158553129 / 500000000000000 : ℝ) ≤ - (2265460100659609485607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (148511511467127 / 1000000000000000 : ℝ)) (q := - (627130158553129 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (627130158553129 / 4000000000000000 : ℚ)) + (r' := (627130158553129 / 500000000000000 : ℚ)) + (U := (-(18528955308340390514393 / 10000000000000000000000 : ℚ))) + (U' := (2265460100659609485607 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (148511511467127 / 1000000000000000 : ℚ)) + (q := (627130158553129 / 4000000000000000 : ℚ)) + (U := (-(18528955308340390514393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_8 : Uω (aρ 8) (bρ 8) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -1862,25 +1678,21 @@ lemma U_285_8 : have hlg : Real.log (2294203357321019 / 20000000000000000 : ℝ) ≤ (-(21653466102551587295531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2294203357321019 / 20000000000000000 : ℝ) = - (2294203357321019 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2294203357321019 / 1250000000000000 : ℚ)) - (U := (6072421109448412704469 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2294203357321019 / 1250000000000000 : ℝ) ≤ - (6072421109448412704469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231802332641661 / 2500000000000000 : ℝ)) (q := - (2294203357321019 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2294203357321019 / 20000000000000000 : ℚ)) + (r' := (2294203357321019 / 1250000000000000 : ℚ)) + (U := (-(21653466102551587295531 / 10000000000000000000000 : ℚ))) + (U' := (6072421109448412704469 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3797734194143 / 16000000000000 : ℚ)) + (s := (231802332641661 / 2500000000000000 : ℚ)) + (q := (2294203357321019 / 20000000000000000 : ℚ)) + (U := (-(21653466102551587295531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_285_9 : Uω (aρ 9) (bρ 9) (3797734194143 / 16000000000000 : ℝ) ≤ @@ -2012,25 +1824,21 @@ lemma U_286_1 : have hlg : Real.log (4660684702538611 / 20000000000000000 : ℝ) ≤ (-(728284951777396434499 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4660684702538611 / 20000000000000000 : ℝ) = - (4660684702538611 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4660684702538611 / 2500000000000000 : ℚ)) - (U := (311435818672603565501 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4660684702538611 / 2500000000000000 : ℝ) ≤ - (311435818672603565501 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2330272976104861 / 10000000000000000 : ℝ)) (q := - (4660684702538611 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4660684702538611 / 20000000000000000 : ℚ)) + (r' := (4660684702538611 / 2500000000000000 : ℚ)) + (U := (-(728284951777396434499 / 500000000000000000000 : ℚ))) + (U' := (311435818672603565501 / 500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (2330272976104861 / 10000000000000000 : ℚ)) + (q := (4660684702538611 / 20000000000000000 : ℚ)) + (U := (-(728284951777396434499 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_2 : Uω (aρ 2) (bρ 2) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2038,25 +1846,21 @@ lemma U_286_2 : have hlg : Real.log (4612365355916907 / 20000000000000000 : ℝ) ≤ (-(14669914549627046428131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4612365355916907 / 20000000000000000 : ℝ) = - (4612365355916907 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4612365355916907 / 2500000000000000 : ℚ)) - (U := (6124500859372953571869 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4612365355916907 / 2500000000000000 : ℝ) ≤ - (6124500859372953571869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2305722641993157 / 10000000000000000 : ℝ)) (q := - (4612365355916907 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4612365355916907 / 20000000000000000 : ℚ)) + (r' := (4612365355916907 / 2500000000000000 : ℚ)) + (U := (-(14669914549627046428131 / 10000000000000000000000 : ℚ))) + (U' := (6124500859372953571869 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (2305722641993157 / 10000000000000000 : ℚ)) + (q := (4612365355916907 / 20000000000000000 : ℚ)) + (U := (-(14669914549627046428131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_3 : Uω (aρ 3) (bρ 3) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2064,25 +1868,21 @@ lemma U_286_3 : have hlg : Real.log (2257608130047833 / 10000000000000000 : ℝ) ≤ (-(1488279188913710560159 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2257608130047833 / 10000000000000000 : ℝ) = - (2257608130047833 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2257608130047833 / 1250000000000000 : ℚ)) - (U := (591162351986289439841 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2257608130047833 / 1250000000000000 : ℝ) ≤ - (591162351986289439841 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (563992413130479 / 2500000000000000 : ℝ)) (q := - (2257608130047833 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2257608130047833 / 10000000000000000 : ℚ)) + (r' := (2257608130047833 / 1250000000000000 : ℚ)) + (U := (-(1488279188913710560159 / 1000000000000000000000 : ℚ))) + (U' := (591162351986289439841 / 1000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (563992413130479 / 2500000000000000 : ℚ)) + (q := (2257608130047833 / 10000000000000000 : ℚ)) + (U := (-(1488279188913710560159 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_4 : Uω (aρ 4) (bρ 4) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2090,25 +1890,21 @@ lemma U_286_4 : have hlg : Real.log (4352235772568247 / 20000000000000000 : ℝ) ≤ (-(7625212945029603857267 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4352235772568247 / 20000000000000000 : ℝ) = - (4352235772568247 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4352235772568247 / 2500000000000000 : ℚ)) - (U := (2771994759470396142733 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4352235772568247 / 2500000000000000 : ℝ) ≤ - (2771994759470396142733 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2171283346059497 / 10000000000000000 : ℝ)) (q := - (4352235772568247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4352235772568247 / 20000000000000000 : ℚ)) + (r' := (4352235772568247 / 2500000000000000 : ℚ)) + (U := (-(7625212945029603857267 / 5000000000000000000000 : ℚ))) + (U' := (2771994759470396142733 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (2171283346059497 / 10000000000000000 : ℚ)) + (q := (4352235772568247 / 20000000000000000 : ℚ)) + (U := (-(7625212945029603857267 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_5 : Uω (aρ 5) (bρ 5) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2116,24 +1912,21 @@ lemma U_286_5 : have hlg : Real.log (51244289419121 / 250000000000000 : ℝ) ≤ (-(1981070914050747589499 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (51244289419121 / 250000000000000 : ℝ) = (51244289419121 / 31250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51244289419121 / 31250000000000 : ℚ)) - (U := (618231012074252410501 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (51244289419121 / 31250000000000 : ℝ) ≤ - (618231012074252410501 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203678064635593 / 1000000000000000 : ℝ)) (q := - (51244289419121 / 250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51244289419121 / 250000000000000 : ℚ)) + (r' := (51244289419121 / 31250000000000 : ℚ)) + (U := (-(1981070914050747589499 / 1250000000000000000000 : ℚ))) + (U' := (618231012074252410501 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (203678064635593 / 1000000000000000 : ℚ)) + (q := (51244289419121 / 250000000000000 : ℚ)) + (U := (-(1981070914050747589499 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_6 : Uω (aρ 6) (bρ 6) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2141,25 +1934,21 @@ lemma U_286_6 : have hlg : Real.log (3725155877604123 / 20000000000000000 : ℝ) ≤ (-(16806235754814884325851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3725155877604123 / 20000000000000000 : ℝ) = - (3725155877604123 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3725155877604123 / 2500000000000000 : ℚ)) - (U := (3988179654185115674149 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3725155877604123 / 2500000000000000 : ℝ) ≤ - (3988179654185115674149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1829633745570373 / 10000000000000000 : ℝ)) (q := - (3725155877604123 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3725155877604123 / 20000000000000000 : ℚ)) + (r' := (3725155877604123 / 2500000000000000 : ℚ)) + (U := (-(16806235754814884325851 / 10000000000000000000000 : ℚ))) + (U' := (3988179654185115674149 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (1829633745570373 / 10000000000000000 : ℚ)) + (q := (3725155877604123 / 20000000000000000 : ℚ)) + (U := (-(16806235754814884325851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_7 : Uω (aρ 7) (bρ 7) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2167,25 +1956,21 @@ lemma U_286_7 : have hlg : Real.log (1590320402548059 / 10000000000000000 : ℝ) ≤ (-(18386495852461762688133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1590320402548059 / 10000000000000000 : ℝ) = - (1590320402548059 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1590320402548059 / 1250000000000000 : ℚ)) - (U := (2407919556538237311867 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1590320402548059 / 1250000000000000 : ℝ) ≤ - (2407919556538237311867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (47149376681949 / 312500000000000 : ℝ)) (q := - (1590320402548059 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1590320402548059 / 10000000000000000 : ℚ)) + (r' := (1590320402548059 / 1250000000000000 : ℚ)) + (U := (-(18386495852461762688133 / 10000000000000000000000 : ℚ))) + (U' := (2407919556538237311867 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (47149376681949 / 312500000000000 : ℚ)) + (q := (1590320402548059 / 10000000000000000 : ℚ)) + (U := (-(18386495852461762688133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_8 : Uω (aρ 8) (bρ 8) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2193,25 +1978,21 @@ lemma U_286_8 : have hlg : Real.log (2346689798958173 / 20000000000000000 : ℝ) ≤ (-(2678408166937960326061 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2346689798958173 / 20000000000000000 : ℝ) = - (2346689798958173 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2346689798958173 / 1250000000000000 : ℚ)) - (U := (787327734562039673939 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2346689798958173 / 1250000000000000 : ℝ) ≤ - (787327734562039673939 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (958370699024423 / 10000000000000000 : ℝ)) (q := - (2346689798958173 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2346689798958173 / 20000000000000000 : ℚ)) + (r' := (2346689798958173 / 1250000000000000 : ℚ)) + (U := (-(2678408166937960326061 / 1250000000000000000000 : ℚ))) + (U' := (787327734562039673939 / 1250000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (383185431123 / 1600000000000 : ℚ)) + (s := (958370699024423 / 10000000000000000 : ℚ)) + (q := (2346689798958173 / 20000000000000000 : ℚ)) + (U := (-(2678408166937960326061 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_286_9 : Uω (aρ 9) (bρ 9) (383185431123 / 1600000000000 : ℝ) ≤ @@ -2343,25 +2124,21 @@ lemma U_287_1 : have hlg : Real.log (4703336107131151 / 20000000000000000 : ℝ) ≤ (-(7237301029131155242153 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4703336107131151 / 20000000000000000 : ℝ) = - (4703336107131151 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4703336107131151 / 2500000000000000 : ℚ)) - (U := (3159906675368844757847 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4703336107131151 / 2500000000000000 : ℝ) ≤ - (3159906675368844757847 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1175799653759013 / 5000000000000000 : ℝ)) (q := - (4703336107131151 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4703336107131151 / 20000000000000000 : ℚ)) + (r' := (4703336107131151 / 2500000000000000 : ℚ)) + (U := (-(7237301029131155242153 / 5000000000000000000000 : ℚ))) + (U' := (3159906675368844757847 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (1175799653759013 / 5000000000000000 : ℚ)) + (q := (4703336107131151 / 20000000000000000 : ℚ)) + (U := (-(7237301029131155242153 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_2 : Uω (aρ 2) (bρ 2) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2369,25 +2146,21 @@ lemma U_287_2 : have hlg : Real.log (931004786760537 / 4000000000000000 : ℝ) ≤ (-(3644463051331309478819 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (931004786760537 / 4000000000000000 : ℝ) = - (931004786760537 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (931004786760537 / 500000000000000 : ℚ)) - (U := (1554140800918690521181 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (931004786760537 / 500000000000000 : ℝ) ≤ - (1554140800918690521181 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58176403667489 / 250000000000000 : ℝ)) (q := - (931004786760537 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (931004786760537 / 4000000000000000 : ℚ)) + (r' := (931004786760537 / 500000000000000 : ℚ)) + (U := (-(3644463051331309478819 / 2500000000000000000000 : ℚ))) + (U' := (1554140800918690521181 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (58176403667489 / 250000000000000 : ℚ)) + (q := (931004786760537 / 4000000000000000 : ℚ)) + (U := (-(3644463051331309478819 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_3 : Uω (aρ 3) (bρ 3) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2395,25 +2168,21 @@ lemma U_287_3 : have hlg : Real.log (4557897092353209 / 20000000000000000 : ℝ) ≤ (-(2957741839148582854709 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4557897092353209 / 20000000000000000 : ℝ) = - (4557897092353209 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4557897092353209 / 2500000000000000 : ℚ)) - (U := (1201141242651417145291 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4557897092353209 / 2500000000000000 : ℝ) ≤ - (1201141242651417145291 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (569331352900021 / 2500000000000000 : ℝ)) (q := - (4557897092353209 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4557897092353209 / 20000000000000000 : ℚ)) + (r' := (4557897092353209 / 2500000000000000 : ℚ)) + (U := (-(2957741839148582854709 / 2000000000000000000000 : ℚ))) + (U' := (1201141242651417145291 / 2000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (569331352900021 / 2500000000000000 : ℚ)) + (q := (4557897092353209 / 20000000000000000 : ℚ)) + (U := (-(2957741839148582854709 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_4 : Uω (aρ 4) (bρ 4) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2421,25 +2190,21 @@ lemma U_287_4 : have hlg : Real.log (1098744989336193 / 5000000000000000 : ℝ) ≤ (-(378817325494630744883 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1098744989336193 / 5000000000000000 : ℝ) = - (1098744989336193 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1098744989336193 / 625000000000000 : ℚ)) - (U := (141043059730369255117 / 250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1098744989336193 / 625000000000000 : ℝ) ≤ - (141043059730369255117 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2192702457656647 / 10000000000000000 : ℝ)) (q := - (1098744989336193 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1098744989336193 / 5000000000000000 : ℚ)) + (r' := (1098744989336193 / 625000000000000 : ℚ)) + (U := (-(378817325494630744883 / 250000000000000000000 : ℚ))) + (U' := (141043059730369255117 / 250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (2192702457656647 / 10000000000000000 : ℚ)) + (q := (1098744989336193 / 5000000000000000 : ℚ)) + (U := (-(378817325494630744883 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_5 : Uω (aρ 5) (bρ 5) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2447,25 +2212,21 @@ lemma U_287_5 : have hlg : Real.log (828492498694077 / 4000000000000000 : ℝ) ≤ (-(3936104641443346695053 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (828492498694077 / 4000000000000000 : ℝ) = - (828492498694077 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (828492498694077 / 500000000000000 : ℚ)) - (U := (1262499210806653304947 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (828492498694077 / 500000000000000 : ℝ) ≤ - (1262499210806653304947 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102918745655863 / 500000000000000 : ℝ)) (q := - (828492498694077 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (828492498694077 / 4000000000000000 : ℚ)) + (r' := (828492498694077 / 500000000000000 : ℚ)) + (U := (-(3936104641443346695053 / 2500000000000000000000 : ℚ))) + (U' := (1262499210806653304947 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (102918745655863 / 500000000000000 : ℚ)) + (q := (828492498694077 / 4000000000000000 : ℚ)) + (U := (-(3936104641443346695053 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_6 : Uω (aρ 6) (bρ 6) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2473,25 +2234,21 @@ lemma U_287_6 : have hlg : Real.log (3768564974754009 / 20000000000000000 : ℝ) ≤ (-(8345189935393049647993 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3768564974754009 / 20000000000000000 : ℝ) = - (3768564974754009 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3768564974754009 / 2500000000000000 : ℚ)) - (U := (2052017769106950352007 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3768564974754009 / 2500000000000000 : ℝ) ≤ - (2052017769106950352007 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (462929442385221 / 2500000000000000 : ℝ)) (q := - (3768564974754009 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3768564974754009 / 20000000000000000 : ℚ)) + (r' := (3768564974754009 / 2500000000000000 : ℚ)) + (U := (-(8345189935393049647993 / 5000000000000000000000 : ℚ))) + (U' := (2052017769106950352007 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (462929442385221 / 2500000000000000 : ℚ)) + (q := (3768564974754009 / 20000000000000000 : ℚ)) + (U := (-(8345189935393049647993 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_7 : Uω (aρ 7) (bρ 7) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2499,25 +2256,21 @@ lemma U_287_7 : have hlg : Real.log (129022484854003 / 800000000000000 : ℝ) ≤ (-(18246250365212857194421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (129022484854003 / 800000000000000 : ℝ) = - (129022484854003 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (129022484854003 / 100000000000000 : ℚ)) - (U := (2548165043787142805579 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (129022484854003 / 100000000000000 : ℝ) ≤ - (2548165043787142805579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (30647525937939 / 200000000000000 : ℝ)) (q := - (129022484854003 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (129022484854003 / 800000000000000 : ℚ)) + (r' := (129022484854003 / 100000000000000 : ℚ)) + (U := (-(18246250365212857194421 / 10000000000000000000000 : ℚ))) + (U' := (2548165043787142805579 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (30647525937939 / 200000000000000 : ℚ)) + (q := (129022484854003 / 800000000000000 : ℚ)) + (U := (-(18246250365212857194421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_8 : Uω (aρ 8) (bρ 8) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2525,25 +2278,21 @@ lemma U_287_8 : have hlg : Real.log (2398654369369711 / 20000000000000000 : ℝ) ≤ (-(1060412185914542412997 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2398654369369711 / 20000000000000000 : ℝ) = - (2398654369369711 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2398654369369711 / 1250000000000000 : ℚ)) - (U := (325882174685457587003 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2398654369369711 / 1250000000000000 : ℝ) ≤ - (325882174685457587003 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (494505098128293 / 5000000000000000 : ℝ)) (q := - (2398654369369711 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2398654369369711 / 20000000000000000 : ℚ)) + (r' := (2398654369369711 / 1250000000000000 : ℚ)) + (U := (-(1060412185914542412997 / 500000000000000000000 : ℚ))) + (U' := (325882174685457587003 / 500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3865974428317 / 16000000000000 : ℚ)) + (s := (494505098128293 / 5000000000000000 : ℚ)) + (q := (2398654369369711 / 20000000000000000 : ℚ)) + (U := (-(1060412185914542412997 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_287_9 : Uω (aρ 9) (bρ 9) (3865974428317 / 16000000000000 : ℝ) ≤ @@ -2674,25 +2423,21 @@ lemma U_288_1 : have hlg : Real.log (4745987489107963 / 20000000000000000 : ℝ) ≤ (-(7192163754279661846917 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4745987489107963 / 20000000000000000 : ℝ) = - (4745987489107963 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4745987489107963 / 2500000000000000 : ℚ)) - (U := (3205043950220338153083 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4745987489107963 / 2500000000000000 : ℝ) ≤ - (3205043950220338153083 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2372925616315463 / 10000000000000000 : ℝ)) (q := - (4745987489107963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4745987489107963 / 20000000000000000 : ℚ)) + (r' := (4745987489107963 / 2500000000000000 : ℚ)) + (U := (-(7192163754279661846917 / 5000000000000000000000 : ℚ))) + (U' := (3205043950220338153083 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (2372925616315463 / 10000000000000000 : ℚ)) + (q := (4745987489107963 / 20000000000000000 : ℚ)) + (U := (-(7192163754279661846917 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_2 : Uω (aρ 2) (bρ 2) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2700,25 +2445,21 @@ lemma U_288_2 : have hlg : Real.log (2348841179264741 / 10000000000000000 : ℝ) ≤ (-(7243315004429613191293 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2348841179264741 / 10000000000000000 : ℝ) = - (2348841179264741 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2348841179264741 / 1250000000000000 : ℚ)) - (U := (3153892700070386808707 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2348841179264741 / 1250000000000000 : ℝ) ≤ - (3153892700070386808707 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1174194749123491 / 5000000000000000 : ℝ)) (q := - (2348841179264741 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2348841179264741 / 10000000000000000 : ℚ)) + (r' := (2348841179264741 / 1250000000000000 : ℚ)) + (U := (-(7243315004429613191293 / 5000000000000000000000 : ℚ))) + (U' := (3153892700070386808707 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (1174194749123491 / 5000000000000000 : ℚ)) + (q := (2348841179264741 / 10000000000000000 : ℚ)) + (U := (-(7243315004429613191293 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_3 : Uω (aρ 3) (bρ 3) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2726,25 +2467,21 @@ lemma U_288_3 : have hlg : Real.log (2300288677424663 / 10000000000000000 : ℝ) ≤ (-(14695504652313017170091 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2300288677424663 / 10000000000000000 : ℝ) = - (2300288677424663 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2300288677424663 / 1250000000000000 : ℚ)) - (U := (6098910756686982829909 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2300288677424663 / 1250000000000000 : ℝ) ≤ - (6098910756686982829909 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1149340300458413 / 5000000000000000 : ℝ)) (q := - (2300288677424663 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2300288677424663 / 10000000000000000 : ℚ)) + (r' := (2300288677424663 / 1250000000000000 : ℚ)) + (U := (-(14695504652313017170091 / 10000000000000000000000 : ℚ))) + (U' := (6098910756686982829909 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (1149340300458413 / 5000000000000000 : ℚ)) + (q := (2300288677424663 / 10000000000000000 : ℚ)) + (U := (-(14695504652313017170091 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_4 : Uω (aρ 4) (bρ 4) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2752,25 +2489,21 @@ lemma U_288_4 : have hlg : Real.log (2218861163342389 / 10000000000000000 : ℝ) ≤ (-(15055910174395545613739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2218861163342389 / 10000000000000000 : ℝ) = - (2218861163342389 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2218861163342389 / 1250000000000000 : ℚ)) - (U := (5738505234604454386261 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2218861163342389 / 1250000000000000 : ℝ) ≤ - (5738505234604454386261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1107059876908639 / 5000000000000000 : ℝ)) (q := - (2218861163342389 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2218861163342389 / 10000000000000000 : ℚ)) + (r' := (2218861163342389 / 1250000000000000 : ℚ)) + (U := (-(15055910174395545613739 / 10000000000000000000000 : ℚ))) + (U' := (5738505234604454386261 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (1107059876908639 / 5000000000000000 : ℚ)) + (q := (2218861163342389 / 10000000000000000 : ℚ)) + (U := (-(15055910174395545613739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_5 : Uω (aρ 5) (bρ 5) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2778,25 +2511,21 @@ lemma U_288_5 : have hlg : Real.log (1046344069675191 / 5000000000000000 : ℝ) ≤ (-(7820678307979677280879 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1046344069675191 / 5000000000000000 : ℝ) = - (1046344069675191 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1046344069675191 / 625000000000000 : ℚ)) - (U := (2576529396520322719121 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1046344069675191 / 625000000000000 : ℝ) ≤ - (2576529396520322719121 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (259995453146033 / 1250000000000000 : ℝ)) (q := - (1046344069675191 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1046344069675191 / 5000000000000000 : ℚ)) + (r' := (1046344069675191 / 625000000000000 : ℚ)) + (U := (-(7820678307979677280879 / 5000000000000000000000 : ℚ))) + (U' := (2576529396520322719121 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (259995453146033 / 1250000000000000 : ℚ)) + (q := (1046344069675191 / 5000000000000000 : ℚ)) + (U := (-(7820678307979677280879 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_6 : Uω (aρ 6) (bρ 6) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2804,25 +2533,21 @@ lemma U_288_6 : have hlg : Real.log (762391297944483 / 4000000000000000 : ℝ) ≤ (-(8287948505380436413979 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (762391297944483 / 4000000000000000 : ℝ) = - (762391297944483 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (762391297944483 / 500000000000000 : ℚ)) - (U := (2109259199119563586021 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (762391297944483 / 500000000000000 : ℝ) ≤ - (2109259199119563586021 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (374756842265983 / 2000000000000000 : ℝ)) (q := - (762391297944483 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (762391297944483 / 4000000000000000 : ℚ)) + (r' := (762391297944483 / 500000000000000 : ℚ)) + (U := (-(8287948505380436413979 / 5000000000000000000000 : ℚ))) + (U' := (2109259199119563586021 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (374756842265983 / 2000000000000000 : ℚ)) + (q := (762391297944483 / 4000000000000000 : ℚ)) + (U := (-(8287948505380436413979 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_7 : Uω (aρ 7) (bρ 7) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2830,25 +2555,21 @@ lemma U_288_7 : have hlg : Real.log (408802233372463 / 2500000000000000 : ℝ) ≤ (-(2263518134952506017373 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (408802233372463 / 2500000000000000 : ℝ) = - (408802233372463 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (408802233372463 / 312500000000000 : ℚ)) - (U := (335783791172493982627 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (408802233372463 / 312500000000000 : ℝ) ≤ - (335783791172493982627 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (388976742336801 / 2500000000000000 : ℝ)) (q := - (408802233372463 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (408802233372463 / 2500000000000000 : ℚ)) + (r' := (408802233372463 / 312500000000000 : ℚ)) + (U := (-(2263518134952506017373 / 1250000000000000000000 : ℚ))) + (U' := (335783791172493982627 / 1250000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (388976742336801 / 2500000000000000 : ℚ)) + (q := (408802233372463 / 2500000000000000 : ℚ)) + (U := (-(2263518134952506017373 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_8 : Uω (aρ 8) (bρ 8) (975023636351 / 4000000000000 : ℝ) ≤ @@ -2856,25 +2577,21 @@ lemma U_288_8 : have hlg : Real.log (2450144136751753 / 20000000000000000 : ℝ) ≤ (-(5248963545902056685773 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2450144136751753 / 20000000000000000 : ℝ) = - (2450144136751753 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2450144136751753 / 1250000000000000 : ℚ)) - (U := (1682508257097943314227 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2450144136751753 / 1250000000000000 : ℝ) ≤ - (1682508257097943314227 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1019174890459253 / 10000000000000000 : ℝ)) (q := - (2450144136751753 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2450144136751753 / 20000000000000000 : ℚ)) + (r' := (2450144136751753 / 1250000000000000 : ℚ)) + (U := (-(5248963545902056685773 / 2500000000000000000000 : ℚ))) + (U' := (1682508257097943314227 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (975023636351 / 4000000000000 : ℚ)) + (s := (1019174890459253 / 10000000000000000 : ℚ)) + (q := (2450144136751753 / 20000000000000000 : ℚ)) + (U := (-(5248963545902056685773 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_288_9 : Uω (aρ 9) (bρ 9) (975023636351 / 4000000000000 : ℝ) ≤ @@ -3006,25 +2723,21 @@ lemma U_289_1 : have hlg : Real.log (598579856134173 / 2500000000000000 : ℝ) ≤ (-(2858972133708537061617 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (598579856134173 / 2500000000000000 : ℝ) = - (598579856134173 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (598579856134173 / 312500000000000 : ℚ)) - (U := (1299910948091462938383 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (598579856134173 / 312500000000000 : ℝ) ≤ - (1299910948091462938383 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2394251903101509 / 10000000000000000 : ℝ)) (q := - (598579856134173 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (598579856134173 / 2500000000000000 : ℚ)) + (r' := (598579856134173 / 312500000000000 : ℚ)) + (U := (-(2858972133708537061617 / 2000000000000000000000 : ℚ))) + (U' := (1299910948091462938383 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (2394251903101509 / 10000000000000000 : ℚ)) + (q := (598579856134173 / 2500000000000000 : ℚ)) + (U := (-(2858972133708537061617 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_2 : Uω (aρ 2) (bρ 2) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3032,25 +2745,21 @@ lemma U_289_2 : have hlg : Real.log (2370170317116863 / 10000000000000000 : ℝ) ≤ (-(3599058189717142384657 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2370170317116863 / 10000000000000000 : ℝ) = - (2370170317116863 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2370170317116863 / 1250000000000000 : ℚ)) - (U := (1599545662532857615343 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2370170317116863 / 1250000000000000 : ℝ) ≤ - (1599545662532857615343 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2369722700771851 / 10000000000000000 : ℝ)) (q := - (2370170317116863 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2370170317116863 / 10000000000000000 : ℚ)) + (r' := (2370170317116863 / 1250000000000000 : ℚ)) + (U := (-(3599058189717142384657 / 2500000000000000000000 : ℚ))) + (U' := (1599545662532857615343 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (2369722700771851 / 10000000000000000 : ℚ)) + (q := (2370170317116863 / 10000000000000000 : ℚ)) + (U := (-(3599058189717142384657 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_3 : Uω (aρ 3) (bρ 3) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3058,25 +2767,21 @@ lemma U_289_3 : have hlg : Real.log (4643257063317437 / 20000000000000000 : ℝ) ≤ (-(7301580997444027247323 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4643257063317437 / 20000000000000000 : ℝ) = - (4643257063317437 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4643257063317437 / 2500000000000000 : ℚ)) - (U := (3095626707055972752677 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4643257063317437 / 2500000000000000 : ℝ) ≤ - (3095626707055972752677 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1160017618102781 / 5000000000000000 : ℝ)) (q := - (4643257063317437 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4643257063317437 / 20000000000000000 : ℚ)) + (r' := (4643257063317437 / 2500000000000000 : ℚ)) + (U := (-(7301580997444027247323 / 5000000000000000000000 : ℚ))) + (U' := (3095626707055972752677 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (1160017618102781 / 5000000000000000 : ℚ)) + (q := (4643257063317437 / 20000000000000000 : ℚ)) + (U := (-(7301580997444027247323 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_4 : Uω (aρ 4) (bρ 4) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3084,25 +2789,21 @@ lemma U_289_4 : have hlg : Real.log (4480462932766027 / 20000000000000000 : ℝ) ≤ (-(1496005898479066858877 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4480462932766027 / 20000000000000000 : ℝ) = - (4480462932766027 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4480462932766027 / 2500000000000000 : ℚ)) - (U := (583435642420933141123 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4480462932766027 / 2500000000000000 : ℝ) ≤ - (583435642420933141123 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (139720955419947 / 625000000000000 : ℝ)) (q := - (4480462932766027 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4480462932766027 / 20000000000000000 : ℚ)) + (r' := (4480462932766027 / 2500000000000000 : ℚ)) + (U := (-(1496005898479066858877 / 1000000000000000000000 : ℚ))) + (U' := (583435642420933141123 / 1000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (139720955419947 / 625000000000000 : ℚ)) + (q := (4480462932766027 / 20000000000000000 : ℚ)) + (U := (-(1496005898479066858877 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_5 : Uω (aρ 5) (bρ 5) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3110,25 +2811,21 @@ lemma U_289_5 : have hlg : Real.log (4228284680407637 / 20000000000000000 : ℝ) ≤ (-(3884839687161393204871 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4228284680407637 / 20000000000000000 : ℝ) = - (4228284680407637 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4228284680407637 / 2500000000000000 : ℚ)) - (U := (1313764165088606795129 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4228284680407637 / 2500000000000000 : ℝ) ≤ - (1313764165088606795129 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1050773476847881 / 5000000000000000 : ℝ)) (q := - (4228284680407637 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4228284680407637 / 20000000000000000 : ℚ)) + (r' := (4228284680407637 / 2500000000000000 : ℚ)) + (U := (-(3884839687161393204871 / 2500000000000000000000 : ℚ))) + (U' := (1313764165088606795129 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (1050773476847881 / 5000000000000000 : ℚ)) + (q := (4228284680407637 / 20000000000000000 : ℚ)) + (U := (-(3884839687161393204871 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_6 : Uω (aρ 6) (bρ 6) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3136,25 +2833,21 @@ lemma U_289_6 : have hlg : Real.log (3855331036449663 / 20000000000000000 : ℝ) ≤ (-(16462753974742707140679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3855331036449663 / 20000000000000000 : ℝ) = - (3855331036449663 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3855331036449663 / 2500000000000000 : ℚ)) - (U := (4331661434257292859321 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3855331036449663 / 2500000000000000 : ℝ) ≤ - (4331661434257292859321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (473958421219447 / 2500000000000000 : ℝ)) (q := - (3855331036449663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3855331036449663 / 20000000000000000 : ℚ)) + (r' := (3855331036449663 / 2500000000000000 : ℚ)) + (U := (-(16462753974742707140679 / 10000000000000000000000 : ℚ))) + (U' := (4331661434257292859321 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (473958421219447 / 2500000000000000 : ℚ)) + (q := (3855331036449663 / 20000000000000000 : ℚ)) + (U := (-(16462753974742707140679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_7 : Uω (aρ 7) (bρ 7) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3162,25 +2855,21 @@ lemma U_289_7 : have hlg : Real.log (3315210972743653 / 20000000000000000 : ℝ) ≤ (-(17972110093080970712811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3315210972743653 / 20000000000000000 : ℝ) = - (3315210972743653 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3315210972743653 / 2500000000000000 : ℚ)) - (U := (2822305315919029287189 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3315210972743653 / 2500000000000000 : ℝ) ≤ - (2822305315919029287189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (789687500965889 / 5000000000000000 : ℝ)) (q := - (3315210972743653 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3315210972743653 / 20000000000000000 : ℚ)) + (r' := (3315210972743653 / 2500000000000000 : ℚ)) + (U := (-(17972110093080970712811 / 10000000000000000000000 : ℚ))) + (U' := (2822305315919029287189 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (789687500965889 / 5000000000000000 : ℚ)) + (q := (3315210972743653 / 20000000000000000 : ℚ)) + (U := (-(17972110093080970712811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_8 : Uω (aρ 8) (bρ 8) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3188,25 +2877,21 @@ lemma U_289_8 : have hlg : Real.log (2501200065417611 / 20000000000000000 : ℝ) ≤ (-(519740407477164840823 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2501200065417611 / 20000000000000000 : ℝ) = - (2501200065417611 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2501200065417611 / 2500000000000000 : ℚ)) - (U := (119977747835159177 / 250000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (2501200065417611 / 2500000000000000 : ℝ) ≤ - (119977747835159177 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (131113218243217 / 1250000000000000 : ℝ)) (q := - (2501200065417611 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2501200065417611 / 20000000000000000 : ℚ)) + (r' := (2501200065417611 / 2500000000000000 : ℚ)) + (U := (-(519740407477164840823 / 250000000000000000000 : ℚ))) + (U' := (119977747835159177 / 250000000000000000000 : ℚ)) + 3 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3934214662491 / 16000000000000 : ℚ)) + (s := (131113218243217 / 1250000000000000 : ℚ)) + (q := (2501200065417611 / 20000000000000000 : ℚ)) + (U := (-(519740407477164840823 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_289_9 : Uω (aρ 9) (bρ 9) (3934214662491 / 16000000000000 : ℝ) ≤ @@ -3338,25 +3023,21 @@ lemma U_290_1 : have hlg : Real.log (966258037522081 / 4000000000000000 : ℝ) ≤ (-(14206187211916833637463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (966258037522081 / 4000000000000000 : ℝ) = - (966258037522081 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (966258037522081 / 500000000000000 : ℚ)) - (U := (6588228197083166362537 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (966258037522081 / 500000000000000 : ℝ) ≤ - (6588228197083166362537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (483115633691831 / 2000000000000000 : ℝ)) (q := - (966258037522081 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (966258037522081 / 4000000000000000 : ℚ)) + (r' := (966258037522081 / 500000000000000 : ℚ)) + (U := (-(14206187211916833637463 / 10000000000000000000000 : ℚ))) + (U' := (6588228197083166362537 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (483115633691831 / 2000000000000000 : ℚ)) + (q := (966258037522081 / 4000000000000000 : ℚ)) + (U := (-(14206187211916833637463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_2 : Uω (aρ 2) (bρ 2) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3364,25 +3045,21 @@ lemma U_290_2 : have hlg : Real.log (4782998764904191 / 20000000000000000 : ℝ) ≤ (-(14306645663022064867043 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4782998764904191 / 20000000000000000 : ℝ) = - (4782998764904191 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4782998764904191 / 2500000000000000 : ℚ)) - (U := (6487769745977935132957 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4782998764904191 / 2500000000000000 : ℝ) ≤ - (6487769745977935132957 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2391055758262941 / 10000000000000000 : ℝ)) (q := - (4782998764904191 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4782998764904191 / 20000000000000000 : ℚ)) + (r' := (4782998764904191 / 2500000000000000 : ℚ)) + (U := (-(14306645663022064867043 / 10000000000000000000000 : ℚ))) + (U' := (6487769745977935132957 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (2391055758262941 / 10000000000000000 : ℚ)) + (q := (4782998764904191 / 20000000000000000 : ℚ)) + (U := (-(14306645663022064867043 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_3 : Uω (aρ 3) (bρ 3) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3390,24 +3067,21 @@ lemma U_290_3 : have hlg : Real.log (146435507278643 / 625000000000000 : ℝ) ≤ (-(1813958175975205347013 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (146435507278643 / 625000000000000 : ℝ) = (146435507278643 / 78125000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (146435507278643 / 78125000000000 : ℚ)) - (U := (785343750149794652987 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (146435507278643 / 78125000000000 : ℝ) ≤ - (785343750149794652987 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1170694666312663 / 5000000000000000 : ℝ)) (q := - (146435507278643 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (146435507278643 / 625000000000000 : ℚ)) + (r' := (146435507278643 / 78125000000000 : ℚ)) + (U := (-(1813958175975205347013 / 1250000000000000000000 : ℚ))) + (U' := (785343750149794652987 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (1170694666312663 / 5000000000000000 : ℚ)) + (q := (146435507278643 / 625000000000000 : ℚ)) + (U := (-(1813958175975205347013 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_4 : Uω (aρ 4) (bρ 4) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3415,25 +3089,21 @@ lemma U_290_4 : have hlg : Real.log (2261600912890833 / 10000000000000000 : ℝ) ≤ (-(92907010073051215021 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2261600912890833 / 10000000000000000 : ℝ) = - (2261600912890833 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2261600912890833 / 1250000000000000 : ℚ)) - (U := (37058086233198784979 / 62500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2261600912890833 / 1250000000000000 : ℝ) ≤ - (37058086233198784979 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (282118638319427 / 1250000000000000 : ℝ)) (q := - (2261600912890833 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2261600912890833 / 10000000000000000 : ℚ)) + (r' := (2261600912890833 / 1250000000000000 : ℚ)) + (U := (-(92907010073051215021 / 62500000000000000000 : ℚ))) + (U' := (37058086233198784979 / 62500000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (282118638319427 / 1250000000000000 : ℚ)) + (q := (2261600912890833 / 10000000000000000 : ℚ)) + (U := (-(92907010073051215021 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_5 : Uω (aρ 5) (bρ 5) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3441,25 +3111,21 @@ lemma U_290_5 : have hlg : Real.log (2135593931387483 / 10000000000000000 : ℝ) ≤ (-(15438402962172249138387 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2135593931387483 / 10000000000000000 : ℝ) = - (2135593931387483 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2135593931387483 / 1250000000000000 : ℚ)) - (U := (5356012446827750861613 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2135593931387483 / 1250000000000000 : ℝ) ≤ - (5356012446827750861613 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (530781265720929 / 2500000000000000 : ℝ)) (q := - (2135593931387483 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2135593931387483 / 10000000000000000 : ℚ)) + (r' := (2135593931387483 / 1250000000000000 : ℚ)) + (U := (-(15438402962172249138387 / 10000000000000000000000 : ℚ))) + (U' := (5356012446827750861613 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (530781265720929 / 2500000000000000 : ℚ)) + (q := (2135593931387483 / 10000000000000000 : ℚ)) + (U := (-(15438402962172249138387 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_6 : Uω (aρ 6) (bρ 6) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3467,24 +3133,21 @@ lemma U_290_6 : have hlg : Real.log (60917018752829 / 312500000000000 : ℝ) ≤ (-(4087729696628356463639 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (60917018752829 / 312500000000000 : ℝ) = (60917018752829 / 39062500000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (60917018752829 / 39062500000000 : ℚ)) - (U := (1110874155621643536361 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (60917018752829 / 39062500000000 : ℝ) ≤ - (1110874155621643536361 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (958933387714903 / 5000000000000000 : ℝ)) (q := - (60917018752829 / 312500000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (60917018752829 / 312500000000000 : ℚ)) + (r' := (60917018752829 / 39062500000000 : ℚ)) + (U := (-(4087729696628356463639 / 2500000000000000000000 : ℚ))) + (U' := (1110874155621643536361 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (958933387714903 / 5000000000000000 : ℚ)) + (q := (60917018752829 / 312500000000000 : ℚ)) + (U := (-(4087729696628356463639 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_7 : Uω (aρ 7) (bρ 7) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3492,25 +3155,21 @@ lemma U_290_7 : have hlg : Real.log (335994419017261 / 2000000000000000 : ℝ) ≤ (-(1783807909004666494059 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (335994419017261 / 2000000000000000 : ℝ) = - (335994419017261 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (335994419017261 / 250000000000000 : ℚ)) - (U := (295633631895333505941 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (335994419017261 / 250000000000000 : ℝ) ≤ - (295633631895333505941 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (20034789327267 / 125000000000000 : ℝ)) (q := - (335994419017261 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (335994419017261 / 2000000000000000 : ℚ)) + (r' := (335994419017261 / 250000000000000 : ℚ)) + (U := (-(1783807909004666494059 / 1000000000000000000000 : ℚ))) + (U' := (295633631895333505941 / 1000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (20034789327267 / 125000000000000 : ℚ)) + (q := (335994419017261 / 2000000000000000 : ℚ)) + (U := (-(1783807909004666494059 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_8 : Uω (aρ 8) (bρ 8) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3518,25 +3177,21 @@ lemma U_290_8 : have hlg : Real.log (2551858043370813 / 20000000000000000 : ℝ) ≤ (-(1286819084048231859999 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2551858043370813 / 20000000000000000 : ℝ) = - (2551858043370813 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2551858043370813 / 2500000000000000 : ℚ)) - (U := (12831879014268140001 / 625000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2551858043370813 / 2500000000000000 : ℝ) ≤ - (12831879014268140001 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1078238650719563 / 10000000000000000 : ℝ)) (q := - (2551858043370813 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2551858043370813 / 20000000000000000 : ℚ)) + (r' := (2551858043370813 / 2500000000000000 : ℚ)) + (U := (-(1286819084048231859999 / 625000000000000000000 : ℚ))) + (U' := (12831879014268140001 / 625000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1984167389789 / 8000000000000 : ℚ)) + (s := (1078238650719563 / 10000000000000000 : ℚ)) + (q := (2551858043370813 / 20000000000000000 : ℚ)) + (U := (-(1286819084048231859999 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_290_9 : Uω (aρ 9) (bρ 9) (1984167389789 / 8000000000000 : ℝ) ≤ @@ -3668,25 +3323,21 @@ lemma U_291_1 : have hlg : Real.log (4916592802630059 / 20000000000000000 : ℝ) ≤ (-(3507791254907928832507 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4916592802630059 / 20000000000000000 : ℝ) = - (4916592802630059 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4916592802630059 / 2500000000000000 : ℚ)) - (U := (1690812597342071167493 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4916592802630059 / 2500000000000000 : ℝ) ≤ - (1690812597342071167493 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2458230637120059 / 10000000000000000 : ℝ)) (q := - (4916592802630059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4916592802630059 / 20000000000000000 : ℚ)) + (r' := (4916592802630059 / 2500000000000000 : ℚ)) + (U := (-(3507791254907928832507 / 2500000000000000000000 : ℚ))) + (U' := (1690812597342071167493 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (2458230637120059 / 10000000000000000 : ℚ)) + (q := (4916592802630059 / 20000000000000000 : ℚ)) + (U := (-(3507791254907928832507 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_2 : Uω (aρ 2) (bρ 2) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3694,25 +3345,21 @@ lemma U_291_2 : have hlg : Real.log (4868314606399477 / 20000000000000000 : ℝ) ≤ (-(7064922361463546649243 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4868314606399477 / 20000000000000000 : ℝ) = - (4868314606399477 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4868314606399477 / 2500000000000000 : ℚ)) - (U := (3332285343036453350757 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4868314606399477 / 2500000000000000 : ℝ) ≤ - (3332285343036453350757 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2433721453399477 / 10000000000000000 : ℝ)) (q := - (4868314606399477 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4868314606399477 / 20000000000000000 : ℚ)) + (r' := (4868314606399477 / 2500000000000000 : ℚ)) + (U := (-(7064922361463546649243 / 5000000000000000000000 : ℚ))) + (U' := (3332285343036453350757 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (2433721453399477 / 10000000000000000 : ℚ)) + (q := (4868314606399477 / 20000000000000000 : ℚ)) + (U := (-(7064922361463546649243 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_3 : Uω (aρ 3) (bρ 3) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3720,25 +3367,21 @@ lemma U_291_3 : have hlg : Real.log (2385646506713341 / 10000000000000000 : ℝ) ≤ (-(14331149326100729740711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2385646506713341 / 10000000000000000 : ℝ) = - (2385646506713341 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2385646506713341 / 1250000000000000 : ℚ)) - (U := (6463266082899270259289 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2385646506713341 / 1250000000000000 : ℝ) ≤ - (6463266082899270259289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1192047983388341 / 5000000000000000 : ℝ)) (q := - (2385646506713341 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2385646506713341 / 10000000000000000 : ℚ)) + (r' := (2385646506713341 / 1250000000000000 : ℚ)) + (U := (-(14331149326100729740711 / 10000000000000000000000 : ℚ))) + (U' := (6463266082899270259289 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (1192047983388341 / 5000000000000000 : ℚ)) + (q := (2385646506713341 / 10000000000000000 : ℚ)) + (U := (-(14331149326100729740711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_4 : Uω (aρ 4) (bρ 4) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3746,25 +3389,21 @@ lemma U_291_4 : have hlg : Real.log (2304337332011151 / 10000000000000000 : ℝ) ≤ (-(14677919486345039845707 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2304337332011151 / 10000000000000000 : ℝ) = - (2304337332011151 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2304337332011151 / 1250000000000000 : ℚ)) - (U := (6116495922654960154293 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2304337332011151 / 1250000000000000 : ℝ) ≤ - (6116495922654960154293 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1149885899218651 / 5000000000000000 : ℝ)) (q := - (2304337332011151 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2304337332011151 / 10000000000000000 : ℚ)) + (r' := (2304337332011151 / 1250000000000000 : ℚ)) + (U := (-(14677919486345039845707 / 10000000000000000000000 : ℚ))) + (U' := (6116495922654960154293 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (1149885899218651 / 5000000000000000 : ℚ)) + (q := (2304337332011151 / 10000000000000000 : ℚ)) + (U := (-(14677919486345039845707 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_5 : Uω (aρ 5) (bρ 5) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3772,25 +3411,21 @@ lemma U_291_5 : have hlg : Real.log (2178489596664727 / 10000000000000000 : ℝ) ≤ (-(3047906602216523433211 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2178489596664727 / 10000000000000000 : ℝ) = - (2178489596664727 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2178489596664727 / 1250000000000000 : ℚ)) - (U := (1110976479583476566789 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2178489596664727 / 1250000000000000 : ℝ) ≤ - (1110976479583476566789 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1083133123539727 / 5000000000000000 : ℝ)) (q := - (2178489596664727 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2178489596664727 / 10000000000000000 : ℚ)) + (r' := (2178489596664727 / 1250000000000000 : ℚ)) + (U := (-(3047906602216523433211 / 2000000000000000000000 : ℚ))) + (U' := (1110976479583476566789 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (1083133123539727 / 5000000000000000 : ℚ)) + (q := (2178489596664727 / 10000000000000000 : ℚ)) + (U := (-(3047906602216523433211 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_6 : Uω (aρ 6) (bρ 6) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3798,25 +3433,21 @@ lemma U_291_6 : have hlg : Real.log (3985358586130907 / 20000000000000000 : ℝ) ≤ (-(2016381225759584278767 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3985358586130907 / 20000000000000000 : ℝ) = - (3985358586130907 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3985358586130907 / 2500000000000000 : ℚ)) - (U := (582920700365415721233 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3985358586130907 / 2500000000000000 : ℝ) ≤ - (582920700365415721233 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1961886015020907 / 10000000000000000 : ℝ)) (q := - (3985358586130907 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3985358586130907 / 20000000000000000 : ℚ)) + (r' := (3985358586130907 / 2500000000000000 : ℚ)) + (U := (-(2016381225759584278767 / 1250000000000000000000 : ℚ))) + (U' := (582920700365415721233 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (1961886015020907 / 10000000000000000 : ℚ)) + (q := (3985358586130907 / 20000000000000000 : ℚ)) + (U := (-(2016381225759584278767 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_7 : Uω (aρ 7) (bρ 7) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3824,25 +3455,21 @@ lemma U_291_7 : have hlg : Real.log (689848230502033 / 4000000000000000 : ℝ) ≤ (-(8787890108594326096779 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (689848230502033 / 4000000000000000 : ℝ) = - (689848230502033 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (689848230502033 / 500000000000000 : ℚ)) - (U := (1609317595905673903221 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (689848230502033 / 500000000000000 : ℝ) ≤ - (1609317595905673903221 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (329885992432033 / 2000000000000000 : ℝ)) (q := - (689848230502033 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (689848230502033 / 4000000000000000 : ℚ)) + (r' := (689848230502033 / 500000000000000 : ℚ)) + (U := (-(8787890108594326096779 / 5000000000000000000000 : ℚ))) + (U' := (1609317595905673903221 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (329885992432033 / 2000000000000000 : ℚ)) + (q := (689848230502033 / 4000000000000000 : ℚ)) + (U := (-(8787890108594326096779 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_8 : Uω (aρ 8) (bρ 8) (504571876719 / 2000000000000 : ℝ) ≤ @@ -3850,25 +3477,21 @@ lemma U_291_8 : have hlg : Real.log (2652103060454627 / 20000000000000000 : ℝ) ≤ (-(20203793397973935609921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2652103060454627 / 20000000000000000 : ℝ) = - (2652103060454627 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2652103060454627 / 2500000000000000 : ℚ)) - (U := (590622011026064390079 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2652103060454627 / 2500000000000000 : ℝ) ≤ - (590622011026064390079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1135833521444627 / 10000000000000000 : ℝ)) (q := - (2652103060454627 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2652103060454627 / 20000000000000000 : ℚ)) + (r' := (2652103060454627 / 2500000000000000 : ℚ)) + (U := (-(20203793397973935609921 / 10000000000000000000000 : ℚ))) + (U' := (590622011026064390079 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (504571876719 / 2000000000000 : ℚ)) + (s := (1135833521444627 / 10000000000000000 : ℚ)) + (q := (2652103060454627 / 20000000000000000 : ℚ)) + (U := (-(20203793397973935609921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_291_9 : Uω (aρ 9) (bρ 9) (504571876719 / 2000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U24.lean b/LeanPool/Zeta5Irrational/Table/U24.lean index 99df604cd9..87f32de68b 100644 --- a/LeanPool/Zeta5Irrational/Table/U24.lean +++ b/LeanPool/Zeta5Irrational/Table/U24.lean @@ -24,25 +24,21 @@ lemma U_292_1 : have hlg : Real.log (2500947669219157 / 10000000000000000 : ℝ) ≤ (-(3464788411850854761307 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2500947669219157 / 10000000000000000 : ℝ) = - (2500947669219157 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2500947669219157 / 2500000000000000 : ℚ)) - (U := (947489649145238693 / 2500000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (2500947669219157 / 2500000000000000 : ℝ) ≤ - (947489649145238693 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (625220756642391 / 2500000000000000 : ℝ)) (q := - (2500947669219157 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2500947669219157 / 10000000000000000 : ℚ)) + (r' := (2500947669219157 / 2500000000000000 : ℚ)) + (U := (-(3464788411850854761307 / 2500000000000000000000 : ℚ))) + (U' := (947489649145238693 / 2500000000000000000000 : ℚ)) + 2 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (625220756642391 / 2500000000000000 : ℚ)) + (q := (2500947669219157 / 10000000000000000 : ℚ)) + (U := (-(3464788411850854761307 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_2 : Uω (aρ 2) (bρ 2) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_292_2 : have hlg : Real.log (2476814956106143 / 10000000000000000 : ℝ) ≤ (-(3489029123349057418429 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2476814956106143 / 10000000000000000 : ℝ) = - (2476814956106143 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2476814956106143 / 1250000000000000 : ℚ)) - (U := (1709574728900942581571 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2476814956106143 / 1250000000000000 : ℝ) ≤ - (1709574728900942581571 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (77387081651673 / 312500000000000 : ℝ)) (q := - (2476814956106143 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2476814956106143 / 10000000000000000 : ℚ)) + (r' := (2476814956106143 / 1250000000000000 : ℚ)) + (U := (-(3489029123349057418429 / 2500000000000000000000 : ℚ))) + (U' := (1709574728900942581571 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (77387081651673 / 312500000000000 : ℚ)) + (q := (2476814956106143 / 10000000000000000 : ℚ)) + (U := (-(3489029123349057418429 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_3 : Uω (aρ 3) (bρ 3) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_292_3 : have hlg : Real.log (303540487944847 / 1250000000000000 : ℝ) ≤ (-(14153838244717469109831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (303540487944847 / 1250000000000000 : ℝ) = - (303540487944847 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (303540487944847 / 156250000000000 : ℚ)) - (U := (6640577164282530890169 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (303540487944847 / 156250000000000 : ℝ) ≤ - (6640577164282530890169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1213400307054401 / 5000000000000000 : ℝ)) (q := - (303540487944847 / 1250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (303540487944847 / 1250000000000000 : ℚ)) + (r' := (303540487944847 / 156250000000000 : ℚ)) + (U := (-(14153838244717469109831 / 10000000000000000000000 : ℚ))) + (U' := (6640577164282530890169 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (1213400307054401 / 5000000000000000 : ℚ)) + (q := (303540487944847 / 1250000000000000 : ℚ)) + (U := (-(14153838244717469109831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_4 : Uω (aρ 4) (bρ 4) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_292_4 : have hlg : Real.log (938828241337921 / 4000000000000000 : ℝ) ≤ (-(3623542733545598920361 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (938828241337921 / 4000000000000000 : ℝ) = - (938828241337921 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (938828241337921 / 500000000000000 : ℚ)) - (U := (1575061118704401079639 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (938828241337921 / 500000000000000 : ℝ) ≤ - (1575061118704401079639 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (468517638949171 / 2000000000000000 : ℝ)) (q := - (938828241337921 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (938828241337921 / 4000000000000000 : ℚ)) + (r' := (938828241337921 / 500000000000000 : ℚ)) + (U := (-(3623542733545598920361 / 2500000000000000000000 : ℚ))) + (U' := (1575061118704401079639 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (468517638949171 / 2000000000000000 : ℚ)) + (q := (938828241337921 / 4000000000000000 : ℚ)) + (U := (-(3623542733545598920361 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_5 : Uω (aρ 5) (bρ 5) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -128,24 +112,21 @@ lemma U_292_5 : have hlg : Real.log (138835983024799 / 625000000000000 : ℝ) ≤ (-(3761145976967960412099 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (138835983024799 / 625000000000000 : ℝ) = (138835983024799 / 78125000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (138835983024799 / 78125000000000 : ℚ)) - (U := (1437457875282039587901 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (138835983024799 / 78125000000000 : ℝ) ≤ - (1437457875282039587901 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1104694182092409 / 5000000000000000 : ℝ)) (q := - (138835983024799 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (138835983024799 / 625000000000000 : ℚ)) + (r' := (138835983024799 / 78125000000000 : ℚ)) + (U := (-(3761145976967960412099 / 2500000000000000000000 : ℚ))) + (U' := (1437457875282039587901 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (1104694182092409 / 5000000000000000 : ℚ)) + (q := (138835983024799 / 625000000000000 : ℚ)) + (U := (-(3761145976967960412099 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_6 : Uω (aρ 6) (bρ 6) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -153,25 +134,21 @@ lemma U_292_6 : have hlg : Real.log (2035984408317511 / 10000000000000000 : ℝ) ≤ (-(1989507064440686596057 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2035984408317511 / 10000000000000000 : ℝ) = - (2035984408317511 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2035984408317511 / 1250000000000000 : ℚ)) - (U := (609794861684313403943 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2035984408317511 / 1250000000000000 : ℝ) ≤ - (609794861684313403943 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (31341345299473 / 156250000000000 : ℝ)) (q := - (2035984408317511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2035984408317511 / 10000000000000000 : ℚ)) + (r' := (2035984408317511 / 1250000000000000 : ℚ)) + (U := (-(1989507064440686596057 / 1250000000000000000000 : ℚ))) + (U' := (609794861684313403943 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (31341345299473 / 156250000000000 : ℚ)) + (q := (2035984408317511 / 10000000000000000 : ℚ)) + (U := (-(1989507064440686596057 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_7 : Uω (aρ 7) (bρ 7) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -179,25 +156,21 @@ lemma U_292_7 : have hlg : Real.log (3538327680625391 / 20000000000000000 : ℝ) ≤ (-(8660390319253113093879 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3538327680625391 / 20000000000000000 : ℝ) = - (3538327680625391 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3538327680625391 / 2500000000000000 : ℚ)) - (U := (1736817385246886906121 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3538327680625391 / 2500000000000000 : ℝ) ≤ - (1736817385246886906121 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1695866343916641 / 10000000000000000 : ℝ)) (q := - (3538327680625391 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3538327680625391 / 20000000000000000 : ℚ)) + (r' := (3538327680625391 / 2500000000000000 : ℚ)) + (U := (-(8660390319253113093879 / 5000000000000000000000 : ℚ))) + (U' := (1736817385246886906121 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (1695866343916641 / 10000000000000000 : ℚ)) + (q := (3538327680625391 / 20000000000000000 : ℚ)) + (U := (-(8660390319253113093879 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_8 : Uω (aρ 8) (bρ 8) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -205,25 +178,21 @@ lemma U_292_8 : have hlg : Real.log (2751092096951029 / 20000000000000000 : ℝ) ≤ (-(3967468627530778132021 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2751092096951029 / 20000000000000000 : ℝ) = - (2751092096951029 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2751092096951029 / 2500000000000000 : ℚ)) - (U := (191414454269221867979 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2751092096951029 / 2500000000000000 : ℝ) ≤ - (191414454269221867979 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1192172411582279 / 10000000000000000 : ℝ)) (q := - (2751092096951029 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2751092096951029 / 20000000000000000 : ℚ)) + (r' := (2751092096951029 / 2500000000000000 : ℚ)) + (U := (-(3967468627530778132021 / 2000000000000000000000 : ℚ))) + (U' := (191414454269221867979 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2052407623963 / 8000000000000 : ℚ)) + (s := (1192172411582279 / 10000000000000000 : ℚ)) + (q := (2751092096951029 / 20000000000000000 : ℚ)) + (U := (-(3967468627530778132021 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_292_9 : Uω (aρ 9) (bρ 9) (2052407623963 / 8000000000000 : ℝ) ≤ @@ -355,25 +324,21 @@ lemma U_293_1 : have hlg : Real.log (1271799449755011 / 5000000000000000 : ℝ) ≤ (-(13690051247136983319469 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1271799449755011 / 5000000000000000 : ℝ) = - (1271799449755011 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1271799449755011 / 1250000000000000 : ℚ)) - (U := (172892358863016680531 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1271799449755011 / 1250000000000000 : ℝ) ≤ - (172892358863016680531 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79485479399767 / 312500000000000 : ℝ)) (q := - (1271799449755011 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1271799449755011 / 5000000000000000 : ℚ)) + (r' := (1271799449755011 / 1250000000000000 : ℚ)) + (U := (-(13690051247136983319469 / 10000000000000000000000 : ℚ))) + (U' := (172892358863016680531 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (41730554821 / 160000000000 : ℚ)) + (s := (79485479399767 / 312500000000000 : ℚ)) + (q := (1271799449755011 / 5000000000000000 : ℚ)) + (U := (-(13690051247136983319469 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_2 : Uω (aρ 2) (bρ 2) (41730554821 / 160000000000 : ℝ) ≤ @@ -381,25 +346,21 @@ lemma U_293_2 : have hlg : Real.log (5038944709561171 / 20000000000000000 : ℝ) ≤ (-(13785355958980859419847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5038944709561171 / 20000000000000000 : ℝ) = - (5038944709561171 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5038944709561171 / 5000000000000000 : ℚ)) - (U := (77587647019140580153 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5038944709561171 / 5000000000000000 : ℝ) ≤ - (77587647019140580153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2519051263843671 / 10000000000000000 : ℝ)) (q := - (5038944709561171 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5038944709561171 / 20000000000000000 : ℚ)) + (r' := (5038944709561171 / 5000000000000000 : ℚ)) + (U := (-(13785355958980859419847 / 10000000000000000000000 : ℚ))) + (U' := (77587647019140580153 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (41730554821 / 160000000000 : ℚ)) + (s := (2519051263843671 / 10000000000000000 : ℚ)) + (q := (5038944709561171 / 20000000000000000 : ℚ)) + (U := (-(13785355958980859419847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_3 : Uω (aρ 3) (bρ 3) (41730554821 / 160000000000 : ℝ) ≤ @@ -407,25 +368,21 @@ lemma U_293_3 : have hlg : Real.log (4942000717062239 / 20000000000000000 : ℝ) ≤ (-(13979620201121910036697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4942000717062239 / 20000000000000000 : ℝ) = - (4942000717062239 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4942000717062239 / 2500000000000000 : ℚ)) - (U := (6814795207878089963303 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4942000717062239 / 2500000000000000 : ℝ) ≤ - (6814795207878089963303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2469503377694739 / 10000000000000000 : ℝ)) (q := - (4942000717062239 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4942000717062239 / 20000000000000000 : ℚ)) + (r' := (4942000717062239 / 2500000000000000 : ℚ)) + (U := (-(13979620201121910036697 / 10000000000000000000000 : ℚ))) + (U' := (6814795207878089963303 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (41730554821 / 160000000000 : ℚ)) + (s := (2469503377694739 / 10000000000000000 : ℚ)) + (q := (4942000717062239 / 20000000000000000 : ℚ)) + (U := (-(13979620201121910036697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_4 : Uω (aρ 4) (bρ 4) (41730554821 / 160000000000 : ℝ) ≤ @@ -433,25 +390,21 @@ lemma U_293_4 : have hlg : Real.log (298725112049267 / 1250000000000000 : ℝ) ≤ (-(2862750073378134468569 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (298725112049267 / 1250000000000000 : ℝ) = - (298725112049267 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (298725112049267 / 156250000000000 : ℚ)) - (U := (1296133008421865531431 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (298725112049267 / 156250000000000 : ℝ) ≤ - (1296133008421865531431 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (596349658621443 / 2500000000000000 : ℝ)) (q := - (298725112049267 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (298725112049267 / 1250000000000000 : ℚ)) + (r' := (298725112049267 / 156250000000000 : ℚ)) + (U := (-(2862750073378134468569 / 2000000000000000000000 : ℚ))) + (U' := (1296133008421865531431 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (41730554821 / 160000000000 : ℚ)) + (s := (596349658621443 / 2500000000000000 : ℚ)) + (q := (298725112049267 / 1250000000000000 : ℚ)) + (U := (-(2862750073378134468569 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_5 : Uω (aρ 5) (bρ 5) (41730554821 / 160000000000 : ℝ) ≤ @@ -459,25 +412,21 @@ lemma U_293_5 : have hlg : Real.log (4528505748238879 / 20000000000000000 : ℝ) ≤ (-(14853402445948760473001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4528505748238879 / 20000000000000000 : ℝ) = - (4528505748238879 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4528505748238879 / 2500000000000000 : ℚ)) - (U := (5941012963051239526999 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4528505748238879 / 2500000000000000 : ℝ) ≤ - (5941012963051239526999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2252492509271379 / 10000000000000000 : ℝ)) (q := - (4528505748238879 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4528505748238879 / 20000000000000000 : ℚ)) + (r' := (4528505748238879 / 2500000000000000 : ℚ)) + (U := (-(14853402445948760473001 / 10000000000000000000000 : ℚ))) + (U' := (5941012963051239526999 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (41730554821 / 160000000000 : ℚ)) + (s := (2252492509271379 / 10000000000000000 : ℚ)) + (q := (4528505748238879 / 20000000000000000 : ℚ)) + (U := (-(14853402445948760473001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_6 : Uω (aρ 6) (bρ 6) (41730554821 / 160000000000 : ℝ) ≤ @@ -485,25 +434,21 @@ lemma U_293_6 : have hlg : Real.log (831704739547529 / 4000000000000000 : ℝ) ≤ (-(15705721418374445952343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (831704739547529 / 4000000000000000 : ℝ) = - (831704739547529 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (831704739547529 / 500000000000000 : ℚ)) - (U := (5088693990625554047657 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (831704739547529 / 500000000000000 : ℝ) ≤ - (5088693990625554047657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (409950166782029 / 2000000000000000 : ℝ)) (q := - (831704739547529 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (831704739547529 / 4000000000000000 : ℚ)) + (r' := (831704739547529 / 500000000000000 : ℚ)) + (U := (-(15705721418374445952343 / 10000000000000000000000 : ℚ))) + (U' := (5088693990625554047657 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (41730554821 / 160000000000 : ℚ)) + (s := (409950166782029 / 2000000000000000 : ℚ)) + (q := (831704739547529 / 4000000000000000 : ℚ)) + (U := (-(15705721418374445952343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_7 : Uω (aρ 7) (bρ 7) (41730554821 / 160000000000 : ℝ) ≤ @@ -511,25 +456,21 @@ lemma U_293_7 : have hlg : Real.log (3627220602139997 / 20000000000000000 : ℝ) ≤ (-(2134081990146632886253 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3627220602139997 / 20000000000000000 : ℝ) = - (3627220602139997 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3627220602139997 / 2500000000000000 : ℚ)) - (U := (465219935978367113747 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3627220602139997 / 2500000000000000 : ℝ) ≤ - (465219935978367113747 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1742109119072497 / 10000000000000000 : ℝ)) (q := - (3627220602139997 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3627220602139997 / 20000000000000000 : ℚ)) + (r' := (3627220602139997 / 2500000000000000 : ℚ)) + (U := (-(2134081990146632886253 / 1250000000000000000000 : ℚ))) + (U' := (465219935978367113747 / 1250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (41730554821 / 160000000000 : ℚ)) + (s := (1742109119072497 / 10000000000000000 : ℚ)) + (q := (3627220602139997 / 20000000000000000 : ℚ)) + (U := (-(2134081990146632886253 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_8 : Uω (aρ 8) (bρ 8) (41730554821 / 160000000000 : ℝ) ≤ @@ -537,25 +478,21 @@ lemma U_293_8 : have hlg : Real.log (1424497670143987 / 10000000000000000 : ℝ) ≤ (-(19487658528202780408503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1424497670143987 / 10000000000000000 : ℝ) = - (1424497670143987 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1424497670143987 / 1250000000000000 : ℚ)) - (U := (1306756880797219591497 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1424497670143987 / 1250000000000000 : ℝ) ≤ - (1306756880797219591497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (623712754280237 / 5000000000000000 : ℝ)) (q := - (1424497670143987 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1424497670143987 / 10000000000000000 : ℚ)) + (r' := (1424497670143987 / 1250000000000000 : ℚ)) + (U := (-(19487658528202780408503 / 10000000000000000000000 : ℚ))) + (U' := (1306756880797219591497 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (41730554821 / 160000000000 : ℚ)) + (s := (623712754280237 / 5000000000000000 : ℚ)) + (q := (1424497670143987 / 10000000000000000 : ℚ)) + (U := (-(19487658528202780408503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_293_9 : Uω (aρ 9) (bρ 9) (41730554821 / 160000000000 : ℝ) ≤ @@ -688,25 +625,21 @@ lemma U_294_1 : have hlg : Real.log (1051560501830063 / 4000000000000000 : ℝ) ≤ (-(13360191075021170630243 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1051560501830063 / 4000000000000000 : ℝ) = - (1051560501830063 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1051560501830063 / 1000000000000000 : ℚ)) - (U := (502752530978829369757 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1051560501830063 / 1000000000000000 : ℝ) ≤ - (502752530978829369757 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (525767951641063 / 2000000000000000 : ℝ)) (q := - (1051560501830063 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1051560501830063 / 4000000000000000 : ℚ)) + (r' := (1051560501830063 / 1000000000000000 : ℚ)) + (U := (-(13360191075021170630243 / 10000000000000000000000 : ℚ))) + (U' := (502752530978829369757 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (525767951641063 / 2000000000000000 : ℚ)) + (q := (1051560501830063 / 4000000000000000 : ℚ)) + (U := (-(13360191075021170630243 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_2 : Uω (aρ 2) (bρ 2) (269345996903 / 1000000000000 : ℝ) ≤ @@ -714,25 +647,21 @@ lemma U_294_2 : have hlg : Real.log (2604786439411037 / 10000000000000000 : ℝ) ≤ (-(26904688033233695969 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2604786439411037 / 10000000000000000 : ℝ) = - (2604786439411037 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2604786439411037 / 2500000000000000 : ℚ)) - (U := (821199178766304031 / 20000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2604786439411037 / 2500000000000000 : ℝ) ≤ - (821199178766304031 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1302189570193537 / 5000000000000000 : ℝ)) (q := - (2604786439411037 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2604786439411037 / 10000000000000000 : ℚ)) + (r' := (2604786439411037 / 2500000000000000 : ℚ)) + (U := (-(26904688033233695969 / 20000000000000000000 : ℚ))) + (U' := (821199178766304031 / 20000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (1302189570193537 / 5000000000000000 : ℚ)) + (q := (2604786439411037 / 10000000000000000 : ℚ)) + (U := (-(26904688033233695969 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_3 : Uω (aρ 3) (bρ 3) (269345996903 / 1000000000000 : ℝ) ≤ @@ -740,25 +669,21 @@ lemma U_294_3 : have hlg : Real.log (102254025270581 / 400000000000000 : ℝ) ≤ (-(3410010963726477067487 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (102254025270581 / 400000000000000 : ℝ) = - (102254025270581 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (102254025270581 / 100000000000000 : ℚ)) - (U := (55724937773522932513 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (102254025270581 / 100000000000000 : ℝ) ≤ - (55724937773522932513 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (51098072628881 / 200000000000000 : ℝ)) (q := - (102254025270581 / 400000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (102254025270581 / 400000000000000 : ℚ)) + (r' := (102254025270581 / 100000000000000 : ℚ)) + (U := (-(3410010963726477067487 / 2500000000000000000000 : ℚ))) + (U' := (55724937773522932513 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (51098072628881 / 200000000000000 : ℚ)) + (q := (102254025270581 / 400000000000000 : ℚ)) + (U := (-(3410010963726477067487 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_4 : Uω (aρ 4) (bρ 4) (269345996903 / 1000000000000 : ℝ) ≤ @@ -766,25 +691,21 @@ lemma U_294_4 : have hlg : Real.log (4950506333616661 / 20000000000000000 : ℝ) ≤ (-(13962424118052550522617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4950506333616661 / 20000000000000000 : ℝ) = - (4950506333616661 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4950506333616661 / 2500000000000000 : ℚ)) - (U := (6831991290947449477383 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4950506333616661 / 2500000000000000 : ℝ) ≤ - (6831991290947449477383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2471002882596661 / 10000000000000000 : ℝ)) (q := - (4950506333616661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4950506333616661 / 20000000000000000 : ℚ)) + (r' := (4950506333616661 / 2500000000000000 : ℚ)) + (U := (-(13962424118052550522617 / 10000000000000000000000 : ℚ))) + (U' := (6831991290947449477383 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (2471002882596661 / 10000000000000000 : ℚ)) + (q := (4950506333616661 / 20000000000000000 : ℚ)) + (U := (-(13962424118052550522617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_5 : Uω (aρ 5) (bρ 5) (269345996903 / 1000000000000 : ℝ) ≤ @@ -792,24 +713,21 @@ lemma U_294_5 : have hlg : Real.log (36718471793851 / 156250000000000 : ℝ) ≤ (-(14481773407649457578313 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (36718471793851 / 156250000000000 : ℝ) = (36718471793851 / 19531250000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36718471793851 / 19531250000000 : ℚ)) - (U := (6312642001350542421687 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (36718471793851 / 19531250000000 : ℝ) ≤ - (6312642001350542421687 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292331357240991 / 1250000000000000 : ℝ)) (q := - (36718471793851 / 156250000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36718471793851 / 156250000000000 : ℚ)) + (r' := (36718471793851 / 19531250000000 : ℚ)) + (U := (-(14481773407649457578313 / 10000000000000000000000 : ℚ))) + (U' := (6312642001350542421687 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (292331357240991 / 1250000000000000 : ℚ)) + (q := (36718471793851 / 156250000000000 : ℚ)) + (U := (-(14481773407649457578313 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_6 : Uω (aρ 6) (bρ 6) (269345996903 / 1000000000000 : ℝ) ≤ @@ -817,25 +735,21 @@ lemma U_294_6 : have hlg : Real.log (2165740525370507 / 10000000000000000 : ℝ) ≤ (-(1529822745192444888481 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2165740525370507 / 10000000000000000 : ℝ) = - (2165740525370507 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2165740525370507 / 1250000000000000 : ℚ)) - (U := (549618795707555111519 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2165740525370507 / 1250000000000000 : ℝ) ≤ - (549618795707555111519 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1068703947098007 / 5000000000000000 : ℝ)) (q := - (2165740525370507 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2165740525370507 / 10000000000000000 : ℚ)) + (r' := (2165740525370507 / 1250000000000000 : ℚ)) + (U := (-(1529822745192444888481 / 1000000000000000000000 : ℚ))) + (U' := (549618795707555111519 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (1068703947098007 / 5000000000000000 : ℚ)) + (q := (2165740525370507 / 10000000000000000 : ℚ)) + (U := (-(1529822745192444888481 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_7 : Uω (aρ 7) (bρ 7) (269345996903 / 1000000000000 : ℝ) ≤ @@ -843,25 +757,21 @@ lemma U_294_7 : have hlg : Real.log (3804484142218451 / 20000000000000000 : ℝ) ≤ (-(16595518643128249441507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3804484142218451 / 20000000000000000 : ℝ) = - (3804484142218451 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3804484142218451 / 2500000000000000 : ℚ)) - (U := (4198896765871750558493 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3804484142218451 / 2500000000000000 : ℝ) ≤ - (4198896765871750558493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1834072366433451 / 10000000000000000 : ℝ)) (q := - (3804484142218451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3804484142218451 / 20000000000000000 : ℚ)) + (r' := (3804484142218451 / 2500000000000000 : ℚ)) + (U := (-(16595518643128249441507 / 10000000000000000000000 : ℚ))) + (U' := (4198896765871750558493 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (1834072366433451 / 10000000000000000 : ℚ)) + (q := (3804484142218451 / 20000000000000000 : ℚ)) + (U := (-(16595518643128249441507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_8 : Uω (aρ 8) (bρ 8) (269345996903 / 1000000000000 : ℝ) ≤ @@ -869,25 +779,21 @@ lemma U_294_8 : have hlg : Real.log (3042073168366019 / 20000000000000000 : ℝ) ≤ (-(18831930265090184175181 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3042073168366019 / 20000000000000000 : ℝ) = - (3042073168366019 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3042073168366019 / 2500000000000000 : ℚ)) - (U := (1962485143909815824819 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3042073168366019 / 2500000000000000 : ℝ) ≤ - (1962485143909815824819 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1355203043921019 / 10000000000000000 : ℝ)) (q := - (3042073168366019 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3042073168366019 / 20000000000000000 : ℚ)) + (r' := (3042073168366019 / 2500000000000000 : ℚ)) + (U := (-(18831930265090184175181 / 10000000000000000000000 : ℚ))) + (U' := (1962485143909815824819 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (269345996903 / 1000000000000 : ℚ)) + (s := (1355203043921019 / 10000000000000000 : ℚ)) + (q := (3042073168366019 / 20000000000000000 : ℚ)) + (U := (-(18831930265090184175181 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_294_9 : Uω (aρ 9) (bρ 9) (269345996903 / 1000000000000 : ℝ) ≤ @@ -1019,25 +925,21 @@ lemma U_295_1 : have hlg : Real.log (10612786717365443 / 40000000000000000 : ℝ) ≤ (-(265363977074615904323 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10612786717365443 / 40000000000000000 : ℝ) = - (10612786717365443 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10612786717365443 / 10000000000000000 : ℚ)) - (U := (11894895045384095677 / 200000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10612786717365443 / 10000000000000000 : ℝ) ≤ - (11894895045384095677 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2653135746096159 / 10000000000000000 : ℝ)) (q := - (10612786717365443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10612786717365443 / 40000000000000000 : ℚ)) + (r' := (10612786717365443 / 10000000000000000 : ℚ)) + (U := (-(265363977074615904323 / 200000000000000000000 : ℚ))) + (U' := (11894895045384095677 / 200000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (2653135746096159 / 10000000000000000 : ℚ)) + (q := (10612786717365443 / 40000000000000000 : ℚ)) + (U := (-(265363977074615904323 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_2 : Uω (aρ 2) (bρ 2) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1045,25 +947,21 @@ lemma U_295_2 : have hlg : Real.log (10516340261626047 / 40000000000000000 : ℝ) ≤ (-(6679745953429830672479 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10516340261626047 / 40000000000000000 : ℝ) = - (10516340261626047 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10516340261626047 / 10000000000000000 : ℚ)) - (U := (251725849570169327521 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10516340261626047 / 10000000000000000 : ℝ) ≤ - (251725849570169327521 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2628681530736461 / 10000000000000000 : ℝ)) (q := - (10516340261626047 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10516340261626047 / 40000000000000000 : ℚ)) + (r' := (10516340261626047 / 10000000000000000 : ℚ)) + (U := (-(6679745953429830672479 / 5000000000000000000000 : ℚ))) + (U' := (251725849570169327521 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (2628681530736461 / 10000000000000000 : ℚ)) + (q := (10516340261626047 / 40000000000000000 : ℚ)) + (U := (-(6679745953429830672479 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_3 : Uω (aρ 3) (bρ 3) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1071,25 +969,21 @@ lemma U_295_3 : have hlg : Real.log (10322636493641941 / 40000000000000000 : ℝ) ≤ (-(13545402519784924013857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10322636493641941 / 40000000000000000 : ℝ) = - (10322636493641941 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10322636493641941 / 10000000000000000 : ℚ)) - (U := (317541086215075986143 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10322636493641941 / 10000000000000000 : ℝ) ≤ - (317541086215075986143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (322403219136801 / 1250000000000000 : ℝ)) (q := - (10322636493641941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10322636493641941 / 40000000000000000 : ℚ)) + (r' := (10322636493641941 / 10000000000000000 : ℚ)) + (U := (-(13545402519784924013857 / 10000000000000000000000 : ℚ))) + (U' := (317541086215075986143 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (322403219136801 / 1250000000000000 : ℚ)) + (q := (10322636493641941 / 40000000000000000 : ℚ)) + (U := (-(13545402519784924013857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_4 : Uω (aρ 4) (bρ 4) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1097,25 +991,21 @@ lemma U_295_4 : have hlg : Real.log (9998357638502501 / 40000000000000000 : ℝ) ≤ (-(6932293049890189446321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9998357638502501 / 40000000000000000 : ℝ) = - (9998357638502501 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9998357638502501 / 5000000000000000 : ℚ)) - (U := (3464914654609810553679 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9998357638502501 / 5000000000000000 : ℝ) ≤ - (3464914654609810553679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (311922563323711 / 1250000000000000 : ℝ)) (q := - (9998357638502501 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9998357638502501 / 40000000000000000 : ℚ)) + (r' := (9998357638502501 / 5000000000000000 : ℚ)) + (U := (-(6932293049890189446321 / 5000000000000000000000 : ℚ))) + (U' := (3464914654609810553679 / 5000000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (311922563323711 / 1250000000000000 : ℚ)) + (q := (9998357638502501 / 40000000000000000 : ℚ)) + (U := (-(6932293049890189446321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_5 : Uω (aρ 5) (bρ 5) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1123,25 +1013,21 @@ lemma U_295_5 : have hlg : Real.log (9497574219890053 / 40000000000000000 : ℝ) ≤ (-(1437843032608491819939 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9497574219890053 / 40000000000000000 : ℝ) = - (9497574219890053 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9497574219890053 / 5000000000000000 : ℚ)) - (U := (641598508291508180061 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9497574219890053 / 5000000000000000 : ℝ) ≤ - (641598508291508180061 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73849334894327 / 312500000000000 : ℝ)) (q := - (9497574219890053 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9497574219890053 / 40000000000000000 : ℚ)) + (r' := (9497574219890053 / 5000000000000000 : ℚ)) + (U := (-(1437843032608491819939 / 1000000000000000000000 : ℚ))) + (U' := (641598508291508180061 / 1000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (73849334894327 / 312500000000000 : ℚ)) + (q := (9497574219890053 / 40000000000000000 : ℚ)) + (U := (-(1437843032608491819939 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_6 : Uω (aρ 6) (bρ 6) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1149,25 +1035,21 @@ lemma U_295_6 : have hlg : Real.log (8761415055219761 / 40000000000000000 : ℝ) ≤ (-(15185220254473415163101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8761415055219761 / 40000000000000000 : ℝ) = - (8761415055219761 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8761415055219761 / 5000000000000000 : ℚ)) - (U := (5609195154526584836899 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8761415055219761 / 5000000000000000 : ℝ) ≤ - (5609195154526584836899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1081169754711659 / 5000000000000000 : ℝ)) (q := - (8761415055219761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8761415055219761 / 40000000000000000 : ℚ)) + (r' := (8761415055219761 / 5000000000000000 : ℚ)) + (U := (-(15185220254473415163101 / 10000000000000000000000 : ℚ))) + (U' := (5609195154526584836899 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (1081169754711659 / 5000000000000000 : ℚ)) + (q := (8761415055219761 / 40000000000000000 : ℚ)) + (U := (-(15185220254473415163101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_7 : Uω (aρ 7) (bρ 7) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1175,25 +1057,21 @@ lemma U_295_7 : have hlg : Real.log (7709710815941033 / 40000000000000000 : ℝ) ≤ (-(3292797548244679441269 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7709710815941033 / 40000000000000000 : ℝ) = - (7709710815941033 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7709710815941033 / 5000000000000000 : ℚ)) - (U := (866085533555320558731 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7709710815941033 / 5000000000000000 : ℝ) ≤ - (866085533555320558731 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (930074385271977 / 5000000000000000 : ℝ)) (q := - (7709710815941033 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7709710815941033 / 40000000000000000 : ℚ)) + (r' := (7709710815941033 / 5000000000000000 : ℚ)) + (U := (-(3292797548244679441269 / 2000000000000000000000 : ℚ))) + (U' := (866085533555320558731 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (930074385271977 / 5000000000000000 : ℚ)) + (q := (7709710815941033 / 40000000000000000 : ℚ)) + (U := (-(3292797548244679441269 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_8 : Uω (aρ 8) (bρ 8) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1201,25 +1079,21 @@ lemma U_295_8 : have hlg : Real.log (1238596676944277 / 8000000000000000 : ℝ) ≤ (-(18654625142945181295753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1238596676944277 / 8000000000000000 : ℝ) = - (1238596676944277 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1238596676944277 / 1000000000000000 : ℚ)) - (U := (2139790266054818704247 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1238596676944277 / 1000000000000000 : ℝ) ≤ - (2139790266054818704247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138532670627413 / 1000000000000000 : ℝ)) (q := - (1238596676944277 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1238596676944277 / 8000000000000000 : ℚ)) + (r' := (1238596676944277 / 1000000000000000 : ℚ)) + (U := (-(18654625142945181295753 / 10000000000000000000000 : ℚ))) + (U' := (2139790266054818704247 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (138532670627413 / 1000000000000000 : ℚ)) + (q := (1238596676944277 / 8000000000000000 : ℚ)) + (U := (-(18654625142945181295753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_9 : Uω (aρ 9) (bρ 9) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1227,25 +1101,21 @@ lemma U_295_9 : have hlg : Real.log (3254158843654867 / 40000000000000000 : ℝ) ≤ (-(12544728152889271956379 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3254158843654867 / 40000000000000000 : ℝ) = - (3254158843654867 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3254158843654867 / 2500000000000000 : ℚ)) - (U := (1318215453110728043621 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3254158843654867 / 2500000000000000 : ℝ) ≤ - (1318215453110728043621 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256880064100871 / 10000000000000000 : ℝ)) (q := - (3254158843654867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3254158843654867 / 40000000000000000 : ℚ)) + (r' := (3254158843654867 / 2500000000000000 : ℚ)) + (U := (-(12544728152889271956379 / 5000000000000000000000 : ℚ))) + (U' := (1318215453110728043621 / 5000000000000000000000 : ℚ)) + 4 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8696815458149 / 32000000000000 : ℚ)) + (s := (256880064100871 / 10000000000000000 : ℚ)) + (q := (3254158843654867 / 40000000000000000 : ℚ)) + (U := (-(12544728152889271956379 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_295_10 : Uω (aρ 10) (bρ 10) (8696815458149 / 32000000000000 : ℝ) ≤ @@ -1372,25 +1242,21 @@ lemma U_296_1 : have hlg : Real.log (5354984187775611 / 20000000000000000 : ℝ) ≤ (-(6588522609675428053601 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5354984187775611 / 20000000000000000 : ℝ) = - (5354984187775611 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5354984187775611 / 5000000000000000 : ℚ)) - (U := (342949193324571946399 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5354984187775611 / 5000000000000000 : ℝ) ≤ - (342949193324571946399 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1338715856773743 / 5000000000000000 : ℝ)) (q := - (5354984187775611 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5354984187775611 / 20000000000000000 : ℚ)) + (r' := (5354984187775611 / 5000000000000000 : ℚ)) + (U := (-(6588522609675428053601 / 5000000000000000000000 : ℚ))) + (U' := (342949193324571946399 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (1338715856773743 / 5000000000000000 : ℚ)) + (q := (5354984187775611 / 20000000000000000 : ℚ)) + (U := (-(6588522609675428053601 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_2 : Uω (aρ 2) (bρ 2) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1398,25 +1264,21 @@ lemma U_296_2 : have hlg : Real.log (1326691811223351 / 5000000000000000 : ℝ) ≤ (-(1326749428282152019991 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1326691811223351 / 5000000000000000 : ℝ) = - (1326691811223351 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1326691811223351 / 1250000000000000 : ℚ)) - (U := (59544932317847980009 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1326691811223351 / 1250000000000000 : ℝ) ≤ - (59544932317847980009 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2652983783175279 / 10000000000000000 : ℝ)) (q := - (1326691811223351 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1326691811223351 / 5000000000000000 : ℚ)) + (r' := (1326691811223351 / 1250000000000000 : ℚ)) + (U := (-(1326749428282152019991 / 1000000000000000000000 : ℚ))) + (U' := (59544932317847980009 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (2652983783175279 / 10000000000000000 : ℚ)) + (q := (1326691811223351 / 5000000000000000 : ℚ)) + (U := (-(1326749428282152019991 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_3 : Uω (aρ 3) (bρ 3) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1424,25 +1286,21 @@ lemma U_296_3 : have hlg : Real.log (130248368026923 / 500000000000000 : ℝ) ≤ (-(6725824734455487825467 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (130248368026923 / 500000000000000 : ℝ) = - (130248368026923 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (130248368026923 / 125000000000000 : ℚ)) - (U := (205647068544512174533 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (130248368026923 / 125000000000000 : ℝ) ≤ - (205647068544512174533 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (520709473141759 / 2000000000000000 : ℝ)) (q := - (130248368026923 / 500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (130248368026923 / 500000000000000 : ℚ)) + (r' := (130248368026923 / 125000000000000 : ℚ)) + (U := (-(6725824734455487825467 / 5000000000000000000000 : ℚ))) + (U' := (205647068544512174533 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (520709473141759 / 2000000000000000 : ℚ)) + (q := (130248368026923 / 500000000000000 : ℚ)) + (U := (-(6725824734455487825467 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_4 : Uω (aρ 4) (bρ 4) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1450,25 +1308,21 @@ lemma U_296_4 : have hlg : Real.log (5047849706220241 / 20000000000000000 : ℝ) ≤ (-(3441924802935448534447 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5047849706220241 / 20000000000000000 : ℝ) = - (5047849706220241 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5047849706220241 / 5000000000000000 : ℚ)) - (U := (23811098564551465553 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5047849706220241 / 5000000000000000 : ℝ) ≤ - (23811098564551465553 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (629939132979279 / 2500000000000000 : ℝ)) (q := - (5047849706220241 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5047849706220241 / 20000000000000000 : ℚ)) + (r' := (5047849706220241 / 5000000000000000 : ℚ)) + (U := (-(3441924802935448534447 / 2500000000000000000000 : ℚ))) + (U' := (23811098564551465553 / 2500000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (629939132979279 / 2500000000000000 : ℚ)) + (q := (5047849706220241 / 20000000000000000 : ℚ)) + (U := (-(3441924802935448534447 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_5 : Uω (aρ 5) (bρ 5) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1476,25 +1330,21 @@ lemma U_296_5 : have hlg : Real.log (4797605066056417 / 20000000000000000 : ℝ) ≤ (-(1784519279932689038239 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4797605066056417 / 20000000000000000 : ℝ) = - (4797605066056417 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4797605066056417 / 2500000000000000 : ℚ)) - (U := (814782646192310961761 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4797605066056417 / 2500000000000000 : ℝ) ≤ - (814782646192310961761 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (596925452772073 / 2500000000000000 : ℝ)) (q := - (4797605066056417 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4797605066056417 / 20000000000000000 : ℚ)) + (r' := (4797605066056417 / 2500000000000000 : ℚ)) + (U := (-(1784519279932689038239 / 1250000000000000000000 : ℚ))) + (U' := (814782646192310961761 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (596925452772073 / 2500000000000000 : ℚ)) + (q := (4797605066056417 / 20000000000000000 : ℚ)) + (U := (-(1784519279932689038239 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_6 : Uω (aρ 6) (bρ 6) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1502,25 +1352,21 @@ lemma U_296_6 : have hlg : Real.log (1107479918431881 / 5000000000000000 : ℝ) ≤ (-(3768377053057300971997 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1107479918431881 / 5000000000000000 : ℝ) = - (1107479918431881 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1107479918431881 / 625000000000000 : ℚ)) - (U := (1430226799192699028003 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1107479918431881 / 625000000000000 : ℝ) ≤ - (1430226799192699028003 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2187256793899399 / 10000000000000000 : ℝ)) (q := - (1107479918431881 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1107479918431881 / 5000000000000000 : ℚ)) + (r' := (1107479918431881 / 625000000000000 : ℚ)) + (U := (-(3768377053057300971997 / 2500000000000000000000 : ℚ))) + (U' := (1430226799192699028003 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (2187256793899399 / 10000000000000000 : ℚ)) + (q := (1107479918431881 / 5000000000000000 : ℚ)) + (U := (-(3768377053057300971997 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_7 : Uω (aρ 7) (bρ 7) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1528,25 +1374,21 @@ lemma U_296_7 : have hlg : Real.log (976294774346881 / 5000000000000000 : ℝ) ≤ (-(16334286269266483063657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (976294774346881 / 5000000000000000 : ℝ) = - (976294774346881 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (976294774346881 / 625000000000000 : ℚ)) - (U := (4460129139733516936343 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (976294774346881 / 625000000000000 : ℝ) ≤ - (4460129139733516936343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1886177598319399 / 10000000000000000 : ℝ)) (q := - (976294774346881 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (976294774346881 / 5000000000000000 : ℚ)) + (r' := (976294774346881 / 625000000000000 : ℚ)) + (U := (-(16334286269266483063657 / 10000000000000000000000 : ℚ))) + (U' := (4460129139733516936343 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (1886177598319399 / 10000000000000000 : ℚ)) + (q := (976294774346881 / 5000000000000000 : ℚ)) + (U := (-(16334286269266483063657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_8 : Uω (aρ 8) (bρ 8) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1554,24 +1396,21 @@ lemma U_296_8 : have hlg : Real.log (49229470375789 / 312500000000000 : ℝ) ≤ (-(4620280082110656607647 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (49229470375789 / 312500000000000 : ℝ) = (49229470375789 / 39062500000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49229470375789 / 39062500000000 : ℚ)) - (U := (578323770139343392353 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (49229470375789 / 39062500000000 : ℝ) ≤ - (578323770139343392353 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1415226256322371 / 10000000000000000 : ℝ)) (q := - (49229470375789 / 312500000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49229470375789 / 312500000000000 : ℚ)) + (r' := (49229470375789 / 39062500000000 : ℚ)) + (U := (-(4620280082110656607647 / 2500000000000000000000 : ℚ))) + (U' := (578323770139343392353 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (1415226256322371 / 10000000000000000 : ℚ)) + (q := (49229470375789 / 312500000000000 : ℚ)) + (U := (-(4620280082110656607647 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_9 : Uω (aρ 9) (bρ 9) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1579,24 +1418,21 @@ lemma U_296_9 : have hlg : Real.log (43984965283121 / 500000000000000 : ℝ) ≤ (-(24307602199671372227129 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (43984965283121 / 500000000000000 : ℝ) = (43984965283121 / 31250000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43984965283121 / 31250000000000 : ℚ)) - (U := (3418285012328627772871 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (43984965283121 / 31250000000000 : ℝ) ≤ - (3418285012328627772871 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (72980878391343 / 2000000000000000 : ℝ)) (q := - (43984965283121 / 500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43984965283121 / 500000000000000 : ℚ)) + (r' := (43984965283121 / 31250000000000 : ℚ)) + (U := (-(24307602199671372227129 / 10000000000000000000000 : ℚ))) + (U' := (3418285012328627772871 / 10000000000000000000000 : ℚ)) + 4 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4387279507701 / 16000000000000 : ℚ)) + (s := (72980878391343 / 2000000000000000 : ℚ)) + (q := (43984965283121 / 500000000000000 : ℚ)) + (U := (-(24307602199671372227129 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_296_10 : Uω (aρ 10) (bρ 10) (4387279507701 / 16000000000000 : ℝ) ≤ @@ -1723,25 +1559,21 @@ lemma U_297_1 : have hlg : Real.log (2161429998792163 / 8000000000000000 : ℝ) ≤ (-(13086715020354936082899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2161429998792163 / 8000000000000000 : ℝ) = - (2161429998792163 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2161429998792163 / 2000000000000000 : ℚ)) - (U := (776228585645063917101 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2161429998792163 / 2000000000000000 : ℝ) ≤ - (776228585645063917101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8442898940971 / 31250000000000 : ℝ)) (q := - (2161429998792163 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2161429998792163 / 8000000000000000 : ℚ)) + (r' := (2161429998792163 / 2000000000000000 : ℚ)) + (U := (-(13086715020354936082899 / 10000000000000000000000 : ℚ))) + (U' := (776228585645063917101 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (8442898940971 / 31250000000000 : ℚ)) + (q := (2161429998792163 / 8000000000000000 : ℚ)) + (U := (-(13086715020354936082899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_2 : Uω (aρ 2) (bρ 2) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1749,25 +1581,21 @@ lemma U_297_2 : have hlg : Real.log (10710728449637483 / 40000000000000000 : ℝ) ≤ (-(3294083889020482951309 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10710728449637483 / 40000000000000000 : ℝ) = - (10710728449637483 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10710728449637483 / 10000000000000000 : ℚ)) - (U := (171652012479517048691 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10710728449637483 / 10000000000000000 : ℝ) ≤ - (171652012479517048691 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1338642950729527 / 5000000000000000 : ℝ)) (q := - (10710728449637483 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10710728449637483 / 40000000000000000 : ℚ)) + (r' := (10710728449637483 / 10000000000000000 : ℚ)) + (U := (-(3294083889020482951309 / 2500000000000000000000 : ℚ))) + (U' := (171652012479517048691 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (1338642950729527 / 5000000000000000 : ℚ)) + (q := (10710728449637483 / 40000000000000000 : ℚ)) + (U := (-(3294083889020482951309 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_3 : Uω (aρ 3) (bρ 3) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1775,25 +1603,21 @@ lemma U_297_3 : have hlg : Real.log (10517101400861367 / 40000000000000000 : ℝ) ≤ (-(13358768164879755402591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10517101400861367 / 40000000000000000 : ℝ) = - (10517101400861367 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10517101400861367 / 10000000000000000 : ℚ)) - (U := (504175441120244597409 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10517101400861367 / 10000000000000000 : ℝ) ≤ - (504175441120244597409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (656967120855249 / 2500000000000000 : ℝ)) (q := - (10517101400861367 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10517101400861367 / 40000000000000000 : ℚ)) + (r' := (10517101400861367 / 10000000000000000 : ℚ)) + (U := (-(13358768164879755402591 / 10000000000000000000000 : ℚ))) + (U' := (504175441120244597409 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (656967120855249 / 2500000000000000 : ℚ)) + (q := (10517101400861367 / 40000000000000000 : ℚ)) + (U := (-(13358768164879755402591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_4 : Uω (aρ 4) (bρ 4) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1801,25 +1625,21 @@ lemma U_297_4 : have hlg : Real.log (10193038080950819 / 40000000000000000 : ℝ) ≤ (-(13671745074242828367393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10193038080950819 / 40000000000000000 : ℝ) = - (10193038080950819 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10193038080950819 / 10000000000000000 : ℚ)) - (U := (191198531757171632607 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10193038080950819 / 10000000000000000 : ℝ) ≤ - (191198531757171632607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1272065502265361 / 5000000000000000 : ℝ)) (q := - (10193038080950819 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10193038080950819 / 40000000000000000 : ℚ)) + (r' := (10193038080950819 / 10000000000000000 : ℚ)) + (U := (-(13671745074242828367393 / 10000000000000000000000 : ℚ))) + (U' := (191198531757171632607 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (1272065502265361 / 5000000000000000 : ℚ)) + (q := (10193038080950819 / 40000000000000000 : ℚ)) + (U := (-(13671745074242828367393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_5 : Uω (aρ 5) (bρ 5) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1827,25 +1647,21 @@ lemma U_297_5 : have hlg : Real.log (9692836806498103 / 40000000000000000 : ℝ) ≤ (-(14174923141875718530619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9692836806498103 / 40000000000000000 : ℝ) = - (9692836806498103 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9692836806498103 / 5000000000000000 : ℚ)) - (U := (6619492267124281469381 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9692836806498103 / 5000000000000000 : ℝ) ≤ - (6619492267124281469381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (603055071659841 / 2500000000000000 : ℝ)) (q := - (9692836806498103 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9692836806498103 / 40000000000000000 : ℚ)) + (r' := (9692836806498103 / 5000000000000000 : ℚ)) + (U := (-(14174923141875718530619 / 10000000000000000000000 : ℚ))) + (U' := (6619492267124281469381 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (603055071659841 / 2500000000000000 : ℚ)) + (q := (9692836806498103 / 40000000000000000 : ℚ)) + (U := (-(14174923141875718530619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_6 : Uω (aρ 6) (bρ 6) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1853,25 +1669,21 @@ lemma U_297_6 : have hlg : Real.log (8958235946698503 / 40000000000000000 : ℝ) ≤ (-(14963061266796872825393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8958235946698503 / 40000000000000000 : ℝ) = - (8958235946698503 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8958235946698503 / 5000000000000000 : ℚ)) - (U := (5831354142203127174607 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8958235946698503 / 5000000000000000 : ℝ) ≤ - (5831354142203127174607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (553040057969891 / 2500000000000000 : ℝ)) (q := - (8958235946698503 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8958235946698503 / 40000000000000000 : ℚ)) + (r' := (8958235946698503 / 5000000000000000 : ℚ)) + (U := (-(14963061266796872825393 / 10000000000000000000000 : ℚ))) + (U' := (5831354142203127174607 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (553040057969891 / 2500000000000000 : ℚ)) + (q := (8958235946698503 / 40000000000000000 : ℚ)) + (U := (-(14963061266796872825393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_7 : Uω (aρ 7) (bρ 7) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1879,25 +1691,21 @@ lemma U_297_7 : have hlg : Real.log (7910914306669263 / 40000000000000000 : ℝ) ≤ (-(1620636089527790470651 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7910914306669263 / 40000000000000000 : ℝ) = - (7910914306669263 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7910914306669263 / 5000000000000000 : ℚ)) - (U := (458805451372209529349 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7910914306669263 / 5000000000000000 : ℝ) ≤ - (458805451372209529349 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (119510049539059 / 625000000000000 : ℝ)) (q := - (7910914306669263 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7910914306669263 / 40000000000000000 : ℚ)) + (r' := (7910914306669263 / 5000000000000000 : ℚ)) + (U := (-(1620636089527790470651 / 1000000000000000000000 : ℚ))) + (U' := (458805451372209529349 / 1000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (119510049539059 / 625000000000000 : ℚ)) + (q := (7910914306669263 / 40000000000000000 : ℚ)) + (U := (-(1620636089527790470651 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_8 : Uω (aρ 8) (bρ 8) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1905,25 +1713,21 @@ lemma U_297_8 : have hlg : Real.log (6409340632257907 / 40000000000000000 : ℝ) ≤ (-(4577807632937310211223 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6409340632257907 / 40000000000000000 : ℝ) = - (6409340632257907 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6409340632257907 / 5000000000000000 : ℚ)) - (U := (620796219312689788777 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6409340632257907 / 5000000000000000 : ℝ) ≤ - (620796219312689788777 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (722457803379633 / 5000000000000000 : ℝ)) (q := - (6409340632257907 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6409340632257907 / 40000000000000000 : ℚ)) + (r' := (6409340632257907 / 5000000000000000 : ℚ)) + (U := (-(4577807632937310211223 / 2500000000000000000000 : ℚ))) + (U' := (620796219312689788777 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (722457803379633 / 5000000000000000 : ℚ)) + (q := (6409340632257907 / 40000000000000000 : ℚ)) + (U := (-(4577807632937310211223 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_9 : Uω (aρ 9) (bρ 9) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -1931,25 +1735,21 @@ lemma U_297_9 : have hlg : Real.log (3735361084134731 / 40000000000000000 : ℝ) ≤ (-(23710349633563607825731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3735361084134731 / 40000000000000000 : ℝ) = - (3735361084134731 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3735361084134731 / 2500000000000000 : ℚ)) - (U := (4015537578436392174269 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3735361084134731 / 2500000000000000 : ℝ) ≤ - (4015537578436392174269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (224445730528839 / 5000000000000000 : ℝ)) (q := - (3735361084134731 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3735361084134731 / 40000000000000000 : ℚ)) + (r' := (3735361084134731 / 2500000000000000 : ℚ)) + (U := (-(23710349633563607825731 / 10000000000000000000000 : ℚ))) + (U' := (4015537578436392174269 / 10000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1770460514531 / 6400000000000 : ℚ)) + (s := (224445730528839 / 5000000000000000 : ℚ)) + (q := (3735361084134731 / 40000000000000000 : ℚ)) + (U := (-(23710349633563607825731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_297_10 : Uω (aρ 10) (bρ 10) (1770460514531 / 6400000000000 : ℝ) ≤ @@ -2077,25 +1877,21 @@ lemma U_298_1 : have hlg : Real.log (21711481577166763 / 80000000000000000 : ℝ) ≤ (-(6520927042978397703819 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21711481577166763 / 80000000000000000 : ℝ) = - (21711481577166763 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21711481577166763 / 20000000000000000 : ℚ)) - (U := (410544760021602296181 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21711481577166763 / 20000000000000000 : ℝ) ≤ - (410544760021602296181 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1356937813800611 / 5000000000000000 : ℝ)) (q := - (21711481577166763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21711481577166763 / 80000000000000000 : ℚ)) + (r' := (21711481577166763 / 20000000000000000 : ℚ)) + (U := (-(6520927042978397703819 / 5000000000000000000000 : ℚ))) + (U' := (410544760021602296181 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (1356937813800611 / 5000000000000000 : ℚ)) + (q := (21711481577166763 / 80000000000000000 : ℚ)) + (U := (-(6520927042978397703819 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_2 : Uω (aρ 2) (bρ 2) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2103,25 +1899,21 @@ lemma U_298_2 : have hlg : Real.log (21518650662438987 / 80000000000000000 : ℝ) ≤ (-(13131066023857589108797 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21518650662438987 / 80000000000000000 : ℝ) = - (21518650662438987 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21518650662438987 / 20000000000000000 : ℚ)) - (U := (731877582142410891203 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21518650662438987 / 20000000000000000 : ℝ) ≤ - (731877582142410891203 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1344718455714639 / 5000000000000000 : ℝ)) (q := - (21518650662438987 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21518650662438987 / 80000000000000000 : ℚ)) + (r' := (21518650662438987 / 20000000000000000 : ℚ)) + (U := (-(13131066023857589108797 / 10000000000000000000000 : ℚ))) + (U' := (731877582142410891203 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (1344718455714639 / 5000000000000000 : ℚ)) + (q := (21518650662438987 / 80000000000000000 : ℚ)) + (U := (-(13131066023857589108797 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_3 : Uω (aρ 3) (bρ 3) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2129,25 +1921,21 @@ lemma U_298_3 : have hlg : Real.log (21131434035174243 / 80000000000000000 : ℝ) ≤ (-(13312649375703026812221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21131434035174243 / 80000000000000000 : ℝ) = - (21131434035174243 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21131434035174243 / 20000000000000000 : ℚ)) - (U := (550294230296973187779 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21131434035174243 / 20000000000000000 : ℝ) ≤ - (550294230296973187779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (660007215240773 / 2500000000000000 : ℝ)) (q := - (21131434035174243 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21131434035174243 / 80000000000000000 : ℚ)) + (r' := (21131434035174243 / 20000000000000000 : ℚ)) + (U := (-(13312649375703026812221 / 10000000000000000000000 : ℚ))) + (U' := (550294230296973187779 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (660007215240773 / 2500000000000000 : ℚ)) + (q := (21131434035174243 / 80000000000000000 : ℚ)) + (U := (-(13312649375703026812221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_4 : Uω (aρ 4) (bρ 4) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2155,25 +1943,21 @@ lemma U_298_4 : have hlg : Real.log (20483412556860871 / 80000000000000000 : ℝ) ≤ (-(13624112191107404353649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20483412556860871 / 80000000000000000 : ℝ) = - (20483412556860871 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20483412556860871 / 20000000000000000 : ℚ)) - (U := (238831414892595646351 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20483412556860871 / 20000000000000000 : ℝ) ≤ - (238831414892595646351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2556317672449749 / 10000000000000000 : ℝ)) (q := - (20483412556860871 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20483412556860871 / 80000000000000000 : ℚ)) + (r' := (20483412556860871 / 20000000000000000 : ℚ)) + (U := (-(13624112191107404353649 / 10000000000000000000000 : ℚ))) + (U' := (238831414892595646351 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (2556317672449749 / 10000000000000000 : ℚ)) + (q := (20483412556860871 / 80000000000000000 : ℚ)) + (U := (-(13624112191107404353649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_5 : Uω (aρ 5) (bρ 5) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2181,25 +1965,21 @@ lemma U_298_5 : have hlg : Real.log (19483293534172267 / 80000000000000000 : ℝ) ≤ (-(2824938554749409884513 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19483293534172267 / 80000000000000000 : ℝ) = - (19483293534172267 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19483293534172267 / 10000000000000000 : ℚ)) - (U := (1333944527050590115487 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19483293534172267 / 10000000000000000 : ℝ) ≤ - (1333944527050590115487 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1212238918056299 / 5000000000000000 : ℝ)) (q := - (19483293534172267 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19483293534172267 / 80000000000000000 : ℚ)) + (r' := (19483293534172267 / 10000000000000000 : ℚ)) + (U := (-(2824938554749409884513 / 2000000000000000000000 : ℚ))) + (U' := (1333944527050590115487 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (1212238918056299 / 5000000000000000 : ℚ)) + (q := (19483293534172267 / 80000000000000000 : ℚ)) + (U := (-(2824938554749409884513 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_6 : Uω (aρ 6) (bρ 6) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2207,25 +1987,21 @@ lemma U_298_6 : have hlg : Real.log (18014848304206023 / 80000000000000000 : ℝ) ≤ (-(14908303102564459612481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18014848304206023 / 80000000000000000 : ℝ) = - (18014848304206023 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18014848304206023 / 10000000000000000 : ℚ)) - (U := (5886112306435540387519 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18014848304206023 / 10000000000000000 : ℝ) ≤ - (5886112306435540387519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2224606903761037 / 10000000000000000 : ℝ)) (q := - (18014848304206023 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18014848304206023 / 80000000000000000 : ℚ)) + (r' := (18014848304206023 / 10000000000000000 : ℚ)) + (U := (-(14908303102564459612481 / 10000000000000000000000 : ℚ))) + (U' := (5886112306435540387519 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (2224606903761037 / 10000000000000000 : ℚ)) + (q := (18014848304206023 / 80000000000000000 : ℚ)) + (U := (-(14908303102564459612481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_7 : Uω (aρ 7) (bρ 7) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2233,25 +2009,21 @@ lemma U_298_7 : have hlg : Real.log (3184463717036787 / 16000000000000000 : ℝ) ≤ (-(16143048243093906018401 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3184463717036787 / 16000000000000000 : ℝ) = - (3184463717036787 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3184463717036787 / 2000000000000000 : ℚ)) - (U := (4651367165906093981599 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3184463717036787 / 2000000000000000 : ℝ) ≤ - (4651367165906093981599 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (385027170953103 / 2000000000000000 : ℝ)) (q := - (3184463717036787 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3184463717036787 / 16000000000000000 : ℚ)) + (r' := (3184463717036787 / 2000000000000000 : ℚ)) + (U := (-(16143048243093906018401 / 10000000000000000000000 : ℚ))) + (U' := (4651367165906093981599 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (385027170953103 / 2000000000000000 : ℚ)) + (q := (3184463717036787 / 16000000000000000 : ℚ)) + (U := (-(16143048243093906018401 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_8 : Uω (aρ 8) (bρ 8) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2259,25 +2031,21 @@ lemma U_298_8 : have hlg : Real.log (12926350436089839 / 80000000000000000 : ℝ) ≤ (-(18227587364746944480603 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12926350436089839 / 80000000000000000 : ℝ) = - (12926350436089839 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12926350436089839 / 10000000000000000 : ℚ)) - (U := (2566828044253055519397 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12926350436089839 / 10000000000000000 : ℝ) ≤ - (2566828044253055519397 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1459685468831991 / 10000000000000000 : ℝ)) (q := - (12926350436089839 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12926350436089839 / 80000000000000000 : ℚ)) + (r' := (12926350436089839 / 10000000000000000 : ℚ)) + (U := (-(18227587364746944480603 / 10000000000000000000000 : ℚ))) + (U' := (2566828044253055519397 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (1459685468831991 / 10000000000000000 : ℚ)) + (q := (12926350436089839 / 80000000000000000 : ℚ)) + (U := (-(18227587364746944480603 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_9 : Uω (aρ 9) (bρ 9) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2285,25 +2053,21 @@ lemma U_298_9 : have hlg : Real.log (7667434863188171 / 80000000000000000 : ℝ) ≤ (-(2345044511846416428901 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (7667434863188171 / 80000000000000000 : ℝ) = - (7667434863188171 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7667434863188171 / 5000000000000000 : ℚ)) - (U := (427544209353583571099 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7667434863188171 / 5000000000000000 : ℝ) ≤ - (427544209353583571099 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242961101983287 / 5000000000000000 : ℝ)) (q := - (7667434863188171 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7667434863188171 / 80000000000000000 : ℚ)) + (r' := (7667434863188171 / 5000000000000000 : ℚ)) + (U := (-(2345044511846416428901 / 1000000000000000000000 : ℚ))) + (U' := (427544209353583571099 / 1000000000000000000000 : ℚ)) + 4 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17782348702563 / 64000000000000 : ℚ)) + (s := (242961101983287 / 5000000000000000 : ℚ)) + (q := (7667434863188171 / 80000000000000000 : ℚ)) + (U := (-(2345044511846416428901 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_298_10 : Uω (aρ 10) (bρ 10) (17782348702563 / 64000000000000 : ℝ) ≤ @@ -2430,25 +2194,21 @@ lemma U_299_1 : have hlg : Real.log (2726082893414437 / 10000000000000000 : ℝ) ≤ (-(6498596756097873732649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2726082893414437 / 10000000000000000 : ℝ) = - (2726082893414437 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2726082893414437 / 2500000000000000 : ℚ)) - (U := (432875046902126267351 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2726082893414437 / 2500000000000000 : ℝ) ≤ - (432875046902126267351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (340752948664703 / 1250000000000000 : ℝ)) (q := - (2726082893414437 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2726082893414437 / 10000000000000000 : ℚ)) + (r' := (2726082893414437 / 2500000000000000 : ℚ)) + (U := (-(6498596756097873732649 / 5000000000000000000000 : ℚ))) + (U' := (432875046902126267351 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (340752948664703 / 1250000000000000 : ℚ)) + (q := (2726082893414437 / 10000000000000000 : ℚ)) + (U := (-(6498596756097873732649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_2 : Uω (aρ 2) (bρ 2) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2456,25 +2216,21 @@ lemma U_299_2 : have hlg : Real.log (5403961074209407 / 20000000000000000 : ℝ) ≤ (-(327150014026541970697 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5403961074209407 / 20000000000000000 : ℝ) = - (5403961074209407 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5403961074209407 / 5000000000000000 : ℚ)) - (U := (19423576123458029303 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5403961074209407 / 5000000000000000 : ℝ) ≤ - (19423576123458029303 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2701587889208157 / 10000000000000000 : ℝ)) (q := - (5403961074209407 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5403961074209407 / 20000000000000000 : ℚ)) + (r' := (5403961074209407 / 5000000000000000 : ℚ)) + (U := (-(327150014026541970697 / 250000000000000000000 : ℚ))) + (U' := (19423576123458029303 / 250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (2701587889208157 / 10000000000000000 : ℚ)) + (q := (5403961074209407 / 20000000000000000 : ℚ)) + (U := (-(327150014026541970697 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_3 : Uω (aρ 3) (bρ 3) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2482,25 +2238,21 @@ lemma U_299_3 : have hlg : Real.log (5307166198497323 / 20000000000000000 : ℝ) ≤ (-(1658342816041916903219 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5307166198497323 / 20000000000000000 : ℝ) = - (5307166198497323 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5307166198497323 / 5000000000000000 : ℚ)) - (U := (74525134708083096781 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5307166198497323 / 5000000000000000 : ℝ) ≤ - (74525134708083096781 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2652189119846073 / 10000000000000000 : ℝ)) (q := - (5307166198497323 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5307166198497323 / 20000000000000000 : ℚ)) + (r' := (5307166198497323 / 5000000000000000 : ℚ)) + (U := (-(1658342816041916903219 / 1250000000000000000000 : ℚ))) + (U' := (74525134708083096781 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (2652189119846073 / 10000000000000000 : ℚ)) + (q := (5307166198497323 / 20000000000000000 : ℚ)) + (U := (-(1658342816041916903219 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_4 : Uω (aρ 4) (bρ 4) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2508,24 +2260,21 @@ lemma U_299_4 : have hlg : Real.log (80393544784709 / 312500000000000 : ℝ) ≤ (-(2715341168884718786139 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (80393544784709 / 312500000000000 : ℝ) = (80393544784709 / 78125000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80393544784709 / 78125000000000 : ℚ)) - (U := (57247552315281213861 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (80393544784709 / 78125000000000 : ℝ) ≤ - (57247552315281213861 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1284251984317563 / 5000000000000000 : ℝ)) (q := - (80393544784709 / 312500000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80393544784709 / 312500000000000 : ℚ)) + (r' := (80393544784709 / 78125000000000 : ℚ)) + (U := (-(2715341168884718786139 / 2000000000000000000000 : ℚ))) + (U' := (57247552315281213861 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (1284251984317563 / 5000000000000000 : ℚ)) + (q := (80393544784709 / 312500000000000 : ℚ)) + (U := (-(2715341168884718786139 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_5 : Uω (aρ 5) (bρ 5) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2533,25 +2282,21 @@ lemma U_299_5 : have hlg : Real.log (4895227260949929 / 20000000000000000 : ℝ) ≤ (-(14074715707090353918203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4895227260949929 / 20000000000000000 : ℝ) = - (4895227260949929 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4895227260949929 / 2500000000000000 : ℚ)) - (U := (6719699701909646081797 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4895227260949929 / 2500000000000000 : ℝ) ≤ - (6719699701909646081797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2436734282698679 / 10000000000000000 : ℝ)) (q := - (4895227260949929 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4895227260949929 / 20000000000000000 : ℚ)) + (r' := (4895227260949929 / 2500000000000000 : ℚ)) + (U := (-(14074715707090353918203 / 10000000000000000000000 : ℚ))) + (U' := (6719699701909646081797 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (2436734282698679 / 10000000000000000 : ℚ)) + (q := (4895227260949929 / 20000000000000000 : ℚ)) + (U := (-(14074715707090353918203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_6 : Uω (aρ 6) (bρ 6) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2559,25 +2304,21 @@ lemma U_299_6 : have hlg : Real.log (2264151444451861 / 10000000000000000 : ℝ) ≤ (-(7426925208423690697017 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2264151444451861 / 10000000000000000 : ℝ) = - (2264151444451861 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2264151444451861 / 1250000000000000 : ℚ)) - (U := (2970282496076309302983 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2264151444451861 / 1250000000000000 : ℝ) ≤ - (2970282496076309302983 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (279631285724059 / 1250000000000000 : ℝ)) (q := - (2264151444451861 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2264151444451861 / 10000000000000000 : ℚ)) + (r' := (2264151444451861 / 1250000000000000 : ℚ)) + (U := (-(7426925208423690697017 / 5000000000000000000000 : ℚ))) + (U' := (2970282496076309302983 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (279631285724059 / 1250000000000000 : ℚ)) + (q := (2264151444451861 / 10000000000000000 : ℚ)) + (U := (-(7426925208423690697017 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_7 : Uω (aρ 7) (bρ 7) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2585,25 +2326,21 @@ lemma U_299_7 : have hlg : Real.log (2002845705585937 / 10000000000000000 : ℝ) ≤ (-(3216032140314322800777 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2002845705585937 / 10000000000000000 : ℝ) = - (2002845705585937 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2002845705585937 / 1250000000000000 : ℚ)) - (U := (942850941485677199223 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2002845705585937 / 1250000000000000 : ℝ) ≤ - (942850941485677199223 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121131261801289 / 625000000000000 : ℝ)) (q := - (2002845705585937 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2002845705585937 / 10000000000000000 : ℚ)) + (r' := (2002845705585937 / 1250000000000000 : ℚ)) + (U := (-(3216032140314322800777 / 2000000000000000000000 : ℚ))) + (U' := (942850941485677199223 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (121131261801289 / 625000000000000 : ℚ)) + (q := (2002845705585937 / 10000000000000000 : ℚ)) + (U := (-(3216032140314322800777 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_8 : Uω (aρ 8) (bρ 8) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2611,24 +2348,21 @@ lemma U_299_8 : have hlg : Real.log (81461425667013 / 500000000000000 : ℝ) ≤ (-(18144784941387903088781 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (81461425667013 / 500000000000000 : ℝ) = (81461425667013 / 62500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (81461425667013 / 62500000000000 : ℚ)) - (U := (2649630467612096911219 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (81461425667013 / 62500000000000 : ℝ) ≤ - (2649630467612096911219 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (147440745566927 / 1000000000000000 : ℝ)) (q := - (81461425667013 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (81461425667013 / 500000000000000 : ℚ)) + (r' := (81461425667013 / 62500000000000 : ℚ)) + (U := (-(18144784941387903088781 / 10000000000000000000000 : ℚ))) + (U' := (2649630467612096911219 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (147440745566927 / 1000000000000000 : ℚ)) + (q := (81461425667013 / 500000000000000 : ℚ)) + (U := (-(18144784941387903088781 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_9 : Uω (aρ 9) (bρ 9) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2636,24 +2370,21 @@ lemma U_299_9 : have hlg : Real.log (98184580963581 / 1000000000000000 : ℝ) ≤ (-(11604530457872435747047 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (98184580963581 / 1000000000000000 : ℝ) = (98184580963581 / 62500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (98184580963581 / 62500000000000 : ℚ)) - (U := (2258413148127564252953 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (98184580963581 / 62500000000000 : ℝ) ≤ - (2258413148127564252953 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (52060767662037 / 1000000000000000 : ℝ)) (q := - (98184580963581 / 1000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (98184580963581 / 1000000000000000 : ℚ)) + (r' := (98184580963581 / 62500000000000 : ℚ)) + (U := (-(11604530457872435747047 / 5000000000000000000000 : ℚ))) + (U' := (2258413148127564252953 / 5000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2232511532477 / 8000000000000 : ℚ)) + (s := (52060767662037 / 1000000000000000 : ℚ)) + (q := (98184580963581 / 1000000000000000 : ℚ)) + (U := (-(11604530457872435747047 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_299_10 : Uω (aρ 10) (bρ 10) (2232511532477 / 8000000000000 : ℝ) ≤ @@ -2780,25 +2511,21 @@ lemma U_300_1 : have hlg : Real.log (21905844698621997 / 80000000000000000 : ℝ) ≤ (-(12952731517223761911667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21905844698621997 / 80000000000000000 : ℝ) = - (21905844698621997 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21905844698621997 / 20000000000000000 : ℚ)) - (U := (910212088776238088333 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21905844698621997 / 20000000000000000 : ℝ) ≤ - (910212088776238088333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (684542886580867 / 2500000000000000 : ℝ)) (q := - (21905844698621997 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21905844698621997 / 80000000000000000 : ℚ)) + (r' := (21905844698621997 / 20000000000000000 : ℚ)) + (U := (-(12952731517223761911667 / 10000000000000000000000 : ℚ))) + (U' := (910212088776238088333 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (684542886580867 / 2500000000000000 : ℚ)) + (q := (21905844698621997 / 80000000000000000 : ℚ)) + (U := (-(12952731517223761911667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_2 : Uω (aρ 2) (bρ 2) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2806,25 +2533,21 @@ lemma U_300_2 : have hlg : Real.log (21713037804200553 / 80000000000000000 : ℝ) ≤ (-(1630142166947326220879 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21713037804200553 / 80000000000000000 : ℝ) = - (21713037804200553 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21713037804200553 / 20000000000000000 : ℚ)) - (U := (102725783802673779121 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21713037804200553 / 20000000000000000 : ℝ) ≤ - (102725783802673779121 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2713738835228107 / 10000000000000000 : ℝ)) (q := - (21713037804200553 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21713037804200553 / 80000000000000000 : ℚ)) + (r' := (21713037804200553 / 20000000000000000 : ℚ)) + (U := (-(1630142166947326220879 / 1250000000000000000000 : ℚ))) + (U' := (102725783802673779121 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (2713738835228107 / 10000000000000000 : ℚ)) + (q := (21713037804200553 / 80000000000000000 : ℚ)) + (U := (-(1630142166947326220879 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_3 : Uω (aρ 3) (bρ 3) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2832,25 +2555,21 @@ lemma U_300_3 : have hlg : Real.log (21325895084666693 / 80000000000000000 : ℝ) ≤ (-(13221045681674648191651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21325895084666693 / 80000000000000000 : ℝ) = - (21325895084666693 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21325895084666693 / 20000000000000000 : ℚ)) - (U := (641897924325351808349 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21325895084666693 / 20000000000000000 : ℝ) ≤ - (641897924325351808349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1332174630847321 / 5000000000000000 : ℝ)) (q := - (21325895084666693 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21325895084666693 / 80000000000000000 : ℚ)) + (r' := (21325895084666693 / 20000000000000000 : ℚ)) + (U := (-(13221045681674648191651 / 10000000000000000000000 : ℚ))) + (U' := (641897924325351808349 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (1332174630847321 / 5000000000000000 : ℚ)) + (q := (21325895084666693 / 80000000000000000 : ℚ)) + (U := (-(13221045681674648191651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_4 : Uω (aρ 4) (bρ 4) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2858,25 +2577,21 @@ lemma U_300_4 : have hlg : Real.log (20678080907039941 / 80000000000000000 : ℝ) ≤ (-(3382380970715133003067 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20678080907039941 / 80000000000000000 : ℝ) = - (20678080907039941 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20678080907039941 / 20000000000000000 : ℚ)) - (U := (83354930784866996933 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20678080907039941 / 20000000000000000 : ℝ) ≤ - (83354930784866996933 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1290344949176477 / 5000000000000000 : ℝ)) (q := - (20678080907039941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20678080907039941 / 80000000000000000 : ℚ)) + (r' := (20678080907039941 / 20000000000000000 : ℚ)) + (U := (-(3382380970715133003067 / 2500000000000000000000 : ℚ))) + (U' := (83354930784866996933 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (1290344949176477 / 5000000000000000 : ℚ)) + (q := (20678080907039941 / 80000000000000000 : ℚ)) + (U := (-(3382380970715133003067 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_5 : Uω (aρ 5) (bρ 5) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2884,25 +2599,21 @@ lemma U_300_5 : have hlg : Real.log (787140808324557 / 3200000000000000 : ℝ) ≤ (-(1753123672217734173881 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (787140808324557 / 3200000000000000 : ℝ) = - (787140808324557 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (787140808324557 / 400000000000000 : ℚ)) - (U := (846178253907265826119 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (787140808324557 / 400000000000000 : ℝ) ≤ - (846178253907265826119 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48979792859129 / 200000000000000 : ℝ)) (q := - (787140808324557 / 3200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (787140808324557 / 3200000000000000 : ℚ)) + (r' := (787140808324557 / 400000000000000 : ℚ)) + (U := (-(1753123672217734173881 / 1250000000000000000000 : ℚ))) + (U' := (846178253907265826119 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (48979792859129 / 200000000000000 : ℚ)) + (q := (787140808324557 / 3200000000000000 : ℚ)) + (U := (-(1753123672217734173881 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_6 : Uω (aρ 6) (bρ 6) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2910,25 +2621,21 @@ lemma U_300_6 : have hlg : Real.log (3642312373200597 / 16000000000000000 : ℝ) ≤ (-(14799699741453893134069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3642312373200597 / 16000000000000000 : ℝ) = - (3642312373200597 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3642312373200597 / 2000000000000000 : ℚ)) - (U := (5994715667546106865931 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3642312373200597 / 2000000000000000 : ℝ) ≤ - (5994715667546106865931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (449898086513743 / 2000000000000000 : ℝ)) (q := - (3642312373200597 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3642312373200597 / 16000000000000000 : ℚ)) + (r' := (3642312373200597 / 2000000000000000 : ℚ)) + (U := (-(14799699741453893134069 / 10000000000000000000000 : ℚ))) + (U' := (5994715667546106865931 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (449898086513743 / 2000000000000000 : ℚ)) + (q := (3642312373200597 / 16000000000000000 : ℚ)) + (U := (-(14799699741453893134069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_7 : Uω (aρ 7) (bρ 7) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2936,25 +2643,21 @@ lemma U_300_7 : have hlg : Real.log (3224634129455817 / 16000000000000000 : ℝ) ≤ (-(320353845175740239713 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3224634129455817 / 16000000000000000 : ℝ) = - (3224634129455817 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3224634129455817 / 2000000000000000 : ℚ)) - (U := (95534463004259760287 / 200000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3224634129455817 / 2000000000000000 : ℝ) ≤ - (95534463004259760287 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (97552700432387 / 500000000000000 : ℝ)) (q := - (3224634129455817 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3224634129455817 / 16000000000000000 : ℚ)) + (r' := (3224634129455817 / 2000000000000000 : ℚ)) + (U := (-(320353845175740239713 / 200000000000000000000 : ℚ))) + (U' := (95534463004259760287 / 200000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (97552700432387 / 500000000000000 : ℚ)) + (q := (3224634129455817 / 16000000000000000 : ℚ)) + (U := (-(320353845175740239713 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_8 : Uω (aρ 8) (bρ 8) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2962,25 +2665,21 @@ lemma U_300_8 : have hlg : Real.log (13141119956302201 / 80000000000000000 : ℝ) ≤ (-(18062803918743756208487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13141119956302201 / 80000000000000000 : ℝ) = - (13141119956302201 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13141119956302201 / 10000000000000000 : ℚ)) - (U := (2731611490256243791513 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13141119956302201 / 10000000000000000 : ℝ) ≤ - (2731611490256243791513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1489082987243519 / 10000000000000000 : ℝ)) (q := - (13141119956302201 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13141119956302201 / 80000000000000000 : ℚ)) + (r' := (13141119956302201 / 10000000000000000 : ℚ)) + (U := (-(18062803918743756208487 / 10000000000000000000000 : ℚ))) + (U' := (2731611490256243791513 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (1489082987243519 / 10000000000000000 : ℚ)) + (q := (13141119956302201 / 80000000000000000 : ℚ)) + (U := (-(18062803918743756208487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_9 : Uω (aρ 9) (bρ 9) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -2988,25 +2687,21 @@ lemma U_300_9 : have hlg : Real.log (1606896336678253 / 16000000000000000 : ℝ) ≤ (-(22982841438817210519433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1606896336678253 / 16000000000000000 : ℝ) = - (1606896336678253 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1606896336678253 / 1000000000000000 : ℚ)) - (U := (4743045773182789480567 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1606896336678253 / 1000000000000000 : ℝ) ≤ - (4743045773182789480567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110677809475157 / 2000000000000000 : ℝ)) (q := - (1606896336678253 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1606896336678253 / 16000000000000000 : ℚ)) + (r' := (1606896336678253 / 1000000000000000 : ℚ)) + (U := (-(22982841438817210519433 / 10000000000000000000000 : ℚ))) + (U' := (4743045773182789480567 / 10000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17937835817069 / 64000000000000 : ℚ)) + (s := (110677809475157 / 2000000000000000 : ℚ)) + (q := (1606896336678253 / 16000000000000000 : ℚ)) + (U := (-(22982841438817210519433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_300_10 : Uω (aρ 10) (bρ 10) (17937835817069 / 64000000000000 : ℝ) ≤ @@ -3134,25 +2829,21 @@ lemma U_301_1 : have hlg : Real.log (11001513115667967 / 40000000000000000 : ℝ) ≤ (-(12908466342858148682791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11001513115667967 / 40000000000000000 : ℝ) = - (11001513115667967 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11001513115667967 / 10000000000000000 : ℚ)) - (U := (954477263141851317209 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11001513115667967 / 10000000000000000 : ℝ) ≤ - (954477263141851317209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2750319498681171 / 10000000000000000 : ℝ)) (q := - (11001513115667967 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11001513115667967 / 40000000000000000 : ℚ)) + (r' := (11001513115667967 / 10000000000000000 : ℚ)) + (U := (-(12908466342858148682791 / 10000000000000000000000 : ℚ))) + (U' := (954477263141851317209 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (2750319498681171 / 10000000000000000 : ℚ)) + (q := (11001513115667967 / 40000000000000000 : ℚ)) + (U := (-(12908466342858148682791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_2 : Uω (aρ 2) (bρ 2) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3160,25 +2851,21 @@ lemma U_301_2 : have hlg : Real.log (10905115593113297 / 40000000000000000 : ℝ) ≤ (-(12996474539862435628569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10905115593113297 / 40000000000000000 : ℝ) = - (10905115593113297 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10905115593113297 / 10000000000000000 : ℚ)) - (U := (866469066137564371431 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10905115593113297 / 10000000000000000 : ℝ) ≤ - (866469066137564371431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (681472437478459 / 2500000000000000 : ℝ)) (q := - (10905115593113297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10905115593113297 / 40000000000000000 : ℚ)) + (r' := (10905115593113297 / 10000000000000000 : ℚ)) + (U := (-(12996474539862435628569 / 10000000000000000000000 : ℚ))) + (U' := (866469066137564371431 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (681472437478459 / 2500000000000000 : ℚ)) + (q := (10905115593113297 / 40000000000000000 : ℚ)) + (U := (-(12996474539862435628569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_3 : Uω (aρ 3) (bρ 3) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3186,25 +2873,21 @@ lemma U_301_3 : have hlg : Real.log (10711562456793547 / 40000000000000000 : ℝ) ≤ (-(1646944615148955121397 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10711562456793547 / 40000000000000000 : ℝ) = - (10711562456793547 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10711562456793547 / 10000000000000000 : ℚ)) - (U := (85923335601044878603 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10711562456793547 / 10000000000000000 : ℝ) ≤ - (85923335601044878603 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2676509288103961 / 10000000000000000 : ℝ)) (q := - (10711562456793547 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10711562456793547 / 40000000000000000 : ℚ)) + (r' := (10711562456793547 / 10000000000000000 : ℚ)) + (U := (-(1646944615148955121397 / 1250000000000000000000 : ℚ))) + (U' := (85923335601044878603 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (2676509288103961 / 10000000000000000 : ℚ)) + (q := (10711562456793547 / 40000000000000000 : ℚ)) + (U := (-(1646944615148955121397 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_4 : Uω (aρ 4) (bρ 4) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3212,25 +2895,21 @@ lemma U_301_4 : have hlg : Real.log (415508258079839 / 1600000000000000 : ℝ) ≤ (-(1348256418568254684709 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (415508258079839 / 1600000000000000 : ℝ) = - (415508258079839 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (415508258079839 / 400000000000000 : ℚ)) - (U := (38037942031745315291 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (415508258079839 / 400000000000000 : ℝ) ≤ - (38037942031745315291 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103715018670807 / 400000000000000 : ℝ)) (q := - (415508258079839 / 1600000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (415508258079839 / 1600000000000000 : ℚ)) + (r' := (415508258079839 / 400000000000000 : ℚ)) + (U := (-(1348256418568254684709 / 1000000000000000000000 : ℚ))) + (U' := (38037942031745315291 / 1000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (103715018670807 / 400000000000000 : ℚ)) + (q := (415508258079839 / 1600000000000000 : ℚ)) + (U := (-(1348256418568254684709 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_5 : Uω (aρ 5) (bρ 5) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3238,25 +2917,21 @@ lemma U_301_5 : have hlg : Real.log (1977612709202521 / 8000000000000000 : ℝ) ≤ (-(3493877815151177753499 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1977612709202521 / 8000000000000000 : ℝ) = - (1977612709202521 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1977612709202521 / 1000000000000000 : ℚ)) - (U := (1704726037098822246501 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1977612709202521 / 1000000000000000 : ℝ) ≤ - (1704726037098822246501 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (246124393311349 / 1000000000000000 : ℝ)) (q := - (1977612709202521 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1977612709202521 / 8000000000000000 : ℚ)) + (r' := (1977612709202521 / 1000000000000000 : ℚ)) + (U := (-(3493877815151177753499 / 2500000000000000000000 : ℚ))) + (U' := (1704726037098822246501 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (246124393311349 / 1000000000000000 : ℚ)) + (q := (1977612709202521 / 8000000000000000 : ℚ)) + (U := (-(3493877815151177753499 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_6 : Uω (aρ 6) (bρ 6) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3264,25 +2939,21 @@ lemma U_301_6 : have hlg : Real.log (9154949724444683 / 40000000000000000 : ℝ) ≤ (-(737292383409021471139 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9154949724444683 / 40000000000000000 : ℝ) = - (9154949724444683 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9154949724444683 / 5000000000000000 : ℚ)) - (U := (302428387040978528861 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9154949724444683 / 5000000000000000 : ℝ) ≤ - (302428387040978528861 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2261927397469529 / 10000000000000000 : ℝ)) (q := - (9154949724444683 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9154949724444683 / 40000000000000000 : ℚ)) + (r' := (9154949724444683 / 5000000000000000 : ℚ)) + (U := (-(737292383409021471139 / 500000000000000000000 : ℚ))) + (U' := (302428387040978528861 / 500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (2261927397469529 / 10000000000000000 : ℚ)) + (q := (9154949724444683 / 40000000000000000 : ℚ)) + (U := (-(737292383409021471139 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_7 : Uω (aρ 7) (bρ 7) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3290,25 +2961,21 @@ lemma U_301_7 : have hlg : Real.log (8111767212567727 / 40000000000000000 : ℝ) ≤ (-(7977818517863032778631 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8111767212567727 / 40000000000000000 : ℝ) = - (8111767212567727 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8111767212567727 / 5000000000000000 : ℚ)) - (U := (2419389186636967221369 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8111767212567727 / 5000000000000000 : ℝ) ≤ - (2419389186636967221369 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1963997522291051 / 10000000000000000 : ℝ)) (q := - (8111767212567727 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8111767212567727 / 40000000000000000 : ℚ)) + (r' := (8111767212567727 / 5000000000000000 : ℚ)) + (U := (-(7977818517863032778631 / 5000000000000000000000 : ℚ))) + (U' := (2419389186636967221369 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (1963997522291051 / 10000000000000000 : ℚ)) + (q := (8111767212567727 / 40000000000000000 : ℚ)) + (U := (-(7977818517863032778631 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_8 : Uω (aρ 8) (bρ 8) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3316,25 +2983,21 @@ lemma U_301_8 : have hlg : Real.log (6624115712704663 / 40000000000000000 : ℝ) ≤ (-(3596325135396607525091 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6624115712704663 / 40000000000000000 : ℝ) = - (6624115712704663 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6624115712704663 / 5000000000000000 : ℚ)) - (U := (562557946403392474909 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6624115712704663 / 5000000000000000 : ℝ) ≤ - (562557946403392474909 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1503713423699519 / 10000000000000000 : ℝ)) (q := - (6624115712704663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6624115712704663 / 40000000000000000 : ℚ)) + (r' := (6624115712704663 / 5000000000000000 : ℚ)) + (U := (-(3596325135396607525091 / 2000000000000000000000 : ℚ))) + (U' := (562557946403392474909 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (1503713423699519 / 10000000000000000 : ℚ)) + (q := (6624115712704663 / 40000000000000000 : ℚ)) + (U := (-(3596325135396607525091 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_9 : Uω (aρ 9) (bρ 9) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3342,25 +3005,21 @@ lemma U_301_9 : have hlg : Real.log (4103931064846051 / 40000000000000000 : ℝ) ≤ (-(2276934142411561312073 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4103931064846051 / 40000000000000000 : ℝ) = - (4103931064846051 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4103931064846051 / 2500000000000000 : ℚ)) - (U := (495654578788438687927 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4103931064846051 / 2500000000000000 : ℝ) ≤ - (495654578788438687927 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (584586728130213 / 10000000000000000 : ℝ)) (q := - (4103931064846051 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4103931064846051 / 40000000000000000 : ℚ)) + (r' := (4103931064846051 / 2500000000000000 : ℚ)) + (U := (-(2276934142411561312073 / 1000000000000000000000 : ℚ))) + (U' := (495654578788438687927 / 1000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9007789687161 / 32000000000000 : ℚ)) + (s := (584586728130213 / 10000000000000000 : ℚ)) + (q := (4103931064846051 / 40000000000000000 : ℚ)) + (U := (-(2276934142411561312073 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_301_10 : Uω (aρ 10) (bρ 10) (9007789687161 / 32000000000000 : ℝ) ≤ @@ -3488,25 +3147,21 @@ lemma U_302_1 : have hlg : Real.log (4420041549140519 / 16000000000000000 : ℝ) ≤ (-(6432198127082150183279 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4420041549140519 / 16000000000000000 : ℝ) = - (4420041549140519 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4420041549140519 / 4000000000000000 : ℚ)) - (U := (499273675917849816721 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4420041549140519 / 4000000000000000 : ℝ) ≤ - (499273675917849816721 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (552493489290411 / 2000000000000000 : ℝ)) (q := - (4420041549140519 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4420041549140519 / 16000000000000000 : ℚ)) + (r' := (4420041549140519 / 4000000000000000 : ℚ)) + (U := (-(6432198127082150183279 / 5000000000000000000000 : ℚ))) + (U' := (499273675917849816721 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (552493489290411 / 2000000000000000 : ℚ)) + (q := (4420041549140519 / 16000000000000000 : ℚ)) + (U := (-(6432198127082150183279 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_2 : Uω (aρ 2) (bρ 2) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3514,25 +3169,21 @@ lemma U_302_2 : have hlg : Real.log (21907424444584411 / 80000000000000000 : ℝ) ≤ (-(1619001298812421734721 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21907424444584411 / 80000000000000000 : ℝ) = - (21907424444584411 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21907424444584411 / 20000000000000000 : ℚ)) - (U := (113866651937578265279 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21907424444584411 / 20000000000000000 : ℝ) ≤ - (113866651937578265279 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2738040633682509 / 10000000000000000 : ℝ)) (q := - (21907424444584411 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21907424444584411 / 80000000000000000 : ℚ)) + (r' := (21907424444584411 / 20000000000000000 : ℚ)) + (U := (-(1619001298812421734721 / 1250000000000000000000 : ℚ))) + (U' := (113866651937578265279 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (2738040633682509 / 10000000000000000 : ℚ)) + (q := (21907424444584411 / 80000000000000000 : ℚ)) + (U := (-(1619001298812421734721 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_3 : Uω (aρ 3) (bρ 3) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3540,25 +3191,21 @@ lemma U_302_3 : have hlg : Real.log (21520354287015651 / 80000000000000000 : ℝ) ≤ (-(6565137179223193084959 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21520354287015651 / 80000000000000000 : ℝ) = - (21520354287015651 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21520354287015651 / 20000000000000000 : ℚ)) - (U := (366334623776806915041 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21520354287015651 / 20000000000000000 : ℝ) ≤ - (366334623776806915041 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2688669200640319 / 10000000000000000 : ℝ)) (q := - (21520354287015651 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21520354287015651 / 80000000000000000 : ℚ)) + (r' := (21520354287015651 / 20000000000000000 : ℚ)) + (U := (-(6565137179223193084959 / 5000000000000000000000 : ℚ))) + (U' := (366334623776806915041 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (2688669200640319 / 10000000000000000 : ℚ)) + (q := (21520354287015651 / 80000000000000000 : ℚ)) + (U := (-(6565137179223193084959 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_4 : Uω (aρ 4) (bρ 4) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3566,25 +3213,21 @@ lemma U_302_4 : have hlg : Real.log (20872743476022003 / 80000000000000000 : ℝ) ≤ (-(335895616554249685107 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20872743476022003 / 80000000000000000 : ℝ) = - (20872743476022003 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20872743476022003 / 20000000000000000 : ℚ)) - (U := (10677973595750314893 / 250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20872743476022003 / 20000000000000000 : ℝ) ≤ - (10677973595750314893 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2605060678956907 / 10000000000000000 : ℝ)) (q := - (20872743476022003 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20872743476022003 / 80000000000000000 : ℚ)) + (r' := (20872743476022003 / 20000000000000000 : ℚ)) + (U := (-(335895616554249685107 / 250000000000000000000 : ℚ))) + (U' := (10677973595750314893 / 250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (2605060678956907 / 10000000000000000 : ℚ)) + (q := (20872743476022003 / 80000000000000000 : ℚ)) + (U := (-(335895616554249685107 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_5 : Uω (aρ 5) (bρ 5) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3592,25 +3235,21 @@ lemma U_302_5 : have hlg : Real.log (19873729759151967 / 80000000000000000 : ℝ) ≤ (-(6963139434426427686679 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19873729759151967 / 80000000000000000 : ℝ) = - (19873729759151967 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19873729759151967 / 10000000000000000 : ℚ)) - (U := (3434068270073572313321 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19873729759151967 / 10000000000000000 : ℝ) ≤ - (3434068270073572313321 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1236748584537199 / 5000000000000000 : ℝ)) (q := - (19873729759151967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19873729759151967 / 80000000000000000 : ℚ)) + (r' := (19873729759151967 / 10000000000000000 : ℚ)) + (U := (-(6963139434426427686679 / 5000000000000000000000 : ℚ))) + (U' := (3434068270073572313321 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (1236748584537199 / 5000000000000000 : ℚ)) + (q := (19873729759151967 / 80000000000000000 : ℚ)) + (U := (-(6963139434426427686679 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_6 : Uω (aρ 6) (bρ 6) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3618,25 +3257,21 @@ lemma U_302_6 : have hlg : Real.log (18408224513068699 / 80000000000000000 : ℝ) ≤ (-(14692290847409693047619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18408224513068699 / 80000000000000000 : ℝ) = - (18408224513068699 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18408224513068699 / 10000000000000000 : ℚ)) - (U := (6102124561590306952381 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18408224513068699 / 10000000000000000 : ℝ) ≤ - (6102124561590306952381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2274361232693581 / 10000000000000000 : ℝ)) (q := - (18408224513068699 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18408224513068699 / 80000000000000000 : ℚ)) + (r' := (18408224513068699 / 10000000000000000 : ℚ)) + (U := (-(14692290847409693047619 / 10000000000000000000000 : ℚ))) + (U' := (6102124561590306952381 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (2274361232693581 / 10000000000000000 : ℚ)) + (q := (18408224513068699 / 80000000000000000 : ℚ)) + (U := (-(14692290847409693047619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_7 : Uω (aρ 7) (bρ 7) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3644,25 +3279,21 @@ lemma U_302_7 : have hlg : Real.log (16323857787985871 / 80000000000000000 : ℝ) ≤ (-(7946994641123173545093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16323857787985871 / 80000000000000000 : ℝ) = - (16323857787985871 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16323857787985871 / 10000000000000000 : ℚ)) - (U := (2450213063376826454907 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16323857787985871 / 10000000000000000 : ℝ) ≤ - (2450213063376826454907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (988465466091437 / 5000000000000000 : ℝ)) (q := - (16323857787985871 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16323857787985871 / 80000000000000000 : ℚ)) + (r' := (16323857787985871 / 10000000000000000 : ℚ)) + (U := (-(7946994641123173545093 / 5000000000000000000000 : ℚ))) + (U' := (2450213063376826454907 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (988465466091437 / 5000000000000000 : ℚ)) + (q := (16323857787985871 / 80000000000000000 : ℚ)) + (U := (-(7946994641123173545093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_8 : Uω (aρ 8) (bρ 8) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3670,25 +3301,21 @@ lemma U_302_8 : have hlg : Real.log (13355167728518967 / 80000000000000000 : ℝ) ≤ (-(3580246456361628938953 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13355167728518967 / 80000000000000000 : ℝ) = - (13355167728518967 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13355167728518967 / 10000000000000000 : ℚ)) - (U := (578636625438371061047 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13355167728518967 / 10000000000000000 : ℝ) ≤ - (578636625438371061047 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (379575017164037 / 2500000000000000 : ℝ)) (q := - (13355167728518967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13355167728518967 / 80000000000000000 : ℚ)) + (r' := (13355167728518967 / 10000000000000000 : ℚ)) + (U := (-(3580246456361628938953 / 2000000000000000000000 : ℚ))) + (U' := (578636625438371061047 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (379575017164037 / 2500000000000000 : ℚ)) + (q := (13355167728518967 / 80000000000000000 : ℚ)) + (U := (-(3580246456361628938953 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_9 : Uω (aρ 9) (bρ 9) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3696,25 +3323,21 @@ lemma U_302_9 : have hlg : Real.log (8375872928878307 / 80000000000000000 : ℝ) ≤ (-(11283356655203721398811 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8375872928878307 / 80000000000000000 : ℝ) = - (8375872928878307 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8375872928878307 / 5000000000000000 : ℚ)) - (U := (2579586950796278601189 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8375872928878307 / 5000000000000000 : ℝ) ≤ - (2579586950796278601189 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (614441997105983 / 10000000000000000 : ℝ)) (q := - (8375872928878307 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8375872928878307 / 80000000000000000 : ℚ)) + (r' := (8375872928878307 / 5000000000000000 : ℚ)) + (U := (-(11283356655203721398811 / 5000000000000000000000 : ℚ))) + (U' := (2579586950796278601189 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (723732917263 / 2560000000000 : ℚ)) + (s := (614441997105983 / 10000000000000000 : ℚ)) + (q := (8375872928878307 / 80000000000000000 : ℚ)) + (U := (-(11283356655203721398811 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_302_10 : Uω (aρ 10) (bρ 10) (723732917263 / 2560000000000 : ℝ) ≤ @@ -3840,25 +3463,21 @@ lemma U_303_1 : have hlg : Real.log (5549347310490741 / 20000000000000000 : ℝ) ≤ (-(12820519539047609253381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5549347310490741 / 20000000000000000 : ℝ) = - (5549347310490741 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5549347310490741 / 5000000000000000 : ℚ)) - (U := (1042424066952390746619 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5549347310490741 / 5000000000000000 : ℝ) ≤ - (1042424066952390746619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1387307694848183 / 5000000000000000 : ℝ)) (q := - (5549347310490741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5549347310490741 / 20000000000000000 : ℚ)) + (r' := (5549347310490741 / 5000000000000000 : ℚ)) + (U := (-(12820519539047609253381 / 10000000000000000000000 : ℚ))) + (U' := (1042424066952390746619 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (1387307694848183 / 5000000000000000 : ℚ)) + (q := (5549347310490741 / 20000000000000000 : ℚ)) + (U := (-(12820519539047609253381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_2 : Uω (aρ 2) (bρ 2) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3866,25 +3485,21 @@ lemma U_303_2 : have hlg : Real.log (1100230879045659 / 4000000000000000 : ℝ) ≤ (-(12907743127780000518383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1100230879045659 / 4000000000000000 : ℝ) = - (1100230879045659 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1100230879045659 / 1000000000000000 : ℚ)) - (U := (955200478219999481617 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1100230879045659 / 1000000000000000 : ℝ) ≤ - (955200478219999481617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (34377393586799 / 125000000000000 : ℝ)) (q := - (1100230879045659 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1100230879045659 / 4000000000000000 : ℚ)) + (r' := (1100230879045659 / 1000000000000000 : ℚ)) + (U := (-(12907743127780000518383 / 10000000000000000000000 : ℚ))) + (U' := (955200478219999481617 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (34377393586799 / 125000000000000 : ℚ)) + (q := (1100230879045659 / 4000000000000000 : ℚ)) + (U := (-(12907743127780000518383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_3 : Uω (aρ 3) (bρ 3) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3892,25 +3507,21 @@ lemma U_303_3 : have hlg : Real.log (2702197901388079 / 10000000000000000 : ℝ) ≤ (-(6542598065307995406991 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2702197901388079 / 10000000000000000 : ℝ) = - (2702197901388079 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2702197901388079 / 2500000000000000 : ℚ)) - (U := (388873737692004593009 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2702197901388079 / 2500000000000000 : ℝ) ≤ - (388873737692004593009 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2700829000841783 / 10000000000000000 : ℝ)) (q := - (2702197901388079 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2702197901388079 / 10000000000000000 : ℚ)) + (r' := (2702197901388079 / 2500000000000000 : ℚ)) + (U := (-(6542598065307995406991 / 5000000000000000000000 : ℚ))) + (U' := (388873737692004593009 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (2700829000841783 / 10000000000000000 : ℚ)) + (q := (2702197901388079 / 10000000000000000 : ℚ)) + (U := (-(6542598065307995406991 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_4 : Uω (aρ 4) (bρ 4) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3918,25 +3529,21 @@ lemma U_303_4 : have hlg : Real.log (655314770094759 / 2500000000000000 : ℝ) ≤ (-(13389303251053762690677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (655314770094759 / 2500000000000000 : ℝ) = - (655314770094759 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (655314770094759 / 625000000000000 : ℚ)) - (U := (473640354946237309323 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (655314770094759 / 625000000000000 : ℝ) ≤ - (473640354946237309323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2617245539888697 / 10000000000000000 : ℝ)) (q := - (655314770094759 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (655314770094759 / 2500000000000000 : ℚ)) + (r' := (655314770094759 / 625000000000000 : ℚ)) + (U := (-(13389303251053762690677 / 10000000000000000000000 : ℚ))) + (U' := (473640354946237309323 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (2617245539888697 / 10000000000000000 : ℚ)) + (q := (655314770094759 / 2500000000000000 : ℚ)) + (U := (-(13389303251053762690677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_5 : Uω (aρ 5) (bρ 5) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3944,25 +3551,21 @@ lemma U_303_5 : have hlg : Real.log (1248208016990797 / 5000000000000000 : ℝ) ≤ (-(13877289753155558398313 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1248208016990797 / 5000000000000000 : ℝ) = - (1248208016990797 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1248208016990797 / 625000000000000 : ℚ)) - (U := (6917125655844441601687 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (1248208016990797 / 625000000000000 : ℝ) ≤ - (6917125655844441601687 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2485749366428813 / 10000000000000000 : ℝ)) (q := - (1248208016990797 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1248208016990797 / 5000000000000000 : ℚ)) + (r' := (1248208016990797 / 625000000000000 : ℚ)) + (U := (-(13877289753155558398313 / 10000000000000000000000 : ℚ))) + (U' := (6917125655844441601687 / 10000000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (2485749366428813 / 10000000000000000 : ℚ)) + (q := (1248208016990797 / 5000000000000000 : ℚ)) + (U := (-(13877289753155558398313 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_6 : Uω (aρ 6) (bρ 6) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3970,25 +3573,21 @@ lemma U_303_6 : have hlg : Real.log (4626634315685649 / 20000000000000000 : ℝ) ≤ (-(7319512993375079674599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4626634315685649 / 20000000000000000 : ℝ) = - (4626634315685649 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4626634315685649 / 2500000000000000 : ℚ)) - (U := (3077694711124920325401 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4626634315685649 / 2500000000000000 : ℝ) ≤ - (3077694711124920325401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1143395994645637 / 5000000000000000 : ℝ)) (q := - (4626634315685649 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4626634315685649 / 20000000000000000 : ℚ)) + (r' := (4626634315685649 / 2500000000000000 : ℚ)) + (U := (-(7319512993375079674599 / 5000000000000000000000 : ℚ))) + (U' := (3077694711124920325401 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (1143395994645637 / 5000000000000000 : ℚ)) + (q := (4626634315685649 / 20000000000000000 : ℚ)) + (U := (-(7319512993375079674599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_7 : Uω (aρ 7) (bρ 7) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -3996,25 +3595,21 @@ lemma U_303_7 : have hlg : Real.log (205301769048547 / 1000000000000000 : ℝ) ≤ (-(15832743373195214114231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (205301769048547 / 1000000000000000 : ℝ) = - (205301769048547 / 125000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (205301769048547 / 125000000000000 : ℚ)) - (U := (4961672035804785885769 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (205301769048547 / 125000000000000 : ℝ) ≤ - (4961672035804785885769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397970887067313 / 2000000000000000 : ℝ)) (q := - (205301769048547 / 1000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (205301769048547 / 1000000000000000 : ℚ)) + (r' := (205301769048547 / 125000000000000 : ℚ)) + (U := (-(15832743373195214114231 / 10000000000000000000000 : ℚ))) + (U' := (4961672035804785885769 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (397970887067313 / 2000000000000000 : ℚ)) + (q := (205301769048547 / 1000000000000000 : ℚ)) + (U := (-(15832743373195214114231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_8 : Uω (aρ 8) (bρ 8) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -4022,25 +3617,21 @@ lemma U_303_8 : have hlg : Real.log (3365483466576571 / 20000000000000000 : ℝ) ≤ (-(8910803224689173136883 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3365483466576571 / 20000000000000000 : ℝ) = - (3365483466576571 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3365483466576571 / 2500000000000000 : ℚ)) - (U := (1486404479810826863117 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3365483466576571 / 2500000000000000 : ℝ) ≤ - (1486404479810826863117 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (383211043070549 / 2500000000000000 : ℝ)) (q := - (3365483466576571 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3365483466576571 / 20000000000000000 : ℚ)) + (r' := (3365483466576571 / 2500000000000000 : ℚ)) + (U := (-(8910803224689173136883 / 5000000000000000000000 : ℚ))) + (U' := (1486404479810826863117 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (383211043070549 / 2500000000000000 : ℚ)) + (q := (3365483466576571 / 20000000000000000 : ℚ)) + (U := (-(8910803224689173136883 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_9 : Uω (aρ 9) (bρ 9) (4542766622207 / 16000000000000 : ℝ) ≤ @@ -4048,25 +3639,21 @@ lemma U_303_9 : have hlg : Real.log (533703873898957 / 5000000000000000 : ℝ) ≤ (-(11186760242463115104121 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (533703873898957 / 5000000000000000 : ℝ) = - (533703873898957 / 312500000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (533703873898957 / 312500000000000 : ℚ)) - (U := (2676183363536884895879 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (533703873898957 / 312500000000000 : ℝ) ≤ - (2676183363536884895879 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (643141829661453 / 10000000000000000 : ℝ)) (q := - (533703873898957 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (533703873898957 / 5000000000000000 : ℚ)) + (r' := (533703873898957 / 312500000000000 : ℚ)) + (U := (-(11186760242463115104121 / 5000000000000000000000 : ℚ))) + (U' := (2676183363536884895879 / 5000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4542766622207 / 16000000000000 : ℚ)) + (s := (643141829661453 / 10000000000000000 : ℚ)) + (q := (533703873898957 / 5000000000000000 : ℚ)) + (U := (-(11186760242463115104121 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_303_10 : Uω (aρ 10) (bρ 10) (4542766622207 / 16000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U25.lean b/LeanPool/Zeta5Irrational/Table/U25.lean index a9d6e4507f..51c995a4e1 100644 --- a/LeanPool/Zeta5Irrational/Table/U25.lean +++ b/LeanPool/Zeta5Irrational/Table/U25.lean @@ -24,25 +24,21 @@ lemma U_304_1 : have hlg : Real.log (44491959966754893 / 160000000000000000 : ℝ) ≤ (-(319966329192450738377 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44491959966754893 / 160000000000000000 : ℝ) = - (44491959966754893 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44491959966754893 / 40000000000000000 : ℚ)) - (U := (26607260957549261623 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44491959966754893 / 40000000000000000 : ℝ) ≤ - (26607260957549261623 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (695172339909899 / 2500000000000000 : ℝ)) (q := - (44491959966754893 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44491959966754893 / 160000000000000000 : ℚ)) + (r' := (44491959966754893 / 40000000000000000 : ℚ)) + (U := (-(319966329192450738377 / 250000000000000000000 : ℚ))) + (U' := (26607260957549261623 / 250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (695172339909899 / 2500000000000000 : ℚ)) + (q := (44491959966754893 / 160000000000000000 : ℚ)) + (U := (-(319966329192450738377 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_2 : Uω (aρ 2) (bρ 2) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_304_2 : have hlg : Real.log (44106428207642013 / 160000000000000000 : ℝ) ≤ (-(12885682785381020929319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44106428207642013 / 160000000000000000 : ℝ) = - (44106428207642013 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44106428207642013 / 40000000000000000 : ℚ)) - (U := (977260820618979070681 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44106428207642013 / 40000000000000000 : ℝ) ≤ - (977260820618979070681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1378133451130243 / 5000000000000000 : ℝ)) (q := - (44106428207642013 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44106428207642013 / 160000000000000000 : ℚ)) + (r' := (44106428207642013 / 40000000000000000 : ℚ)) + (U := (-(12885682785381020929319 / 10000000000000000000000 : ℚ))) + (U' := (977260820618979070681 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (1378133451130243 / 5000000000000000 : ℚ)) + (q := (44106428207642013 / 160000000000000000 : ℚ)) + (U := (-(12885682785381020929319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_3 : Uω (aρ 3) (bρ 3) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_304_3 : have hlg : Real.log (8666479002615649 / 32000000000000000 : ℝ) ≤ (-(13062733067052531422153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8666479002615649 / 32000000000000000 : ℝ) = - (8666479002615649 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8666479002615649 / 8000000000000000 : ℚ)) - (U := (800210538947468577847 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8666479002615649 / 8000000000000000 : ℝ) ≤ - (800210538947468577847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (541381771858003 / 2000000000000000 : ℝ)) (q := - (8666479002615649 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8666479002615649 / 32000000000000000 : ℚ)) + (r' := (8666479002615649 / 8000000000000000 : ℚ)) + (U := (-(13062733067052531422153 / 10000000000000000000000 : ℚ))) + (U' := (800210538947468577847 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (541381771858003 / 2000000000000000 : ℚ)) + (q := (8666479002615649 / 32000000000000000 : ℚ)) + (U := (-(13062733067052531422153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_4 : Uω (aρ 4) (bρ 4) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_304_4 : have hlg : Real.log (42037473411546381 / 160000000000000000 : ℝ) ≤ (-(2673224740282882651271 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42037473411546381 / 160000000000000000 : ℝ) = - (42037473411546381 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42037473411546381 / 40000000000000000 : ℚ)) - (U := (99363980917117348729 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42037473411546381 / 40000000000000000 : ℝ) ≤ - (99363980917117348729 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (655834460040883 / 2500000000000000 : ℝ)) (q := - (42037473411546381 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42037473411546381 / 160000000000000000 : ℚ)) + (r' := (42037473411546381 / 40000000000000000 : ℚ)) + (U := (-(2673224740282882651271 / 2000000000000000000000 : ℚ))) + (U' := (99363980917117348729 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (655834460040883 / 2500000000000000 : ℚ)) + (q := (42037473411546381 / 160000000000000000 : ℚ)) + (U := (-(2673224740282882651271 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_5 : Uω (aρ 5) (bρ 5) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_304_5 : have hlg : Real.log (40040251978887333 / 160000000000000000 : ℝ) ≤ (-(13852885671077141140659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40040251978887333 / 160000000000000000 : ℝ) = - (40040251978887333 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40040251978887333 / 40000000000000000 : ℚ)) - (U := (10057934922858859341 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (40040251978887333 / 40000000000000000 : ℝ) ≤ - (10057934922858859341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2491875080416151 / 10000000000000000 : ℝ)) (q := - (40040251978887333 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40040251978887333 / 160000000000000000 : ℚ)) + (r' := (40040251978887333 / 40000000000000000 : ℚ)) + (U := (-(13852885671077141140659 / 10000000000000000000000 : ℚ))) + (U' := (10057934922858859341 / 10000000000000000000000 : ℚ)) + 2 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (2491875080416151 / 10000000000000000 : ℚ)) + (q := (40040251978887333 / 160000000000000000 : ℚ)) + (U := (-(13852885671077141140659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_6 : Uω (aρ 6) (bρ 6) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_304_6 : have hlg : Real.log (37111378164456861 / 160000000000000000 : ℝ) ≤ (-(14612502027911626169787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (37111378164456861 / 160000000000000000 : ℝ) = - (37111378164456861 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37111378164456861 / 20000000000000000 : ℚ)) - (U := (6181913381088373830213 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37111378164456861 / 20000000000000000 : ℝ) ≤ - (6181913381088373830213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1146503114376171 / 5000000000000000 : ℝ)) (q := - (37111378164456861 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37111378164456861 / 160000000000000000 : ℚ)) + (r' := (37111378164456861 / 20000000000000000 : ℚ)) + (U := (-(14612502027911626169787 / 10000000000000000000000 : ℚ))) + (U' := (6181913381088373830213 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (1146503114376171 / 5000000000000000 : ℚ)) + (q := (37111378164456861 / 160000000000000000 : ℚ)) + (U := (-(14612502027911626169787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_7 : Uω (aρ 7) (bρ 7) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_304_7 : have hlg : Real.log (32948537544495549 / 160000000000000000 : ℝ) ≤ (-(7901134692862773503333 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (32948537544495549 / 160000000000000000 : ℝ) = - (32948537544495549 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32948537544495549 / 20000000000000000 : ℚ)) - (U := (2496073011637226496667 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32948537544495549 / 20000000000000000 : ℝ) ≤ - (2496073011637226496667 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (998156266008589 / 5000000000000000 : ℝ)) (q := - (32948537544495549 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32948537544495549 / 160000000000000000 : ℚ)) + (r' := (32948537544495549 / 20000000000000000 : ℚ)) + (U := (-(7901134692862773503333 / 5000000000000000000000 : ℚ))) + (U' := (2496073011637226496667 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (998156266008589 / 5000000000000000 : ℚ)) + (q := (32948537544495549 / 160000000000000000 : ℚ)) + (U := (-(7901134692862773503333 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_8 : Uω (aρ 8) (bρ 8) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_304_8 : have hlg : Real.log (27030509260586877 / 160000000000000000 : ℝ) ≤ (-(4445519034434660549931 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (27030509260586877 / 160000000000000000 : ℝ) = - (27030509260586877 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27030509260586877 / 20000000000000000 : ℚ)) - (U := (753084817815339450069 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27030509260586877 / 20000000000000000 : ℝ) ≤ - (753084817815339450069 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (770050323934297 / 5000000000000000 : ℝ)) (q := - (27030509260586877 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27030509260586877 / 160000000000000000 : ℚ)) + (r' := (27030509260586877 / 20000000000000000 : ℚ)) + (U := (-(4445519034434660549931 / 2500000000000000000000 : ℚ))) + (U' := (753084817815339450069 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (770050323934297 / 5000000000000000 : ℚ)) + (q := (27030509260586877 / 160000000000000000 : ℚ)) + (U := (-(4445519034434660549931 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_9 : Uω (aρ 9) (bρ 9) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_304_9 : have hlg : Real.log (17238827114719109 / 160000000000000000 : ℝ) ≤ (-(4456019168123497172333 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17238827114719109 / 160000000000000000 : ℝ) = - (17238827114719109 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17238827114719109 / 10000000000000000 : ℚ)) - (U := (1089158274276502827667 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17238827114719109 / 10000000000000000 : ℝ) ≤ - (1089158274276502827667 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (657106007995123 / 10000000000000000 : ℝ)) (q := - (17238827114719109 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17238827114719109 / 160000000000000000 : ℚ)) + (r' := (17238827114719109 / 10000000000000000 : ℚ)) + (U := (-(4456019168123497172333 / 2000000000000000000000 : ℚ))) + (U' := (1089158274276502827667 / 2000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (36419876534909 / 128000000000000 : ℚ)) + (s := (657106007995123 / 10000000000000000 : ℚ)) + (q := (17238827114719109 / 160000000000000000 : ℚ)) + (U := (-(4456019168123497172333 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_304_10 : Uω (aρ 10) (bρ 10) (36419876534909 / 128000000000000 : ℝ) ≤ @@ -378,25 +342,21 @@ lemma U_305_1 : have hlg : Real.log (22294570720353829 / 80000000000000000 : ℝ) ≤ (-(12776834507854284359341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22294570720353829 / 80000000000000000 : ℝ) = - (22294570720353829 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22294570720353829 / 20000000000000000 : ℚ)) - (U := (1086109098145715640659 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22294570720353829 / 20000000000000000 : ℝ) ≤ - (1086109098145715640659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2786763328473301 / 10000000000000000 : ℝ)) (q := - (22294570720353829 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22294570720353829 / 80000000000000000 : ℚ)) + (r' := (22294570720353829 / 20000000000000000 : ℚ)) + (U := (-(12776834507854284359341 / 10000000000000000000000 : ℚ))) + (U' := (1086109098145715640659 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (2786763328473301 / 10000000000000000 : ℚ)) + (q := (22294570720353829 / 80000000000000000 : ℚ)) + (U := (-(12776834507854284359341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_2 : Uω (aρ 2) (bρ 2) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -404,25 +364,21 @@ lemma U_305_2 : have hlg : Real.log (884072423872929 / 3200000000000000 : ℝ) ≤ (-(200994859613764106703 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (884072423872929 / 3200000000000000 : ℝ) = - (884072423872929 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (884072423872929 / 800000000000000 : ℚ)) - (U := (15613634229985893297 / 156250000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (884072423872929 / 800000000000000 : ℝ) ≤ - (15613634229985893297 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55246846202013 / 200000000000000 : ℝ)) (q := - (884072423872929 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (884072423872929 / 3200000000000000 : ℚ)) + (r' := (884072423872929 / 800000000000000 : ℚ)) + (U := (-(200994859613764106703 / 156250000000000000000 : ℚ))) + (U' := (15613634229985893297 / 156250000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (55246846202013 / 200000000000000 : ℚ)) + (q := (884072423872929 / 3200000000000000 : ℚ)) + (U := (-(200994859613764106703 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_3 : Uω (aρ 3) (bρ 3) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -430,25 +386,21 @@ lemma U_305_3 : have hlg : Real.log (21714811691895949 / 80000000000000000 : ℝ) ≤ (-(13040320400032887200957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21714811691895949 / 80000000000000000 : ℝ) = - (21714811691895949 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21714811691895949 / 20000000000000000 : ℚ)) - (U := (822623205967112799043 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21714811691895949 / 20000000000000000 : ℝ) ≤ - (822623205967112799043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2712988690218831 / 10000000000000000 : ℝ)) (q := - (21714811691895949 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21714811691895949 / 80000000000000000 : ℚ)) + (r' := (21714811691895949 / 20000000000000000 : ℚ)) + (U := (-(13040320400032887200957 / 10000000000000000000000 : ℚ))) + (U' := (822623205967112799043 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (2712988690218831 / 10000000000000000 : ℚ)) + (q := (21714811691895949 / 80000000000000000 : ℚ)) + (U := (-(13040320400032887200957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_4 : Uω (aρ 4) (bρ 4) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -456,25 +408,21 @@ lemma U_305_4 : have hlg : Real.log (842696016982221 / 3200000000000000 : ℝ) ≤ (-(13342997919963146336917 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (842696016982221 / 3200000000000000 : ℝ) = - (842696016982221 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (842696016982221 / 800000000000000 : ℚ)) - (U := (519945686036853663083 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (842696016982221 / 800000000000000 : ℝ) ≤ - (519945686036853663083 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105177202177949 / 400000000000000 : ℝ)) (q := - (842696016982221 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (842696016982221 / 3200000000000000 : ℚ)) + (r' := (842696016982221 / 800000000000000 : ℚ)) + (U := (-(13342997919963146336917 / 10000000000000000000000 : ℚ))) + (U' := (519945686036853663083 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (105177202177949 / 400000000000000 : ℚ)) + (q := (842696016982221 / 3200000000000000 : ℚ)) + (U := (-(13342997919963146336917 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_5 : Uω (aρ 5) (bρ 5) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -482,25 +430,21 @@ lemma U_305_5 : have hlg : Real.log (20068922691257481 / 80000000000000000 : ℝ) ≤ (-(3457135375880206226739 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20068922691257481 / 80000000000000000 : ℝ) = - (20068922691257481 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20068922691257481 / 20000000000000000 : ℚ)) - (U := (8600525619793773261 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20068922691257481 / 20000000000000000 : ℝ) ≤ - (8600525619793773261 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1249000270229607 / 5000000000000000 : ℝ)) (q := - (20068922691257481 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20068922691257481 / 80000000000000000 : ℚ)) + (r' := (20068922691257481 / 20000000000000000 : ℚ)) + (U := (-(3457135375880206226739 / 2500000000000000000000 : ℚ))) + (U' := (8600525619793773261 / 2500000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (1249000270229607 / 5000000000000000 : ℚ)) + (q := (20068922691257481 / 80000000000000000 : ℚ)) + (U := (-(3457135375880206226739 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_6 : Uω (aρ 6) (bρ 6) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -508,25 +452,21 @@ lemma U_305_6 : have hlg : Real.log (3720967579529317 / 16000000000000000 : ℝ) ≤ (-(7293024924857735976821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3720967579529317 / 16000000000000000 : ℝ) = - (3720967579529317 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3720967579529317 / 2000000000000000 : ℚ)) - (U := (3104182779642264023179 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3720967579529317 / 2000000000000000 : ℝ) ≤ - (3104182779642264023179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (229921971719649 / 1000000000000000 : ℝ)) (q := - (3720967579529317 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3720967579529317 / 16000000000000000 : ℚ)) + (r' := (3720967579529317 / 2000000000000000 : ℚ)) + (U := (-(7293024924857735976821 / 5000000000000000000000 : ℚ))) + (U' := (3104182779642264023179 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (229921971719649 / 1000000000000000 : ℚ)) + (q := (3720967579529317 / 16000000000000000 : ℚ)) + (U := (-(7293024924857735976821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_7 : Uω (aρ 7) (bρ 7) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -534,25 +474,21 @@ lemma U_305_7 : have hlg : Real.log (16524386399945949 / 80000000000000000 : ℝ) ≤ (-(31543787609354435141 / 20000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16524386399945949 / 80000000000000000 : ℝ) = - (16524386399945949 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16524386399945949 / 10000000000000000 : ℚ)) - (U := (10045043208645564859 / 20000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16524386399945949 / 10000000000000000 : ℝ) ≤ - (10045043208645564859 / 20000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2002768223531331 / 10000000000000000 : ℝ)) (q := - (16524386399945949 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16524386399945949 / 80000000000000000 : ℚ)) + (r' := (16524386399945949 / 10000000000000000 : ℚ)) + (U := (-(31543787609354435141 / 20000000000000000000 : ℚ))) + (U' := (10045043208645564859 / 20000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (2002768223531331 / 10000000000000000 : ℚ)) + (q := (16524386399945949 / 80000000000000000 : ℚ)) + (U := (-(31543787609354435141 / 20000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_8 : Uω (aρ 8) (bρ 8) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -560,25 +496,21 @@ lemma U_305_8 : have hlg : Real.log (13568534637119313 / 80000000000000000 : ℝ) ≤ (-(17742731513520089426687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13568534637119313 / 80000000000000000 : ℝ) = - (13568534637119313 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13568534637119313 / 10000000000000000 : ℚ)) - (U := (3051683895479910573313 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13568534637119313 / 10000000000000000 : ℝ) ≤ - (3051683895479910573313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24177295846323 / 156250000000000 : ℝ)) (q := - (13568534637119313 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13568534637119313 / 80000000000000000 : ℚ)) + (r' := (13568534637119313 / 10000000000000000 : ℚ)) + (U := (-(17742731513520089426687 / 10000000000000000000000 : ℚ))) + (U' := (3051683895479910573313 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (24177295846323 / 156250000000000 : ℚ)) + (q := (13568534637119313 / 80000000000000000 : ℚ)) + (U := (-(17742731513520089426687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_9 : Uω (aρ 9) (bρ 9) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -586,25 +518,21 @@ lemma U_305_9 : have hlg : Real.log (8698622542271477 / 80000000000000000 : ℝ) ≤ (-(2218861948983381281 / 1000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (8698622542271477 / 80000000000000000 : ℝ) = - (8698622542271477 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8698622542271477 / 5000000000000000 : ℚ)) - (U := (553726772216618719 / 1000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8698622542271477 / 5000000000000000 : ℝ) ≤ - (553726772216618719 / 1000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (670834538812713 / 10000000000000000 : ℝ)) (q := - (8698622542271477 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8698622542271477 / 80000000000000000 : ℚ)) + (r' := (8698622542271477 / 5000000000000000 : ℚ)) + (U := (-(2218861948983381281 / 1000000000000000000 : ℚ))) + (U' := (553726772216618719 / 1000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18248810046081 / 64000000000000 : ℚ)) + (s := (670834538812713 / 10000000000000000 : ℚ)) + (q := (8698622542271477 / 80000000000000000 : ℚ)) + (U := (-(2218861948983381281 / 1000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_305_10 : Uω (aρ 10) (bρ 10) (18248810046081 / 64000000000000 : ℝ) ≤ @@ -731,25 +659,21 @@ lemma U_306_1 : have hlg : Real.log (44686322905842127 / 160000000000000000 : ℝ) ≤ (-(6377531675875982707461 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44686322905842127 / 160000000000000000 : ℝ) = - (44686322905842127 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44686322905842127 / 40000000000000000 : ℚ)) - (U := (553940127124017292539 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44686322905842127 / 40000000000000000 : ℝ) ≤ - (553940127124017292539 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2792837296204719 / 10000000000000000 : ℝ)) (q := - (44686322905842127 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44686322905842127 / 160000000000000000 : ℚ)) + (r' := (44686322905842127 / 40000000000000000 : ℚ)) + (U := (-(6377531675875982707461 / 5000000000000000000000 : ℚ))) + (U' := (553940127124017292539 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (2792837296204719 / 10000000000000000 : ℚ)) + (q := (44686322905842127 / 160000000000000000 : ℚ)) + (U := (-(6377531675875982707461 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_2 : Uω (aρ 2) (bρ 2) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -757,25 +681,21 @@ lemma U_306_2 : have hlg : Real.log (44300814120233439 / 160000000000000000 : ℝ) ≤ (-(802606725249877005899 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44300814120233439 / 160000000000000000 : ℝ) = - (44300814120233439 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44300814120233439 / 40000000000000000 : ℚ)) - (U := (63827250125122994101 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44300814120233439 / 40000000000000000 : ℝ) ≤ - (63827250125122994101 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2768417710513633 / 10000000000000000 : ℝ)) (q := - (44300814120233439 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44300814120233439 / 160000000000000000 : ℚ)) + (r' := (44300814120233439 / 40000000000000000 : ℚ)) + (U := (-(802606725249877005899 / 625000000000000000000 : ℚ))) + (U' := (63827250125122994101 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (2768417710513633 / 10000000000000000 : ℚ)) + (q := (44300814120233439 / 160000000000000000 : ℚ)) + (U := (-(802606725249877005899 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_3 : Uω (aρ 3) (bρ 3) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -783,25 +703,21 @@ lemma U_306_3 : have hlg : Real.log (43526851535827023 / 160000000000000000 : ℝ) ≤ (-(2603591580741016814553 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43526851535827023 / 160000000000000000 : ℝ) = - (43526851535827023 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43526851535827023 / 40000000000000000 : ℚ)) - (U := (168997140458983185447 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43526851535827023 / 40000000000000000 : ℝ) ≤ - (168997140458983185447 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2719068493812831 / 10000000000000000 : ℝ)) (q := - (43526851535827023 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43526851535827023 / 160000000000000000 : ℚ)) + (r' := (43526851535827023 / 40000000000000000 : ℚ)) + (U := (-(2603591580741016814553 / 2000000000000000000000 : ℚ))) + (U' := (168997140458983185447 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (2719068493812831 / 10000000000000000 : ℚ)) + (q := (43526851535827023 / 160000000000000000 : ℚ)) + (U := (-(2603591580741016814553 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_4 : Uω (aρ 4) (bρ 4) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -809,25 +725,21 @@ lemma U_306_4 : have hlg : Real.log (42232127603529111 / 160000000000000000 : ℝ) ≤ (-(13319925657080517909239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42232127603529111 / 160000000000000000 : ℝ) = - (42232127603529111 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42232127603529111 / 40000000000000000 : ℚ)) - (U := (543017948919482090761 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42232127603529111 / 40000000000000000 : ℝ) ≤ - (543017948919482090761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (164720136458787 / 625000000000000 : ℝ)) (q := - (42232127603529111 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42232127603529111 / 160000000000000000 : ℚ)) + (r' := (42232127603529111 / 40000000000000000 : ℚ)) + (U := (-(13319925657080517909239 / 10000000000000000000000 : ℚ))) + (U' := (543017948919482090761 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (164720136458787 / 625000000000000 : ℚ)) + (q := (42232127603529111 / 160000000000000000 : ℚ)) + (U := (-(13319925657080517909239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_5 : Uω (aρ 5) (bρ 5) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -835,25 +747,21 @@ lemma U_306_5 : have hlg : Real.log (40235436769496831 / 160000000000000000 : ℝ) ≤ (-(13804256957131762695407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40235436769496831 / 160000000000000000 : ℝ) = - (40235436769496831 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40235436769496831 / 40000000000000000 : ℚ)) - (U := (58686648868237304593 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40235436769496831 / 40000000000000000 : ℝ) ≤ - (58686648868237304593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2504125748421557 / 10000000000000000 : ℝ)) (q := - (40235436769496831 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40235436769496831 / 160000000000000000 : ℚ)) + (r' := (40235436769496831 / 40000000000000000 : ℚ)) + (U := (-(13804256957131762695407 / 10000000000000000000000 : ℚ))) + (U' := (58686648868237304593 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (2504125748421557 / 10000000000000000 : ℚ)) + (q := (40235436769496831 / 160000000000000000 : ℚ)) + (U := (-(13804256957131762695407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_6 : Uω (aρ 6) (bρ 6) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -861,25 +769,21 @@ lemma U_306_6 : have hlg : Real.log (7461593493314523 / 32000000000000000 : ℝ) ≤ (-(14559669056125745715263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7461593493314523 / 32000000000000000 : ℝ) = - (7461593493314523 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7461593493314523 / 4000000000000000 : ℚ)) - (U := (6234746352874254284737 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7461593493314523 / 4000000000000000 : ℝ) ≤ - (6234746352874254284737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (230543246069603 / 1000000000000000 : ℝ)) (q := - (7461593493314523 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7461593493314523 / 32000000000000000 : ℚ)) + (r' := (7461593493314523 / 4000000000000000 : ℚ)) + (U := (-(14559669056125745715263 / 10000000000000000000000 : ℚ))) + (U' := (6234746352874254284737 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (230543246069603 / 1000000000000000 : ℚ)) + (q := (7461593493314523 / 32000000000000000 : ℚ)) + (U := (-(14559669056125745715263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_7 : Uω (aρ 7) (bρ 7) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -887,25 +791,21 @@ lemma U_306_7 : have hlg : Real.log (1325959559977023 / 6400000000000000 : ℝ) ≤ (-(3148323192084140152897 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1325959559977023 / 6400000000000000 : ℝ) = - (1325959559977023 / 800000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1325959559977023 / 800000000000000 : ℚ)) - (U := (1010559889715859847103 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1325959559977023 / 800000000000000 : ℝ) ≤ - (1010559889715859847103 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40184430661253 / 200000000000000 : ℝ)) (q := - (1325959559977023 / 6400000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1325959559977023 / 6400000000000000 : ℚ)) + (r' := (1325959559977023 / 800000000000000 : ℚ)) + (U := (-(3148323192084140152897 / 2000000000000000000000 : ℚ))) + (U' := (1010559889715859847103 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (40184430661253 / 200000000000000 : ℚ)) + (q := (1325959559977023 / 6400000000000000 : ℚ)) + (U := (-(3148323192084140152897 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_8 : Uω (aρ 8) (bρ 8) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -913,25 +813,21 @@ lemma U_306_8 : have hlg : Real.log (27243548913441479 / 160000000000000000 : ℝ) ≤ (-(3540714116985614482459 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (27243548913441479 / 160000000000000000 : ℝ) = - (27243548913441479 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27243548913441479 / 20000000000000000 : ℚ)) - (U := (618168964814385517541 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27243548913441479 / 20000000000000000 : ℝ) ≤ - (618168964814385517541 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (777291586827319 / 5000000000000000 : ℝ)) (q := - (27243548913441479 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27243548913441479 / 160000000000000000 : ℚ)) + (r' := (27243548913441479 / 20000000000000000 : ℚ)) + (U := (-(3540714116985614482459 / 2000000000000000000000 : ℚ))) + (U' := (618168964814385517541 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (777291586827319 / 5000000000000000 : ℚ)) + (q := (27243548913441479 / 160000000000000000 : ℚ)) + (U := (-(3540714116985614482459 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_9 : Uω (aρ 9) (bρ 9) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -939,25 +835,21 @@ lemma U_306_9 : have hlg : Real.log (17553891330828439 / 160000000000000000 : ℝ) ≤ (-(2209898160607914061911 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17553891330828439 / 160000000000000000 : ℝ) = - (17553891330828439 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17553891330828439 / 10000000000000000 : ℚ)) - (U := (562690560592085938089 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17553891330828439 / 10000000000000000 : ℝ) ≤ - (562690560592085938089 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85542700523501 / 1250000000000000 : ℝ)) (q := - (17553891330828439 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17553891330828439 / 160000000000000000 : ℚ)) + (r' := (17553891330828439 / 10000000000000000 : ℚ)) + (U := (-(2209898160607914061911 / 1000000000000000000000 : ℚ))) + (U' := (562690560592085938089 / 1000000000000000000000 : ℚ)) + 4 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (7315072729883 / 25600000000000 : ℚ)) + (s := (85542700523501 / 1250000000000000 : ℚ)) + (q := (17553891330828439 / 160000000000000000 : ℚ)) + (U := (-(2209898160607914061911 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_306_10 : Uω (aρ 10) (bρ 10) (7315072729883 / 25600000000000 : ℝ) ≤ @@ -1084,25 +976,21 @@ lemma U_307_1 : have hlg : Real.log (11195876090553929 / 40000000000000000 : ℝ) ≤ (-(3183334873245216212523 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11195876090553929 / 40000000000000000 : ℝ) = - (11195876090553929 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11195876090553929 / 10000000000000000 : ℚ)) - (U := (282401028254783787477 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11195876090553929 / 10000000000000000 : ℝ) ≤ - (282401028254783787477 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2798911262841027 / 10000000000000000 : ℝ)) (q := - (11195876090553929 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11195876090553929 / 40000000000000000 : ℚ)) + (r' := (11195876090553929 / 10000000000000000 : ℚ)) + (U := (-(3183334873245216212523 / 2500000000000000000000 : ℚ))) + (U' := (282401028254783787477 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (2798911262841027 / 10000000000000000 : ℚ)) + (q := (11195876090553929 / 40000000000000000 : ℚ)) + (U := (-(3183334873245216212523 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_2 : Uω (aρ 2) (bρ 2) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1110,25 +998,21 @@ lemma U_307_2 : have hlg : Real.log (11099501746948329 / 40000000000000000 : ℝ) ≤ (-(12819792339455511980223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11099501746948329 / 40000000000000000 : ℝ) = - (11099501746948329 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11099501746948329 / 10000000000000000 : ℚ)) - (U := (1043151266544488019777 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11099501746948329 / 10000000000000000 : ℝ) ≤ - (1043151266544488019777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2774493103548227 / 10000000000000000 : ℝ)) (q := - (11099501746948329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11099501746948329 / 40000000000000000 : ℚ)) + (r' := (11099501746948329 / 10000000000000000 : ℚ)) + (U := (-(12819792339455511980223 / 10000000000000000000000 : ℚ))) + (U' := (1043151266544488019777 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (2774493103548227 / 10000000000000000 : ℚ)) + (q := (11099501746948329 / 40000000000000000 : ℚ)) + (U := (-(12819792339455511980223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_3 : Uω (aρ 3) (bρ 3) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1136,25 +1020,21 @@ lemma U_307_3 : have hlg : Real.log (10906019867661809 / 40000000000000000 : ℝ) ≤ (-(3248911338433372805021 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10906019867661809 / 40000000000000000 : ℝ) = - (10906019867661809 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10906019867661809 / 10000000000000000 : ℚ)) - (U := (216824563066627194979 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10906019867661809 / 10000000000000000 : ℝ) ≤ - (216824563066627194979 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2725148270254967 / 10000000000000000 : ℝ)) (q := - (10906019867661809 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10906019867661809 / 40000000000000000 : ℚ)) + (r' := (10906019867661809 / 10000000000000000 : ℚ)) + (U := (-(3248911338433372805021 / 2500000000000000000000 : ℚ))) + (U' := (216824563066627194979 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (2725148270254967 / 10000000000000000 : ℚ)) + (q := (10906019867661809 / 40000000000000000 : ℚ)) + (U := (-(3248911338433372805021 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_4 : Uω (aρ 4) (bρ 4) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1162,25 +1042,21 @@ lemma U_307_4 : have hlg : Real.log (10582363419881751 / 40000000000000000 : ℝ) ≤ (-(6648453332443258315593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10582363419881751 / 40000000000000000 : ℝ) = - (10582363419881751 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10582363419881751 / 10000000000000000 : ℚ)) - (U := (283018470556741684407 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10582363419881751 / 10000000000000000 : ℝ) ≤ - (283018470556741684407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1320807113714969 / 5000000000000000 : ℝ)) (q := - (10582363419881751 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10582363419881751 / 40000000000000000 : ℚ)) + (r' := (10582363419881751 / 10000000000000000 : ℚ)) + (U := (-(6648453332443258315593 / 5000000000000000000000 : ℚ))) + (U' := (283018470556741684407 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (1320807113714969 / 5000000000000000 : ℚ)) + (q := (10582363419881751 / 40000000000000000 : ℚ)) + (U := (-(6648453332443258315593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_5 : Uω (aρ 5) (bρ 5) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1188,25 +1064,21 @@ lemma U_307_5 : have hlg : Real.log (2016651307729763 / 8000000000000000 : ℝ) ≤ (-(13780031738160772080827 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2016651307729763 / 8000000000000000 : ℝ) = - (2016651307729763 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2016651307729763 / 2000000000000000 : ℚ)) - (U := (82911867839227919173 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2016651307729763 / 2000000000000000 : ℝ) ≤ - (82911867839227919173 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (251025070614847 / 1000000000000000 : ℝ)) (q := - (2016651307729763 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2016651307729763 / 8000000000000000 : ℚ)) + (r' := (2016651307729763 / 2000000000000000 : ℚ)) + (U := (-(13780031738160772080827 / 10000000000000000000000 : ℚ))) + (U' := (82911867839227919173 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (251025070614847 / 1000000000000000 : ℚ)) + (q := (2016651307729763 / 8000000000000000 : ℚ)) + (U := (-(13780031738160772080827 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_6 : Uω (aρ 6) (bρ 6) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1214,25 +1086,21 @@ lemma U_307_6 : have hlg : Real.log (1870312661317283 / 8000000000000000 : ℝ) ≤ (-(14533359254442350572721 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1870312661317283 / 8000000000000000 : ℝ) = - (1870312661317283 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1870312661317283 / 1000000000000000 : ℚ)) - (U := (6261056154557649427279 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1870312661317283 / 1000000000000000 : ℝ) ≤ - (6261056154557649427279 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231164446525727 / 1000000000000000 : ℝ)) (q := - (1870312661317283 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1870312661317283 / 8000000000000000 : ℚ)) + (r' := (1870312661317283 / 1000000000000000 : ℚ)) + (U := (-(14533359254442350572721 / 10000000000000000000000 : ℚ))) + (U' := (6261056154557649427279 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (231164446525727 / 1000000000000000 : ℚ)) + (q := (1870312661317283 / 8000000000000000 : ℚ)) + (U := (-(14533359254442350572721 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_7 : Uω (aρ 7) (bρ 7) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1240,25 +1108,21 @@ lemma U_307_7 : have hlg : Real.log (8312296581530601 / 40000000000000000 : ℝ) ≤ (-(628457407618548892479 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8312296581530601 / 40000000000000000 : ℝ) = - (8312296581530601 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8312296581530601 / 5000000000000000 : ℚ)) - (U := (203319208741451107521 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8312296581530601 / 5000000000000000 : ℝ) ≤ - (203319208741451107521 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2015672483489363 / 10000000000000000 : ℝ)) (q := - (8312296581530601 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8312296581530601 / 40000000000000000 : ℚ)) + (r' := (8312296581530601 / 5000000000000000 : ℚ)) + (U := (-(628457407618548892479 / 400000000000000000000 : ℚ))) + (U' := (203319208741451107521 / 400000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (2015672483489363 / 10000000000000000 : ℚ)) + (q := (8312296581530601 / 40000000000000000 : ℚ)) + (U := (-(628457407618548892479 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_8 : Uω (aρ 8) (bρ 8) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1266,25 +1130,21 @@ lemma U_307_8 : have hlg : Real.log (1367497464768901 / 8000000000000000 : ℝ) ≤ (-(17664591395044278791573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1367497464768901 / 8000000000000000 : ℝ) = - (1367497464768901 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1367497464768901 / 1000000000000000 : ℚ)) - (U := (3129824013955721208427 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1367497464768901 / 1000000000000000 : ℝ) ≤ - (3129824013955721208427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (312361901197263 / 2000000000000000 : ℝ)) (q := - (1367497464768901 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1367497464768901 / 8000000000000000 : ℚ)) + (r' := (1367497464768901 / 1000000000000000 : ℚ)) + (U := (-(17664591395044278791573 / 10000000000000000000000 : ℚ))) + (U' := (3129824013955721208427 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (312361901197263 / 2000000000000000 : ℚ)) + (q := (1367497464768901 / 8000000000000000 : ℚ)) + (U := (-(17664591395044278791573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_9 : Uω (aρ 9) (bρ 9) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1292,25 +1152,21 @@ lemma U_307_9 : have hlg : Real.log (4427217190492359 / 40000000000000000 : ℝ) ≤ (-(1375692650065395914491 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4427217190492359 / 40000000000000000 : ℝ) = - (4427217190492359 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4427217190492359 / 2500000000000000 : ℚ)) - (U := (357175300684604085509 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4427217190492359 / 2500000000000000 : ℝ) ≤ - (357175300684604085509 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (348820033835121 / 5000000000000000 : ℝ)) (q := - (4427217190492359 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4427217190492359 / 40000000000000000 : ℚ)) + (r' := (4427217190492359 / 2500000000000000 : ℚ)) + (U := (-(1375692650065395914491 / 625000000000000000000 : ℚ))) + (U' := (357175300684604085509 / 625000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9163276801667 / 32000000000000 : ℚ)) + (s := (348820033835121 / 5000000000000000 : ℚ)) + (q := (4427217190492359 / 40000000000000000 : ℚ)) + (U := (-(1375692650065395914491 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_307_10 : Uω (aρ 10) (bρ 10) (9163276801667 / 32000000000000 : ℝ) ≤ @@ -1437,25 +1293,21 @@ lemma U_308_1 : have hlg : Real.log (44880685809885337 / 160000000000000000 : ℝ) ≤ (-(1588957840809154527443 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44880685809885337 / 160000000000000000 : ℝ) = - (44880685809885337 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44880685809885337 / 40000000000000000 : ℚ)) - (U := (143910109940845472557 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44880685809885337 / 40000000000000000 : ℝ) ≤ - (143910109940845472557 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2804985228389339 / 10000000000000000 : ℝ)) (q := - (44880685809885337 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44880685809885337 / 160000000000000000 : ℚ)) + (r' := (44880685809885337 / 40000000000000000 : ℚ)) + (U := (-(1588957840809154527443 / 1250000000000000000000 : ℚ))) + (U' := (143910109940845472557 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (2804985228389339 / 10000000000000000 : ℚ)) + (q := (44880685809885337 / 160000000000000000 : ℚ)) + (U := (-(1588957840809154527443 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_2 : Uω (aρ 2) (bρ 2) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1463,25 +1315,21 @@ lemma U_308_2 : have hlg : Real.log (8899039959342597 / 32000000000000000 : ℝ) ≤ (-(2559585002193774210817 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8899039959342597 / 32000000000000000 : ℝ) = - (8899039959342597 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8899039959342597 / 8000000000000000 : ℚ)) - (U := (213003719006225789183 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8899039959342597 / 8000000000000000 : ℝ) ≤ - (213003719006225789183 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (556113697850559 / 2000000000000000 : ℝ)) (q := - (8899039959342597 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8899039959342597 / 32000000000000000 : ℚ)) + (r' := (8899039959342597 / 8000000000000000 : ℚ)) + (U := (-(2559585002193774210817 / 2000000000000000000000 : ℚ))) + (U' := (213003719006225789183 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (556113697850559 / 2000000000000000 : ℚ)) + (q := (8899039959342597 / 32000000000000000 : ℚ)) + (U := (-(2559585002193774210817 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_3 : Uω (aρ 3) (bρ 3) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1489,25 +1337,21 @@ lemma U_308_3 : have hlg : Real.log (43721307189703121 / 160000000000000000 : ℝ) ≤ (-(12973382527285262823649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43721307189703121 / 160000000000000000 : ℝ) = - (43721307189703121 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43721307189703121 / 40000000000000000 : ℚ)) - (U := (889561078714737176351 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43721307189703121 / 40000000000000000 : ℝ) ≤ - (889561078714737176351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1365614009863281 / 5000000000000000 : ℝ)) (q := - (43721307189703121 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43721307189703121 / 160000000000000000 : ℚ)) + (r' := (43721307189703121 / 40000000000000000 : ℚ)) + (U := (-(12973382527285262823649 / 10000000000000000000000 : ℚ))) + (U' := (889561078714737176351 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (1365614009863281 / 5000000000000000 : ℚ)) + (q := (43721307189703121 / 160000000000000000 : ℚ)) + (U := (-(12973382527285262823649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_4 : Uω (aρ 4) (bρ 4) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1515,25 +1359,21 @@ lemma U_308_4 : have hlg : Real.log (42426779081787617 / 160000000000000000 : ℝ) ≤ (-(6636970348612193216359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42426779081787617 / 160000000000000000 : ℝ) = - (42426779081787617 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42426779081787617 / 40000000000000000 : ℚ)) - (U := (294501454387806783641 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42426779081787617 / 40000000000000000 : ℝ) ≤ - (294501454387806783641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661926546825531 / 2500000000000000 : ℝ)) (q := - (42426779081787617 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42426779081787617 / 160000000000000000 : ℚ)) + (r' := (42426779081787617 / 40000000000000000 : ℚ)) + (U := (-(6636970348612193216359 / 5000000000000000000000 : ℚ))) + (U' := (294501454387806783641 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (661926546825531 / 2500000000000000 : ℚ)) + (q := (42426779081787617 / 160000000000000000 : ℚ)) + (U := (-(6636970348612193216359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_5 : Uω (aρ 5) (bρ 5) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1541,25 +1381,21 @@ lemma U_308_5 : have hlg : Real.log (40430613552428249 / 160000000000000000 : ℝ) ≤ (-(13755865555041763943411 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40430613552428249 / 160000000000000000 : ℝ) = - (40430613552428249 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40430613552428249 / 40000000000000000 : ℚ)) - (U := (107078050958236056589 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40430613552428249 / 40000000000000000 : ℝ) ≤ - (107078050958236056589 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2516375415467203 / 10000000000000000 : ℝ)) (q := - (40430613552428249 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40430613552428249 / 160000000000000000 : ℚ)) + (r' := (40430613552428249 / 40000000000000000 : ℚ)) + (U := (-(13755865555041763943411 / 10000000000000000000000 : ℚ))) + (U' := (107078050958236056589 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (2516375415467203 / 10000000000000000 : ℚ)) + (q := (40430613552428249 / 160000000000000000 : ℚ)) + (U := (-(13755865555041763943411 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_6 : Uω (aρ 6) (bρ 6) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1567,25 +1403,21 @@ lemma U_308_6 : have hlg : Real.log (37504533122141969 / 160000000000000000 : ℝ) ≤ (-(7253560027631494245037 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (37504533122141969 / 160000000000000000 : ℝ) = - (37504533122141969 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37504533122141969 / 20000000000000000 : ℚ)) - (U := (3143647676868505754963 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37504533122141969 / 20000000000000000 : ℝ) ≤ - (3143647676868505754963 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1158927868410709 / 5000000000000000 : ℝ)) (q := - (37504533122141969 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37504533122141969 / 160000000000000000 : ℚ)) + (r' := (37504533122141969 / 20000000000000000 : ℚ)) + (U := (-(7253560027631494245037 / 5000000000000000000000 : ℚ))) + (U' := (3143647676868505754963 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (1158927868410709 / 5000000000000000 : ℚ)) + (q := (37504533122141969 / 160000000000000000 : ℚ)) + (U := (-(7253560027631494245037 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_7 : Uω (aρ 7) (bρ 7) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1593,25 +1425,21 @@ lemma U_308_7 : have hlg : Real.log (33349364960606209 / 160000000000000000 : ℝ) ≤ (-(7840675419673181174101 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33349364960606209 / 160000000000000000 : ℝ) = - (33349364960606209 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33349364960606209 / 20000000000000000 : ℚ)) - (U := (2556532284826818825899 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33349364960606209 / 20000000000000000 : ℝ) ≤ - (2556532284826818825899 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252765137173681 / 1250000000000000 : ℝ)) (q := - (33349364960606209 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33349364960606209 / 160000000000000000 : ℚ)) + (r' := (33349364960606209 / 20000000000000000 : ℚ)) + (U := (-(7840675419673181174101 / 5000000000000000000000 : ℚ))) + (U' := (2556532284826818825899 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (252765137173681 / 1250000000000000 : ℚ)) + (q := (33349364960606209 / 160000000000000000 : ℚ)) + (U := (-(7840675419673181174101 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_8 : Uω (aρ 8) (bρ 8) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1619,25 +1447,21 @@ lemma U_308_8 : have hlg : Real.log (27456271515134017 / 160000000000000000 : ℝ) ≤ (-(8812896010485875851931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (27456271515134017 / 160000000000000000 : ℝ) = - (27456271515134017 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27456271515134017 / 20000000000000000 : ℚ)) - (U := (1584311694014124148069 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27456271515134017 / 20000000000000000 : ℝ) ≤ - (1584311694014124148069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98064129252839 / 625000000000000 : ℝ)) (q := - (27456271515134017 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27456271515134017 / 160000000000000000 : ℚ)) + (r' := (27456271515134017 / 20000000000000000 : ℚ)) + (U := (-(8812896010485875851931 / 5000000000000000000000 : ℚ))) + (U' := (1584311694014124148069 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (98064129252839 / 625000000000000 : ℚ)) + (q := (27456271515134017 / 160000000000000000 : ℚ)) + (U := (-(8812896010485875851931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_9 : Uω (aρ 9) (bρ 9) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1645,25 +1469,21 @@ lemma U_308_9 : have hlg : Real.log (17862271052765049 / 160000000000000000 : ℝ) ≤ (-(2740603860275247694661 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (17862271052765049 / 160000000000000000 : ℝ) = - (17862271052765049 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17862271052765049 / 10000000000000000 : ℚ)) - (U := (725132041224752305339 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17862271052765049 / 10000000000000000 : ℝ) ≤ - (725132041224752305339 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (710741638609303 / 10000000000000000 : ℝ)) (q := - (17862271052765049 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17862271052765049 / 160000000000000000 : ℚ)) + (r' := (17862271052765049 / 10000000000000000 : ℚ)) + (U := (-(2740603860275247694661 / 1250000000000000000000 : ℚ))) + (U' := (725132041224752305339 / 1250000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (36730850763921 / 128000000000000 : ℚ)) + (s := (710741638609303 / 10000000000000000 : ℚ)) + (q := (17862271052765049 / 160000000000000000 : ℚ)) + (U := (-(2740603860275247694661 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_308_10 : Uω (aρ 10) (bρ 10) (36730850763921 / 128000000000000 : ℝ) ≤ @@ -1791,25 +1611,21 @@ lemma U_309_1 : have hlg : Real.log (22488933624453707 / 80000000000000000 : ℝ) ≤ (-(396563526515380477321 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22488933624453707 / 80000000000000000 : ℝ) = - (22488933624453707 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22488933624453707 / 20000000000000000 : ℚ)) - (U := (36653461172119522679 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22488933624453707 / 20000000000000000 : ℝ) ≤ - (36653461172119522679 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (702764798214177 / 2500000000000000 : ℝ)) (q := - (22488933624453707 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22488933624453707 / 80000000000000000 : ℚ)) + (r' := (22488933624453707 / 20000000000000000 : ℚ)) + (U := (-(396563526515380477321 / 312500000000000000000 : ℚ))) + (U' := (36653461172119522679 / 312500000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (702764798214177 / 2500000000000000 : ℚ)) + (q := (22488933624453707 / 80000000000000000 : ℚ)) + (U := (-(396563526515380477321 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_2 : Uω (aρ 2) (bρ 2) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1817,25 +1633,21 @@ lemma U_309_2 : have hlg : Real.log (22296196273687991 / 80000000000000000 : ℝ) ≤ (-(12776105409233890902293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22296196273687991 / 80000000000000000 : ℝ) = - (22296196273687991 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22296196273687991 / 20000000000000000 : ℚ)) - (U := (1086838196766109097707 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22296196273687991 / 20000000000000000 : ℝ) ≤ - (1086838196766109097707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2786643867675279 / 10000000000000000 : ℝ)) (q := - (22296196273687991 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22296196273687991 / 80000000000000000 : ℚ)) + (r' := (22296196273687991 / 20000000000000000 : ℚ)) + (U := (-(12776105409233890902293 / 10000000000000000000000 : ℚ))) + (U' := (1086838196766109097707 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (2786643867675279 / 10000000000000000 : ℚ)) + (q := (22296196273687991 / 80000000000000000 : ℚ)) + (U := (-(12776105409233890902293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_3 : Uω (aρ 3) (bρ 3) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1843,25 +1655,21 @@ lemma U_309_3 : have hlg : Real.log (876370693888647 / 3200000000000000 : ℝ) ≤ (-(12951169203016937992483 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (876370693888647 / 3200000000000000 : ℝ) = - (876370693888647 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (876370693888647 / 800000000000000 : ℚ)) - (U := (911774402983062007517 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (876370693888647 / 800000000000000 : ℝ) ≤ - (911774402983062007517 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109492309696293 / 400000000000000 : ℝ)) (q := - (876370693888647 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (876370693888647 / 3200000000000000 : ℚ)) + (r' := (876370693888647 / 800000000000000 : ℚ)) + (U := (-(12951169203016937992483 / 10000000000000000000000 : ℚ))) + (U' := (911774402983062007517 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (109492309696293 / 400000000000000 : ℚ)) + (q := (876370693888647 / 3200000000000000 : ℚ)) + (U := (-(12951169203016937992483 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_4 : Uω (aρ 4) (bρ 4) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1869,25 +1677,21 @@ lemma U_309_4 : have hlg : Real.log (21262051907475379 / 80000000000000000 : ℝ) ≤ (-(13251027509644650616501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21262051907475379 / 80000000000000000 : ℝ) = - (21262051907475379 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21262051907475379 / 20000000000000000 : ℚ)) - (U := (611916096355349383499 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21262051907475379 / 20000000000000000 : ℝ) ≤ - (611916096355349383499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1326899031768563 / 5000000000000000 : ℝ)) (q := - (21262051907475379 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21262051907475379 / 80000000000000000 : ℚ)) + (r' := (21262051907475379 / 20000000000000000 : ℚ)) + (U := (-(13251027509644650616501 / 10000000000000000000000 : ℚ))) + (U' := (611916096355349383499 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (1326899031768563 / 5000000000000000 : ℚ)) + (q := (21262051907475379 / 80000000000000000 : ℚ)) + (U := (-(13251027509644650616501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_5 : Uω (aρ 5) (bρ 5) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1895,25 +1699,21 @@ lemma U_309_5 : have hlg : Real.log (20264099488735607 / 80000000000000000 : ℝ) ≤ (-(13731758118370003654299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20264099488735607 / 80000000000000000 : ℝ) = - (20264099488735607 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20264099488735607 / 20000000000000000 : ℚ)) - (U := (131185487629996345701 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20264099488735607 / 20000000000000000 : ℝ) ≤ - (131185487629996345701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2522499878187183 / 10000000000000000 : ℝ)) (q := - (20264099488735607 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20264099488735607 / 80000000000000000 : ℚ)) + (r' := (20264099488735607 / 20000000000000000 : ℚ)) + (U := (-(13731758118370003654299 / 10000000000000000000000 : ℚ))) + (U' := (131185487629996345701 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (2522499878187183 / 10000000000000000 : ℚ)) + (q := (20264099488735607 / 80000000000000000 : ℚ)) + (U := (-(13731758118370003654299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_6 : Uω (aρ 6) (bρ 6) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1921,25 +1721,21 @@ lemma U_309_6 : have hlg : Real.log (18801403600488763 / 80000000000000000 : ℝ) ≤ (-(905059442027853315307 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18801403600488763 / 80000000000000000 : ℝ) = - (18801403600488763 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18801403600488763 / 10000000000000000 : ℚ)) - (U := (394591521034646684693 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18801403600488763 / 10000000000000000 : ℝ) ≤ - (394591521034646684693 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36313535644773 / 156250000000000 : ℝ)) (q := - (18801403600488763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18801403600488763 / 80000000000000000 : ℚ)) + (r' := (18801403600488763 / 10000000000000000 : ℚ)) + (U := (-(905059442027853315307 / 625000000000000000000 : ℚ))) + (U' := (394591521034646684693 / 625000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (36313535644773 / 156250000000000 : ℚ)) + (q := (18801403600488763 / 80000000000000000 : ℚ)) + (U := (-(905059442027853315307 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_7 : Uω (aρ 7) (bρ 7) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1947,25 +1743,21 @@ lemma U_309_7 : have hlg : Real.log (3344952508113903 / 16000000000000000 : ℝ) ≤ (-(2445525352896588967 / 1562500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3344952508113903 / 16000000000000000 : ℝ) = - (3344952508113903 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3344952508113903 / 2000000000000000 : ℚ)) - (U := (803602054759661033 / 1562500000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3344952508113903 / 2000000000000000 : ℝ) ≤ - (803602054759661033 / 1562500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101428369852283 / 500000000000000 : ℝ)) (q := - (3344952508113903 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3344952508113903 / 16000000000000000 : ℚ)) + (r' := (3344952508113903 / 2000000000000000 : ℚ)) + (U := (-(2445525352896588967 / 1562500000000000000 : ℚ))) + (U' := (803602054759661033 / 1562500000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (101428369852283 / 500000000000000 : ℚ)) + (q := (3344952508113903 / 16000000000000000 : ℚ)) + (U := (-(2445525352896588967 / 1562500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_8 : Uω (aρ 8) (bρ 8) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1973,25 +1765,21 @@ lemma U_309_8 : have hlg : Real.log (13781258323136651 / 80000000000000000 : ℝ) ≤ (-(8793585286503424790819 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13781258323136651 / 80000000000000000 : ℝ) = - (13781258323136651 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13781258323136651 / 10000000000000000 : ℚ)) - (U := (1603622417996575209181 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13781258323136651 / 10000000000000000 : ℝ) ≤ - (1603622417996575209181 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (394058248506861 / 2500000000000000 : ℝ)) (q := - (13781258323136651 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13781258323136651 / 80000000000000000 : ℚ)) + (r' := (13781258323136651 / 10000000000000000 : ℚ)) + (U := (-(8793585286503424790819 / 5000000000000000000000 : ℚ))) + (U' := (1603622417996575209181 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (394058248506861 / 2500000000000000 : ℚ)) + (q := (13781258323136651 / 80000000000000000 : ℚ)) + (U := (-(8793585286503424790819 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_9 : Uω (aρ 9) (bρ 9) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -1999,25 +1787,21 @@ lemma U_309_9 : have hlg : Real.log (9007091878016507 / 80000000000000000 : ℝ) ≤ (-(873605752059970258149 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9007091878016507 / 80000000000000000 : ℝ) = - (9007091878016507 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9007091878016507 / 5000000000000000 : ℚ)) - (U := (235429736420029741851 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9007091878016507 / 5000000000000000 : ℝ) ≤ - (235429736420029741851 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45228563194213 / 625000000000000 : ℝ)) (q := - (9007091878016507 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9007091878016507 / 80000000000000000 : ℚ)) + (r' := (9007091878016507 / 5000000000000000 : ℚ)) + (U := (-(873605752059970258149 / 400000000000000000000 : ℚ))) + (U' := (235429736420029741851 / 400000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18404297160587 / 64000000000000 : ℚ)) + (s := (45228563194213 / 625000000000000 : ℚ)) + (q := (9007091878016507 / 80000000000000000 : ℚ)) + (U := (-(873605752059970258149 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_309_10 : Uω (aρ 10) (bρ 10) (18404297160587 / 64000000000000 : ℝ) ≤ @@ -2143,25 +1927,21 @@ lemma U_310_1 : have hlg : Real.log (45075048679337883 / 160000000000000000 : ℝ) ≤ (-(791778103538758106661 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45075048679337883 / 160000000000000000 : ℝ) = - (45075048679337883 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45075048679337883 / 40000000000000000 : ℚ)) - (U := (74655871836241893339 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45075048679337883 / 40000000000000000 : ℝ) ≤ - (74655871836241893339 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1408566578125063 / 5000000000000000 : ℝ)) (q := - (45075048679337883 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45075048679337883 / 160000000000000000 : ℚ)) + (r' := (45075048679337883 / 40000000000000000 : ℚ)) + (U := (-(791778103538758106661 / 625000000000000000000 : ℚ))) + (U' := (74655871836241893339 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (1408566578125063 / 5000000000000000 : ℚ)) + (q := (45075048679337883 / 160000000000000000 : ℚ)) + (U := (-(791778103538758106661 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_2 : Uω (aρ 2) (bρ 2) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2169,25 +1949,21 @@ lemma U_310_2 : have hlg : Real.log (44689585240162523 / 160000000000000000 : ℝ) ≤ (-(797145832894660626739 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44689585240162523 / 160000000000000000 : ℝ) = - (44689585240162523 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44689585240162523 / 40000000000000000 : ℚ)) - (U := (69288142480339373261 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44689585240162523 / 40000000000000000 : ℝ) ≤ - (69288142480339373261 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1396359619431603 / 5000000000000000 : ℝ)) (q := - (44689585240162523 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44689585240162523 / 160000000000000000 : ℚ)) + (r' := (44689585240162523 / 40000000000000000 : ℚ)) + (U := (-(797145832894660626739 / 625000000000000000000 : ℚ))) + (U' := (69288142480339373261 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (1396359619431603 / 5000000000000000 : ℚ)) + (q := (44689585240162523 / 160000000000000000 : ℚ)) + (U := (-(797145832894660626739 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_3 : Uω (aρ 3) (bρ 3) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2195,25 +1971,21 @@ lemma U_310_3 : have hlg : Real.log (43915761986259859 / 160000000000000000 : ℝ) ≤ (-(12929005161061176723777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43915761986259859 / 160000000000000000 : ℝ) = - (43915761986259859 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43915761986259859 / 40000000000000000 : ℚ)) - (U := (933938444938823276223 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43915761986259859 / 40000000000000000 : ℝ) ≤ - (933938444938823276223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2743387438475373 / 10000000000000000 : ℝ)) (q := - (43915761986259859 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43915761986259859 / 160000000000000000 : ℚ)) + (r' := (43915761986259859 / 40000000000000000 : ℚ)) + (U := (-(12929005161061176723777 / 10000000000000000000000 : ℚ))) + (U' := (933938444938823276223 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (2743387438475373 / 10000000000000000 : ℚ)) + (q := (43915761986259859 / 160000000000000000 : ℚ)) + (U := (-(12929005161061176723777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_4 : Uω (aρ 4) (bρ 4) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2221,25 +1993,21 @@ lemma U_310_4 : have hlg : Real.log (42621427883613691 / 160000000000000000 : ℝ) ≤ (-(1322816685938930461697 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42621427883613691 / 160000000000000000 : ℝ) = - (42621427883613691 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42621427883613691 / 40000000000000000 : ℚ)) - (U := (63477674661069538303 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42621427883613691 / 40000000000000000 : ℝ) ≤ - (63477674661069538303 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1329944928354801 / 5000000000000000 : ℝ)) (q := - (42621427883613691 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42621427883613691 / 160000000000000000 : ℚ)) + (r' := (42621427883613691 / 40000000000000000 : ℚ)) + (U := (-(1322816685938930461697 / 1000000000000000000000 : ℚ))) + (U' := (63477674661069538303 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (1329944928354801 / 5000000000000000 : ℚ)) + (q := (42621427883613691 / 160000000000000000 : ℚ)) + (U := (-(1322816685938930461697 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_5 : Uω (aρ 5) (bρ 5) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2247,25 +2015,21 @@ lemma U_310_5 : have hlg : Real.log (40625782444058779 / 160000000000000000 : ℝ) ≤ (-(13707709140880624061209 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40625782444058779 / 160000000000000000 : ℝ) = - (40625782444058779 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40625782444058779 / 40000000000000000 : ℚ)) - (U := (155234465119375938791 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40625782444058779 / 40000000000000000 : ℝ) ≤ - (155234465119375938791 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1264312048050119 / 5000000000000000 : ℝ)) (q := - (40625782444058779 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40625782444058779 / 160000000000000000 : ℚ)) + (r' := (40625782444058779 / 40000000000000000 : ℚ)) + (U := (-(13707709140880624061209 / 10000000000000000000000 : ℚ))) + (U' := (155234465119375938791 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (1264312048050119 / 5000000000000000 : ℚ)) + (q := (40625782444058779 / 160000000000000000 : ℚ)) + (U := (-(13707709140880624061209 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_6 : Uω (aρ 6) (bρ 6) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2273,25 +2037,21 @@ lemma U_310_6 : have hlg : Real.log (37701075509361619 / 160000000000000000 : ℝ) ≤ (-(289097038461433344131 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (37701075509361619 / 160000000000000000 : ℝ) = - (37701075509361619 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37701075509361619 / 20000000000000000 : ℚ)) - (U := (126791269718566655869 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37701075509361619 / 20000000000000000 : ℝ) ≤ - (126791269718566655869 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2330276104403093 / 10000000000000000 : ℝ)) (q := - (37701075509361619 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37701075509361619 / 160000000000000000 : ℚ)) + (r' := (37701075509361619 / 20000000000000000 : ℚ)) + (U := (-(289097038461433344131 / 200000000000000000000 : ℚ))) + (U' := (126791269718566655869 / 200000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (2330276104403093 / 10000000000000000 : ℚ)) + (q := (37701075509361619 / 160000000000000000 : ℚ)) + (U := (-(289097038461433344131 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_7 : Uω (aρ 7) (bρ 7) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2299,25 +2059,21 @@ lemma U_310_7 : have hlg : Real.log (33549666863660643 / 160000000000000000 : ℝ) ≤ (-(3124293761267432852327 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33549666863660643 / 160000000000000000 : ℝ) = - (33549666863660643 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33549666863660643 / 20000000000000000 : ℚ)) - (U := (1034589320532567147673 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33549666863660643 / 20000000000000000 : ℝ) ≤ - (1034589320532567147673 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2035011404450471 / 10000000000000000 : ℝ)) (q := - (33549666863660643 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33549666863660643 / 160000000000000000 : ℚ)) + (r' := (33549666863660643 / 20000000000000000 : ℚ)) + (U := (-(3124293761267432852327 / 2000000000000000000000 : ℚ))) + (U' := (1034589320532567147673 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (2035011404450471 / 10000000000000000 : ℚ)) + (q := (33549666863660643 / 160000000000000000 : ℚ)) + (U := (-(3124293761267432852327 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_8 : Uω (aρ 8) (bρ 8) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2325,25 +2081,21 @@ lemma U_310_8 : have hlg : Real.log (5533737148278807 / 32000000000000000 : ℝ) ≤ (-(877436259691853950059 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5533737148278807 / 32000000000000000 : ℝ) = - (5533737148278807 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5533737148278807 / 4000000000000000 : ℚ)) - (U := (162284510758146049941 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5533737148278807 / 4000000000000000 : ℝ) ≤ - (162284510758146049941 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (316686083101429 / 2000000000000000 : ℝ)) (q := - (5533737148278807 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5533737148278807 / 32000000000000000 : ℚ)) + (r' := (5533737148278807 / 4000000000000000 : ℚ)) + (U := (-(877436259691853950059 / 500000000000000000000 : ℚ))) + (U' := (162284510758146049941 / 500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (316686083101429 / 2000000000000000 : ℚ)) + (q := (5533737148278807 / 32000000000000000 : ℚ)) + (U := (-(877436259691853950059 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_9 : Uω (aρ 9) (bρ 9) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2351,25 +2103,21 @@ lemma U_310_9 : have hlg : Real.log (18164685248242899 / 160000000000000000 : ℝ) ≤ (-(1087847238022731517901 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (18164685248242899 / 160000000000000000 : ℝ) = - (18164685248242899 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18164685248242899 / 10000000000000000 : ℚ)) - (U := (298447122577268482099 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18164685248242899 / 10000000000000000 : ℝ) ≤ - (298447122577268482099 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (736395982223253 / 10000000000000000 : ℝ)) (q := - (18164685248242899 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18164685248242899 / 160000000000000000 : ℚ)) + (r' := (18164685248242899 / 10000000000000000 : ℚ)) + (U := (-(1087847238022731517901 / 500000000000000000000 : ℚ))) + (U' := (298447122577268482099 / 500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (36886337878427 / 128000000000000 : ℚ)) + (s := (736395982223253 / 10000000000000000 : ℚ)) + (q := (18164685248242899 / 160000000000000000 : ℚ)) + (U := (-(1087847238022731517901 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_310_10 : Uω (aρ 10) (bρ 10) (36886337878427 / 128000000000000 : ℝ) ≤ @@ -2497,25 +2245,21 @@ lemma U_311_1 : have hlg : Real.log (5646528762654023 / 20000000000000000 : ℝ) ≤ (-(632345647487376720253 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5646528762654023 / 20000000000000000 : ℝ) = - (5646528762654023 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5646528762654023 / 5000000000000000 : ℚ)) - (U := (60801532812623279747 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5646528762654023 / 5000000000000000 : ℝ) ≤ - (60801532812623279747 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2823207118576523 / 10000000000000000 : ℝ)) (q := - (5646528762654023 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5646528762654023 / 20000000000000000 : ℚ)) + (r' := (5646528762654023 / 5000000000000000 : ℚ)) + (U := (-(632345647487376720253 / 500000000000000000000 : ℚ))) + (U' := (60801532812623279747 / 500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (231025508973 / 800000000000 : ℚ)) + (s := (2823207118576523 / 10000000000000000 : ℚ)) + (q := (5646528762654023 / 20000000000000000 : ℚ)) + (U := (-(632345647487376720253 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_2 : Uω (aρ 2) (bρ 2) (231025508973 / 800000000000 : ℝ) ≤ @@ -2523,25 +2267,21 @@ lemma U_311_2 : have hlg : Real.log (2799173617215593 / 10000000000000000 : ℝ) ≤ (-(6366304277815616426409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2799173617215593 / 10000000000000000 : ℝ) = - (2799173617215593 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2799173617215593 / 2500000000000000 : ℚ)) - (U := (565167525184383573591 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2799173617215593 / 2500000000000000 : ℝ) ≤ - (565167525184383573591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1399397301431843 / 5000000000000000 : ℝ)) (q := - (2799173617215593 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2799173617215593 / 10000000000000000 : ℚ)) + (r' := (2799173617215593 / 2500000000000000 : ℚ)) + (U := (-(6366304277815616426409 / 5000000000000000000000 : ℚ))) + (U' := (565167525184383573591 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (231025508973 / 800000000000 : ℚ)) + (s := (1399397301431843 / 5000000000000000 : ℚ)) + (q := (2799173617215593 / 10000000000000000 : ℚ)) + (U := (-(6366304277815616426409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_3 : Uω (aρ 3) (bρ 3) (231025508973 / 800000000000 : ℝ) ≤ @@ -2549,25 +2289,21 @@ lemma U_311_3 : have hlg : Real.log (2750811816662373 / 10000000000000000 : ℝ) ≤ (-(12906890183013655558881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2750811816662373 / 10000000000000000 : ℝ) = - (2750811816662373 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2750811816662373 / 2500000000000000 : ℚ)) - (U := (956053422986344441119 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2750811816662373 / 2500000000000000 : ℝ) ≤ - (956053422986344441119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1374733554053623 / 5000000000000000 : ℝ)) (q := - (2750811816662373 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2750811816662373 / 10000000000000000 : ℚ)) + (r' := (2750811816662373 / 2500000000000000 : ℚ)) + (U := (-(12906890183013655558881 / 10000000000000000000000 : ℚ))) + (U' := (956053422986344441119 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (231025508973 / 800000000000 : ℚ)) + (s := (1374733554053623 / 5000000000000000 : ℚ)) + (q := (2750811816662373 / 10000000000000000 : ℚ)) + (U := (-(12906890183013655558881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_4 : Uω (aρ 4) (bρ 4) (231025508973 / 800000000000 : ℝ) ≤ @@ -2575,25 +2311,21 @@ lemma U_311_4 : have hlg : Real.log (2669921955770723 / 10000000000000000 : ℝ) ≤ (-(3301339626344053614233 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2669921955770723 / 10000000000000000 : ℝ) = - (2669921955770723 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2669921955770723 / 2500000000000000 : ℚ)) - (U := (164396275155946385767 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2669921955770723 / 2500000000000000 : ℝ) ≤ - (164396275155946385767 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1332990783694473 / 5000000000000000 : ℝ)) (q := - (2669921955770723 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2669921955770723 / 10000000000000000 : ℚ)) + (r' := (2669921955770723 / 2500000000000000 : ℚ)) + (U := (-(3301339626344053614233 / 2500000000000000000000 : ℚ))) + (U' := (164396275155946385767 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (231025508973 / 800000000000 : ℚ)) + (s := (1332990783694473 / 5000000000000000 : ℚ)) + (q := (2669921955770723 / 10000000000000000 : ℚ)) + (U := (-(3301339626344053614233 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_5 : Uω (aρ 5) (bρ 5) (231025508973 / 800000000000 : ℝ) ≤ @@ -2601,25 +2333,21 @@ lemma U_311_5 : have hlg : Real.log (159075640493697 / 625000000000000 : ℝ) ≤ (-(3420929584356858442139 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (159075640493697 / 625000000000000 : ℝ) = - (159075640493697 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (159075640493697 / 156250000000000 : ℚ)) - (U := (44806317143141557861 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (159075640493697 / 156250000000000 : ℝ) ≤ - (44806317143141557861 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (633687017745201 / 2500000000000000 : ℝ)) (q := - (159075640493697 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (159075640493697 / 625000000000000 : ℚ)) + (r' := (159075640493697 / 156250000000000 : ℚ)) + (U := (-(3420929584356858442139 / 2500000000000000000000 : ℚ))) + (U' := (44806317143141557861 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (231025508973 / 800000000000 : ℚ)) + (s := (633687017745201 / 2500000000000000 : ℚ)) + (q := (159075640493697 / 625000000000000 : ℚ)) + (U := (-(3420929584356858442139 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_6 : Uω (aρ 6) (bρ 6) (231025508973 / 800000000000 : ℝ) ≤ @@ -2627,25 +2355,21 @@ lemma U_311_6 : have hlg : Real.log (944983452332593 / 4000000000000000 : ℝ) ≤ (-(14428822227409249675339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (944983452332593 / 4000000000000000 : ℝ) = - (944983452332593 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (944983452332593 / 500000000000000 : ℚ)) - (U := (6365593181590750324661 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (944983452332593 / 500000000000000 : ℝ) ≤ - (6365593181590750324661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (467297042397093 / 2000000000000000 : ℝ)) (q := - (944983452332593 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (944983452332593 / 4000000000000000 : ℚ)) + (r' := (944983452332593 / 500000000000000 : ℚ)) + (U := (-(14428822227409249675339 / 10000000000000000000000 : ℚ))) + (U' := (6365593181590750324661 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (231025508973 / 800000000000 : ℚ)) + (s := (467297042397093 / 2000000000000000 : ℚ)) + (q := (944983452332593 / 4000000000000000 : ℚ)) + (U := (-(14428822227409249675339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_7 : Uω (aρ 7) (bρ 7) (231025508973 / 800000000000 : ℝ) ≤ @@ -2653,25 +2377,21 @@ lemma U_311_7 : have hlg : Real.log (841244762045679 / 4000000000000000 : ℝ) ≤ (-(15591669847770762946373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (841244762045679 / 4000000000000000 : ℝ) = - (841244762045679 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (841244762045679 / 500000000000000 : ℚ)) - (U := (5202745561229237053627 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (841244762045679 / 500000000000000 : ℝ) ≤ - (5202745561229237053627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (408290628262179 / 2000000000000000 : ℝ)) (q := - (841244762045679 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (841244762045679 / 4000000000000000 : ℚ)) + (r' := (841244762045679 / 500000000000000 : ℚ)) + (U := (-(15591669847770762946373 / 10000000000000000000000 : ℚ))) + (U' := (5202745561229237053627 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (231025508973 / 800000000000 : ℚ)) + (s := (408290628262179 / 2000000000000000 : ℚ)) + (q := (841244762045679 / 4000000000000000 : ℚ)) + (U := (-(15591669847770762946373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_8 : Uω (aρ 8) (bρ 8) (231025508973 / 800000000000 : ℝ) ≤ @@ -2679,25 +2399,21 @@ lemma U_311_8 : have hlg : Real.log (3471847479083373 / 20000000000000000 : ℝ) ≤ (-(8755227028881924606817 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3471847479083373 / 20000000000000000 : ℝ) = - (3471847479083373 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3471847479083373 / 2500000000000000 : ℚ)) - (U := (1641980675618075393183 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3471847479083373 / 2500000000000000 : ℝ) ≤ - (1641980675618075393183 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1590618461505873 / 10000000000000000 : ℝ)) (q := - (3471847479083373 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3471847479083373 / 20000000000000000 : ℚ)) + (r' := (3471847479083373 / 2500000000000000 : ℚ)) + (U := (-(8755227028881924606817 / 5000000000000000000000 : ℚ))) + (U' := (1641980675618075393183 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (231025508973 / 800000000000 : ℚ)) + (s := (1590618461505873 / 10000000000000000 : ℚ)) + (q := (3471847479083373 / 20000000000000000 : ℚ)) + (U := (-(8755227028881924606817 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_9 : Uω (aρ 9) (bρ 9) (231025508973 / 800000000000 : ℝ) ≤ @@ -2705,25 +2421,21 @@ lemma U_311_9 : have hlg : Real.log (2289230942307729 / 20000000000000000 : ℝ) ≤ (-(1083758172203001746681 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2289230942307729 / 20000000000000000 : ℝ) = - (2289230942307729 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2289230942307729 / 1250000000000000 : ℚ)) - (U := (302536188396998253319 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2289230942307729 / 1250000000000000 : ℝ) ≤ - (302536188396998253319 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (748967553090229 / 10000000000000000 : ℝ)) (q := - (2289230942307729 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2289230942307729 / 20000000000000000 : ℚ)) + (r' := (2289230942307729 / 1250000000000000 : ℚ)) + (U := (-(1083758172203001746681 / 500000000000000000000 : ℚ))) + (U' := (302536188396998253319 / 500000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (231025508973 / 800000000000 : ℚ)) + (s := (748967553090229 / 10000000000000000 : ℚ)) + (q := (2289230942307729 / 20000000000000000 : ℚ)) + (U := (-(1083758172203001746681 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_311_10 : Uω (aρ 10) (bρ 10) (231025508973 / 800000000000 : ℝ) ≤ @@ -2850,25 +2562,21 @@ lemma U_312_1 : have hlg : Real.log (45269411514645309 / 160000000000000000 : ℝ) ≤ (-(12625422528061556459799 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45269411514645309 / 160000000000000000 : ℝ) = - (45269411514645309 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45269411514645309 / 40000000000000000 : ℚ)) - (U := (1237521077938443540201 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45269411514645309 / 40000000000000000 : ℝ) ≤ - (1237521077938443540201 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2829281079842773 / 10000000000000000 : ℝ)) (q := - (45269411514645309 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45269411514645309 / 160000000000000000 : ℚ)) + (r' := (45269411514645309 / 40000000000000000 : ℚ)) + (U := (-(12625422528061556459799 / 10000000000000000000000 : ℚ))) + (U' := (1237521077938443540201 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (2829281079842773 / 10000000000000000 : ℚ)) + (q := (45269411514645309 / 160000000000000000 : ℚ)) + (U := (-(12625422528061556459799 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_2 : Uω (aρ 2) (bρ 2) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -2876,25 +2584,21 @@ lemma U_312_2 : have hlg : Real.log (1795358818144421 / 6400000000000000 : ℝ) ≤ (-(12710930891948740915369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1795358818144421 / 6400000000000000 : ℝ) = - (1795358818144421 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1795358818144421 / 1600000000000000 : ℚ)) - (U := (1152012714051259084631 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1795358818144421 / 1600000000000000 : ℝ) ≤ - (1152012714051259084631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (112194798388937 / 400000000000000 : ℝ)) (q := - (1795358818144421 / 6400000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1795358818144421 / 6400000000000000 : ℚ)) + (r' := (1795358818144421 / 1600000000000000 : ℚ)) + (U := (-(12710930891948740915369 / 10000000000000000000000 : ℚ))) + (U' := (1152012714051259084631 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (112194798388937 / 400000000000000 : ℚ)) + (q := (1795358818144421 / 6400000000000000 : ℚ)) + (U := (-(12710930891948740915369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_3 : Uω (aρ 3) (bρ 3) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -2902,25 +2606,21 @@ lemma U_312_3 : have hlg : Real.log (44110215936846533 / 160000000000000000 : ℝ) ≤ (-(12884824051920100839147 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44110215936846533 / 160000000000000000 : ℝ) = - (44110215936846533 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44110215936846533 / 40000000000000000 : ℚ)) - (U := (978119554079899160853 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44110215936846533 / 40000000000000000 : ℝ) ≤ - (978119554079899160853 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1377773375738963 / 5000000000000000 : ℝ)) (q := - (44110215936846533 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44110215936846533 / 160000000000000000 : ℚ)) + (r' := (44110215936846533 / 40000000000000000 : ℚ)) + (U := (-(12884824051920100839147 / 10000000000000000000000 : ℚ))) + (U' := (978119554079899160853 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (1377773375738963 / 5000000000000000 : ℚ)) + (q := (44110215936846533 / 160000000000000000 : ℚ)) + (U := (-(12884824051920100839147 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_4 : Uω (aρ 4) (bρ 4) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -2928,25 +2628,21 @@ lemma U_312_4 : have hlg : Real.log (42816074045617973 / 160000000000000000 : ℝ) ≤ (-(1318260220818366757497 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42816074045617973 / 160000000000000000 : ℝ) = - (42816074045617973 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42816074045617973 / 40000000000000000 : ℚ)) - (U := (68034139781633242503 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42816074045617973 / 40000000000000000 : ℝ) ≤ - (68034139781633242503 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (668018299034839 / 2500000000000000 : ℝ)) (q := - (42816074045617973 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42816074045617973 / 160000000000000000 : ℚ)) + (r' := (42816074045617973 / 40000000000000000 : ℚ)) + (U := (-(1318260220818366757497 / 1000000000000000000000 : ℚ))) + (U' := (68034139781633242503 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (668018299034839 / 2500000000000000 : ℚ)) + (q := (42816074045617973 / 160000000000000000 : ℚ)) + (U := (-(1318260220818366757497 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_5 : Uω (aρ 5) (bρ 5) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -2954,25 +2650,21 @@ lemma U_312_5 : have hlg : Real.log (40820943558512269 / 160000000000000000 : ℝ) ≤ (-(13659785424961961456927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40820943558512269 / 160000000000000000 : ℝ) = - (40820943558512269 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40820943558512269 / 40000000000000000 : ℚ)) - (U := (203158181038038543073 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40820943558512269 / 40000000000000000 : ℝ) ≤ - (203158181038038543073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2540871804586143 / 10000000000000000 : ℝ)) (q := - (40820943558512269 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40820943558512269 / 160000000000000000 : ℚ)) + (r' := (40820943558512269 / 40000000000000000 : ℚ)) + (U := (-(13659785424961961456927 / 10000000000000000000000 : ℚ))) + (U' := (203158181038038543073 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (2540871804586143 / 10000000000000000 : ℚ)) + (q := (40820943558512269 / 160000000000000000 : ℚ)) + (U := (-(13659785424961961456927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_6 : Uω (aρ 6) (bρ 6) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -2980,25 +2672,21 @@ lemma U_312_6 : have hlg : Real.log (7579518999664049 / 32000000000000000 : ℝ) ≤ (-(14402861608877604147629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7579518999664049 / 32000000000000000 : ℝ) = - (7579518999664049 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7579518999664049 / 4000000000000000 : ℚ)) - (U := (6391553800122395852371 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7579518999664049 / 4000000000000000 : ℝ) ≤ - (6391553800122395852371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117134680485107 / 500000000000000 : ℝ)) (q := - (7579518999664049 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7579518999664049 / 32000000000000000 : ℚ)) + (r' := (7579518999664049 / 4000000000000000 : ℚ)) + (U := (-(14402861608877604147629 / 10000000000000000000000 : ℚ))) + (U' := (6391553800122395852371 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (117134680485107 / 500000000000000 : ℚ)) + (q := (7579518999664049 / 32000000000000000 : ℚ)) + (U := (-(14402861608877604147629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_7 : Uω (aρ 7) (bρ 7) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -3006,25 +2694,21 @@ lemma U_312_7 : have hlg : Real.log (33749896107048941 / 160000000000000000 : ℝ) ≤ (-(7780982377249255875523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33749896107048941 / 160000000000000000 : ℝ) = - (33749896107048941 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33749896107048941 / 20000000000000000 : ℚ)) - (U := (2616225327250744124477 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33749896107048941 / 20000000000000000 : ℝ) ≤ - (2616225327250744124477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2047892629053227 / 10000000000000000 : ℝ)) (q := - (33749896107048941 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33749896107048941 / 160000000000000000 : ℚ)) + (r' := (33749896107048941 / 20000000000000000 : ℚ)) + (U := (-(7780982377249255875523 / 5000000000000000000000 : ℚ))) + (U' := (2616225327250744124477 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (2047892629053227 / 10000000000000000 : ℚ)) + (q := (33749896107048941 / 160000000000000000 : ℚ)) + (U := (-(7780982377249255875523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_8 : Uω (aρ 8) (bρ 8) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -3032,25 +2716,21 @@ lemma U_312_8 : have hlg : Real.log (27880799932356629 / 160000000000000000 : ℝ) ≤ (-(17472355369949165105051 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (27880799932356629 / 160000000000000000 : ℝ) = - (27880799932356629 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27880799932356629 / 20000000000000000 : ℚ)) - (U := (3322060039050834894949 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27880799932356629 / 20000000000000000 : ℝ) ≤ - (3322060039050834894949 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99862328659793 / 625000000000000 : ℝ)) (q := - (27880799932356629 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27880799932356629 / 160000000000000000 : ℚ)) + (r' := (27880799932356629 / 20000000000000000 : ℚ)) + (U := (-(17472355369949165105051 / 10000000000000000000000 : ℚ))) + (U' := (3322060039050834894949 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (99862328659793 / 625000000000000 : ℚ)) + (q := (27880799932356629 / 160000000000000000 : ℚ)) + (U := (-(17472355369949165105051 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_9 : Uω (aρ 9) (bρ 9) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -3058,24 +2738,21 @@ lemma U_312_9 : have hlg : Real.log (29538779142381 / 256000000000000 : ℝ) ≤ (-(10797367480776861680277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (29538779142381 / 256000000000000 : ℝ) = (29538779142381 / 16000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29538779142381 / 16000000000000 : ℚ)) - (U := (3065576125223138319723 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (29538779142381 / 16000000000000 : ℝ) ≤ - (3065576125223138319723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1218208025393 / 16000000000000 : ℝ)) (q := - (29538779142381 / 256000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29538779142381 / 256000000000000 : ℚ)) + (r' := (29538779142381 / 16000000000000 : ℚ)) + (U := (-(10797367480776861680277 / 5000000000000000000000 : ℚ))) + (U' := (3065576125223138319723 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37041824992933 / 128000000000000 : ℚ)) + (s := (1218208025393 / 16000000000000 : ℚ)) + (q := (29538779142381 / 256000000000000 : ℚ)) + (U := (-(10797367480776861680277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_312_10 : Uω (aρ 10) (bρ 10) (37041824992933 / 128000000000000 : ℝ) ≤ @@ -3204,25 +2881,21 @@ lemma U_313_1 : have hlg : Real.log (22683296459815877 / 80000000000000000 : ℝ) ≤ (-(1575497274129372754583 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22683296459815877 / 80000000000000000 : ℝ) = - (22683296459815877 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22683296459815877 / 20000000000000000 : ℚ)) - (U := (157370676620627245417 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22683296459815877 / 20000000000000000 : ℝ) ≤ - (157370676620627245417 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (354419380006961 / 1250000000000000 : ℝ)) (q := - (22683296459815877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22683296459815877 / 80000000000000000 : ℚ)) + (r' := (22683296459815877 / 20000000000000000 : ℚ)) + (U := (-(1575497274129372754583 / 1250000000000000000000 : ℚ))) + (U' := (157370676620627245417 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (354419380006961 / 1250000000000000 : ℚ)) + (q := (22683296459815877 / 80000000000000000 : ℚ)) + (U := (-(1575497274129372754583 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_2 : Uω (aρ 2) (bρ 2) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3230,25 +2903,21 @@ lemma U_313_2 : have hlg : Real.log (22490581487508013 / 80000000000000000 : ℝ) ≤ (-(12689300131364860125261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22490581487508013 / 80000000000000000 : ℝ) = - (22490581487508013 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22490581487508013 / 20000000000000000 : ℚ)) - (U := (1173643474635139874739 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22490581487508013 / 20000000000000000 : ℝ) ≤ - (1173643474635139874739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1405472654744361 / 5000000000000000 : ℝ)) (q := - (22490581487508013 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22490581487508013 / 80000000000000000 : ℚ)) + (r' := (22490581487508013 / 20000000000000000 : ℚ)) + (U := (-(12689300131364860125261 / 10000000000000000000000 : ℚ))) + (U' := (1173643474635139874739 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (1405472654744361 / 5000000000000000 : ℚ)) + (q := (22490581487508013 / 80000000000000000 : ℚ)) + (U := (-(12689300131364860125261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_3 : Uω (aρ 3) (bρ 3) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3256,25 +2925,21 @@ lemma U_313_3 : have hlg : Real.log (22103721299196533 / 80000000000000000 : ℝ) ≤ (-(6431403276131736116647 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22103721299196533 / 80000000000000000 : ℝ) = - (22103721299196533 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22103721299196533 / 20000000000000000 : ℚ)) - (U := (500068526868263883353 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22103721299196533 / 20000000000000000 : ℝ) ≤ - (500068526868263883353 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (690406592190213 / 2500000000000000 : ℝ)) (q := - (22103721299196533 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22103721299196533 / 80000000000000000 : ℚ)) + (r' := (22103721299196533 / 20000000000000000 : ℚ)) + (U := (-(6431403276131736116647 / 5000000000000000000000 : ℚ))) + (U' := (500068526868263883353 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (690406592190213 / 2500000000000000 : ℚ)) + (q := (22103721299196533 / 80000000000000000 : ℚ)) + (U := (-(6431403276131736116647 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_4 : Uω (aρ 4) (bρ 4) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3282,25 +2947,21 @@ lemma U_313_4 : have hlg : Real.log (21456698073972669 / 80000000000000000 : ℝ) ≤ (-(1644987216254391239947 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21456698073972669 / 80000000000000000 : ℝ) = - (21456698073972669 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21456698073972669 / 20000000000000000 : ℚ)) - (U := (87880734495608760053 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21456698073972669 / 20000000000000000 : ℝ) ≤ - (87880734495608760053 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1339082371759943 / 5000000000000000 : ℝ)) (q := - (21456698073972669 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21456698073972669 / 80000000000000000 : ℚ)) + (r' := (21456698073972669 / 20000000000000000 : ℚ)) + (U := (-(1644987216254391239947 / 1250000000000000000000 : ℚ))) + (U' := (87880734495608760053 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (1339082371759943 / 5000000000000000 : ℚ)) + (q := (21456698073972669 / 80000000000000000 : ℚ)) + (U := (-(1644987216254391239947 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_5 : Uω (aρ 5) (bρ 5) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3308,25 +2969,21 @@ lemma U_313_5 : have hlg : Real.log (20459260617179309 / 80000000000000000 : ℝ) ≤ (-(13635910122512783687653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20459260617179309 / 80000000000000000 : ℝ) = - (20459260617179309 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20459260617179309 / 20000000000000000 : ℚ)) - (U := (227033483487216312347 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20459260617179309 / 20000000000000000 : ℝ) ≤ - (227033483487216312347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1273497649328273 / 5000000000000000 : ℝ)) (q := - (20459260617179309 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20459260617179309 / 80000000000000000 : ℚ)) + (r' := (20459260617179309 / 20000000000000000 : ℚ)) + (U := (-(13635910122512783687653 / 10000000000000000000000 : ℚ))) + (U' := (227033483487216312347 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (1273497649328273 / 5000000000000000 : ℚ)) + (q := (20459260617179309 / 80000000000000000 : ℚ)) + (U := (-(13635910122512783687653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_6 : Uω (aρ 6) (bρ 6) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3334,25 +2991,21 @@ lemma U_313_6 : have hlg : Real.log (18997923134720613 / 80000000000000000 : ℝ) ≤ (-(898560605875719717287 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18997923134720613 / 80000000000000000 : ℝ) = - (18997923134720613 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18997923134720613 / 10000000000000000 : ℚ)) - (U := (401090357186780282713 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18997923134720613 / 10000000000000000 : ℝ) ≤ - (401090357186780282713 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (146806331448867 / 625000000000000 : ℝ)) (q := - (18997923134720613 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18997923134720613 / 80000000000000000 : ℚ)) + (r' := (18997923134720613 / 10000000000000000 : ℚ)) + (U := (-(898560605875719717287 / 625000000000000000000 : ℚ))) + (U' := (401090357186780282713 / 625000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (146806331448867 / 625000000000000 : ℚ)) + (q := (18997923134720613 / 80000000000000000 : ℚ)) + (U := (-(898560605875719717287 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_7 : Uω (aρ 7) (bρ 7) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3360,25 +3013,21 @@ lemma U_313_7 : have hlg : Real.log (16924991954263829 / 80000000000000000 : ℝ) ≤ (-(155323529047166465161 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16924991954263829 / 80000000000000000 : ℝ) = - (16924991954263829 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16924991954263829 / 10000000000000000 : ℚ)) - (U := (52620625042833534839 / 100000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16924991954263829 / 10000000000000000 : ℝ) ≤ - (52620625042833534839 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (513582472206919 / 2500000000000000 : ℝ)) (q := - (16924991954263829 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16924991954263829 / 80000000000000000 : ℚ)) + (r' := (16924991954263829 / 10000000000000000 : ℚ)) + (U := (-(155323529047166465161 / 100000000000000000000 : ℚ))) + (U' := (52620625042833534839 / 100000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (513582472206919 / 2500000000000000 : ℚ)) + (q := (16924991954263829 / 80000000000000000 : ℚ)) + (U := (-(155323529047166465161 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_8 : Uω (aρ 8) (bρ 8) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3386,25 +3035,21 @@ lemma U_313_8 : have hlg : Real.log (13993373516662809 / 80000000000000000 : ℝ) ≤ (-(17434427365685407335693 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13993373516662809 / 80000000000000000 : ℝ) = - (13993373516662809 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13993373516662809 / 10000000000000000 : ℚ)) - (U := (3359988043314592664307 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13993373516662809 / 10000000000000000 : ℝ) ≤ - (3359988043314592664307 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1604966930767421 / 10000000000000000 : ℝ)) (q := - (13993373516662809 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13993373516662809 / 80000000000000000 : ℚ)) + (r' := (13993373516662809 / 10000000000000000 : ℚ)) + (U := (-(17434427365685407335693 / 10000000000000000000000 : ℚ))) + (U' := (3359988043314592664307 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (1604966930767421 / 10000000000000000 : ℚ)) + (q := (13993373516662809 / 80000000000000000 : ℚ)) + (U := (-(17434427365685407335693 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_9 : Uω (aρ 9) (bρ 9) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3412,25 +3057,21 @@ lemma U_313_9 : have hlg : Real.log (9304207395734157 / 80000000000000000 : ℝ) ≤ (-(10757799638185708569451 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9304207395734157 / 80000000000000000 : ℝ) = - (9304207395734157 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9304207395734157 / 5000000000000000 : ℚ)) - (U := (3105143967814291430549 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9304207395734157 / 5000000000000000 : ℝ) ≤ - (3105143967814291430549 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (386820514447629 / 5000000000000000 : ℝ)) (q := - (9304207395734157 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9304207395734157 / 80000000000000000 : ℚ)) + (r' := (9304207395734157 / 5000000000000000 : ℚ)) + (U := (-(10757799638185708569451 / 5000000000000000000000 : ℚ))) + (U' := (3105143967814291430549 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18559784275093 / 64000000000000 : ℚ)) + (s := (386820514447629 / 5000000000000000 : ℚ)) + (q := (9304207395734157 / 80000000000000000 : ℚ)) + (U := (-(10757799638185708569451 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_313_10 : Uω (aρ 10) (bρ 10) (18559784275093 / 64000000000000 : ℝ) ≤ @@ -3557,25 +3198,21 @@ lemma U_314_1 : have hlg : Real.log (45463774316245559 / 160000000000000000 : ℝ) ≤ (-(2516515949483040556447 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45463774316245559 / 160000000000000000 : ℝ) = - (45463774316245559 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45463774316245559 / 40000000000000000 : ℚ)) - (U := (256072771716959443553 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45463774316245559 / 40000000000000000 : ℝ) ≤ - (256072771716959443553 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2841428999222023 / 10000000000000000 : ℝ)) (q := - (45463774316245559 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45463774316245559 / 160000000000000000 : ℚ)) + (r' := (45463774316245559 / 40000000000000000 : ℚ)) + (U := (-(2516515949483040556447 / 2000000000000000000000 : ℚ))) + (U' := (256072771716959443553 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2841428999222023 / 10000000000000000 : ℚ)) + (q := (45463774316245559 / 160000000000000000 : ℚ)) + (U := (-(2516515949483040556447 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_2 : Uω (aρ 2) (bρ 2) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3583,25 +3220,21 @@ lemma U_314_2 : have hlg : Real.log (45078355440033207 / 160000000000000000 : ℝ) ≤ (-(6333858035649365264693 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45078355440033207 / 160000000000000000 : ℝ) = - (45078355440033207 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45078355440033207 / 40000000000000000 : ℚ)) - (U := (597613767350634735307 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45078355440033207 / 40000000000000000 : ℝ) ≤ - (597613767350634735307 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2817020652205479 / 10000000000000000 : ℝ)) (q := - (45078355440033207 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45078355440033207 / 160000000000000000 : ℚ)) + (r' := (45078355440033207 / 40000000000000000 : ℚ)) + (U := (-(6333858035649365264693 / 5000000000000000000000 : ℚ))) + (U' := (597613767350634735307 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2817020652205479 / 10000000000000000 : ℚ)) + (q := (45078355440033207 / 160000000000000000 : ℚ)) + (U := (-(6333858035649365264693 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_3 : Uω (aρ 3) (bρ 3) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3609,25 +3242,21 @@ lemma U_314_3 : have hlg : Real.log (44304669052612903 / 160000000000000000 : ℝ) ≤ (-(2568167493990255296731 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44304669052612903 / 160000000000000000 : ℝ) = - (44304669052612903 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44304669052612903 / 40000000000000000 : ℚ)) - (U := (204421227209744703269 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44304669052612903 / 40000000000000000 : ℝ) ≤ - (204421227209744703269 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2767705960127941 / 10000000000000000 : ℝ)) (q := - (44304669052612903 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44304669052612903 / 160000000000000000 : ℚ)) + (r' := (44304669052612903 / 40000000000000000 : ℚ)) + (U := (-(2568167493990255296731 / 2000000000000000000000 : ℚ))) + (U' := (204421227209744703269 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2767705960127941 / 10000000000000000 : ℚ)) + (q := (44304669052612903 / 160000000000000000 : ℚ)) + (U := (-(2568167493990255296731 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_4 : Uω (aρ 4) (bρ 4) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3635,25 +3264,21 @@ lemma U_314_4 : have hlg : Real.log (8602143520749091 / 32000000000000000 : ℝ) ≤ (-(2627448966956830868993 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8602143520749091 / 32000000000000000 : ℝ) = - (8602143520749091 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8602143520749091 / 8000000000000000 : ℚ)) - (U := (145139754243169131007 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8602143520749091 / 8000000000000000 : ℝ) ≤ - (145139754243169131007 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268425621008451 / 1000000000000000 : ℝ)) (q := - (8602143520749091 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8602143520749091 / 32000000000000000 : ℚ)) + (r' := (8602143520749091 / 8000000000000000 : ℚ)) + (U := (-(2627448966956830868993 / 2000000000000000000000 : ℚ))) + (U' := (145139754243169131007 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (268425621008451 / 1000000000000000 : ℚ)) + (q := (8602143520749091 / 32000000000000000 : ℚ)) + (U := (-(2627448966956830868993 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_5 : Uω (aρ 5) (bρ 5) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3661,25 +3286,21 @@ lemma U_314_5 : have hlg : Real.log (41016097007713719 / 160000000000000000 : ℝ) ≤ (-(13612092151165089101821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41016097007713719 / 160000000000000000 : ℝ) = - (41016097007713719 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41016097007713719 / 40000000000000000 : ℚ)) - (U := (250851454834910898179 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41016097007713719 / 40000000000000000 : ℝ) ≤ - (250851454834910898179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2553118554915543 / 10000000000000000 : ℝ)) (q := - (41016097007713719 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41016097007713719 / 160000000000000000 : ℚ)) + (r' := (41016097007713719 / 40000000000000000 : ℚ)) + (U := (-(13612092151165089101821 / 10000000000000000000000 : ℚ))) + (U' := (250851454834910898179 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2553118554915543 / 10000000000000000 : ℚ)) + (q := (41016097007713719 / 160000000000000000 : ℚ)) + (U := (-(13612092151165089101821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_6 : Uω (aρ 6) (bρ 6) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3687,25 +3308,21 @@ lemma U_314_6 : have hlg : Real.log (38094091951216839 / 160000000000000000 : ℝ) ≤ (-(14351146112426458858217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (38094091951216839 / 160000000000000000 : ℝ) = - (38094091951216839 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38094091951216839 / 20000000000000000 : ℚ)) - (U := (6443269296573541141783 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38094091951216839 / 20000000000000000 : ℝ) ≤ - (6443269296573541141783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2355108297993433 / 10000000000000000 : ℝ)) (q := - (38094091951216839 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38094091951216839 / 160000000000000000 : ℚ)) + (r' := (38094091951216839 / 20000000000000000 : ℚ)) + (U := (-(14351146112426458858217 / 10000000000000000000000 : ℚ))) + (U' := (6443269296573541141783 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2355108297993433 / 10000000000000000 : ℚ)) + (q := (38094091951216839 / 160000000000000000 : ℚ)) + (U := (-(14351146112426458858217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_7 : Uω (aρ 7) (bρ 7) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3713,25 +3330,21 @@ lemma U_314_7 : have hlg : Real.log (33950054053292631 / 160000000000000000 : ℝ) ≤ (-(15502833683064404763959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33950054053292631 / 160000000000000000 : ℝ) = - (33950054053292631 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33950054053292631 / 20000000000000000 : ℚ)) - (U := (5291581725935595236041 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33950054053292631 / 20000000000000000 : ℝ) ≤ - (5291581725935595236041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2060764941512907 / 10000000000000000 : ℝ)) (q := - (33950054053292631 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33950054053292631 / 160000000000000000 : ℚ)) + (r' := (33950054053292631 / 20000000000000000 : ℚ)) + (U := (-(15502833683064404763959 / 10000000000000000000000 : ℚ))) + (U' := (5291581725935595236041 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (2060764941512907 / 10000000000000000 : ℚ)) + (q := (33950054053292631 / 160000000000000000 : ℚ)) + (U := (-(15502833683064404763959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_8 : Uω (aρ 8) (bρ 8) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3739,25 +3352,21 @@ lemma U_314_8 : have hlg : Real.log (28092622109523383 / 160000000000000000 : ℝ) ≤ (-(695866732387491057881 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (28092622109523383 / 160000000000000000 : ℝ) = - (28092622109523383 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28092622109523383 / 20000000000000000 : ℚ)) - (U := (135909883972508942119 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28092622109523383 / 20000000000000000 : ℝ) ≤ - (135909883972508942119 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1612127599881751 / 10000000000000000 : ℝ)) (q := - (28092622109523383 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28092622109523383 / 160000000000000000 : ℚ)) + (r' := (28092622109523383 / 20000000000000000 : ℚ)) + (U := (-(695866732387491057881 / 400000000000000000000 : ℚ))) + (U' := (135909883972508942119 / 400000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (1612127599881751 / 10000000000000000 : ℚ)) + (q := (28092622109523383 / 160000000000000000 : ℚ)) + (U := (-(695866732387491057881 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_9 : Uω (aρ 9) (bρ 9) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3765,25 +3374,21 @@ lemma U_314_9 : have hlg : Real.log (18753937738718031 / 160000000000000000 : ℝ) ≤ (-(21437700710955841835511 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (18753937738718031 / 160000000000000000 : ℝ) = - (18753937738718031 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18753937738718031 / 10000000000000000 : ℚ)) - (U := (6288186501044158164489 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18753937738718031 / 10000000000000000 : ℝ) ≤ - (6288186501044158164489 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (392878840945541 / 5000000000000000 : ℝ)) (q := - (18753937738718031 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18753937738718031 / 160000000000000000 : ℚ)) + (r' := (18753937738718031 / 10000000000000000 : ℚ)) + (U := (-(21437700710955841835511 / 10000000000000000000000 : ℚ))) + (U' := (6288186501044158164489 / 10000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37197312107439 / 128000000000000 : ℚ)) + (s := (392878840945541 / 5000000000000000 : ℚ)) + (q := (18753937738718031 / 160000000000000000 : ℚ)) + (U := (-(21437700710955841835511 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_314_10 : Uω (aρ 10) (bρ 10) (37197312107439 / 128000000000000 : ℝ) ≤ @@ -3911,25 +3516,21 @@ lemma U_315_1 : have hlg : Real.log (11390238926135077 / 40000000000000000 : ℝ) ≤ (-(1256122699521332861959 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11390238926135077 / 40000000000000000 : ℝ) = - (11390238926135077 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11390238926135077 / 10000000000000000 : ℚ)) - (U := (130171661078667138041 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11390238926135077 / 10000000000000000 : ℝ) ≤ - (130171661078667138041 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (711875739337119 / 2500000000000000 : ℝ)) (q := - (11390238926135077 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11390238926135077 / 40000000000000000 : ℚ)) + (r' := (11390238926135077 / 10000000000000000 : ℚ)) + (U := (-(1256122699521332861959 / 1000000000000000000000 : ℚ))) + (U' := (130171661078667138041 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (711875739337119 / 2500000000000000 : ℚ)) + (q := (11390238926135077 / 40000000000000000 : ℚ)) + (U := (-(1256122699521332861959 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_2 : Uω (aρ 2) (bρ 2) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -3937,25 +3538,21 @@ lemma U_315_2 : have hlg : Real.log (11293886962256527 / 40000000000000000 : ℝ) ≤ (-(790386156904967377561 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11293886962256527 / 40000000000000000 : ℝ) = - (11293886962256527 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11293886962256527 / 10000000000000000 : ℚ)) - (U := (76047818470032622439 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11293886962256527 / 10000000000000000 : ℝ) ≤ - (76047818470032622439 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2823095987919201 / 10000000000000000 : ℝ)) (q := - (11293886962256527 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11293886962256527 / 40000000000000000 : ℚ)) + (r' := (11293886962256527 / 10000000000000000 : ℚ)) + (U := (-(790386156904967377561 / 625000000000000000000 : ℚ))) + (U' := (76047818470032622439 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (2823095987919201 / 10000000000000000 : ℚ)) + (q := (11293886962256527 / 40000000000000000 : ℚ)) + (U := (-(790386156904967377561 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_3 : Uω (aρ 3) (bρ 3) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -3963,25 +3560,21 @@ lemma U_315_3 : have hlg : Real.log (11100473825217321 / 40000000000000000 : ℝ) ≤ (-(6409458296151520141253 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11100473825217321 / 40000000000000000 : ℝ) = - (11100473825217321 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11100473825217321 / 10000000000000000 : ℚ)) - (U := (522013506848479858747 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11100473825217321 / 10000000000000000 : ℝ) ≤ - (522013506848479858747 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1386892762874799 / 5000000000000000 : ℝ)) (q := - (11100473825217321 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11100473825217321 / 40000000000000000 : ℚ)) + (r' := (11100473825217321 / 10000000000000000 : ℚ)) + (U := (-(6409458296151520141253 / 5000000000000000000000 : ℚ))) + (U' := (522013506848479858747 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (1386892762874799 / 5000000000000000 : ℚ)) + (q := (11100473825217321 / 40000000000000000 : ℚ)) + (U := (-(6409458296151520141253 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_4 : Uω (aρ 4) (bρ 4) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -3989,25 +3582,21 @@ lemma U_315_4 : have hlg : Real.log (431080384174099 / 1600000000000000 : ℝ) ≤ (-(1311464328789948097699 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (431080384174099 / 1600000000000000 : ℝ) = - (431080384174099 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (431080384174099 / 400000000000000 : ℚ)) - (U := (74830031810051902301 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (431080384174099 / 400000000000000 : ℝ) ≤ - (74830031810051902301 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (107613903855287 / 400000000000000 : ℝ)) (q := - (431080384174099 / 1600000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (431080384174099 / 1600000000000000 : ℚ)) + (r' := (431080384174099 / 400000000000000 : ℚ)) + (U := (-(1311464328789948097699 / 1000000000000000000000 : ℚ))) + (U' := (74830031810051902301 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (107613903855287 / 400000000000000 : ℚ)) + (q := (431080384174099 / 1600000000000000 : ℚ)) + (U := (-(1311464328789948097699 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_5 : Uω (aρ 5) (bρ 5) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -4015,25 +3604,21 @@ lemma U_315_5 : have hlg : Real.log (411136708922333 / 1600000000000000 : ℝ) ≤ (-(13588331234040514537341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (411136708922333 / 1600000000000000 : ℝ) = - (411136708922333 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (411136708922333 / 400000000000000 : ℚ)) - (U := (274612371959485462659 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (411136708922333 / 400000000000000 : ℝ) ≤ - (274612371959485462659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25592415750701 / 100000000000000 : ℝ)) (q := - (411136708922333 / 1600000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (411136708922333 / 1600000000000000 : ℚ)) + (r' := (411136708922333 / 400000000000000 : ℚ)) + (U := (-(13588331234040514537341 / 10000000000000000000000 : ℚ))) + (U' := (274612371959485462659 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (25592415750701 / 100000000000000 : ℚ)) + (q := (411136708922333 / 1600000000000000 : ℚ)) + (U := (-(13588331234040514537341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_6 : Uω (aρ 6) (bρ 6) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -4041,25 +3626,21 @@ lemma U_315_6 : have hlg : Real.log (9548083021930961 / 40000000000000000 : ℝ) ≤ (-(7162695248392099559029 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9548083021930961 / 40000000000000000 : ℝ) = - (9548083021930961 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9548083021930961 / 5000000000000000 : ℚ)) - (U := (3234512456107900440971 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9548083021930961 / 5000000000000000 : ℝ) ≤ - (3234512456107900440971 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1180657299823209 / 5000000000000000 : ℝ)) (q := - (9548083021930961 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9548083021930961 / 40000000000000000 : ℚ)) + (r' := (9548083021930961 / 5000000000000000 : ℚ)) + (U := (-(7162695248392099559029 / 5000000000000000000000 : ℚ))) + (U' := (3234512456107900440971 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (1180657299823209 / 5000000000000000 : ℚ)) + (q := (9548083021930961 / 40000000000000000 : ℚ)) + (U := (-(7162695248392099559029 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_7 : Uω (aρ 7) (bρ 7) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -4067,25 +3648,21 @@ lemma U_315_7 : have hlg : Real.log (8512526676559121 / 40000000000000000 : ℝ) ≤ (-(15473406480532042506811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8512526676559121 / 40000000000000000 : ℝ) = - (8512526676559121 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8512526676559121 / 5000000000000000 : ℚ)) - (U := (5321008928467957493189 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8512526676559121 / 5000000000000000 : ℝ) ≤ - (5321008928467957493189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1033598903860249 / 5000000000000000 : ℝ)) (q := - (8512526676559121 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8512526676559121 / 40000000000000000 : ℚ)) + (r' := (8512526676559121 / 5000000000000000 : ℚ)) + (U := (-(15473406480532042506811 / 10000000000000000000000 : ℚ))) + (U' := (5321008928467957493189 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (1033598903860249 / 5000000000000000 : ℚ)) + (q := (8512526676559121 / 40000000000000000 : ℚ)) + (U := (-(15473406480532042506811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_8 : Uω (aρ 8) (bρ 8) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -4093,25 +3670,21 @@ lemma U_315_8 : have hlg : Real.log (7049606529114841 / 40000000000000000 : ℝ) ≤ (-(8679538247702567513831 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7049606529114841 / 40000000000000000 : ℝ) = - (7049606529114841 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7049606529114841 / 5000000000000000 : ℚ)) - (U := (1717669456797432486169 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7049606529114841 / 5000000000000000 : ℝ) ≤ - (1717669456797432486169 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (809639692669179 / 5000000000000000 : ℝ)) (q := - (7049606529114841 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7049606529114841 / 40000000000000000 : ℚ)) + (r' := (7049606529114841 / 5000000000000000 : ℚ)) + (U := (-(8679538247702567513831 / 5000000000000000000000 : ℚ))) + (U' := (1717669456797432486169 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (809639692669179 / 5000000000000000 : ℚ)) + (q := (7049606529114841 / 40000000000000000 : ℚ)) + (U := (-(8679538247702567513831 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_9 : Uω (aρ 9) (bρ 9) (9318763916173 / 32000000000000 : ℝ) ≤ @@ -4119,25 +3692,21 @@ lemma U_315_9 : have hlg : Real.log (4724589607413553 / 40000000000000000 : ℝ) ≤ (-(21360987514744639833261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4724589607413553 / 40000000000000000 : ℝ) = - (4724589607413553 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4724589607413553 / 2500000000000000 : ℚ)) - (U := (6364899697255360166739 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4724589607413553 / 2500000000000000 : ℝ) ≤ - (6364899697255360166739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (398868276423857 / 5000000000000000 : ℝ)) (q := - (4724589607413553 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4724589607413553 / 40000000000000000 : ℚ)) + (r' := (4724589607413553 / 2500000000000000 : ℚ)) + (U := (-(21360987514744639833261 / 10000000000000000000000 : ℚ))) + (U' := (6364899697255360166739 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9318763916173 / 32000000000000 : ℚ)) + (s := (398868276423857 / 5000000000000000 : ℚ)) + (q := (4724589607413553 / 40000000000000000 : ℚ)) + (U := (-(21360987514744639833261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_315_10 : Uω (aρ 10) (bρ 10) (9318763916173 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U26.lean b/LeanPool/Zeta5Irrational/Table/U26.lean index 419a8c5abb..7da290f461 100644 --- a/LeanPool/Zeta5Irrational/Table/U26.lean +++ b/LeanPool/Zeta5Irrational/Table/U26.lean @@ -24,25 +24,21 @@ lemma U_316_1 : have hlg : Real.log (45658137084569129 / 160000000000000000 : ℝ) ≤ (-(313497993542335413487 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45658137084569129 / 160000000000000000 : ℝ) = - (45658137084569129 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45658137084569129 / 40000000000000000 : ℚ)) - (U := (33075596607664586513 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45658137084569129 / 40000000000000000 : ℝ) ≤ - (33075596607664586513 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (356697114305211 / 1250000000000000 : ℝ)) (q := - (45658137084569129 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45658137084569129 / 160000000000000000 : ℚ)) + (r' := (45658137084569129 / 40000000000000000 : ℚ)) + (U := (-(313497993542335413487 / 250000000000000000000 : ℚ))) + (U' := (33075596607664586513 / 250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (356697114305211 / 1250000000000000 : ℚ)) + (q := (45658137084569129 / 160000000000000000 : ℚ)) + (U := (-(313497993542335413487 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_2 : Uω (aρ 2) (bρ 2) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_316_2 : have hlg : Real.log (45272740202355649 / 160000000000000000 : ℝ) ≤ (-(12624687248934936222979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45272740202355649 / 160000000000000000 : ℝ) = - (45272740202355649 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45272740202355649 / 40000000000000000 : ℚ)) - (U := (1238256357065063777021 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45272740202355649 / 40000000000000000 : ℝ) ≤ - (1238256357065063777021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2829171316675003 / 10000000000000000 : ℝ)) (q := - (45272740202355649 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45272740202355649 / 160000000000000000 : ℚ)) + (r' := (45272740202355649 / 40000000000000000 : ℚ)) + (U := (-(12624687248934936222979 / 10000000000000000000000 : ℚ))) + (U' := (1238256357065063777021 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (2829171316675003 / 10000000000000000 : ℚ)) + (q := (45272740202355649 / 160000000000000000 : ℚ)) + (U := (-(12624687248934936222979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_3 : Uω (aρ 3) (bρ 3) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_316_3 : have hlg : Real.log (44499121344513537 / 160000000000000000 : ℝ) ≤ (-(12797043708037897056853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44499121344513537 / 160000000000000000 : ℝ) = - (44499121344513537 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44499121344513537 / 40000000000000000 : ℚ)) - (U := (1065899897962102943147 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44499121344513537 / 40000000000000000 : ℝ) ≤ - (1065899897962102943147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2779865065794739 / 10000000000000000 : ℝ)) (q := - (44499121344513537 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44499121344513537 / 160000000000000000 : ℚ)) + (r' := (44499121344513537 / 40000000000000000 : ℚ)) + (U := (-(12797043708037897056853 / 10000000000000000000000 : ℚ))) + (U' := (1065899897962102943147 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (2779865065794739 / 10000000000000000 : ℚ)) + (q := (44499121344513537 / 160000000000000000 : ℚ)) + (U := (-(12797043708037897056853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_4 : Uω (aρ 4) (bρ 4) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_316_4 : have hlg : Real.log (43205358593290521 / 160000000000000000 : ℝ) ≤ (-(13092092856450291711527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43205358593290521 / 160000000000000000 : ℝ) = - (43205358593290521 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43205358593290521 / 40000000000000000 : ℚ)) - (U := (770850749549708288473 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43205358593290521 / 40000000000000000 : ℝ) ≤ - (770850749549708288473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1348219451478431 / 5000000000000000 : ℝ)) (q := - (43205358593290521 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43205358593290521 / 160000000000000000 : ℚ)) + (r' := (43205358593290521 / 40000000000000000 : ℚ)) + (U := (-(13092092856450291711527 / 10000000000000000000000 : ℚ))) + (U' := (770850749549708288473 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (1348219451478431 / 5000000000000000 : ℚ)) + (q := (43205358593290521 / 160000000000000000 : ℚ)) + (U := (-(13092092856450291711527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_5 : Uω (aρ 5) (bρ 5) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_316_5 : have hlg : Real.log (41211242901442193 / 160000000000000000 : ℝ) ≤ (-(13564627096277214139309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41211242901442193 / 160000000000000000 : ℝ) = - (41211242901442193 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41211242901442193 / 40000000000000000 : ℚ)) - (U := (298316509722785860691 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41211242901442193 / 40000000000000000 : ℝ) ≤ - (298316509722785860691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2565364360810821 / 10000000000000000 : ℝ)) (q := - (41211242901442193 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41211242901442193 / 160000000000000000 : ℚ)) + (r' := (41211242901442193 / 40000000000000000 : ℚ)) + (U := (-(13564627096277214139309 / 10000000000000000000000 : ℚ))) + (U' := (298316509722785860691 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (2565364360810821 / 10000000000000000 : ℚ)) + (q := (41211242901442193 / 160000000000000000 : ℚ)) + (U := (-(13564627096277214139309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_6 : Uω (aρ 6) (bρ 6) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_316_6 : have hlg : Real.log (38290566722571937 / 160000000000000000 : ℝ) ≤ (-(14299702482758872198407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (38290566722571937 / 160000000000000000 : ℝ) = - (38290566722571937 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38290566722571937 / 20000000000000000 : ℚ)) - (U := (6494712926241127801593 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38290566722571937 / 20000000000000000 : ℝ) ≤ - (6494712926241127801593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2367520213592039 / 10000000000000000 : ℝ)) (q := - (38290566722571937 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38290566722571937 / 160000000000000000 : ℚ)) + (r' := (38290566722571937 / 20000000000000000 : ℚ)) + (U := (-(14299702482758872198407 / 10000000000000000000000 : ℚ))) + (U' := (6494712926241127801593 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (2367520213592039 / 10000000000000000 : ℚ)) + (q := (38290566722571937 / 160000000000000000 : ℚ)) + (U := (-(14299702482758872198407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_7 : Uω (aρ 7) (bρ 7) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_316_7 : have hlg : Real.log (34150142030150001 / 160000000000000000 : ℝ) ≤ (-(7722035347185278864809 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34150142030150001 / 160000000000000000 : ℝ) = - (34150142030150001 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34150142030150001 / 20000000000000000 : ℚ)) - (U := (2675172357314721135191 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34150142030150001 / 20000000000000000 : ℝ) ≤ - (2675172357314721135191 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2073628507799297 / 10000000000000000 : ℝ)) (q := - (34150142030150001 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34150142030150001 / 160000000000000000 : ℚ)) + (r' := (34150142030150001 / 20000000000000000 : ℚ)) + (U := (-(7722035347185278864809 / 5000000000000000000000 : ℚ))) + (U' := (2675172357314721135191 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (2073628507799297 / 10000000000000000 : ℚ)) + (q := (34150142030150001 / 160000000000000000 : ℚ)) + (U := (-(7722035347185278864809 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_8 : Uω (aρ 8) (bρ 8) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_316_8 : have hlg : Real.log (28304159991661457 / 160000000000000000 : ℝ) ≤ (-(17321650244358947368713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (28304159991661457 / 160000000000000000 : ℝ) = - (28304159991661457 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28304159991661457 / 20000000000000000 : ℚ)) - (U := (3472765164641052631287 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28304159991661457 / 20000000000000000 : ℝ) ≤ - (3472765164641052631287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1626422404328229 / 10000000000000000 : ℝ)) (q := - (28304159991661457 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28304159991661457 / 160000000000000000 : ℚ)) + (r' := (28304159991661457 / 20000000000000000 : ℚ)) + (U := (-(17321650244358947368713 / 10000000000000000000000 : ℚ))) + (U' := (3472765164641052631287 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (1626422404328229 / 10000000000000000 : ℚ)) + (q := (28304159991661457 / 160000000000000000 : ℚ)) + (U := (-(17321650244358947368713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_9 : Uω (aρ 9) (bρ 9) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_316_9 : have hlg : Real.log (19041725792516417 / 160000000000000000 : ℝ) ≤ (-(2128541148575158751237 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19041725792516417 / 160000000000000000 : ℝ) = - (19041725792516417 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19041725792516417 / 10000000000000000 : ℚ)) - (U := (644047572624841248763 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19041725792516417 / 10000000000000000 : ℝ) ≤ - (644047572624841248763 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (809583757795099 / 10000000000000000 : ℝ)) (q := - (19041725792516417 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19041725792516417 / 160000000000000000 : ℚ)) + (r' := (19041725792516417 / 10000000000000000 : ℚ)) + (U := (-(2128541148575158751237 / 1000000000000000000000 : ℚ))) + (U' := (644047572624841248763 / 1000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (7470559844389 / 25600000000000 : ℚ)) + (s := (809583757795099 / 10000000000000000 : ℚ)) + (q := (19041725792516417 / 160000000000000000 : ℚ)) + (U := (-(2128541148575158751237 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_316_10 : Uω (aρ 10) (bρ 10) (7470559844389 / 25600000000000 : ℝ) ≤ @@ -377,25 +341,21 @@ lemma U_317_1 : have hlg : Real.log (22877659228192339 / 80000000000000000 : ℝ) ≤ (-(1564832224170227175487 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22877659228192339 / 80000000000000000 : ℝ) = - (22877659228192339 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22877659228192339 / 20000000000000000 : ℚ)) - (U := (168035726579772824513 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22877659228192339 / 20000000000000000 : ℝ) ≤ - (168035726579772824513 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2859650870508241 / 10000000000000000 : ℝ)) (q := - (22877659228192339 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22877659228192339 / 80000000000000000 : ℚ)) + (r' := (22877659228192339 / 20000000000000000 : ℚ)) + (U := (-(1564832224170227175487 / 1250000000000000000000 : ℚ))) + (U' := (168035726579772824513 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (2859650870508241 / 10000000000000000 : ℚ)) + (q := (22877659228192339 / 80000000000000000 : ℚ)) + (U := (-(1564832224170227175487 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_2 : Uω (aρ 2) (bρ 2) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -403,25 +363,21 @@ lemma U_317_2 : have hlg : Real.log (22684966250189827 / 80000000000000000 : ℝ) ≤ (-(12603242087980496131311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22684966250189827 / 80000000000000000 : ℝ) = - (22684966250189827 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22684966250189827 / 20000000000000000 : ℚ)) - (U := (1259701518019503868689 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22684966250189827 / 20000000000000000 : ℝ) ≤ - (1259701518019503868689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2835246638517613 / 10000000000000000 : ℝ)) (q := - (22684966250189827 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22684966250189827 / 80000000000000000 : ℚ)) + (r' := (22684966250189827 / 20000000000000000 : ℚ)) + (U := (-(12603242087980496131311 / 10000000000000000000000 : ℚ))) + (U' := (1259701518019503868689 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (2835246638517613 / 10000000000000000 : ℚ)) + (q := (22684966250189827 / 80000000000000000 : ℚ)) + (U := (-(12603242087980496131311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_3 : Uω (aρ 3) (bρ 3) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -429,25 +385,21 @@ lemma U_317_3 : have hlg : Real.log (22298173592442603 / 80000000000000000 : ℝ) ≤ (-(51100874429049288073 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22298173592442603 / 80000000000000000 : ℝ) = - (22298173592442603 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22298173592442603 / 20000000000000000 : ℚ)) - (U := (4350899994950711927 / 40000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22298173592442603 / 20000000000000000 : ℝ) ≤ - (4350899994950711927 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2785944580430807 / 10000000000000000 : ℝ)) (q := - (22298173592442603 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22298173592442603 / 80000000000000000 : ℚ)) + (r' := (22298173592442603 / 20000000000000000 : ℚ)) + (U := (-(51100874429049288073 / 40000000000000000000 : ℚ))) + (U' := (4350899994950711927 / 40000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (2785944580430807 / 10000000000000000 : ℚ)) + (q := (22298173592442603 / 80000000000000000 : ℚ)) + (U := (-(51100874429049288073 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_4 : Uω (aρ 4) (bρ 4) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -455,25 +407,21 @@ lemma U_317_4 : have hlg : Real.log (21651339067849943 / 80000000000000000 : ℝ) ≤ (-(653479665454582040087 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21651339067849943 / 80000000000000000 : ℝ) = - (21651339067849943 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21651339067849943 / 20000000000000000 : ℚ)) - (U := (39667514845417959913 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21651339067849943 / 20000000000000000 : ℝ) ≤ - (39667514845417959913 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1351265065173821 / 5000000000000000 : ℝ)) (q := - (21651339067849943 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21651339067849943 / 80000000000000000 : ℚ)) + (r' := (21651339067849943 / 20000000000000000 : ℚ)) + (U := (-(653479665454582040087 / 500000000000000000000 : ℚ))) + (U' := (39667514845417959913 / 500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (1351265065173821 / 5000000000000000 : ℚ)) + (q := (21651339067849943 / 80000000000000000 : ℚ)) + (U := (-(653479665454582040087 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_5 : Uω (aρ 5) (bρ 5) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -481,25 +429,21 @@ lemma U_317_5 : have hlg : Real.log (4130881304873591 / 16000000000000000 : ℝ) ≤ (-(13540979465010177493251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4130881304873591 / 16000000000000000 : ℝ) = - (4130881304873591 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4130881304873591 / 4000000000000000 : ℚ)) - (U := (321964140989822506749 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4130881304873591 / 4000000000000000 : ℝ) ≤ - (321964140989822506749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (514297382762429 / 2000000000000000 : ℝ)) (q := - (4130881304873591 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4130881304873591 / 16000000000000000 : ℚ)) + (r' := (4130881304873591 / 4000000000000000 : ℚ)) + (U := (-(13540979465010177493251 / 10000000000000000000000 : ℚ))) + (U' := (321964140989822506749 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (514297382762429 / 2000000000000000 : ℚ)) + (q := (4130881304873591 / 16000000000000000 : ℚ)) + (U := (-(13540979465010177493251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_6 : Uω (aρ 6) (bρ 6) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -507,25 +451,21 @@ lemma U_317_6 : have hlg : Real.log (19194397949454987 / 80000000000000000 : ℝ) ≤ (-(14274081709003551513581 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19194397949454987 / 80000000000000000 : ℝ) = - (19194397949454987 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19194397949454987 / 10000000000000000 : ℚ)) - (U := (6520333699996448486419 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19194397949454987 / 10000000000000000 : ℝ) ≤ - (6520333699996448486419 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2373725145223903 / 10000000000000000 : ℝ)) (q := - (19194397949454987 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19194397949454987 / 80000000000000000 : ℚ)) + (r' := (19194397949454987 / 10000000000000000 : ℚ)) + (U := (-(14274081709003551513581 / 10000000000000000000000 : ℚ))) + (U' := (6520333699996448486419 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (2373725145223903 / 10000000000000000 : ℚ)) + (q := (19194397949454987 / 80000000000000000 : ℚ)) + (U := (-(14274081709003551513581 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_7 : Uω (aρ 7) (bρ 7) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -533,25 +473,21 @@ lemma U_317_7 : have hlg : Real.log (17125080092878191 / 80000000000000000 : ℝ) ≤ (-(3853706432000757266593 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17125080092878191 / 80000000000000000 : ℝ) = - (17125080092878191 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17125080092878191 / 10000000000000000 : ℚ)) - (U := (1344897420249242733407 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17125080092878191 / 10000000000000000 : ℝ) ≤ - (1344897420249242733407 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260007132729963 / 1250000000000000 : ℝ)) (q := - (17125080092878191 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17125080092878191 / 80000000000000000 : ℚ)) + (r' := (17125080092878191 / 10000000000000000 : ℚ)) + (U := (-(3853706432000757266593 / 2500000000000000000000 : ℚ))) + (U' := (1344897420249242733407 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (260007132729963 / 1250000000000000 : ℚ)) + (q := (17125080092878191 / 80000000000000000 : ℚ)) + (U := (-(3853706432000757266593 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_8 : Uω (aρ 8) (bρ 8) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -559,25 +495,21 @@ lemma U_317_8 : have hlg : Real.log (14204912327560163 / 80000000000000000 : ℝ) ≤ (-(1728438790549203311371 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14204912327560163 / 80000000000000000 : ℝ) = - (14204912327560163 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14204912327560163 / 10000000000000000 : ℚ)) - (U := (351002750350796688629 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14204912327560163 / 10000000000000000 : ℝ) ≤ - (351002750350796688629 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1633556771850197 / 10000000000000000 : ℝ)) (q := - (14204912327560163 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14204912327560163 / 80000000000000000 : ℚ)) + (r' := (14204912327560163 / 10000000000000000 : ℚ)) + (U := (-(1728438790549203311371 / 1000000000000000000000 : ℚ))) + (U' := (351002750350796688629 / 1000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (1633556771850197 / 10000000000000000 : ℚ)) + (q := (14204912327560163 / 80000000000000000 : ℚ)) + (U := (-(1728438790549203311371 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_9 : Uω (aρ 9) (bρ 9) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -585,25 +517,21 @@ lemma U_317_9 : have hlg : Real.log (9592042704887499 / 80000000000000000 : ℝ) ≤ (-(21210927637829035889281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9592042704887499 / 80000000000000000 : ℝ) = - (9592042704887499 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9592042704887499 / 5000000000000000 : ℚ)) - (U := (6514959574170964110719 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9592042704887499 / 5000000000000000 : ℝ) ≤ - (6514959574170964110719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (821304994542031 / 10000000000000000 : ℝ)) (q := - (9592042704887499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9592042704887499 / 80000000000000000 : ℚ)) + (r' := (9592042704887499 / 5000000000000000 : ℚ)) + (U := (-(21210927637829035889281 / 10000000000000000000000 : ℚ))) + (U' := (6514959574170964110719 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18715271389599 / 64000000000000 : ℚ)) + (s := (821304994542031 / 10000000000000000 : ℚ)) + (q := (9592042704887499 / 80000000000000000 : ℚ)) + (U := (-(21210927637829035889281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_317_10 : Uω (aρ 10) (bρ 10) (18715271389599 / 64000000000000 : ℝ) ≤ @@ -728,25 +656,21 @@ lemma U_318_1 : have hlg : Real.log (45852499820039187 / 160000000000000000 : ℝ) ≤ (-(2499488191591324361 / 2000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45852499820039187 / 160000000000000000 : ℝ) = - (45852499820039187 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45852499820039187 / 40000000000000000 : ℚ)) - (U := (273100529608675639 / 2000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45852499820039187 / 40000000000000000 : ℝ) ≤ - (273100529608675639 / 2000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (358215603194333 / 1250000000000000 : ℝ)) (q := - (45852499820039187 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45852499820039187 / 160000000000000000 : ℚ)) + (r' := (45852499820039187 / 40000000000000000 : ℚ)) + (U := (-(2499488191591324361 / 2000000000000000000 : ℚ))) + (U' := (273100529608675639 / 2000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (358215603194333 / 1250000000000000 : ℚ)) + (q := (45852499820039187 / 160000000000000000 : ℚ)) + (U := (-(2499488191591324361 / 2000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_2 : Uω (aρ 2) (bρ 2) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -754,25 +678,21 @@ lemma U_318_2 : have hlg : Real.log (45467124743452883 / 160000000000000000 : ℝ) ≤ (-(3145460707552018440057 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45467124743452883 / 160000000000000000 : ℝ) = - (45467124743452883 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45467124743452883 / 40000000000000000 : ℚ)) - (U := (320275193947981559943 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45467124743452883 / 40000000000000000 : ℝ) ≤ - (320275193947981559943 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177582622093211 / 625000000000000 : ℝ)) (q := - (45467124743452883 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45467124743452883 / 160000000000000000 : ℚ)) + (r' := (45467124743452883 / 40000000000000000 : ℚ)) + (U := (-(3145460707552018440057 / 2500000000000000000000 : ℚ))) + (U' := (320275193947981559943 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (177582622093211 / 625000000000000 : ℚ)) + (q := (45467124743452883 / 160000000000000000 : ℚ)) + (U := (-(3145460707552018440057 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_3 : Uω (aρ 3) (bρ 3) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -780,25 +700,21 @@ lemma U_318_3 : have hlg : Real.log (44693572823312123 / 160000000000000000 : ℝ) ≤ (-(797090067591125847769 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44693572823312123 / 160000000000000000 : ℝ) = - (44693572823312123 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44693572823312123 / 40000000000000000 : ℚ)) - (U := (69343907783874152231 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44693572823312123 / 40000000000000000 : ℝ) ≤ - (69343907783874152231 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2792024069823781 / 10000000000000000 : ℝ)) (q := - (44693572823312123 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44693572823312123 / 160000000000000000 : ℚ)) + (r' := (44693572823312123 / 40000000000000000 : ℚ)) + (U := (-(797090067591125847769 / 625000000000000000000 : ℚ))) + (U' := (69343907783874152231 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (2792024069823781 / 10000000000000000 : ℚ)) + (q := (44693572823312123 / 160000000000000000 : ℚ)) + (U := (-(797090067591125847769 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_4 : Uω (aρ 4) (bρ 4) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -806,25 +722,21 @@ lemma U_318_4 : have hlg : Real.log (43399997048911691 / 160000000000000000 : ℝ) ≤ (-(652357220802502956437 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43399997048911691 / 160000000000000000 : ℝ) = - (43399997048911691 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43399997048911691 / 40000000000000000 : ℚ)) - (U := (40789959497497043563 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43399997048911691 / 40000000000000000 : ℝ) ≤ - (40789959497497043563 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2708621279088727 / 10000000000000000 : ℝ)) (q := - (43399997048911691 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43399997048911691 / 160000000000000000 : ℚ)) + (r' := (43399997048911691 / 40000000000000000 : ℚ)) + (U := (-(652357220802502956437 / 500000000000000000000 : ℚ))) + (U' := (40789959497497043563 / 500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (2708621279088727 / 10000000000000000 : ℚ)) + (q := (43399997048911691 / 160000000000000000 : ℚ)) + (U := (-(652357220802502956437 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_5 : Uω (aρ 5) (bρ 5) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -832,25 +744,21 @@ lemma U_318_5 : have hlg : Real.log (41406381347382187 / 160000000000000000 : ℝ) ≤ (-(13517388069351791248559 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41406381347382187 / 160000000000000000 : ℝ) = - (41406381347382187 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41406381347382187 / 40000000000000000 : ℚ)) - (U := (345555536648208751441 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41406381347382187 / 40000000000000000 : ℝ) ≤ - (345555536648208751441 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2577609235732539 / 10000000000000000 : ℝ)) (q := - (41406381347382187 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41406381347382187 / 160000000000000000 : ℚ)) + (r' := (41406381347382187 / 40000000000000000 : ℚ)) + (U := (-(13517388069351791248559 / 10000000000000000000000 : ℚ))) + (U' := (345555536648208751441 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (2577609235732539 / 10000000000000000 : ℚ)) + (q := (41406381347382187 / 160000000000000000 : ℚ)) + (U := (-(13517388069351791248559 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_6 : Uω (aρ 6) (bρ 6) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -858,25 +766,21 @@ lemma U_318_6 : have hlg : Real.log (38487019659432091 / 160000000000000000 : ℝ) ≤ (-(14248527817117285144357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (38487019659432091 / 160000000000000000 : ℝ) = - (38487019659432091 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38487019659432091 / 20000000000000000 : ℚ)) - (U := (6545887591882714855643 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38487019659432091 / 20000000000000000 : ℝ) ≤ - (6545887591882714855643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2379929399878777 / 10000000000000000 : ℝ)) (q := - (38487019659432091 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38487019659432091 / 160000000000000000 : ℚ)) + (r' := (38487019659432091 / 20000000000000000 : ℚ)) + (U := (-(14248527817117285144357 / 10000000000000000000000 : ℚ))) + (U' := (6545887591882714855643 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (2379929399878777 / 10000000000000000 : ℚ)) + (q := (38487019659432091 / 160000000000000000 : ℚ)) + (U := (-(14248527817117285144357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_7 : Uω (aρ 7) (bρ 7) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -884,25 +788,21 @@ lemma U_318_7 : have hlg : Real.log (6870032266348943 / 32000000000000000 : ℝ) ≤ (-(7692835495468796043633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6870032266348943 / 32000000000000000 : ℝ) = - (6870032266348943 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6870032266348943 / 4000000000000000 : ℚ)) - (U := (2704372209031203956367 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6870032266348943 / 4000000000000000 : ℝ) ≤ - (2704372209031203956367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (417296697935571 / 2000000000000000 : ℝ)) (q := - (6870032266348943 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6870032266348943 / 32000000000000000 : ℚ)) + (r' := (6870032266348943 / 4000000000000000 : ℚ)) + (U := (-(7692835495468796043633 / 5000000000000000000000 : ℚ))) + (U' := (2704372209031203956367 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (417296697935571 / 2000000000000000 : ℚ)) + (q := (6870032266348943 / 32000000000000000 : ℚ)) + (U := (-(7692835495468796043633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_8 : Uω (aρ 8) (bρ 8) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -910,25 +810,21 @@ lemma U_318_8 : have hlg : Real.log (28515421009719987 / 160000000000000000 : ℝ) ≤ (-(431182196363598939487 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (28515421009719987 / 160000000000000000 : ℝ) = - (28515421009719987 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28515421009719987 / 20000000000000000 : ℚ)) - (U := (88678188861401060513 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28515421009719987 / 20000000000000000 : ℝ) ≤ - (88678188861401060513 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410170650191191 / 2500000000000000 : ℝ)) (q := - (28515421009719987 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28515421009719987 / 160000000000000000 : ℚ)) + (r' := (28515421009719987 / 20000000000000000 : ℚ)) + (U := (-(431182196363598939487 / 250000000000000000000 : ℚ))) + (U' := (88678188861401060513 / 250000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (410170650191191 / 2500000000000000 : ℚ)) + (q := (28515421009719987 / 160000000000000000 : ℚ)) + (U := (-(431182196363598939487 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_9 : Uω (aρ 9) (bρ 9) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -936,25 +832,21 @@ lemma U_318_9 : have hlg : Real.log (19325479826693587 / 160000000000000000 : ℝ) ≤ (-(21137493907044255191037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19325479826693587 / 160000000000000000 : ℝ) = - (19325479826693587 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19325479826693587 / 10000000000000000 : ℚ)) - (U := (6588393304955744808963 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19325479826693587 / 10000000000000000 : ℝ) ≤ - (6588393304955744808963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (406692178343 / 4882812500000 : ℝ)) (q := - (19325479826693587 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19325479826693587 / 160000000000000000 : ℚ)) + (r' := (19325479826693587 / 10000000000000000 : ℚ)) + (U := (-(21137493907044255191037 / 10000000000000000000000 : ℚ))) + (U' := (6588393304955744808963 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37508286336451 / 128000000000000 : ℚ)) + (s := (406692178343 / 4882812500000 : ℚ)) + (q := (19325479826693587 / 160000000000000000 : ℚ)) + (U := (-(21137493907044255191037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_318_10 : Uω (aρ 10) (bρ 10) (37508286336451 / 128000000000000 : ℝ) ≤ @@ -1081,25 +973,21 @@ lemma U_319_1 : have hlg : Real.log (1148742029389611 / 4000000000000000 : ℝ) ≤ (-(2495253808887446669611 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1148742029389611 / 4000000000000000 : ℝ) = - (1148742029389611 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1148742029389611 / 1000000000000000 : ℚ)) - (U := (277334912312553330389 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1148742029389611 / 1000000000000000 : ℝ) ≤ - (277334912312553330389 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (287179877958743 / 1000000000000000 : ℝ)) (q := - (1148742029389611 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1148742029389611 / 4000000000000000 : ℚ)) + (r' := (1148742029389611 / 1000000000000000 : ℚ)) + (U := (-(2495253808887446669611 / 2000000000000000000000 : ℚ))) + (U' := (277334912312553330389 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (287179877958743 / 1000000000000000 : ℚ)) + (q := (1148742029389611 / 4000000000000000 : ℚ)) + (U := (-(2495253808887446669611 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_2 : Uω (aρ 2) (bρ 2) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1107,25 +995,21 @@ lemma U_319_2 : have hlg : Real.log (1423884904122721 / 5000000000000000 : ℝ) ≤ (-(2512097855895038717213 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1423884904122721 / 5000000000000000 : ℝ) = - (1423884904122721 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1423884904122721 / 1250000000000000 : ℚ)) - (U := (260490865304961282787 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1423884904122721 / 1250000000000000 : ℝ) ≤ - (260490865304961282787 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2847397261640259 / 10000000000000000 : ℝ)) (q := - (1423884904122721 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1423884904122721 / 5000000000000000 : ℚ)) + (r' := (1423884904122721 / 1250000000000000 : ℚ)) + (U := (-(2512097855895038717213 / 2000000000000000000000 : ℚ))) + (U' := (260490865304961282787 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (2847397261640259 / 10000000000000000 : ℚ)) + (q := (1423884904122721 / 5000000000000000 : ℚ)) + (U := (-(2512097855895038717213 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_3 : Uω (aρ 3) (bρ 3) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1133,25 +1017,21 @@ lemma U_319_3 : have hlg : Real.log (223953991305553 / 800000000000000 : ℝ) ≤ (-(12731710923469879778623 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (223953991305553 / 800000000000000 : ℝ) = - (223953991305553 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (223953991305553 / 200000000000000 : ℚ)) - (U := (1131232682530120221377 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (223953991305553 / 200000000000000 : ℝ) ≤ - (1131232682530120221377 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13990517670691 / 50000000000000 : ℝ)) (q := - (223953991305553 / 800000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (223953991305553 / 800000000000000 : ℚ)) + (r' := (223953991305553 / 200000000000000 : ℚ)) + (U := (-(12731710923469879778623 / 10000000000000000000000 : ℚ))) + (U' := (1131232682530120221377 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (13990517670691 / 50000000000000 : ℚ)) + (q := (223953991305553 / 800000000000000 : ℚ)) + (U := (-(12731710923469879778623 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_4 : Uω (aρ 4) (bρ 4) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1159,25 +1039,21 @@ lemma U_319_4 : have hlg : Real.log (2718582208572577 / 10000000000000000 : ℝ) ≤ (-(3256186487277326469717 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2718582208572577 / 10000000000000000 : ℝ) = - (2718582208572577 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2718582208572577 / 2500000000000000 : ℚ)) - (U := (209549414222673530283 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2718582208572577 / 2500000000000000 : ℝ) ≤ - (209549414222673530283 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2714712349709529 / 10000000000000000 : ℝ)) (q := - (2718582208572577 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2718582208572577 / 10000000000000000 : ℚ)) + (r' := (2718582208572577 / 2500000000000000 : ℚ)) + (U := (-(3256186487277326469717 / 2500000000000000000000 : ℚ))) + (U' := (209549414222673530283 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (2714712349709529 / 10000000000000000 : ℚ)) + (q := (2718582208572577 / 10000000000000000 : ℚ)) + (U := (-(3256186487277326469717 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_5 : Uω (aρ 5) (bρ 5) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1185,25 +1061,21 @@ lemma U_319_5 : have hlg : Real.log (5187993476315311 / 20000000000000000 : ℝ) ≤ (-(421682895011645082857 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5187993476315311 / 20000000000000000 : ℝ) = - (5187993476315311 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5187993476315311 / 5000000000000000 : ℚ)) - (U := (11534092675854917143 / 312500000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5187993476315311 / 5000000000000000 : ℝ) ≤ - (11534092675854917143 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1291865664107343 / 5000000000000000 : ℝ)) (q := - (5187993476315311 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5187993476315311 / 20000000000000000 : ℚ)) + (r' := (5187993476315311 / 5000000000000000 : ℚ)) + (U := (-(421682895011645082857 / 312500000000000000000 : ℚ))) + (U' := (11534092675854917143 / 312500000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (1291865664107343 / 5000000000000000 : ℚ)) + (q := (5187993476315311 / 20000000000000000 : ℚ)) + (U := (-(421682895011645082857 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_6 : Uω (aρ 6) (bρ 6) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1211,25 +1083,21 @@ lemma U_319_6 : have hlg : Real.log (4823154755797971 / 20000000000000000 : ℝ) ≤ (-(2844608090322516779093 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4823154755797971 / 20000000000000000 : ℝ) = - (4823154755797971 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4823154755797971 / 2500000000000000 : ℚ)) - (U := (1314274991477483220907 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4823154755797971 / 2500000000000000 : ℝ) ≤ - (1314274991477483220907 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1193066491418673 / 5000000000000000 : ℝ)) (q := - (4823154755797971 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4823154755797971 / 20000000000000000 : ℚ)) + (r' := (4823154755797971 / 2500000000000000 : ℚ)) + (U := (-(2844608090322516779093 / 2000000000000000000000 : ℚ))) + (U' := (1314274991477483220907 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (1193066491418673 / 5000000000000000 : ℚ)) + (q := (4823154755797971 / 20000000000000000 : ℚ)) + (U := (-(2844608090322516779093 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_7 : Uω (aρ 7) (bρ 7) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1237,25 +1105,21 @@ lemma U_319_7 : have hlg : Real.log (1076567050775089 / 5000000000000000 : ℝ) ≤ (-(15356605898681968251623 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1076567050775089 / 5000000000000000 : ℝ) = - (1076567050775089 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1076567050775089 / 625000000000000 : ℚ)) - (U := (5437809510318031748377 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1076567050775089 / 625000000000000 : ℝ) ≤ - (5437809510318031748377 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2092907810899731 / 10000000000000000 : ℝ)) (q := - (1076567050775089 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1076567050775089 / 5000000000000000 : ℚ)) + (r' := (1076567050775089 / 625000000000000 : ℚ)) + (U := (-(15356605898681968251623 / 10000000000000000000000 : ℚ))) + (U' := (5437809510318031748377 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (2092907810899731 / 10000000000000000 : ℚ)) + (q := (1076567050775089 / 5000000000000000 : ℚ)) + (U := (-(15356605898681968251623 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_8 : Uω (aρ 8) (bρ 8) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1263,25 +1127,21 @@ lemma U_319_8 : have hlg : Real.log (3577618742706903 / 20000000000000000 : ℝ) ≤ (-(17210348493441849799951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3577618742706903 / 20000000000000000 : ℝ) = - (3577618742706903 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3577618742706903 / 2500000000000000 : ℚ)) - (U := (3584066915558150200049 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3577618742706903 / 2500000000000000 : ℝ) ≤ - (3584066915558150200049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (823900000923139 / 5000000000000000 : ℝ)) (q := - (3577618742706903 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3577618742706903 / 20000000000000000 : ℚ)) + (r' := (3577618742706903 / 2500000000000000 : ℚ)) + (U := (-(17210348493441849799951 / 10000000000000000000000 : ℚ))) + (U' := (3584066915558150200049 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (823900000923139 / 5000000000000000 : ℚ)) + (q := (3577618742706903 / 20000000000000000 : ℚ)) + (U := (-(17210348493441849799951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_9 : Uω (aρ 9) (bρ 9) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1289,23 +1149,21 @@ lemma U_319_9 : have hlg : Real.log (9504857824393 / 78125000000000 : ℝ) ≤ (-(5266267722922526326391 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show (9504857824393 / 78125000000000 : ℝ) = (9504857824393 / 4882812500000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9504857824393 / 4882812500000 : ℚ)) - (U := (1665204080077473673609 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9504857824393 / 4882812500000 : ℝ) ≤ - (1665204080077473673609 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (844390490543983 / 10000000000000000 : ℝ)) (q := - (9504857824393 / 78125000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9504857824393 / 78125000000000 : ℚ)) + (r' := (9504857824393 / 4882812500000 : ℚ)) + (U := (-(5266267722922526326391 / 2500000000000000000000 : ℚ))) + (U' := (1665204080077473673609 / 2500000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4698253736713 / 16000000000000 : ℚ)) + (s := (844390490543983 / 10000000000000000 : ℚ)) + (q := (9504857824393 / 78125000000000 : ℚ)) + (U := (-(5266267722922526326391 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_319_10 : Uω (aρ 10) (bρ 10) (4698253736713 / 16000000000000 : ℝ) ≤ @@ -1431,25 +1289,21 @@ lemma U_320_1 : have hlg : Real.log (46046862523071781 / 160000000000000000 : ℝ) ≤ (-(3113785465743511281037 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46046862523071781 / 160000000000000000 : ℝ) = - (46046862523071781 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46046862523071781 / 40000000000000000 : ℚ)) - (U := (351950435756488718963 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46046862523071781 / 40000000000000000 : ℝ) ≤ - (351950435756488718963 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2877872732612957 / 10000000000000000 : ℝ)) (q := - (46046862523071781 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46046862523071781 / 160000000000000000 : ℚ)) + (r' := (46046862523071781 / 40000000000000000 : ℚ)) + (U := (-(3113785465743511281037 / 2500000000000000000000 : ℚ))) + (U' := (351950435756488718963 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (2877872732612957 / 10000000000000000 : ℚ)) + (q := (46046862523071781 / 160000000000000000 : ℚ)) + (U := (-(3113785465743511281037 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_2 : Uω (aρ 2) (bρ 2) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1457,25 +1311,21 @@ lemma U_320_2 : have hlg : Real.log (9132301813230193 / 32000000000000000 : ℝ) ≤ (-(12539181240894190232013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9132301813230193 / 32000000000000000 : ℝ) = - (9132301813230193 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9132301813230193 / 8000000000000000 : ℚ)) - (U := (1323762365105809767987 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9132301813230193 / 8000000000000000 : ℝ) ≤ - (1323762365105809767987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (570694512601571 / 2000000000000000 : ℝ)) (q := - (9132301813230193 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9132301813230193 / 32000000000000000 : ℚ)) + (r' := (9132301813230193 / 8000000000000000 : ℚ)) + (U := (-(12539181240894190232013 / 10000000000000000000000 : ℚ))) + (U' := (1323762365105809767987 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (570694512601571 / 2000000000000000 : ℚ)) + (q := (9132301813230193 / 32000000000000000 : ℚ)) + (U := (-(12539181240894190232013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_3 : Uω (aρ 3) (bρ 3) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1483,25 +1333,21 @@ lemma U_320_3 : have hlg : Real.log (1795520939983421 / 6400000000000000 : ℝ) ≤ (-(198594186367096513121 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1795520939983421 / 6400000000000000 : ℝ) = - (1795520939983421 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1795520939983421 / 1600000000000000 : ℚ)) - (U := (18014307476653486879 / 156250000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1795520939983421 / 1600000000000000 : ℝ) ≤ - (18014307476653486879 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (112167318941487 / 400000000000000 : ℝ)) (q := - (1795520939983421 / 6400000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1795520939983421 / 6400000000000000 : ℚ)) + (r' := (1795520939983421 / 1600000000000000 : ℚ)) + (U := (-(198594186367096513121 / 156250000000000000000 : ℚ))) + (U' := (18014307476653486879 / 156250000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (112167318941487 / 400000000000000 : ℚ)) + (q := (1795520939983421 / 6400000000000000 : ℚ)) + (U := (-(198594186367096513121 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_4 : Uω (aρ 4) (bρ 4) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1509,25 +1355,21 @@ lemma U_320_4 : have hlg : Real.log (43594633004645821 / 160000000000000000 : ℝ) ≤ (-(13002397681596293197851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43594633004645821 / 160000000000000000 : ℝ) = - (43594633004645821 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43594633004645821 / 40000000000000000 : ℚ)) - (U := (860545924403706802149 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43594633004645821 / 40000000000000000 : ℝ) ≤ - (860545924403706802149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (340100417841839 / 1250000000000000 : ℝ)) (q := - (43594633004645821 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43594633004645821 / 160000000000000000 : ℚ)) + (r' := (43594633004645821 / 40000000000000000 : ℚ)) + (U := (-(13002397681596293197851 / 10000000000000000000000 : ℚ))) + (U' := (860545924403706802149 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (340100417841839 / 1250000000000000 : ℚ)) + (q := (43594633004645821 / 160000000000000000 : ℚ)) + (U := (-(13002397681596293197851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_5 : Uω (aρ 5) (bρ 5) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1535,25 +1377,21 @@ lemma U_320_5 : have hlg : Real.log (41601512451173557 / 160000000000000000 : ℝ) ≤ (-(2694074582216508070629 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41601512451173557 / 160000000000000000 : ℝ) = - (41601512451173557 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41601512451173557 / 40000000000000000 : ℚ)) - (U := (78514138983491929371 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41601512451173557 / 40000000000000000 : ℝ) ≤ - (78514138983491929371 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2589853192885679 / 10000000000000000 : ℝ)) (q := - (41601512451173557 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41601512451173557 / 160000000000000000 : ℚ)) + (r' := (41601512451173557 / 40000000000000000 : ℚ)) + (U := (-(2694074582216508070629 / 2000000000000000000000 : ℚ))) + (U' := (78514138983491929371 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (2589853192885679 / 10000000000000000 : ℚ)) + (q := (41601512451173557 / 160000000000000000 : ℚ)) + (U := (-(2694074582216508070629 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_6 : Uω (aρ 6) (bρ 6) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1561,25 +1399,21 @@ lemma U_320_6 : have hlg : Real.log (38683451101567717 / 160000000000000000 : ℝ) ≤ (-(7098809629941692031279 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (38683451101567717 / 160000000000000000 : ℝ) = - (38683451101567717 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38683451101567717 / 20000000000000000 : ℚ)) - (U := (3298398074558307968721 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38683451101567717 / 20000000000000000 : ℝ) ≤ - (3298398074558307968721 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2392335899324949 / 10000000000000000 : ℝ)) (q := - (38683451101567717 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38683451101567717 / 160000000000000000 : ℚ)) + (r' := (38683451101567717 / 20000000000000000 : ℚ)) + (U := (-(7098809629941692031279 / 5000000000000000000000 : ℚ))) + (U' := (3298398074558307968721 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (2392335899324949 / 10000000000000000 : ℚ)) + (q := (38683451101567717 / 160000000000000000 : ℚ)) + (U := (-(7098809629941692031279 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_7 : Uω (aρ 7) (bρ 7) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1587,25 +1421,21 @@ lemma U_320_7 : have hlg : Real.log (6910022643929929 / 32000000000000000 : ℝ) ≤ (-(1532762987265952141441 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6910022643929929 / 32000000000000000 : ℝ) = - (6910022643929929 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6910022643929929 / 4000000000000000 : ℚ)) - (U := (546678553634047858559 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6910022643929929 / 4000000000000000 : ℝ) ≤ - (546678553634047858559 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (209933004484519 / 1000000000000000 : ℝ)) (q := - (6910022643929929 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6910022643929929 / 32000000000000000 : ℚ)) + (r' := (6910022643929929 / 4000000000000000 : ℚ)) + (U := (-(1532762987265952141441 / 1000000000000000000000 : ℚ))) + (U' := (546678553634047858559 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (209933004484519 / 1000000000000000 : ℚ)) + (q := (6910022643929929 / 32000000000000000 : ℚ)) + (U := (-(1532762987265952141441 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_8 : Uω (aρ 8) (bρ 8) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1613,25 +1443,21 @@ lemma U_320_8 : have hlg : Real.log (5745282464167273 / 32000000000000000 : ℝ) ≤ (-(8586784124854736362831 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5745282464167273 / 32000000000000000 : ℝ) = - (5745282464167273 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5745282464167273 / 4000000000000000 : ℚ)) - (U := (1810423579645263637169 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5745282464167273 / 4000000000000000 : ℝ) ≤ - (1810423579645263637169 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (165490908383353 / 1000000000000000 : ℝ)) (q := - (5745282464167273 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5745282464167273 / 32000000000000000 : ℚ)) + (r' := (5745282464167273 / 4000000000000000 : ℚ)) + (U := (-(8586784124854736362831 / 5000000000000000000000 : ℚ))) + (U' := (1810423579645263637169 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (165490908383353 / 1000000000000000 : ℚ)) + (q := (5745282464167273 / 32000000000000000 : ℚ)) + (U := (-(8586784124854736362831 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_9 : Uω (aρ 9) (bρ 9) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1639,25 +1465,21 @@ lemma U_320_9 : have hlg : Real.log (19605529662034021 / 160000000000000000 : ℝ) ≤ (-(1312101351333463023481 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (19605529662034021 / 160000000000000000 : ℝ) = - (19605529662034021 / 10000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19605529662034021 / 10000000000000000 : ℚ)) - (U := (420766599416536976519 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19605529662034021 / 10000000000000000 : ℝ) ≤ - (420766599416536976519 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (855764379843237 / 10000000000000000 : ℝ)) (q := - (19605529662034021 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19605529662034021 / 160000000000000000 : ℚ)) + (r' := (19605529662034021 / 10000000000000000 : ℚ)) + (U := (-(1312101351333463023481 / 625000000000000000000 : ℚ))) + (U' := (420766599416536976519 / 625000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37663773450957 / 128000000000000 : ℚ)) + (s := (855764379843237 / 10000000000000000 : ℚ)) + (q := (19605529662034021 / 160000000000000000 : ℚ)) + (U := (-(1312101351333463023481 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_320_10 : Uω (aρ 10) (bρ 10) (37663773450957 / 128000000000000 : ℝ) ≤ @@ -1785,25 +1607,21 @@ lemma U_321_1 : have hlg : Real.log (23072021931276057 / 80000000000000000 : ℝ) ≤ (-(12434059224938226750533 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23072021931276057 / 80000000000000000 : ℝ) = - (23072021931276057 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23072021931276057 / 20000000000000000 : ℚ)) - (U := (1428884381061773249467 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23072021931276057 / 20000000000000000 : ℝ) ≤ - (1428884381061773249467 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (360493335579701 / 1250000000000000 : ℝ)) (q := - (23072021931276057 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23072021931276057 / 80000000000000000 : ℚ)) + (r' := (23072021931276057 / 20000000000000000 : ℚ)) + (U := (-(12434059224938226750533 / 10000000000000000000000 : ℚ))) + (U' := (1428884381061773249467 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (360493335579701 / 1250000000000000 : ℚ)) + (q := (23072021931276057 / 80000000000000000 : ℚ)) + (U := (-(12434059224938226750533 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_2 : Uω (aρ 2) (bρ 2) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1811,25 +1629,21 @@ lemma U_321_2 : have hlg : Real.log (22879350573235169 / 80000000000000000 : ℝ) ≤ (-(12517918520821526742451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22879350573235169 / 80000000000000000 : ℝ) = - (22879350573235169 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22879350573235169 / 20000000000000000 : ℚ)) - (U := (1345025085178473257549 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22879350573235169 / 20000000000000000 : ℝ) ≤ - (1345025085178473257549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1429773928818693 / 5000000000000000 : ℝ)) (q := - (22879350573235169 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22879350573235169 / 80000000000000000 : ℚ)) + (r' := (22879350573235169 / 20000000000000000 : ℚ)) + (U := (-(12517918520821526742451 / 10000000000000000000000 : ℚ))) + (U' := (1345025085178473257549 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (1429773928818693 / 5000000000000000 : ℚ)) + (q := (22879350573235169 / 80000000000000000 : ℚ)) + (U := (-(12517918520821526742451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_3 : Uω (aρ 3) (bρ 3) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1837,25 +1651,21 @@ lemma U_321_3 : have hlg : Real.log (22492624270015249 / 80000000000000000 : ℝ) ≤ (-(1268839188906676708531 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22492624270015249 / 80000000000000000 : ℝ) = - (22492624270015249 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22492624270015249 / 20000000000000000 : ℚ)) - (U := (117455171693323291469 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22492624270015249 / 20000000000000000 : ℝ) ≤ - (117455171693323291469 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1405131194091203 / 5000000000000000 : ℝ)) (q := - (22492624270015249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22492624270015249 / 80000000000000000 : ℚ)) + (r' := (22492624270015249 / 20000000000000000 : ℚ)) + (U := (-(1268839188906676708531 / 1000000000000000000000 : ℚ))) + (U' := (117455171693323291469 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (1405131194091203 / 5000000000000000 : ℚ)) + (q := (22492624270015249 / 80000000000000000 : ℚ)) + (U := (-(1268839188906676708531 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_4 : Uω (aρ 4) (bρ 4) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1863,25 +1673,21 @@ lemma U_321_4 : have hlg : Real.log (21845975027762613 / 80000000000000000 : ℝ) ≤ (-(3245024847091790789197 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21845975027762613 / 80000000000000000 : ℝ) = - (21845975027762613 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21845975027762613 / 20000000000000000 : ℚ)) - (U := (220711054408209210803 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21845975027762613 / 20000000000000000 : ℝ) ≤ - (220711054408209210803 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2726894258684247 / 10000000000000000 : ℝ)) (q := - (21845975027762613 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21845975027762613 / 80000000000000000 : ℚ)) + (r' := (21845975027762613 / 20000000000000000 : ℚ)) + (U := (-(3245024847091790789197 / 2500000000000000000000 : ℚ))) + (U' := (220711054408209210803 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (2726894258684247 / 10000000000000000 : ℚ)) + (q := (21845975027762613 / 80000000000000000 : ℚ)) + (U := (-(3245024847091790789197 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_5 : Uω (aρ 5) (bρ 5) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1889,25 +1695,21 @@ lemma U_321_5 : have hlg : Real.log (20849537641114421 / 80000000000000000 : ℝ) ≤ (-(3361737154102947906173 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20849537641114421 / 80000000000000000 : ℝ) = - (20849537641114421 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20849537641114421 / 20000000000000000 : ℚ)) - (U := (103998747397052093827 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20849537641114421 / 20000000000000000 : ℝ) ≤ - (103998747397052093827 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2595974831357199 / 10000000000000000 : ℝ)) (q := - (20849537641114421 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20849537641114421 / 80000000000000000 : ℚ)) + (r' := (20849537641114421 / 20000000000000000 : ℚ)) + (U := (-(3361737154102947906173 / 2500000000000000000000 : ℚ))) + (U' := (103998747397052093827 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (2595974831357199 / 10000000000000000 : ℚ)) + (q := (20849537641114421 / 80000000000000000 : ℚ)) + (U := (-(3361737154102947906173 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_6 : Uω (aρ 6) (bρ 6) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1915,25 +1717,21 @@ lemma U_321_6 : have hlg : Real.log (19390829433174889 / 80000000000000000 : ℝ) ≤ (-(2834452778434685974403 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19390829433174889 / 80000000000000000 : ℝ) = - (19390829433174889 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19390829433174889 / 10000000000000000 : ℚ)) - (U := (1324430303365314025597 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19390829433174889 / 10000000000000000 : ℝ) ≤ - (1324430303365314025597 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (599634538628079 / 2500000000000000 : ℝ)) (q := - (19390829433174889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19390829433174889 / 80000000000000000 : ℚ)) + (r' := (19390829433174889 / 10000000000000000 : ℚ)) + (U := (-(2834452778434685974403 / 2000000000000000000000 : ℚ))) + (U' := (1324430303365314025597 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (599634538628079 / 2500000000000000 : ℚ)) + (q := (19390829433174889 / 80000000000000000 : ℚ)) + (U := (-(2834452778434685974403 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_7 : Uω (aρ 7) (bρ 7) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1941,25 +1739,21 @@ lemma U_321_7 : have hlg : Real.log (3465006426906649 / 16000000000000000 : ℝ) ≤ (-(3059748468025370392999 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3465006426906649 / 16000000000000000 : ℝ) = - (3465006426906649 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3465006426906649 / 2000000000000000 : ℚ)) - (U := (1099134613774629607001 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3465006426906649 / 2000000000000000 : ℝ) ≤ - (1099134613774629607001 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421150042122381 / 2000000000000000 : ℝ)) (q := - (3465006426906649 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3465006426906649 / 16000000000000000 : ℚ)) + (r' := (3465006426906649 / 2000000000000000 : ℚ)) + (U := (-(3059748468025370392999 / 2000000000000000000000 : ℚ))) + (U' := (1099134613774629607001 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (421150042122381 / 2000000000000000 : ℚ)) + (q := (3465006426906649 / 16000000000000000 : ℚ)) + (U := (-(3059748468025370392999 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_8 : Uω (aρ 8) (bρ 8) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1967,25 +1761,21 @@ lemma U_321_8 : have hlg : Real.log (14415904500640873 / 80000000000000000 : ℝ) ≤ (-(4284236393973365117899 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14415904500640873 / 80000000000000000 : ℝ) = - (14415904500640873 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14415904500640873 / 10000000000000000 : ℚ)) - (U := (914367458276634882101 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14415904500640873 / 10000000000000000 : ℝ) ≤ - (914367458276634882101 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (415502488369703 / 2500000000000000 : ℝ)) (q := - (14415904500640873 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14415904500640873 / 80000000000000000 : ℚ)) + (r' := (14415904500640873 / 10000000000000000 : ℚ)) + (U := (-(4284236393973365117899 / 2500000000000000000000 : ℚ))) + (U' := (914367458276634882101 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (415502488369703 / 2500000000000000 : ℚ)) + (q := (14415904500640873 / 80000000000000000 : ℚ)) + (U := (-(4284236393973365117899 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_9 : Uω (aρ 9) (bρ 9) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -1993,25 +1783,21 @@ lemma U_321_9 : have hlg : Real.log (9872128646489561 / 80000000000000000 : ℝ) ≤ (-(326923614860068943593 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (9872128646489561 / 80000000000000000 : ℝ) = - (9872128646489561 / 5000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9872128646489561 / 5000000000000000 : ℚ)) - (U := (106293372827431056407 / 156250000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9872128646489561 / 5000000000000000 : ℝ) ≤ - (106293372827431056407 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (108378952287623 / 1250000000000000 : ℝ)) (q := - (9872128646489561 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9872128646489561 / 80000000000000000 : ℚ)) + (r' := (9872128646489561 / 5000000000000000 : ℚ)) + (U := (-(326923614860068943593 / 156250000000000000000 : ℚ))) + (U' := (106293372827431056407 / 156250000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (3774151700821 / 12800000000000 : ℚ)) + (s := (108378952287623 / 1250000000000000 : ℚ)) + (q := (9872128646489561 / 80000000000000000 : ℚ)) + (U := (-(326923614860068943593 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_321_10 : Uω (aρ 10) (bρ 10) (3774151700821 / 12800000000000 : ℝ) ≤ @@ -2139,25 +1925,21 @@ lemma U_322_1 : have hlg : Real.log (46241225194075943 / 160000000000000000 : ℝ) ≤ (-(496520837715664407951 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46241225194075943 / 160000000000000000 : ℝ) = - (46241225194075943 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46241225194075943 / 40000000000000000 : ℚ)) - (U := (57996906524335592049 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46241225194075943 / 40000000000000000 : ℝ) ≤ - (57996906524335592049 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180626289729231 / 625000000000000 : ℝ)) (q := - (46241225194075943 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46241225194075943 / 160000000000000000 : ℚ)) + (r' := (46241225194075943 / 40000000000000000 : ℚ)) + (U := (-(496520837715664407951 / 400000000000000000000 : ℚ))) + (U' := (57996906524335592049 / 400000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (180626289729231 / 625000000000000 : ℚ)) + (q := (46241225194075943 / 160000000000000000 : ℚ)) + (U := (-(496520837715664407951 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_2 : Uω (aρ 2) (bρ 2) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2165,25 +1947,21 @@ lemma U_322_2 : have hlg : Real.log (45855893173228023 / 160000000000000000 : ℝ) ≤ (-(124967009268472262333 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45855893173228023 / 160000000000000000 : ℝ) = - (45855893173228023 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45855893173228023 / 40000000000000000 : ℚ)) - (U := (13662426791527737667 / 100000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45855893173228023 / 40000000000000000 : ℝ) ≤ - (13662426791527737667 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1432811572785853 / 5000000000000000 : ℝ)) (q := - (45855893173228023 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45855893173228023 / 160000000000000000 : ℚ)) + (r' := (45855893173228023 / 40000000000000000 : ℚ)) + (U := (-(124967009268472262333 / 100000000000000000000 : ℚ))) + (U' := (13662426791527737667 / 100000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (1432811572785853 / 5000000000000000 : ℚ)) + (q := (45855893173228023 / 160000000000000000 : ℚ)) + (U := (-(124967009268472262333 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_3 : Uω (aρ 3) (bρ 3) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2191,25 +1969,21 @@ lemma U_322_3 : have hlg : Real.log (45082473383727919 / 160000000000000000 : ℝ) ≤ (-(253336052101030294349 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45082473383727919 / 160000000000000000 : ℝ) = - (45082473383727919 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45082473383727919 / 40000000000000000 : ℚ)) - (U := (23922820018969705651 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45082473383727919 / 40000000000000000 : ℝ) ≤ - (23922820018969705651 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2816341778234193 / 10000000000000000 : ℝ)) (q := - (45082473383727919 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45082473383727919 / 160000000000000000 : ℚ)) + (r' := (45082473383727919 / 40000000000000000 : ℚ)) + (U := (-(253336052101030294349 / 200000000000000000000 : ℚ))) + (U' := (23922820018969705651 / 200000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (2816341778234193 / 10000000000000000 : ℚ)) + (q := (45082473383727919 / 160000000000000000 : ℚ)) + (U := (-(253336052101030294349 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_4 : Uω (aρ 4) (bρ 4) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2217,25 +1991,21 @@ lemma U_322_4 : have hlg : Real.log (43789266493922071 / 160000000000000000 : ℝ) ≤ (-(6478925422896764806271 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43789266493922071 / 160000000000000000 : ℝ) = - (43789266493922071 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43789266493922071 / 40000000000000000 : ℚ)) - (U := (452546380103235193729 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43789266493922071 / 40000000000000000 : ℝ) ≤ - (452546380103235193729 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1366492549036731 / 5000000000000000 : ℝ)) (q := - (43789266493922071 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43789266493922071 / 160000000000000000 : ℚ)) + (r' := (43789266493922071 / 40000000000000000 : ℚ)) + (U := (-(6478925422896764806271 / 5000000000000000000000 : ℚ))) + (U' := (452546380103235193729 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (1366492549036731 / 5000000000000000 : ℚ)) + (q := (43789266493922071 / 160000000000000000 : ℚ)) + (U := (-(6478925422896764806271 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_5 : Uω (aρ 5) (bρ 5) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2243,25 +2013,21 @@ lemma U_322_5 : have hlg : Real.log (41796636316459999 / 160000000000000000 : ℝ) ≤ (-(13423579493192682497527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41796636316459999 / 160000000000000000 : ℝ) = - (41796636316459999 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41796636316459999 / 40000000000000000 : ℚ)) - (U := (439364112807317502473 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41796636316459999 / 40000000000000000 : ℝ) ≤ - (439364112807317502473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2602096245225703 / 10000000000000000 : ℝ)) (q := - (41796636316459999 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41796636316459999 / 160000000000000000 : ℚ)) + (r' := (41796636316459999 / 40000000000000000 : ℚ)) + (U := (-(13423579493192682497527 / 10000000000000000000000 : ℚ))) + (U' := (439364112807317502473 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (2602096245225703 / 10000000000000000 : ℚ)) + (q := (41796636316459999 / 160000000000000000 : ℚ)) + (U := (-(13423579493192682497527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_6 : Uω (aρ 6) (bρ 6) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2269,25 +2035,21 @@ lemma U_322_6 : have hlg : Real.log (38879861381664647 / 160000000000000000 : ℝ) ≤ (-(2829394800309022849977 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (38879861381664647 / 160000000000000000 : ℝ) = - (38879861381664647 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38879861381664647 / 20000000000000000 : ℚ)) - (U := (1329488281490977150023 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38879861381664647 / 20000000000000000 : ℝ) ≤ - (1329488281490977150023 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (601184938379071 / 2500000000000000 : ℝ)) (q := - (38879861381664647 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38879861381664647 / 160000000000000000 : ℚ)) + (r' := (38879861381664647 / 20000000000000000 : ℚ)) + (U := (-(2829394800309022849977 / 2000000000000000000000 : ℚ))) + (U' := (1329488281490977150023 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (601184938379071 / 2500000000000000 : ℚ)) + (q := (38879861381664647 / 160000000000000000 : ℚ)) + (U := (-(2829394800309022849977 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_7 : Uω (aρ 7) (bρ 7) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2295,25 +2057,21 @@ lemma U_322_7 : have hlg : Real.log (6949999784785659 / 32000000000000000 : ℝ) ≤ (-(15269942734092825618979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6949999784785659 / 32000000000000000 : ℝ) = - (6949999784785659 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6949999784785659 / 4000000000000000 : ℚ)) - (U := (5524472674907174381021 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6949999784785659 / 4000000000000000 : ℝ) ≤ - (5524472674907174381021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (52804208176481 / 250000000000000 : ℝ)) (q := - (6949999784785659 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6949999784785659 / 32000000000000000 : ℚ)) + (r' := (6949999784785659 / 4000000000000000 : ℚ)) + (U := (-(15269942734092825618979 / 10000000000000000000000 : ℚ))) + (U' := (5524472674907174381021 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (52804208176481 / 250000000000000 : ℚ)) + (q := (6949999784785659 / 32000000000000000 : ℚ)) + (U := (-(15269942734092825618979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_8 : Uω (aρ 8) (bρ 8) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2321,25 +2079,21 @@ lemma U_322_8 : have hlg : Real.log (28937140821498503 / 160000000000000000 : ℝ) ≤ (-(1710047894900604801367 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (28937140821498503 / 160000000000000000 : ℝ) = - (28937140821498503 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28937140821498503 / 20000000000000000 : ℚ)) - (U := (369393645999395198633 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28937140821498503 / 20000000000000000 : ℝ) ≤ - (369393645999395198633 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (417275678898879 / 2500000000000000 : ℝ)) (q := - (28937140821498503 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28937140821498503 / 160000000000000000 : ℚ)) + (r' := (28937140821498503 / 20000000000000000 : ℚ)) + (U := (-(1710047894900604801367 / 1000000000000000000000 : ℚ))) + (U' := (369393645999395198633 / 1000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (417275678898879 / 2500000000000000 : ℚ)) + (q := (28937140821498503 / 160000000000000000 : ℚ)) + (U := (-(1710047894900604801367 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_9 : Uω (aρ 9) (bρ 9) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2347,25 +2101,21 @@ lemma U_322_9 : have hlg : Real.log (3976432911427427 / 32000000000000000 : ℝ) ≤ (-(20853507377490201335747 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (3976432911427427 / 32000000000000000 : ℝ) = - (3976432911427427 / 2000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3976432911427427 / 2000000000000000 : ℚ)) - (U := (6872379834509798664253 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3976432911427427 / 2000000000000000 : ℝ) ≤ - (6872379834509798664253 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (175639262182069 / 2000000000000000 : ℝ)) (q := - (3976432911427427 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3976432911427427 / 32000000000000000 : ℚ)) + (r' := (3976432911427427 / 2000000000000000 : ℚ)) + (U := (-(20853507377490201335747 / 10000000000000000000000 : ℚ))) + (U' := (6872379834509798664253 / 10000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37819260565463 / 128000000000000 : ℚ)) + (s := (175639262182069 / 2000000000000000 : ℚ)) + (q := (3976432911427427 / 32000000000000000 : ℚ)) + (U := (-(20853507377490201335747 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_322_10 : Uω (aρ 10) (bρ 10) (37819260565463 / 128000000000000 : ℝ) ≤ @@ -2493,25 +2243,21 @@ lemma U_323_1 : have hlg : Real.log (11584601629423329 / 40000000000000000 : ℝ) ≤ (-(3098006707644175633397 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11584601629423329 / 40000000000000000 : ℝ) = - (11584601629423329 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11584601629423329 / 10000000000000000 : ℚ)) - (U := (367729193855824366603 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11584601629423329 / 10000000000000000 : ℝ) ≤ - (367729193855824366603 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2896094585709477 / 10000000000000000 : ℝ)) (q := - (11584601629423329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11584601629423329 / 40000000000000000 : ℚ)) + (r' := (11584601629423329 / 10000000000000000 : ℚ)) + (U := (-(3098006707644175633397 / 2500000000000000000000 : ℚ))) + (U' := (367729193855824366603 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (2896094585709477 / 10000000000000000 : ℚ)) + (q := (11584601629423329 / 40000000000000000 : ℚ)) + (U := (-(3098006707644175633397 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_2 : Uω (aρ 2) (bρ 2) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2519,25 +2265,21 @@ lemma U_323_2 : have hlg : Real.log (11488271286690993 / 40000000000000000 : ℝ) ≤ (-(12475528267784406772859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11488271286690993 / 40000000000000000 : ℝ) = - (11488271286690993 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11488271286690993 / 10000000000000000 : ℚ)) - (U := (1387415338215593227141 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11488271286690993 / 10000000000000000 : ℝ) ≤ - (1387415338215593227141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2871698426853309 / 10000000000000000 : ℝ)) (q := - (11488271286690993 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11488271286690993 / 40000000000000000 : ℚ)) + (r' := (11488271286690993 / 10000000000000000 : ℚ)) + (U := (-(12475528267784406772859 / 10000000000000000000000 : ℚ))) + (U' := (1387415338215593227141 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (2871698426853309 / 10000000000000000 : ℚ)) + (q := (11488271286690993 / 40000000000000000 : ℚ)) + (U := (-(12475528267784406772859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_3 : Uω (aρ 3) (bρ 3) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2545,25 +2287,21 @@ lemma U_323_3 : have hlg : Real.log (11294924507987287 / 40000000000000000 : ℝ) ≤ (-(2529051974725758156739 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11294924507987287 / 40000000000000000 : ℝ) = - (11294924507987287 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11294924507987287 / 10000000000000000 : ℚ)) - (U := (243536746474241843261 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11294924507987287 / 10000000000000000 : ℝ) ≤ - (243536746474241843261 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44100330372679 / 156250000000000 : ℝ)) (q := - (11294924507987287 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11294924507987287 / 40000000000000000 : ℚ)) + (r' := (11294924507987287 / 10000000000000000 : ℚ)) + (U := (-(2529051974725758156739 / 2000000000000000000000 : ℚ))) + (U' := (243536746474241843261 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (44100330372679 / 156250000000000 : ℚ)) + (q := (11294924507987287 / 40000000000000000 : ℚ)) + (U := (-(2529051974725758156739 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_4 : Uω (aρ 4) (bρ 4) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2571,25 +2309,21 @@ lemma U_323_4 : have hlg : Real.log (10971645580980563 / 40000000000000000 : ℝ) ≤ (-(6467825915874434987103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10971645580980563 / 40000000000000000 : ℝ) = - (10971645580980563 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10971645580980563 / 10000000000000000 : ℚ)) - (U := (463645887125565012897 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10971645580980563 / 10000000000000000 : ℝ) ≤ - (463645887125565012897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1369537930706547 / 5000000000000000 : ℝ)) (q := - (10971645580980563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10971645580980563 / 40000000000000000 : ℚ)) + (r' := (10971645580980563 / 10000000000000000 : ℚ)) + (U := (-(6467825915874434987103 / 5000000000000000000000 : ℚ))) + (U' := (463645887125565012897 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (1369537930706547 / 5000000000000000 : ℚ)) + (q := (10971645580980563 / 40000000000000000 : ℚ)) + (U := (-(6467825915874434987103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_5 : Uω (aρ 5) (bρ 5) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2597,25 +2331,21 @@ lemma U_323_5 : have hlg : Real.log (10473548891629579 / 40000000000000000 : ℝ) ≤ (-(13400265280141196180749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10473548891629579 / 40000000000000000 : ℝ) = - (10473548891629579 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10473548891629579 / 10000000000000000 : ℚ)) - (U := (462678325858803819251 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10473548891629579 / 10000000000000000 : ℝ) ≤ - (462678325858803819251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1304108718036301 / 5000000000000000 : ℝ)) (q := - (10473548891629579 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10473548891629579 / 40000000000000000 : ℚ)) + (r' := (10473548891629579 / 10000000000000000 : ℚ)) + (U := (-(13400265280141196180749 / 10000000000000000000000 : ℚ))) + (U' := (462678325858803819251 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (1304108718036301 / 5000000000000000 : ℚ)) + (q := (10473548891629579 / 40000000000000000 : ℚ)) + (U := (-(13400265280141196180749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_6 : Uω (aρ 6) (bρ 6) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2623,25 +2353,21 @@ lemma U_323_6 : have hlg : Real.log (9744514672005377 / 40000000000000000 : ℝ) ≤ (-(1412174924384875215969 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9744514672005377 / 40000000000000000 : ℝ) = - (9744514672005377 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9744514672005377 / 5000000000000000 : ℚ)) - (U := (667266616515124784031 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9744514672005377 / 5000000000000000 : ℝ) ≤ - (667266616515124784031 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2410940701400501 / 10000000000000000 : ℝ)) (q := - (9744514672005377 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9744514672005377 / 40000000000000000 : ℚ)) + (r' := (9744514672005377 / 5000000000000000 : ℚ)) + (U := (-(1412174924384875215969 / 1000000000000000000000 : ℚ))) + (U' := (667266616515124784031 / 1000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (2410940701400501 / 10000000000000000 : ℚ)) + (q := (9744514672005377 / 40000000000000000 : ℚ)) + (U := (-(1412174924384875215969 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_7 : Uω (aρ 7) (bρ 7) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2649,25 +2375,21 @@ lemma U_323_7 : have hlg : Real.log (8712479333308459 / 40000000000000000 : ℝ) ≤ (-(15241230493239060186719 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8712479333308459 / 40000000000000000 : ℝ) = - (8712479333308459 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8712479333308459 / 5000000000000000 : ℚ)) - (U := (5553184915760939813281 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8712479333308459 / 5000000000000000 : ℝ) ≤ - (5553184915760939813281 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1059292206406021 / 5000000000000000 : ℝ)) (q := - (8712479333308459 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8712479333308459 / 40000000000000000 : ℚ)) + (r' := (8712479333308459 / 5000000000000000 : ℚ)) + (U := (-(15241230493239060186719 / 10000000000000000000000 : ℚ))) + (U' := (5553184915760939813281 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (1059292206406021 / 5000000000000000 : ℚ)) + (q := (8712479333308459 / 40000000000000000 : ℚ)) + (U := (-(15241230493239060186719 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_8 : Uω (aρ 8) (bρ 8) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2675,25 +2397,21 @@ lemma U_323_8 : have hlg : Real.log (7260602151212977 / 40000000000000000 : ℝ) ≤ (-(8532083434991892629273 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7260602151212977 / 40000000000000000 : ℝ) = - (7260602151212977 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7260602151212977 / 5000000000000000 : ℚ)) - (U := (1865124269508107370727 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7260602151212977 / 5000000000000000 : ℝ) ≤ - (1865124269508107370727 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1676187473104301 / 10000000000000000 : ℝ)) (q := - (7260602151212977 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7260602151212977 / 40000000000000000 : ℚ)) + (r' := (7260602151212977 / 5000000000000000 : ℚ)) + (U := (-(8532083434991892629273 / 5000000000000000000000 : ℚ))) + (U' := (1865124269508107370727 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (1676187473104301 / 10000000000000000 : ℚ)) + (q := (7260602151212977 / 40000000000000000 : ℚ)) + (U := (-(8532083434991892629273 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_9 : Uω (aρ 9) (bρ 9) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2701,25 +2419,21 @@ lemma U_323_9 : have hlg : Real.log (5004820588425443 / 40000000000000000 : ℝ) ≤ (-(20784778876778594280753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5004820588425443 / 40000000000000000 : ℝ) = - (5004820588425443 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5004820588425443 / 5000000000000000 : ℚ)) - (U := (9636532221405719247 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (5004820588425443 / 5000000000000000 : ℝ) ≤ - (9636532221405719247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (444631160035267 / 5000000000000000 : ℝ)) (q := - (5004820588425443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5004820588425443 / 40000000000000000 : ℚ)) + (r' := (5004820588425443 / 5000000000000000 : ℚ)) + (U := (-(20784778876778594280753 / 10000000000000000000000 : ℚ))) + (U' := (9636532221405719247 / 10000000000000000000000 : ℚ)) + 3 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9474251030679 / 32000000000000 : ℚ)) + (s := (444631160035267 / 5000000000000000 : ℚ)) + (q := (5004820588425443 / 40000000000000000 : ℚ)) + (U := (-(20784778876778594280753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_323_10 : Uω (aρ 10) (bρ 10) (9474251030679 / 32000000000000 : ℝ) ≤ @@ -2846,25 +2560,21 @@ lemma U_324_1 : have hlg : Real.log (46435587833453881 / 160000000000000000 : ℝ) ≤ (-(1546384587863347391307 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46435587833453881 / 160000000000000000 : ℝ) = - (46435587833453881 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46435587833453881 / 40000000000000000 : ℚ)) - (U := (186483362886652608693 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46435587833453881 / 40000000000000000 : ℝ) ≤ - (186483362886652608693 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2902168534769157 / 10000000000000000 : ℝ)) (q := - (46435587833453881 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46435587833453881 / 160000000000000000 : ℚ)) + (r' := (46435587833453881 / 40000000000000000 : ℚ)) + (U := (-(1546384587863347391307 / 1250000000000000000000 : ℚ))) + (U' := (186483362886652608693 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (2902168534769157 / 10000000000000000 : ℚ)) + (q := (46435587833453881 / 160000000000000000 : ℚ)) + (U := (-(1546384587863347391307 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_2 : Uω (aρ 2) (bρ 2) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -2872,25 +2582,21 @@ lemma U_324_2 : have hlg : Real.log (46050277067415249 / 160000000000000000 : ℝ) ≤ (-(12454400353658942523317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46050277067415249 / 160000000000000000 : ℝ) = - (46050277067415249 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46050277067415249 / 40000000000000000 : ℚ)) - (U := (1408543252341057476683 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46050277067415249 / 40000000000000000 : ℝ) ≤ - (1408543252341057476683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (359721712690541 / 1250000000000000 : ℝ)) (q := - (46050277067415249 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46050277067415249 / 160000000000000000 : ℚ)) + (r' := (46050277067415249 / 40000000000000000 : ℚ)) + (U := (-(12454400353658942523317 / 10000000000000000000000 : ℚ))) + (U' := (1408543252341057476683 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (359721712690541 / 1250000000000000 : ℚ)) + (q := (46050277067415249 / 160000000000000000 : ℚ)) + (U := (-(12454400353658942523317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_3 : Uω (aρ 3) (bρ 3) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -2898,25 +2604,21 @@ lemma U_324_3 : have hlg : Real.log (362215379887637 / 1280000000000000 : ℝ) ≤ (-(6311881747142055395947 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (362215379887637 / 1280000000000000 : ℝ) = - (362215379887637 / 320000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (362215379887637 / 320000000000000 : ℚ)) - (U := (619590055857944604053 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (362215379887637 / 320000000000000 : ℝ) ≤ - (619590055857944604053 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11314001940767 / 40000000000000 : ℝ)) (q := - (362215379887637 / 1280000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (362215379887637 / 1280000000000000 : ℚ)) + (r' := (362215379887637 / 320000000000000 : ℚ)) + (U := (-(6311881747142055395947 / 5000000000000000000000 : ℚ))) + (U' := (619590055857944604053 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (11314001940767 / 40000000000000 : ℚ)) + (q := (362215379887637 / 1280000000000000 : ℚ)) + (U := (-(6311881747142055395947 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_4 : Uω (aρ 4) (bρ 4) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -2924,25 +2626,21 @@ lemma U_324_4 : have hlg : Real.log (43983897549575361 / 160000000000000000 : ℝ) ≤ (-(6456751062797533349511 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43983897549575361 / 160000000000000000 : ℝ) = - (43983897549575361 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43983897549575361 / 40000000000000000 : ℚ)) - (U := (474720740202466650489 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43983897549575361 / 40000000000000000 : ℝ) ≤ - (474720740202466650489 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1372583274604671 / 5000000000000000 : ℝ)) (q := - (43983897549575361 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43983897549575361 / 160000000000000000 : ℚ)) + (r' := (43983897549575361 / 40000000000000000 : ℚ)) + (U := (-(6456751062797533349511 / 5000000000000000000000 : ℚ))) + (U' := (474720740202466650489 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (1372583274604671 / 5000000000000000 : ℚ)) + (q := (43983897549575361 / 160000000000000000 : ℚ)) + (U := (-(6456751062797533349511 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_5 : Uω (aρ 5) (bρ 5) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -2950,25 +2648,21 @@ lemma U_324_5 : have hlg : Real.log (41991753044936137 / 160000000000000000 : ℝ) ≤ (-(1337700571783894728703 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41991753044936137 / 160000000000000000 : ℝ) = - (41991753044936137 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41991753044936137 / 40000000000000000 : ℚ)) - (U := (48593788816105271297 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41991753044936137 / 40000000000000000 : ℝ) ≤ - (48593788816105271297 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2614338405464439 / 10000000000000000 : ℝ)) (q := - (41991753044936137 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41991753044936137 / 160000000000000000 : ℚ)) + (r' := (41991753044936137 / 40000000000000000 : ℚ)) + (U := (-(1337700571783894728703 / 1000000000000000000000 : ℚ))) + (U' := (48593788816105271297 / 1000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (2614338405464439 / 10000000000000000 : ℚ)) + (q := (41991753044936137 / 160000000000000000 : ℚ)) + (U := (-(1337700571783894728703 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_6 : Uω (aρ 6) (bρ 6) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -2976,25 +2670,21 @@ lemma U_324_6 : have hlg : Real.log (39076250825509641 / 160000000000000000 : ℝ) ≤ (-(704829463884613062753 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (39076250825509641 / 160000000000000000 : ℝ) = - (39076250825509641 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39076250825509641 / 20000000000000000 : ℚ)) - (U := (334891306565386937247 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39076250825509641 / 20000000000000000 : ℝ) ≤ - (334891306565386937247 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2417141003176127 / 10000000000000000 : ℝ)) (q := - (39076250825509641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39076250825509641 / 160000000000000000 : ℚ)) + (r' := (39076250825509641 / 20000000000000000 : ℚ)) + (U := (-(704829463884613062753 / 500000000000000000000 : ℚ))) + (U' := (334891306565386937247 / 500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (2417141003176127 / 10000000000000000 : ℚ)) + (q := (39076250825509641 / 160000000000000000 : ℚ)) + (U := (-(704829463884613062753 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_7 : Uω (aρ 7) (bρ 7) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -3002,25 +2692,21 @@ lemma U_324_7 : have hlg : Real.log (34949819644135537 / 160000000000000000 : ℝ) ≤ (-(15212605061841808395923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34949819644135537 / 160000000000000000 : ℝ) = - (34949819644135537 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34949819644135537 / 20000000000000000 : ℚ)) - (U := (5581810347158191604077 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34949819644135537 / 20000000000000000 : ℝ) ≤ - (5581810347158191604077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (531249621566091 / 2500000000000000 : ℝ)) (q := - (34949819644135537 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34949819644135537 / 160000000000000000 : ℚ)) + (r' := (34949819644135537 / 20000000000000000 : ℚ)) + (U := (-(15212605061841808395923 / 10000000000000000000000 : ℚ))) + (U' := (5581810347158191604077 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (531249621566091 / 2500000000000000 : ℚ)) + (q := (34949819644135537 / 160000000000000000 : ℚ)) + (U := (-(15212605061841808395923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_8 : Uω (aρ 8) (bρ 8) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -3028,25 +2714,21 @@ lemma U_324_8 : have hlg : Real.log (29147613159923817 / 160000000000000000 : ℝ) ≤ (-(17028007863161623062419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (29147613159923817 / 160000000000000000 : ℝ) = - (29147613159923817 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29147613159923817 / 20000000000000000 : ℚ)) - (U := (3766407545838376937581 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29147613159923817 / 20000000000000000 : ℝ) ≤ - (3766407545838376937581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1683264327077899 / 10000000000000000 : ℝ)) (q := - (29147613159923817 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29147613159923817 / 160000000000000000 : ℚ)) + (r' := (29147613159923817 / 20000000000000000 : ℚ)) + (U := (-(17028007863161623062419 / 10000000000000000000000 : ℚ))) + (U' := (3766407545838376937581 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (1683264327077899 / 10000000000000000 : ℚ)) + (q := (29147613159923817 / 160000000000000000 : ℚ)) + (U := (-(17028007863161623062419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_9 : Uω (aρ 9) (bρ 9) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -3054,25 +2736,21 @@ lemma U_324_9 : have hlg : Real.log (20155639796037609 / 160000000000000000 : ℝ) ≤ (-(4143379349202316265587 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (20155639796037609 / 160000000000000000 : ℝ) = - (20155639796037609 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20155639796037609 / 20000000000000000 : ℚ)) - (U := (15503732597683734413 / 2000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20155639796037609 / 20000000000000000 : ℝ) ≤ - (15503732597683734413 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (900233284952123 / 10000000000000000 : ℝ)) (q := - (20155639796037609 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20155639796037609 / 160000000000000000 : ℚ)) + (r' := (20155639796037609 / 20000000000000000 : ℚ)) + (U := (-(4143379349202316265587 / 2000000000000000000000 : ℚ))) + (U' := (15503732597683734413 / 2000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (37974747679969 / 128000000000000 : ℚ)) + (s := (900233284952123 / 10000000000000000 : ℚ)) + (q := (20155639796037609 / 160000000000000000 : ℚ)) + (U := (-(4143379349202316265587 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_324_10 : Uω (aρ 10) (bρ 10) (37974747679969 / 128000000000000 : ℝ) ≤ @@ -3200,25 +2878,21 @@ lemma U_325_1 : have hlg : Real.log (23266384570703427 / 80000000000000000 : ℝ) ≤ (-(12350170375956099393281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23266384570703427 / 80000000000000000 : ℝ) = - (23266384570703427 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23266384570703427 / 20000000000000000 : ℚ)) - (U := (1512773230043900606719 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23266384570703427 / 20000000000000000 : ℝ) ≤ - (1512773230043900606719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (363530310356611 / 1250000000000000 : ℝ)) (q := - (23266384570703427 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23266384570703427 / 80000000000000000 : ℚ)) + (r' := (23266384570703427 / 20000000000000000 : ℚ)) + (U := (-(12350170375956099393281 / 10000000000000000000000 : ℚ))) + (U' := (1512773230043900606719 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (363530310356611 / 1250000000000000 : ℚ)) + (q := (23266384570703427 / 80000000000000000 : ℚ)) + (U := (-(12350170375956099393281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_2 : Uω (aρ 2) (bρ 2) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3226,25 +2900,21 @@ lemma U_325_2 : have hlg : Real.log (23073734467758043 / 80000000000000000 : ℝ) ≤ (-(248666339913984400827 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23073734467758043 / 80000000000000000 : ℝ) = - (23073734467758043 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23073734467758043 / 20000000000000000 : ℚ)) - (U := (28592532206015599173 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23073734467758043 / 20000000000000000 : ℝ) ≤ - (28592532206015599173 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1441924484813271 / 5000000000000000 : ℝ)) (q := - (23073734467758043 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23073734467758043 / 80000000000000000 : ℚ)) + (r' := (23073734467758043 / 20000000000000000 : ℚ)) + (U := (-(248666339913984400827 / 200000000000000000000 : ℚ))) + (U' := (28592532206015599173 / 200000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (1441924484813271 / 5000000000000000 : ℚ)) + (q := (23073734467758043 / 80000000000000000 : ℚ)) + (U := (-(248666339913984400827 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_3 : Uω (aρ 3) (bρ 3) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3252,25 +2922,21 @@ lemma U_325_3 : have hlg : Real.log (22687073373496971 / 80000000000000000 : ℝ) ≤ (-(2520462653559380998639 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22687073373496971 / 80000000000000000 : ℝ) = - (22687073373496971 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22687073373496971 / 20000000000000000 : ℚ)) - (U := (252126067640619001361 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22687073373496971 / 20000000000000000 : ℝ) ≤ - (252126067640619001361 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1417289901205637 / 5000000000000000 : ℝ)) (q := - (22687073373496971 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22687073373496971 / 80000000000000000 : ℚ)) + (r' := (22687073373496971 / 20000000000000000 : ℚ)) + (U := (-(2520462653559380998639 / 2000000000000000000000 : ℚ))) + (U' := (252126067640619001361 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (1417289901205637 / 5000000000000000 : ℚ)) + (q := (22687073373496971 / 80000000000000000 : ℚ)) + (U := (-(2520462653559380998639 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_4 : Uω (aρ 4) (bρ 4) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3278,25 +2944,21 @@ lemma U_325_4 : have hlg : Real.log (22040606087447539 / 80000000000000000 : ℝ) ≤ (-(12891401508169105599223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22040606087447539 / 80000000000000000 : ℝ) = - (22040606087447539 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22040606087447539 / 20000000000000000 : ℚ)) - (U := (971542097830894400777 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22040606087447539 / 20000000000000000 : ℝ) ≤ - (971542097830894400777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (687814290490979 / 2500000000000000 : ℝ)) (q := - (22040606087447539 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22040606087447539 / 80000000000000000 : ℚ)) + (r' := (22040606087447539 / 20000000000000000 : ℚ)) + (U := (-(12891401508169105599223 / 10000000000000000000000 : ℚ))) + (U' := (971542097830894400777 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (687814290490979 / 2500000000000000 : ℚ)) + (q := (22040606087447539 / 80000000000000000 : ℚ)) + (U := (-(12891401508169105599223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_5 : Uω (aρ 5) (bρ 5) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3304,25 +2966,21 @@ lemma U_325_5 : have hlg : Real.log (21044654382064131 / 80000000000000000 : ℝ) ≤ (-(3338450137178833629859 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21044654382064131 / 80000000000000000 : ℝ) = - (21044654382064131 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21044654382064131 / 20000000000000000 : ℚ)) - (U := (127285764321166370141 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (21044654382064131 / 20000000000000000 : ℝ) ≤ - (127285764321166370141 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (327557394369133 / 1250000000000000 : ℝ)) (q := - (21044654382064131 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21044654382064131 / 80000000000000000 : ℚ)) + (r' := (21044654382064131 / 20000000000000000 : ℚ)) + (U := (-(3338450137178833629859 / 2500000000000000000000 : ℚ))) + (U' := (127285764321166370141 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (327557394369133 / 1250000000000000 : ℚ)) + (q := (21044654382064131 / 80000000000000000 : ℚ)) + (U := (-(3338450137178833629859 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_6 : Uω (aρ 6) (bρ 6) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3330,25 +2988,21 @@ lemma U_325_6 : have hlg : Real.log (19587218916901939 / 80000000000000000 : ℝ) ≤ (-(1758936720551409517731 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19587218916901939 / 80000000000000000 : ℝ) = - (19587218916901939 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19587218916901939 / 10000000000000000 : ℚ)) - (U := (840365205573590482269 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19587218916901939 / 10000000000000000 : ℝ) ≤ - (840365205573590482269 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (605835165950629 / 2500000000000000 : ℝ)) (q := - (19587218916901939 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19587218916901939 / 80000000000000000 : ℚ)) + (r' := (19587218916901939 / 10000000000000000 : ℚ)) + (U := (-(1758936720551409517731 / 1250000000000000000000 : ℚ))) + (U' := (840365205573590482269 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (605835165950629 / 2500000000000000 : ℚ)) + (q := (19587218916901939 / 80000000000000000 : ℚ)) + (U := (-(1758936720551409517731 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_7 : Uω (aρ 7) (bρ 7) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3356,25 +3010,21 @@ lemma U_325_7 : have hlg : Real.log (17524853000984307 / 80000000000000000 : ℝ) ≤ (-(15184065889695235582767 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17524853000984307 / 80000000000000000 : ℝ) = - (17524853000984307 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17524853000984307 / 10000000000000000 : ℚ)) - (U := (5610349519304764417233 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17524853000984307 / 10000000000000000 : ℝ) ≤ - (5610349519304764417233 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (532852641395777 / 2500000000000000 : ℝ)) (q := - (17524853000984307 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17524853000984307 / 80000000000000000 : ℚ)) + (r' := (17524853000984307 / 10000000000000000 : ℚ)) + (U := (-(15184065889695235582767 / 10000000000000000000000 : ℚ))) + (U' := (5610349519304764417233 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (532852641395777 / 2500000000000000 : ℚ)) + (q := (17524853000984307 / 80000000000000000 : ℚ)) + (U := (-(15184065889695235582767 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_8 : Uω (aρ 8) (bρ 8) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3382,25 +3032,21 @@ lemma U_325_8 : have hlg : Real.log (14626377640430259 / 80000000000000000 : ℝ) ≤ (-(8496000237880936070873 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14626377640430259 / 80000000000000000 : ℝ) = - (14626377640430259 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14626377640430259 / 10000000000000000 : ℚ)) - (U := (1901207466619063929127 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14626377640430259 / 10000000000000000 : ℝ) ≤ - (1901207466619063929127 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (422583344196149 / 2500000000000000 : ℝ)) (q := - (14626377640430259 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14626377640430259 / 80000000000000000 : ℚ)) + (r' := (14626377640430259 / 10000000000000000 : ℚ)) + (U := (-(8496000237880936070873 / 5000000000000000000000 : ℚ))) + (U' := (1901207466619063929127 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (422583344196149 / 2500000000000000 : ℚ)) + (q := (14626377640430259 / 80000000000000000 : ℚ)) + (U := (-(8496000237880936070873 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_9 : Uω (aρ 9) (bρ 9) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3408,25 +3054,21 @@ lemma U_325_9 : have hlg : Real.log (10145632175558567 / 80000000000000000 : ℝ) ≤ (-(10324916742774442850357 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10145632175558567 / 80000000000000000 : ℝ) = - (10145632175558567 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10145632175558567 / 10000000000000000 : ℚ)) - (U := (72290961725557149643 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10145632175558567 / 10000000000000000 : ℝ) ≤ - (72290961725557149643 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (911112638926673 / 10000000000000000 : ℝ)) (q := - (10145632175558567 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10145632175558567 / 80000000000000000 : ℚ)) + (r' := (10145632175558567 / 10000000000000000 : ℚ)) + (U := (-(10324916742774442850357 / 5000000000000000000000 : ℚ))) + (U' := (72290961725557149643 / 5000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19026245618611 / 64000000000000 : ℚ)) + (s := (911112638926673 / 10000000000000000 : ℚ)) + (q := (10145632175558567 / 80000000000000000 : ℚ)) + (U := (-(10324916742774442850357 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_325_10 : Uω (aρ 10) (bρ 10) (19026245618611 / 64000000000000 : ℝ) ≤ @@ -3554,25 +3196,21 @@ lemma U_326_1 : have hlg : Real.log (46629950441601067 / 160000000000000000 : ℝ) ≤ (-(308232691673755184269 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46629950441601067 / 160000000000000000 : ℝ) = - (46629950441601067 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46629950441601067 / 40000000000000000 : ℚ)) - (U := (38340898476244815731 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46629950441601067 / 40000000000000000 : ℝ) ≤ - (38340898476244815731 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1457158214983387 / 5000000000000000 : ℝ)) (q := - (46629950441601067 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46629950441601067 / 160000000000000000 : ℚ)) + (r' := (46629950441601067 / 40000000000000000 : ℚ)) + (U := (-(308232691673755184269 / 250000000000000000000 : ℚ))) + (U' := (38340898476244815731 / 250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (1457158214983387 / 5000000000000000 : ℚ)) + (q := (46629950441601067 / 160000000000000000 : ℚ)) + (U := (-(308232691673755184269 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_2 : Uω (aρ 2) (bρ 2) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3580,25 +3218,21 @@ lemma U_326_2 : have hlg : Real.log (46244660751397899 / 160000000000000000 : ℝ) ≤ (-(775767375395375690883 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46244660751397899 / 160000000000000000 : ℝ) = - (46244660751397899 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46244660751397899 / 40000000000000000 : ℚ)) - (U := (90666599979624309117 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46244660751397899 / 40000000000000000 : ℝ) ≤ - (90666599979624309117 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1444962115600689 / 5000000000000000 : ℝ)) (q := - (46244660751397899 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46244660751397899 / 160000000000000000 : ℚ)) + (r' := (46244660751397899 / 40000000000000000 : ℚ)) + (U := (-(775767375395375690883 / 625000000000000000000 : ℚ))) + (U' := (90666599979624309117 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (1444962115600689 / 5000000000000000 : ℚ)) + (q := (46244660751397899 / 160000000000000000 : ℚ)) + (U := (-(775767375395375690883 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_3 : Uω (aρ 3) (bρ 3) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3606,25 +3240,21 @@ lemma U_326_3 : have hlg : Real.log (45471370816306019 / 160000000000000000 : ℝ) ≤ (-(2516181799245877235259 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45471370816306019 / 160000000000000000 : ℝ) = - (45471370816306019 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45471370816306019 / 40000000000000000 : ℚ)) - (U := (256406921954122764741 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45471370816306019 / 40000000000000000 : ℝ) ≤ - (256406921954122764741 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2840659095664893 / 10000000000000000 : ℝ)) (q := - (45471370816306019 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45471370816306019 / 160000000000000000 : ℚ)) + (r' := (45471370816306019 / 40000000000000000 : ℚ)) + (U := (-(2516181799245877235259 / 2000000000000000000000 : ℚ))) + (U' := (256406921954122764741 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (2840659095664893 / 10000000000000000 : ℚ)) + (q := (45471370816306019 / 160000000000000000 : ℚ)) + (U := (-(2516181799245877235259 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_4 : Uω (aρ 4) (bρ 4) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3632,25 +3262,21 @@ lemma U_326_4 : have hlg : Real.log (44178526203859579 / 160000000000000000 : ℝ) ≤ (-(12869349761769917993087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44178526203859579 / 160000000000000000 : ℝ) = - (44178526203859579 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44178526203859579 / 40000000000000000 : ℚ)) - (U := (993593844230082006913 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44178526203859579 / 40000000000000000 : ℝ) ≤ - (993593844230082006913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (344668462521761 / 1250000000000000 : ℝ)) (q := - (44178526203859579 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44178526203859579 / 160000000000000000 : ℚ)) + (r' := (44178526203859579 / 40000000000000000 : ℚ)) + (U := (-(12869349761769917993087 / 10000000000000000000000 : ℚ))) + (U' := (993593844230082006913 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (344668462521761 / 1250000000000000 : ℚ)) + (q := (44178526203859579 / 160000000000000000 : ℚ)) + (U := (-(12869349761769917993087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_5 : Uω (aρ 5) (bρ 5) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3658,25 +3284,21 @@ lemma U_326_5 : have hlg : Real.log (42186862736393331 / 160000000000000000 : ℝ) ≤ (-(533225980681196273301 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42186862736393331 / 160000000000000000 : ℝ) = - (42186862736393331 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42186862736393331 / 40000000000000000 : ℚ)) - (U := (21291763558803726699 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42186862736393331 / 40000000000000000 : ℝ) ≤ - (21291763558803726699 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2626579686075807 / 10000000000000000 : ℝ)) (q := - (42186862736393331 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42186862736393331 / 160000000000000000 : ℚ)) + (r' := (42186862736393331 / 40000000000000000 : ℚ)) + (U := (-(533225980681196273301 / 400000000000000000000 : ℚ))) + (U' := (21291763558803726699 / 400000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (2626579686075807 / 10000000000000000 : ℚ)) + (q := (42186862736393331 / 160000000000000000 : ℚ)) + (U := (-(533225980681196273301 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_6 : Uω (aρ 6) (bρ 6) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3684,25 +3306,21 @@ lemma U_326_6 : have hlg : Real.log (39272619752170011 / 160000000000000000 : ℝ) ≤ (-(3511615592009915733251 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (39272619752170011 / 160000000000000000 : ℝ) = - (39272619752170011 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39272619752170011 / 20000000000000000 : ℚ)) - (U := (1686988260240084266749 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39272619752170011 / 20000000000000000 : ℝ) ≤ - (1686988260240084266749 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (607384922046973 / 2500000000000000 : ℝ)) (q := - (39272619752170011 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39272619752170011 / 160000000000000000 : ℚ)) + (r' := (39272619752170011 / 20000000000000000 : ℚ)) + (U := (-(3511615592009915733251 / 2500000000000000000000 : ℚ))) + (U' := (1686988260240084266749 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (607384922046973 / 2500000000000000 : ℚ)) + (q := (39272619752170011 / 160000000000000000 : ℚ)) + (U := (-(3511615592009915733251 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_7 : Uω (aρ 7) (bρ 7) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3710,25 +3328,21 @@ lemma U_326_7 : have hlg : Real.log (35149576550279731 / 160000000000000000 : ℝ) ≤ (-(473612888501125712317 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35149576550279731 / 160000000000000000 : ℝ) = - (35149576550279731 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35149576550279731 / 20000000000000000 : ℚ)) - (U := (176212593030124287683 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35149576550279731 / 20000000000000000 : ℝ) ≤ - (176212593030124287683 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2137820668711607 / 10000000000000000 : ℝ)) (q := - (35149576550279731 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35149576550279731 / 160000000000000000 : ℚ)) + (r' := (35149576550279731 / 20000000000000000 : ℚ)) + (U := (-(473612888501125712317 / 312500000000000000000 : ℚ))) + (U' := (176212593030124287683 / 312500000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (2137820668711607 / 10000000000000000 : ℚ)) + (q := (35149576550279731 / 160000000000000000 : ℚ)) + (U := (-(473612888501125712317 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_8 : Uω (aρ 8) (bρ 8) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3736,25 +3350,21 @@ lemma U_326_8 : have hlg : Real.log (29357835747710419 / 160000000000000000 : ℝ) ≤ (-(16956143277397500307727 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (29357835747710419 / 160000000000000000 : ℝ) = - (29357835747710419 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29357835747710419 / 20000000000000000 : ℚ)) - (U := (3838272131602499692273 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29357835747710419 / 20000000000000000 : ℝ) ≤ - (3838272131602499692273 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1697394719730443 / 10000000000000000 : ℝ)) (q := - (29357835747710419 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29357835747710419 / 160000000000000000 : ℚ)) + (r' := (29357835747710419 / 20000000000000000 : ℚ)) + (U := (-(16956143277397500307727 / 10000000000000000000000 : ℚ))) + (U' := (3838272131602499692273 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (1697394719730443 / 10000000000000000 : ℚ)) + (q := (29357835747710419 / 160000000000000000 : ℚ)) + (U := (-(16956143277397500307727 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_9 : Uω (aρ 9) (bρ 9) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3762,25 +3372,21 @@ lemma U_326_9 : have hlg : Real.log (817047278612811 / 6400000000000000 : ℝ) ≤ (-(20583563068231126965171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (817047278612811 / 6400000000000000 : ℝ) = - (817047278612811 / 800000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (817047278612811 / 800000000000000 : ℚ)) - (U := (210852340768873034829 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (817047278612811 / 800000000000000 : ℝ) ≤ - (210852340768873034829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36876145011667 / 400000000000000 : ℝ)) (q := - (817047278612811 / 6400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (817047278612811 / 6400000000000000 : ℚ)) + (r' := (817047278612811 / 800000000000000 : ℚ)) + (U := (-(20583563068231126965171 / 10000000000000000000000 : ℚ))) + (U' := (210852340768873034829 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1525209391779 / 5120000000000 : ℚ)) + (s := (36876145011667 / 400000000000000 : ℚ)) + (q := (817047278612811 / 6400000000000000 : ℚ)) + (U := (-(20583563068231126965171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_326_10 : Uω (aρ 10) (bρ 10) (1525209391779 / 5120000000000 : ℝ) ≤ @@ -3906,25 +3512,21 @@ lemma U_327_1 : have hlg : Real.log (730111433345077 / 2500000000000000 : ℝ) ≤ (-(492339535770254087997 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (730111433345077 / 2500000000000000 : ℝ) = - (730111433345077 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (730111433345077 / 625000000000000 : ℚ)) - (U := (62178208469745912003 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (730111433345077 / 625000000000000 : ℝ) ≤ - (62178208469745912003 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1460195188058433 / 5000000000000000 : ℝ)) (q := - (730111433345077 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (730111433345077 / 2500000000000000 : ℚ)) + (r' := (730111433345077 / 625000000000000 : ℚ)) + (U := (-(492339535770254087997 / 400000000000000000000 : ℚ))) + (U' := (62178208469745912003 / 400000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (1460195188058433 / 5000000000000000 : ℚ)) + (q := (730111433345077 / 2500000000000000 : ℚ)) + (U := (-(492339535770254087997 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_2 : Uω (aρ 2) (bρ 2) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -3932,25 +3534,21 @@ lemma U_327_2 : have hlg : Real.log (2896365782211833 / 10000000000000000 : ℝ) ≤ (-(12391283199142446414239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2896365782211833 / 10000000000000000 : ℝ) = - (2896365782211833 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2896365782211833 / 2500000000000000 : ℚ)) - (U := (1471660406857553585761 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2896365782211833 / 2500000000000000 : ℝ) ≤ - (1471660406857553585761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (723999871572479 / 2500000000000000 : ℝ)) (q := - (2896365782211833 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2896365782211833 / 10000000000000000 : ℚ)) + (r' := (2896365782211833 / 2500000000000000 : ℚ)) + (U := (-(12391283199142446414239 / 10000000000000000000000 : ℚ))) + (U' := (1471660406857553585761 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (723999871572479 / 2500000000000000 : ℚ)) + (q := (2896365782211833 / 10000000000000000 : ℚ)) + (U := (-(12391283199142446414239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_3 : Uω (aρ 3) (bρ 3) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -3958,25 +3556,21 @@ lemma U_327_3 : have hlg : Real.log (1139214867377979 / 4000000000000000 : ℝ) ≤ (-(12559550482915562925899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1139214867377979 / 4000000000000000 : ℝ) = - (1139214867377979 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1139214867377979 / 1000000000000000 : ℚ)) - (U := (1303393123084437074101 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1139214867377979 / 1000000000000000 : ℝ) ≤ - (1303393123084437074101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (569347673021229 / 2000000000000000 : ℝ)) (q := - (1139214867377979 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1139214867377979 / 4000000000000000 : ℚ)) + (r' := (1139214867377979 / 1000000000000000 : ℚ)) + (U := (-(12559550482915562925899 / 10000000000000000000000 : ℚ))) + (U' := (1303393123084437074101 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (569347673021229 / 2000000000000000 : ℚ)) + (q := (1139214867377979 / 4000000000000000 : ℚ)) + (U := (-(12559550482915562925899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_4 : Uω (aρ 4) (bρ 4) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -3984,25 +3578,21 @@ lemma U_327_4 : have hlg : Real.log (5534479955051489 / 20000000000000000 : ℝ) ≤ (-(2569469334029075128739 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5534479955051489 / 20000000000000000 : ℝ) = - (5534479955051489 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5534479955051489 / 5000000000000000 : ℚ)) - (U := (203119387170924871261 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5534479955051489 / 5000000000000000 : ℝ) ≤ - (203119387170924871261 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2763438164332739 / 10000000000000000 : ℝ)) (q := - (5534479955051489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5534479955051489 / 20000000000000000 : ℚ)) + (r' := (5534479955051489 / 5000000000000000 : ℚ)) + (U := (-(2569469334029075128739 / 2000000000000000000000 : ℚ))) + (U' := (203119387170924871261 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (2763438164332739 / 10000000000000000 : ℚ)) + (q := (5534479955051489 / 20000000000000000 : ℚ)) + (U := (-(2569469334029075128739 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_5 : Uω (aρ 5) (bρ 5) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -4010,25 +3600,21 @@ lemma U_327_5 : have hlg : Real.log (1057110374347879 / 4000000000000000 : ℝ) ≤ (-(532302094754197904583 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1057110374347879 / 4000000000000000 : ℝ) = - (1057110374347879 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1057110374347879 / 1000000000000000 : ℚ)) - (U := (22215649485802095417 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1057110374347879 / 1000000000000000 : ℝ) ≤ - (22215649485802095417 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (526540000071129 / 2000000000000000 : ℝ)) (q := - (1057110374347879 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1057110374347879 / 4000000000000000 : ℚ)) + (r' := (1057110374347879 / 1000000000000000 : ℚ)) + (U := (-(532302094754197904583 / 400000000000000000000 : ℚ))) + (U' := (22215649485802095417 / 400000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (526540000071129 / 2000000000000000 : ℚ)) + (q := (1057110374347879 / 4000000000000000 : ℚ)) + (U := (-(532302094754197904583 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_6 : Uω (aρ 6) (bρ 6) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -4036,24 +3622,21 @@ lemma U_327_6 : have hlg : Real.log (30758434858961 / 125000000000000 : ℝ) ≤ (-(3505373688820111534097 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (30758434858961 / 125000000000000 : ℝ) = (30758434858961 / 15625000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30758434858961 / 15625000000000 : ℚ)) - (U := (1693230163429888465903 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (30758434858961 / 15625000000000 : ℝ) ≤ - (1693230163429888465903 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243573808119001 / 1000000000000000 : ℝ)) (q := - (30758434858961 / 125000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30758434858961 / 125000000000000 : ℚ)) + (r' := (30758434858961 / 15625000000000 : ℚ)) + (U := (-(3505373688820111534097 / 2500000000000000000000 : ℚ))) + (U' := (1693230163429888465903 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (243573808119001 / 1000000000000000 : ℚ)) + (q := (30758434858961 / 125000000000000 : ℚ)) + (U := (-(3505373688820111534097 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_7 : Uω (aρ 7) (bρ 7) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -4061,25 +3644,21 @@ lemma U_327_7 : have hlg : Real.log (2203089464428441 / 10000000000000000 : ℝ) ≤ (-(15127244149469302294097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2203089464428441 / 10000000000000000 : ℝ) = - (2203089464428441 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2203089464428441 / 1250000000000000 : ℚ)) - (U := (5667171259530697705903 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2203089464428441 / 1250000000000000 : ℝ) ≤ - (5667171259530697705903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (536057203343283 / 2500000000000000 : ℝ)) (q := - (2203089464428441 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2203089464428441 / 10000000000000000 : ℚ)) + (r' := (2203089464428441 / 1250000000000000 : ℚ)) + (U := (-(15127244149469302294097 / 10000000000000000000000 : ℚ))) + (U' := (5667171259530697705903 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (536057203343283 / 2500000000000000 : ℚ)) + (q := (2203089464428441 / 10000000000000000 : ℚ)) + (U := (-(15127244149469302294097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_8 : Uω (aρ 8) (bρ 8) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -4087,25 +3666,21 @@ lemma U_327_8 : have hlg : Real.log (920714228960997 / 5000000000000000 : ℝ) ≤ (-(52876358936216522127 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (920714228960997 / 5000000000000000 : ℝ) = - (920714228960997 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (920714228960997 / 625000000000000 : ℚ)) - (U := (12106189216908477873 / 31250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (920714228960997 / 625000000000000 : ℝ) ≤ - (12106189216908477873 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (852224225850119 / 5000000000000000 : ℝ)) (q := - (920714228960997 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (920714228960997 / 5000000000000000 : ℚ)) + (r' := (920714228960997 / 625000000000000 : ℚ)) + (U := (-(52876358936216522127 / 31250000000000000000 : ℚ))) + (U' := (12106189216908477873 / 31250000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (852224225850119 / 5000000000000000 : ℚ)) + (q := (920714228960997 / 5000000000000000 : ℚ)) + (U := (-(52876358936216522127 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_9 : Uω (aρ 9) (bρ 9) (2387998646983 / 8000000000000 : ℝ) ≤ @@ -4113,25 +3688,21 @@ lemma U_327_9 : have hlg : Real.log (642513036818419 / 5000000000000000 : ℝ) ≤ (-(4103612166609828334827 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (642513036818419 / 5000000000000000 : ℝ) = - (642513036818419 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (642513036818419 / 625000000000000 : ℚ)) - (U := (55270915190171665173 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (642513036818419 / 625000000000000 : ℝ) ≤ - (55270915190171665173 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (466304655744963 / 5000000000000000 : ℝ)) (q := - (642513036818419 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (642513036818419 / 5000000000000000 : ℚ)) + (r' := (642513036818419 / 625000000000000 : ℚ)) + (U := (-(4103612166609828334827 / 2000000000000000000000 : ℚ))) + (U' := (55270915190171665173 / 2000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2387998646983 / 8000000000000 : ℚ)) + (s := (466304655744963 / 5000000000000000 : ℚ)) + (q := (642513036818419 / 5000000000000000 : ℚ)) + (U := (-(4103612166609828334827 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_327_10 : Uω (aρ 10) (bρ 10) (2387998646983 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U27.lean b/LeanPool/Zeta5Irrational/Table/U27.lean index f19be05673..a6bfb29d9e 100644 --- a/LeanPool/Zeta5Irrational/Table/U27.lean +++ b/LeanPool/Zeta5Irrational/Table/U27.lean @@ -24,25 +24,21 @@ lemma U_328_1 : have hlg : Real.log (46824313018906437 / 160000000000000000 : ℝ) ≤ (-(12287712377373996090711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46824313018906437 / 160000000000000000 : ℝ) = - (46824313018906437 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46824313018906437 / 40000000000000000 : ℚ)) - (U := (1575231228626003909289 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46824313018906437 / 40000000000000000 : ℝ) ≤ - (1575231228626003909289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (731616080327291 / 2500000000000000 : ℝ)) (q := - (46824313018906437 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46824313018906437 / 160000000000000000 : ℚ)) + (r' := (46824313018906437 / 40000000000000000 : ℚ)) + (U := (-(12287712377373996090711 / 10000000000000000000000 : ℚ))) + (U' := (1575231228626003909289 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (731616080327291 / 2500000000000000 : ℚ)) + (q := (46824313018906437 / 160000000000000000 : ℚ)) + (U := (-(12287712377373996090711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_2 : Uω (aρ 2) (bρ 2) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_328_2 : have hlg : Real.log (46439044227816253 / 160000000000000000 : ℝ) ≤ (-(6185166194462050153967 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46439044227816253 / 160000000000000000 : ℝ) = - (46439044227816253 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46439044227816253 / 40000000000000000 : ℚ)) - (U := (746305608537949846033 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46439044227816253 / 40000000000000000 : ℝ) ≤ - (746305608537949846033 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2902074734932891 / 10000000000000000 : ℝ)) (q := - (46439044227816253 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46439044227816253 / 160000000000000000 : ℚ)) + (r' := (46439044227816253 / 40000000000000000 : ℚ)) + (U := (-(6185166194462050153967 / 5000000000000000000000 : ℚ))) + (U' := (746305608537949846033 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (2902074734932891 / 10000000000000000 : ℚ)) + (q := (46439044227816253 / 160000000000000000 : ℚ)) + (U := (-(6185166194462050153967 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_3 : Uω (aρ 3) (bρ 3) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_328_3 : have hlg : Real.log (45665818384651213 / 160000000000000000 : ℝ) ≤ (-(12538237532450347374363 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45665818384651213 / 160000000000000000 : ℝ) = - (45665818384651213 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45665818384651213 / 40000000000000000 : ℚ)) - (U := (1324706073549652625637 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45665818384651213 / 40000000000000000 : ℝ) ≤ - (1324706073549652625637 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2852817610887261 / 10000000000000000 : ℝ)) (q := - (45665818384651213 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45665818384651213 / 160000000000000000 : ℚ)) + (r' := (45665818384651213 / 40000000000000000 : ℚ)) + (U := (-(12538237532450347374363 / 10000000000000000000000 : ℚ))) + (U' := (1324706073549652625637 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (2852817610887261 / 10000000000000000 : ℚ)) + (q := (45665818384651213 / 160000000000000000 : ℚ)) + (U := (-(12538237532450347374363 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_4 : Uω (aρ 4) (bρ 4) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_328_4 : have hlg : Real.log (44373152488460389 / 160000000000000000 : ℝ) ≤ (-(12825392018479425605597 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44373152488460389 / 160000000000000000 : ℝ) = - (44373152488460389 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44373152488460389 / 40000000000000000 : ℚ)) - (U := (1037551587520574394403 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44373152488460389 / 40000000000000000 : ℝ) ≤ - (1037551587520574394403 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (346191069366051 / 1250000000000000 : ℝ)) (q := - (44373152488460389 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44373152488460389 / 160000000000000000 : ℚ)) + (r' := (44373152488460389 / 40000000000000000 : ℚ)) + (U := (-(12825392018479425605597 / 10000000000000000000000 : ℚ))) + (U' := (1037551587520574394403 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (346191069366051 / 1250000000000000 : ℚ)) + (q := (44373152488460389 / 160000000000000000 : ℚ)) + (U := (-(12825392018479425605597 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_5 : Uω (aρ 5) (bρ 5) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_328_5 : have hlg : Real.log (42381965488764117 / 160000000000000000 : ℝ) ≤ (-(6642254426029126533917 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42381965488764117 / 160000000000000000 : ℝ) = - (42381965488764117 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42381965488764117 / 40000000000000000 : ℚ)) - (U := (289217376970873466083 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42381965488764117 / 40000000000000000 : ℝ) ≤ - (289217376970873466083 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1319410049650687 / 5000000000000000 : ℝ)) (q := - (42381965488764117 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42381965488764117 / 160000000000000000 : ℚ)) + (r' := (42381965488764117 / 40000000000000000 : ℚ)) + (U := (-(6642254426029126533917 / 5000000000000000000000 : ℚ))) + (U' := (289217376970873466083 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (1319410049650687 / 5000000000000000 : ℚ)) + (q := (42381965488764117 / 160000000000000000 : ℚ)) + (U := (-(6642254426029126533917 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_6 : Uω (aρ 6) (bρ 6) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_328_6 : have hlg : Real.log (39468968474167621 / 160000000000000000 : ℝ) ≤ (-(13996590595477121154087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (39468968474167621 / 160000000000000000 : ℝ) = - (39468968474167621 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39468968474167621 / 20000000000000000 : ℚ)) - (U := (6797824813522878845913 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39468968474167621 / 20000000000000000 : ℝ) ≤ - (6797824813522878845913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (610483961904203 / 2500000000000000 : ℝ)) (q := - (39468968474167621 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39468968474167621 / 160000000000000000 : ℚ)) + (r' := (39468968474167621 / 20000000000000000 : ℚ)) + (U := (-(13996590595477121154087 / 10000000000000000000000 : ℚ))) + (U' := (6797824813522878845913 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (610483961904203 / 2500000000000000 : ℚ)) + (q := (39468968474167621 / 160000000000000000 : ℚ)) + (U := (-(13996590595477121154087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_7 : Uω (aρ 7) (bρ 7) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_328_7 : have hlg : Real.log (35349270783747821 / 160000000000000000 : ℝ) ≤ (-(7549480253947935622409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35349270783747821 / 160000000000000000 : ℝ) = - (35349270783747821 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35349270783747821 / 20000000000000000 : ℚ)) - (U := (2847727450552064377591 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35349270783747821 / 20000000000000000 : ℝ) ≤ - (2847727450552064377591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2150635017074337 / 10000000000000000 : ℝ)) (q := - (35349270783747821 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35349270783747821 / 160000000000000000 : ℚ)) + (r' := (35349270783747821 / 20000000000000000 : ℚ)) + (U := (-(7549480253947935622409 / 5000000000000000000000 : ℚ))) + (U' := (2847727450552064377591 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (2150635017074337 / 10000000000000000 : ℚ)) + (q := (35349270783747821 / 160000000000000000 : ℚ)) + (U := (-(7549480253947935622409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_8 : Uω (aρ 8) (bρ 8) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_328_8 : have hlg : Real.log (29567814770811661 / 160000000000000000 : ℝ) ≤ (-(16884873835296377582209 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (29567814770811661 / 160000000000000000 : ℝ) = - (29567814770811661 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29567814770811661 / 20000000000000000 : ℚ)) - (U := (3909541573703622417791 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29567814770811661 / 20000000000000000 : ℝ) ≤ - (3909541573703622417791 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1711494666797317 / 10000000000000000 : ℝ)) (q := - (29567814770811661 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29567814770811661 / 160000000000000000 : ℚ)) + (r' := (29567814770811661 / 20000000000000000 : ℚ)) + (U := (-(16884873835296377582209 / 10000000000000000000000 : ℚ))) + (U' := (3909541573703622417791 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (1711494666797317 / 10000000000000000 : ℚ)) + (q := (29567814770811661 / 160000000000000000 : ℚ)) + (U := (-(16884873835296377582209 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_9 : Uω (aρ 9) (bρ 9) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_328_9 : have hlg : Real.log (4138798645103481 / 32000000000000000 : ℝ) ≤ (-(4090660677271729170247 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4138798645103481 / 32000000000000000 : ℝ) = - (4138798645103481 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4138798645103481 / 4000000000000000 : ℚ)) - (U := (68222404528270829753 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4138798645103481 / 4000000000000000 : ℝ) ≤ - (68222404528270829753 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188646520399107 / 2000000000000000 : ℝ)) (q := - (4138798645103481 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4138798645103481 / 32000000000000000 : ℚ)) + (r' := (4138798645103481 / 4000000000000000 : ℚ)) + (U := (-(4090660677271729170247 / 2000000000000000000000 : ℚ))) + (U' := (68222404528270829753 / 2000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38285721908981 / 128000000000000 : ℚ)) + (s := (188646520399107 / 2000000000000000 : ℚ)) + (q := (4138798645103481 / 32000000000000000 : ℚ)) + (U := (-(4090660677271729170247 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_328_10 : Uω (aρ 10) (bρ 10) (38285721908981 / 128000000000000 : ℝ) ≤ @@ -379,25 +343,21 @@ lemma U_329_1 : have hlg : Real.log (23460747148056609 / 80000000000000000 : ℝ) ≤ (-(6133489718462708656097 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23460747148056609 / 80000000000000000 : ℝ) = - (23460747148056609 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23460747148056609 / 20000000000000000 : ℚ)) - (U := (797982084537291343903 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23460747148056609 / 20000000000000000 : ℝ) ≤ - (797982084537291343903 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2932538265549621 / 10000000000000000 : ℝ)) (q := - (23460747148056609 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23460747148056609 / 80000000000000000 : ℚ)) + (r' := (23460747148056609 / 20000000000000000 : ℚ)) + (U := (-(6133489718462708656097 / 5000000000000000000000 : ℚ))) + (U' := (797982084537291343903 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (2932538265549621 / 10000000000000000 : ℚ)) + (q := (23460747148056609 / 80000000000000000 : ℚ)) + (U := (-(6133489718462708656097 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_2 : Uω (aρ 2) (bρ 2) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -405,25 +365,21 @@ lemma U_329_2 : have hlg : Real.log (23268117944500921 / 80000000000000000 : ℝ) ≤ (-(12349425391609171288573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23268117944500921 / 80000000000000000 : ℝ) = - (23268117944500921 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23268117944500921 / 20000000000000000 : ℚ)) - (U := (1513518214390828711427 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23268117944500921 / 20000000000000000 : ℝ) ≤ - (1513518214390828711427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2908149977170699 / 10000000000000000 : ℝ)) (q := - (23268117944500921 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23268117944500921 / 80000000000000000 : ℚ)) + (r' := (23268117944500921 / 20000000000000000 : ℚ)) + (U := (-(12349425391609171288573 / 10000000000000000000000 : ℚ))) + (U' := (1513518214390828711427 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (2908149977170699 / 10000000000000000 : ℚ)) + (q := (23268117944500921 / 80000000000000000 : ℚ)) + (U := (-(12349425391609171288573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_3 : Uω (aρ 3) (bρ 3) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -431,25 +387,21 @@ lemma U_329_3 : have hlg : Real.log (22881520943054829 / 80000000000000000 : ℝ) ≤ (-(6258484975339397372699 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22881520943054829 / 80000000000000000 : ℝ) = - (22881520943054829 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22881520943054829 / 20000000000000000 : ℚ)) - (U := (672986827660602627301 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22881520943054829 / 20000000000000000 : ℝ) ≤ - (672986827660602627301 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (357362104144897 / 1250000000000000 : ℝ)) (q := - (22881520943054829 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22881520943054829 / 80000000000000000 : ℚ)) + (r' := (22881520943054829 / 20000000000000000 : ℚ)) + (U := (-(6258484975339397372699 / 5000000000000000000000 : ℚ))) + (U' := (672986827660602627301 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (357362104144897 / 1250000000000000 : ℚ)) + (q := (22881520943054829 / 80000000000000000 : ℚ)) + (U := (-(6258484975339397372699 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_4 : Uω (aρ 4) (bρ 4) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -457,25 +409,21 @@ lemma U_329_4 : have hlg : Real.log (4447046475187897 / 16000000000000000 : ℝ) ≤ (-(640174279668968429527 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4447046475187897 / 16000000000000000 : ℝ) = - (4447046475187897 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4447046475187897 / 4000000000000000 : ℚ)) - (U := (52972900631031570473 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4447046475187897 / 4000000000000000 : ℝ) ≤ - (52972900631031570473 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138780943622267 / 500000000000000 : ℝ)) (q := - (4447046475187897 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4447046475187897 / 16000000000000000 : ℚ)) + (r' := (4447046475187897 / 4000000000000000 : ℚ)) + (U := (-(640174279668968429527 / 500000000000000000000 : ℚ))) + (U' := (52972900631031570473 / 500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (138780943622267 / 500000000000000 : ℚ)) + (q := (4447046475187897 / 16000000000000000 : ℚ)) + (U := (-(640174279668968429527 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_5 : Uω (aρ 5) (bρ 5) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -483,25 +431,21 @@ lemma U_329_5 : have hlg : Real.log (21239757146449213 / 80000000000000000 : ℝ) ≤ (-(13261518716286128424891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21239757146449213 / 80000000000000000 : ℝ) = - (21239757146449213 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21239757146449213 / 20000000000000000 : ℚ)) - (U := (601424889713871575109 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21239757146449213 / 20000000000000000 : ℝ) ≤ - (601424889713871575109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661234996101943 / 2500000000000000 : ℝ)) (q := - (21239757146449213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21239757146449213 / 80000000000000000 : ℚ)) + (r' := (21239757146449213 / 20000000000000000 : ℚ)) + (U := (-(13261518716286128424891 / 10000000000000000000000 : ℚ))) + (U' := (601424889713871575109 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (661234996101943 / 2500000000000000 : ℚ)) + (q := (21239757146449213 / 80000000000000000 : ℚ)) + (U := (-(13261518716286128424891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_6 : Uω (aρ 6) (bρ 6) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -509,25 +453,21 @@ lemma U_329_6 : have hlg : Real.log (19783567677166397 / 80000000000000000 : ℝ) ≤ (-(13971749560585366629263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19783567677166397 / 80000000000000000 : ℝ) = - (19783567677166397 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19783567677166397 / 10000000000000000 : ℚ)) - (U := (6822665848414633370737 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19783567677166397 / 10000000000000000 : ℝ) ≤ - (6822665848414633370737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (612033248056767 / 2500000000000000 : ℝ)) (q := - (19783567677166397 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19783567677166397 / 80000000000000000 : ℚ)) + (r' := (19783567677166397 / 10000000000000000 : ℚ)) + (U := (-(13971749560585366629263 / 10000000000000000000000 : ℚ))) + (U' := (6822665848414633370737 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (612033248056767 / 2500000000000000 : ℚ)) + (q := (19783567677166397 / 80000000000000000 : ℚ)) + (U := (-(13971749560585366629263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_7 : Uω (aρ 7) (bρ 7) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -535,25 +475,21 @@ lemma U_329_7 : have hlg : Real.log (3544909474730529 / 16000000000000000 : ℝ) ≤ (-(15070760978440686554333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3544909474730529 / 16000000000000000 : ℝ) = - (3544909474730529 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3544909474730529 / 2000000000000000 : ℚ)) - (U := (5723654430559313445667 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3544909474730529 / 2000000000000000 : ℝ) ≤ - (5723654430559313445667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (215703929710863 / 1000000000000000 : ℝ)) (q := - (3544909474730529 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3544909474730529 / 16000000000000000 : ℚ)) + (r' := (3544909474730529 / 2000000000000000 : ℚ)) + (U := (-(15070760978440686554333 / 10000000000000000000000 : ℚ))) + (U' := (5723654430559313445667 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (215703929710863 / 1000000000000000 : ℚ)) + (q := (3544909474730529 / 16000000000000000 : ℚ)) + (U := (-(15070760978440686554333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_8 : Uω (aρ 8) (bρ 8) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -561,25 +497,21 @@ lemma U_329_8 : have hlg : Real.log (14836357409786957 / 80000000000000000 : ℝ) ≤ (-(2106182354807468528861 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14836357409786957 / 80000000000000000 : ℝ) = - (14836357409786957 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14836357409786957 / 10000000000000000 : ℚ)) - (U := (493119571317531471139 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14836357409786957 / 10000000000000000 : ℝ) ≤ - (493119571317531471139 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53704170546319 / 312500000000000 : ℝ)) (q := - (14836357409786957 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14836357409786957 / 80000000000000000 : ℚ)) + (r' := (14836357409786957 / 10000000000000000 : ℚ)) + (U := (-(2106182354807468528861 / 1250000000000000000000 : ℚ))) + (U' := (493119571317531471139 / 1250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (53704170546319 / 312500000000000 : ℚ)) + (q := (14836357409786957 / 80000000000000000 : ℚ)) + (U := (-(2106182354807468528861 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_9 : Uω (aρ 9) (bρ 9) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -587,25 +519,21 @@ lemma U_329_9 : have hlg : Real.log (2082693213296429 / 16000000000000000 : ℝ) ≤ (-(20389268512107521157571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2082693213296429 / 16000000000000000 : ℝ) = - (2082693213296429 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2082693213296429 / 2000000000000000 : ℚ)) - (U := (405146896892478842429 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2082693213296429 / 2000000000000000 : ℝ) ≤ - (405146896892478842429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (190755250003201 / 2000000000000000 : ℝ)) (q := - (2082693213296429 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2082693213296429 / 16000000000000000 : ℚ)) + (r' := (2082693213296429 / 2000000000000000 : ℚ)) + (U := (-(20389268512107521157571 / 10000000000000000000000 : ℚ))) + (U' := (405146896892478842429 / 10000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19181732733117 / 64000000000000 : ℚ)) + (s := (190755250003201 / 2000000000000000 : ℚ)) + (q := (2082693213296429 / 16000000000000000 : ℚ)) + (U := (-(20389268512107521157571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_329_10 : Uω (aρ 10) (bρ 10) (19181732733117 / 64000000000000 : ℝ) ≤ @@ -731,25 +659,21 @@ lemma U_330_1 : have hlg : Real.log (47018675565752471 / 160000000000000000 : ℝ) ≤ (-(61231446973232137127 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47018675565752471 / 160000000000000000 : ℝ) = - (47018675565752471 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47018675565752471 / 40000000000000000 : ℚ)) - (U := (8083271056767862873 / 50000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (47018675565752471 / 40000000000000000 : ℝ) ≤ - (8083271056767862873 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2938612208844137 / 10000000000000000 : ℝ)) (q := - (47018675565752471 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47018675565752471 / 160000000000000000 : ℚ)) + (r' := (47018675565752471 / 40000000000000000 : ℚ)) + (U := (-(61231446973232137127 / 50000000000000000000 : ℚ))) + (U' := (8083271056767862873 / 50000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (2938612208844137 / 10000000000000000 : ℚ)) + (q := (47018675565752471 / 160000000000000000 : ℚ)) + (U := (-(61231446973232137127 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_2 : Uω (aρ 2) (bρ 2) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -757,25 +681,21 @@ lemma U_330_2 : have hlg : Real.log (46633427499266559 / 160000000000000000 : ℝ) ≤ (-(12328562024288774376437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46633427499266559 / 160000000000000000 : ℝ) = - (46633427499266559 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46633427499266559 / 40000000000000000 : ℚ)) - (U := (1534381581711225623563 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46633427499266559 / 40000000000000000 : ℝ) ≤ - (1534381581711225623563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1457112606521699 / 5000000000000000 : ℝ)) (q := - (46633427499266559 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46633427499266559 / 160000000000000000 : ℚ)) + (r' := (46633427499266559 / 40000000000000000 : ℚ)) + (U := (-(12328562024288774376437 / 10000000000000000000000 : ℚ))) + (U' := (1534381581711225623563 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (1457112606521699 / 5000000000000000 : ℚ)) + (q := (46633427499266559 / 160000000000000000 : ℚ)) + (U := (-(12328562024288774376437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_3 : Uω (aρ 3) (bρ 3) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -783,25 +703,21 @@ lemma U_330_3 : have hlg : Real.log (45860265200691719 / 160000000000000000 : ℝ) ≤ (-(3123936886171363010597 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45860265200691719 / 160000000000000000 : ℝ) = - (45860265200691719 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45860265200691719 / 40000000000000000 : ℚ)) - (U := (341799015328636989403 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45860265200691719 / 40000000000000000 : ℝ) ≤ - (341799015328636989403 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2864976032071543 / 10000000000000000 : ℝ)) (q := - (45860265200691719 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45860265200691719 / 160000000000000000 : ℚ)) + (r' := (45860265200691719 / 40000000000000000 : ℚ)) + (U := (-(3123936886171363010597 / 2500000000000000000000 : ℚ))) + (U' := (341799015328636989403 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (2864976032071543 / 10000000000000000 : ℚ)) + (q := (45860265200691719 / 160000000000000000 : ℚ)) + (U := (-(3123936886171363010597 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_4 : Uω (aρ 4) (bρ 4) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -809,25 +725,21 @@ lemma U_330_4 : have hlg : Real.log (44567776434507663 / 160000000000000000 : ℝ) ≤ (-(1278162718286327350039 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44567776434507663 / 160000000000000000 : ℝ) = - (44567776434507663 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44567776434507663 / 40000000000000000 : ℚ)) - (U := (108131642313672649961 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44567776434507663 / 40000000000000000 : ℝ) ≤ - (108131642313672649961 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (173856819835221 / 625000000000000 : ℝ)) (q := - (44567776434507663 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44567776434507663 / 160000000000000000 : ℚ)) + (r' := (44567776434507663 / 40000000000000000 : ℚ)) + (U := (-(1278162718286327350039 / 1000000000000000000000 : ℚ))) + (U' := (108131642313672649961 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (173856819835221 / 625000000000000 : ℚ)) + (q := (44567776434507663 / 160000000000000000 : ℚ)) + (U := (-(1278162718286327350039 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_5 : Uω (aρ 5) (bρ 5) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -835,25 +747,21 @@ lemma U_330_5 : have hlg : Real.log (42577061398165479 / 160000000000000000 : ℝ) ≤ (-(3309645428236645038509 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42577061398165479 / 160000000000000000 : ℝ) = - (42577061398165479 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42577061398165479 / 40000000000000000 : ℚ)) - (U := (156090473263354961491 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42577061398165479 / 40000000000000000 : ℝ) ≤ - (156090473263354961491 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2651059657155763 / 10000000000000000 : ℝ)) (q := - (42577061398165479 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42577061398165479 / 160000000000000000 : ℚ)) + (r' := (42577061398165479 / 40000000000000000 : ℚ)) + (U := (-(3309645428236645038509 / 2500000000000000000000 : ℚ))) + (U' := (156090473263354961491 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (2651059657155763 / 10000000000000000 : ℚ)) + (q := (42577061398165479 / 160000000000000000 : ℚ)) + (U := (-(3309645428236645038509 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_6 : Uω (aρ 6) (bρ 6) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -861,25 +769,21 @@ lemma U_330_6 : have hlg : Real.log (7933059459529491 / 32000000000000000 : ℝ) ≤ (-(2789394265029026856113 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7933059459529491 / 32000000000000000 : ℝ) = - (7933059459529491 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7933059459529491 / 4000000000000000 : ℚ)) - (U := (1369488816770973143887 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7933059459529491 / 4000000000000000 : ℝ) ≤ - (1369488816770973143887 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (245432951973101 / 1000000000000000 : ℝ)) (q := - (7933059459529491 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7933059459529491 / 32000000000000000 : ℚ)) + (r' := (7933059459529491 / 4000000000000000 : ℚ)) + (U := (-(2789394265029026856113 / 2000000000000000000000 : ℚ))) + (U' := (1369488816770973143887 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (245432951973101 / 1000000000000000 : ℚ)) + (q := (7933059459529491 / 32000000000000000 : ℚ)) + (U := (-(2789394265029026856113 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_7 : Uω (aρ 7) (bρ 7) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -887,25 +791,21 @@ lemma U_330_7 : have hlg : Real.log (35548903458195263 / 160000000000000000 : ℝ) ≤ (-(15042645037382581962017 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35548903458195263 / 160000000000000000 : ℝ) = - (35548903458195263 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35548903458195263 / 20000000000000000 : ℚ)) - (U := (5751770371617418037983 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35548903458195263 / 20000000000000000 : ℝ) ≤ - (5751770371617418037983 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1081720835279743 / 5000000000000000 : ℝ)) (q := - (35548903458195263 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35548903458195263 / 160000000000000000 : ℚ)) + (r' := (35548903458195263 / 20000000000000000 : ℚ)) + (U := (-(15042645037382581962017 / 10000000000000000000000 : ℚ))) + (U' := (5751770371617418037983 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (1081720835279743 / 5000000000000000 : ℚ)) + (q := (35548903458195263 / 160000000000000000 : ℚ)) + (U := (-(15042645037382581962017 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_8 : Uω (aρ 8) (bρ 8) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -913,25 +813,21 @@ lemma U_330_8 : have hlg : Real.log (29777556199880767 / 160000000000000000 : ℝ) ≤ (-(67256754094232746029 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (29777556199880767 / 160000000000000000 : ℝ) = - (29777556199880767 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29777556199880767 / 20000000000000000 : ℚ)) - (U := (15920907541767253971 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29777556199880767 / 20000000000000000 : ℝ) ≤ - (15920907541767253971 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (862782457305087 / 5000000000000000 : ℝ)) (q := - (29777556199880767 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29777556199880767 / 160000000000000000 : ℚ)) + (r' := (29777556199880767 / 20000000000000000 : ℚ)) + (U := (-(67256754094232746029 / 40000000000000000000 : ℚ))) + (U' := (15920907541767253971 / 40000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (862782457305087 / 5000000000000000 : ℚ)) + (q := (29777556199880767 / 160000000000000000 : ℚ)) + (U := (-(67256754094232746029 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_9 : Uω (aρ 9) (bρ 9) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -939,25 +835,21 @@ lemma U_330_9 : have hlg : Real.log (4191850960248571 / 32000000000000000 : ℝ) ≤ (-(5081483772522509532501 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4191850960248571 / 32000000000000000 : ℝ) = - (4191850960248571 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4191850960248571 / 4000000000000000 : ℚ)) - (U := (117120079727490467499 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4191850960248571 / 4000000000000000 : ℝ) ≤ - (117120079727490467499 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (192848573628087 / 2000000000000000 : ℝ)) (q := - (4191850960248571 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4191850960248571 / 32000000000000000 : ℚ)) + (r' := (4191850960248571 / 4000000000000000 : ℚ)) + (U := (-(5081483772522509532501 / 2500000000000000000000 : ℚ))) + (U' := (117120079727490467499 / 2500000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38441209023487 / 128000000000000 : ℚ)) + (s := (192848573628087 / 2000000000000000 : ℚ)) + (q := (4191850960248571 / 32000000000000000 : ℚ)) + (U := (-(5081483772522509532501 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_330_10 : Uω (aρ 10) (bρ 10) (38441209023487 / 128000000000000 : ℝ) ≤ @@ -1084,25 +976,21 @@ lemma U_331_1 : have hlg : Real.log (11778964206967761 / 40000000000000000 : ℝ) ≤ (-(6112821036688579436813 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11778964206967761 / 40000000000000000 : ℝ) = - (11778964206967761 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11778964206967761 / 10000000000000000 : ℚ)) - (U := (818650766311420563187 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11778964206967761 / 10000000000000000 : ℝ) ≤ - (818650766311420563187 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (368085768899821 / 1250000000000000 : ℝ)) (q := - (11778964206967761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11778964206967761 / 40000000000000000 : ℚ)) + (r' := (11778964206967761 / 10000000000000000 : ℚ)) + (U := (-(6112821036688579436813 / 5000000000000000000000 : ℚ))) + (U' := (818650766311420563187 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (368085768899821 / 1250000000000000 : ℚ)) + (q := (11778964206967761 / 40000000000000000 : ℚ)) + (U := (-(6112821036688579436813 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_2 : Uω (aρ 2) (bρ 2) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1110,25 +998,21 @@ lemma U_331_2 : have hlg : Real.log (11682654764732049 / 40000000000000000 : ℝ) ≤ (-(12307742105197329123461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11682654764732049 / 40000000000000000 : ℝ) = - (11682654764732049 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11682654764732049 / 10000000000000000 : ℚ)) - (U := (1555201500802670876539 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11682654764732049 / 10000000000000000 : ℝ) ≤ - (1555201500802670876539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (365037555323839 / 1250000000000000 : ℝ)) (q := - (11682654764732049 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11682654764732049 / 40000000000000000 : ℚ)) + (r' := (11682654764732049 / 10000000000000000 : ℚ)) + (U := (-(12307742105197329123461 / 10000000000000000000000 : ℚ))) + (U' := (1555201500802670876539 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (365037555323839 / 1250000000000000 : ℚ)) + (q := (11682654764732049 / 40000000000000000 : ℚ)) + (U := (-(12307742105197329123461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_3 : Uω (aρ 3) (bρ 3) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1136,25 +1020,21 @@ lemma U_331_3 : have hlg : Real.log (11489372082396121 / 40000000000000000 : ℝ) ≤ (-(3118642530695954496121 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11489372082396121 / 40000000000000000 : ℝ) = - (11489372082396121 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11489372082396121 / 10000000000000000 : ℚ)) - (U := (347093370804045503879 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11489372082396121 / 10000000000000000 : ℝ) ≤ - (347093370804045503879 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (717763801943187 / 2500000000000000 : ℝ)) (q := - (11489372082396121 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11489372082396121 / 40000000000000000 : ℚ)) + (r' := (11489372082396121 / 10000000000000000 : ℚ)) + (U := (-(3118642530695954496121 / 2500000000000000000000 : ℚ))) + (U' := (347093370804045503879 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (717763801943187 / 2500000000000000 : ℚ)) + (q := (11489372082396121 / 40000000000000000 : ℚ)) + (U := (-(3118642530695954496121 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_4 : Uω (aρ 4) (bρ 4) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1162,25 +1042,21 @@ lemma U_331_4 : have hlg : Real.log (2233254377007643 / 8000000000000000 : ℝ) ≤ (-(12759816576347544304649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2233254377007643 / 8000000000000000 : ℝ) = - (2233254377007643 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2233254377007643 / 2000000000000000 : ℚ)) - (U := (1103127029652455695351 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2233254377007643 / 2000000000000000 : ℝ) ≤ - (1103127029652455695351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (557559858031759 / 2000000000000000 : ℝ)) (q := - (2233254377007643 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2233254377007643 / 8000000000000000 : ℚ)) + (r' := (2233254377007643 / 2000000000000000 : ℚ)) + (U := (-(12759816576347544304649 / 10000000000000000000000 : ℚ))) + (U' := (1103127029652455695351 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (557559858031759 / 2000000000000000 : ℚ)) + (q := (2233254377007643 / 8000000000000000 : ℚ)) + (U := (-(12759816576347544304649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_5 : Uω (aρ 5) (bρ 5) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1188,25 +1064,21 @@ lemma U_331_5 : have hlg : Real.log (10668651704075777 / 40000000000000000 : ℝ) ≤ (-(2643139519038542533491 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10668651704075777 / 40000000000000000 : ℝ) = - (10668651704075777 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10668651704075777 / 10000000000000000 : ℚ)) - (U := (129449202161457466509 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10668651704075777 / 10000000000000000 : ℝ) ≤ - (129449202161457466509 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83036847469143 / 312500000000000 : ℝ)) (q := - (10668651704075777 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10668651704075777 / 40000000000000000 : ℚ)) + (r' := (10668651704075777 / 10000000000000000 : ℚ)) + (U := (-(2643139519038542533491 / 2000000000000000000000 : ℚ))) + (U' := (129449202161457466509 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (83036847469143 / 312500000000000 : ℚ)) + (q := (10668651704075777 / 40000000000000000 : ℚ)) + (U := (-(2643139519038542533491 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_6 : Uω (aρ 6) (bρ 6) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1214,25 +1086,21 @@ lemma U_331_6 : have hlg : Real.log (9940863585352533 / 40000000000000000 : ℝ) ≤ (-(2784451113250624090057 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9940863585352533 / 40000000000000000 : ℝ) = - (9940863585352533 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9940863585352533 / 5000000000000000 : ℚ)) - (U := (1374431968549375909943 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9940863585352533 / 5000000000000000 : ℝ) ≤ - (1374431968549375909943 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1230262717395477 / 5000000000000000 : ℝ)) (q := - (9940863585352533 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9940863585352533 / 40000000000000000 : ℚ)) + (r' := (9940863585352533 / 5000000000000000 : ℚ)) + (U := (-(2784451113250624090057 / 2000000000000000000000 : ℚ))) + (U' := (1374431968549375909943 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (1230262717395477 / 5000000000000000 : ℚ)) + (q := (9940863585352533 / 40000000000000000 : ℚ)) + (U := (-(2784451113250624090057 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_7 : Uω (aρ 7) (bρ 7) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1240,25 +1108,21 @@ lemma U_331_7 : have hlg : Real.log (356486970514321 / 1600000000000000 : ℝ) ≤ (-(15014612166085188211901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (356486970514321 / 1600000000000000 : ℝ) = - (356486970514321 / 200000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (356486970514321 / 200000000000000 : ℚ)) - (U := (5779803242914811788099 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (356486970514321 / 200000000000000 : ℝ) ≤ - (5779803242914811788099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21698421543037 / 100000000000000 : ℝ)) (q := - (356486970514321 / 1600000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (356486970514321 / 1600000000000000 : ℚ)) + (r' := (356486970514321 / 200000000000000 : ℚ)) + (U := (-(15014612166085188211901 / 10000000000000000000000 : ℚ))) + (U' := (5779803242914811788099 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (21698421543037 / 100000000000000 : ℚ)) + (q := (356486970514321 / 1600000000000000 : ℚ)) + (U := (-(15014612166085188211901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_8 : Uω (aρ 8) (bρ 8) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1266,25 +1130,21 @@ lemma U_331_8 : have hlg : Real.log (7470584906506009 / 40000000000000000 : ℝ) ≤ (-(2097382695647042841857 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7470584906506009 / 40000000000000000 : ℝ) = - (7470584906506009 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7470584906506009 / 5000000000000000 : ℚ)) - (U := (501919230477957158143 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7470584906506009 / 5000000000000000 : ℝ) ≤ - (501919230477957158143 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (433147281866923 / 2500000000000000 : ℝ)) (q := - (7470584906506009 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7470584906506009 / 40000000000000000 : ℚ)) + (r' := (7470584906506009 / 5000000000000000 : ℚ)) + (U := (-(2097382695647042841857 / 1250000000000000000000 : ℚ))) + (U' := (501919230477957158143 / 1250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (433147281866923 / 2500000000000000 : ℚ)) + (q := (7470584906506009 / 40000000000000000 : ℚ)) + (U := (-(2097382695647042841857 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_9 : Uω (aρ 9) (bρ 9) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1292,25 +1152,21 @@ lemma U_331_9 : have hlg : Real.log (5272745270945327 / 40000000000000000 : ℝ) ≤ (-(20263283021367291826911 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5272745270945327 / 40000000000000000 : ℝ) = - (5272745270945327 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5272745270945327 / 5000000000000000 : ℚ)) - (U := (531132387632708173089 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5272745270945327 / 5000000000000000 : ℝ) ≤ - (531132387632708173089 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (974634938047351 / 10000000000000000 : ℝ)) (q := - (5272745270945327 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5272745270945327 / 40000000000000000 : ℚ)) + (r' := (5272745270945327 / 5000000000000000 : ℚ)) + (U := (-(20263283021367291826911 / 10000000000000000000000 : ℚ))) + (U' := (531132387632708173089 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1925947629037 / 6400000000000 : ℚ)) + (s := (974634938047351 / 10000000000000000 : ℚ)) + (q := (5272745270945327 / 40000000000000000 : ℚ)) + (U := (-(20263283021367291826911 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_331_10 : Uω (aρ 10) (bρ 10) (1925947629037 / 6400000000000 : ℝ) ≤ @@ -1437,25 +1293,21 @@ lemma U_332_1 : have hlg : Real.log (4731021932973151 / 16000000000000000 : ℝ) ≤ (-(6092237445347728784389 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4731021932973151 / 16000000000000000 : ℝ) = - (4731021932973151 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4731021932973151 / 4000000000000000 : ℚ)) - (U := (839234357652271215611 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4731021932973151 / 4000000000000000 : ℝ) ≤ - (839234357652271215611 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (591366806622069 / 2000000000000000 : ℝ)) (q := - (4731021932973151 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4731021932973151 / 16000000000000000 : ℚ)) + (r' := (4731021932973151 / 4000000000000000 : ℚ)) + (U := (-(6092237445347728784389 / 5000000000000000000000 : ℚ))) + (U' := (839234357652271215611 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (591366806622069 / 2000000000000000 : ℚ)) + (q := (4731021932973151 / 16000000000000000 : ℚ)) + (U := (-(6092237445347728784389 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_2 : Uω (aρ 2) (bρ 2) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1463,25 +1315,21 @@ lemma U_332_2 : have hlg : Real.log (23462501013850143 / 80000000000000000 : ℝ) ≤ (-(12266231890298508999037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23462501013850143 / 80000000000000000 : ℝ) = - (23462501013850143 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23462501013850143 / 20000000000000000 : ℚ)) - (U := (1596711715701491000963 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23462501013850143 / 20000000000000000 : ℝ) ≤ - (1596711715701491000963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1466225441433221 / 5000000000000000 : ℝ)) (q := - (23462501013850143 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23462501013850143 / 80000000000000000 : ℚ)) + (r' := (23462501013850143 / 20000000000000000 : ℚ)) + (U := (-(12266231890298508999037 / 10000000000000000000000 : ℚ))) + (U' := (1596711715701491000963 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (1466225441433221 / 5000000000000000 : ℚ)) + (q := (23462501013850143 / 80000000000000000 : ℚ)) + (U := (-(12266231890298508999037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_3 : Uω (aρ 3) (bρ 3) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1489,25 +1337,21 @@ lemma U_332_3 : have hlg : Real.log (923038680700007 / 3200000000000000 : ℝ) ≤ (-(6216174735296002445103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (923038680700007 / 3200000000000000 : ℝ) = - (923038680700007 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (923038680700007 / 800000000000000 : ℚ)) - (U := (715297067703997554897 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (923038680700007 / 800000000000000 : ℝ) ≤ - (715297067703997554897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57664269802579 / 200000000000000 : ℝ)) (q := - (923038680700007 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (923038680700007 / 3200000000000000 : ℚ)) + (r' := (923038680700007 / 800000000000000 : ℚ)) + (U := (-(6216174735296002445103 / 5000000000000000000000 : ℚ))) + (U' := (715297067703997554897 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (57664269802579 / 200000000000000 : ℚ)) + (q := (923038680700007 / 3200000000000000 : ℚ)) + (U := (-(6216174735296002445103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_4 : Uω (aρ 4) (bρ 4) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1515,25 +1359,21 @@ lemma U_332_4 : have hlg : Real.log (22429854017776247 / 80000000000000000 : ℝ) ≤ (-(12716337939900776348663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22429854017776247 / 80000000000000000 : ℝ) = - (22429854017776247 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22429854017776247 / 20000000000000000 : ℚ)) - (U := (1146605666099223651337 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22429854017776247 / 20000000000000000 : ℝ) ≤ - (1146605666099223651337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (349997427657871 / 1250000000000000 : ℝ)) (q := - (22429854017776247 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22429854017776247 / 80000000000000000 : ℚ)) + (r' := (22429854017776247 / 20000000000000000 : ℚ)) + (U := (-(12716337939900776348663 / 10000000000000000000000 : ℚ))) + (U' := (1146605666099223651337 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (349997427657871 / 1250000000000000 : ℚ)) + (q := (22429854017776247 / 80000000000000000 : ℚ)) + (U := (-(12716337939900776348663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_5 : Uω (aρ 5) (bρ 5) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1541,25 +1381,21 @@ lemma U_332_5 : have hlg : Real.log (21434846318800643 / 80000000000000000 : ℝ) ≤ (-(3292521759420410891227 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21434846318800643 / 80000000000000000 : ℝ) = - (21434846318800643 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21434846318800643 / 20000000000000000 : ℚ)) - (U := (173214142079589108773 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21434846318800643 / 20000000000000000 : ℝ) ≤ - (173214142079589108773 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2669417415854067 / 10000000000000000 : ℝ)) (q := - (21434846318800643 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21434846318800643 / 80000000000000000 : ℚ)) + (r' := (21434846318800643 / 20000000000000000 : ℚ)) + (U := (-(3292521759420410891227 / 2500000000000000000000 : ℚ))) + (U' := (173214142079589108773 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (2669417415854067 / 10000000000000000 : ℚ)) + (q := (21434846318800643 / 80000000000000000 : ℚ)) + (U := (-(3292521759420410891227 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_6 : Uω (aρ 6) (bρ 6) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1567,25 +1403,21 @@ lemma U_332_6 : have hlg : Real.log (19979876938793223 / 80000000000000000 : ℝ) ≤ (-(6936505099560823511611 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19979876938793223 / 80000000000000000 : ℝ) = - (19979876938793223 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19979876938793223 / 10000000000000000 : ℚ)) - (U := (3460702604939176488389 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (19979876938793223 / 10000000000000000 : ℝ) ≤ - (3460702604939176488389 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (618228861498053 / 2500000000000000 : ℝ)) (q := - (19979876938793223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19979876938793223 / 80000000000000000 : ℚ)) + (r' := (19979876938793223 / 10000000000000000 : ℚ)) + (U := (-(6936505099560823511611 / 5000000000000000000000 : ℚ))) + (U' := (3460702604939176488389 / 5000000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (618228861498053 / 2500000000000000 : ℚ)) + (q := (19979876938793223 / 80000000000000000 : ℚ)) + (U := (-(6936505099560823511611 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_7 : Uω (aρ 7) (bρ 7) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1593,25 +1425,21 @@ lemma U_332_7 : have hlg : Real.log (17924119708444467 / 80000000000000000 : ℝ) ≤ (-(14958793583244939740179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17924119708444467 / 80000000000000000 : ℝ) = - (17924119708444467 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17924119708444467 / 10000000000000000 : ℚ)) - (U := (5835621825755060259821 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17924119708444467 / 10000000000000000 : ℝ) ≤ - (5835621825755060259821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2182637519165023 / 10000000000000000 : ℝ)) (q := - (17924119708444467 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17924119708444467 / 80000000000000000 : ℚ)) + (r' := (17924119708444467 / 10000000000000000 : ℚ)) + (U := (-(14958793583244939740179 / 10000000000000000000000 : ℚ))) + (U' := (5835621825755060259821 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (2182637519165023 / 10000000000000000 : ℚ)) + (q := (17924119708444467 / 80000000000000000 : ℚ)) + (U := (-(14958793583244939740179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_8 : Uω (aρ 8) (bρ 8) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1619,25 +1447,21 @@ lemma U_332_8 : have hlg : Real.log (15045867705964499 / 80000000000000000 : ℝ) ≤ (-(8354616257164736756719 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15045867705964499 / 80000000000000000 : ℝ) = - (15045867705964499 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15045867705964499 / 10000000000000000 : ℚ)) - (U := (2042591447335263243281 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15045867705964499 / 10000000000000000 : ℝ) ≤ - (2042591447335263243281 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1746616169885031 / 10000000000000000 : ℝ)) (q := - (15045867705964499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15045867705964499 / 80000000000000000 : ℚ)) + (r' := (15045867705964499 / 10000000000000000 : ℚ)) + (U := (-(8354616257164736756719 / 5000000000000000000000 : ℚ))) + (U' := (2042591447335263243281 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (1746616169885031 / 10000000000000000 : ℚ)) + (q := (15045867705964499 / 80000000000000000 : ℚ)) + (U := (-(8354616257164736756719 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_9 : Uω (aρ 9) (bρ 9) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1645,25 +1469,21 @@ lemma U_332_9 : have hlg : Real.log (10676359544252443 / 80000000000000000 : ℝ) ≤ (-(5034986812783164747793 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10676359544252443 / 80000000000000000 : ℝ) = - (10676359544252443 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10676359544252443 / 10000000000000000 : ℚ)) - (U := (163617039466835252207 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10676359544252443 / 10000000000000000 : ℝ) ≤ - (163617039466835252207 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (995204757817017 / 10000000000000000 : ℝ)) (q := - (10676359544252443 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10676359544252443 / 80000000000000000 : ℚ)) + (r' := (10676359544252443 / 10000000000000000 : ℚ)) + (U := (-(5034986812783164747793 / 2500000000000000000000 : ℚ))) + (U' := (163617039466835252207 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19337219847623 / 64000000000000 : ℚ)) + (s := (995204757817017 / 10000000000000000 : ℚ)) + (q := (10676359544252443 / 80000000000000000 : ℚ)) + (U := (-(5034986812783164747793 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_332_10 : Uω (aρ 10) (bρ 10) (19337219847623 / 64000000000000 : ℝ) ≤ @@ -1790,25 +1610,21 @@ lemma U_333_1 : have hlg : Real.log (2969036362628849 / 10000000000000000 : ℝ) ≤ (-(2428695298668879795403 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2969036362628849 / 10000000000000000 : ℝ) = - (2969036362628849 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2969036362628849 / 2500000000000000 : ℚ)) - (U := (343893422531120204597 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2969036362628849 / 2500000000000000 : ℝ) ≤ - (343893422531120204597 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2968981911330823 / 10000000000000000 : ℝ)) (q := - (2969036362628849 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2969036362628849 / 10000000000000000 : ℚ)) + (r' := (2969036362628849 / 2500000000000000 : ℚ)) + (U := (-(2428695298668879795403 / 2000000000000000000000 : ℚ))) + (U' := (343893422531120204597 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (2968981911330823 / 10000000000000000 : ℚ)) + (q := (2969036362628849 / 10000000000000000 : ℚ)) + (U := (-(2428695298668879795403 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_2 : Uω (aρ 2) (bρ 2) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1816,25 +1632,21 @@ lemma U_333_2 : have hlg : Real.log (235596923989041 / 800000000000000 : ℝ) ≤ (-(6112446657647581372819 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (235596923989041 / 800000000000000 : ℝ) = - (235596923989041 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (235596923989041 / 200000000000000 : ℚ)) - (U := (819025145352418627181 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (235596923989041 / 200000000000000 : ℝ) ≤ - (819025145352418627181 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58892025966183 / 200000000000000 : ℝ)) (q := - (235596923989041 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (235596923989041 / 800000000000000 : ℚ)) + (r' := (235596923989041 / 200000000000000 : ℚ)) + (U := (-(6112446657647581372819 / 5000000000000000000000 : ℚ))) + (U' := (819025145352418627181 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (58892025966183 / 200000000000000 : ℚ)) + (q := (235596923989041 / 800000000000000 : ℚ)) + (U := (-(6112446657647581372819 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_3 : Uω (aρ 3) (bρ 3) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1842,25 +1654,21 @@ lemma U_333_3 : have hlg : Real.log (5793297376456881 / 20000000000000000 : ℝ) ≤ (-(12390306484797001658741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5793297376456881 / 20000000000000000 : ℝ) = - (5793297376456881 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5793297376456881 / 5000000000000000 : ℚ)) - (U := (1472637121202998341259 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5793297376456881 / 5000000000000000 : ℝ) ≤ - (1472637121202998341259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1447685840695003 / 5000000000000000 : ℝ)) (q := - (5793297376456881 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5793297376456881 / 20000000000000000 : ℚ)) + (r' := (5793297376456881 / 5000000000000000 : ℚ)) + (U := (-(12390306484797001658741 / 10000000000000000000000 : ℚ))) + (U' := (1472637121202998341259 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (1447685840695003 / 5000000000000000 : ℚ)) + (q := (5793297376456881 / 20000000000000000 : ℚ)) + (U := (-(12390306484797001658741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_4 : Uω (aρ 4) (bρ 4) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1868,25 +1676,21 @@ lemma U_333_4 : have hlg : Real.log (351986923967741 / 1250000000000000 : ℝ) ≤ (-(6336524013436370123083 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (351986923967741 / 1250000000000000 : ℝ) = - (351986923967741 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (351986923967741 / 312500000000000 : ℚ)) - (U := (594947789563629876917 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (351986923967741 / 312500000000000 : ℝ) ≤ - (594947789563629876917 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2812159269481981 / 10000000000000000 : ℝ)) (q := - (351986923967741 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (351986923967741 / 1250000000000000 : ℚ)) + (r' := (351986923967741 / 312500000000000 : ℚ)) + (U := (-(6336524013436370123083 / 5000000000000000000000 : ℚ))) + (U' := (594947789563629876917 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (2812159269481981 / 10000000000000000 : ℚ)) + (q := (351986923967741 / 1250000000000000 : ℚ)) + (U := (-(6336524013436370123083 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_5 : Uω (aρ 5) (bρ 5) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1894,25 +1698,21 @@ lemma U_333_5 : have hlg : Real.log (5383096481069049 / 20000000000000000 : ℝ) ≤ (-(13124685103260900577841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5383096481069049 / 20000000000000000 : ℝ) = - (5383096481069049 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5383096481069049 / 5000000000000000 : ℚ)) - (U := (738258502739099422159 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5383096481069049 / 5000000000000000 : ℝ) ≤ - (738258502739099422159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1340827443201087 / 5000000000000000 : ℝ)) (q := - (5383096481069049 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5383096481069049 / 20000000000000000 : ℚ)) + (r' := (5383096481069049 / 5000000000000000 : ℚ)) + (U := (-(13124685103260900577841 / 10000000000000000000000 : ℚ))) + (U' := (738258502739099422159 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (1340827443201087 / 5000000000000000 : ℚ)) + (q := (5383096481069049 / 20000000000000000 : ℚ)) + (U := (-(13124685103260900577841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_6 : Uω (aρ 6) (bρ 6) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1920,25 +1720,21 @@ lemma U_333_6 : have hlg : Real.log (5019504281721021 / 20000000000000000 : ℝ) ≤ (-(1728001366084479726809 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5019504281721021 / 20000000000000000 : ℝ) = - (5019504281721021 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5019504281721021 / 5000000000000000 : ℚ)) - (U := (4866584665520273191 / 1250000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5019504281721021 / 5000000000000000 : ℝ) ≤ - (4866584665520273191 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1242651531097073 / 5000000000000000 : ℝ)) (q := - (5019504281721021 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5019504281721021 / 20000000000000000 : ℚ)) + (r' := (5019504281721021 / 5000000000000000 : ℚ)) + (U := (-(1728001366084479726809 / 1250000000000000000000 : ℚ))) + (U' := (4866584665520273191 / 1250000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (1242651531097073 / 5000000000000000 : ℚ)) + (q := (5019504281721021 / 20000000000000000 : ℚ)) + (U := (-(1728001366084479726809 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_7 : Uω (aρ 7) (bρ 7) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1946,25 +1742,21 @@ lemma U_333_7 : have hlg : Real.log (450596536145979 / 2000000000000000 : ℝ) ≤ (-(7451650589987120200889 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (450596536145979 / 2000000000000000 : ℝ) = - (450596536145979 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (450596536145979 / 250000000000000 : ℚ)) - (U := (2945557114512879799111 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (450596536145979 / 250000000000000 : ℝ) ≤ - (2945557114512879799111 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (439085104538583 / 2000000000000000 : ℝ)) (q := - (450596536145979 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (450596536145979 / 2000000000000000 : ℚ)) + (r' := (450596536145979 / 250000000000000 : ℚ)) + (U := (-(7451650589987120200889 / 5000000000000000000000 : ℚ))) + (U' := (2945557114512879799111 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (439085104538583 / 2000000000000000 : ℚ)) + (q := (450596536145979 / 2000000000000000 : ℚ)) + (U := (-(7451650589987120200889 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_8 : Uω (aρ 8) (bρ 8) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1972,25 +1764,21 @@ lemma U_333_8 : have hlg : Real.log (1893806728199749 / 10000000000000000 : ℝ) ≤ (-(16639961469023081417581 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1893806728199749 / 10000000000000000 : ℝ) = - (1893806728199749 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1893806728199749 / 1250000000000000 : ℚ)) - (U := (4154453939976918582419 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1893806728199749 / 1250000000000000 : ℝ) ≤ - (4154453939976918582419 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1760615268972623 / 10000000000000000 : ℝ)) (q := - (1893806728199749 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1893806728199749 / 10000000000000000 : ℚ)) + (r' := (1893806728199749 / 1250000000000000 : ℚ)) + (U := (-(16639961469023081417581 / 10000000000000000000000 : ℚ))) + (U' := (4154453939976918582419 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (1760615268972623 / 10000000000000000 : ℚ)) + (q := (1893806728199749 / 10000000000000000 : ℚ)) + (U := (-(16639961469023081417581 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_9 : Uω (aρ 9) (bρ 9) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -1998,25 +1786,21 @@ lemma U_333_9 : have hlg : Real.log (168845988894201 / 1250000000000000 : ℝ) ≤ (-(2502389798007060102871 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (168845988894201 / 1250000000000000 : ℝ) = - (168845988894201 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (168845988894201 / 156250000000000 : ℚ)) - (U := (96912128117939897129 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (168845988894201 / 156250000000000 : ℝ) ≤ - (96912128117939897129 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1015503263240341 / 10000000000000000 : ℝ)) (q := - (168845988894201 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (168845988894201 / 1250000000000000 : ℚ)) + (r' := (168845988894201 / 156250000000000 : ℚ)) + (U := (-(2502389798007060102871 / 1250000000000000000000 : ℚ))) + (U' := (96912128117939897129 / 1250000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4853740851219 / 16000000000000 : ℚ)) + (s := (1015503263240341 / 10000000000000000 : ℚ)) + (q := (168845988894201 / 1250000000000000 : ℚ)) + (U := (-(2502389798007060102871 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_333_10 : Uω (aρ 10) (bρ 10) (4853740851219 / 16000000000000 : ℝ) ≤ @@ -2143,25 +1927,21 @@ lemma U_334_1 : have hlg : Real.log (23849472122611141 / 80000000000000000 : ℝ) ≤ (-(12102645502884357136123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23849472122611141 / 80000000000000000 : ℝ) = - (23849472122611141 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23849472122611141 / 20000000000000000 : ℚ)) - (U := (1760298103115642863877 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23849472122611141 / 20000000000000000 : ℝ) ≤ - (1760298103115642863877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2981129785905129 / 10000000000000000 : ℝ)) (q := - (23849472122611141 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23849472122611141 / 80000000000000000 : ℚ)) + (r' := (23849472122611141 / 20000000000000000 : ℚ)) + (U := (-(12102645502884357136123 / 10000000000000000000000 : ℚ))) + (U' := (1760298103115642863877 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (2981129785905129 / 10000000000000000 : ℚ)) + (q := (23849472122611141 / 80000000000000000 : ℚ)) + (U := (-(12102645502884357136123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_2 : Uω (aρ 2) (bρ 2) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2169,25 +1949,21 @@ lemma U_334_2 : have hlg : Real.log (23656883685850549 / 80000000000000000 : ℝ) ≤ (-(6091862483132022743739 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23656883685850549 / 80000000000000000 : ℝ) = - (23656883685850549 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23656883685850549 / 20000000000000000 : ℚ)) - (U := (839609319867977256261 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23656883685850549 / 20000000000000000 : ℝ) ≤ - (839609319867977256261 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2956751689224981 / 10000000000000000 : ℝ)) (q := - (23656883685850549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23656883685850549 / 80000000000000000 : ℚ)) + (r' := (23656883685850549 / 20000000000000000 : ℚ)) + (U := (-(6091862483132022743739 / 5000000000000000000000 : ℚ))) + (U' := (839609319867977256261 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (2956751689224981 / 10000000000000000 : ℚ)) + (q := (23656883685850549 / 80000000000000000 : ℚ)) + (U := (-(6091862483132022743739 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_3 : Uω (aρ 3) (bρ 3) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2195,25 +1971,21 @@ lemma U_334_3 : have hlg : Real.log (23270411634345401 / 80000000000000000 : ℝ) ≤ (-(12348439675099821250339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23270411634345401 / 80000000000000000 : ℝ) = - (23270411634345401 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23270411634345401 / 20000000000000000 : ℚ)) - (U := (1514503930900178749661 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23270411634345401 / 20000000000000000 : ℝ) ≤ - (1514503930900178749661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1453764891349347 / 5000000000000000 : ℝ)) (q := - (23270411634345401 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23270411634345401 / 80000000000000000 : ℚ)) + (r' := (23270411634345401 / 20000000000000000 : ℚ)) + (U := (-(12348439675099821250339 / 10000000000000000000000 : ℚ))) + (U' := (1514503930900178749661 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (1453764891349347 / 5000000000000000 : ℚ)) + (q := (23270411634345401 / 80000000000000000 : ℚ)) + (U := (-(12348439675099821250339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_4 : Uω (aρ 4) (bρ 4) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2221,25 +1993,21 @@ lemma U_334_4 : have hlg : Real.log (22624471133193121 / 80000000000000000 : ℝ) ≤ (-(6314972600848446314769 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22624471133193121 / 80000000000000000 : ℝ) = - (22624471133193121 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22624471133193121 / 20000000000000000 : ℚ)) - (U := (616499202151553685231 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22624471133193121 / 20000000000000000 : ℝ) ≤ - (616499202151553685231 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (353042354809453 / 1250000000000000 : ℝ)) (q := - (22624471133193121 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22624471133193121 / 80000000000000000 : ℚ)) + (r' := (22624471133193121 / 20000000000000000 : ℚ)) + (U := (-(6314972600848446314769 / 5000000000000000000000 : ℚ))) + (U' := (616499202151553685231 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (353042354809453 / 1250000000000000 : ℚ)) + (q := (22624471133193121 / 80000000000000000 : ℚ)) + (U := (-(6314972600848446314769 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_5 : Uω (aρ 5) (bρ 5) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2247,25 +2015,21 @@ lemma U_334_5 : have hlg : Real.log (21629922269621181 / 80000000000000000 : ℝ) ≤ (-(13079489878329665778293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21629922269621181 / 80000000000000000 : ℝ) = - (21629922269621181 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21629922269621181 / 20000000000000000 : ℚ)) - (U := (783453727670334221707 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21629922269621181 / 20000000000000000 : ℝ) ≤ - (783453727670334221707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2693891541917639 / 10000000000000000 : ℝ)) (q := - (21629922269621181 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21629922269621181 / 80000000000000000 : ℚ)) + (r' := (21629922269621181 / 20000000000000000 : ℚ)) + (U := (-(13079489878329665778293 / 10000000000000000000000 : ℚ))) + (U' := (783453727670334221707 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (2693891541917639 / 10000000000000000 : ℚ)) + (q := (21629922269621181 / 80000000000000000 : ℚ)) + (U := (-(13079489878329665778293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_6 : Uω (aρ 6) (bρ 6) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2273,25 +2037,21 @@ lemma U_334_6 : have hlg : Real.log (20176147877517449 / 80000000000000000 : ℝ) ≤ (-(13775255255809352500289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20176147877517449 / 80000000000000000 : ℝ) = - (20176147877517449 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20176147877517449 / 20000000000000000 : ℚ)) - (U := (87688350190647499711 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20176147877517449 / 20000000000000000 : ℝ) ≤ - (87688350190647499711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1248844159515853 / 5000000000000000 : ℝ)) (q := - (20176147877517449 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20176147877517449 / 80000000000000000 : ℚ)) + (r' := (20176147877517449 / 20000000000000000 : ℚ)) + (U := (-(13775255255809352500289 / 10000000000000000000000 : ℚ))) + (U' := (87688350190647499711 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (1248844159515853 / 5000000000000000 : ℚ)) + (q := (20176147877517449 / 80000000000000000 : ℚ)) + (U := (-(13775255255809352500289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_7 : Uω (aρ 7) (bρ 7) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2299,25 +2059,21 @@ lemma U_334_7 : have hlg : Real.log (3624714849893033 / 16000000000000000 : ℝ) ≤ (-(7424065491729029942457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3624714849893033 / 16000000000000000 : ℝ) = - (3624714849893033 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3624714849893033 / 2000000000000000 : ℚ)) - (U := (2973142212770970057543 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3624714849893033 / 2000000000000000 : ℝ) ≤ - (2973142212770970057543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (441641258555727 / 2000000000000000 : ℝ)) (q := - (3624714849893033 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3624714849893033 / 16000000000000000 : ℚ)) + (r' := (3624714849893033 / 2000000000000000 : ℚ)) + (U := (-(7424065491729029942457 / 5000000000000000000000 : ℚ))) + (U' := (2973142212770970057543 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (441641258555727 / 2000000000000000 : ℚ)) + (q := (3624714849893033 / 16000000000000000 : ℚ)) + (U := (-(7424065491729029942457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_8 : Uω (aρ 8) (bρ 8) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2325,25 +2081,21 @@ lemma U_334_8 : have hlg : Real.log (15254930817135281 / 80000000000000000 : ℝ) ≤ (-(16571238508300731484711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15254930817135281 / 80000000000000000 : ℝ) = - (15254930817135281 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15254930817135281 / 10000000000000000 : ℚ)) - (U := (4223176900699268515289 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15254930817135281 / 10000000000000000 : ℝ) ≤ - (4223176900699268515289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (443646771509041 / 2500000000000000 : ℝ)) (q := - (15254930817135281 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15254930817135281 / 80000000000000000 : ℚ)) + (r' := (15254930817135281 / 10000000000000000 : ℚ)) + (U := (-(16571238508300731484711 / 10000000000000000000000 : ℚ))) + (U' := (4223176900699268515289 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (443646771509041 / 2500000000000000 : ℚ)) + (q := (15254930817135281 / 80000000000000000 : ℚ)) + (U := (-(16571238508300731484711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_9 : Uω (aρ 9) (bρ 9) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2351,25 +2103,21 @@ lemma U_334_9 : have hlg : Real.log (10934905596091849 / 80000000000000000 : ℝ) ≤ (-(9950333064951701404441 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10934905596091849 / 80000000000000000 : ℝ) = - (10934905596091849 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10934905596091849 / 10000000000000000 : ℚ)) - (U := (446874639548298595559 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10934905596091849 / 10000000000000000 : ℝ) ≤ - (446874639548298595559 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (517773204567653 / 5000000000000000 : ℝ)) (q := - (10934905596091849 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10934905596091849 / 80000000000000000 : ℚ)) + (r' := (10934905596091849 / 10000000000000000 : ℚ)) + (U := (-(9950333064951701404441 / 5000000000000000000000 : ℚ))) + (U' := (446874639548298595559 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19492706962129 / 64000000000000 : ℚ)) + (s := (517773204567653 / 5000000000000000 : ℚ)) + (q := (10934905596091849 / 80000000000000000 : ℚ)) + (U := (-(9950333064951701404441 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_334_10 : Uω (aρ 10) (bρ 10) (19492706962129 / 64000000000000 : ℝ) ≤ @@ -2497,25 +2245,21 @@ lemma U_335_1 : have hlg : Real.log (2394665332978437 / 8000000000000000 : ℝ) ≤ (-(12061980557693874766859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2394665332978437 / 8000000000000000 : ℝ) = - (2394665332978437 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2394665332978437 / 2000000000000000 : ℚ)) - (U := (1800963048306125233141 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2394665332978437 / 2000000000000000 : ℝ) ≤ - (1800963048306125233141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (598655531375531 / 2000000000000000 : ℝ)) (q := - (2394665332978437 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2394665332978437 / 8000000000000000 : ℚ)) + (r' := (2394665332978437 / 2000000000000000 : ℚ)) + (U := (-(12061980557693874766859 / 10000000000000000000000 : ℚ))) + (U' := (1800963048306125233141 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (598655531375531 / 2000000000000000 : ℚ)) + (q := (2394665332978437 / 8000000000000000 : ℚ)) + (U := (-(12061980557693874766859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_2 : Uω (aρ 2) (bρ 2) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2523,25 +2267,21 @@ lemma U_335_2 : have hlg : Real.log (11877037437947009 / 40000000000000000 : ℝ) ≤ (-(1517840680835718813187 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11877037437947009 / 40000000000000000 : ℝ) = - (11877037437947009 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11877037437947009 / 10000000000000000 : ℚ)) - (U := (215027269914281186813 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11877037437947009 / 10000000000000000 : ℝ) ≤ - (215027269914281186813 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2968902055915067 / 10000000000000000 : ℝ)) (q := - (11877037437947009 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11877037437947009 / 40000000000000000 : ℚ)) + (r' := (11877037437947009 / 10000000000000000 : ℚ)) + (U := (-(1517840680835718813187 / 1250000000000000000000 : ℚ))) + (U' := (215027269914281186813 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (2968902055915067 / 10000000000000000 : ℚ)) + (q := (11877037437947009 / 40000000000000000 : ℚ)) + (U := (-(1517840680835718813187 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_3 : Uω (aρ 3) (bρ 3) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2549,25 +2289,21 @@ lemma U_335_3 : have hlg : Real.log (11683816703774369 / 40000000000000000 : ℝ) ≤ (-(6153373784945376044151 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11683816703774369 / 40000000000000000 : ℝ) = - (11683816703774369 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11683816703774369 / 10000000000000000 : ℚ)) - (U := (778098018054623955849 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11683816703774369 / 10000000000000000 : ℝ) ≤ - (778098018054623955849 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2919687795178747 / 10000000000000000 : ℝ)) (q := - (11683816703774369 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11683816703774369 / 40000000000000000 : ℚ)) + (r' := (11683816703774369 / 10000000000000000 : ℚ)) + (U := (-(6153373784945376044151 / 5000000000000000000000 : ℚ))) + (U' := (778098018054623955849 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (2919687795178747 / 10000000000000000 : ℚ)) + (q := (11683816703774369 / 40000000000000000 : ℚ)) + (U := (-(6153373784945376044151 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_4 : Uω (aρ 4) (bρ 4) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2575,24 +2311,21 @@ lemma U_335_4 : have hlg : Real.log (90887112119747 / 320000000000000 : ℝ) ≤ (-(12587027850031739223471 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (90887112119747 / 320000000000000 : ℝ) = (90887112119747 / 80000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (90887112119747 / 80000000000000 : ℚ)) - (U := (1275915755968260776529 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (90887112119747 / 80000000000000 : ℝ) ≤ - (1275915755968260776529 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11346072527363 / 40000000000000 : ℝ)) (q := - (90887112119747 / 320000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (90887112119747 / 320000000000000 : ℚ)) + (r' := (90887112119747 / 80000000000000 : ℚ)) + (U := (-(12587027850031739223471 / 10000000000000000000000 : ℚ))) + (U' := (1275915755968260776529 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (11346072527363 / 40000000000000 : ℚ)) + (q := (90887112119747 / 320000000000000 : ℚ)) + (U := (-(12587027850031739223471 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_5 : Uω (aρ 5) (bρ 5) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2600,25 +2333,21 @@ lemma U_335_5 : have hlg : Real.log (10863727699530449 / 40000000000000000 : ℝ) ≤ (-(814656217230021947263 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10863727699530449 / 40000000000000000 : ℝ) = - (10863727699530449 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10863727699530449 / 10000000000000000 : ℚ)) - (U := (51777758144978052737 / 625000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10863727699530449 / 10000000000000000 : ℝ) ≤ - (51777758144978052737 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2706127393456787 / 10000000000000000 : ℝ)) (q := - (10863727699530449 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10863727699530449 / 40000000000000000 : ℚ)) + (r' := (10863727699530449 / 10000000000000000 : ℚ)) + (U := (-(814656217230021947263 / 625000000000000000000 : ℚ))) + (U' := (51777758144978052737 / 625000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (2706127393456787 / 10000000000000000 : ℚ)) + (q := (10863727699530449 / 40000000000000000 : ℚ)) + (U := (-(814656217230021947263 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_6 : Uω (aρ 6) (bρ 6) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2626,25 +2355,21 @@ lemma U_335_6 : have hlg : Real.log (10137134665196471 / 40000000000000000 : ℝ) ≤ (-(1372674072760321762727 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10137134665196471 / 40000000000000000 : ℝ) = - (10137134665196471 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10137134665196471 / 10000000000000000 : ℚ)) - (U := (13620287839678237273 / 1000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10137134665196471 / 10000000000000000 : ℝ) ≤ - (13620287839678237273 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1255035625714899 / 5000000000000000 : ℝ)) (q := - (10137134665196471 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10137134665196471 / 40000000000000000 : ℚ)) + (r' := (10137134665196471 / 10000000000000000 : ℚ)) + (U := (-(1372674072760321762727 / 1000000000000000000000 : ℚ))) + (U' := (13620287839678237273 / 1000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (1255035625714899 / 5000000000000000 : ℚ)) + (q := (10137134665196471 / 40000000000000000 : ℚ)) + (U := (-(1372674072760321762727 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_7 : Uω (aρ 7) (bρ 7) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2652,25 +2377,21 @@ lemma U_335_7 : have hlg : Real.log (9111629309413061 / 40000000000000000 : ℝ) ≤ (-(7396639548000137332547 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9111629309413061 / 40000000000000000 : ℝ) = - (9111629309413061 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9111629309413061 / 5000000000000000 : ℚ)) - (U := (3000568156499862667453 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9111629309413061 / 5000000000000000 : ℝ) ≤ - (3000568156499862667453 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2220979954298093 / 10000000000000000 : ℝ)) (q := - (9111629309413061 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9111629309413061 / 40000000000000000 : ℚ)) + (r' := (9111629309413061 / 5000000000000000 : ℚ)) + (U := (-(7396639548000137332547 / 5000000000000000000000 : ℚ))) + (U' := (3000568156499862667453 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (2220979954298093 / 10000000000000000 : ℚ)) + (q := (9111629309413061 / 40000000000000000 : ℚ)) + (U := (-(7396639548000137332547 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_8 : Uω (aρ 8) (bρ 8) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2678,25 +2399,21 @@ lemma U_335_8 : have hlg : Real.log (7679650619033413 / 40000000000000000 : ℝ) ≤ (-(1031440874701677454237 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7679650619033413 / 40000000000000000 : ℝ) = - (7679650619033413 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7679650619033413 / 5000000000000000 : ℚ)) - (U := (268210088360822545763 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7679650619033413 / 5000000000000000 : ℝ) ≤ - (268210088360822545763 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1788532260448269 / 10000000000000000 : ℝ)) (q := - (7679650619033413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7679650619033413 / 40000000000000000 : ℚ)) + (r' := (7679650619033413 / 5000000000000000 : ℚ)) + (U := (-(1031440874701677454237 / 625000000000000000000 : ℚ))) + (U' := (268210088360822545763 / 625000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (1788532260448269 / 10000000000000000 : ℚ)) + (q := (7679650619033413 / 40000000000000000 : ℚ)) + (U := (-(1031440874701677454237 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_9 : Uω (aρ 9) (bρ 9) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2704,25 +2421,21 @@ lemma U_335_9 : have hlg : Real.log (5531352331295859 / 40000000000000000 : ℝ) ≤ (-(19784471231578686300367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5531352331295859 / 40000000000000000 : ℝ) = - (5531352331295859 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5531352331295859 / 5000000000000000 : ℚ)) - (U := (1009944177421313699633 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5531352331295859 / 5000000000000000 : ℝ) ≤ - (1009944177421313699633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263837186234873 / 2500000000000000 : ℝ)) (q := - (5531352331295859 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5531352331295859 / 40000000000000000 : ℚ)) + (r' := (5531352331295859 / 5000000000000000 : ℚ)) + (U := (-(19784471231578686300367 / 10000000000000000000000 : ℚ))) + (U' := (1009944177421313699633 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9785225259691 / 32000000000000 : ℚ)) + (s := (263837186234873 / 2500000000000000 : ℚ)) + (q := (5531352331295859 / 40000000000000000 : ℚ)) + (U := (-(19784471231578686300367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_335_10 : Uω (aρ 10) (bρ 10) (9785225259691 / 32000000000000 : ℝ) ≤ @@ -2849,25 +2562,21 @@ lemma U_336_1 : have hlg : Real.log (24043834522725183 / 80000000000000000 : ℝ) ≤ (-(12021480312697159223583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24043834522725183 / 80000000000000000 : ℝ) = - (24043834522725183 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24043834522725183 / 20000000000000000 : ℚ)) - (U := (1841463293302840776417 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24043834522725183 / 20000000000000000 : ℝ) ≤ - (1841463293302840776417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3005425524292077 / 10000000000000000 : ℝ)) (q := - (24043834522725183 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24043834522725183 / 80000000000000000 : ℚ)) + (r' := (24043834522725183 / 20000000000000000 : ℚ)) + (U := (-(12021480312697159223583 / 10000000000000000000000 : ℚ))) + (U' := (1841463293302840776417 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (3005425524292077 / 10000000000000000 : ℚ)) + (q := (24043834522725183 / 80000000000000000 : ℚ)) + (U := (-(12021480312697159223583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_2 : Uω (aρ 2) (bρ 2) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -2875,25 +2584,21 @@ lemma U_336_2 : have hlg : Real.log (23851265970219407 / 80000000000000000 : ℝ) ≤ (-(3025473344290043015187 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23851265970219407 / 80000000000000000 : ℝ) = - (23851265970219407 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23851265970219407 / 20000000000000000 : ℚ)) - (U := (440262557209956984813 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23851265970219407 / 20000000000000000 : ℝ) ≤ - (440262557209956984813 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2981052398675633 / 10000000000000000 : ℝ)) (q := - (23851265970219407 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23851265970219407 / 80000000000000000 : ℚ)) + (r' := (23851265970219407 / 20000000000000000 : ℚ)) + (U := (-(3025473344290043015187 / 2500000000000000000000 : ℚ))) + (U' := (440262557209956984813 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (2981052398675633 / 10000000000000000 : ℚ)) + (q := (23851265970219407 / 80000000000000000 : ℚ)) + (U := (-(3025473344290043015187 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_3 : Uω (aρ 3) (bρ 3) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -2901,25 +2606,21 @@ lemma U_336_3 : have hlg : Real.log (23464854829857871 / 80000000000000000 : ℝ) ≤ (-(3066307178984472565569 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23464854829857871 / 80000000000000000 : ℝ) = - (23464854829857871 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23464854829857871 / 20000000000000000 : ℚ)) - (U := (399428722515527434431 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23464854829857871 / 20000000000000000 : ℝ) ≤ - (399428722515527434431 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2931845719935249 / 10000000000000000 : ℝ)) (q := - (23464854829857871 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23464854829857871 / 80000000000000000 : ℚ)) + (r' := (23464854829857871 / 20000000000000000 : ℚ)) + (U := (-(3066307178984472565569 / 2500000000000000000000 : ℚ))) + (U' := (399428722515527434431 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (2931845719935249 / 10000000000000000 : ℚ)) + (q := (23464854829857871 / 80000000000000000 : ℚ)) + (U := (-(3066307178984472565569 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_4 : Uω (aρ 4) (bρ 4) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -2927,25 +2628,21 @@ lemma U_336_4 : have hlg : Real.log (22819083838307347 / 80000000000000000 : ℝ) ≤ (-(12544294378394242768849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22819083838307347 / 80000000000000000 : ℝ) = - (22819083838307347 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22819083838307347 / 20000000000000000 : ℚ)) - (U := (1318649227605757231151 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22819083838307347 / 20000000000000000 : ℝ) ≤ - (1318649227605757231151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1424348576556309 / 5000000000000000 : ℝ)) (q := - (22819083838307347 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22819083838307347 / 80000000000000000 : ℚ)) + (r' := (22819083838307347 / 20000000000000000 : ℚ)) + (U := (-(12544294378394242768849 / 10000000000000000000000 : ℚ))) + (U' := (1318649227605757231151 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (1424348576556309 / 5000000000000000 : ℚ)) + (q := (22819083838307347 / 80000000000000000 : ℚ)) + (U := (-(12544294378394242768849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_5 : Uω (aρ 5) (bρ 5) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -2953,25 +2650,21 @@ lemma U_336_5 : have hlg : Real.log (21824985356021499 / 80000000000000000 : ℝ) ≤ (-(2597942406802438394041 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21824985356021499 / 80000000000000000 : ℝ) = - (21824985356021499 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21824985356021499 / 20000000000000000 : ℚ)) - (U := (174646314397561605959 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21824985356021499 / 20000000000000000 : ℝ) ≤ - (174646314397561605959 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (679590612969039 / 2500000000000000 : ℝ)) (q := - (21824985356021499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21824985356021499 / 80000000000000000 : ℚ)) + (r' := (21824985356021499 / 20000000000000000 : ℚ)) + (U := (-(2597942406802438394041 / 2000000000000000000000 : ℚ))) + (U' := (174646314397561605959 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (679590612969039 / 2500000000000000 : ℚ)) + (q := (21824985356021499 / 80000000000000000 : ℚ)) + (U := (-(2597942406802438394041 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_6 : Uω (aρ 6) (bρ 6) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -2979,25 +2672,21 @@ lemma U_336_6 : have hlg : Real.log (20372381622441031 / 80000000000000000 : ℝ) ≤ (-(6839232463065716702293 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20372381622441031 / 80000000000000000 : ℝ) = - (20372381622441031 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20372381622441031 / 20000000000000000 : ℚ)) - (U := (92239339934283297707 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20372381622441031 / 20000000000000000 : ℝ) ≤ - (92239339934283297707 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2522451893621039 / 10000000000000000 : ℝ)) (q := - (20372381622441031 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20372381622441031 / 80000000000000000 : ℚ)) + (r' := (20372381622441031 / 20000000000000000 : ℚ)) + (U := (-(6839232463065716702293 / 5000000000000000000000 : ℚ))) + (U' := (92239339934283297707 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (2522451893621039 / 10000000000000000 : ℚ)) + (q := (20372381622441031 / 80000000000000000 : ℚ)) + (U := (-(6839232463065716702293 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_7 : Uω (aρ 7) (bρ 7) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -3005,25 +2694,21 @@ lemma U_336_7 : have hlg : Real.log (18322915041725367 / 80000000000000000 : ℝ) ≤ (-(7369370846539389318947 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18322915041725367 / 80000000000000000 : ℝ) = - (18322915041725367 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18322915041725367 / 10000000000000000 : ℚ)) - (U := (3027836857960610681053 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18322915041725367 / 10000000000000000 : ℝ) ≤ - (3027836857960610681053 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2233746629202123 / 10000000000000000 : ℝ)) (q := - (18322915041725367 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18322915041725367 / 80000000000000000 : ℚ)) + (r' := (18322915041725367 / 10000000000000000 : ℚ)) + (U := (-(7369370846539389318947 / 5000000000000000000000 : ℚ))) + (U' := (3027836857960610681053 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (2233746629202123 / 10000000000000000 : ℚ)) + (q := (18322915041725367 / 80000000000000000 : ℚ)) + (U := (-(7369370846539389318947 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_8 : Uω (aρ 8) (bρ 8) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -3031,25 +2716,21 @@ lemma U_336_8 : have hlg : Real.log (15463567561933823 / 80000000000000000 : ℝ) ≤ (-(16435398565581580107231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15463567561933823 / 80000000000000000 : ℝ) = - (15463567561933823 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15463567561933823 / 10000000000000000 : ℚ)) - (U := (4359016843418419892769 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15463567561933823 / 10000000000000000 : ℝ) ≤ - (4359016843418419892769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1802451410594237 / 10000000000000000 : ℝ)) (q := - (15463567561933823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15463567561933823 / 80000000000000000 : ℚ)) + (r' := (15463567561933823 / 10000000000000000 : ℚ)) + (U := (-(16435398565581580107231 / 10000000000000000000000 : ℚ))) + (U' := (4359016843418419892769 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (1802451410594237 / 10000000000000000 : ℚ)) + (q := (15463567561933823 / 80000000000000000 : ℚ)) + (U := (-(16435398565581580107231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_9 : Uω (aρ 9) (bρ 9) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -3057,25 +2738,21 @@ lemma U_336_9 : have hlg : Real.log (2237918744750327 / 16000000000000000 : ℝ) ≤ (-(19670424193114000292823 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2237918744750327 / 16000000000000000 : ℝ) = - (2237918744750327 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2237918744750327 / 2000000000000000 : ℚ)) - (U := (1123991215885999707177 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2237918744750327 / 2000000000000000 : ℝ) ≤ - (1123991215885999707177 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (107492357940869 / 1000000000000000 : ℝ)) (q := - (2237918744750327 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2237918744750327 / 16000000000000000 : ℚ)) + (r' := (2237918744750327 / 2000000000000000 : ℚ)) + (U := (-(19670424193114000292823 / 10000000000000000000000 : ℚ))) + (U' := (1123991215885999707177 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (3929638815327 / 12800000000000 : ℚ)) + (s := (107492357940869 / 1000000000000000 : ℚ)) + (q := (2237918744750327 / 16000000000000000 : ℚ)) + (U := (-(19670424193114000292823 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_336_10 : Uω (aρ 10) (bρ 10) (3929638815327 / 12800000000000 : ℝ) ≤ @@ -3203,25 +2880,21 @@ lemma U_337_1 : have hlg : Real.log (1508813481350341 / 5000000000000000 : ℝ) ≤ (-(11981143439097091459783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1508813481350341 / 5000000000000000 : ℝ) = - (1508813481350341 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1508813481350341 / 1250000000000000 : ℚ)) - (U := (1881800166902908540217 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1508813481350341 / 1250000000000000 : ℝ) ≤ - (1881800166902908540217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (754393347047841 / 2500000000000000 : ℝ)) (q := - (1508813481350341 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1508813481350341 / 5000000000000000 : ℚ)) + (r' := (1508813481350341 / 1250000000000000 : ℚ)) + (U := (-(11981143439097091459783 / 10000000000000000000000 : ℚ))) + (U' := (1881800166902908540217 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (754393347047841 / 2500000000000000 : ℚ)) + (q := (1508813481350341 / 5000000000000000 : ℚ)) + (U := (-(11981143439097091459783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_2 : Uω (aρ 2) (bρ 2) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3229,25 +2902,21 @@ lemma U_337_2 : have hlg : Real.log (748389280312261 / 2500000000000000 : ℝ) ≤ (-(12061227395127781664123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (748389280312261 / 2500000000000000 : ℝ) = - (748389280312261 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (748389280312261 / 625000000000000 : ℚ)) - (U := (1801716210872218335877 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (748389280312261 / 625000000000000 : ℝ) ≤ - (1801716210872218335877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (374150339724761 / 1250000000000000 : ℝ)) (q := - (748389280312261 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (748389280312261 / 2500000000000000 : ℚ)) + (r' := (748389280312261 / 625000000000000 : ℚ)) + (U := (-(12061227395127781664123 / 10000000000000000000000 : ℚ))) + (U' := (1801716210872218335877 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (374150339724761 / 1250000000000000 : ℚ)) + (q := (748389280312261 / 2500000000000000 : ℚ)) + (U := (-(12061227395127781664123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_3 : Uω (aρ 3) (bρ 3) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3255,25 +2924,21 @@ lemma U_337_3 : have hlg : Real.log (5890518976405023 / 20000000000000000 : ℝ) ≤ (-(12223881678082135699073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5890518976405023 / 20000000000000000 : ℝ) = - (5890518976405023 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5890518976405023 / 5000000000000000 : ℚ)) - (U := (1639061927917864300927 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5890518976405023 / 5000000000000000 : ℝ) ≤ - (1639061927917864300927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2944003558055023 / 10000000000000000 : ℝ)) (q := - (5890518976405023 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5890518976405023 / 20000000000000000 : ℚ)) + (r' := (5890518976405023 / 5000000000000000 : ℚ)) + (U := (-(12223881678082135699073 / 10000000000000000000000 : ℚ))) + (U' := (1639061927917864300927 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (2944003558055023 / 10000000000000000 : ℚ)) + (q := (5890518976405023 / 20000000000000000 : ℚ)) + (U := (-(12223881678082135699073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_4 : Uω (aρ 4) (bρ 4) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3281,25 +2946,21 @@ lemma U_337_4 : have hlg : Real.log (5729097143051207 / 20000000000000000 : ℝ) ≤ (-(3125435803450280365889 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5729097143051207 / 20000000000000000 : ℝ) = - (5729097143051207 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5729097143051207 / 5000000000000000 : ℚ)) - (U := (340300098049719634111 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5729097143051207 / 5000000000000000 : ℝ) ≤ - (340300098049719634111 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2860875905766207 / 10000000000000000 : ℝ)) (q := - (5729097143051207 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5729097143051207 / 20000000000000000 : ℚ)) + (r' := (5729097143051207 / 5000000000000000 : ℚ)) + (U := (-(3125435803450280365889 / 2500000000000000000000 : ℚ))) + (U' := (340300098049719634111 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (2860875905766207 / 10000000000000000 : ℚ)) + (q := (5729097143051207 / 20000000000000000 : ℚ)) + (U := (-(3125435803450280365889 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_5 : Uω (aρ 5) (bρ 5) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3307,25 +2968,21 @@ lemma U_337_5 : have hlg : Real.log (1096125609157401 / 4000000000000000 : ℝ) ≤ (-(2589025143491211693361 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1096125609157401 / 4000000000000000 : ℝ) = - (1096125609157401 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1096125609157401 / 1000000000000000 : ℚ)) - (U := (183563577708788306639 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1096125609157401 / 1000000000000000 : ℝ) ≤ - (183563577708788306639 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (546119345567401 / 2000000000000000 : ℝ)) (q := - (1096125609157401 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1096125609157401 / 4000000000000000 : ℚ)) + (r' := (1096125609157401 / 1000000000000000 : ℚ)) + (U := (-(2589025143491211693361 / 2000000000000000000000 : ℚ))) + (U' := (183563577708788306639 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (546119345567401 / 2000000000000000 : ℚ)) + (q := (1096125609157401 / 4000000000000000 : ℚ)) + (U := (-(2589025143491211693361 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_6 : Uω (aρ 6) (bρ 6) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3333,25 +2990,21 @@ lemma U_337_6 : have hlg : Real.log (255881061098649 / 1000000000000000 : ℝ) ≤ (-(13630425470284692729279 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (255881061098649 / 1000000000000000 : ℝ) = - (255881061098649 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (255881061098649 / 250000000000000 : ℚ)) - (U := (232518135715307270721 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (255881061098649 / 250000000000000 : ℝ) ≤ - (232518135715307270721 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (126741513958149 / 500000000000000 : ℝ)) (q := - (255881061098649 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (255881061098649 / 1000000000000000 : ℚ)) + (r' := (255881061098649 / 250000000000000 : ℚ)) + (U := (-(13630425470284692729279 / 10000000000000000000000 : ℚ))) + (U' := (232518135715307270721 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (126741513958149 / 500000000000000 : ℚ)) + (q := (255881061098649 / 1000000000000000 : ℚ)) + (U := (-(13630425470284692729279 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_7 : Uω (aρ 7) (bρ 7) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3359,25 +3012,21 @@ lemma U_337_7 : have hlg : Real.log (4605635998653471 / 20000000000000000 : ℝ) ≤ (-(14684515021464761878583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4605635998653471 / 20000000000000000 : ℝ) = - (4605635998653471 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4605635998653471 / 2500000000000000 : ℚ)) - (U := (6109900387535238121417 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4605635998653471 / 2500000000000000 : ℝ) ≤ - (6109900387535238121417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2246506436603471 / 10000000000000000 : ℝ)) (q := - (4605635998653471 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4605635998653471 / 20000000000000000 : ℚ)) + (r' := (4605635998653471 / 2500000000000000 : ℚ)) + (U := (-(14684515021464761878583 / 10000000000000000000000 : ℚ))) + (U' := (6109900387535238121417 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (2246506436603471 / 10000000000000000 : ℚ)) + (q := (4605635998653471 / 20000000000000000 : ℚ)) + (U := (-(14684515021464761878583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_8 : Uω (aρ 8) (bρ 8) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3385,25 +3034,21 @@ lemma U_337_8 : have hlg : Real.log (3891933045477401 / 20000000000000000 : ℝ) ≤ (-(4092065779282799140011 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3891933045477401 / 20000000000000000 : ℝ) = - (3891933045477401 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3891933045477401 / 2500000000000000 : ℚ)) - (U := (1106538072967200859989 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3891933045477401 / 2500000000000000 : ℝ) ≤ - (1106538072967200859989 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1816345134767401 / 10000000000000000 : ℝ)) (q := - (3891933045477401 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3891933045477401 / 20000000000000000 : ℚ)) + (r' := (3891933045477401 / 2500000000000000 : ℚ)) + (U := (-(4092065779282799140011 / 2500000000000000000000 : ℚ))) + (U' := (1106538072967200859989 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (1816345134767401 / 10000000000000000 : ℚ)) + (q := (3891933045477401 / 20000000000000000 : ℚ)) + (U := (-(4092065779282799140011 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_9 : Uω (aρ 9) (bρ 9) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3411,25 +3056,21 @@ lemma U_337_9 : have hlg : Real.log (2828905403778503 / 20000000000000000 : ℝ) ≤ (-(9779212095280143712081 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2828905403778503 / 20000000000000000 : ℝ) = - (2828905403778503 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2828905403778503 / 2500000000000000 : ℚ)) - (U := (617995609219856287919 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2828905403778503 / 2500000000000000 : ℝ) ≤ - (617995609219856287919 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1094283121428503 / 10000000000000000 : ℝ)) (q := - (2828905403778503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2828905403778503 / 20000000000000000 : ℚ)) + (r' := (2828905403778503 / 2500000000000000 : ℚ)) + (U := (-(9779212095280143712081 / 5000000000000000000000 : ℚ))) + (U' := (617995609219856287919 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (616435551059 / 2000000000000 : ℚ)) + (s := (1094283121428503 / 10000000000000000 : ℚ)) + (q := (2828905403778503 / 20000000000000000 : ℚ)) + (U := (-(9779212095280143712081 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_337_10 : Uω (aρ 10) (bρ 10) (616435551059 / 2000000000000 : ℝ) ≤ @@ -3557,25 +3198,21 @@ lemma U_338_1 : have hlg : Real.log (24238196866594329 / 80000000000000000 : ℝ) ≤ (-(46644408687943654039 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24238196866594329 / 80000000000000000 : ℝ) = - (24238196866594329 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24238196866594329 / 20000000000000000 : ℚ)) - (U := (7507714772993845961 / 39062500000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24238196866594329 / 20000000000000000 : ℝ) ≤ - (7507714772993845961 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3029721248617801 / 10000000000000000 : ℝ)) (q := - (24238196866594329 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24238196866594329 / 80000000000000000 : ℚ)) + (r' := (24238196866594329 / 20000000000000000 : ℚ)) + (U := (-(46644408687943654039 / 39062500000000000000 : ℚ))) + (U' := (7507714772993845961 / 39062500000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (3029721248617801 / 10000000000000000 : ℚ)) + (q := (24238196866594329 / 80000000000000000 : ℚ)) + (U := (-(46644408687943654039 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_2 : Uω (aρ 2) (bρ 2) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3583,25 +3220,21 @@ lemma U_338_2 : have hlg : Real.log (24045647876359661 / 80000000000000000 : ℝ) ≤ (-(12020726154596521413683 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24045647876359661 / 80000000000000000 : ℝ) = - (24045647876359661 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24045647876359661 / 20000000000000000 : ℚ)) - (U := (1842217451403478586317 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24045647876359661 / 20000000000000000 : ℝ) ≤ - (1842217451403478586317 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1502676506784567 / 5000000000000000 : ℝ)) (q := - (24045647876359661 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24045647876359661 / 80000000000000000 : ℚ)) + (r' := (24045647876359661 / 20000000000000000 : ℚ)) + (U := (-(12020726154596521413683 / 10000000000000000000000 : ℚ))) + (U' := (1842217451403478586317 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (1502676506784567 / 5000000000000000 : ℚ)) + (q := (24045647876359661 / 80000000000000000 : ℚ)) + (U := (-(12020726154596521413683 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_3 : Uω (aρ 3) (bρ 3) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3609,25 +3242,21 @@ lemma U_338_3 : have hlg : Real.log (4731859327822229 / 16000000000000000 : ℝ) ≤ (-(2436541007787700471499 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4731859327822229 / 16000000000000000 : ℝ) = - (4731859327822229 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4731859327822229 / 4000000000000000 : ℚ)) - (U := (336047713412299528501 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4731859327822229 / 4000000000000000 : ℝ) ≤ - (336047713412299528501 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (591232262121401 / 2000000000000000 : ℝ)) (q := - (4731859327822229 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4731859327822229 / 16000000000000000 : ℚ)) + (r' := (4731859327822229 / 4000000000000000 : ℚ)) + (U := (-(2436541007787700471499 / 2000000000000000000000 : ℚ))) + (U' := (336047713412299528501 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (591232262121401 / 2000000000000000 : ℚ)) + (q := (4731859327822229 / 16000000000000000 : ℚ)) + (U := (-(2436541007787700471499 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_4 : Uω (aρ 4) (bρ 4) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3635,25 +3264,21 @@ lemma U_338_4 : have hlg : Real.log (23013692245293137 / 80000000000000000 : ℝ) ≤ (-(6229686401708916302631 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23013692245293137 / 80000000000000000 : ℝ) = - (23013692245293137 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23013692245293137 / 20000000000000000 : ℚ)) - (U := (701785401291083697369 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23013692245293137 / 20000000000000000 : ℝ) ≤ - (701785401291083697369 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2873054393217503 / 10000000000000000 : ℝ)) (q := - (23013692245293137 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23013692245293137 / 80000000000000000 : ℚ)) + (r' := (23013692245293137 / 20000000000000000 : ℚ)) + (U := (-(6229686401708916302631 / 5000000000000000000000 : ℚ))) + (U' := (701785401291083697369 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (2873054393217503 / 10000000000000000 : ℚ)) + (q := (23013692245293137 / 80000000000000000 : ℚ)) + (U := (-(6229686401708916302631 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_5 : Uω (aρ 5) (bρ 5) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3661,25 +3286,21 @@ lemma U_338_5 : have hlg : Real.log (22020035922321933 / 80000000000000000 : ℝ) ≤ (-(12900738715110178474141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22020035922321933 / 80000000000000000 : ℝ) = - (22020035922321933 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22020035922321933 / 20000000000000000 : ℚ)) - (U := (962204890889821525859 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22020035922321933 / 20000000000000000 : ℝ) ≤ - (962204890889821525859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1371415115904851 / 5000000000000000 : ℝ)) (q := - (22020035922321933 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22020035922321933 / 80000000000000000 : ℚ)) + (r' := (22020035922321933 / 20000000000000000 : ℚ)) + (U := (-(12900738715110178474141 / 10000000000000000000000 : ℚ))) + (U' := (962204890889821525859 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (1371415115904851 / 5000000000000000 : ℚ)) + (q := (22020035922321933 / 80000000000000000 : ℚ)) + (U := (-(12900738715110178474141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_6 : Uω (aρ 6) (bρ 6) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3687,25 +3308,21 @@ lemma U_338_6 : have hlg : Real.log (20568579258342361 / 80000000000000000 : ℝ) ≤ (-(2716524003002969505043 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20568579258342361 / 80000000000000000 : ℝ) = - (20568579258342361 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20568579258342361 / 20000000000000000 : ℚ)) - (U := (56064718197030494957 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20568579258342361 / 20000000000000000 : ℝ) ≤ - (56064718197030494957 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2547206440954809 / 10000000000000000 : ℝ)) (q := - (20568579258342361 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20568579258342361 / 80000000000000000 : ℚ)) + (r' := (20568579258342361 / 20000000000000000 : ℚ)) + (U := (-(2716524003002969505043 / 2000000000000000000000 : ℚ))) + (U' := (56064718197030494957 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (2547206440954809 / 10000000000000000 : ℚ)) + (q := (20568579258342361 / 80000000000000000 : ℚ)) + (U := (-(2716524003002969505043 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_7 : Uω (aρ 7) (bρ 7) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3713,25 +3330,21 @@ lemma U_338_7 : have hlg : Real.log (18522145942925669 / 80000000000000000 : ℝ) ≤ (-(14630595397403589959339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18522145942925669 / 80000000000000000 : ℝ) = - (18522145942925669 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18522145942925669 / 10000000000000000 : ℚ)) - (U := (6163820011596410040661 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18522145942925669 / 10000000000000000 : ℝ) ≤ - (6163820011596410040661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (564814873215159 / 2500000000000000 : ℝ)) (q := - (18522145942925669 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18522145942925669 / 80000000000000000 : ℚ)) + (r' := (18522145942925669 / 10000000000000000 : ℚ)) + (U := (-(14630595397403589959339 / 10000000000000000000000 : ℚ))) + (U' := (6163820011596410040661 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (564814873215159 / 2500000000000000 : ℚ)) + (q := (18522145942925669 / 80000000000000000 : ℚ)) + (U := (-(14630595397403589959339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_8 : Uω (aρ 8) (bρ 8) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3739,25 +3352,21 @@ lemma U_338_8 : have hlg : Real.log (15671797414192209 / 80000000000000000 : ℝ) ≤ (-(16301638799438157530459 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15671797414192209 / 80000000000000000 : ℝ) = - (15671797414192209 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15671797414192209 / 10000000000000000 : ℚ)) - (U := (4492776609561842469541 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15671797414192209 / 10000000000000000 : ℝ) ≤ - (4492776609561842469541 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1830214012017271 / 10000000000000000 : ℝ)) (q := - (15671797414192209 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15671797414192209 / 80000000000000000 : ℚ)) + (r' := (15671797414192209 / 10000000000000000 : ℚ)) + (U := (-(16301638799438157530459 / 10000000000000000000000 : ℚ))) + (U' := (4492776609561842469541 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (1830214012017271 / 10000000000000000 : ℚ)) + (q := (15671797414192209 / 80000000000000000 : ℚ)) + (U := (-(16301638799438157530459 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_9 : Uω (aρ 9) (bρ 9) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3765,25 +3374,21 @@ lemma U_338_9 : have hlg : Real.log (11440833256812601 / 80000000000000000 : ℝ) ≤ (-(9724189067304602339073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11440833256812601 / 80000000000000000 : ℝ) = - (11440833256812601 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11440833256812601 / 10000000000000000 : ℚ)) - (U := (673018637195397660927 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11440833256812601 / 10000000000000000 : ℝ) ≤ - (673018637195397660927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1113438601032369 / 10000000000000000 : ℝ)) (q := - (11440833256812601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11440833256812601 / 80000000000000000 : ℚ)) + (r' := (11440833256812601 / 10000000000000000 : ℚ)) + (U := (-(9724189067304602339073 / 5000000000000000000000 : ℚ))) + (U' := (673018637195397660927 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19803681191141 / 64000000000000 : ℚ)) + (s := (1113438601032369 / 10000000000000000 : ℚ)) + (q := (11440833256812601 / 80000000000000000 : ℚ)) + (U := (-(9724189067304602339073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_338_10 : Uω (aρ 10) (bρ 10) (19803681191141 / 64000000000000 : ℝ) ≤ @@ -3910,25 +3515,21 @@ lemma U_339_1 : have hlg : Real.log (2433537801785823 / 8000000000000000 : ℝ) ≤ (-(5950477285363575388391 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2433537801785823 / 8000000000000000 : ℝ) = - (2433537801785823 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2433537801785823 / 2000000000000000 : ℚ)) - (U := (980994517636424611609 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2433537801785823 / 2000000000000000 : ℝ) ≤ - (980994517636424611609 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (608373821122599 / 2000000000000000 : ℝ)) (q := - (2433537801785823 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2433537801785823 / 8000000000000000 : ℚ)) + (r' := (2433537801785823 / 2000000000000000 : ℚ)) + (U := (-(5950477285363575388391 / 5000000000000000000000 : ℚ))) + (U' := (980994517636424611609 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (608373821122599 / 2000000000000000 : ℚ)) + (q := (2433537801785823 / 8000000000000000 : ℚ)) + (U := (-(5950477285363575388391 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_2 : Uω (aρ 2) (bρ 2) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -3936,25 +3537,21 @@ lemma U_339_2 : have hlg : Real.log (482856773808993 / 1600000000000000 : ℝ) ≤ (-(5990194162937124877343 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (482856773808993 / 1600000000000000 : ℝ) = - (482856773808993 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (482856773808993 / 400000000000000 : ℚ)) - (U := (941277640062875122657 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (482856773808993 / 400000000000000 : ℝ) ≤ - (941277640062875122657 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (60350065725417 / 200000000000000 : ℝ)) (q := - (482856773808993 / 1600000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (482856773808993 / 1600000000000000 : ℚ)) + (r' := (482856773808993 / 400000000000000 : ℚ)) + (U := (-(5990194162937124877343 / 5000000000000000000000 : ℚ))) + (U' := (941277640062875122657 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (60350065725417 / 200000000000000 : ℚ)) + (q := (482856773808993 / 1600000000000000 : ℚ)) + (U := (-(5990194162937124877343 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_3 : Uω (aρ 3) (bρ 3) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -3962,25 +3559,21 @@ lemma U_339_3 : have hlg : Real.log (2375651703453669 / 8000000000000000 : ℝ) ≤ (-(6070848699301788378207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2375651703453669 / 8000000000000000 : ℝ) = - (2375651703453669 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2375651703453669 / 2000000000000000 : ℚ)) - (U := (860623103698211621793 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2375651703453669 / 2000000000000000 : ℝ) ≤ - (860623103698211621793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (296831897864261 / 1000000000000000 : ℝ)) (q := - (2375651703453669 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2375651703453669 / 8000000000000000 : ℚ)) + (r' := (2375651703453669 / 2000000000000000 : ℚ)) + (U := (-(6070848699301788378207 / 5000000000000000000000 : ℚ))) + (U' := (860623103698211621793 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (296831897864261 / 1000000000000000 : ℚ)) + (q := (2375651703453669 / 8000000000000000 : ℚ)) + (U := (-(6070848699301788378207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_4 : Uω (aρ 4) (bρ 4) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -3988,25 +3581,21 @@ lemma U_339_4 : have hlg : Real.log (11555497435502603 / 40000000000000000 : ℝ) ≤ (-(1552147701776885039179 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11555497435502603 / 40000000000000000 : ℝ) = - (11555497435502603 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11555497435502603 / 10000000000000000 : ℚ)) - (U := (180720248973114960821 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11555497435502603 / 10000000000000000 : ℝ) ≤ - (180720248973114960821 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2885232618824739 / 10000000000000000 : ℝ)) (q := - (11555497435502603 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11555497435502603 / 40000000000000000 : ℚ)) + (r' := (11555497435502603 / 10000000000000000 : ℚ)) + (U := (-(1552147701776885039179 / 1250000000000000000000 : ℚ))) + (U' := (180720248973114960821 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (2885232618824739 / 10000000000000000 : ℚ)) + (q := (11555497435502603 / 40000000000000000 : ℚ)) + (U := (-(1552147701776885039179 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_5 : Uω (aρ 5) (bρ 5) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -4014,25 +3603,21 @@ lemma U_339_5 : have hlg : Real.log (2211755661467821 / 8000000000000000 : ℝ) ≤ (-(6428274620293240149007 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2211755661467821 / 8000000000000000 : ℝ) = - (2211755661467821 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2211755661467821 / 2000000000000000 : ℚ)) - (U := (503197182706759850993 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2211755661467821 / 2000000000000000 : ℝ) ≤ - (503197182706759850993 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (275506297407799 / 1000000000000000 : ℝ)) (q := - (2211755661467821 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2211755661467821 / 8000000000000000 : ℚ)) + (r' := (2211755661467821 / 2000000000000000 : ℚ)) + (U := (-(6428274620293240149007 / 5000000000000000000000 : ℚ))) + (U' := (503197182706759850993 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (275506297407799 / 1000000000000000 : ℚ)) + (q := (2211755661467821 / 8000000000000000 : ℚ)) + (U := (-(6428274620293240149007 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_6 : Uω (aρ 6) (bρ 6) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -4040,25 +3625,21 @@ lemma U_339_6 : have hlg : Real.log (10333332431410249 / 40000000000000000 : ℝ) ≤ (-(13535046250598920676661 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10333332431410249 / 40000000000000000 : ℝ) = - (10333332431410249 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10333332431410249 / 10000000000000000 : ℚ)) - (U := (327897355401079323339 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10333332431410249 / 10000000000000000 : ℝ) ≤ - (327897355401079323339 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1279790205626781 / 5000000000000000 : ℝ)) (q := - (10333332431410249 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10333332431410249 / 40000000000000000 : ℚ)) + (r' := (10333332431410249 / 10000000000000000 : ℚ)) + (U := (-(13535046250598920676661 / 10000000000000000000000 : ℚ))) + (U' := (327897355401079323339 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (1279790205626781 / 5000000000000000 : ℚ)) + (q := (10333332431410249 / 40000000000000000 : ℚ)) + (U := (-(13535046250598920676661 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_7 : Uω (aρ 7) (bρ 7) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -4066,25 +3647,21 @@ lemma U_339_7 : have hlg : Real.log (1862172134140103 / 8000000000000000 : ℝ) ≤ (-(91106120030342734303 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1862172134140103 / 8000000000000000 : ℝ) = - (1862172134140103 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1862172134140103 / 1000000000000000 : ℚ)) - (U := (38858976275907265697 / 62500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1862172134140103 / 1000000000000000 : ℝ) ≤ - (38858976275907265697 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (454401182331739 / 2000000000000000 : ℝ)) (q := - (1862172134140103 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1862172134140103 / 8000000000000000 : ℚ)) + (r' := (1862172134140103 / 1000000000000000 : ℚ)) + (U := (-(91106120030342734303 / 62500000000000000000 : ℚ))) + (U' := (38858976275907265697 / 62500000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (454401182331739 / 2000000000000000 : ℚ)) + (q := (1862172134140103 / 8000000000000000 : ℚ)) + (U := (-(91106120030342734303 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_8 : Uω (aρ 8) (bρ 8) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -4092,25 +3669,21 @@ lemma U_339_8 : have hlg : Real.log (7887882750610003 / 40000000000000000 : ℝ) ≤ (-(16235517004178202317679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7887882750610003 / 40000000000000000 : ℝ) = - (7887882750610003 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7887882750610003 / 5000000000000000 : ℚ)) - (U := (4558898404821797682321 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7887882750610003 / 5000000000000000 : ℝ) ≤ - (4558898404821797682321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1844058602953439 / 10000000000000000 : ℝ)) (q := - (7887882750610003 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7887882750610003 / 40000000000000000 : ℚ)) + (r' := (7887882750610003 / 5000000000000000 : ℚ)) + (U := (-(16235517004178202317679 / 10000000000000000000000 : ℚ))) + (U' := (4558898404821797682321 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (1844058602953439 / 10000000000000000 : ℚ)) + (q := (7887882750610003 / 40000000000000000 : ℚ)) + (U := (-(16235517004178202317679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_9 : Uω (aρ 9) (bρ 9) (9940712374197 / 32000000000000 : ℝ) ≤ @@ -4118,25 +3691,21 @@ lemma U_339_9 : have hlg : Real.log (5782635035815587 / 40000000000000000 : ℝ) ≤ (-(19340199859860171901071 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5782635035815587 / 40000000000000000 : ℝ) = - (5782635035815587 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5782635035815587 / 5000000000000000 : ℚ)) - (U := (1454215549139828098929 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5782635035815587 / 5000000000000000 : ℝ) ≤ - (1454215549139828098929 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1132400373916231 / 10000000000000000 : ℝ)) (q := - (5782635035815587 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5782635035815587 / 40000000000000000 : ℚ)) + (r' := (5782635035815587 / 5000000000000000 : ℚ)) + (U := (-(19340199859860171901071 / 10000000000000000000000 : ℚ))) + (U' := (1454215549139828098929 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9940712374197 / 32000000000000 : ℚ)) + (s := (1132400373916231 / 10000000000000000 : ℚ)) + (q := (5782635035815587 / 40000000000000000 : ℚ)) + (U := (-(19340199859860171901071 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_339_10 : Uω (aρ 10) (bρ 10) (9940712374197 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U28.lean b/LeanPool/Zeta5Irrational/Table/U28.lean index 9ecd7a0688..6f5606eb74 100644 --- a/LeanPool/Zeta5Irrational/Table/U28.lean +++ b/LeanPool/Zeta5Irrational/Table/U28.lean @@ -24,25 +24,21 @@ lemma U_340_1 : have hlg : Real.log (3066217534982953 / 10000000000000000 : ℝ) ≤ (-(369418863686504577121 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3066217534982953 / 10000000000000000 : ℝ) = - (3066217534982953 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3066217534982953 / 2500000000000000 : ℚ)) - (U := (63798124000995422879 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3066217534982953 / 2500000000000000 : ℝ) ≤ - (63798124000995422879 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3066164809472781 / 10000000000000000 : ℝ)) (q := - (3066217534982953 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3066217534982953 / 10000000000000000 : ℚ)) + (r' := (3066217534982953 / 2500000000000000 : ℚ)) + (U := (-(369418863686504577121 / 312500000000000000000 : ℚ))) + (U' := (63798124000995422879 / 312500000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (200369118629 / 640000000000 : ℚ)) + (s := (3066164809472781 / 10000000000000000 : ℚ)) + (q := (3066217534982953 / 10000000000000000 : ℚ)) + (U := (-(369418863686504577121 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_2 : Uω (aρ 2) (bρ 2) (200369118629 / 640000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_340_2 : have hlg : Real.log (6084305011555203 / 20000000000000000 : ℝ) ≤ (-(5950098832509869832131 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6084305011555203 / 20000000000000000 : ℝ) = - (6084305011555203 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6084305011555203 / 5000000000000000 : ℚ)) - (U := (981372970490130167869 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6084305011555203 / 5000000000000000 : ℝ) ≤ - (981372970490130167869 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1520901881786039 / 5000000000000000 : ℝ)) (q := - (6084305011555203 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6084305011555203 / 20000000000000000 : ℚ)) + (r' := (6084305011555203 / 5000000000000000 : ℚ)) + (U := (-(5950098832509869832131 / 5000000000000000000000 : ℚ))) + (U' := (981372970490130167869 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (200369118629 / 640000000000 : ℚ)) + (s := (1520901881786039 / 5000000000000000 : ℚ)) + (q := (6084305011555203 / 20000000000000000 : ℚ)) + (U := (-(5950098832509869832131 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_3 : Uω (aρ 3) (bρ 3) (200369118629 / 640000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_340_3 : have hlg : Real.log (5987739206918011 / 20000000000000000 : ℝ) ≤ (-(1507522950055079918221 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5987739206918011 / 20000000000000000 : ℝ) = - (5987739206918011 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5987739206918011 / 5000000000000000 : ℚ)) - (U := (225345000694920081779 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5987739206918011 / 5000000000000000 : ℝ) ≤ - (225345000694920081779 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1496317032642443 / 5000000000000000 : ℝ)) (q := - (5987739206918011 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5987739206918011 / 20000000000000000 : ℚ)) + (r' := (5987739206918011 / 5000000000000000 : ℚ)) + (U := (-(1507522950055079918221 / 1250000000000000000000 : ℚ))) + (U' := (225345000694920081779 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (200369118629 / 640000000000 : ℚ)) + (s := (1496317032642443 / 5000000000000000 : ℚ)) + (q := (5987739206918011 / 20000000000000000 : ℚ)) + (U := (-(1507522950055079918221 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_4 : Uω (aρ 4) (bρ 4) (200369118629 / 640000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_340_4 : have hlg : Real.log (2913199629113311 / 10000000000000000 : ℝ) ≤ (-(616666543212505308213 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2913199629113311 / 10000000000000000 : ℝ) = - (2913199629113311 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2913199629113311 / 2500000000000000 : ℚ)) - (U := (76480637087494691787 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2913199629113311 / 2500000000000000 : ℝ) ≤ - (76480637087494691787 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2909588297658497 / 10000000000000000 : ℝ)) (q := - (2913199629113311 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2913199629113311 / 10000000000000000 : ℚ)) + (r' := (2913199629113311 / 2500000000000000 : ℚ)) + (U := (-(616666543212505308213 / 500000000000000000000 : ℚ))) + (U' := (76480637087494691787 / 500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (200369118629 / 640000000000 : ℚ)) + (s := (2909588297658497 / 10000000000000000 : ℚ)) + (q := (2913199629113311 / 10000000000000000 : ℚ)) + (U := (-(616666543212505308213 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_5 : Uω (aρ 5) (bρ 5) (200369118629 / 640000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_340_5 : have hlg : Real.log (697268406870141 / 2500000000000000 : ℝ) ≤ (-(3192188962342959562939 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (697268406870141 / 2500000000000000 : ℝ) = - (697268406870141 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (697268406870141 / 625000000000000 : ℚ)) - (U := (273546939157040437061 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (697268406870141 / 625000000000000 : ℝ) ≤ - (273546939157040437061 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2779526213728003 / 10000000000000000 : ℝ)) (q := - (697268406870141 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (697268406870141 / 2500000000000000 : ℚ)) + (r' := (697268406870141 / 625000000000000 : ℚ)) + (U := (-(3192188962342959562939 / 2500000000000000000000 : ℚ))) + (U' := (273546939157040437061 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (200369118629 / 640000000000 : ℚ)) + (s := (2779526213728003 / 10000000000000000 : ℚ)) + (q := (697268406870141 / 2500000000000000 : ℚ)) + (U := (-(3192188962342959562939 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_6 : Uω (aρ 6) (bρ 6) (200369118629 / 640000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_340_6 : have hlg : Real.log (1303925642344057 / 5000000000000000 : ℝ) ≤ (-(13440584727778944987359 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1303925642344057 / 5000000000000000 : ℝ) = - (1303925642344057 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1303925642344057 / 1250000000000000 : ℚ)) - (U := (422358878221055012641 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1303925642344057 / 1250000000000000 : ℝ) ≤ - (422358878221055012641 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2584321903283103 / 10000000000000000 : ℝ)) (q := - (1303925642344057 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1303925642344057 / 5000000000000000 : ℚ)) + (r' := (1303925642344057 / 1250000000000000 : ℚ)) + (U := (-(13440584727778944987359 / 10000000000000000000000 : ℚ))) + (U' := (422358878221055012641 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (200369118629 / 640000000000 : ℚ)) + (s := (2584321903283103 / 10000000000000000 : ℚ)) + (q := (1303925642344057 / 5000000000000000 : ℚ)) + (U := (-(13440584727778944987359 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_7 : Uω (aρ 7) (bρ 7) (200369118629 / 640000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_340_7 : have hlg : Real.log (4705198564048747 / 20000000000000000 : ℝ) ≤ (-(7235321489269726734981 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4705198564048747 / 20000000000000000 : ℝ) = - (4705198564048747 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4705198564048747 / 2500000000000000 : ℚ)) - (U := (3161886215230273265019 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4705198564048747 / 2500000000000000 : ℝ) ≤ - (3161886215230273265019 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1148739639357811 / 5000000000000000 : ℝ)) (q := - (4705198564048747 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4705198564048747 / 20000000000000000 : ℚ)) + (r' := (4705198564048747 / 2500000000000000 : ℚ)) + (U := (-(7235321489269726734981 / 5000000000000000000000 : ℚ))) + (U' := (3161886215230273265019 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (200369118629 / 640000000000 : ℚ)) + (s := (1148739639357811 / 5000000000000000 : ℚ)) + (q := (4705198564048747 / 20000000000000000 : ℚ)) + (U := (-(7235321489269726734981 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_8 : Uω (aρ 8) (bρ 8) (200369118629 / 640000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_340_8 : have hlg : Real.log (1997927357326081 / 10000000000000000 : ℝ) ≤ (-(8052373851717295670201 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1997927357326081 / 10000000000000000 : ℝ) = - (1997927357326081 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1997927357326081 / 1250000000000000 : ℚ)) - (U := (2344833852782704329799 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1997927357326081 / 1250000000000000 : ℝ) ≤ - (2344833852782704329799 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1871677080659037 / 10000000000000000 : ℝ)) (q := - (1997927357326081 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1997927357326081 / 10000000000000000 : ℚ)) + (r' := (1997927357326081 / 1250000000000000 : ℚ)) + (U := (-(8052373851717295670201 / 5000000000000000000000 : ℚ))) + (U' := (2344833852782704329799 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (200369118629 / 640000000000 : ℚ)) + (s := (1871677080659037 / 10000000000000000 : ℚ)) + (q := (1997927357326081 / 10000000000000000 : ℚ)) + (U := (-(8052373851717295670201 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_9 : Uω (aρ 9) (bρ 9) (200369118629 / 640000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_340_9 : have hlg : Real.log (738248097158353 / 5000000000000000 : ℝ) ≤ (-(19129132475187687634013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (738248097158353 / 5000000000000000 : ℝ) = - (738248097158353 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (738248097158353 / 625000000000000 : ℚ)) - (U := (1665282933812312365987 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (738248097158353 / 625000000000000 : ℝ) ≤ - (1665282933812312365987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1169780383000287 / 10000000000000000 : ℝ)) (q := - (738248097158353 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (738248097158353 / 5000000000000000 : ℚ)) + (r' := (738248097158353 / 625000000000000 : ℚ)) + (U := (-(19129132475187687634013 / 10000000000000000000000 : ℚ))) + (U' := (1665282933812312365987 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (200369118629 / 640000000000 : ℚ)) + (s := (1169780383000287 / 10000000000000000 : ℚ)) + (q := (738248097158353 / 5000000000000000 : ℚ)) + (U := (-(19129132475187687634013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_340_10 : Uω (aρ 10) (bρ 10) (200369118629 / 640000000000 : ℝ) ≤ @@ -376,25 +340,21 @@ lemma U_341_1 : have hlg : Real.log (12362051244450521 / 40000000000000000 : ℝ) ≤ (-(11742480570451772639849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12362051244450521 / 40000000000000000 : ℝ) = - (12362051244450521 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12362051244450521 / 10000000000000000 : ℚ)) - (U := (2120463035548227360151 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12362051244450521 / 10000000000000000 : ℝ) ≤ - (2120463035548227360151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3090460500090573 / 10000000000000000 : ℝ)) (q := - (12362051244450521 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12362051244450521 / 40000000000000000 : ℚ)) + (r' := (12362051244450521 / 10000000000000000 : ℚ)) + (U := (-(11742480570451772639849 / 10000000000000000000000 : ℚ))) + (U' := (2120463035548227360151 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (3090460500090573 / 10000000000000000 : ℚ)) + (q := (12362051244450521 / 40000000000000000 : ℚ)) + (U := (-(11742480570451772639849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_2 : Uω (aρ 2) (bρ 2) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -402,25 +362,21 @@ lemma U_341_2 : have hlg : Real.log (12265800522988413 / 40000000000000000 : ℝ) ≤ (-(11820645091192290518187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12265800522988413 / 40000000000000000 : ℝ) = - (12265800522988413 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12265800522988413 / 10000000000000000 : ℚ)) - (U := (2042298514807709481813 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12265800522988413 / 10000000000000000 : ℝ) ≤ - (2042298514807709481813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3066104151869519 / 10000000000000000 : ℝ)) (q := - (12265800522988413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12265800522988413 / 40000000000000000 : ℚ)) + (r' := (12265800522988413 / 10000000000000000 : ℚ)) + (U := (-(11820645091192290518187 / 10000000000000000000000 : ℚ))) + (U' := (2042298514807709481813 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (3066104151869519 / 10000000000000000 : ℚ)) + (q := (12265800522988413 / 40000000000000000 : ℚ)) + (U := (-(11820645091192290518187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_3 : Uω (aρ 3) (bρ 3) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -428,25 +384,21 @@ lemma U_341_3 : have hlg : Real.log (12072697658661663 / 40000000000000000 : ℝ) ≤ (-(11979329423253933029181 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12072697658661663 / 40000000000000000 : ℝ) = - (12072697658661663 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12072697658661663 / 10000000000000000 : ℚ)) - (U := (1883614182746066970819 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12072697658661663 / 10000000000000000 : ℝ) ≤ - (1883614182746066970819 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188559301628509 / 625000000000000 : ℝ)) (q := - (12072697658661663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12072697658661663 / 40000000000000000 : ℚ)) + (r' := (12072697658661663 / 10000000000000000 : ℚ)) + (U := (-(11979329423253933029181 / 10000000000000000000000 : ℚ))) + (U' := (1883614182746066970819 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (188559301628509 / 625000000000000 : ℚ)) + (q := (12072697658661663 / 40000000000000000 : ℚ)) + (U := (-(11979329423253933029181 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_4 : Uω (aρ 4) (bρ 4) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -454,25 +406,21 @@ lemma U_341_4 : have hlg : Real.log (11750097580467091 / 40000000000000000 : ℝ) ≤ (-(12250179083177582271047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11750097580467091 / 40000000000000000 : ℝ) = - (11750097580467091 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11750097580467091 / 10000000000000000 : ℚ)) - (U := (1612764522822417728953 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11750097580467091 / 10000000000000000 : ℝ) ≤ - (1612764522822417728953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1466971484011929 / 5000000000000000 : ℝ)) (q := - (11750097580467091 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11750097580467091 / 40000000000000000 : ℚ)) + (r' := (11750097580467091 / 10000000000000000 : ℚ)) + (U := (-(12250179083177582271047 / 10000000000000000000000 : ℚ))) + (U' := (1612764522822417728953 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (1466971484011929 / 5000000000000000 : ℚ)) + (q := (11750097580467091 / 40000000000000000 : ℚ)) + (U := (-(12250179083177582271047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_5 : Uω (aρ 5) (bρ 5) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -480,25 +428,21 @@ lemma U_341_5 : have hlg : Real.log (450152194268343 / 1600000000000000 : ℝ) ≤ (-(2536346345276691305741 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (450152194268343 / 1600000000000000 : ℝ) = - (450152194268343 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (450152194268343 / 400000000000000 : ℚ)) - (U := (236242375923308694259 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (450152194268343 / 400000000000000 : ℝ) ≤ - (236242375923308694259 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7009966313699 / 25000000000000 : ℝ)) (q := - (450152194268343 / 1600000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (450152194268343 / 1600000000000000 : ℚ)) + (r' := (450152194268343 / 400000000000000 : ℚ)) + (U := (-(2536346345276691305741 / 2000000000000000000000 : ℚ))) + (U' := (236242375923308694259 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (7009966313699 / 25000000000000 : ℚ)) + (q := (450152194268343 / 1600000000000000 : ℚ)) + (U := (-(2536346345276691305741 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_6 : Uω (aρ 6) (bρ 6) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -506,25 +450,21 @@ lemma U_341_6 : have hlg : Real.log (10529461057571289 / 40000000000000000 : ℝ) ≤ (-(13347023103751467493021 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10529461057571289 / 40000000000000000 : ℝ) = - (10529461057571289 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10529461057571289 / 10000000000000000 : ℚ)) - (U := (515920502248532506979 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10529461057571289 / 10000000000000000 : ℝ) ≤ - (515920502248532506979 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2609055001050957 / 10000000000000000 : ℝ)) (q := - (10529461057571289 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10529461057571289 / 40000000000000000 : ℚ)) + (r' := (10529461057571289 / 10000000000000000 : ℚ)) + (U := (-(13347023103751467493021 / 10000000000000000000000 : ℚ))) + (U' := (515920502248532506979 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (2609055001050957 / 10000000000000000 : ℚ)) + (q := (10529461057571289 / 40000000000000000 : ℚ)) + (U := (-(13347023103751467493021 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_7 : Uω (aρ 7) (bρ 7) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -532,25 +472,21 @@ lemma U_341_7 : have hlg : Real.log (9509883087309847 / 40000000000000000 : ℝ) ≤ (-(1795684838138299536907 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9509883087309847 / 40000000000000000 : ℝ) = - (9509883087309847 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9509883087309847 / 5000000000000000 : ℚ)) - (U := (803617087986700463093 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9509883087309847 / 5000000000000000 : ℝ) ≤ - (803617087986700463093 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (580731849170059 / 2500000000000000 : ℝ)) (q := - (9509883087309847 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9509883087309847 / 40000000000000000 : ℚ)) + (r' := (9509883087309847 / 5000000000000000 : ℚ)) + (U := (-(1795684838138299536907 / 1250000000000000000000 : ℚ))) + (U' := (803617087986700463093 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (580731849170059 / 2500000000000000 : ℚ)) + (q := (9509883087309847 / 40000000000000000 : ℚ)) + (U := (-(1795684838138299536907 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_8 : Uω (aρ 8) (bρ 8) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -558,25 +494,21 @@ lemma U_341_8 : have hlg : Real.log (8095354415229067 / 40000000000000000 : ℝ) ≤ (-(1996986356463040772307 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8095354415229067 / 40000000000000000 : ℝ) = - (8095354415229067 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8095354415229067 / 5000000000000000 : ℚ)) - (U := (602315569661959227693 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8095354415229067 / 5000000000000000 : ℝ) ≤ - (602315569661959227693 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (949602355989923 / 5000000000000000 : ℝ)) (q := - (8095354415229067 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8095354415229067 / 40000000000000000 : ℚ)) + (r' := (8095354415229067 / 5000000000000000 : ℚ)) + (U := (-(1996986356463040772307 / 1250000000000000000000 : ℚ))) + (U' := (602315569661959227693 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (949602355989923 / 5000000000000000 : ℚ)) + (q := (8095354415229067 / 40000000000000000 : ℚ)) + (U := (-(1996986356463040772307 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_9 : Uω (aρ 9) (bρ 9) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -584,25 +516,21 @@ lemma U_341_9 : have hlg : Real.log (6027997085228231 / 40000000000000000 : ℝ) ≤ (-(18924646561087487775289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6027997085228231 / 40000000000000000 : ℝ) = - (6027997085228231 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6027997085228231 / 5000000000000000 : ℚ)) - (U := (1869768847912512224711 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6027997085228231 / 5000000000000000 : ℝ) ≤ - (1869768847912512224711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (301622918834857 / 2500000000000000 : ℝ)) (q := - (6027997085228231 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6027997085228231 / 40000000000000000 : ℚ)) + (r' := (6027997085228231 / 5000000000000000 : ℚ)) + (U := (-(18924646561087487775289 / 10000000000000000000000 : ℚ))) + (U' := (1869768847912512224711 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10096199488703 / 32000000000000 : ℚ)) + (s := (301622918834857 / 2500000000000000 : ℚ)) + (q := (6027997085228231 / 40000000000000000 : ℚ)) + (U := (-(18924646561087487775289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_341_10 : Uω (aρ 10) (bρ 10) (10096199488703 / 32000000000000 : ℝ) ≤ @@ -730,25 +658,21 @@ lemma U_342_1 : have hlg : Real.log (6229616161552491 / 20000000000000000 : ℝ) ≤ (-(11664175534405795398607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6229616161552491 / 20000000000000000 : ℝ) = - (6229616161552491 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6229616161552491 / 5000000000000000 : ℚ)) - (U := (2198768071594204601393 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6229616161552491 / 5000000000000000 : ℝ) ≤ - (2198768071594204601393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3114756177776241 / 10000000000000000 : ℝ)) (q := - (6229616161552491 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6229616161552491 / 20000000000000000 : ℚ)) + (r' := (6229616161552491 / 5000000000000000 : ℚ)) + (U := (-(11664175534405795398607 / 10000000000000000000000 : ℚ))) + (U' := (2198768071594204601393 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (3114756177776241 / 10000000000000000 : ℚ)) + (q := (6229616161552491 / 20000000000000000 : ℚ)) + (U := (-(11664175534405795398607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_2 : Uω (aρ 2) (bρ 2) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -756,25 +680,21 @@ lemma U_342_2 : have hlg : Real.log (309074771226449 / 1000000000000000 : ℝ) ≤ (-(5870860263786756796371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (309074771226449 / 1000000000000000 : ℝ) = - (309074771226449 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (309074771226449 / 250000000000000 : ℚ)) - (U := (1060611539213243203629 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (309074771226449 / 250000000000000 : ℝ) ≤ - (1060611539213243203629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (309040445326273 / 1000000000000000 : ℝ)) (q := - (309074771226449 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (309074771226449 / 1000000000000000 : ℚ)) + (r' := (309074771226449 / 250000000000000 : ℚ)) + (U := (-(5870860263786756796371 / 5000000000000000000000 : ℚ))) + (U' := (1060611539213243203629 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (309040445326273 / 1000000000000000 : ℚ)) + (q := (309074771226449 / 1000000000000000 : ℚ)) + (U := (-(5870860263786756796371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_3 : Uω (aρ 3) (bρ 3) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -782,25 +702,21 @@ lemma U_342_3 : have hlg : Real.log (1216991626737721 / 4000000000000000 : ℝ) ≤ (-(2974781067166648350813 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1216991626737721 / 4000000000000000 : ℝ) = - (1216991626737721 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1216991626737721 / 1000000000000000 : ℚ)) - (U := (490954834333351649187 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1216991626737721 / 1000000000000000 : ℝ) ≤ - (490954834333351649187 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (608252653754471 / 2000000000000000 : ℝ)) (q := - (1216991626737721 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1216991626737721 / 4000000000000000 : ℚ)) + (r' := (1216991626737721 / 1000000000000000 : ℚ)) + (U := (-(2974781067166648350813 / 2500000000000000000000 : ℚ))) + (U' := (490954834333351649187 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (608252653754471 / 2000000000000000 : ℚ)) + (q := (1216991626737721 / 4000000000000000 : ℚ)) + (U := (-(2974781067166648350813 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_4 : Uω (aρ 4) (bρ 4) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -808,25 +724,21 @@ lemma U_342_4 : have hlg : Real.log (740462167334903 / 2500000000000000 : ℝ) ≤ (-(6083857343180408154369 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (740462167334903 / 2500000000000000 : ℝ) = - (740462167334903 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (740462167334903 / 625000000000000 : ℚ)) - (U := (847614459819591845631 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (740462167334903 / 625000000000000 : ℝ) ≤ - (847614459819591845631 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1479148327413987 / 5000000000000000 : ℝ)) (q := - (740462167334903 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (740462167334903 / 2500000000000000 : ℚ)) + (r' := (740462167334903 / 625000000000000 : ℚ)) + (U := (-(6083857343180408154369 / 5000000000000000000000 : ℚ))) + (U' := (847614459819591845631 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (1479148327413987 / 5000000000000000 : ℚ)) + (q := (740462167334903 / 2500000000000000 : ℚ)) + (U := (-(6083857343180408154369 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_5 : Uω (aρ 5) (bρ 5) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -834,25 +746,21 @@ lemma U_342_5 : have hlg : Real.log (2837827374905103 / 10000000000000000 : ℝ) ≤ (-(12595463419058547117867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2837827374905103 / 10000000000000000 : ℝ) = - (2837827374905103 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2837827374905103 / 2500000000000000 : ℚ)) - (U := (1267480186941452882133 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2837827374905103 / 2500000000000000 : ℝ) ≤ - (1267480186941452882133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (707110996323489 / 2500000000000000 : ℝ)) (q := - (2837827374905103 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2837827374905103 / 10000000000000000 : ℚ)) + (r' := (2837827374905103 / 2500000000000000 : ℚ)) + (U := (-(12595463419058547117867 / 10000000000000000000000 : ℚ))) + (U' := (1267480186941452882133 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (707110996323489 / 2500000000000000 : ℚ)) + (q := (2837827374905103 / 10000000000000000 : ℚ)) + (U := (-(12595463419058547117867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_6 : Uω (aρ 6) (bρ 6) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -860,25 +768,21 @@ lemma U_342_6 : have hlg : Real.log (664218791302243 / 2500000000000000 : ℝ) ≤ (-(6627172050807757955697 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (664218791302243 / 2500000000000000 : ℝ) = - (664218791302243 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (664218791302243 / 625000000000000 : ℚ)) - (U := (304299752192242044303 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (664218791302243 / 625000000000000 : ℝ) ≤ - (304299752192242044303 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1316889970520847 / 5000000000000000 : ℝ)) (q := - (664218791302243 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (664218791302243 / 2500000000000000 : ℚ)) + (r' := (664218791302243 / 625000000000000 : ℚ)) + (U := (-(6627172050807757955697 / 5000000000000000000000 : ℚ))) + (U' := (304299752192242044303 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (1316889970520847 / 5000000000000000 : ℚ)) + (q := (664218791302243 / 2500000000000000 : ℚ)) + (U := (-(6627172050807757955697 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_7 : Uω (aρ 7) (bρ 7) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -886,25 +790,21 @@ lemma U_342_7 : have hlg : Real.log (1201165023752779 / 5000000000000000 : ℝ) ≤ (-(14261459727060855781449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1201165023752779 / 5000000000000000 : ℝ) = - (1201165023752779 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1201165023752779 / 625000000000000 : ℚ)) - (U := (6532955681939144218551 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1201165023752779 / 625000000000000 : ℝ) ≤ - (6532955681939144218551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1174175543197433 / 5000000000000000 : ℝ)) (q := - (1201165023752779 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1201165023752779 / 5000000000000000 : ℚ)) + (r' := (1201165023752779 / 625000000000000 : ℚ)) + (U := (-(14261459727060855781449 / 10000000000000000000000 : ℚ))) + (U' := (6532955681939144218551 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (1174175543197433 / 5000000000000000 : ℚ)) + (q := (1201165023752779 / 5000000000000000 : ℚ)) + (U := (-(14261459727060855781449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_8 : Uω (aρ 8) (bρ 8) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -912,25 +812,21 @@ lemma U_342_8 : have hlg : Real.log (2049706374098079 / 10000000000000000 : ℝ) ≤ (-(990555338418671925963 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2049706374098079 / 10000000000000000 : ℝ) = - (2049706374098079 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2049706374098079 / 1250000000000000 : ℚ)) - (U := (309095624643828074037 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2049706374098079 / 1250000000000000 : ℝ) ≤ - (309095624643828074037 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (481661347729977 / 2500000000000000 : ℝ)) (q := - (2049706374098079 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2049706374098079 / 10000000000000000 : ℚ)) + (r' := (2049706374098079 / 1250000000000000 : ℚ)) + (U := (-(990555338418671925963 / 625000000000000000000 : ℚ))) + (U' := (309095624643828074037 / 625000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (481661347729977 / 2500000000000000 : ℚ)) + (q := (2049706374098079 / 10000000000000000 : ℚ)) + (U := (-(990555338418671925963 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_9 : Uω (aρ 9) (bρ 9) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -938,25 +834,21 @@ lemma U_342_9 : have hlg : Real.log (192149703196409 / 1250000000000000 : ℝ) ≤ (-(4681560142880333083387 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (192149703196409 / 1250000000000000 : ℝ) = - (192149703196409 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192149703196409 / 156250000000000 : ℚ)) - (U := (517043709369666916613 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (192149703196409 / 156250000000000 : ℝ) ≤ - (517043709369666916613 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (621296761113147 / 5000000000000000 : ℝ)) (q := - (192149703196409 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192149703196409 / 1250000000000000 : ℚ)) + (r' := (192149703196409 / 156250000000000 : ℚ)) + (U := (-(4681560142880333083387 / 2500000000000000000000 : ℚ))) + (U' := (517043709369666916613 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2543485761489 / 8000000000000 : ℚ)) + (s := (621296761113147 / 5000000000000000 : ℚ)) + (q := (192149703196409 / 1250000000000000 : ℚ)) + (U := (-(4681560142880333083387 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_342_10 : Uω (aρ 10) (bρ 10) (2543485761489 / 8000000000000 : ℝ) ≤ @@ -1084,25 +976,21 @@ lemma U_343_1 : have hlg : Real.log (12556413376495749 / 40000000000000000 : ℝ) ≤ (-(5793239462649911037 / 5000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12556413376495749 / 40000000000000000 : ℝ) = - (12556413376495749 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12556413376495749 / 10000000000000000 : ℚ)) - (U := (1138232340350088963 / 5000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12556413376495749 / 10000000000000000 : ℝ) ≤ - (1138232340350088963 / 5000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1569525921415031 / 5000000000000000 : ℝ)) (q := - (12556413376495749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12556413376495749 / 40000000000000000 : ℚ)) + (r' := (12556413376495749 / 10000000000000000 : ℚ)) + (U := (-(5793239462649911037 / 5000000000000000000 : ℚ))) + (U' := (1138232340350088963 / 5000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (1569525921415031 / 5000000000000000 : ℚ)) + (q := (12556413376495749 / 40000000000000000 : ℚ)) + (U := (-(5793239462649911037 / 5000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_2 : Uω (aρ 2) (bρ 2) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1110,25 +998,21 @@ lemma U_343_2 : have hlg : Real.log (12460181005387103 / 40000000000000000 : ℝ) ≤ (-(2332682826846300534697 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12460181005387103 / 40000000000000000 : ℝ) = - (12460181005387103 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12460181005387103 / 10000000000000000 : ℚ)) - (U := (439905894353699465303 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12460181005387103 / 10000000000000000 : ℝ) ≤ - (439905894353699465303 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3114704669785739 / 10000000000000000 : ℝ)) (q := - (12460181005387103 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12460181005387103 / 40000000000000000 : ℚ)) + (r' := (12460181005387103 / 10000000000000000 : ℚ)) + (U := (-(2332682826846300534697 / 2000000000000000000000 : ℚ))) + (U' := (439905894353699465303 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (3114704669785739 / 10000000000000000 : ℚ)) + (q := (12460181005387103 / 40000000000000000 : ℚ)) + (U := (-(2332682826846300534697 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_3 : Uω (aρ 3) (bρ 3) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1136,25 +1020,21 @@ lemma U_343_3 : have hlg : Real.log (12267134255118471 / 40000000000000000 : ℝ) ≤ (-(2954889447974945029483 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12267134255118471 / 40000000000000000 : ℝ) = - (12267134255118471 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12267134255118471 / 10000000000000000 : ℚ)) - (U := (510846453525054970517 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12267134255118471 / 10000000000000000 : ℝ) ≤ - (510846453525054970517 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3065577401001423 / 10000000000000000 : ℝ)) (q := - (12267134255118471 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12267134255118471 / 40000000000000000 : ℚ)) + (r' := (12267134255118471 / 10000000000000000 : ℚ)) + (U := (-(2954889447974945029483 / 2500000000000000000000 : ℚ))) + (U' := (510846453525054970517 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (3065577401001423 / 10000000000000000 : ℚ)) + (q := (12267134255118471 / 40000000000000000 : ℚ)) + (U := (-(2954889447974945029483 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_4 : Uω (aρ 4) (bρ 4) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1162,25 +1042,21 @@ lemma U_343_4 : have hlg : Real.log (2388937971062537 / 8000000000000000 : ℝ) ≤ (-(6042963187737180019357 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2388937971062537 / 8000000000000000 : ℝ) = - (2388937971062537 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2388937971062537 / 2000000000000000 : ℚ)) - (U := (888508615262819980643 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2388937971062537 / 2000000000000000 : ℝ) ≤ - (888508615262819980643 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (298264938216353 / 1000000000000000 : ℝ)) (q := - (2388937971062537 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2388937971062537 / 8000000000000000 : ℚ)) + (r' := (2388937971062537 / 2000000000000000 : ℚ)) + (U := (-(6042963187737180019357 / 5000000000000000000000 : ℚ))) + (U' := (888508615262819980643 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (298264938216353 / 1000000000000000 : ℚ)) + (q := (2388937971062537 / 8000000000000000 : ℚ)) + (U := (-(6042963187737180019357 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_5 : Uω (aρ 5) (bρ 5) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1188,25 +1064,21 @@ lemma U_343_5 : have hlg : Real.log (457952343414123 / 1600000000000000 : ℝ) ≤ (-(12509937826887110023689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (457952343414123 / 1600000000000000 : ℝ) = - (457952343414123 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (457952343414123 / 400000000000000 : ℚ)) - (U := (1353005779112889976311 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (457952343414123 / 400000000000000 : ℝ) ≤ - (1353005779112889976311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114115946660749 / 400000000000000 : ℝ)) (q := - (457952343414123 / 1600000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (457952343414123 / 1600000000000000 : ℚ)) + (r' := (457952343414123 / 400000000000000 : ℚ)) + (U := (-(12509937826887110023689 / 10000000000000000000000 : ℚ))) + (U' := (1353005779112889976311 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (114115946660749 / 400000000000000 : ℚ)) + (q := (457952343414123 / 1600000000000000 : ℚ)) + (U := (-(12509937826887110023689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_6 : Uω (aρ 6) (bρ 6) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1214,25 +1086,21 @@ lemma U_343_6 : have hlg : Real.log (10725524403767141 / 40000000000000000 : ℝ) ≤ (-(13162530945191651836923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10725524403767141 / 40000000000000000 : ℝ) = - (10725524403767141 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10725524403767141 / 10000000000000000 : ℚ)) - (U := (700412660808348163077 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10725524403767141 / 10000000000000000 : ℝ) ≤ - (700412660808348163077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1329248475432879 / 5000000000000000 : ℝ)) (q := - (10725524403767141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10725524403767141 / 40000000000000000 : ℚ)) + (r' := (10725524403767141 / 10000000000000000 : ℚ)) + (U := (-(13162530945191651836923 / 10000000000000000000000 : ℚ))) + (U' := (700412660808348163077 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (1329248475432879 / 5000000000000000 : ℚ)) + (q := (10725524403767141 / 40000000000000000 : ℚ)) + (U := (-(13162530945191651836923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_7 : Uω (aρ 7) (bρ 7) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1240,25 +1108,21 @@ lemma U_343_7 : have hlg : Real.log (9708710006044581 / 40000000000000000 : ℝ) ≤ (-(14158560319631239190253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9708710006044581 / 40000000000000000 : ℝ) = - (9708710006044581 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9708710006044581 / 5000000000000000 : ℚ)) - (U := (6635855089368760809747 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9708710006044581 / 5000000000000000 : ℝ) ≤ - (6635855089368760809747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1186875566382239 / 5000000000000000 : ℝ)) (q := - (9708710006044581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9708710006044581 / 40000000000000000 : ℚ)) + (r' := (9708710006044581 / 5000000000000000 : ℚ)) + (U := (-(14158560319631239190253 / 10000000000000000000000 : ℚ))) + (U' := (6635855089368760809747 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (1186875566382239 / 5000000000000000 : ℚ)) + (q := (9708710006044581 / 40000000000000000 : ℚ)) + (U := (-(14158560319631239190253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_8 : Uω (aρ 8) (bρ 8) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1266,25 +1130,21 @@ lemma U_343_8 : have hlg : Real.log (1660425999879923 / 8000000000000000 : ℝ) ≤ (-(15723673450207903387083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1660425999879923 / 8000000000000000 : ℝ) = - (1660425999879923 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1660425999879923 / 1000000000000000 : ℚ)) - (U := (5070741958792096612917 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1660425999879923 / 1000000000000000 : ℝ) ≤ - (5070741958792096612917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (390800556156399 / 2000000000000000 : ℝ)) (q := - (1660425999879923 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1660425999879923 / 8000000000000000 : ℚ)) + (r' := (1660425999879923 / 1000000000000000 : ℚ)) + (U := (-(15723673450207903387083 / 10000000000000000000000 : ℚ))) + (U' := (5070741958792096612917 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (390800556156399 / 2000000000000000 : ℚ)) + (q := (1660425999879923 / 8000000000000000 : ℚ)) + (U := (-(15723673450207903387083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_9 : Uω (aρ 9) (bρ 9) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1292,25 +1152,21 @@ lemma U_343_9 : have hlg : Real.log (6268468315680387 / 40000000000000000 : ℝ) ≤ (-(741338966521064763589 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6268468315680387 / 40000000000000000 : ℝ) = - (6268468315680387 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6268468315680387 / 5000000000000000 : ℚ)) - (U := (90437649838935236411 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6268468315680387 / 5000000000000000 : ℝ) ≤ - (90437649838935236411 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1278137567282381 / 10000000000000000 : ℝ)) (q := - (6268468315680387 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6268468315680387 / 40000000000000000 : ℚ)) + (r' := (6268468315680387 / 5000000000000000 : ℚ)) + (U := (-(741338966521064763589 / 400000000000000000000 : ℚ))) + (U' := (90437649838935236411 / 400000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10251686603209 / 32000000000000 : ℚ)) + (s := (1278137567282381 / 10000000000000000 : ℚ)) + (q := (6268468315680387 / 40000000000000000 : ℚ)) + (U := (-(741338966521064763589 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_343_10 : Uω (aρ 10) (bρ 10) (10251686603209 / 32000000000000 : ℝ) ≤ @@ -1437,25 +1293,21 @@ lemma U_344_1 : have hlg : Real.log (3163398601301231 / 10000000000000000 : ℝ) ≤ (-(2301876272154925326387 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3163398601301231 / 10000000000000000 : ℝ) = - (3163398601301231 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3163398601301231 / 2500000000000000 : ℚ)) - (U := (470712449045074673613 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3163398601301231 / 2500000000000000 : ℝ) ≤ - (470712449045074673613 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3163347495543087 / 10000000000000000 : ℝ)) (q := - (3163398601301231 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3163398601301231 / 10000000000000000 : ℚ)) + (r' := (3163398601301231 / 2500000000000000 : ℚ)) + (U := (-(2301876272154925326387 / 2000000000000000000000 : ℚ))) + (U' := (470712449045074673613 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (3163347495543087 / 10000000000000000 : ℚ)) + (q := (3163398601301231 / 10000000000000000 : ℚ)) + (U := (-(2301876272154925326387 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_2 : Uω (aρ 2) (bρ 2) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1463,25 +1315,21 @@ lemma U_344_2 : have hlg : Real.log (6278685497958957 / 20000000000000000 : ℝ) ≤ (-(11585716300751941489211 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6278685497958957 / 20000000000000000 : ℝ) = - (6278685497958957 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6278685497958957 / 5000000000000000 : ℚ)) - (U := (2277227305248058510789 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6278685497958957 / 5000000000000000 : ℝ) ≤ - (2277227305248058510789 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1569502401704791 / 5000000000000000 : ℝ)) (q := - (6278685497958957 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6278685497958957 / 20000000000000000 : ℚ)) + (r' := (6278685497958957 / 5000000000000000 : ℚ)) + (U := (-(11585716300751941489211 / 10000000000000000000000 : ℚ))) + (U' := (2277227305248058510789 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (1569502401704791 / 5000000000000000 : ℚ)) + (q := (6278685497958957 / 20000000000000000 : ℚ)) + (U := (-(11585716300751941489211 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_3 : Uω (aρ 3) (bρ 3) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1489,25 +1337,21 @@ lemma U_344_3 : have hlg : Real.log (6182175818272327 / 20000000000000000 : ℝ) ≤ (-(11740619893739643235129 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6182175818272327 / 20000000000000000 : ℝ) = - (6182175818272327 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6182175818272327 / 5000000000000000 : ℚ)) - (U := (2122323712260356764871 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6182175818272327 / 5000000000000000 : ℝ) ≤ - (2122323712260356764871 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (386236403759119 / 1250000000000000 : ℝ)) (q := - (6182175818272327 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6182175818272327 / 20000000000000000 : ℚ)) + (r' := (6182175818272327 / 5000000000000000 : ℚ)) + (U := (-(11740619893739643235129 / 10000000000000000000000 : ℚ))) + (U' := (2122323712260356764871 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (386236403759119 / 1250000000000000 : ℚ)) + (q := (6182175818272327 / 20000000000000000 : ℚ)) + (U := (-(11740619893739643235129 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_4 : Uω (aρ 4) (bρ 4) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1515,25 +1359,21 @@ lemma U_344_4 : have hlg : Real.log (3010495790238087 / 10000000000000000 : ℝ) ≤ (-(240096062582495861523 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3010495790238087 / 10000000000000000 : ℝ) = - (3010495790238087 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3010495790238087 / 2500000000000000 : ℚ)) - (U := (37162809537504138477 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3010495790238087 / 2500000000000000 : ℝ) ≤ - (37162809537504138477 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3007001173341799 / 10000000000000000 : ℝ)) (q := - (3010495790238087 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3010495790238087 / 10000000000000000 : ℚ)) + (r' := (3010495790238087 / 2500000000000000 : ℚ)) + (U := (-(240096062582495861523 / 200000000000000000000 : ℚ))) + (U' := (37162809537504138477 / 200000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (3007001173341799 / 10000000000000000 : ℚ)) + (q := (3010495790238087 / 10000000000000000 : ℚ)) + (U := (-(240096062582495861523 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_5 : Uω (aρ 5) (bρ 5) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1541,25 +1381,21 @@ lemma U_344_5 : have hlg : Real.log (5773151127799207 / 20000000000000000 : ℝ) ≤ (-(6212571094579826978127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5773151127799207 / 20000000000000000 : ℝ) = - (5773151127799207 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5773151127799207 / 5000000000000000 : ℚ)) - (U := (718900708420173021873 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5773151127799207 / 5000000000000000 : ℝ) ≤ - (718900708420173021873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (359668829999979 / 1250000000000000 : ℝ)) (q := - (5773151127799207 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5773151127799207 / 20000000000000000 : ℚ)) + (r' := (5773151127799207 / 5000000000000000 : ℚ)) + (U := (-(6212571094579826978127 / 5000000000000000000000 : ℚ))) + (U' := (718900708420173021873 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (359668829999979 / 1250000000000000 : ℚ)) + (q := (5773151127799207 / 20000000000000000 : ℚ)) + (U := (-(6212571094579826978127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_6 : Uω (aρ 6) (bρ 6) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1567,25 +1403,21 @@ lemma U_344_6 : have hlg : Real.log (676470795291817 / 2500000000000000 : ℝ) ≤ (-(13071567339577674235373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (676470795291817 / 2500000000000000 : ℝ) = - (676470795291817 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (676470795291817 / 625000000000000 : ℚ)) - (U := (791376266422325764627 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (676470795291817 / 625000000000000 : ℝ) ≤ - (791376266422325764627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2683206249675161 / 10000000000000000 : ℝ)) (q := - (676470795291817 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (676470795291817 / 2500000000000000 : ℚ)) + (r' := (676470795291817 / 625000000000000 : ℚ)) + (U := (-(13071567339577674235373 / 10000000000000000000000 : ℚ))) + (U' := (791376266422325764627 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (2683206249675161 / 10000000000000000 : ℚ)) + (q := (676470795291817 / 2500000000000000 : ℚ)) + (U := (-(13071567339577674235373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_7 : Uω (aρ 7) (bρ 7) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1593,25 +1425,21 @@ lemma U_344_7 : have hlg : Real.log (2452013509319447 / 10000000000000000 : ℝ) ≤ (-(14056755646450440234437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2452013509319447 / 10000000000000000 : ℝ) = - (2452013509319447 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2452013509319447 / 1250000000000000 : ℚ)) - (U := (6737659762549559765563 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2452013509319447 / 1250000000000000 : ℝ) ≤ - (6737659762549559765563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2399128286739519 / 10000000000000000 : ℝ)) (q := - (2452013509319447 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2452013509319447 / 10000000000000000 : ℚ)) + (r' := (2452013509319447 / 1250000000000000 : ℚ)) + (U := (-(14056755646450440234437 / 10000000000000000000000 : ℚ))) + (U' := (6737659762549559765563 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (2399128286739519 / 10000000000000000 : ℚ)) + (q := (2452013509319447 / 10000000000000000 : ℚ)) + (U := (-(14056755646450440234437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_8 : Uω (aρ 8) (bρ 8) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1619,25 +1447,21 @@ lemma U_344_8 : have hlg : Real.log (4202637412278987 / 20000000000000000 : ℝ) ≤ (-(195002498657717841121 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4202637412278987 / 20000000000000000 : ℝ) = - (4202637412278987 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4202637412278987 / 2500000000000000 : ℚ)) - (U := (64927693954782158879 / 125000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4202637412278987 / 2500000000000000 : ℝ) ≤ - (64927693954782158879 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (495320082929903 / 2500000000000000 : ℝ)) (q := - (4202637412278987 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4202637412278987 / 20000000000000000 : ℚ)) + (r' := (4202637412278987 / 2500000000000000 : ℚ)) + (U := (-(195002498657717841121 / 125000000000000000000 : ℚ))) + (U' := (64927693954782158879 / 125000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (495320082929903 / 2500000000000000 : ℚ)) + (q := (4202637412278987 / 20000000000000000 : ℚ)) + (U := (-(195002498657717841121 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_9 : Uω (aρ 9) (bρ 9) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1645,25 +1469,21 @@ lemma U_344_9 : have hlg : Real.log (798390139546971 / 5000000000000000 : ℝ) ≤ (-(3669191631964464684769 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (798390139546971 / 5000000000000000 : ℝ) = - (798390139546971 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (798390139546971 / 625000000000000 : ℚ)) - (U := (489691449835535315231 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (798390139546971 / 625000000000000 : ℝ) ≤ - (489691449835535315231 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1313169105988509 / 10000000000000000 : ℝ)) (q := - (798390139546971 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (798390139546971 / 5000000000000000 : ℚ)) + (r' := (798390139546971 / 625000000000000 : ℚ)) + (U := (-(3669191631964464684769 / 2000000000000000000000 : ℚ))) + (U' := (489691449835535315231 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5164715080231 / 16000000000000 : ℚ)) + (s := (1313169105988509 / 10000000000000000 : ℚ)) + (q := (798390139546971 / 5000000000000000 : ℚ)) + (U := (-(3669191631964464684769 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_344_10 : Uω (aρ 10) (bρ 10) (5164715080231 / 16000000000000 : ℝ) ≤ @@ -1789,25 +1609,21 @@ lemma U_345_1 : have hlg : Real.log (3211989097704713 / 10000000000000000 : ℝ) ≤ (-(11356946906342816493083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3211989097704713 / 10000000000000000 : ℝ) = - (3211989097704713 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3211989097704713 / 2500000000000000 : ℚ)) - (U := (2505996699657183506917 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3211989097704713 / 2500000000000000 : ℝ) ≤ - (2505996699657183506917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1605969382533463 / 5000000000000000 : ℝ)) (q := - (3211989097704713 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3211989097704713 / 10000000000000000 : ℚ)) + (r' := (3211989097704713 / 2500000000000000 : ℚ)) + (U := (-(11356946906342816493083 / 10000000000000000000000 : ℚ))) + (U' := (2505996699657183506917 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (1605969382533463 / 5000000000000000 : ℚ)) + (q := (3211989097704713 / 10000000000000000 : ℚ)) + (U := (-(11356946906342816493083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_2 : Uω (aρ 2) (bρ 2) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1815,25 +1631,21 @@ lemma U_345_2 : have hlg : Real.log (6375875247375869 / 20000000000000000 : ℝ) ≤ (-(11432108977075101674191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6375875247375869 / 20000000000000000 : ℝ) = - (6375875247375869 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6375875247375869 / 5000000000000000 : ℚ)) - (U := (2430834628924898325809 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6375875247375869 / 5000000000000000 : ℝ) ≤ - (2430834628924898325809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3187604829543369 / 10000000000000000 : ℝ)) (q := - (6375875247375869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6375875247375869 / 20000000000000000 : ℚ)) + (r' := (6375875247375869 / 5000000000000000 : ℚ)) + (U := (-(11432108977075101674191 / 10000000000000000000000 : ℚ))) + (U' := (2430834628924898325809 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (3187604829543369 / 10000000000000000 : ℚ)) + (q := (6375875247375869 / 20000000000000000 : ℚ)) + (U := (-(11432108977075101674191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_3 : Uω (aρ 3) (bρ 3) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1841,25 +1653,21 @@ lemma U_345_3 : have hlg : Real.log (3139696159204113 / 10000000000000000 : ℝ) ≤ (-(5792295309103324570207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3139696159204113 / 10000000000000000 : ℝ) = - (3139696159204113 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3139696159204113 / 2500000000000000 : ℚ)) - (U := (1139176493896675429793 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3139696159204113 / 2500000000000000 : ℝ) ≤ - (1139176493896675429793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1569259003462863 / 5000000000000000 : ℝ)) (q := - (3139696159204113 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3139696159204113 / 10000000000000000 : ℚ)) + (r' := (3139696159204113 / 2500000000000000 : ℚ)) + (U := (-(5792295309103324570207 / 5000000000000000000000 : ℚ))) + (U' := (1139176493896675429793 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (1569259003462863 / 5000000000000000 : ℚ)) + (q := (3139696159204113 / 10000000000000000 : ℚ)) + (U := (-(5792295309103324570207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_4 : Uω (aρ 4) (bρ 4) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1867,25 +1675,21 @@ lemma U_345_4 : have hlg : Real.log (6118282167169283 / 20000000000000000 : ℝ) ≤ (-(11844509075501430543993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6118282167169283 / 20000000000000000 : ℝ) = - (6118282167169283 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6118282167169283 / 5000000000000000 : ℚ)) - (U := (2018434530498569456007 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6118282167169283 / 5000000000000000 : ℝ) ≤ - (2018434530498569456007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3055702036751783 / 10000000000000000 : ℝ)) (q := - (6118282167169283 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6118282167169283 / 20000000000000000 : ℚ)) + (r' := (6118282167169283 / 5000000000000000 : ℚ)) + (U := (-(11844509075501430543993 / 10000000000000000000000 : ℚ))) + (U' := (2018434530498569456007 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (3055702036751783 / 10000000000000000 : ℚ)) + (q := (6118282167169283 / 20000000000000000 : ℚ)) + (U := (-(11844509075501430543993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_5 : Uω (aρ 5) (bρ 5) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1893,25 +1697,21 @@ lemma U_345_5 : have hlg : Real.log (5870636946319773 / 20000000000000000 : ℝ) ≤ (-(2451538272676043922751 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5870636946319773 / 20000000000000000 : ℝ) = - (5870636946319773 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5870636946319773 / 5000000000000000 : ℚ)) - (U := (321050448523956077249 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5870636946319773 / 5000000000000000 : ℝ) ≤ - (321050448523956077249 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2926246735237273 / 10000000000000000 : ℝ)) (q := - (5870636946319773 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5870636946319773 / 20000000000000000 : ℚ)) + (r' := (5870636946319773 / 5000000000000000 : ℚ)) + (U := (-(2451538272676043922751 / 2000000000000000000000 : ℚ))) + (U' := (321050448523956077249 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (2926246735237273 / 10000000000000000 : ℚ)) + (q := (5870636946319773 / 20000000000000000 : ℚ)) + (U := (-(2451538272676043922751 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_6 : Uω (aρ 6) (bρ 6) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1919,25 +1719,21 @@ lemma U_345_6 : have hlg : Real.log (2754876193420369 / 10000000000000000 : ℝ) ≤ (-(50359866786970237563 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2754876193420369 / 10000000000000000 : ℝ) = - (2754876193420369 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2754876193420369 / 2500000000000000 : ℚ)) - (U := (3792256673967262437 / 39062500000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2754876193420369 / 2500000000000000 : ℝ) ≤ - (3792256673967262437 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1366301275449119 / 5000000000000000 : ℝ)) (q := - (2754876193420369 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2754876193420369 / 10000000000000000 : ℚ)) + (r' := (2754876193420369 / 2500000000000000 : ℚ)) + (U := (-(50359866786970237563 / 39062500000000000000 : ℚ))) + (U' := (3792256673967262437 / 39062500000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (1366301275449119 / 5000000000000000 : ℚ)) + (q := (2754876193420369 / 10000000000000000 : ℚ)) + (U := (-(50359866786970237563 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_7 : Uω (aρ 7) (bρ 7) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1945,25 +1741,21 @@ lemma U_345_7 : have hlg : Real.log (2501652608850121 / 10000000000000000 : ℝ) ≤ (-(3464083838632482367617 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2501652608850121 / 10000000000000000 : ℝ) = - (2501652608850121 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2501652608850121 / 2500000000000000 : ℚ)) - (U := (1652062867517632383 / 2500000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (2501652608850121 / 2500000000000000 : ℝ) ≤ - (1652062867517632383 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1224908381258871 / 5000000000000000 : ℝ)) (q := - (2501652608850121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2501652608850121 / 10000000000000000 : ℚ)) + (r' := (2501652608850121 / 2500000000000000 : ℚ)) + (U := (-(3464083838632482367617 / 2500000000000000000000 : ℚ))) + (U' := (1652062867517632383 / 2500000000000000000000 : ℚ)) + 2 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (1224908381258871 / 5000000000000000 : ℚ)) + (q := (2501652608850121 / 10000000000000000 : ℚ)) + (U := (-(3464083838632482367617 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_8 : Uω (aρ 8) (bρ 8) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1971,25 +1763,21 @@ lemma U_345_8 : have hlg : Real.log (1076388887398653 / 5000000000000000 : ℝ) ≤ (-(7679130478477478291329 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1076388887398653 / 5000000000000000 : ℝ) = - (1076388887398653 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1076388887398653 / 625000000000000 : ℚ)) - (U := (2718077226022521708671 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1076388887398653 / 625000000000000 : ℝ) ≤ - (2718077226022521708671 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (127225546609507 / 625000000000000 : ℝ)) (q := - (1076388887398653 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1076388887398653 / 5000000000000000 : ℚ)) + (r' := (1076388887398653 / 625000000000000 : ℚ)) + (U := (-(7679130478477478291329 / 5000000000000000000000 : ℚ))) + (U' := (2718077226022521708671 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (127225546609507 / 625000000000000 : ℚ)) + (q := (1076388887398653 / 5000000000000000 : ℚ)) + (U := (-(7679130478477478291329 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_9 : Uω (aρ 9) (bρ 9) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -1997,24 +1785,21 @@ lemma U_345_9 : have hlg : Real.log (25865868672333 / 156250000000000 : ℝ) ≤ (-(449633250021974099083 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25865868672333 / 156250000000000 : ℝ) = (25865868672333 / 19531250000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25865868672333 / 19531250000000 : ℚ)) - (U := (70227135203025900917 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25865868672333 / 19531250000000 : ℝ) ≤ - (70227135203025900917 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (345462503644031 / 2500000000000000 : ℝ)) (q := - (25865868672333 / 156250000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25865868672333 / 156250000000000 : ℚ)) + (r' := (25865868672333 / 19531250000000 : ℚ)) + (U := (-(449633250021974099083 / 250000000000000000000 : ℚ))) + (U' := (70227135203025900917 / 250000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1310614659371 / 4000000000000 : ℚ)) + (s := (345462503644031 / 2500000000000000 : ℚ)) + (q := (25865868672333 / 156250000000000 : ℚ)) + (U := (-(449633250021974099083 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_345_10 : Uω (aρ 10) (bρ 10) (1310614659371 / 4000000000000 : ℝ) ≤ @@ -2141,25 +1926,21 @@ lemma U_346_1 : have hlg : Real.log (326057957106513 / 1000000000000000 : ℝ) ≤ (-(1400850162952081230453 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (326057957106513 / 1000000000000000 : ℝ) = - (326057957106513 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (326057957106513 / 250000000000000 : ℚ)) - (U := (332017787797918769547 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (326057957106513 / 250000000000000 : ℝ) ≤ - (332017787797918769547 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (652105997700927 / 2000000000000000 : ℝ)) (q := - (326057957106513 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (326057957106513 / 1000000000000000 : ℚ)) + (r' := (326057957106513 / 250000000000000 : ℚ)) + (U := (-(1400850162952081230453 / 1250000000000000000000 : ℚ))) + (U' := (332017787797918769547 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (652105997700927 / 2000000000000000 : ℚ)) + (q := (326057957106513 / 1000000000000000 : ℚ)) + (U := (-(1400850162952081230453 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_2 : Uω (aρ 2) (bρ 2) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2167,25 +1948,21 @@ lemma U_346_2 : have hlg : Real.log (647306468737741 / 2000000000000000 : ℝ) ≤ (-(11280826001053343395199 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (647306468737741 / 2000000000000000 : ℝ) = - (647306468737741 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (647306468737741 / 500000000000000 : ℚ)) - (U := (2582117604946656604801 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (647306468737741 / 500000000000000 : ℝ) ≤ - (2582117604946656604801 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (647240909252357 / 2000000000000000 : ℝ)) (q := - (647306468737741 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (647306468737741 / 2000000000000000 : ℚ)) + (r' := (647306468737741 / 500000000000000 : ℚ)) + (U := (-(11280826001053343395199 / 10000000000000000000000 : ℚ))) + (U' := (2582117604946656604801 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (647240909252357 / 2000000000000000 : ℚ)) + (q := (647306468737741 / 2000000000000000 : ℚ)) + (U := (-(11280826001053343395199 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_3 : Uω (aρ 3) (bρ 3) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2193,24 +1970,21 @@ lemma U_346_3 : have hlg : Real.log (25506430753241 / 80000000000000 : ℝ) ≤ (-(228619205476329618989 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25506430753241 / 80000000000000 : ℝ) = (25506430753241 / 20000000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25506430753241 / 20000000000000 : ℚ)) - (U := (48639666643670381011 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25506430753241 / 20000000000000 : ℝ) ≤ - (48639666643670381011 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25497149228357 / 80000000000000 : ℝ)) (q := - (25506430753241 / 80000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25506430753241 / 80000000000000 : ℚ)) + (r' := (25506430753241 / 20000000000000 : ℚ)) + (U := (-(228619205476329618989 / 200000000000000000000 : ℚ))) + (U' := (48639666643670381011 / 200000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (25497149228357 / 80000000000000 : ℚ)) + (q := (25506430753241 / 80000000000000 : ℚ)) + (U := (-(228619205476329618989 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_4 : Uω (aρ 4) (bρ 4) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2218,25 +1992,21 @@ lemma U_346_4 : have hlg : Real.log (621556927077899 / 2000000000000000 : ℝ) ≤ (-(11686749560023923541033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (621556927077899 / 2000000000000000 : ℝ) = - (621556927077899 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (621556927077899 / 500000000000000 : ℚ)) - (U := (2176194045976076458967 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (621556927077899 / 500000000000000 : ℝ) ≤ - (2176194045976076458967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (620879883415673 / 2000000000000000 : ℝ)) (q := - (621556927077899 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (621556927077899 / 2000000000000000 : ℚ)) + (r' := (621556927077899 / 500000000000000 : ℚ)) + (U := (-(11686749560023923541033 / 10000000000000000000000 : ℚ))) + (U' := (2176194045976076458967 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (620879883415673 / 2000000000000000 : ℚ)) + (q := (621556927077899 / 2000000000000000 : ℚ)) + (U := (-(11686749560023923541033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_5 : Uω (aρ 5) (bρ 5) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2244,25 +2014,21 @@ lemma U_346_5 : have hlg : Real.log (5968112726004279 / 20000000000000000 : ℝ) ≤ (-(12093015219054816054701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5968112726004279 / 20000000000000000 : ℝ) = - (5968112726004279 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5968112726004279 / 5000000000000000 : ℚ)) - (U := (1769928386945183945299 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5968112726004279 / 5000000000000000 : ℝ) ≤ - (1769928386945183945299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1487566395819327 / 5000000000000000 : ℝ)) (q := - (5968112726004279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5968112726004279 / 20000000000000000 : ℚ)) + (r' := (5968112726004279 / 5000000000000000 : ℚ)) + (U := (-(12093015219054816054701 / 10000000000000000000000 : ℚ))) + (U' := (1769928386945183945299 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (1487566395819327 / 5000000000000000 : ℚ)) + (q := (5968112726004279 / 20000000000000000 : ℚ)) + (U := (-(12093015219054816054701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_6 : Uω (aρ 6) (bρ 6) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2270,25 +2036,21 @@ lemma U_346_6 : have hlg : Real.log (5607710002359903 / 20000000000000000 : ℝ) ≤ (-(6357949180291555523893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5607710002359903 / 20000000000000000 : ℝ) = - (5607710002359903 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5607710002359903 / 5000000000000000 : ℚ)) - (U := (573522622708444476107 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5607710002359903 / 5000000000000000 : ℝ) ≤ - (573522622708444476107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1390985221567139 / 5000000000000000 : ℝ)) (q := - (5607710002359903 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5607710002359903 / 20000000000000000 : ℚ)) + (r' := (5607710002359903 / 5000000000000000 : ℚ)) + (U := (-(6357949180291555523893 / 5000000000000000000000 : ℚ))) + (U' := (573522622708444476107 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (1390985221567139 / 5000000000000000 : ℚ)) + (q := (5607710002359903 / 20000000000000000 : ℚ)) + (U := (-(6357949180291555523893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_7 : Uω (aρ 7) (bρ 7) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2296,23 +2058,21 @@ lemma U_346_7 : have hlg : Real.log (2551250044033 / 10000000000000 : ℝ) ≤ (-(6830008200364275306877 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (2551250044033 / 10000000000000 : ℝ) = (2551250044033 / 2500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2551250044033 / 2500000000000 : ℚ)) - (U := (101463602635724693123 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2551250044033 / 2500000000000 : ℝ) ≤ - (101463602635724693123 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (20003375276803 / 80000000000000 : ℝ)) (q := - (2551250044033 / 10000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2551250044033 / 10000000000000 : ℚ)) + (r' := (2551250044033 / 2500000000000 : ℚ)) + (U := (-(6830008200364275306877 / 5000000000000000000000 : ℚ))) + (U' := (101463602635724693123 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (20003375276803 / 80000000000000 : ℚ)) + (q := (2551250044033 / 10000000000000 : ℚ)) + (U := (-(6830008200364275306877 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_8 : Uω (aρ 8) (bρ 8) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2320,25 +2080,21 @@ lemma U_346_8 : have hlg : Real.log (4408191068221703 / 20000000000000000 : ℝ) ≤ (-(7561339280388101403409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4408191068221703 / 20000000000000000 : ℝ) = - (4408191068221703 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4408191068221703 / 2500000000000000 : ℚ)) - (U := (2835868424111898596591 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4408191068221703 / 2500000000000000 : ℝ) ≤ - (2835868424111898596591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1044827270548039 / 5000000000000000 : ℝ)) (q := - (4408191068221703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4408191068221703 / 20000000000000000 : ℚ)) + (r' := (4408191068221703 / 2500000000000000 : ℚ)) + (U := (-(7561339280388101403409 / 5000000000000000000000 : ℚ))) + (U' := (2835868424111898596591 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (1044827270548039 / 5000000000000000 : ℚ)) + (q := (4408191068221703 / 20000000000000000 : ℚ)) + (U := (-(7561339280388101403409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_9 : Uω (aρ 9) (bρ 9) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2346,25 +2102,21 @@ lemma U_346_9 : have hlg : Real.log (428309575689891 / 2500000000000000 : ℝ) ≤ (-(2756562137920207449 / 1562500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (428309575689891 / 2500000000000000 : ℝ) = - (428309575689891 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (428309575689891 / 312500000000000 : ℚ)) - (U := (492565269736042551 / 1562500000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (428309575689891 / 312500000000000 : ℝ) ≤ - (492565269736042551 / 1562500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1448905706753503 / 10000000000000000 : ℝ)) (q := - (428309575689891 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (428309575689891 / 2500000000000000 : ℚ)) + (r' := (428309575689891 / 312500000000000 : ℚ)) + (U := (-(2756562137920207449 / 1562500000000000000 : ℚ))) + (U' := (492565269736042551 / 1562500000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5320202194737 / 16000000000000 : ℚ)) + (s := (1448905706753503 / 10000000000000000 : ℚ)) + (q := (428309575689891 / 2500000000000000 : ℚ)) + (U := (-(2756562137920207449 / 1562500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_346_10 : Uω (aρ 10) (bρ 10) (5320202194737 / 16000000000000 : ℝ) ≤ @@ -2491,25 +2243,21 @@ lemma U_347_1 : have hlg : Real.log (1323668008959031 / 4000000000000000 : ℝ) ≤ (-(5529438415241096726837 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1323668008959031 / 4000000000000000 : ℝ) = - (1323668008959031 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1323668008959031 / 1000000000000000 : ℚ)) - (U := (1402033387758903273163 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1323668008959031 / 1000000000000000 : ℝ) ≤ - (1402033387758903273163 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661824233577281 / 2000000000000000 : ℝ)) (q := - (1323668008959031 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1323668008959031 / 4000000000000000 : ℚ)) + (r' := (1323668008959031 / 1000000000000000 : ℚ)) + (U := (-(5529438415241096726837 / 5000000000000000000000 : ℚ))) + (U' := (1402033387758903273163 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (661824233577281 / 2000000000000000 : ℚ)) + (q := (1323668008959031 / 4000000000000000 : ℚ)) + (U := (-(5529438415241096726837 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_2 : Uω (aρ 2) (bρ 2) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2517,25 +2265,21 @@ lemma U_347_2 : have hlg : Real.log (3285126915848639 / 10000000000000000 : ℝ) ≤ (-(2782949515805895480333 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3285126915848639 / 10000000000000000 : ℝ) = - (3285126915848639 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3285126915848639 / 2500000000000000 : ℚ)) - (U := (682786385694104519667 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3285126915848639 / 2500000000000000 : ℝ) ≤ - (682786385694104519667 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102650123978079 / 312500000000000 : ℝ)) (q := - (3285126915848639 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3285126915848639 / 10000000000000000 : ℚ)) + (r' := (3285126915848639 / 2500000000000000 : ℚ)) + (U := (-(2782949515805895480333 / 2500000000000000000000 : ℚ))) + (U' := (682786385694104519667 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (102650123978079 / 312500000000000 : ℚ)) + (q := (3285126915848639 / 10000000000000000 : ℚ)) + (U := (-(2782949515805895480333 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_3 : Uω (aρ 3) (bρ 3) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2543,25 +2287,21 @@ lemma U_347_3 : have hlg : Real.log (1294764395786463 / 4000000000000000 : ℝ) ≤ (-(2819914039390198190657 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1294764395786463 / 4000000000000000 : ℝ) = - (1294764395786463 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1294764395786463 / 1000000000000000 : ℚ)) - (U := (645821862109801809343 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1294764395786463 / 1000000000000000 : ℝ) ≤ - (645821862109801809343 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (647153644176713 / 2000000000000000 : ℝ)) (q := - (1294764395786463 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1294764395786463 / 4000000000000000 : ℚ)) + (r' := (1294764395786463 / 1000000000000000 : ℚ)) + (U := (-(2819914039390198190657 / 2500000000000000000000 : ℚ))) + (U' := (645821862109801809343 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (647153644176713 / 2000000000000000 : ℚ)) + (q := (1294764395786463 / 4000000000000000 : ℚ)) + (U := (-(2819914039390198190657 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_4 : Uω (aρ 4) (bρ 4) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2569,25 +2309,21 @@ lemma U_347_4 : have hlg : Real.log (6312853052686849 / 20000000000000000 : ℝ) ≤ (-(1153144550858087381687 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6312853052686849 / 20000000000000000 : ℝ) = - (6312853052686849 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6312853052686849 / 5000000000000000 : ℚ)) - (U := (233149809741912618313 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6312853052686849 / 5000000000000000 : ℝ) ≤ - (233149809741912618313 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3153093475703099 / 10000000000000000 : ℝ)) (q := - (6312853052686849 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6312853052686849 / 20000000000000000 : ℚ)) + (r' := (6312853052686849 / 5000000000000000 : ℚ)) + (U := (-(1153144550858087381687 / 1000000000000000000000 : ℚ))) + (U' := (233149809741912618313 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (3153093475703099 / 10000000000000000 : ℚ)) + (q := (6312853052686849 / 20000000000000000 : ℚ)) + (U := (-(1153144550858087381687 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_5 : Uω (aρ 5) (bρ 5) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2595,25 +2331,21 @@ lemma U_347_5 : have hlg : Real.log (303278947685773 / 1000000000000000 : ℝ) ≤ (-(1193102277038038876959 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (303278947685773 / 1000000000000000 : ℝ) = - (303278947685773 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (303278947685773 / 250000000000000 : ℚ)) - (U := (193192083561961123041 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (303278947685773 / 250000000000000 : ℝ) ≤ - (193192083561961123041 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (302400929606671 / 1000000000000000 : ℝ)) (q := - (303278947685773 / 1000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (303278947685773 / 1000000000000000 : ℚ)) + (r' := (303278947685773 / 250000000000000 : ℚ)) + (U := (-(1193102277038038876959 / 1000000000000000000000 : ℚ))) + (U' := (193192083561961123041 / 1000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (302400929606671 / 1000000000000000 : ℚ)) + (q := (303278947685773 / 1000000000000000 : ℚ)) + (U := (-(1193102277038038876959 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_6 : Uω (aρ 6) (bρ 6) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2621,25 +2353,21 @@ lemma U_347_6 : have hlg : Real.log (228225627797769 / 800000000000000 : ℝ) ≤ (-(6271384959581393181183 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (228225627797769 / 800000000000000 : ℝ) = - (228225627797769 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (228225627797769 / 200000000000000 : ℚ)) - (U := (660086843418606818817 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (228225627797769 / 200000000000000 : ℝ) ≤ - (660086843418606818817 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (113252456497419 / 400000000000000 : ℝ)) (q := - (228225627797769 / 800000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (228225627797769 / 800000000000000 : ℚ)) + (r' := (228225627797769 / 200000000000000 : ℚ)) + (U := (-(6271384959581393181183 / 5000000000000000000000 : ℚ))) + (U' := (660086843418606818817 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (113252456497419 / 400000000000000 : ℚ)) + (q := (228225627797769 / 800000000000000 : ℚ)) + (U := (-(6271384959581393181183 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_7 : Uω (aρ 7) (bρ 7) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2647,25 +2375,21 @@ lemma U_347_7 : have hlg : Real.log (1300404147227207 / 5000000000000000 : ℝ) ≤ (-(2693525626556395372243 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1300404147227207 / 5000000000000000 : ℝ) = - (1300404147227207 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1300404147227207 / 1250000000000000 : ℚ)) - (U := (79063094643604627757 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1300404147227207 / 1250000000000000 : ℝ) ≤ - (79063094643604627757 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1275474343580039 / 5000000000000000 : ℝ)) (q := - (1300404147227207 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1300404147227207 / 5000000000000000 : ℚ)) + (r' := (1300404147227207 / 1250000000000000 : ℚ)) + (U := (-(2693525626556395372243 / 2000000000000000000000 : ℚ))) + (U' := (79063094643604627757 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (1275474343580039 / 5000000000000000 : ℚ)) + (q := (1300404147227207 / 5000000000000000 : ℚ)) + (U := (-(2693525626556395372243 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_8 : Uω (aρ 8) (bρ 8) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2673,25 +2397,21 @@ lemma U_347_8 : have hlg : Real.log (4510565346553517 / 20000000000000000 : ℝ) ≤ (-(14893097731127274734401 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4510565346553517 / 20000000000000000 : ℝ) = - (4510565346553517 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4510565346553517 / 2500000000000000 : ℚ)) - (U := (5901317677872725265599 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4510565346553517 / 2500000000000000 : ℝ) ≤ - (5901317677872725265599 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2143439096144767 / 10000000000000000 : ℝ)) (q := - (4510565346553517 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4510565346553517 / 20000000000000000 : ℚ)) + (r' := (4510565346553517 / 2500000000000000 : ℚ)) + (U := (-(14893097731127274734401 / 10000000000000000000000 : ℚ))) + (U' := (5901317677872725265599 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (2143439096144767 / 10000000000000000 : ℚ)) + (q := (4510565346553517 / 20000000000000000 : ℚ)) + (U := (-(14893097731127274734401 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_9 : Uω (aρ 9) (bρ 9) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2699,25 +2419,21 @@ lemma U_347_9 : have hlg : Real.log (3540712685782171 / 20000000000000000 : ℝ) ≤ (-(17314042422240819869213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3540712685782171 / 20000000000000000 : ℝ) = - (3540712685782171 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3540712685782171 / 2500000000000000 : ℚ)) - (U := (3480372986759180130787 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3540712685782171 / 2500000000000000 : ℝ) ≤ - (3480372986759180130787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1514552063733421 / 10000000000000000 : ℝ)) (q := - (3540712685782171 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3540712685782171 / 20000000000000000 : ℚ)) + (r' := (3540712685782171 / 2500000000000000 : ℚ)) + (U := (-(17314042422240819869213 / 10000000000000000000000 : ℚ))) + (U' := (3480372986759180130787 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (539794575199 / 1600000000000 : ℚ)) + (s := (1514552063733421 / 10000000000000000 : ℚ)) + (q := (3540712685782171 / 20000000000000000 : ℚ)) + (U := (-(17314042422240819869213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_347_10 : Uω (aρ 10) (bρ 10) (539794575199 / 1600000000000 : ℝ) ≤ @@ -2844,25 +2560,21 @@ lemma U_348_1 : have hlg : Real.log (6715520905316779 / 20000000000000000 : ℝ) ≤ (-(2728277181692807866107 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6715520905316779 / 20000000000000000 : ℝ) = - (6715520905316779 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6715520905316779 / 5000000000000000 : ℚ)) - (U := (737458719807192133893 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6715520905316779 / 5000000000000000 : ℝ) ≤ - (737458719807192133893 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (419714038140613 / 1250000000000000 : ℝ)) (q := - (6715520905316779 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6715520905316779 / 20000000000000000 : ℚ)) + (r' := (6715520905316779 / 5000000000000000 : ℚ)) + (U := (-(2728277181692807866107 / 2500000000000000000000 : ℚ))) + (U' := (737458719807192133893 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (419714038140613 / 1250000000000000 : ℚ)) + (q := (6715520905316779 / 20000000000000000 : ℚ)) + (U := (-(2728277181692807866107 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_2 : Uω (aρ 2) (bρ 2) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -2870,25 +2582,21 @@ lemma U_348_2 : have hlg : Real.log (6667442693268163 / 20000000000000000 : ℝ) ≤ (-(10984958909324133836937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6667442693268163 / 20000000000000000 : ℝ) = - (6667442693268163 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6667442693268163 / 5000000000000000 : ℚ)) - (U := (2877984696675866163063 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6667442693268163 / 5000000000000000 : ℝ) ≤ - (2877984696675866163063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (208337694099143 / 625000000000000 : ℝ)) (q := - (6667442693268163 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6667442693268163 / 20000000000000000 : ℚ)) + (r' := (6667442693268163 / 5000000000000000 : ℚ)) + (U := (-(10984958909324133836937 / 10000000000000000000000 : ℚ))) + (U' := (2877984696675866163063 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (208337694099143 / 625000000000000 : ℚ)) + (q := (6667442693268163 / 20000000000000000 : ℚ)) + (U := (-(10984958909324133836937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_3 : Uω (aρ 3) (bρ 3) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -2896,25 +2604,21 @@ lemma U_348_3 : have hlg : Real.log (6571035238209801 / 20000000000000000 : ℝ) ≤ (-(1113060882446734250669 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6571035238209801 / 20000000000000000 : ℝ) = - (6571035238209801 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6571035238209801 / 5000000000000000 : ℚ)) - (U := (273233478153265749331 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6571035238209801 / 5000000000000000 : ℝ) ≤ - (273233478153265749331 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1642195878438963 / 5000000000000000 : ℝ)) (q := - (6571035238209801 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6571035238209801 / 20000000000000000 : ℚ)) + (r' := (6571035238209801 / 5000000000000000 : ℚ)) + (U := (-(1113060882446734250669 / 1000000000000000000000 : ℚ))) + (U' := (273233478153265749331 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (1642195878438963 / 5000000000000000 : ℚ)) + (q := (6571035238209801 / 20000000000000000 : ℚ)) + (U := (-(1113060882446734250669 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_4 : Uω (aρ 4) (bρ 4) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -2922,25 +2626,21 @@ lemma U_348_4 : have hlg : Real.log (200316677013947 / 625000000000000 : ℝ) ≤ (-(5689260749156044347883 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (200316677013947 / 625000000000000 : ℝ) = - (200316677013947 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (200316677013947 / 156250000000000 : ℚ)) - (U := (1242211053843955652117 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (200316677013947 / 156250000000000 : ℝ) ≤ - (1242211053843955652117 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3201784364179429 / 10000000000000000 : ℝ)) (q := - (200316677013947 / 625000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (200316677013947 / 625000000000000 : ℚ)) + (r' := (200316677013947 / 156250000000000 : ℚ)) + (U := (-(5689260749156044347883 / 5000000000000000000000 : ℚ))) + (U' := (1242211053843955652117 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (3201784364179429 / 10000000000000000 : ℚ)) + (q := (200316677013947 / 625000000000000 : ℚ)) + (U := (-(5689260749156044347883 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_5 : Uω (aρ 5) (bρ 5) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -2948,25 +2648,21 @@ lemma U_348_5 : have hlg : Real.log (385189755328009 / 1250000000000000 : ℝ) ≤ (-(470865098371135128527 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (385189755328009 / 1250000000000000 : ℝ) = - (385189755328009 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (385189755328009 / 312500000000000 : ℚ)) - (U := (83652645868864871473 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (385189755328009 / 312500000000000 : ℝ) ≤ - (83652645868864871473 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3072876704316269 / 10000000000000000 : ℝ)) (q := - (385189755328009 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (385189755328009 / 1250000000000000 : ℚ)) + (r' := (385189755328009 / 312500000000000 : ℚ)) + (U := (-(470865098371135128527 / 400000000000000000000 : ℚ))) + (U' := (83652645868864871473 / 400000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (3072876704316269 / 10000000000000000 : ℚ)) + (q := (385189755328009 / 1250000000000000 : ℚ)) + (U := (-(470865098371135128527 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_6 : Uω (aρ 6) (bρ 6) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -2974,25 +2670,21 @@ lemma U_348_6 : have hlg : Real.log (290177292402339 / 1000000000000000 : ℝ) ≤ (-(12372631891703963693447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (290177292402339 / 1000000000000000 : ℝ) = - (290177292402339 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (290177292402339 / 250000000000000 : ℚ)) - (U := (1490311714296036306553 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (290177292402339 / 250000000000000 : ℝ) ≤ - (1490311714296036306553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (576125368450981 / 2000000000000000 : ℝ)) (q := - (290177292402339 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (290177292402339 / 1000000000000000 : ℚ)) + (r' := (290177292402339 / 250000000000000 : ℚ)) + (U := (-(12372631891703963693447 / 10000000000000000000000 : ℚ))) + (U' := (1490311714296036306553 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (576125368450981 / 2000000000000000 : ℚ)) + (q := (290177292402339 / 1000000000000000 : ℚ)) + (U := (-(12372631891703963693447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_7 : Uω (aρ 7) (bρ 7) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -3000,25 +2692,21 @@ lemma U_348_7 : have hlg : Real.log (1325164821681037 / 5000000000000000 : ℝ) ≤ (-(6639505332453721451779 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1325164821681037 / 5000000000000000 : ℝ) = - (1325164821681037 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1325164821681037 / 1250000000000000 : ℚ)) - (U := (291966470546278548221 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1325164821681037 / 1250000000000000 : ℝ) ≤ - (291966470546278548221 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2601401661692273 / 10000000000000000 : ℝ)) (q := - (1325164821681037 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1325164821681037 / 5000000000000000 : ℚ)) + (r' := (1325164821681037 / 1250000000000000 : ℚ)) + (U := (-(6639505332453721451779 / 5000000000000000000000 : ℚ))) + (U' := (291966470546278548221 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (2601401661692273 / 10000000000000000 : ℚ)) + (q := (1325164821681037 / 5000000000000000 : ℚ)) + (U := (-(6639505332453721451779 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_8 : Uω (aρ 8) (bρ 8) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -3026,25 +2714,21 @@ lemma U_348_8 : have hlg : Real.log (1153174392758377 / 5000000000000000 : ℝ) ≤ (-(14669194304964489016403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1153174392758377 / 5000000000000000 : ℝ) = - (1153174392758377 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1153174392758377 / 625000000000000 : ℚ)) - (U := (6125221104035510983597 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1153174392758377 / 625000000000000 : ℝ) ≤ - (6125221104035510983597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2196981597341633 / 10000000000000000 : ℝ)) (q := - (1153174392758377 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1153174392758377 / 5000000000000000 : ℚ)) + (r' := (1153174392758377 / 625000000000000 : ℚ)) + (U := (-(14669194304964489016403 / 10000000000000000000000 : ℚ))) + (U' := (6125221104035510983597 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (2196981597341633 / 10000000000000000 : ℚ)) + (q := (1153174392758377 / 5000000000000000 : ℚ)) + (U := (-(14669194304964489016403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_9 : Uω (aρ 9) (bρ 9) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -3052,25 +2736,21 @@ lemma U_348_9 : have hlg : Real.log (730743044471017 / 4000000000000000 : ℝ) ≤ (-(2124984692148639207169 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (730743044471017 / 4000000000000000 : ℝ) = - (730743044471017 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (730743044471017 / 500000000000000 : ℚ)) - (U := (474317233976360792831 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (730743044471017 / 500000000000000 : ℝ) ≤ - (474317233976360792831 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (157896487702321 / 1000000000000000 : ℝ)) (q := - (730743044471017 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (730743044471017 / 4000000000000000 : ℚ)) + (r' := (730743044471017 / 500000000000000 : ℚ)) + (U := (-(2124984692148639207169 / 1250000000000000000000 : ℚ))) + (U' := (474317233976360792831 / 1250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5475689309243 / 16000000000000 : ℚ)) + (s := (157896487702321 / 1000000000000000 : ℚ)) + (q := (730743044471017 / 4000000000000000 : ℚ)) + (U := (-(2124984692148639207169 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_348_10 : Uω (aρ 10) (bρ 10) (5475689309243 / 16000000000000 : ℝ) ≤ @@ -3196,25 +2876,21 @@ lemma U_349_1 : have hlg : Real.log (6812701725498661 / 20000000000000000 : ℝ) ≤ (-(2692358756001912750639 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6812701725498661 / 20000000000000000 : ℝ) = - (6812701725498661 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6812701725498661 / 5000000000000000 : ℚ)) - (U := (773377145498087249361 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6812701725498661 / 5000000000000000 : ℝ) ≤ - (773377145498087249361 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3406303402023661 / 10000000000000000 : ℝ)) (q := - (6812701725498661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6812701725498661 / 20000000000000000 : ℚ)) + (r' := (6812701725498661 / 5000000000000000 : ℚ)) + (U := (-(2692358756001912750639 / 2500000000000000000000 : ℚ))) + (U' := (773377145498087249361 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (86772388539 / 250000000000 : ℚ)) + (s := (3406303402023661 / 10000000000000000 : ℚ)) + (q := (6812701725498661 / 20000000000000000 : ℚ)) + (U := (-(2692358756001912750639 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_2 : Uω (aρ 2) (bρ 2) (86772388539 / 250000000000 : ℝ) ≤ @@ -3222,25 +2898,21 @@ lemma U_349_2 : have hlg : Real.log (6764631284279317 / 20000000000000000 : ℝ) ≤ (-(2710061290822971316719 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6764631284279317 / 20000000000000000 : ℝ) = - (6764631284279317 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6764631284279317 / 5000000000000000 : ℚ)) - (U := (755674610677028683281 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6764631284279317 / 5000000000000000 : ℝ) ≤ - (755674610677028683281 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3382001973314317 / 10000000000000000 : ℝ)) (q := - (6764631284279317 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6764631284279317 / 20000000000000000 : ℚ)) + (r' := (6764631284279317 / 5000000000000000 : ℚ)) + (U := (-(2710061290822971316719 / 2500000000000000000000 : ℚ))) + (U' := (755674610677028683281 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (86772388539 / 250000000000 : ℚ)) + (s := (3382001973314317 / 10000000000000000 : ℚ)) + (q := (6764631284279317 / 20000000000000000 : ℚ)) + (U := (-(2710061290822971316719 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_3 : Uω (aρ 3) (bρ 3) (86772388539 / 250000000000 : ℝ) ≤ @@ -3248,25 +2920,21 @@ lemma U_349_3 : have hlg : Real.log (1333649502255977 / 4000000000000000 : ℝ) ≤ (-(2745937973915816665167 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1333649502255977 / 4000000000000000 : ℝ) = - (1333649502255977 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1333649502255977 / 1000000000000000 : ℚ)) - (U := (719797927584183334833 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1333649502255977 / 1000000000000000 : ℝ) ≤ - (719797927584183334833 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (666602861332977 / 2000000000000000 : ℝ)) (q := - (1333649502255977 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1333649502255977 / 4000000000000000 : ℚ)) + (r' := (1333649502255977 / 1000000000000000 : ℚ)) + (U := (-(2745937973915816665167 / 2500000000000000000000 : ℚ))) + (U' := (719797927584183334833 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (86772388539 / 250000000000 : ℚ)) + (s := (666602861332977 / 2000000000000000 : ℚ)) + (q := (1333649502255977 / 4000000000000000 : ℚ)) + (U := (-(2745937973915816665167 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_4 : Uω (aρ 4) (bρ 4) (86772388539 / 250000000000 : ℝ) ≤ @@ -3274,25 +2942,21 @@ lemma U_349_4 : have hlg : Real.log (3253705624260179 / 10000000000000000 : ℝ) ≤ (-(1403488191972210064163 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3253705624260179 / 10000000000000000 : ℝ) = - (3253705624260179 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3253705624260179 / 2500000000000000 : ℚ)) - (U := (329379758777789935837 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3253705624260179 / 2500000000000000 : ℝ) ≤ - (329379758777789935837 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1625236112485179 / 5000000000000000 : ℝ)) (q := - (3253705624260179 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3253705624260179 / 10000000000000000 : ℚ)) + (r' := (3253705624260179 / 2500000000000000 : ℚ)) + (U := (-(1403488191972210064163 / 1250000000000000000000 : ℚ))) + (U' := (329379758777789935837 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (86772388539 / 250000000000 : ℚ)) + (s := (1625236112485179 / 5000000000000000 : ℚ)) + (q := (3253705624260179 / 10000000000000000 : ℚ)) + (U := (-(1403488191972210064163 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_5 : Uω (aρ 5) (bρ 5) (86772388539 / 250000000000 : ℝ) ≤ @@ -3300,25 +2964,21 @@ lemma U_349_5 : have hlg : Real.log (626048454777501 / 2000000000000000 : ℝ) ≤ (-(181480419862451201021 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (626048454777501 / 2000000000000000 : ℝ) = - (626048454777501 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (626048454777501 / 500000000000000 : ℚ)) - (U := (35128073981298798979 / 156250000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (626048454777501 / 500000000000000 : ℝ) ≤ - (35128073981298798979 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (312173544356001 / 1000000000000000 : ℝ)) (q := - (626048454777501 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (626048454777501 / 2000000000000000 : ℚ)) + (r' := (626048454777501 / 500000000000000 : ℚ)) + (U := (-(181480419862451201021 / 156250000000000000000 : ℚ))) + (U' := (35128073981298798979 / 156250000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (86772388539 / 250000000000 : ℚ)) + (s := (312173544356001 / 1000000000000000 : ℚ)) + (q := (626048454777501 / 2000000000000000 : ℚ)) + (U := (-(181480419862451201021 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_6 : Uω (aρ 6) (bρ 6) (86772388539 / 250000000000 : ℝ) ≤ @@ -3326,25 +2986,21 @@ lemma U_349_6 : have hlg : Real.log (590142675128467 / 2000000000000000 : ℝ) ≤ (-(488215251642030165167 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (590142675128467 / 2000000000000000 : ℝ) = - (590142675128467 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (590142675128467 / 500000000000000 : ℚ)) - (U := (66302492597969834833 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (590142675128467 / 500000000000000 : ℝ) ≤ - (66302492597969834833 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292991802220967 / 1000000000000000 : ℝ)) (q := - (590142675128467 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (590142675128467 / 2000000000000000 : ℚ)) + (r' := (590142675128467 / 500000000000000 : ℚ)) + (U := (-(488215251642030165167 / 400000000000000000000 : ℚ))) + (U' := (66302492597969834833 / 400000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (86772388539 / 250000000000 : ℚ)) + (s := (292991802220967 / 1000000000000000 : ℚ)) + (q := (590142675128467 / 2000000000000000 : ℚ)) + (U := (-(488215251642030165167 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_7 : Uω (aρ 7) (bρ 7) (86772388539 / 250000000000 : ℝ) ≤ @@ -3352,25 +3008,21 @@ lemma U_349_7 : have hlg : Real.log (1079926478810777 / 4000000000000000 : ℝ) ≤ (-(3273503492390745150533 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1079926478810777 / 4000000000000000 : ℝ) = - (1079926478810777 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1079926478810777 / 1000000000000000 : ℚ)) - (U := (192232409109254849467 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1079926478810777 / 1000000000000000 : ℝ) ≤ - (192232409109254849467 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (530357009147777 / 2000000000000000 : ℝ)) (q := - (1079926478810777 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1079926478810777 / 4000000000000000 : ℚ)) + (r' := (1079926478810777 / 1000000000000000 : ℚ)) + (U := (-(3273503492390745150533 / 2500000000000000000000 : ℚ))) + (U' := (192232409109254849467 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (86772388539 / 250000000000 : ℚ)) + (s := (530357009147777 / 2000000000000000 : ℚ)) + (q := (1079926478810777 / 4000000000000000 : ℚ)) + (U := (-(3273503492390745150533 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_8 : Uω (aρ 8) (bρ 8) (86772388539 / 250000000000 : ℝ) ≤ @@ -3378,25 +3030,21 @@ lemma U_349_8 : have hlg : Real.log (294662813728397 / 1250000000000000 : ℝ) ≤ (-(3612667828037066073951 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (294662813728397 / 1250000000000000 : ℝ) = - (294662813728397 / 156250000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (294662813728397 / 156250000000000 : ℚ)) - (U := (1585936024212933926049 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (294662813728397 / 156250000000000 : ℝ) ≤ - (1585936024212933926049 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (281287415334919 / 1250000000000000 : ℝ)) (q := - (294662813728397 / 1250000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (294662813728397 / 1250000000000000 : ℚ)) + (r' := (294662813728397 / 156250000000000 : ℚ)) + (U := (-(3612667828037066073951 / 2500000000000000000000 : ℚ))) + (U' := (1585936024212933926049 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (86772388539 / 250000000000 : ℚ)) + (s := (281287415334919 / 1250000000000000 : ℚ)) + (q := (294662813728397 / 1250000000000000 : ℚ)) + (U := (-(3612667828037066073951 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_9 : Uω (aρ 9) (bρ 9) (86772388539 / 250000000000 : ℝ) ≤ @@ -3404,25 +3052,21 @@ lemma U_349_9 : have hlg : Real.log (3765629365421181 / 20000000000000000 : ℝ) ≤ (-(16698172633618705145123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3765629365421181 / 20000000000000000 : ℝ) = - (3765629365421181 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3765629365421181 / 2500000000000000 : ℚ)) - (U := (4096242775381294854877 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3765629365421181 / 2500000000000000 : ℝ) ≤ - (4096242775381294854877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1642289296806181 / 10000000000000000 : ℝ)) (q := - (3765629365421181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3765629365421181 / 20000000000000000 : ℚ)) + (r' := (3765629365421181 / 2500000000000000 : ℚ)) + (U := (-(16698172633618705145123 / 10000000000000000000000 : ℚ))) + (U' := (4096242775381294854877 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (86772388539 / 250000000000 : ℚ)) + (s := (1642289296806181 / 10000000000000000 : ℚ)) + (q := (3765629365421181 / 20000000000000000 : ℚ)) + (U := (-(16698172633618705145123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_349_10 : Uω (aρ 10) (bρ 10) (86772388539 / 250000000000 : ℝ) ≤ @@ -3548,25 +3192,21 @@ lemma U_350_1 : have hlg : Real.log (13730051335768191 / 40000000000000000 : ℝ) ≤ (-(10692924948722708581073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13730051335768191 / 40000000000000000 : ℝ) = - (13730051335768191 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13730051335768191 / 10000000000000000 : ℚ)) - (U := (3170018657277291418927 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13730051335768191 / 10000000000000000 : ℝ) ≤ - (3170018657277291418927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1716232867476579 / 5000000000000000 : ℝ)) (q := - (13730051335768191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13730051335768191 / 40000000000000000 : ℚ)) + (r' := (13730051335768191 / 10000000000000000 : ℚ)) + (U := (-(10692924948722708581073 / 10000000000000000000000 : ℚ))) + (U' := (3170018657277291418927 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (1716232867476579 / 5000000000000000 : ℚ)) + (q := (13730051335768191 / 40000000000000000 : ℚ)) + (U := (-(10692924948722708581073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_2 : Uω (aρ 2) (bρ 2) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3574,25 +3214,21 @@ lemma U_350_2 : have hlg : Real.log (13633918637464121 / 40000000000000000 : ℝ) ≤ (-(5381593741458052326591 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13633918637464121 / 40000000000000000 : ℝ) = - (13633918637464121 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13633918637464121 / 10000000000000000 : ℚ)) - (U := (1549878061541947673409 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13633918637464121 / 10000000000000000 : ℝ) ≤ - (1549878061541947673409 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3408168398311123 / 10000000000000000 : ℝ)) (q := - (13633918637464121 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13633918637464121 / 40000000000000000 : ℚ)) + (r' := (13633918637464121 / 10000000000000000 : ℚ)) + (U := (-(5381593741458052326591 / 5000000000000000000000 : ℚ))) + (U' := (1549878061541947673409 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (3408168398311123 / 10000000000000000 : ℚ)) + (q := (13633918637464121 / 40000000000000000 : ℚ)) + (U := (-(5381593741458052326591 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_3 : Uω (aρ 3) (bρ 3) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3600,25 +3236,21 @@ lemma U_350_3 : have hlg : Real.log (13441176022308067 / 40000000000000000 : ℝ) ≤ (-(10905566206672627143071 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13441176022308067 / 40000000000000000 : ℝ) = - (13441176022308067 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13441176022308067 / 10000000000000000 : ℚ)) - (U := (2957377399327372856929 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13441176022308067 / 10000000000000000 : ℝ) ≤ - (2957377399327372856929 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (419899149635387 / 1250000000000000 : ℝ)) (q := - (13441176022308067 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13441176022308067 / 40000000000000000 : ℚ)) + (r' := (13441176022308067 / 10000000000000000 : ℚ)) + (U := (-(10905566206672627143071 / 10000000000000000000000 : ℚ))) + (U' := (2957377399327372856929 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (419899149635387 / 1250000000000000 : ℚ)) + (q := (13441176022308067 / 40000000000000000 : ℚ)) + (U := (-(10905566206672627143071 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_4 : Uω (aρ 4) (bρ 4) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3626,25 +3258,21 @@ lemma U_350_4 : have hlg : Real.log (2623914439939867 / 8000000000000000 : ℝ) ≤ (-(11147742773399472978853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2623914439939867 / 8000000000000000 : ℝ) = - (2623914439939867 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2623914439939867 / 2000000000000000 : ℚ)) - (U := (2715200832600527021147 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2623914439939867 / 2000000000000000 : ℝ) ≤ - (2715200832600527021147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (327668546684373 / 1000000000000000 : ℝ)) (q := - (2623914439939867 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2623914439939867 / 8000000000000000 : ℚ)) + (r' := (2623914439939867 / 2000000000000000 : ℚ)) + (U := (-(11147742773399472978853 / 10000000000000000000000 : ℚ))) + (U' := (2715200832600527021147 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (327668546684373 / 1000000000000000 : ℚ)) + (q := (2623914439939867 / 8000000000000000 : ℚ)) + (U := (-(11147742773399472978853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_5 : Uω (aρ 5) (bρ 5) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3652,25 +3280,21 @@ lemma U_350_5 : have hlg : Real.log (12625898322004909 / 40000000000000000 : ℝ) ≤ (-(5765646633728764278609 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12625898322004909 / 40000000000000000 : ℝ) = - (12625898322004909 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12625898322004909 / 10000000000000000 : ℚ)) - (U := (1165825169271235721391 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12625898322004909 / 10000000000000000 : ℝ) ≤ - (1165825169271235721391 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3148038447331517 / 10000000000000000 : ℝ)) (q := - (12625898322004909 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12625898322004909 / 40000000000000000 : ℚ)) + (r' := (12625898322004909 / 10000000000000000 : ℚ)) + (U := (-(5765646633728764278609 / 5000000000000000000000 : ℚ))) + (U' := (1165825169271235721391 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (3148038447331517 / 10000000000000000 : ℚ)) + (q := (12625898322004909 / 40000000000000000 : ℚ)) + (U := (-(5765646633728764278609 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_6 : Uω (aρ 6) (bρ 6) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3678,25 +3302,21 @@ lemma U_350_6 : have hlg : Real.log (11908236058652281 / 40000000000000000 : ℝ) ≤ (-(12116491871022092607709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11908236058652281 / 40000000000000000 : ℝ) = - (11908236058652281 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11908236058652281 / 10000000000000000 : ℚ)) - (U := (1746451734977907392291 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11908236058652281 / 10000000000000000 : ℝ) ≤ - (1746451734977907392291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2956447690795203 / 10000000000000000 : ℝ)) (q := - (11908236058652281 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11908236058652281 / 40000000000000000 : ℚ)) + (r' := (11908236058652281 / 10000000000000000 : ℚ)) + (U := (-(12116491871022092607709 / 10000000000000000000000 : ℚ))) + (U' := (1746451734977907392291 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (2956447690795203 / 10000000000000000 : ℚ)) + (q := (11908236058652281 / 40000000000000000 : ℚ)) + (U := (-(12116491871022092607709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_7 : Uω (aρ 7) (bρ 7) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3704,25 +3324,21 @@ lemma U_350_7 : have hlg : Real.log (10905787816146419 / 40000000000000000 : ℝ) ≤ (-(12995858129784667405647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10905787816146419 / 40000000000000000 : ℝ) = - (10905787816146419 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10905787816146419 / 10000000000000000 : ℚ)) - (U := (867085476215332594353 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10905787816146419 / 10000000000000000 : ℝ) ≤ - (867085476215332594353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (41857577348473 / 156250000000000 : ℝ)) (q := - (10905787816146419 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10905787816146419 / 40000000000000000 : ℚ)) + (r' := (10905787816146419 / 10000000000000000 : ℚ)) + (U := (-(12995858129784667405647 / 10000000000000000000000 : ℚ))) + (U' := (867085476215332594353 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (41857577348473 / 156250000000000 : ℚ)) + (q := (10905787816146419 / 40000000000000000 : ℚ)) + (U := (-(12995858129784667405647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_8 : Uω (aρ 8) (bρ 8) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3730,24 +3346,21 @@ lemma U_350_8 : have hlg : Real.log (76310181146337 / 320000000000000 : ℝ) ≤ (-(7167573149467358629037 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (76310181146337 / 320000000000000 : ℝ) = (76310181146337 / 40000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (76310181146337 / 40000000000000 : ℚ)) - (U := (3229634555032641370963 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (76310181146337 / 40000000000000 : ℝ) ≤ - (3229634555032641370963 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18231352121721 / 80000000000000 : ℝ)) (q := - (76310181146337 / 320000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (76310181146337 / 320000000000000 : ℚ)) + (r' := (76310181146337 / 40000000000000 : ℚ)) + (U := (-(7167573149467358629037 / 5000000000000000000000 : ℚ))) + (U' := (3229634555032641370963 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (18231352121721 / 80000000000000 : ℚ)) + (q := (76310181146337 / 320000000000000 : ℚ)) + (U := (-(7167573149467358629037 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_9 : Uω (aρ 9) (bρ 9) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3755,25 +3368,21 @@ lemma U_350_9 : have hlg : Real.log (7650957145470101 / 40000000000000000 : ℝ) ≤ (-(8270243481336133218047 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7650957145470101 / 40000000000000000 : ℝ) = - (7650957145470101 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7650957145470101 / 5000000000000000 : ℚ)) - (U := (2126964223163866781953 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7650957145470101 / 5000000000000000 : ℝ) ≤ - (2126964223163866781953 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1675976894664113 / 10000000000000000 : ℝ)) (q := - (7650957145470101 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7650957145470101 / 40000000000000000 : ℚ)) + (r' := (7650957145470101 / 5000000000000000 : ℚ)) + (U := (-(8270243481336133218047 / 5000000000000000000000 : ℚ))) + (U' := (2126964223163866781953 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (1675976894664113 / 10000000000000000 : ℚ)) + (q := (7650957145470101 / 40000000000000000 : ℚ)) + (U := (-(8270243481336133218047 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_10 : Uω (aρ 10) (bρ 10) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3781,26 +3390,21 @@ lemma U_350_10 : have hlg : Real.log (4126711735908559 / 40000000000000000 : ℝ) ≤ (-(2271398553081343851221 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4126711735908559 / 40000000000000000 : ℝ) = - (4126711735908559 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4126711735908559 / 2500000000000000 : ℚ)) - (U := (501190168118656148779 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4126711735908559 / 2500000000000000 : ℝ) ≤ - (501190168118656148779 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (151206611689171 / 5000000000000000 : ℝ)) (q := - (4126711735908559 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4126711735908559 / 40000000000000000 : ℚ)) + (r' := (4126711735908559 / 2500000000000000 : ℚ)) + (U := (-(2271398553081343851221 / 1000000000000000000000 : ℚ))) + (U' := (501190168118656148779 / 1000000000000000000000 : ℚ)) + 4 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11190582883251 / 32000000000000 : ℚ)) + (s := (151206611689171 / 5000000000000000 : ℚ)) + (q := (4126711735908559 / 40000000000000000 : ℚ)) + (U := (-(2271398553081343851221 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_350_11 : Uω (aρ 11) (bρ 11) (11190582883251 / 32000000000000 : ℝ) ≤ @@ -3923,25 +3527,21 @@ lemma U_351_1 : have hlg : Real.log (6917349599324441 / 20000000000000000 : ℝ) ≤ (-(2123399165295955899713 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6917349599324441 / 20000000000000000 : ℝ) = - (6917349599324441 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6917349599324441 / 5000000000000000 : ℚ)) - (U := (649189555904044100287 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6917349599324441 / 5000000000000000 : ℝ) ≤ - (649189555904044100287 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1729314028468783 / 5000000000000000 : ℝ)) (q := - (6917349599324441 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6917349599324441 / 20000000000000000 : ℚ)) + (r' := (6917349599324441 / 5000000000000000 : ℚ)) + (U := (-(2123399165295955899713 / 2000000000000000000000 : ℚ))) + (U' := (649189555904044100287 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (1729314028468783 / 5000000000000000 : ℚ)) + (q := (6917349599324441 / 20000000000000000 : ℚ)) + (U := (-(2123399165295955899713 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_2 : Uω (aρ 2) (bρ 2) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -3949,25 +3549,21 @@ lemma U_351_2 : have hlg : Real.log (1373857455962341 / 4000000000000000 : ℝ) ≤ (-(2671679790056744699741 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1373857455962341 / 4000000000000000 : ℝ) = - (1373857455962341 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1373857455962341 / 1000000000000000 : ℚ)) - (U := (794056111443255300259 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1373857455962341 / 1000000000000000 : ℝ) ≤ - (794056111443255300259 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (343433474993483 / 1000000000000000 : ℝ)) (q := - (1373857455962341 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1373857455962341 / 4000000000000000 : ℚ)) + (r' := (1373857455962341 / 1000000000000000 : ℚ)) + (U := (-(2671679790056744699741 / 2500000000000000000000 : ℚ))) + (U' := (794056111443255300259 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (343433474993483 / 1000000000000000 : ℚ)) + (q := (1373857455962341 / 4000000000000000 : ℚ)) + (U := (-(2671679790056744699741 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_3 : Uω (aρ 3) (bρ 3) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -3975,25 +3571,21 @@ lemma U_351_3 : have hlg : Real.log (3386464121925491 / 10000000000000000 : ℝ) ≤ (-(10827987472984737147193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3386464121925491 / 10000000000000000 : ℝ) = - (3386464121925491 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3386464121925491 / 2500000000000000 : ℚ)) - (U := (3034956133015262852807 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3386464121925491 / 2500000000000000 : ℝ) ≤ - (3034956133015262852807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3385371820324107 / 10000000000000000 : ℝ)) (q := - (3386464121925491 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3386464121925491 / 10000000000000000 : ℚ)) + (r' := (3386464121925491 / 2500000000000000 : ℚ)) + (U := (-(10827987472984737147193 / 10000000000000000000000 : ℚ))) + (U' := (3034956133015262852807 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (3385371820324107 / 10000000000000000 : ℚ)) + (q := (3386464121925491 / 10000000000000000 : ℚ)) + (U := (-(10827987472984737147193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_4 : Uω (aρ 4) (bρ 4) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4001,25 +3593,21 @@ lemma U_351_4 : have hlg : Real.log (826520016553917 / 2500000000000000 : ℝ) ≤ (-(5534109374562723863797 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (826520016553917 / 2500000000000000 : ℝ) = - (826520016553917 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (826520016553917 / 625000000000000 : ℚ)) - (U := (1397362428437276136203 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (826520016553917 / 625000000000000 : ℝ) ≤ - (1397362428437276136203 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3302897889969461 / 10000000000000000 : ℝ)) (q := - (826520016553917 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (826520016553917 / 2500000000000000 : ℚ)) + (r' := (826520016553917 / 625000000000000 : ℚ)) + (U := (-(5534109374562723863797 / 5000000000000000000000 : ℚ))) + (U' := (1397362428437276136203 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (3302897889969461 / 10000000000000000 : ℚ)) + (q := (826520016553917 / 2500000000000000 : ℚ)) + (U := (-(5534109374562723863797 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_5 : Uω (aρ 5) (bρ 5) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4027,25 +3615,21 @@ lemma U_351_5 : have hlg : Real.log (3182705718651991 / 10000000000000000 : ℝ) ≤ (-(2862133506329783265521 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3182705718651991 / 10000000000000000 : ℝ) = - (3182705718651991 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3182705718651991 / 2500000000000000 : ℚ)) - (U := (603602395170216734479 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3182705718651991 / 2500000000000000 : ℝ) ≤ - (603602395170216734479 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3174339114177107 / 10000000000000000 : ℝ)) (q := - (3182705718651991 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3182705718651991 / 10000000000000000 : ℚ)) + (r' := (3182705718651991 / 2500000000000000 : ℚ)) + (U := (-(2862133506329783265521 / 2500000000000000000000 : ℚ))) + (U' := (603602395170216734479 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (3174339114177107 / 10000000000000000 : ℚ)) + (q := (3182705718651991 / 10000000000000000 : ℚ)) + (U := (-(2862133506329783265521 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_6 : Uω (aρ 6) (bρ 6) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4053,25 +3637,21 @@ lemma U_351_6 : have hlg : Real.log (300340140298413 / 1000000000000000 : ℝ) ≤ (-(6014198225391302158967 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (300340140298413 / 1000000000000000 : ℝ) = - (300340140298413 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (300340140298413 / 250000000000000 : ℚ)) - (U := (917273577608697841033 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (300340140298413 / 250000000000000 : ℝ) ≤ - (917273577608697841033 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (596594171596277 / 2000000000000000 : ℝ)) (q := - (300340140298413 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (300340140298413 / 1000000000000000 : ℚ)) + (r' := (300340140298413 / 250000000000000 : ℚ)) + (U := (-(6014198225391302158967 / 5000000000000000000000 : ℚ))) + (U' := (917273577608697841033 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (596594171596277 / 2000000000000000 : ℚ)) + (q := (300340140298413 / 1000000000000000 : ℚ)) + (U := (-(6014198225391302158967 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_7 : Uω (aρ 7) (bρ 7) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4079,25 +3659,21 @@ lemma U_351_7 : have hlg : Real.log (5506136953700713 / 20000000000000000 : ℝ) ≤ (-(50385507542380392039 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5506136953700713 / 20000000000000000 : ℝ) = - (5506136953700713 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5506136953700713 / 5000000000000000 : ℚ)) - (U := (3766615918557107961 / 39062500000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5506136953700713 / 5000000000000000 : ℝ) ≤ - (3766615918557107961 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1352983193236919 / 5000000000000000 : ℝ)) (q := - (5506136953700713 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5506136953700713 / 20000000000000000 : ℚ)) + (r' := (5506136953700713 / 5000000000000000 : ℚ)) + (U := (-(50385507542380392039 / 39062500000000000000 : ℚ))) + (U' := (3766615918557107961 / 39062500000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (1352983193236919 / 5000000000000000 : ℚ)) + (q := (5506136953700713 / 20000000000000000 : ℚ)) + (U := (-(50385507542380392039 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_8 : Uω (aρ 8) (bρ 8) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4105,25 +3681,21 @@ lemma U_351_8 : have hlg : Real.log (4824109267652769 / 20000000000000000 : ℝ) ≤ (-(2844212325531341812721 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4824109267652769 / 20000000000000000 : ℝ) = - (4824109267652769 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4824109267652769 / 2500000000000000 : ℚ)) - (U := (1314670756268658187279 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4824109267652769 / 2500000000000000 : ℝ) ≤ - (1314670756268658187279 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1153740175882947 / 5000000000000000 : ℝ)) (q := - (4824109267652769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4824109267652769 / 20000000000000000 : ℚ)) + (r' := (4824109267652769 / 2500000000000000 : ℚ)) + (U := (-(2844212325531341812721 / 2000000000000000000000 : ℚ))) + (U' := (1314670756268658187279 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (1153740175882947 / 5000000000000000 : ℚ)) + (q := (4824109267652769 / 20000000000000000 : ℚ)) + (U := (-(2844212325531341812721 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_9 : Uω (aρ 9) (bρ 9) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4131,25 +3703,21 @@ lemma U_351_9 : have hlg : Real.log (3885064301949891 / 20000000000000000 : ℝ) ≤ (-(4096481844382657276603 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3885064301949891 / 20000000000000000 : ℝ) = - (3885064301949891 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3885064301949891 / 2500000000000000 : ℚ)) - (U := (1102122007867342723397 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3885064301949891 / 2500000000000000 : ℝ) ≤ - (1102122007867342723397 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (213675126802877 / 1250000000000000 : ℝ)) (q := - (3885064301949891 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3885064301949891 / 20000000000000000 : ℚ)) + (r' := (3885064301949891 / 2500000000000000 : ℚ)) + (U := (-(4096481844382657276603 / 2500000000000000000000 : ℚ))) + (U' := (1102122007867342723397 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (213675126802877 / 1250000000000000 : ℚ)) + (q := (3885064301949891 / 20000000000000000 : ℚ)) + (U := (-(4096481844382657276603 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_10 : Uω (aρ 10) (bρ 10) (1127430003351 / 3200000000000 : ℝ) ≤ @@ -4157,25 +3725,21 @@ lemma U_351_10 : have hlg : Real.log (221637849617413 / 2000000000000000 : ℝ) ≤ (-(219985771669146987571 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (221637849617413 / 2000000000000000 : ℝ) = - (221637849617413 / 125000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (221637849617413 / 125000000000000 : ℚ)) - (U := (57273100450853012429 / 100000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (221637849617413 / 125000000000000 : ℝ) ≤ - (57273100450853012429 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85854848428451 / 2000000000000000 : ℝ)) (q := - (221637849617413 / 2000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (221637849617413 / 2000000000000000 : ℚ)) + (r' := (221637849617413 / 125000000000000 : ℚ)) + (U := (-(219985771669146987571 / 100000000000000000000 : ℚ))) + (U' := (57273100450853012429 / 100000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1127430003351 / 3200000000000 : ℚ)) + (s := (85854848428451 / 2000000000000000 : ℚ)) + (q := (221637849617413 / 2000000000000000 : ℚ)) + (U := (-(219985771669146987571 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_351_11 : Uω (aρ 11) (bρ 11) (1127430003351 / 3200000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U29.lean b/LeanPool/Zeta5Irrational/Table/U29.lean index e35c4edf29..5c99be25ca 100644 --- a/LeanPool/Zeta5Irrational/Table/U29.lean +++ b/LeanPool/Zeta5Irrational/Table/U29.lean @@ -24,25 +24,21 @@ lemma U_352_1 : have hlg : Real.log (13939347040132423 / 40000000000000000 : ℝ) ≤ (-(10541638900952844384301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13939347040132423 / 40000000000000000 : ℝ) = - (13939347040132423 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13939347040132423 / 10000000000000000 : ℚ)) - (U := (3321304705047155615699 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13939347040132423 / 10000000000000000 : ℝ) ≤ - (3321304705047155615699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3484790368223399 / 10000000000000000 : ℝ)) (q := - (13939347040132423 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13939347040132423 / 40000000000000000 : ℚ)) + (r' := (13939347040132423 / 10000000000000000 : ℚ)) + (U := (-(10541638900952844384301 / 10000000000000000000000 : ℚ))) + (U' := (3321304705047155615699 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (3484790368223399 / 10000000000000000 : ℚ)) + (q := (13939347040132423 / 40000000000000000 : ℚ)) + (U := (-(10541638900952844384301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_2 : Uω (aρ 2) (bρ 2) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_352_2 : have hlg : Real.log (13843230338365333 / 40000000000000000 : ℝ) ≤ (-(1061083124688201051313 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13843230338365333 / 40000000000000000 : ℝ) = - (13843230338365333 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13843230338365333 / 10000000000000000 : ℚ)) - (U := (325211235911798948687 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13843230338365333 / 10000000000000000 : ℝ) ≤ - (325211235911798948687 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1730250514924927 / 5000000000000000 : ℝ)) (q := - (13843230338365333 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13843230338365333 / 40000000000000000 : ℚ)) + (r' := (13843230338365333 / 10000000000000000 : ℚ)) + (U := (-(1061083124688201051313 / 1000000000000000000000 : ℚ))) + (U' := (325211235911798948687 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (1730250514924927 / 5000000000000000 : ℚ)) + (q := (13843230338365333 / 40000000000000000 : ℚ)) + (U := (-(1061083124688201051313 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_3 : Uω (aρ 3) (bρ 3) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_352_3 : have hlg : Real.log (2730107286208521 / 8000000000000000 : ℝ) ≤ (-(2150201267515562619751 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2730107286208521 / 8000000000000000 : ℝ) = - (2730107286208521 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2730107286208521 / 2000000000000000 : ℚ)) - (U := (622387453684437380249 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2730107286208521 / 2000000000000000 : ℝ) ≤ - (622387453684437380249 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (341155018253849 / 1000000000000000 : ℝ)) (q := - (2730107286208521 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2730107286208521 / 8000000000000000 : ℚ)) + (r' := (2730107286208521 / 2000000000000000 : ℚ)) + (U := (-(2150201267515562619751 / 2000000000000000000000 : ℚ))) + (U' := (622387453684437380249 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (341155018253849 / 1000000000000000 : ℚ)) + (q := (2730107286208521 / 8000000000000000 : ℚ)) + (U := (-(2150201267515562619751 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_4 : Uω (aρ 4) (bρ 4) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_352_4 : have hlg : Real.log (13329066731210191 / 40000000000000000 : ℝ) ≤ (-(5494661672584152532607 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13329066731210191 / 40000000000000000 : ℝ) = - (13329066731210191 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13329066731210191 / 10000000000000000 : ℚ)) - (U := (1436810130415847467393 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13329066731210191 / 10000000000000000 : ℝ) ≤ - (1436810130415847467393 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3329109513687283 / 10000000000000000 : ℝ)) (q := - (13329066731210191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13329066731210191 / 40000000000000000 : ℚ)) + (r' := (13329066731210191 / 10000000000000000 : ℚ)) + (U := (-(5494661672584152532607 / 5000000000000000000000 : ℚ))) + (U' := (1436810130415847467393 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (3329109513687283 / 10000000000000000 : ℚ)) + (q := (13329066731210191 / 40000000000000000 : ℚ)) + (U := (-(5494661672584152532607 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_5 : Uω (aρ 5) (bρ 5) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_352_5 : have hlg : Real.log (12835742868578809 / 40000000000000000 : ℝ) ≤ (-(5683228812996067015517 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12835742868578809 / 40000000000000000 : ℝ) = - (12835742868578809 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12835742868578809 / 10000000000000000 : ℚ)) - (U := (1248242990003932984483 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12835742868578809 / 10000000000000000 : ℝ) ≤ - (1248242990003932984483 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100019921928331 / 312500000000000 : ℝ)) (q := - (12835742868578809 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12835742868578809 / 40000000000000000 : ℚ)) + (r' := (12835742868578809 / 10000000000000000 : ℚ)) + (U := (-(5683228812996067015517 / 5000000000000000000000 : ℚ))) + (U' := (1248242990003932984483 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (100019921928331 / 312500000000000 : ℚ)) + (q := (12835742868578809 / 40000000000000000 : ℚ)) + (U := (-(5683228812996067015517 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_6 : Uω (aρ 6) (bρ 6) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_352_6 : have hlg : Real.log (12118962506210219 / 40000000000000000 : ℝ) ≤ (-(5970540392073785020387 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12118962506210219 / 40000000000000000 : ℝ) = - (12118962506210219 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12118962506210219 / 10000000000000000 : ℚ)) - (U := (960931410926214979613 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12118962506210219 / 10000000000000000 : ℝ) ≤ - (960931410926214979613 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3009487695662297 / 10000000000000000 : ℝ)) (q := - (12118962506210219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12118962506210219 / 40000000000000000 : ℚ)) + (r' := (12118962506210219 / 10000000000000000 : ℚ)) + (U := (-(5970540392073785020387 / 5000000000000000000000 : ℚ))) + (U' := (960931410926214979613 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (3009487695662297 / 10000000000000000 : ℚ)) + (q := (12118962506210219 / 40000000000000000 : ℚ)) + (U := (-(5970540392073785020387 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_7 : Uω (aρ 7) (bρ 7) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_352_7 : have hlg : Real.log (11118724159886299 / 40000000000000000 : ℝ) ≤ (-(6401244525886062483541 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11118724159886299 / 40000000000000000 : ℝ) = - (11118724159886299 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11118724159886299 / 10000000000000000 : ℚ)) - (U := (530227277113937516459 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11118724159886299 / 10000000000000000 : ℝ) ≤ - (530227277113937516459 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2733029903260337 / 10000000000000000 : ℝ)) (q := - (11118724159886299 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11118724159886299 / 40000000000000000 : ℚ)) + (r' := (11118724159886299 / 10000000000000000 : ℚ)) + (U := (-(6401244525886062483541 / 5000000000000000000000 : ℚ))) + (U' := (530227277113937516459 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (2733029903260337 / 10000000000000000 : ℚ)) + (q := (11118724159886299 / 40000000000000000 : ℚ)) + (U := (-(6401244525886062483541 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_8 : Uω (aρ 8) (bρ 8) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_352_8 : have hlg : Real.log (9757551996349087 / 40000000000000000 : ℝ) ≤ (-(2821675808831815775213 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9757551996349087 / 40000000000000000 : ℝ) = - (9757551996349087 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9757551996349087 / 5000000000000000 : ℚ)) - (U := (1337207272968184224787 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9757551996349087 / 5000000000000000 : ℝ) ≤ - (1337207272968184224787 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2335985472831731 / 10000000000000000 : ℝ)) (q := - (9757551996349087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9757551996349087 / 40000000000000000 : ℚ)) + (r' := (9757551996349087 / 5000000000000000 : ℚ)) + (U := (-(2821675808831815775213 / 2000000000000000000000 : ℚ))) + (U' := (1337207272968184224787 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (2335985472831731 / 10000000000000000 : ℚ)) + (q := (9757551996349087 / 40000000000000000 : ℚ)) + (U := (-(2821675808831815775213 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_9 : Uω (aρ 9) (bρ 9) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_352_9 : have hlg : Real.log (7888803428680491 / 40000000000000000 : ℝ) ≤ (-(4058587466679611612501 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7888803428680491 / 40000000000000000 : ℝ) = - (7888803428680491 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7888803428680491 / 5000000000000000 : ℚ)) - (U := (1140016385570388387499 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7888803428680491 / 5000000000000000 : ℝ) ≤ - (1140016385570388387499 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1742576817357433 / 10000000000000000 : ℝ)) (q := - (7888803428680491 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7888803428680491 / 40000000000000000 : ℚ)) + (r' := (7888803428680491 / 5000000000000000 : ℚ)) + (U := (-(4058587466679611612501 / 2500000000000000000000 : ℚ))) + (U' := (1140016385570388387499 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (1742576817357433 / 10000000000000000 : ℚ)) + (q := (7888803428680491 / 40000000000000000 : ℚ)) + (U := (-(4058587466679611612501 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_10 : Uω (aρ 10) (bρ 10) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_352_10 : have hlg : Real.log (4681932791743299 / 40000000000000000 : ℝ) ≤ (-(10725842193563147263599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (4681932791743299 / 40000000000000000 : ℝ) = - (4681932791743299 / 2500000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4681932791743299 / 2500000000000000 : ℚ)) - (U := (3137101412436852736401 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4681932791743299 / 2500000000000000 : ℝ) ≤ - (3137101412436852736401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (527700532383837 / 10000000000000000 : ℝ)) (q := - (4681932791743299 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4681932791743299 / 40000000000000000 : ℚ)) + (r' := (4681932791743299 / 2500000000000000 : ℚ)) + (U := (-(10725842193563147263599 / 5000000000000000000000 : ℚ))) + (U' := (3137101412436852736401 / 5000000000000000000000 : ℚ)) + 4 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11358017183769 / 32000000000000 : ℚ)) + (s := (527700532383837 / 10000000000000000 : ℚ)) + (q := (4681932791743299 / 40000000000000000 : ℚ)) + (U := (-(10725842193563147263599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_352_11 : Uω (aρ 11) (bρ 11) (11358017183769 / 32000000000000 : ℝ) ≤ @@ -400,25 +359,21 @@ lemma U_353_1 : have hlg : Real.log (27983341906000601 / 80000000000000000 : ℝ) ≤ (-(10504172329495590335047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27983341906000601 / 80000000000000000 : ℝ) = - (27983341906000601 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27983341906000601 / 20000000000000000 : ℚ)) - (U := (3358771276504409664953 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27983341906000601 / 20000000000000000 : ℝ) ≤ - (3358771276504409664953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3497871519929369 / 10000000000000000 : ℝ)) (q := - (27983341906000601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27983341906000601 / 80000000000000000 : ℚ)) + (r' := (27983341906000601 / 20000000000000000 : ℚ)) + (U := (-(10504172329495590335047 / 10000000000000000000000 : ℚ))) + (U' := (3358771276504409664953 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (3497871519929369 / 10000000000000000 : ℚ)) + (q := (27983341906000601 / 80000000000000000 : ℚ)) + (U := (-(10504172329495590335047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_2 : Uω (aρ 2) (bρ 2) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -426,25 +381,21 @@ lemma U_353_2 : have hlg : Real.log (27791116349935233 / 80000000000000000 : ℝ) ≤ (-(10573102202839460368983 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27791116349935233 / 80000000000000000 : ℝ) = - (27791116349935233 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27791116349935233 / 20000000000000000 : ℚ)) - (U := (3289841403160539631017 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27791116349935233 / 20000000000000000 : ℝ) ≤ - (3289841403160539631017 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3473584143423027 / 10000000000000000 : ℝ)) (q := - (27791116349935233 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27791116349935233 / 80000000000000000 : ℚ)) + (r' := (27791116349935233 / 20000000000000000 : ℚ)) + (U := (-(10573102202839460368983 / 10000000000000000000000 : ℚ))) + (U' := (3289841403160539631017 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (3473584143423027 / 10000000000000000 : ℚ)) + (q := (27791116349935233 / 80000000000000000 : ℚ)) + (U := (-(10573102202839460368983 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_3 : Uω (aρ 3) (bρ 3) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -452,25 +403,21 @@ lemma U_353_3 : have hlg : Real.log (27405752421368369 / 80000000000000000 : ℝ) ≤ (-(5356368502045391193103 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27405752421368369 / 80000000000000000 : ℝ) = - (27405752421368369 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27405752421368369 / 20000000000000000 : ℚ)) - (U := (1575103300954608806897 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27405752421368369 / 20000000000000000 : ℝ) ≤ - (1575103300954608806897 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3424639267631311 / 10000000000000000 : ℝ)) (q := - (27405752421368369 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27405752421368369 / 80000000000000000 : ℚ)) + (r' := (27405752421368369 / 20000000000000000 : ℚ)) + (U := (-(5356368502045391193103 / 5000000000000000000000 : ℚ))) + (U' := (1575103300954608806897 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (3424639267631311 / 10000000000000000 : ℚ)) + (q := (27405752421368369 / 80000000000000000 : ℚ)) + (U := (-(5356368502045391193103 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_4 : Uω (aρ 4) (bρ 4) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -478,25 +425,21 @@ lemma U_353_4 : have hlg : Real.log (5352575750633297 / 16000000000000000 : ℝ) ≤ (-(684381767471699544513 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5352575750633297 / 16000000000000000 : ℝ) = - (5352575750633297 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5352575750633297 / 4000000000000000 : ℚ)) - (U := (182052207903300455487 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5352575750633297 / 4000000000000000 : ℝ) ≤ - (182052207903300455487 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (41777687895573 / 125000000000000 : ℝ)) (q := - (5352575750633297 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5352575750633297 / 16000000000000000 : ℚ)) + (r' := (5352575750633297 / 4000000000000000 : ℚ)) + (U := (-(684381767471699544513 / 625000000000000000000 : ℚ))) + (U' := (182052207903300455487 / 625000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (41777687895573 / 125000000000000 : ℚ)) + (q := (5352575750633297 / 16000000000000000 : ℚ)) + (U := (-(684381767471699544513 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_5 : Uω (aρ 5) (bρ 5) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -504,25 +447,21 @@ lemma U_353_5 : have hlg : Real.log (25776402382098673 / 80000000000000000 : ℝ) ≤ (-(11325671971142371422989 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25776402382098673 / 80000000000000000 : ℝ) = - (25776402382098673 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25776402382098673 / 20000000000000000 : ℚ)) - (U := (2537271634857628577011 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25776402382098673 / 20000000000000000 : ℝ) ≤ - (2537271634857628577011 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3213785858213887 / 10000000000000000 : ℝ)) (q := - (25776402382098673 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25776402382098673 / 80000000000000000 : ℚ)) + (r' := (25776402382098673 / 20000000000000000 : ℚ)) + (U := (-(11325671971142371422989 / 10000000000000000000000 : ℚ))) + (U' := (2537271634857628577011 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (3213785858213887 / 10000000000000000 : ℚ)) + (q := (25776402382098673 / 80000000000000000 : ℚ)) + (U := (-(11325671971142371422989 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_6 : Uω (aρ 6) (bρ 6) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -530,25 +469,21 @@ lemma U_353_6 : have hlg : Real.log (24343272620661961 / 80000000000000000 : ℝ) ≤ (-(11897711012095434041723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24343272620661961 / 80000000000000000 : ℝ) = - (24343272620661961 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24343272620661961 / 20000000000000000 : ℚ)) - (U := (1965232593904565958277 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24343272620661961 / 20000000000000000 : ℝ) ≤ - (1965232593904565958277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3022743792994709 / 10000000000000000 : ℝ)) (q := - (24343272620661961 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24343272620661961 / 80000000000000000 : ℚ)) + (r' := (24343272620661961 / 20000000000000000 : ℚ)) + (U := (-(11897711012095434041723 / 10000000000000000000000 : ℚ))) + (U' := (1965232593904565958277 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (3022743792994709 / 10000000000000000 : ℚ)) + (q := (24343272620661961 / 80000000000000000 : ℚ)) + (U := (-(11897711012095434041723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_7 : Uω (aρ 7) (bρ 7) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -556,25 +491,21 @@ lemma U_353_7 : have hlg : Real.log (22343872355375393 / 80000000000000000 : ℝ) ≤ (-(6377372591149652653381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22343872355375393 / 80000000000000000 : ℝ) = - (22343872355375393 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22343872355375393 / 20000000000000000 : ℚ)) - (U := (554099211850347346619 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22343872355375393 / 20000000000000000 : ℝ) ≤ - (554099211850347346619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2746555107433067 / 10000000000000000 : ℝ)) (q := - (22343872355375393 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22343872355375393 / 80000000000000000 : ℚ)) + (r' := (22343872355375393 / 20000000000000000 : ℚ)) + (U := (-(6377372591149652653381 / 5000000000000000000000 : ℚ))) + (U' := (554099211850347346619 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (2746555107433067 / 10000000000000000 : ℚ)) + (q := (22343872355375393 / 80000000000000000 : ℚ)) + (U := (-(6377372591149652653381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_8 : Uω (aρ 8) (bρ 8) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -582,25 +513,21 @@ lemma U_353_8 : have hlg : Real.log (19624355687976101 / 80000000000000000 : ℝ) ≤ (-(878284501219037432057 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19624355687976101 / 80000000000000000 : ℝ) = - (19624355687976101 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19624355687976101 / 10000000000000000 : ℚ)) - (U := (421366461843462567943 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19624355687976101 / 10000000000000000 : ℝ) ≤ - (421366461843462567943 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (587554397980811 / 2500000000000000 : ℝ)) (q := - (19624355687976101 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19624355687976101 / 80000000000000000 : ℚ)) + (r' := (19624355687976101 / 10000000000000000 : ℚ)) + (U := (-(878284501219037432057 / 625000000000000000000 : ℚ))) + (U' := (421366461843462567943 / 625000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (587554397980811 / 2500000000000000 : ℚ)) + (q := (19624355687976101 / 80000000000000000 : ℚ)) + (U := (-(878284501219037432057 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_9 : Uω (aρ 9) (bρ 9) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -608,25 +535,21 @@ lemma U_353_9 : have hlg : Real.log (15895926785369481 / 80000000000000000 : ℝ) ≤ (-(8079818672537926407997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15895926785369481 / 80000000000000000 : ℝ) = - (15895926785369481 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15895926785369481 / 10000000000000000 : ℚ)) - (U := (2317389031962073592003 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15895926785369481 / 10000000000000000 : ℝ) ≤ - (2317389031962073592003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1759075994631589 / 10000000000000000 : ℝ)) (q := - (15895926785369481 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15895926785369481 / 80000000000000000 : ℚ)) + (r' := (15895926785369481 / 10000000000000000 : ℚ)) + (U := (-(8079818672537926407997 / 5000000000000000000000 : ℚ))) + (U' := (2317389031962073592003 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (1759075994631589 / 10000000000000000 : ℚ)) + (q := (15895926785369481 / 80000000000000000 : ℚ)) + (U := (-(8079818672537926407997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_10 : Uω (aρ 10) (bρ 10) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -634,26 +557,21 @@ lemma U_353_10 : have hlg : Real.log (1917902491631817 / 16000000000000000 : ℝ) ≤ (-(10606782922981723231029 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (1917902491631817 / 16000000000000000 : ℝ) = - (1917902491631817 / 1000000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1917902491631817 / 1000000000000000 : ℚ)) - (U := (3256160683018276768971 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1917902491631817 / 1000000000000000 : ℝ) ≤ - (3256160683018276768971 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57103144632399 / 1000000000000000 : ℝ)) (q := - (1917902491631817 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1917902491631817 / 16000000000000000 : ℚ)) + (r' := (1917902491631817 / 1000000000000000 : ℚ)) + (U := (-(10606782922981723231029 / 5000000000000000000000 : ℚ))) + (U' := (3256160683018276768971 / 5000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22799751517797 / 64000000000000 : ℚ)) + (s := (57103144632399 / 1000000000000000 : ℚ)) + (q := (1917902491631817 / 16000000000000000 : ℚ)) + (U := (-(10606782922981723231029 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_353_11 : Uω (aρ 11) (bρ 11) (22799751517797 / 64000000000000 : ℝ) ≤ @@ -775,25 +693,21 @@ lemma U_354_1 : have hlg : Real.log (7021997430348573 / 20000000000000000 : ℝ) ≤ (-(5233422806154407011667 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7021997430348573 / 20000000000000000 : ℝ) = - (7021997430348573 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7021997430348573 / 5000000000000000 : ℚ)) - (U := (1698048996845592988333 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7021997430348573 / 5000000000000000 : ℝ) ≤ - (1698048996845592988333 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3510952669049823 / 10000000000000000 : ℝ)) (q := - (7021997430348573 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7021997430348573 / 20000000000000000 : ℚ)) + (r' := (7021997430348573 / 5000000000000000 : ℚ)) + (U := (-(5233422806154407011667 / 5000000000000000000000 : ℚ))) + (U' := (1698048996845592988333 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (3510952669049823 / 10000000000000000 : ℚ)) + (q := (7021997430348573 / 20000000000000000 : ℚ)) + (U := (-(5233422806154407011667 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_2 : Uω (aρ 2) (bρ 2) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -801,25 +715,21 @@ lemma U_354_2 : have hlg : Real.log (1743485747114849 / 5000000000000000 : ℝ) ≤ (-(2107102999367314674609 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1743485747114849 / 5000000000000000 : ℝ) = - (1743485747114849 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1743485747114849 / 1250000000000000 : ℚ)) - (U := (665485721832685325391 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1743485747114849 / 1250000000000000 : ℝ) ≤ - (665485721832685325391 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1743333619835323 / 5000000000000000 : ℝ)) (q := - (1743485747114849 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1743485747114849 / 5000000000000000 : ℚ)) + (r' := (1743485747114849 / 1250000000000000 : ℚ)) + (U := (-(2107102999367314674609 / 2000000000000000000000 : ℚ))) + (U' := (665485721832685325391 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (1743333619835323 / 5000000000000000 : ℚ)) + (q := (1743485747114849 / 5000000000000000 : ℚ)) + (U := (-(2107102999367314674609 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_3 : Uω (aρ 3) (bρ 3) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -827,25 +737,21 @@ lemma U_354_3 : have hlg : Real.log (1719401983032041 / 5000000000000000 : ℝ) ≤ (-(2668653414571848144461 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1719401983032041 / 5000000000000000 : ℝ) = - (1719401983032041 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1719401983032041 / 1250000000000000 : ℚ)) - (U := (797082486928151855539 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1719401983032041 / 1250000000000000 : ℝ) ≤ - (797082486928151855539 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1718864144844707 / 5000000000000000 : ℝ)) (q := - (1719401983032041 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1719401983032041 / 5000000000000000 : ℚ)) + (r' := (1719401983032041 / 1250000000000000 : ℚ)) + (U := (-(2668653414571848144461 / 2500000000000000000000 : ℚ))) + (U' := (797082486928151855539 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (1718864144844707 / 5000000000000000 : ℚ)) + (q := (1719401983032041 / 5000000000000000 : ℚ)) + (U := (-(2668653414571848144461 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_4 : Uω (aρ 4) (bρ 4) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -853,25 +759,21 @@ lemma U_354_4 : have hlg : Real.log (671690581810577 / 2000000000000000 : ℝ) ≤ (-(218220933654013876573 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (671690581810577 / 2000000000000000 : ℝ) = - (671690581810577 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (671690581810577 / 500000000000000 : ℚ)) - (U := (59037938465986123427 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (671690581810577 / 500000000000000 : ℝ) ≤ - (59037938465986123427 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (167766017836601 / 500000000000000 : ℝ)) (q := - (671690581810577 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (671690581810577 / 2000000000000000 : ℚ)) + (r' := (671690581810577 / 500000000000000 : ℚ)) + (U := (-(218220933654013876573 / 200000000000000000000 : ℚ))) + (U' := (59037938465986123427 / 200000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (167766017836601 / 500000000000000 : ℚ)) + (q := (671690581810577 / 2000000000000000 : ℚ)) + (U := (-(218220933654013876573 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_5 : Uω (aρ 5) (bρ 5) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -879,25 +781,21 @@ lemma U_354_5 : have hlg : Real.log (3235164603842813 / 10000000000000000 : ℝ) ≤ (-(5642526418193389259393 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3235164603842813 / 10000000000000000 : ℝ) = - (3235164603842813 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3235164603842813 / 2500000000000000 : ℚ)) - (U := (1288945384806610740607 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3235164603842813 / 2500000000000000 : ℝ) ≤ - (1288945384806610740607 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (806733416411719 / 2500000000000000 : ℝ)) (q := - (3235164603842813 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3235164603842813 / 10000000000000000 : ℚ)) + (r' := (3235164603842813 / 2500000000000000 : ℚ)) + (U := (-(5642526418193389259393 / 5000000000000000000000 : ℚ))) + (U' := (1288945384806610740607 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (806733416411719 / 2500000000000000 : ℚ)) + (q := (3235164603842813 / 10000000000000000 : ℚ)) + (U := (-(5642526418193389259393 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_6 : Uω (aρ 6) (bρ 6) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -905,25 +803,21 @@ lemma U_354_6 : have hlg : Real.log (1528038384146267 / 5000000000000000 : ℝ) ≤ (-(2963632752427058012139 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1528038384146267 / 5000000000000000 : ℝ) = - (1528038384146267 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1528038384146267 / 1250000000000000 : ℚ)) - (U := (502103149072941987861 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1528038384146267 / 1250000000000000 : ℝ) ≤ - (502103149072941987861 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1517999184843159 / 5000000000000000 : ℝ)) (q := - (1528038384146267 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1528038384146267 / 5000000000000000 : ℚ)) + (r' := (1528038384146267 / 1250000000000000 : ℚ)) + (U := (-(2963632752427058012139 / 2500000000000000000000 : ℚ))) + (U' := (502103149072941987861 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (1517999184843159 / 5000000000000000 : ℚ)) + (q := (1528038384146267 / 5000000000000000 : ℚ)) + (U := (-(2963632752427058012139 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_7 : Uω (aρ 7) (bρ 7) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -931,25 +825,21 @@ lemma U_354_7 : have hlg : Real.log (5612569813918199 / 20000000000000000 : ℝ) ≤ (-(12707235810376217255869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5612569813918199 / 20000000000000000 : ℝ) = - (5612569813918199 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5612569813918199 / 5000000000000000 : ℚ)) - (U := (1155707795623782744131 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5612569813918199 / 5000000000000000 : ℝ) ≤ - (1155707795623782744131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2760076027779449 / 10000000000000000 : ℝ)) (q := - (5612569813918199 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5612569813918199 / 20000000000000000 : ℚ)) + (r' := (5612569813918199 / 5000000000000000 : ℚ)) + (U := (-(12707235810376217255869 / 10000000000000000000000 : ℚ))) + (U' := (1155707795623782744131 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (2760076027779449 / 10000000000000000 : ℚ)) + (q := (5612569813918199 / 20000000000000000 : ℚ)) + (U := (-(12707235810376217255869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_8 : Uω (aρ 8) (bρ 8) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -957,24 +847,21 @@ lemma U_354_8 : have hlg : Real.log (123334713659413 / 500000000000000 : ℝ) ≤ (-(13997061889017450904763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (123334713659413 / 500000000000000 : ℝ) = (123334713659413 / 62500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123334713659413 / 62500000000000 : ℚ)) - (U := (6797353519982549095237 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (123334713659413 / 62500000000000 : ℝ) ≤ - (6797353519982549095237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (236443641157777 / 1000000000000000 : ℝ)) (q := - (123334713659413 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123334713659413 / 500000000000000 : ℚ)) + (r' := (123334713659413 / 62500000000000 : ℚ)) + (U := (-(13997061889017450904763 / 10000000000000000000000 : ℚ))) + (U' := (6797353519982549095237 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (236443641157777 / 1000000000000000 : ℚ)) + (q := (123334713659413 / 500000000000000 : ℚ)) + (U := (-(13997061889017450904763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_9 : Uω (aρ 9) (bρ 9) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -982,23 +869,21 @@ lemma U_354_9 : have hlg : Real.log (3127738069893 / 15625000000000 : ℝ) ≤ (-(4021405282280517378607 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show (3127738069893 / 15625000000000 : ℝ) = (3127738069893 / 1953125000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3127738069893 / 1953125000000 : ℚ)) - (U := (1177198569969482621393 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3127738069893 / 1953125000000 : ℝ) ≤ - (1177198569969482621393 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177551822302429 / 1000000000000000 : ℝ)) (q := - (3127738069893 / 15625000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3127738069893 / 15625000000000 : ℚ)) + (r' := (3127738069893 / 1953125000000 : ℚ)) + (U := (-(4021405282280517378607 / 2500000000000000000000 : ℚ))) + (U' := (1177198569969482621393 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (177551822302429 / 1000000000000000 : ℚ)) + (q := (3127738069893 / 15625000000000 : ℚ)) + (U := (-(4021405282280517378607 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_10 : Uω (aρ 10) (bρ 10) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -1006,26 +891,21 @@ lemma U_354_10 : have hlg : Real.log (2451005913054431 / 20000000000000000 : ℝ) ≤ (-(2099233755464236526453 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 4 - (show - (2451005913054431 / 20000000000000000 : ℝ) = - (2451005913054431 / 1250000000000000 : ℝ) / 2 ^ 4 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2451005913054431 / 1250000000000000 : ℚ)) - (U := (673354965735763473547 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2451005913054431 / 1250000000000000 : ℝ) ≤ - (673354965735763473547 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (611578440110681 / 10000000000000000 : ℝ)) (q := - (2451005913054431 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2451005913054431 / 20000000000000000 : ℚ)) + (r' := (2451005913054431 / 1250000000000000 : ℚ)) + (U := (-(2099233755464236526453 / 1000000000000000000000 : ℚ))) + (U' := (673354965735763473547 / 1000000000000000000000 : ℚ)) + 4 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2860433583507 / 8000000000000 : ℚ)) + (s := (611578440110681 / 10000000000000000 : ℚ)) + (q := (2451005913054431 / 20000000000000000 : ℚ)) + (U := (-(2099233755464236526453 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_354_11 : Uω (aρ 11) (bρ 11) (2860433583507 / 8000000000000 : ℝ) ≤ @@ -1146,25 +1026,21 @@ lemma U_355_1 : have hlg : Real.log (28192637526561087 / 80000000000000000 : ℝ) ≤ (-(10429657709158020939677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28192637526561087 / 80000000000000000 : ℝ) = - (28192637526561087 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28192637526561087 / 20000000000000000 : ℚ)) - (U := (3433285896841979060323 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28192637526561087 / 20000000000000000 : ℝ) ≤ - (3433285896841979060323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3524033815613553 / 10000000000000000 : ℝ)) (q := - (28192637526561087 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28192637526561087 / 80000000000000000 : ℚ)) + (r' := (28192637526561087 / 20000000000000000 : ℚ)) + (U := (-(10429657709158020939677 / 10000000000000000000000 : ℚ))) + (U' := (3433285896841979060323 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (3524033815613553 / 10000000000000000 : ℚ)) + (q := (28192637526561087 / 80000000000000000 : ℚ)) + (U := (-(10429657709158020939677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_2 : Uω (aρ 2) (bρ 2) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1172,25 +1048,21 @@ lemma U_355_2 : have hlg : Real.log (28000427489214943 / 80000000000000000 : ℝ) ≤ (-(10498068566233714828257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28000427489214943 / 80000000000000000 : ℝ) = - (28000427489214943 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28000427489214943 / 20000000000000000 : ℚ)) - (U := (3364875039766285171743 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28000427489214943 / 20000000000000000 : ℝ) ≤ - (3364875039766285171743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3499750318787017 / 10000000000000000 : ℝ)) (q := - (28000427489214943 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28000427489214943 / 80000000000000000 : ℚ)) + (r' := (28000427489214943 / 20000000000000000 : ℚ)) + (U := (-(10498068566233714828257 / 10000000000000000000000 : ℚ))) + (U' := (3364875039766285171743 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (3499750318787017 / 10000000000000000 : ℚ)) + (q := (28000427489214943 / 80000000000000000 : ℚ)) + (U := (-(10498068566233714828257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_3 : Uω (aρ 3) (bρ 3) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1198,25 +1070,21 @@ lemma U_355_3 : have hlg : Real.log (1104604431455487 / 3200000000000000 : ℝ) ≤ (-(10636635189896886432221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1104604431455487 / 3200000000000000 : ℝ) = - (1104604431455487 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1104604431455487 / 800000000000000 : ℚ)) - (U := (3226308416103113567779 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1104604431455487 / 800000000000000 : ℝ) ≤ - (3226308416103113567779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138032689977203 / 400000000000000 : ℝ)) (q := - (1104604431455487 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1104604431455487 / 3200000000000000 : ℚ)) + (r' := (1104604431455487 / 800000000000000 : ℚ)) + (U := (-(10636635189896886432221 / 10000000000000000000000 : ℚ))) + (U' := (3226308416103113567779 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (138032689977203 / 400000000000000 : ℚ)) + (q := (1104604431455487 / 3200000000000000 : ℚ)) + (U := (-(10636635189896886432221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_4 : Uω (aρ 4) (bρ 4) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1224,25 +1092,21 @@ lemma U_355_4 : have hlg : Real.log (26972367029194927 / 80000000000000000 : ℝ) ≤ (-(10872137355885766455087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26972367029194927 / 80000000000000000 : ℝ) = - (26972367029194927 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26972367029194927 / 20000000000000000 : ℚ)) - (U := (2990806250114233544913 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26972367029194927 / 20000000000000000 : ℝ) ≤ - (2990806250114233544913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3368425491197013 / 10000000000000000 : ℝ)) (q := - (26972367029194927 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26972367029194927 / 80000000000000000 : ℚ)) + (r' := (26972367029194927 / 20000000000000000 : ℚ)) + (U := (-(10872137355885766455087 / 10000000000000000000000 : ℚ))) + (U' := (2990806250114233544913 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (3368425491197013 / 10000000000000000 : ℚ)) + (q := (26972367029194927 / 80000000000000000 : ℚ)) + (U := (-(10872137355885766455087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_5 : Uω (aρ 5) (bρ 5) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1250,25 +1114,21 @@ lemma U_355_5 : have hlg : Real.log (25986229109825939 / 80000000000000000 : ℝ) ≤ (-(11244598860684962943507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25986229109825939 / 80000000000000000 : ℝ) = - (25986229109825939 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25986229109825939 / 20000000000000000 : ℚ)) - (U := (2618344745315037056493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25986229109825939 / 20000000000000000 : ℝ) ≤ - (2618344745315037056493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1620040465344883 / 5000000000000000 : ℝ)) (q := - (25986229109825939 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25986229109825939 / 80000000000000000 : ℚ)) + (r' := (25986229109825939 / 20000000000000000 : ℚ)) + (U := (-(11244598860684962943507 / 10000000000000000000000 : ℚ))) + (U' := (2618344745315037056493 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (1620040465344883 / 5000000000000000 : ℚ)) + (q := (25986229109825939 / 80000000000000000 : ℚ)) + (U := (-(11244598860684962943507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_6 : Uω (aρ 6) (bρ 6) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1276,25 +1136,21 @@ lemma U_355_6 : have hlg : Real.log (24553949668774967 / 80000000000000000 : ℝ) ≤ (-(11811539102151936781149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24553949668774967 / 80000000000000000 : ℝ) = - (24553949668774967 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24553949668774967 / 20000000000000000 : ℚ)) - (U := (2051404503848063218851 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24553949668774967 / 20000000000000000 : ℝ) ≤ - (2051404503848063218851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3049251445567023 / 10000000000000000 : ℝ)) (q := - (24553949668774967 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24553949668774967 / 80000000000000000 : ℚ)) + (r' := (24553949668774967 / 20000000000000000 : ℚ)) + (U := (-(11811539102151936781149 / 10000000000000000000000 : ℚ))) + (U' := (2051404503848063218851 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (3049251445567023 / 10000000000000000 : ℚ)) + (q := (24553949668774967 / 80000000000000000 : ℚ)) + (U := (-(11811539102151936781149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_7 : Uω (aρ 7) (bρ 7) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1302,25 +1158,21 @@ lemma U_355_7 : have hlg : Real.log (22556669271262279 / 80000000000000000 : ℝ) ≤ (-(12659958571089790164417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22556669271262279 / 80000000000000000 : ℝ) = - (22556669271262279 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22556669271262279 / 20000000000000000 : ℚ)) - (U := (1202985034910209835583 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22556669271262279 / 20000000000000000 : ℝ) ≤ - (1202985034910209835583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2773592726948851 / 10000000000000000 : ℝ)) (q := - (22556669271262279 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22556669271262279 / 80000000000000000 : ℚ)) + (r' := (22556669271262279 / 20000000000000000 : ℚ)) + (U := (-(12659958571089790164417 / 10000000000000000000000 : ℚ))) + (U' := (1202985034910209835583 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (2773592726948851 / 10000000000000000 : ℚ)) + (q := (22556669271262279 / 80000000000000000 : ℚ)) + (U := (-(12659958571089790164417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_8 : Uω (aρ 8) (bρ 8) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1328,25 +1180,21 @@ lemma U_355_8 : have hlg : Real.log (19842700439289387 / 80000000000000000 : ℝ) ≤ (-(435684509515087757189 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19842700439289387 / 80000000000000000 : ℝ) = - (19842700439289387 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19842700439289387 / 10000000000000000 : ℚ)) - (U := (214140972016162242811 / 312500000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19842700439289387 / 10000000000000000 : ℝ) ≤ - (214140972016162242811 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (594660542573907 / 2500000000000000 : ℝ)) (q := - (19842700439289387 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19842700439289387 / 80000000000000000 : ℚ)) + (r' := (19842700439289387 / 10000000000000000 : ℚ)) + (U := (-(435684509515087757189 / 312500000000000000000 : ℚ))) + (U' := (214140972016162242811 / 312500000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (594660542573907 / 2500000000000000 : ℚ)) + (q := (19842700439289387 / 80000000000000000 : ℚ)) + (U := (-(435684509515087757189 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_9 : Uω (aρ 9) (bρ 9) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1354,25 +1202,21 @@ lemma U_355_9 : have hlg : Real.log (16131889525455431 / 80000000000000000 : ℝ) ≤ (-(16012286050680742624031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16131889525455431 / 80000000000000000 : ℝ) = - (16131889525455431 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16131889525455431 / 10000000000000000 : ℚ)) - (U := (4782129358319257375969 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16131889525455431 / 10000000000000000 : ℝ) ≤ - (4782129358319257375969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1791905070197139 / 10000000000000000 : ℝ)) (q := - (16131889525455431 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16131889525455431 / 80000000000000000 : ℚ)) + (r' := (16131889525455431 / 10000000000000000 : ℚ)) + (U := (-(16012286050680742624031 / 10000000000000000000000 : ℚ))) + (U' := (4782129358319257375969 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (1791905070197139 / 10000000000000000 : ℚ)) + (q := (16131889525455431 / 80000000000000000 : ℚ)) + (U := (-(16012286050680742624031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_10 : Uω (aρ 10) (bρ 10) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1380,26 +1224,21 @@ lemma U_355_10 : have hlg : Real.log (10009484372873479 / 80000000000000000 : ℝ) ≤ (-(20784935530951146153959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10009484372873479 / 80000000000000000 : ℝ) = - (10009484372873479 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10009484372873479 / 10000000000000000 : ℚ)) - (U := (9479878048853846041 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (10009484372873479 / 10000000000000000 : ℝ) ≤ - (9479878048853846041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (649862815546651 / 10000000000000000 : ℝ)) (q := - (10009484372873479 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10009484372873479 / 80000000000000000 : ℚ)) + (r' := (10009484372873479 / 10000000000000000 : ℚ)) + (U := (-(20784935530951146153959 / 10000000000000000000000 : ℚ))) + (U' := (9479878048853846041 / 10000000000000000000000 : ℚ)) + 3 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4593437163663 / 12800000000000 : ℚ)) + (s := (649862815546651 / 10000000000000000 : ℚ)) + (q := (10009484372873479 / 80000000000000000 : ℚ)) + (U := (-(20784935530951146153959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_355_11 : Uω (aρ 11) (bρ 11) (4593437163663 / 12800000000000 : ℝ) ≤ @@ -1522,25 +1361,21 @@ lemma U_356_1 : have hlg : Real.log (14148642660807227 / 40000000000000000 : ℝ) ≤ (-(1299075948921488108637 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14148642660807227 / 40000000000000000 : ℝ) = - (14148642660807227 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14148642660807227 / 10000000000000000 : ℚ)) - (U := (433792001828511891363 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14148642660807227 / 10000000000000000 : ℝ) ≤ - (433792001828511891363 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1768557479824463 / 5000000000000000 : ℝ)) (q := - (14148642660807227 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14148642660807227 / 40000000000000000 : ℚ)) + (r' := (14148642660807227 / 10000000000000000 : ℚ)) + (U := (-(1299075948921488108637 / 1250000000000000000000 : ℚ))) + (U' := (433792001828511891363 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (1768557479824463 / 5000000000000000 : ℚ)) + (q := (14148642660807227 / 40000000000000000 : ℚ)) + (U := (-(1299075948921488108637 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_2 : Uω (aρ 2) (bρ 2) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1548,25 +1383,21 @@ lemma U_356_2 : have hlg : Real.log (14052541478416471 / 40000000000000000 : ℝ) ≤ (-(1046076186029057426927 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14052541478416471 / 40000000000000000 : ℝ) = - (14052541478416471 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14052541478416471 / 10000000000000000 : ℚ)) - (U := (340218174570942573073 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14052541478416471 / 10000000000000000 : ℝ) ≤ - (340218174570942573073 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (878208345240887 / 2500000000000000 : ℝ)) (q := - (14052541478416471 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14052541478416471 / 40000000000000000 : ℚ)) + (r' := (14052541478416471 / 10000000000000000 : ℚ)) + (U := (-(1046076186029057426927 / 1000000000000000000000 : ℚ))) + (U' := (340218174570942573073 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (878208345240887 / 2500000000000000 : ℚ)) + (q := (14052541478416471 / 40000000000000000 : ℚ)) + (U := (-(1046076186029057426927 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_3 : Uω (aρ 3) (bρ 3) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1574,25 +1405,21 @@ lemma U_356_3 : have hlg : Real.log (554395791956353 / 1600000000000000 : ℝ) ≤ (-(662425031329633293843 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (554395791956353 / 1600000000000000 : ℝ) = - (554395791956353 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (554395791956353 / 400000000000000 : ℚ)) - (U := (204008944045366706157 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (554395791956353 / 400000000000000 : ℝ) ≤ - (204008944045366706157 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138556245902389 / 400000000000000 : ℝ)) (q := - (554395791956353 / 1600000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (554395791956353 / 1600000000000000 : ℚ)) + (r' := (554395791956353 / 400000000000000 : ℚ)) + (U := (-(662425031329633293843 / 625000000000000000000 : ℚ))) + (U' := (204008944045366706157 / 625000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (138556245902389 / 400000000000000 : ℚ)) + (q := (554395791956353 / 1600000000000000 : ℚ)) + (U := (-(662425031329633293843 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_4 : Uω (aρ 4) (bρ 4) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1600,25 +1427,21 @@ lemma U_356_4 : have hlg : Real.log (13538555016173533 / 40000000000000000 : ℝ) ≤ (-(5416689557187702177793 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13538555016173533 / 40000000000000000 : ℝ) = - (13538555016173533 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13538555016173533 / 10000000000000000 : ℚ)) - (U := (1514782245812297822207 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13538555016173533 / 10000000000000000 : ℝ) ≤ - (1514782245812297822207 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3381530437257079 / 10000000000000000 : ℝ)) (q := - (13538555016173533 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13538555016173533 / 40000000000000000 : ℚ)) + (r' := (13538555016173533 / 10000000000000000 : ℚ)) + (U := (-(5416689557187702177793 / 5000000000000000000000 : ℚ))) + (U' := (1514782245812297822207 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (3381530437257079 / 10000000000000000 : ℚ)) + (q := (13538555016173533 / 40000000000000000 : ℚ)) + (U := (-(5416689557187702177793 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_5 : Uω (aρ 5) (bρ 5) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1626,25 +1449,21 @@ lemma U_356_5 : have hlg : Real.log (13045569622826253 / 40000000000000000 : ℝ) ≤ (-(2240861739939409583837 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13045569622826253 / 40000000000000000 : ℝ) = - (13045569622826253 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13045569622826253 / 10000000000000000 : ℚ)) - (U := (531726981260590416163 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13045569622826253 / 10000000000000000 : ℝ) ≤ - (531726981260590416163 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3253227659918439 / 10000000000000000 : ℝ)) (q := - (13045569622826253 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13045569622826253 / 40000000000000000 : ℚ)) + (r' := (13045569622826253 / 10000000000000000 : ℚ)) + (U := (-(2240861739939409583837 / 2000000000000000000000 : ℚ))) + (U' := (531726981260590416163 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (3253227659918439 / 10000000000000000 : ℚ)) + (q := (13045569622826253 / 40000000000000000 : ℚ)) + (U := (-(2240861739939409583837 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_6 : Uω (aρ 6) (bρ 6) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1652,25 +1471,21 @@ lemma U_356_6 : have hlg : Real.log (12329639632951857 / 40000000000000000 : ℝ) ≤ (-(5884366818469516185671 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12329639632951857 / 40000000000000000 : ℝ) = - (12329639632951857 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12329639632951857 / 10000000000000000 : ℚ)) - (U := (1047104984530483814329 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12329639632951857 / 10000000000000000 : ℝ) ≤ - (1047104984530483814329 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3062503040121241 / 10000000000000000 : ℝ)) (q := - (12329639632951857 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12329639632951857 / 40000000000000000 : ℚ)) + (r' := (12329639632951857 / 10000000000000000 : ℚ)) + (U := (-(5884366818469516185671 / 5000000000000000000000 : ℚ))) + (U' := (1047104984530483814329 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (3062503040121241 / 10000000000000000 : ℚ)) + (q := (12329639632951857 / 40000000000000000 : ℚ)) + (U := (-(5884366818469516185671 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_7 : Uω (aρ 7) (bρ 7) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1678,25 +1493,21 @@ lemma U_356_7 : have hlg : Real.log (11331521323901253 / 40000000000000000 : ℝ) ≤ (-(6306455568069282526061 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11331521323901253 / 40000000000000000 : ℝ) = - (11331521323901253 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11331521323901253 / 10000000000000000 : ℚ)) - (U := (625016234930717473939 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11331521323901253 / 10000000000000000 : ℝ) ≤ - (625016234930717473939 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2787105266355939 / 10000000000000000 : ℝ)) (q := - (11331521323901253 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11331521323901253 / 40000000000000000 : ℚ)) + (r' := (11331521323901253 / 10000000000000000 : ℚ)) + (U := (-(6306455568069282526061 / 5000000000000000000000 : ℚ))) + (U' := (625016234930717473939 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (2787105266355939 / 10000000000000000 : ℚ)) + (q := (11331521323901253 / 40000000000000000 : ℚ)) + (U := (-(6306455568069282526061 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_8 : Uω (aρ 8) (bρ 8) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1704,25 +1515,21 @@ lemma U_356_8 : have hlg : Real.log (9975897689903237 / 40000000000000000 : ℝ) ≤ (-(13887075006321262224287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9975897689903237 / 40000000000000000 : ℝ) = - (9975897689903237 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9975897689903237 / 5000000000000000 : ℚ)) - (U := (6907340402678737775713 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9975897689903237 / 5000000000000000 : ℝ) ≤ - (6907340402678737775713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2392835100696931 / 10000000000000000 : ℝ)) (q := - (9975897689903237 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9975897689903237 / 40000000000000000 : ℚ)) + (r' := (9975897689903237 / 5000000000000000 : ℚ)) + (U := (-(13887075006321262224287 / 10000000000000000000000 : ℚ))) + (U' := (6907340402678737775713 / 10000000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (2392835100696931 / 10000000000000000 : ℚ)) + (q := (9975897689903237 / 40000000000000000 : ℚ)) + (U := (-(13887075006321262224287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_9 : Uω (aρ 9) (bρ 9) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1730,25 +1537,21 @@ lemma U_356_9 : have hlg : Real.log (8124772315387749 / 40000000000000000 : ℝ) ≤ (-(15939617482324508012211 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8124772315387749 / 40000000000000000 : ℝ) = - (8124772315387749 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8124772315387749 / 5000000000000000 : ℚ)) - (U := (4854797926675491987789 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8124772315387749 / 5000000000000000 : ℝ) ≤ - (4854797926675491987789 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1808238041799187 / 10000000000000000 : ℝ)) (q := - (8124772315387749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8124772315387749 / 40000000000000000 : ℚ)) + (r' := (8124772315387749 / 5000000000000000 : ℚ)) + (U := (-(15939617482324508012211 / 10000000000000000000000 : ℚ))) + (U' := (4854797926675491987789 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (1808238041799187 / 10000000000000000 : ℚ)) + (q := (8124772315387749 / 40000000000000000 : ℚ)) + (U := (-(15939617482324508012211 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_10 : Uω (aρ 10) (bρ 10) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1756,26 +1559,21 @@ lemma U_356_10 : have hlg : Real.log (1020740972669511 / 8000000000000000 : ℝ) ≤ (-(102945636677137892163 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1020740972669511 / 8000000000000000 : ℝ) = - (1020740972669511 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1020740972669511 / 1000000000000000 : ℚ)) - (U := (1026440367862107837 / 50000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1020740972669511 / 1000000000000000 : ℝ) ≤ - (1026440367862107837 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68626334927409 / 1000000000000000 : ℝ)) (q := - (1020740972669511 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1020740972669511 / 8000000000000000 : ℚ)) + (r' := (1020740972669511 / 1000000000000000 : ℚ)) + (U := (-(102945636677137892163 / 50000000000000000000 : ℚ))) + (U' := (1026440367862107837 / 50000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11525451484287 / 32000000000000 : ℚ)) + (s := (68626334927409 / 1000000000000000 : ℚ)) + (q := (1020740972669511 / 8000000000000000 : ℚ)) + (U := (-(102945636677137892163 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_356_11 : Uω (aρ 11) (bρ 11) (11525451484287 / 32000000000000 : ℝ) ≤ @@ -1896,25 +1694,21 @@ lemma U_357_1 : have hlg : Real.log (5680386621333237 / 16000000000000000 : ℝ) ≤ (-(5177847120835798780771 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5680386621333237 / 16000000000000000 : ℝ) = - (5680386621333237 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5680386621333237 / 4000000000000000 : ℚ)) - (U := (1753624682164201219229 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5680386621333237 / 4000000000000000 : ℝ) ≤ - (1753624682164201219229 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (355019610118389 / 1000000000000000 : ℝ)) (q := - (5680386621333237 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5680386621333237 / 16000000000000000 : ℚ)) + (r' := (5680386621333237 / 4000000000000000 : ℚ)) + (U := (-(5177847120835798780771 / 5000000000000000000000 : ℚ))) + (U' := (1753624682164201219229 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (355019610118389 / 1000000000000000 : ℚ)) + (q := (5680386621333237 / 16000000000000000 : ℚ)) + (U := (-(5177847120835798780771 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_2 : Uω (aρ 2) (bρ 2) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -1922,25 +1716,21 @@ lemma U_357_2 : have hlg : Real.log (28209738357445857 / 80000000000000000 : ℝ) ≤ (-(10423593839989125093553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28209738357445857 / 80000000000000000 : ℝ) = - (28209738357445857 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28209738357445857 / 20000000000000000 : ℚ)) - (U := (3439349766010874906447 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28209738357445857 / 20000000000000000 : ℝ) ≤ - (3439349766010874906447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (440739553298601 / 1250000000000000 : ℝ)) (q := - (28209738357445857 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28209738357445857 / 80000000000000000 : ℚ)) + (r' := (28209738357445857 / 20000000000000000 : ℚ)) + (U := (-(10423593839989125093553 / 10000000000000000000000 : ℚ))) + (U' := (3439349766010874906447 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (440739553298601 / 1250000000000000 : ℚ)) + (q := (28209738357445857 / 80000000000000000 : ℚ)) + (U := (-(10423593839989125093553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_3 : Uω (aρ 3) (bρ 3) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -1948,25 +1738,21 @@ lemma U_357_3 : have hlg : Real.log (5564893633117449 / 16000000000000000 : ℝ) ≤ (-(2640277126802199692219 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5564893633117449 / 16000000000000000 : ℝ) = - (5564893633117449 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5564893633117449 / 4000000000000000 : ℚ)) - (U := (825458774697800307781 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5564893633117449 / 4000000000000000 : ℝ) ≤ - (825458774697800307781 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (695398996954831 / 2000000000000000 : ℝ)) (q := - (5564893633117449 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5564893633117449 / 16000000000000000 : ℚ)) + (r' := (5564893633117449 / 4000000000000000 : ℚ)) + (U := (-(2640277126802199692219 / 2500000000000000000000 : ℚ))) + (U' := (825458774697800307781 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (695398996954831 / 2000000000000000 : ℚ)) + (q := (5564893633117449 / 16000000000000000 : ℚ)) + (U := (-(2640277126802199692219 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_4 : Uω (aρ 4) (bρ 4) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -1974,25 +1760,21 @@ lemma U_357_4 : have hlg : Real.log (27181852290607513 / 80000000000000000 : ℝ) ≤ (-(1349346348405073664153 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27181852290607513 / 80000000000000000 : ℝ) = - (27181852290607513 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27181852290607513 / 20000000000000000 : ℚ)) - (U := (383521602344926335847 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27181852290607513 / 20000000000000000 : ℝ) ≤ - (383521602344926335847 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1697317598547111 / 5000000000000000 : ℝ)) (q := - (27181852290607513 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27181852290607513 / 80000000000000000 : ℚ)) + (r' := (27181852290607513 / 20000000000000000 : ℚ)) + (U := (-(1349346348405073664153 / 1250000000000000000000 : ℚ))) + (U' := (383521602344926335847 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (1697317598547111 / 5000000000000000 : ℚ)) + (q := (27181852290607513 / 80000000000000000 : ℚ)) + (U := (-(1349346348405073664153 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_5 : Uω (aρ 5) (bρ 5) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2000,25 +1782,21 @@ lemma U_357_5 : have hlg : Real.log (26196047264101189 / 80000000000000000 : ℝ) ≤ (-(11164181025510258405207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26196047264101189 / 80000000000000000 : ℝ) = - (26196047264101189 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26196047264101189 / 20000000000000000 : ℚ)) - (U := (2698762580489741594793 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26196047264101189 / 20000000000000000 : ℝ) ≤ - (2698762580489741594793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3266373859802641 / 10000000000000000 : ℝ)) (q := - (26196047264101189 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26196047264101189 / 80000000000000000 : ℚ)) + (r' := (26196047264101189 / 20000000000000000 : ℚ)) + (U := (-(11164181025510258405207 / 10000000000000000000000 : ℚ))) + (U' := (2698762580489741594793 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (3266373859802641 / 10000000000000000 : ℚ)) + (q := (26196047264101189 / 80000000000000000 : ℚ)) + (U := (-(11164181025510258405207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_6 : Uω (aρ 6) (bρ 6) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2026,25 +1804,21 @@ lemma U_357_6 : have hlg : Real.log (24764603014312389 / 80000000000000000 : ℝ) ≤ (-(5863056491764085571929 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24764603014312389 / 80000000000000000 : ℝ) = - (24764603014312389 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24764603014312389 / 20000000000000000 : ℚ)) - (U := (1068415311235914428071 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24764603014312389 / 20000000000000000 : ℝ) ≤ - (1068415311235914428071 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3075753172495441 / 10000000000000000 : ℝ)) (q := - (24764603014312389 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24764603014312389 / 80000000000000000 : ℚ)) + (r' := (24764603014312389 / 20000000000000000 : ℚ)) + (U := (-(5863056491764085571929 / 5000000000000000000000 : ℚ))) + (U' := (1068415311235914428071 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (3075753172495441 / 10000000000000000 : ℚ)) + (q := (24764603014312389 / 80000000000000000 : ℚ)) + (U := (-(5863056491764085571929 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_7 : Uω (aρ 7) (bρ 7) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2052,25 +1826,21 @@ lemma U_357_7 : have hlg : Real.log (22769399626136197 / 80000000000000000 : ℝ) ≤ (-(12566091213062274615969 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22769399626136197 / 80000000000000000 : ℝ) = - (22769399626136197 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22769399626136197 / 20000000000000000 : ℚ)) - (U := (1296852392937725384031 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22769399626136197 / 20000000000000000 : ℝ) ≤ - (1296852392937725384031 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2800613706211393 / 10000000000000000 : ℝ)) (q := - (22769399626136197 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22769399626136197 / 80000000000000000 : ℚ)) + (r' := (22769399626136197 / 20000000000000000 : ℚ)) + (U := (-(12566091213062274615969 / 10000000000000000000000 : ℚ))) + (U' := (1296852392937725384031 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (2800613706211393 / 10000000000000000 : ℚ)) + (q := (22769399626136197 / 80000000000000000 : ℚ)) + (U := (-(12566091213062274615969 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_8 : Uω (aρ 8) (bρ 8) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2078,25 +1848,21 @@ lemma U_357_8 : have hlg : Real.log (20060839914761097 / 80000000000000000 : ℝ) ≤ (-(13832569823690590154751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20060839914761097 / 80000000000000000 : ℝ) = - (20060839914761097 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20060839914761097 / 20000000000000000 : ℚ)) - (U := (30373782309409845249 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20060839914761097 / 20000000000000000 : ℝ) ≤ - (30373782309409845249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1203507714853809 / 5000000000000000 : ℝ)) (q := - (20060839914761097 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20060839914761097 / 80000000000000000 : ℚ)) + (r' := (20060839914761097 / 20000000000000000 : ℚ)) + (U := (-(13832569823690590154751 / 10000000000000000000000 : ℚ))) + (U' := (30373782309409845249 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (1203507714853809 / 5000000000000000 : ℚ)) + (q := (20060839914761097 / 80000000000000000 : ℚ)) + (U := (-(13832569823690590154751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_9 : Uω (aρ 9) (bρ 9) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2104,25 +1870,21 @@ lemma U_357_9 : have hlg : Real.log (3273398004260377 / 16000000000000000 : ℝ) ≤ (-(7933800655272450017953 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3273398004260377 / 16000000000000000 : ℝ) = - (3273398004260377 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3273398004260377 / 2000000000000000 : ℚ)) - (U := (2463407049227549982047 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3273398004260377 / 2000000000000000 : ℝ) ≤ - (2463407049227549982047 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (364903716940563 / 2000000000000000 : ℝ)) (q := - (3273398004260377 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3273398004260377 / 16000000000000000 : ℚ)) + (r' := (3273398004260377 / 2000000000000000 : ℚ)) + (U := (-(7933800655272450017953 / 5000000000000000000000 : ℚ))) + (U' := (2463407049227549982047 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (364903716940563 / 2000000000000000 : ℚ)) + (q := (3273398004260377 / 16000000000000000 : ℚ)) + (U := (-(7933800655272450017953 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_10 : Uω (aρ 10) (bρ 10) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2130,26 +1892,21 @@ lemma U_357_10 : have hlg : Real.log (2079788226324381 / 16000000000000000 : ℝ) ≤ (-(10201613235986337760123 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2079788226324381 / 16000000000000000 : ℝ) = - (2079788226324381 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2079788226324381 / 2000000000000000 : ℚ)) - (U := (195594468513662239877 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2079788226324381 / 2000000000000000 : ℝ) ≤ - (195594468513662239877 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36053269788891 / 500000000000000 : ℝ)) (q := - (2079788226324381 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2079788226324381 / 16000000000000000 : ℚ)) + (r' := (2079788226324381 / 2000000000000000 : ℚ)) + (U := (-(10201613235986337760123 / 5000000000000000000000 : ℚ))) + (U' := (195594468513662239877 / 5000000000000000000000 : ℚ)) + 3 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23134620118833 / 64000000000000 : ℚ)) + (s := (36053269788891 / 500000000000000 : ℚ)) + (q := (2079788226324381 / 16000000000000000 : ℚ)) + (U := (-(10201613235986337760123 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_357_11 : Uω (aρ 11) (bρ 11) (23134620118833 / 64000000000000 : ℝ) ≤ @@ -2271,25 +2028,21 @@ lemma U_358_1 : have hlg : Real.log (222707663139269 / 625000000000000 : ℝ) ≤ (-(5159458327001527128447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (222707663139269 / 625000000000000 : ℝ) = - (222707663139269 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (222707663139269 / 156250000000000 : ℚ)) - (U := (1772013475998472871553 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (222707663139269 / 156250000000000 : ℝ) ≤ - (1772013475998472871553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3563277240245983 / 10000000000000000 : ℝ)) (q := - (222707663139269 / 625000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (222707663139269 / 625000000000000 : ℚ)) + (r' := (222707663139269 / 156250000000000 : ℚ)) + (U := (-(5159458327001527128447 / 5000000000000000000000 : ℚ))) + (U' := (1772013475998472871553 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (3563277240245983 / 10000000000000000 : ℚ)) + (q := (222707663139269 / 625000000000000 : ℚ)) + (U := (-(5159458327001527128447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_2 : Uω (aρ 2) (bρ 2) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2297,25 +2050,21 @@ lemma U_358_2 : have hlg : Real.log (7078598422949201 / 20000000000000000 : ℝ) ≤ (-(5193281738929938716601 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7078598422949201 / 20000000000000000 : ℝ) = - (7078598422949201 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7078598422949201 / 5000000000000000 : ℚ)) - (U := (1738190064070061283399 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7078598422949201 / 5000000000000000 : ℝ) ≤ - (1738190064070061283399 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55296866488259 / 156250000000000 : ℝ)) (q := - (7078598422949201 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7078598422949201 / 20000000000000000 : ℚ)) + (r' := (7078598422949201 / 5000000000000000 : ℚ)) + (U := (-(5193281738929938716601 / 5000000000000000000000 : ℚ))) + (U' := (1738190064070061283399 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (55296866488259 / 156250000000000 : ℚ)) + (q := (7078598422949201 / 20000000000000000 : ℚ)) + (U := (-(5193281738929938716601 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_3 : Uω (aρ 3) (bρ 3) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2323,25 +2072,21 @@ lemma U_358_3 : have hlg : Real.log (6982286623109339 / 20000000000000000 : ℝ) ≤ (-(10523558134738120583187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6982286623109339 / 20000000000000000 : ℝ) = - (6982286623109339 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6982286623109339 / 5000000000000000 : ℚ)) - (U := (3339385471261879416813 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6982286623109339 / 5000000000000000 : ℝ) ≤ - (3339385471261879416813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1745041880879357 / 5000000000000000 : ℝ)) (q := - (6982286623109339 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6982286623109339 / 20000000000000000 : ℚ)) + (r' := (6982286623109339 / 5000000000000000 : ℚ)) + (U := (-(10523558134738120583187 / 10000000000000000000000 : ℚ))) + (U' := (3339385471261879416813 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (1745041880879357 / 5000000000000000 : ℚ)) + (q := (6982286623109339 / 20000000000000000 : ℚ)) + (U := (-(10523558134738120583187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_4 : Uω (aρ 4) (bρ 4) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2349,25 +2094,21 @@ lemma U_358_4 : have hlg : Real.log (1705412113285619 / 5000000000000000 : ℝ) ≤ (-(10756311217136471123861 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1705412113285619 / 5000000000000000 : ℝ) = - (1705412113285619 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1705412113285619 / 1250000000000000 : ℚ)) - (U := (3106632388863528876139 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1705412113285619 / 1250000000000000 : ℝ) ≤ - (3106632388863528876139 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3407739772856851 / 10000000000000000 : ℝ)) (q := - (1705412113285619 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1705412113285619 / 5000000000000000 : ℚ)) + (r' := (1705412113285619 / 1250000000000000 : ℚ)) + (U := (-(10756311217136471123861 / 10000000000000000000000 : ℚ))) + (U' := (3106632388863528876139 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (3407739772856851 / 10000000000000000 : ℚ)) + (q := (1705412113285619 / 5000000000000000 : ℚ)) + (U := (-(10756311217136471123861 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_5 : Uω (aρ 5) (bρ 5) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2375,25 +2116,21 @@ lemma U_358_5 : have hlg : Real.log (6575238297658749 / 20000000000000000 : ℝ) ≤ (-(1390526815796387017917 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6575238297658749 / 20000000000000000 : ℝ) = - (6575238297658749 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6575238297658749 / 5000000000000000 : ℚ)) - (U := (342341134953612982083 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6575238297658749 / 5000000000000000 : ℝ) ≤ - (342341134953612982083 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (819879884177031 / 2500000000000000 : ℝ)) (q := - (6575238297658749 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6575238297658749 / 20000000000000000 : ℚ)) + (r' := (6575238297658749 / 5000000000000000 : ℚ)) + (U := (-(1390526815796387017917 / 1250000000000000000000 : ℚ))) + (U' := (342341134953612982083 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (819879884177031 / 2500000000000000 : ℚ)) + (q := (6575238297658749 / 20000000000000000 : ℚ)) + (U := (-(1390526815796387017917 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_6 : Uω (aρ 6) (bρ 6) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2401,25 +2138,21 @@ lemma U_358_6 : have hlg : Real.log (6217480247316111 / 20000000000000000 : ℝ) ≤ (-(467347021317313664613 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6217480247316111 / 20000000000000000 : ℝ) = - (6217480247316111 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6217480247316111 / 5000000000000000 : ℚ)) - (U := (87170722922686335387 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6217480247316111 / 5000000000000000 : ℝ) ≤ - (87170722922686335387 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1544500930752743 / 5000000000000000 : ℝ)) (q := - (6217480247316111 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6217480247316111 / 20000000000000000 : ℚ)) + (r' := (6217480247316111 / 5000000000000000 : ℚ)) + (U := (-(467347021317313664613 / 400000000000000000000 : ℚ))) + (U' := (87170722922686335387 / 400000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (1544500930752743 / 5000000000000000 : ℚ)) + (q := (6217480247316111 / 20000000000000000 : ℚ)) + (U := (-(467347021317313664613 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_7 : Uω (aρ 7) (bρ 7) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2427,25 +2160,21 @@ lemma U_358_7 : have hlg : Real.log (228757404424093 / 800000000000000 : ℝ) ≤ (-(6259748272245998521739 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (228757404424093 / 800000000000000 : ℝ) = - (228757404424093 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (228757404424093 / 200000000000000 : ℚ)) - (U := (671723530754001478261 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (228757404424093 / 200000000000000 : ℝ) ≤ - (671723530754001478261 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28141181055517 / 100000000000000 : ℝ)) (q := - (228757404424093 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (228757404424093 / 800000000000000 : ℚ)) + (r' := (228757404424093 / 200000000000000 : ℚ)) + (U := (-(6259748272245998521739 / 5000000000000000000000 : ℚ))) + (U' := (671723530754001478261 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (28141181055517 / 100000000000000 : ℚ)) + (q := (228757404424093 / 800000000000000 : ℚ)) + (U := (-(6259748272245998521739 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_8 : Uω (aρ 8) (bρ 8) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2453,24 +2182,21 @@ lemma U_358_8 : have hlg : Real.log (39394208847257 / 156250000000000 : ℝ) ≤ (-(13778384661680333337793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39394208847257 / 156250000000000 : ℝ) = (39394208847257 / 39062500000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39394208847257 / 39062500000000 : ℚ)) - (U := (84558944319666662207 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (39394208847257 / 39062500000000 : ℝ) ≤ - (84558944319666662207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2421183378738271 / 10000000000000000 : ℝ)) (q := - (39394208847257 / 156250000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39394208847257 / 156250000000000 : ℚ)) + (r' := (39394208847257 / 39062500000000 : ℚ)) + (U := (-(13778384661680333337793 / 10000000000000000000000 : ℚ))) + (U' := (84558944319666662207 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (2421183378738271 / 10000000000000000 : ℚ)) + (q := (39394208847257 / 156250000000000 : ℚ)) + (U := (-(13778384661680333337793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_9 : Uω (aρ 9) (bρ 9) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2478,25 +2204,21 @@ lemma U_358_9 : have hlg : Real.log (412105781538001 / 2000000000000000 : ℝ) ≤ (-(7898111955309340951673 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (412105781538001 / 2000000000000000 : ℝ) = - (412105781538001 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (412105781538001 / 250000000000000 : ℚ)) - (U := (2499095749190659048327 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (412105781538001 / 250000000000000 : ℝ) ≤ - (2499095749190659048327 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (368149618005877 / 2000000000000000 : ℝ)) (q := - (412105781538001 / 2000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (412105781538001 / 2000000000000000 : ℚ)) + (r' := (412105781538001 / 250000000000000 : ℚ)) + (U := (-(7898111955309340951673 / 5000000000000000000000 : ℚ))) + (U' := (2499095749190659048327 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (368149618005877 / 2000000000000000 : ℚ)) + (q := (412105781538001 / 2000000000000000 : ℚ)) + (U := (-(7898111955309340951673 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_10 : Uω (aρ 10) (bρ 10) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2504,26 +2226,21 @@ lemma U_358_10 : have hlg : Real.log (1323120438779999 / 10000000000000000 : ℝ) ≤ (-(10112960883108076518971 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1323120438779999 / 10000000000000000 : ℝ) = - (1323120438779999 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1323120438779999 / 1250000000000000 : ℚ)) - (U := (284246821391923481029 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1323120438779999 / 1250000000000000 : ℝ) ≤ - (284246821391923481029 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (754490185704373 / 10000000000000000 : ℝ)) (q := - (1323120438779999 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1323120438779999 / 10000000000000000 : ℚ)) + (r' := (1323120438779999 / 1250000000000000 : ℚ)) + (U := (-(10112960883108076518971 / 5000000000000000000000 : ℚ))) + (U' := (284246821391923481029 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5804584317273 / 16000000000000 : ℚ)) + (s := (754490185704373 / 10000000000000000 : ℚ)) + (q := (1323120438779999 / 10000000000000000 : ℚ)) + (U := (-(10112960883108076518971 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_358_11 : Uω (aρ 11) (bρ 11) (5804584317273 / 16000000000000 : ℝ) ≤ @@ -2645,25 +2362,21 @@ lemma U_359_1 : have hlg : Real.log (57117809531462451 / 160000000000000000 : ℝ) ≤ (-(5150289229783770027499 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57117809531462451 / 160000000000000000 : ℝ) = - (57117809531462451 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57117809531462451 / 40000000000000000 : ℚ)) - (U := (1781182573216229972501 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57117809531462451 / 40000000000000000 : ℝ) ≤ - (1781182573216229972501 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3569817808858197 / 10000000000000000 : ℝ)) (q := - (57117809531462451 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57117809531462451 / 160000000000000000 : ℚ)) + (r' := (57117809531462451 / 40000000000000000 : ℚ)) + (U := (-(5150289229783770027499 / 5000000000000000000000 : ℚ))) + (U' := (1781182573216229972501 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (3569817808858197 / 10000000000000000 : ℚ)) + (q := (57117809531462451 / 160000000000000000 : ℚ)) + (U := (-(5150289229783770027499 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_2 : Uω (aρ 2) (bρ 2) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2671,25 +2384,21 @@ lemma U_359_2 : have hlg : Real.log (56733442668706523 / 160000000000000000 : ℝ) ≤ (-(5184049800320691189273 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56733442668706523 / 160000000000000000 : ℝ) = - (56733442668706523 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56733442668706523 / 40000000000000000 : ℚ)) - (U := (1747422002679308810727 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56733442668706523 / 40000000000000000 : ℝ) ≤ - (1747422002679308810727 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1772770481761853 / 5000000000000000 : ℝ)) (q := - (56733442668706523 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56733442668706523 / 160000000000000000 : ℚ)) + (r' := (56733442668706523 / 40000000000000000 : ℚ)) + (U := (-(5184049800320691189273 / 5000000000000000000000 : ℚ))) + (U' := (1747422002679308810727 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (1772770481761853 / 5000000000000000 : ℚ)) + (q := (56733442668706523 / 160000000000000000 : ℚ)) + (U := (-(5184049800320691189273 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_3 : Uω (aρ 3) (bρ 3) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2697,25 +2406,21 @@ lemma U_359_3 : have hlg : Real.log (55962971132726131 / 160000000000000000 : ℝ) ≤ (-(10504835724603574181621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55962971132726131 / 160000000000000000 : ℝ) = - (55962971132726131 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55962971132726131 / 40000000000000000 : ℚ)) - (U := (3358107881396425818379 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55962971132726131 / 40000000000000000 : ℝ) ≤ - (3358107881396425818379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3496628127876157 / 10000000000000000 : ℝ)) (q := - (55962971132726131 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55962971132726131 / 160000000000000000 : ℚ)) + (r' := (55962971132726131 / 40000000000000000 : ℚ)) + (U := (-(10504835724603574181621 / 10000000000000000000000 : ℚ))) + (U' := (3358107881396425818379 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (3496628127876157 / 10000000000000000 : ℚ)) + (q := (55962971132726131 / 160000000000000000 : ℚ)) + (U := (-(10504835724603574181621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_4 : Uω (aρ 4) (bρ 4) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2723,25 +2428,21 @@ lemma U_359_4 : have hlg : Real.log (54677928600177467 / 160000000000000000 : ℝ) ≤ (-(2147427371592678436087 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54677928600177467 / 160000000000000000 : ℝ) = - (54677928600177467 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54677928600177467 / 40000000000000000 : ℚ)) - (U := (625161349607321563913 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54677928600177467 / 40000000000000000 : ℝ) ≤ - (625161349607321563913 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1707145996186287 / 5000000000000000 : ℝ)) (q := - (54677928600177467 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54677928600177467 / 160000000000000000 : ℚ)) + (r' := (54677928600177467 / 40000000000000000 : ℚ)) + (U := (-(2147427371592678436087 / 2000000000000000000000 : ℚ))) + (U' := (625161349607321563913 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (1707145996186287 / 5000000000000000 : ℚ)) + (q := (54677928600177467 / 160000000000000000 : ℚ)) + (U := (-(2147427371592678436087 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_5 : Uω (aρ 5) (bρ 5) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2749,25 +2450,21 @@ lemma U_359_5 : have hlg : Real.log (52706810754558643 / 160000000000000000 : ℝ) ≤ (-(11104291311875286283503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52706810754558643 / 160000000000000000 : ℝ) = - (52706810754558643 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52706810754558643 / 40000000000000000 : ℚ)) - (U := (2758652294124713716497 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52706810754558643 / 40000000000000000 : ℝ) ≤ - (2758652294124713716497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3286092181005221 / 10000000000000000 : ℝ)) (q := - (52706810754558643 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52706810754558643 / 160000000000000000 : ℚ)) + (r' := (52706810754558643 / 40000000000000000 : ℚ)) + (U := (-(11104291311875286283503 / 10000000000000000000000 : ℚ))) + (U' := (2758652294124713716497 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (3286092181005221 / 10000000000000000 : ℚ)) + (q := (52706810754558643 / 160000000000000000 : ℚ)) + (U := (-(11104291311875286283503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_6 : Uω (aρ 6) (bρ 6) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2775,25 +2472,21 @@ lemma U_359_6 : have hlg : Real.log (9969031133943807 / 32000000000000000 : ℝ) ≤ (-(11662525011682297601331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9969031133943807 / 32000000000000000 : ℝ) = - (9969031133943807 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9969031133943807 / 8000000000000000 : ℚ)) - (U := (2200418594317702398669 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9969031133943807 / 8000000000000000 : ℝ) ≤ - (2200418594317702398669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (309562567054027 / 1000000000000000 : ℝ)) (q := - (9969031133943807 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9969031133943807 / 32000000000000000 : ℚ)) + (r' := (9969031133943807 / 8000000000000000 : ℚ)) + (U := (-(11662525011682297601331 / 10000000000000000000000 : ℚ))) + (U' := (2200418594317702398669 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (309562567054027 / 1000000000000000 : ℚ)) + (q := (9969031133943807 / 32000000000000000 : ℚ)) + (U := (-(11662525011682297601331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_7 : Uω (aρ 7) (bρ 7) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2801,25 +2494,21 @@ lemma U_359_7 : have hlg : Real.log (45857809724625947 / 160000000000000000 : ℝ) ≤ (-(12496282984634089874379 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45857809724625947 / 160000000000000000 : ℝ) = - (45857809724625947 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45857809724625947 / 40000000000000000 : ℚ)) - (U := (1366660621365910125621 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45857809724625947 / 40000000000000000 : ℝ) ≤ - (1366660621365910125621 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1410434404081817 / 5000000000000000 : ℝ)) (q := - (45857809724625947 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45857809724625947 / 160000000000000000 : ℚ)) + (r' := (45857809724625947 / 40000000000000000 : ℚ)) + (U := (-(12496282984634089874379 / 10000000000000000000000 : ℚ))) + (U' := (1366660621365910125621 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (1410434404081817 / 5000000000000000 : ℚ)) + (q := (45857809724625947 / 160000000000000000 : ℚ)) + (U := (-(12496282984634089874379 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_8 : Uω (aρ 8) (bρ 8) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2827,25 +2516,21 @@ lemma U_359_8 : have hlg : Real.log (40448628276486739 / 160000000000000000 : ℝ) ≤ (-(13751410833669744054049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40448628276486739 / 160000000000000000 : ℝ) = - (40448628276486739 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40448628276486739 / 40000000000000000 : ℚ)) - (U := (111532772330255945951 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40448628276486739 / 40000000000000000 : ℝ) ≤ - (111532772330255945951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2428262778486233 / 10000000000000000 : ℝ)) (q := - (40448628276486739 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40448628276486739 / 160000000000000000 : ℚ)) + (r' := (40448628276486739 / 40000000000000000 : ℚ)) + (U := (-(13751410833669744054049 / 10000000000000000000000 : ℚ))) + (U' := (111532772330255945951 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (2428262778486233 / 10000000000000000 : ℚ)) + (q := (40448628276486739 / 160000000000000000 : ℚ)) + (U := (-(13751410833669744054049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_9 : Uω (aρ 9) (bρ 9) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2853,25 +2538,21 @@ lemma U_359_9 : have hlg : Real.log (33085554011979971 / 160000000000000000 : ℝ) ≤ (-(197009632752461729613 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33085554011979971 / 160000000000000000 : ℝ) = - (33085554011979971 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33085554011979971 / 20000000000000000 : ℚ)) - (U := (62920559860038270387 / 125000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (33085554011979971 / 20000000000000000 : ℝ) ≤ - (62920559860038270387 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1848844123782887 / 10000000000000000 : ℝ)) (q := - (33085554011979971 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33085554011979971 / 160000000000000000 : ℚ)) + (r' := (33085554011979971 / 20000000000000000 : ℚ)) + (U := (-(197009632752461729613 / 125000000000000000000 : ℚ))) + (U' := (62920559860038270387 / 125000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (1848844123782887 / 10000000000000000 : ℚ)) + (q := (33085554011979971 / 160000000000000000 : ℚ)) + (U := (-(197009632752461729613 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_10 : Uω (aρ 10) (bρ 10) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -2879,26 +2560,21 @@ lemma U_359_10 : have hlg : Real.log (21352267909247611 / 160000000000000000 : ℝ) ≤ (-(1258759909477100777669 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (21352267909247611 / 160000000000000000 : ℝ) = - (21352267909247611 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21352267909247611 / 20000000000000000 : ℚ)) - (U := (40891053585399222331 / 625000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21352267909247611 / 20000000000000000 : ℝ) ≤ - (40891053585399222331 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (385371197218171 / 5000000000000000 : ℝ)) (q := - (21352267909247611 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21352267909247611 / 160000000000000000 : ℚ)) + (r' := (21352267909247611 / 20000000000000000 : ℚ)) + (U := (-(1258759909477100777669 / 625000000000000000000 : ℚ))) + (U' := (40891053585399222331 / 625000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (46520391688443 / 128000000000000 : ℚ)) + (s := (385371197218171 / 5000000000000000 : ℚ)) + (q := (21352267909247611 / 160000000000000000 : ℚ)) + (U := (-(1258759909477100777669 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_359_11 : Uω (aρ 11) (bρ 11) (46520391688443 / 128000000000000 : ℝ) ≤ @@ -3021,25 +2697,21 @@ lemma U_360_1 : have hlg : Real.log (28611228647203731 / 80000000000000000 : ℝ) ≤ (-(10282273833372514520303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28611228647203731 / 80000000000000000 : ℝ) = - (28611228647203731 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28611228647203731 / 20000000000000000 : ℚ)) - (U := (3580669772627485479697 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28611228647203731 / 20000000000000000 : ℝ) ≤ - (3580669772627485479697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3576358376862339 / 10000000000000000 : ℝ)) (q := - (28611228647203731 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28611228647203731 / 80000000000000000 : ℚ)) + (r' := (28611228647203731 / 20000000000000000 : ℚ)) + (U := (-(10282273833372514520303 / 10000000000000000000000 : ℚ))) + (U' := (3580669772627485479697 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (3576358376862339 / 10000000000000000 : ℚ)) + (q := (28611228647203731 / 80000000000000000 : ℚ)) + (U := (-(10282273833372514520303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_2 : Uω (aρ 2) (bρ 2) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3047,25 +2719,21 @@ lemma U_360_2 : have hlg : Real.log (28419048960617947 / 80000000000000000 : ℝ) ≤ (-(10349669757811332992301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28419048960617947 / 80000000000000000 : ℝ) = - (28419048960617947 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28419048960617947 / 20000000000000000 : ℚ)) - (U := (3513273848188667007699 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28419048960617947 / 20000000000000000 : ℝ) ≤ - (3513273848188667007699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3552082467725893 / 10000000000000000 : ℝ)) (q := - (28419048960617947 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28419048960617947 / 80000000000000000 : ℚ)) + (r' := (28419048960617947 / 20000000000000000 : ℚ)) + (U := (-(10349669757811332992301 / 10000000000000000000000 : ℚ))) + (U' := (3513273848188667007699 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (3552082467725893 / 10000000000000000 : ℚ)) + (q := (28419048960617947 / 80000000000000000 : ℚ)) + (U := (-(10349669757811332992301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_3 : Uω (aρ 3) (bρ 3) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3073,25 +2741,21 @@ lemma U_360_3 : have hlg : Real.log (28033824581068403 / 80000000000000000 : ℝ) ≤ (-(1310768540370397377601 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28033824581068403 / 80000000000000000 : ℝ) = - (28033824581068403 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28033824581068403 / 20000000000000000 : ℚ)) - (U := (422099410379602622399 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28033824581068403 / 20000000000000000 : ℝ) ≤ - (422099410379602622399 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3503172479188507 / 10000000000000000 : ℝ)) (q := - (28033824581068403 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28033824581068403 / 80000000000000000 : ℚ)) + (r' := (28033824581068403 / 20000000000000000 : ℚ)) + (U := (-(1310768540370397377601 / 1250000000000000000000 : ℚ))) + (U' := (422099410379602622399 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (3503172479188507 / 10000000000000000 : ℚ)) + (q := (28033824581068403 / 80000000000000000 : ℚ)) + (U := (-(1310768540370397377601 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_4 : Uω (aρ 4) (bρ 4) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3099,25 +2763,21 @@ lemma U_360_4 : have hlg : Real.log (1095653384267843 / 3200000000000000 : ℝ) ≤ (-(1071799926009268155151 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1095653384267843 / 3200000000000000 : ℝ) = - (1095653384267843 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1095653384267843 / 800000000000000 : ℚ)) - (U := (314494434590731844849 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1095653384267843 / 800000000000000 : ℝ) ≤ - (314494434590731844849 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (136833766666417 / 400000000000000 : ℝ)) (q := - (1095653384267843 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1095653384267843 / 3200000000000000 : ℚ)) + (r' := (1095653384267843 / 800000000000000 : ℚ)) + (U := (-(1071799926009268155151 / 1000000000000000000000 : ℚ))) + (U' := (314494434590731844849 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (136833766666417 / 400000000000000 : ℚ)) + (q := (1095653384267843 / 3200000000000000 : ℚ)) + (U := (-(1071799926009268155151 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_5 : Uω (aρ 5) (bρ 5) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3125,25 +2785,21 @@ lemma U_360_5 : have hlg : Real.log (26405857050309291 / 80000000000000000 : ℝ) ≤ (-(11084407906422986722507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26405857050309291 / 80000000000000000 : ℝ) = - (26405857050309291 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26405857050309291 / 20000000000000000 : ℚ)) - (U := (2778535699577013277493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26405857050309291 / 20000000000000000 : ℝ) ≤ - (2778535699577013277493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3292664696898729 / 10000000000000000 : ℝ)) (q := - (26405857050309291 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26405857050309291 / 80000000000000000 : ℚ)) + (r' := (26405857050309291 / 20000000000000000 : ℚ)) + (U := (-(11084407906422986722507 / 10000000000000000000000 : ℚ))) + (U' := (2778535699577013277493 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (3292664696898729 / 10000000000000000 : ℚ)) + (q := (26405857050309291 / 80000000000000000 : ℚ)) + (U := (-(11084407906422986722507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_6 : Uω (aρ 6) (bρ 6) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3151,25 +2807,21 @@ lemma U_360_6 : have hlg : Real.log (24975233264729499 / 80000000000000000 : ℝ) ≤ (-(2328283939467763148137 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24975233264729499 / 80000000000000000 : ℝ) = - (24975233264729499 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24975233264729499 / 20000000000000000 : ℚ)) - (U := (444304781732236851863 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24975233264729499 / 20000000000000000 : ℝ) ≤ - (444304781732236851863 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3102249125643781 / 10000000000000000 : ℝ)) (q := - (24975233264729499 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24975233264729499 / 80000000000000000 : ℚ)) + (r' := (24975233264729499 / 20000000000000000 : ℚ)) + (U := (-(2328283939467763148137 / 2000000000000000000000 : ℚ))) + (U' := (444304781732236851863 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (3102249125643781 / 10000000000000000 : ℚ)) + (q := (24975233264729499 / 80000000000000000 : ℚ)) + (U := (-(2328283939467763148137 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_7 : Uω (aρ 7) (bρ 7) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3177,25 +2829,21 @@ lemma U_360_7 : have hlg : Real.log (22982065328186551 / 80000000000000000 : ℝ) ≤ (-(3118281226855059681807 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22982065328186551 / 80000000000000000 : ℝ) = - (22982065328186551 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22982065328186551 / 20000000000000000 : ℚ)) - (U := (347454674644940318193 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22982065328186551 / 20000000000000000 : ℝ) ≤ - (347454674644940318193 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (706904630567011 / 2500000000000000 : ℝ)) (q := - (22982065328186551 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22982065328186551 / 80000000000000000 : ℚ)) + (r' := (22982065328186551 / 20000000000000000 : ℚ)) + (U := (-(3118281226855059681807 / 2500000000000000000000 : ℚ))) + (U' := (347454674644940318193 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (706904630567011 / 2500000000000000 : ℚ)) + (q := (22982065328186551 / 80000000000000000 : ℚ)) + (U := (-(3118281226855059681807 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_8 : Uω (aρ 8) (bρ 8) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3203,25 +2851,21 @@ lemma U_360_8 : have hlg : Real.log (20278781289178551 / 80000000000000000 : ℝ) ≤ (-(13724515514587036197389 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20278781289178551 / 80000000000000000 : ℝ) = - (20278781289178551 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20278781289178551 / 20000000000000000 : ℚ)) - (U := (138428091412963802611 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20278781289178551 / 20000000000000000 : ℝ) ≤ - (138428091412963802611 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (608834790964011 / 2500000000000000 : ℝ)) (q := - (20278781289178551 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20278781289178551 / 80000000000000000 : ℚ)) + (r' := (20278781289178551 / 20000000000000000 : ℚ)) + (U := (-(13724515514587036197389 / 10000000000000000000000 : ℚ))) + (U' := (138428091412963802611 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (608834790964011 / 2500000000000000 : ℚ)) + (q := (20278781289178551 / 80000000000000000 : ℚ)) + (U := (-(13724515514587036197389 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_9 : Uω (aρ 9) (bρ 9) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3229,25 +2873,21 @@ lemma U_360_9 : have hlg : Real.log (16601273704238307 / 80000000000000000 : ℝ) ≤ (-(15725472123040980563639 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16601273704238307 / 80000000000000000 : ℝ) = - (16601273704238307 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16601273704238307 / 10000000000000000 : ℚ)) - (U := (5068943285959019436361 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16601273704238307 / 10000000000000000 : ℝ) ≤ - (5068943285959019436361 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1856927895980983 / 10000000000000000 : ℝ)) (q := - (16601273704238307 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16601273704238307 / 80000000000000000 : ℚ)) + (r' := (16601273704238307 / 10000000000000000 : ℚ)) + (U := (-(15725472123040980563639 / 10000000000000000000000 : ℚ))) + (U' := (5068943285959019436361 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (1856927895980983 / 10000000000000000 : ℚ)) + (q := (16601273704238307 / 80000000000000000 : ℚ)) + (U := (-(15725472123040980563639 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_10 : Uω (aρ 10) (bρ 10) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3255,26 +2895,21 @@ lemma U_360_10 : have hlg : Real.log (10766179120663659 / 80000000000000000 : ℝ) ≤ (-(5014042440673356328323 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (10766179120663659 / 80000000000000000 : ℝ) = - (10766179120663659 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10766179120663659 / 10000000000000000 : ℚ)) - (U := (184561411576643671677 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10766179120663659 / 10000000000000000 : ℝ) ≤ - (184561411576643671677 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (786713283582321 / 10000000000000000 : ℝ)) (q := - (10766179120663659 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10766179120663659 / 80000000000000000 : ℚ)) + (r' := (10766179120663659 / 10000000000000000 : ℚ)) + (U := (-(5014042440673356328323 / 2500000000000000000000 : ℚ))) + (U' := (184561411576643671677 / 2500000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23302054419351 / 64000000000000 : ℚ)) + (s := (786713283582321 / 10000000000000000 : ℚ)) + (q := (10766179120663659 / 80000000000000000 : ℚ)) + (U := (-(5014042440673356328323 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_360_11 : Uω (aρ 11) (bρ 11) (23302054419351 / 64000000000000 : ℝ) ≤ @@ -3397,25 +3032,21 @@ lemma U_361_1 : have hlg : Real.log (57327105052514521 / 160000000000000000 : ℝ) ≤ (-(2052800530549085513821 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57327105052514521 / 160000000000000000 : ℝ) = - (57327105052514521 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57327105052514521 / 40000000000000000 : ℚ)) - (U := (719788190650914486179 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57327105052514521 / 40000000000000000 : ℝ) ≤ - (719788190650914486179 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3582898944261737 / 10000000000000000 : ℝ)) (q := - (57327105052514521 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57327105052514521 / 160000000000000000 : ℚ)) + (r' := (57327105052514521 / 40000000000000000 : ℚ)) + (U := (-(2052800530549085513821 / 2000000000000000000000 : ℚ))) + (U' := (719788190650914486179 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (3582898944261737 / 10000000000000000 : ℚ)) + (q := (57327105052514521 / 160000000000000000 : ℚ)) + (U := (-(2052800530549085513821 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_2 : Uω (aρ 2) (bρ 2) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3423,25 +3054,21 @@ lemma U_361_2 : have hlg : Real.log (56942753141361409 / 160000000000000000 : ℝ) ≤ (-(10331273824108637515949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56942753141361409 / 160000000000000000 : ℝ) = - (56942753141361409 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56942753141361409 / 40000000000000000 : ℚ)) - (U := (3531669781891362484051 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56942753141361409 / 40000000000000000 : ℝ) ≤ - (3531669781891362484051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1779311983938799 / 5000000000000000 : ℝ)) (q := - (56942753141361409 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56942753141361409 / 160000000000000000 : ℚ)) + (r' := (56942753141361409 / 40000000000000000 : ℚ)) + (U := (-(10331273824108637515949 / 10000000000000000000000 : ℚ))) + (U' := (3531669781891362484051 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (1779311983938799 / 5000000000000000 : ℚ)) + (q := (56942753141361409 / 160000000000000000 : ℚ)) + (U := (-(10331273824108637515949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_3 : Uω (aρ 3) (bρ 3) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3449,25 +3076,21 @@ lemma U_361_3 : have hlg : Real.log (56172327073769273 / 160000000000000000 : ℝ) ≤ (-(5233747899529985342477 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56172327073769273 / 160000000000000000 : ℝ) = - (56172327073769273 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56172327073769273 / 40000000000000000 : ℚ)) - (U := (1697723903470014657523 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56172327073769273 / 40000000000000000 : ℝ) ≤ - (1697723903470014657523 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3509716815778581 / 10000000000000000 : ℝ)) (q := - (56172327073769273 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56172327073769273 / 160000000000000000 : ℚ)) + (r' := (56172327073769273 / 40000000000000000 : ℚ)) + (U := (-(5233747899529985342477 / 5000000000000000000000 : ℚ))) + (U' := (1697723903470014657523 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (3509716815778581 / 10000000000000000 : ℚ)) + (q := (56172327073769273 / 160000000000000000 : ℚ)) + (U := (-(5233747899529985342477 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_4 : Uω (aρ 4) (bρ 4) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3475,25 +3098,21 @@ lemma U_361_4 : have hlg : Real.log (54887409466858969 / 160000000000000000 : ℝ) ≤ (-(10698898282584064623033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54887409466858969 / 160000000000000000 : ℝ) = - (54887409466858969 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54887409466858969 / 40000000000000000 : ℚ)) - (U := (3164045323415935376967 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54887409466858969 / 40000000000000000 : ℝ) ≤ - (3164045323415935376967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3427396295979793 / 10000000000000000 : ℝ)) (q := - (54887409466858969 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54887409466858969 / 160000000000000000 : ℚ)) + (r' := (54887409466858969 / 40000000000000000 : ℚ)) + (U := (-(10698898282584064623033 / 10000000000000000000000 : ℚ))) + (U' := (3164045323415935376967 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (3427396295979793 / 10000000000000000 : ℚ)) + (q := (54887409466858969 / 160000000000000000 : ℚ)) + (U := (-(10698898282584064623033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_5 : Uω (aρ 5) (bρ 5) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3501,25 +3120,21 @@ lemma U_361_5 : have hlg : Real.log (52916616425588929 / 160000000000000000 : ℝ) ≤ (-(1383070518809231514651 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52916616425588929 / 160000000000000000 : ℝ) = - (52916616425588929 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52916616425588929 / 40000000000000000 : ℚ)) - (U := (349797431940768485349 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52916616425588929 / 40000000000000000 : ℝ) ≤ - (349797431940768485349 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1649618542578019 / 5000000000000000 : ℝ)) (q := - (52916616425588929 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52916616425588929 / 160000000000000000 : ℚ)) + (r' := (52916616425588929 / 40000000000000000 : ℚ)) + (U := (-(1383070518809231514651 / 1250000000000000000000 : ℚ))) + (U' := (349797431940768485349 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (1649618542578019 / 5000000000000000 : ℚ)) + (q := (52916616425588929 / 160000000000000000 : ℚ)) + (U := (-(1383070518809231514651 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_6 : Uω (aρ 6) (bρ 6) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3527,25 +3142,21 @@ lemma U_361_6 : have hlg : Real.log (50055774575846001 / 160000000000000000 : ℝ) ≤ (-(1452544924334053118787 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (50055774575846001 / 160000000000000000 : ℝ) = - (50055774575846001 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50055774575846001 / 40000000000000000 : ℚ)) - (U := (280323026415946881213 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50055774575846001 / 40000000000000000 : ℝ) ≤ - (280323026415946881213 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (777218057269543 / 2500000000000000 : ℝ)) (q := - (50055774575846001 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50055774575846001 / 160000000000000000 : ℚ)) + (r' := (50055774575846001 / 40000000000000000 : ℚ)) + (U := (-(1452544924334053118787 / 1250000000000000000000 : ℚ))) + (U' := (280323026415946881213 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (777218057269543 / 2500000000000000 : ℚ)) + (q := (50055774575846001 / 160000000000000000 : ℚ)) + (U := (-(1452544924334053118787 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_7 : Uω (aρ 7) (bρ 7) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3553,25 +3164,21 @@ lemma U_361_7 : have hlg : Real.log (46070443736556433 / 160000000000000000 : ℝ) ≤ (-(778126377514180342509 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46070443736556433 / 160000000000000000 : ℝ) = - (46070443736556433 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46070443736556433 / 40000000000000000 : ℚ)) - (U := (88307597860819657491 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46070443736556433 / 40000000000000000 : ℝ) ≤ - (88307597860819657491 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (22143494179117 / 78125000000000 : ℝ)) (q := - (46070443736556433 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46070443736556433 / 160000000000000000 : ℚ)) + (r' := (46070443736556433 / 40000000000000000 : ℚ)) + (U := (-(778126377514180342509 / 625000000000000000000 : ℚ))) + (U' := (88307597860819657491 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (22143494179117 / 78125000000000 : ℚ)) + (q := (46070443736556433 / 160000000000000000 : ℚ)) + (U := (-(778126377514180342509 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_8 : Uω (aρ 8) (bρ 8) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3579,25 +3186,21 @@ lemma U_361_8 : have hlg : Real.log (40666472974807153 / 160000000000000000 : ℝ) ≤ (-(856106138484193971651 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40666472974807153 / 160000000000000000 : ℝ) = - (40666472974807153 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40666472974807153 / 40000000000000000 : ℚ)) - (U := (10327836890806028349 / 625000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40666472974807153 / 40000000000000000 : ℝ) ≤ - (10327836890806028349 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (610603140262079 / 2500000000000000 : ℝ)) (q := - (40666472974807153 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40666472974807153 / 160000000000000000 : ℚ)) + (r' := (40666472974807153 / 40000000000000000 : ℚ)) + (U := (-(856106138484193971651 / 625000000000000000000 : ℚ))) + (U' := (10327836890806028349 / 625000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (610603140262079 / 2500000000000000 : ℚ)) + (q := (40666472974807153 / 160000000000000000 : ℚ)) + (U := (-(856106138484193971651 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_9 : Uω (aρ 9) (bρ 9) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3605,25 +3208,21 @@ lemma U_361_9 : have hlg : Real.log (33319443988064353 / 160000000000000000 : ℝ) ≤ (-(15690326843274616969439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33319443988064353 / 160000000000000000 : ℝ) = - (33319443988064353 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33319443988064353 / 20000000000000000 : ℚ)) - (U := (5104088565725383030561 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33319443988064353 / 20000000000000000 : ℝ) ≤ - (5104088565725383030561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (932499783032733 / 5000000000000000 : ℝ)) (q := - (33319443988064353 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33319443988064353 / 160000000000000000 : ℚ)) + (r' := (33319443988064353 / 20000000000000000 : ℚ)) + (U := (-(15690326843274616969439 / 10000000000000000000000 : ℚ))) + (U' := (5104088565725383030561 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (932499783032733 / 5000000000000000 : ℚ)) + (q := (33319443988064353 / 160000000000000000 : ℚ)) + (U := (-(15690326843274616969439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_10 : Uω (aρ 10) (bρ 10) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3631,26 +3230,21 @@ lemma U_361_10 : have hlg : Real.log (21710332399398641 / 160000000000000000 : ℝ) ≤ (-(19973855197920723312371 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (21710332399398641 / 160000000000000000 : ℝ) = - (21710332399398641 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21710332399398641 / 20000000000000000 : ℚ)) - (U := (820560211079276687629 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21710332399398641 / 20000000000000000 : ℝ) ≤ - (820560211079276687629 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (200604912744313 / 2500000000000000 : ℝ)) (q := - (21710332399398641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21710332399398641 / 160000000000000000 : ℚ)) + (r' := (21710332399398641 / 20000000000000000 : ℚ)) + (U := (-(19973855197920723312371 / 10000000000000000000000 : ℚ))) + (U' := (820560211079276687629 / 10000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (46687825988961 / 128000000000000 : ℚ)) + (s := (200604912744313 / 2500000000000000 : ℚ)) + (q := (21710332399398641 / 160000000000000000 : ℚ)) + (U := (-(19973855197920723312371 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_361_11 : Uω (aρ 11) (bρ 11) (46687825988961 / 128000000000000 : ℝ) ≤ @@ -3773,25 +3367,21 @@ lemma U_362_1 : have hlg : Real.log (14357938201452519 / 40000000000000000 : ℝ) ≤ (-(2049152959136992528997 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14357938201452519 / 40000000000000000 : ℝ) = - (14357938201452519 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14357938201452519 / 10000000000000000 : ℚ)) - (U := (723435762063007471003 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14357938201452519 / 10000000000000000 : ℝ) ≤ - (723435762063007471003 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3589439511059697 / 10000000000000000 : ℝ)) (q := - (14357938201452519 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14357938201452519 / 40000000000000000 : ℚ)) + (r' := (14357938201452519 / 10000000000000000 : ℚ)) + (U := (-(2049152959136992528997 / 2000000000000000000000 : ℚ))) + (U' := (723435762063007471003 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (3589439511059697 / 10000000000000000 : ℚ)) + (q := (14357938201452519 / 40000000000000000 : ℚ)) + (U := (-(2049152959136992528997 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_2 : Uω (aρ 2) (bρ 2) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3799,25 +3389,21 @@ lemma U_362_2 : have hlg : Real.log (2852370416463071 / 8000000000000000 : ℝ) ≤ (-(5156455837481287013357 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2852370416463071 / 8000000000000000 : ℝ) = - (2852370416463071 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2852370416463071 / 2000000000000000 : ℚ)) - (U := (1775015965518712986643 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2852370416463071 / 2000000000000000 : ℝ) ≤ - (1775015965518712986643 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (713033092800223 / 2000000000000000 : ℝ)) (q := - (2852370416463071 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2852370416463071 / 8000000000000000 : ℚ)) + (r' := (2852370416463071 / 2000000000000000 : ℚ)) + (U := (-(5156455837481287013357 / 5000000000000000000000 : ℚ))) + (U' := (1775015965518712986643 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (713033092800223 / 2000000000000000 : ℚ)) + (q := (2852370416463071 / 8000000000000000 : ℚ)) + (U := (-(5156455837481287013357 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_3 : Uω (aρ 3) (bρ 3) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3825,25 +3411,21 @@ lemma U_362_3 : have hlg : Real.log (14069251217070289 / 40000000000000000 : ℝ) ≤ (-(1306109752858577475561 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14069251217070289 / 40000000000000000 : ℝ) = - (14069251217070289 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14069251217070289 / 10000000000000000 : ℚ)) - (U := (426758197891422524439 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14069251217070289 / 10000000000000000 : ℝ) ≤ - (426758197891422524439 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1758130568864291 / 5000000000000000 : ℝ)) (q := - (14069251217070289 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14069251217070289 / 40000000000000000 : ℚ)) + (r' := (14069251217070289 / 10000000000000000 : ℚ)) + (U := (-(1306109752858577475561 / 1250000000000000000000 : ℚ))) + (U' := (426758197891422524439 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (1758130568864291 / 5000000000000000 : ℚ)) + (q := (14069251217070289 / 40000000000000000 : ℚ)) + (U := (-(1306109752858577475561 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_4 : Uω (aρ 4) (bρ 4) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3851,25 +3433,21 @@ lemma U_362_4 : have hlg : Real.log (13748037340659291 / 40000000000000000 : ℝ) ≤ (-(10679833785307686060643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13748037340659291 / 40000000000000000 : ℝ) = - (13748037340659291 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13748037340659291 / 10000000000000000 : ℚ)) - (U := (3183109820692313939357 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13748037340659291 / 10000000000000000 : ℝ) ≤ - (3183109820692313939357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3433948380588083 / 10000000000000000 : ℝ)) (q := - (13748037340659291 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13748037340659291 / 40000000000000000 : ℚ)) + (r' := (13748037340659291 / 10000000000000000 : ℚ)) + (U := (-(10679833785307686060643 / 10000000000000000000000 : ℚ))) + (U' := (3183109820692313939357 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (3433948380588083 / 10000000000000000 : ℚ)) + (q := (13748037340659291 / 40000000000000000 : ℚ)) + (U := (-(10679833785307686060643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_5 : Uω (aρ 5) (bρ 5) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3877,25 +3455,21 @@ lemma U_362_5 : have hlg : Real.log (13255379433889969 / 40000000000000000 : ℝ) ≤ (-(11044759885449248784207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13255379433889969 / 40000000000000000 : ℝ) = - (13255379433889969 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13255379433889969 / 10000000000000000 : ℚ)) - (U := (2818183720550751215793 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13255379433889969 / 10000000000000000 : ℝ) ≤ - (2818183720550751215793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1652904673269211 / 5000000000000000 : ℝ)) (q := - (13255379433889969 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13255379433889969 / 40000000000000000 : ℚ)) + (r' := (13255379433889969 / 10000000000000000 : ℚ)) + (U := (-(11044759885449248784207 / 10000000000000000000000 : ℚ))) + (U' := (2818183720550751215793 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (1652904673269211 / 5000000000000000 : ℚ)) + (q := (13255379433889969 / 40000000000000000 : ℚ)) + (U := (-(11044759885449248784207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_6 : Uω (aρ 6) (bρ 6) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3903,25 +3477,21 @@ lemma U_362_6 : have hlg : Real.log (12540269956705601 / 40000000000000000 : ℝ) ≤ (-(11599343909730129726657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12540269956705601 / 40000000000000000 : ℝ) = - (12540269956705601 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12540269956705601 / 10000000000000000 : ℚ)) - (U := (2263599696269870273343 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12540269956705601 / 10000000000000000 : ℝ) ≤ - (2263599696269870273343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1557747491543119 / 5000000000000000 : ℝ)) (q := - (12540269956705601 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12540269956705601 / 40000000000000000 : ℚ)) + (r' := (12540269956705601 / 10000000000000000 : ℚ)) + (U := (-(11599343909730129726657 / 10000000000000000000000 : ℚ))) + (U' := (2263599696269870273343 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (1557747491543119 / 5000000000000000 : ℚ)) + (q := (12540269956705601 / 40000000000000000 : ℚ)) + (U := (-(11599343909730129726657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_7 : Uω (aρ 7) (bρ 7) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3929,25 +3499,21 @@ lemma U_362_7 : have hlg : Real.log (11544187255281831 / 40000000000000000 : ℝ) ≤ (-(3106743528122563498903 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11544187255281831 / 40000000000000000 : ℝ) = - (11544187255281831 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11544187255281831 / 10000000000000000 : ℚ)) - (U := (358992373377436501097 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11544187255281831 / 10000000000000000 : ℝ) ≤ - (358992373377436501097 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2841115013134353 / 10000000000000000 : ℝ)) (q := - (11544187255281831 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11544187255281831 / 40000000000000000 : ℚ)) + (r' := (11544187255281831 / 10000000000000000 : ℚ)) + (U := (-(3106743528122563498903 / 2500000000000000000000 : ℚ))) + (U' := (358992373377436501097 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (2841115013134353 / 10000000000000000 : ℚ)) + (q := (11544187255281831 / 40000000000000000 : ℚ)) + (U := (-(3106743528122563498903 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_8 : Uω (aρ 8) (bρ 8) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3955,25 +3521,21 @@ lemma U_362_8 : have hlg : Real.log (10193839918233171 / 40000000000000000 : ℝ) ≤ (-(13670958453277325403241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10193839918233171 / 40000000000000000 : ℝ) = - (10193839918233171 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10193839918233171 / 10000000000000000 : ℚ)) - (U := (191985152722674596759 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10193839918233171 / 10000000000000000 : ℝ) ≤ - (191985152722674596759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2449482995950023 / 10000000000000000 : ℝ)) (q := - (10193839918233171 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10193839918233171 / 40000000000000000 : ℚ)) + (r' := (10193839918233171 / 10000000000000000 : ℚ)) + (U := (-(13670958453277325403241 / 10000000000000000000000 : ℚ))) + (U' := (191985152722674596759 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (2449482995950023 / 10000000000000000 : ℚ)) + (q := (10193839918233171 / 40000000000000000 : ℚ)) + (U := (-(13670958453277325403241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_9 : Uω (aρ 9) (bρ 9) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -3981,25 +3543,21 @@ lemma U_362_9 : have hlg : Real.log (1671812250119869 / 8000000000000000 : ℝ) ≤ (-(3913833307851789537159 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1671812250119869 / 8000000000000000 : ℝ) = - (1671812250119869 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1671812250119869 / 1000000000000000 : ℚ)) - (U := (1284770544398210462841 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1671812250119869 / 1000000000000000 : ℝ) ≤ - (1284770544398210462841 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (187305929049311 / 1000000000000000 : ℝ)) (q := - (1671812250119869 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1671812250119869 / 8000000000000000 : ℚ)) + (r' := (1671812250119869 / 1000000000000000 : ℚ)) + (U := (-(3913833307851789537159 / 2500000000000000000000 : ℚ))) + (U' := (1284770544398210462841 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (187305929049311 / 1000000000000000 : ℚ)) + (q := (1671812250119869 / 8000000000000000 : ℚ)) + (U := (-(3913833307851789537159 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_10 : Uω (aρ 10) (bρ 10) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -4007,23 +3565,21 @@ lemma U_362_10 : have hlg : Real.log (8754524920219 / 64000000000000 : ℝ) ≤ (-(9946561910692850307419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show (8754524920219 / 64000000000000 : ℝ) = (8754524920219 / 8000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8754524920219 / 8000000000000 : ℚ)) - (U := (450645793807149692581 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8754524920219 / 8000000000000 : ℝ) ≤ - (450645793807149692581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1308602778011 / 16000000000000 : ℝ)) (q := - (8754524920219 / 64000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8754524920219 / 64000000000000 : ℚ)) + (r' := (8754524920219 / 8000000000000 : ℚ)) + (U := (-(9946561910692850307419 / 5000000000000000000000 : ℚ))) + (U' := (450645793807149692581 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2338577156961 / 6400000000000 : ℚ)) + (s := (1308602778011 / 16000000000000 : ℚ)) + (q := (8754524920219 / 64000000000000 : ℚ)) + (U := (-(9946561910692850307419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_362_11 : Uω (aρ 11) (bρ 11) (2338577156961 / 6400000000000 : ℝ) ≤ @@ -4145,25 +3701,21 @@ lemma U_363_1 : have hlg : Real.log (57536400554320391 / 160000000000000000 : ℝ) ≤ (-(2045512028171230018933 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57536400554320391 / 160000000000000000 : ℝ) = - (57536400554320391 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57536400554320391 / 40000000000000000 : ℚ)) - (U := (727076693028769981067 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57536400554320391 / 40000000000000000 : ℝ) ≤ - (727076693028769981067 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1797990038629751 / 5000000000000000 : ℝ)) (q := - (57536400554320391 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57536400554320391 / 160000000000000000 : ℚ)) + (r' := (57536400554320391 / 40000000000000000 : ℚ)) + (U := (-(2045512028171230018933 / 2000000000000000000000 : ℚ))) + (U' := (727076693028769981067 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (1797990038629751 / 5000000000000000 : ℚ)) + (q := (57536400554320391 / 160000000000000000 : ℚ)) + (U := (-(2045512028171230018933 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_2 : Uω (aρ 2) (bρ 2) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4171,25 +3723,21 @@ lemma U_363_2 : have hlg : Real.log (57152063485113007 / 160000000000000000 : ℝ) ≤ (-(5147291593243858290007 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57152063485113007 / 160000000000000000 : ℝ) = - (57152063485113007 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57152063485113007 / 40000000000000000 : ℚ)) - (U := (1784180209756141709993 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57152063485113007 / 40000000000000000 : ℝ) ≤ - (1784180209756141709993 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3571706956118579 / 10000000000000000 : ℝ)) (q := - (57152063485113007 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57152063485113007 / 160000000000000000 : ℚ)) + (r' := (57152063485113007 / 40000000000000000 : ℚ)) + (U := (-(5147291593243858290007 / 5000000000000000000000 : ℚ))) + (U' := (1784180209756141709993 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (3571706956118579 / 10000000000000000 : ℚ)) + (q := (57152063485113007 / 160000000000000000 : ℚ)) + (U := (-(5147291593243858290007 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_3 : Uω (aρ 3) (bρ 3) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4197,25 +3745,21 @@ lemma U_363_3 : have hlg : Real.log (56381682546325183 / 160000000000000000 : ℝ) ≤ (-(325946714534062058909 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56381682546325183 / 160000000000000000 : ℝ) = - (56381682546325183 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56381682546325183 / 40000000000000000 : ℚ)) - (U := (107270273153437941091 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56381682546325183 / 40000000000000000 : ℝ) ≤ - (107270273153437941091 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3522805445120101 / 10000000000000000 : ℝ)) (q := - (56381682546325183 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56381682546325183 / 160000000000000000 : ℚ)) + (r' := (56381682546325183 / 40000000000000000 : ℚ)) + (U := (-(325946714534062058909 / 312500000000000000000 : ℚ))) + (U' := (107270273153437941091 / 312500000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (3522805445120101 / 10000000000000000 : ℚ)) + (q := (56381682546325183 / 160000000000000000 : ℚ)) + (U := (-(325946714534062058909 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_4 : Uω (aρ 4) (bρ 4) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4223,25 +3767,21 @@ lemma U_363_4 : have hlg : Real.log (55096888902770287 / 160000000000000000 : ℝ) ≤ (-(2665201407234472898471 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55096888902770287 / 160000000000000000 : ℝ) = - (55096888902770287 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55096888902770287 / 40000000000000000 : ℚ)) - (U := (800534494265527101529 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55096888902770287 / 40000000000000000 : ℝ) ≤ - (800534494265527101529 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3440500420740739 / 10000000000000000 : ℝ)) (q := - (55096888902770287 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55096888902770287 / 160000000000000000 : ℚ)) + (r' := (55096888902770287 / 40000000000000000 : ℚ)) + (U := (-(2665201407234472898471 / 2500000000000000000000 : ℚ))) + (U' := (800534494265527101529 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (3440500420740739 / 10000000000000000 : ℚ)) + (q := (55096888902770287 / 160000000000000000 : ℚ)) + (U := (-(2665201407234472898471 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_5 : Uω (aρ 5) (bρ 5) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4249,25 +3789,21 @@ lemma U_363_5 : have hlg : Real.log (53126418036573151 / 160000000000000000 : ℝ) ≤ (-(5512497476862254615211 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (53126418036573151 / 160000000000000000 : ℝ) = - (53126418036573151 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53126418036573151 / 40000000000000000 : ℚ)) - (U := (1418974326137745384789 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53126418036573151 / 40000000000000000 : ℝ) ≤ - (1418974326137745384789 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3312381481801097 / 10000000000000000 : ℝ)) (q := - (53126418036573151 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53126418036573151 / 160000000000000000 : ℚ)) + (r' := (53126418036573151 / 40000000000000000 : ℚ)) + (U := (-(5512497476862254615211 / 5000000000000000000000 : ℚ))) + (U' := (1418974326137745384789 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (3312381481801097 / 10000000000000000 : ℚ)) + (q := (53126418036573151 / 160000000000000000 : ℚ)) + (U := (-(5512497476862254615211 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_6 : Uω (aρ 6) (bρ 6) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4275,25 +3811,21 @@ lemma U_363_6 : have hlg : Real.log (10053276460035483 / 32000000000000000 : ℝ) ≤ (-(11578373049824663123831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10053276460035483 / 32000000000000000 : ℝ) = - (10053276460035483 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10053276460035483 / 8000000000000000 : ℚ)) - (U := (2284570556175336876169 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (10053276460035483 / 8000000000000000 : ℝ) ≤ - (2284570556175336876169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (312211738989163 / 1000000000000000 : ℝ)) (q := - (10053276460035483 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10053276460035483 / 32000000000000000 : ℚ)) + (r' := (10053276460035483 / 8000000000000000 : ℚ)) + (U := (-(11578373049824663123831 / 10000000000000000000000 : ℚ))) + (U' := (2284570556175336876169 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (312211738989163 / 1000000000000000 : ℚ)) + (q := (10053276460035483 / 32000000000000000 : ℚ)) + (U := (-(11578373049824663123831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_7 : Uω (aρ 7) (bρ 7) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4301,25 +3833,21 @@ lemma U_363_7 : have hlg : Real.log (9256609313099763 / 32000000000000000 : ℝ) ≤ (-(12403980855685154507843 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9256609313099763 / 32000000000000000 : ℝ) = - (9256609313099763 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9256609313099763 / 8000000000000000 : ℚ)) - (U := (1458962750314845492157 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9256609313099763 / 8000000000000000 : ℝ) ≤ - (1458962750314845492157 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (569572360763361 / 2000000000000000 : ℝ)) (q := - (9256609313099763 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9256609313099763 / 32000000000000000 : ℚ)) + (r' := (9256609313099763 / 8000000000000000 : ℚ)) + (U := (-(12403980855685154507843 / 10000000000000000000000 : ℚ))) + (U' := (1458962750314845492157 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (569572360763361 / 2000000000000000 : ℚ)) + (q := (9256609313099763 / 32000000000000000 : ℚ)) + (U := (-(12403980855685154507843 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_8 : Uω (aρ 8) (bρ 8) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4327,25 +3855,21 @@ lemma U_363_8 : have hlg : Real.log (40884222877358991 / 160000000000000000 : ℝ) ≤ (-(13644295748051856774619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40884222877358991 / 160000000000000000 : ℝ) = - (40884222877358991 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40884222877358991 / 40000000000000000 : ℚ)) - (U := (218647857948143225381 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40884222877358991 / 40000000000000000 : ℝ) ≤ - (218647857948143225381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2456550494139327 / 10000000000000000 : ℝ)) (q := - (40884222877358991 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40884222877358991 / 160000000000000000 : ℚ)) + (r' := (40884222877358991 / 40000000000000000 : ℚ)) + (U := (-(13644295748051856774619 / 10000000000000000000000 : ℚ))) + (U' := (218647857948143225381 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (2456550494139327 / 10000000000000000 : ℚ)) + (q := (40884222877358991 / 160000000000000000 : ℚ)) + (U := (-(13644295748051856774619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_9 : Uω (aρ 9) (bρ 9) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4353,25 +3877,21 @@ lemma U_363_9 : have hlg : Real.log (6710590335968427 / 32000000000000000 : ℝ) ≤ (-(15620489763713965806193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6710590335968427 / 32000000000000000 : ℝ) = - (6710590335968427 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6710590335968427 / 4000000000000000 : ℚ)) - (U := (5173925645286034193807 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6710590335968427 / 4000000000000000 : ℝ) ≤ - (5173925645286034193807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (47027680570243 / 250000000000000 : ℝ)) (q := - (6710590335968427 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6710590335968427 / 32000000000000000 : ℚ)) + (r' := (6710590335968427 / 4000000000000000 : ℚ)) + (U := (-(15620489763713965806193 / 10000000000000000000000 : ℚ))) + (U' := (5173925645286034193807 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (47027680570243 / 250000000000000 : ℚ)) + (q := (6710590335968427 / 32000000000000000 : ℚ)) + (U := (-(15620489763713965806193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_10 : Uω (aρ 10) (bρ 10) (46855260289479 / 128000000000000 : ℝ) ≤ @@ -4379,26 +3899,21 @@ lemma U_363_10 : have hlg : Real.log (22060408948427751 / 160000000000000000 : ℝ) ≤ (-(3962778525587527231453 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22060408948427751 / 160000000000000000 : ℝ) = - (22060408948427751 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22060408948427751 / 20000000000000000 : ℚ)) - (U := (196104556212472768547 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22060408948427751 / 20000000000000000 : ℝ) ≤ - (196104556212472768547 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (416549207438961 / 5000000000000000 : ℝ)) (q := - (22060408948427751 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22060408948427751 / 160000000000000000 : ℚ)) + (r' := (22060408948427751 / 20000000000000000 : ℚ)) + (U := (-(3962778525587527231453 / 2000000000000000000000 : ℚ))) + (U' := (196104556212472768547 / 2000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (46855260289479 / 128000000000000 : ℚ)) + (s := (416549207438961 / 5000000000000000 : ℚ)) + (q := (22060408948427751 / 160000000000000000 : ℚ)) + (U := (-(3962778525587527231453 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_363_11 : Uω (aρ 11) (bρ 11) (46855260289479 / 128000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U30.lean b/LeanPool/Zeta5Irrational/Table/U30.lean index ee0b700689..ce25525f03 100644 --- a/LeanPool/Zeta5Irrational/Table/U30.lean +++ b/LeanPool/Zeta5Irrational/Table/U30.lean @@ -24,25 +24,21 @@ lemma U_364_1 : have hlg : Real.log (28820524149035761 / 80000000000000000 : ℝ) ≤ (-(1020938856758552771767 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28820524149035761 / 80000000000000000 : ℝ) = - (28820524149035761 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28820524149035761 / 20000000000000000 : ℚ)) - (U := (365355503841447228233 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28820524149035761 / 20000000000000000 : ℝ) ≤ - (365355503841447228233 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3602520642864409 / 10000000000000000 : ℝ)) (q := - (28820524149035761 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28820524149035761 / 80000000000000000 : ℚ)) + (r' := (28820524149035761 / 20000000000000000 : ℚ)) + (U := (-(1020938856758552771767 / 1000000000000000000000 : ℚ))) + (U' := (365355503841447228233 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (3602520642864409 / 10000000000000000 : ℚ)) + (q := (28820524149035761 / 80000000000000000 : ℚ)) + (U := (-(1020938856758552771767 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_2 : Uω (aρ 2) (bρ 2) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_364_2 : have hlg : Real.log (28628359304545961 / 80000000000000000 : ℝ) ≤ (-(1284536029434866094411 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28628359304545961 / 80000000000000000 : ℝ) = - (28628359304545961 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28628359304545961 / 20000000000000000 : ℚ)) - (U := (448331921315133905589 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28628359304545961 / 20000000000000000 : ℝ) ≤ - (448331921315133905589 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3578248444251959 / 10000000000000000 : ℝ)) (q := - (28628359304545961 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28628359304545961 / 80000000000000000 : ℚ)) + (r' := (28628359304545961 / 20000000000000000 : ℚ)) + (U := (-(1284536029434866094411 / 1250000000000000000000 : ℚ))) + (U' := (448331921315133905589 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (3578248444251959 / 10000000000000000 : ℚ)) + (q := (28628359304545961 / 80000000000000000 : ℚ)) + (U := (-(1284536029434866094411 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_3 : Uω (aρ 3) (bρ 3) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_364_3 : have hlg : Real.log (28243180054274613 / 80000000000000000 : ℝ) ≤ (-(2602936549286429362049 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28243180054274613 / 80000000000000000 : ℝ) = - (28243180054274613 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28243180054274613 / 20000000000000000 : ℚ)) - (U := (862799352213570637951 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28243180054274613 / 20000000000000000 : ℝ) ≤ - (862799352213570637951 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1764674869017061 / 5000000000000000 : ℝ)) (q := - (28243180054274613 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28243180054274613 / 80000000000000000 : ℚ)) + (r' := (28243180054274613 / 20000000000000000 : ℚ)) + (U := (-(2602936549286429362049 / 2500000000000000000000 : ℚ))) + (U' := (862799352213570637951 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1764674869017061 / 5000000000000000 : ℚ)) + (q := (28243180054274613 / 80000000000000000 : ℚ)) + (U := (-(2602936549286429362049 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_4 : Uω (aρ 4) (bρ 4) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_364_4 : have hlg : Real.log (27600814044643157 / 80000000000000000 : ℝ) ≤ (-(10641813674947082111827 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27600814044643157 / 80000000000000000 : ℝ) = - (27600814044643157 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27600814044643157 / 20000000000000000 : ℚ)) - (U := (3221129931052917888173 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27600814044643157 / 20000000000000000 : ℝ) ≤ - (3221129931052917888173 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1723526208345629 / 5000000000000000 : ℝ)) (q := - (27600814044643157 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27600814044643157 / 80000000000000000 : ℚ)) + (r' := (27600814044643157 / 20000000000000000 : ℚ)) + (U := (-(10641813674947082111827 / 10000000000000000000000 : ℚ))) + (U' := (3221129931052917888173 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1723526208345629 / 5000000000000000 : ℚ)) + (q := (27600814044643157 / 80000000000000000 : ℚ)) + (U := (-(10641813674947082111827 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_5 : Uω (aρ 5) (bρ 5) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_364_5 : have hlg : Real.log (26615658667311261 / 80000000000000000 : ℝ) ≤ (-(1100526919862125627921 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26615658667311261 / 80000000000000000 : ℝ) = - (26615658667311261 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26615658667311261 / 20000000000000000 : ℚ)) - (U := (285767440737874372079 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26615658667311261 / 20000000000000000 : ℝ) ≤ - (285767440737874372079 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (829738372923321 / 2500000000000000 : ℝ)) (q := - (26615658667311261 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26615658667311261 / 80000000000000000 : ℚ)) + (r' := (26615658667311261 / 20000000000000000 : ℚ)) + (U := (-(1100526919862125627921 / 1000000000000000000000 : ℚ))) + (U' := (285767440737874372079 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (829738372923321 / 2500000000000000 : ℚ)) + (q := (26615658667311261 / 80000000000000000 : ℚ)) + (U := (-(1100526919862125627921 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_6 : Uω (aρ 6) (bρ 6) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_364_6 : have hlg : Real.log (25185841006774341 / 80000000000000000 : ℝ) ≤ (-(11557446623523384046263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25185841006774341 / 80000000000000000 : ℝ) = - (25185841006774341 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25185841006774341 / 20000000000000000 : ℚ)) - (U := (2305496982476615953737 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25185841006774341 / 20000000000000000 : ℝ) ≤ - (2305496982476615953737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1564369725849527 / 5000000000000000 : ℝ)) (q := - (25185841006774341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25185841006774341 / 80000000000000000 : ℚ)) + (r' := (25185841006774341 / 20000000000000000 : ℚ)) + (U := (-(11557446623523384046263 / 10000000000000000000000 : ℚ))) + (U' := (2305496982476615953737 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1564369725849527 / 5000000000000000 : ℚ)) + (q := (25185841006774341 / 80000000000000000 : ℚ)) + (U := (-(11557446623523384046263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_7 : Uω (aρ 7) (bρ 7) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_364_7 : have hlg : Real.log (23194668212276101 / 80000000000000000 : ℝ) ≤ (-(2476208400660810589321 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23194668212276101 / 80000000000000000 : ℝ) = - (23194668212276101 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23194668212276101 / 20000000000000000 : ℚ)) - (U := (296380320539189410679 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23194668212276101 / 20000000000000000 : ℝ) ≤ - (296380320539189410679 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1427303816917247 / 5000000000000000 : ℝ)) (q := - (23194668212276101 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23194668212276101 / 80000000000000000 : ℚ)) + (r' := (23194668212276101 / 20000000000000000 : ℚ)) + (U := (-(2476208400660810589321 / 2000000000000000000000 : ℚ))) + (U' := (296380320539189410679 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1427303816917247 / 5000000000000000 : ℚ)) + (q := (23194668212276101 / 80000000000000000 : ℚ)) + (U := (-(2476208400660810589321 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_8 : Uω (aρ 8) (bρ 8) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_364_8 : have hlg : Real.log (20496531395139397 / 80000000000000000 : ℝ) ≤ (-(1702213703203382586437 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20496531395139397 / 80000000000000000 : ℝ) = - (20496531395139397 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20496531395139397 / 20000000000000000 : ℚ)) - (U := (30654247546617413563 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20496531395139397 / 20000000000000000 : ℝ) ≤ - (30654247546617413563 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1231807540445159 / 5000000000000000 : ℝ)) (q := - (20496531395139397 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20496531395139397 / 80000000000000000 : ℚ)) + (r' := (20496531395139397 / 20000000000000000 : ℚ)) + (U := (-(1702213703203382586437 / 1250000000000000000000 : ℚ))) + (U' := (30654247546617413563 / 1250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1231807540445159 / 5000000000000000 : ℚ)) + (q := (20496531395139397 / 80000000000000000 : ℚ)) + (U := (-(1702213703203382586437 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_9 : Uω (aρ 9) (bρ 9) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_364_9 : have hlg : Real.log (16834782613025601 / 80000000000000000 : ℝ) ≤ (-(155857949416357088431 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16834782613025601 / 80000000000000000 : ℝ) = - (16834782613025601 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16834782613025601 / 10000000000000000 : ℚ)) - (U := (52086204673642911569 / 100000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16834782613025601 / 10000000000000000 : ℝ) ≤ - (52086204673642911569 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1889143513721869 / 10000000000000000 : ℝ)) (q := - (16834782613025601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16834782613025601 / 80000000000000000 : ℚ)) + (r' := (16834782613025601 / 10000000000000000 : ℚ)) + (U := (-(155857949416357088431 / 100000000000000000000 : ℚ))) + (U' := (52086204673642911569 / 100000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (1889143513721869 / 10000000000000000 : ℚ)) + (q := (16834782613025601 / 80000000000000000 : ℚ)) + (U := (-(155857949416357088431 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_10 : Uω (aρ 10) (bρ 10) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_364_10 : have hlg : Real.log (11116361872933557 / 80000000000000000 : ℝ) ≤ (-(19736085683035117132133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (11116361872933557 / 80000000000000000 : ℝ) = - (11116361872933557 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11116361872933557 / 10000000000000000 : ℚ)) - (U := (1058329725964882867867 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11116361872933557 / 10000000000000000 : ℝ) ≤ - (1058329725964882867867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (424048681096929 / 5000000000000000 : ℝ)) (q := - (11116361872933557 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11116361872933557 / 80000000000000000 : ℚ)) + (r' := (11116361872933557 / 10000000000000000 : ℚ)) + (U := (-(19736085683035117132133 / 10000000000000000000000 : ℚ))) + (U' := (1058329725964882867867 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23469488719869 / 64000000000000 : ℚ)) + (s := (424048681096929 / 5000000000000000 : ℚ)) + (q := (11116361872933557 / 80000000000000000 : ℚ)) + (U := (-(19736085683035117132133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_364_11 : Uω (aρ 11) (bρ 11) (23469488719869 / 64000000000000 : ℝ) ≤ @@ -399,25 +358,21 @@ lemma U_365_1 : have hlg : Real.log (57745696037089349 / 160000000000000000 : ℝ) ≤ (-(5095624977928167751467 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57745696037089349 / 160000000000000000 : ℝ) = - (57745696037089349 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57745696037089349 / 40000000000000000 : ℚ)) - (U := (1835846825071832248533 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57745696037089349 / 40000000000000000 : ℝ) ≤ - (1835846825071832248533 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3609061207877653 / 10000000000000000 : ℝ)) (q := - (57745696037089349 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57745696037089349 / 160000000000000000 : ℚ)) + (r' := (57745696037089349 / 40000000000000000 : ℚ)) + (U := (-(5095624977928167751467 / 5000000000000000000000 : ℚ))) + (U' := (1835846825071832248533 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (3609061207877653 / 10000000000000000 : ℚ)) + (q := (57745696037089349 / 160000000000000000 : ℚ)) + (U := (-(5095624977928167751467 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_2 : Uω (aρ 2) (bρ 2) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -425,25 +380,21 @@ lemma U_365_2 : have hlg : Real.log (57361373701372661 / 160000000000000000 : ℝ) ≤ (-(2051605339881276118719 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57361373701372661 / 160000000000000000 : ℝ) = - (57361373701372661 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57361373701372661 / 40000000000000000 : ℚ)) - (U := (720983381318723881281 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57361373701372661 / 40000000000000000 : ℝ) ≤ - (720983381318723881281 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3584789928423067 / 10000000000000000 : ℝ)) (q := - (57361373701372661 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57361373701372661 / 160000000000000000 : ℚ)) + (r' := (57361373701372661 / 40000000000000000 : ℚ)) + (U := (-(2051605339881276118719 / 2000000000000000000000 : ℚ))) + (U' := (720983381318723881281 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (3584789928423067 / 10000000000000000 : ℚ)) + (q := (57361373701372661 / 160000000000000000 : ℚ)) + (U := (-(2051605339881276118719 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_3 : Uω (aρ 3) (bρ 3) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -451,25 +402,21 @@ lemma U_365_3 : have hlg : Real.log (56591037555596373 / 160000000000000000 : ℝ) ≤ (-(5196615945586448281083 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56591037555596373 / 160000000000000000 : ℝ) = - (56591037555596373 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56591037555596373 / 40000000000000000 : ℚ)) - (U := (1734855857413551718917 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56591037555596373 / 40000000000000000 : ℝ) ≤ - (1734855857413551718917 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3535894016551031 / 10000000000000000 : ℝ)) (q := - (56591037555596373 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56591037555596373 / 160000000000000000 : ℚ)) + (r' := (56591037555596373 / 40000000000000000 : ℚ)) + (U := (-(5196615945586448281083 / 5000000000000000000000 : ℚ))) + (U' := (1734855857413551718917 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (3535894016551031 / 10000000000000000 : ℚ)) + (q := (56591037555596373 / 160000000000000000 : ℚ)) + (U := (-(5196615945586448281083 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_4 : Uω (aρ 4) (bρ 4) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -477,25 +424,21 @@ lemma U_365_4 : have hlg : Real.log (55306366924197853 / 160000000000000000 : ℝ) ≤ (-(1327857223199951105543 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55306366924197853 / 160000000000000000 : ℝ) = - (55306366924197853 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55306366924197853 / 40000000000000000 : ℚ)) - (U := (405010727550048894457 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55306366924197853 / 40000000000000000 : ℝ) ≤ - (405010727550048894457 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (215850273043201 / 625000000000000 : ℝ)) (q := - (55306366924197853 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55306366924197853 / 160000000000000000 : ℚ)) + (r' := (55306366924197853 / 40000000000000000 : ℚ)) + (U := (-(1327857223199951105543 / 1250000000000000000000 : ℚ))) + (U' := (405010727550048894457 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (215850273043201 / 625000000000000 : ℚ)) + (q := (55306366924197853 / 160000000000000000 : ℚ)) + (U := (-(1327857223199951105543 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_5 : Uω (aρ 5) (bρ 5) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -503,25 +446,21 @@ lemma U_365_5 : have hlg : Real.log (53336215635654253 / 160000000000000000 : ℝ) ≤ (-(10985582464399812475231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (53336215635654253 / 160000000000000000 : ℝ) = - (53336215635654253 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53336215635654253 / 40000000000000000 : ℚ)) - (U := (2877361141600187524769 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53336215635654253 / 40000000000000000 : ℝ) ≤ - (2877361141600187524769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1662762688479133 / 5000000000000000 : ℝ)) (q := - (53336215635654253 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53336215635654253 / 160000000000000000 : ℚ)) + (r' := (53336215635654253 / 40000000000000000 : ℚ)) + (U := (-(10985582464399812475231 / 10000000000000000000000 : ℚ))) + (U' := (2877361141600187524769 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (1662762688479133 / 5000000000000000 : ℚ)) + (q := (53336215635654253 / 160000000000000000 : ℚ)) + (U := (-(10985582464399812475231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_6 : Uω (aρ 6) (bρ 6) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -529,25 +468,21 @@ lemma U_365_6 : have hlg : Real.log (2019079159376957 / 6400000000000000 : ℝ) ≤ (-(11536564440637285168937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2019079159376957 / 6400000000000000 : ℝ) = - (2019079159376957 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2019079159376957 / 1600000000000000 : ℚ)) - (U := (2326379165362714831063 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2019079159376957 / 1600000000000000 : ℝ) ≤ - (2326379165362714831063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (125414446827779 / 400000000000000 : ℝ)) (q := - (2019079159376957 / 6400000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2019079159376957 / 6400000000000000 : ℚ)) + (r' := (2019079159376957 / 1600000000000000 : ℚ)) + (U := (-(11536564440637285168937 / 10000000000000000000000 : ℚ))) + (U' := (2326379165362714831063 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (125414446827779 / 400000000000000 : ℚ)) + (q := (2019079159376957 / 6400000000000000 : ℚ)) + (U := (-(11536564440637285168937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_7 : Uω (aρ 7) (bρ 7) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -555,25 +490,21 @@ lemma U_365_7 : have hlg : Real.log (46495618652643429 / 160000000000000000 : ℝ) ≤ (-(12358157290836437477463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46495618652643429 / 160000000000000000 : ℝ) = - (46495618652643429 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46495618652643429 / 40000000000000000 : ℚ)) - (U := (1504786315163562522537 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46495618652643429 / 40000000000000000 : ℝ) ≤ - (1504786315163562522537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2861352509981913 / 10000000000000000 : ℝ)) (q := - (46495618652643429 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46495618652643429 / 160000000000000000 : ℚ)) + (r' := (46495618652643429 / 40000000000000000 : ℚ)) + (U := (-(12358157290836437477463 / 10000000000000000000000 : ℚ))) + (U' := (1504786315163562522537 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (2861352509981913 / 10000000000000000 : ℚ)) + (q := (46495618652643429 / 160000000000000000 : ℚ)) + (U := (-(12358157290836437477463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_8 : Uω (aρ 8) (bρ 8) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -581,25 +512,21 @@ lemma U_365_8 : have hlg : Real.log (41101879611489413 / 160000000000000000 : ℝ) ≤ (-(6795599808089037888341 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41101879611489413 / 160000000000000000 : ℝ) = - (41101879611489413 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41101879611489413 / 40000000000000000 : ℚ)) - (U := (135871994910962111659 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41101879611489413 / 40000000000000000 : ℝ) ≤ - (135871994910962111659 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2470676781177661 / 10000000000000000 : ℝ)) (q := - (41101879611489413 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41101879611489413 / 160000000000000000 : ℚ)) + (r' := (41101879611489413 / 40000000000000000 : ℚ)) + (U := (-(6795599808089037888341 / 5000000000000000000000 : ℚ))) + (U' := (135871994910962111659 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (2470676781177661 / 10000000000000000 : ℚ)) + (q := (41101879611489413 / 160000000000000000 : ℚ)) + (U := (-(6795599808089037888341 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_9 : Uω (aρ 9) (bρ 9) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -607,25 +534,21 @@ lemma U_365_9 : have hlg : Real.log (6757217364903913 / 32000000000000000 : ℝ) ≤ (-(3887811822798896889681 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6757217364903913 / 32000000000000000 : ℝ) = - (6757217364903913 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6757217364903913 / 4000000000000000 : ℚ)) - (U := (1310792029451103110319 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6757217364903913 / 4000000000000000 : ℝ) ≤ - (1310792029451103110319 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (189716831116643 / 1000000000000000 : ℝ)) (q := - (6757217364903913 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6757217364903913 / 32000000000000000 : ℚ)) + (r' := (6757217364903913 / 4000000000000000 : ℚ)) + (U := (-(3887811822798896889681 / 2500000000000000000000 : ℚ))) + (U' := (1310792029451103110319 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (189716831116643 / 1000000000000000 : ℚ)) + (q := (6757217364903913 / 32000000000000000 : ℚ)) + (U := (-(3887811822798896889681 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_10 : Uω (aρ 10) (bρ 10) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -633,26 +556,21 @@ lemma U_365_10 : have hlg : Real.log (22403349611579381 / 160000000000000000 : ℝ) ≤ (-(19659633305412022108387 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22403349611579381 / 160000000000000000 : ℝ) = - (22403349611579381 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22403349611579381 / 20000000000000000 : ℚ)) - (U := (1134782103587977891613 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22403349611579381 / 20000000000000000 : ℝ) ≤ - (1134782103587977891613 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (862885193043907 / 10000000000000000 : ℝ)) (q := - (22403349611579381 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22403349611579381 / 160000000000000000 : ℚ)) + (r' := (22403349611579381 / 20000000000000000 : ℚ)) + (U := (-(19659633305412022108387 / 10000000000000000000000 : ℚ))) + (U' := (1134782103587977891613 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47022694589997 / 128000000000000 : ℚ)) + (s := (862885193043907 / 10000000000000000 : ℚ)) + (q := (22403349611579381 / 160000000000000000 : ℚ)) + (U := (-(19659633305412022108387 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_365_11 : Uω (aρ 11) (bρ 11) (47022694589997 / 128000000000000 : ℝ) ≤ @@ -775,25 +693,21 @@ lemma U_366_1 : have hlg : Real.log (1446258594284989 / 4000000000000000 : ℝ) ≤ (-(1017314418630376217589 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1446258594284989 / 4000000000000000 : ℝ) = - (1446258594284989 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1446258594284989 / 1000000000000000 : ℚ)) - (U := (368979941969623782411 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1446258594284989 / 1000000000000000 : ℝ) ≤ - (368979941969623782411 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (723120354460489 / 2000000000000000 : ℝ)) (q := - (1446258594284989 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1446258594284989 / 4000000000000000 : ℚ)) + (r' := (1446258594284989 / 1000000000000000 : ℚ)) + (U := (-(1017314418630376217589 / 1000000000000000000000 : ℚ))) + (U' := (368979941969623782411 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (723120354460489 / 2000000000000000 : ℚ)) + (q := (1446258594284989 / 4000000000000000 : ℚ)) + (U := (-(1017314418630376217589 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_2 : Uω (aρ 2) (bρ 2) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -801,25 +715,21 @@ lemma U_366_2 : have hlg : Real.log (1795813398816513 / 5000000000000000 : ℝ) ≤ (-(10239798456410631867589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1795813398816513 / 5000000000000000 : ℝ) = - (1795813398816513 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1795813398816513 / 1250000000000000 : ℚ)) - (U := (3623145149589368132411 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1795813398816513 / 1250000000000000 : ℝ) ≤ - (3623145149589368132411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (224458213040847 / 625000000000000 : ℝ)) (q := - (1795813398816513 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1795813398816513 / 5000000000000000 : ℚ)) + (r' := (1795813398816513 / 1250000000000000 : ℚ)) + (U := (-(10239798456410631867589 / 10000000000000000000000 : ℚ))) + (U' := (3623145149589368132411 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (224458213040847 / 625000000000000 : ℚ)) + (q := (1795813398816513 / 5000000000000000 : ℚ)) + (U := (-(10239798456410631867589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_3 : Uω (aρ 3) (bρ 3) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -827,23 +737,21 @@ lemma U_366_3 : have hlg : Real.log (11073381814083 / 31250000000000 : ℝ) ≤ (-(64842198875117124881 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (11073381814083 / 31250000000000 : ℝ) = (11073381814083 / 7812500000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11073381814083 / 7812500000000 : ℚ)) - (U := (21801198662382875119 / 62500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (11073381814083 / 7812500000000 : ℝ) ≤ - (21801198662382875119 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177121914037531 / 500000000000000 : ℝ)) (q := - (11073381814083 / 31250000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11073381814083 / 31250000000000 : ℚ)) + (r' := (11073381814083 / 7812500000000 : ℚ)) + (U := (-(64842198875117124881 / 62500000000000000000 : ℚ))) + (U' := (21801198662382875119 / 62500000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (177121914037531 / 500000000000000 : ℚ)) + (q := (11073381814083 / 31250000000000 : ℚ)) + (U := (-(64842198875117124881 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_4 : Uω (aρ 4) (bρ 4) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -851,25 +759,21 @@ lemma U_366_4 : have hlg : Real.log (6926388176187779 / 20000000000000000 : ℝ) ≤ (-(10603937823945748174413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6926388176187779 / 20000000000000000 : ℝ) = - (6926388176187779 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6926388176187779 / 5000000000000000 : ℚ)) - (U := (3259005782054251825587 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6926388176187779 / 5000000000000000 : ℝ) ≤ - (3259005782054251825587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3460156276990279 / 10000000000000000 : ℝ)) (q := - (6926388176187779 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6926388176187779 / 20000000000000000 : ℚ)) + (r' := (6926388176187779 / 5000000000000000 : ℚ)) + (U := (-(10603937823945748174413 / 10000000000000000000000 : ℚ))) + (U' := (3259005782054251825587 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (3460156276990279 / 10000000000000000 : ℚ)) + (q := (6926388176187779 / 20000000000000000 : ℚ)) + (U := (-(10603937823945748174413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_5 : Uω (aρ 5) (bρ 5) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -877,25 +781,21 @@ lemma U_366_5 : have hlg : Real.log (6680139118195949 / 20000000000000000 : ℝ) ≤ (-(2741483649062919691693 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6680139118195949 / 20000000000000000 : ℝ) = - (6680139118195949 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6680139118195949 / 5000000000000000 : ℚ)) - (U := (724252252437080308307 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6680139118195949 / 5000000000000000 : ℝ) ≤ - (724252252437080308307 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3332097138333449 / 10000000000000000 : ℝ)) (q := - (6680139118195949 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6680139118195949 / 20000000000000000 : ℚ)) + (r' := (6680139118195949 / 5000000000000000 : ℚ)) + (U := (-(2741483649062919691693 / 2500000000000000000000 : ℚ))) + (U' := (724252252437080308307 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (3332097138333449 / 10000000000000000 : ℚ)) + (q := (6680139118195949 / 20000000000000000 : ℚ)) + (U := (-(2741483649062919691693 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_6 : Uω (aρ 6) (bρ 6) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -903,25 +803,21 @@ lemma U_366_6 : have hlg : Real.log (6322784153767821 / 20000000000000000 : ℝ) ≤ (-(5757863156105059112447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6322784153767821 / 20000000000000000 : ℝ) = - (6322784153767821 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6322784153767821 / 5000000000000000 : ℚ)) - (U := (1173608646894940887553 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6322784153767821 / 5000000000000000 : ℝ) ≤ - (1173608646894940887553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3141982549045321 / 10000000000000000 : ℝ)) (q := - (6322784153767821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6322784153767821 / 20000000000000000 : ℚ)) + (r' := (6322784153767821 / 5000000000000000 : ℚ)) + (U := (-(5757863156105059112447 / 5000000000000000000000 : ℚ))) + (U' := (1173608646894940887553 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (3141982549045321 / 10000000000000000 : ℚ)) + (q := (6322784153767821 / 20000000000000000 : ℚ)) + (U := (-(5757863156105059112447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_7 : Uω (aρ 7) (bρ 7) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -929,25 +825,21 @@ lemma U_366_7 : have hlg : Real.log (5825236662951187 / 20000000000000000 : ℝ) ≤ (-(3083831613937107456921 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5825236662951187 / 20000000000000000 : ℝ) = - (5825236662951187 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5825236662951187 / 5000000000000000 : ℚ)) - (U := (381904287562892543079 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5825236662951187 / 5000000000000000 : ℝ) ≤ - (381904287562892543079 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2868096438988687 / 10000000000000000 : ℝ)) (q := - (5825236662951187 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5825236662951187 / 20000000000000000 : ℚ)) + (r' := (5825236662951187 / 5000000000000000 : ℚ)) + (U := (-(3083831613937107456921 / 2500000000000000000000 : ℚ))) + (U' := (381904287562892543079 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (2868096438988687 / 10000000000000000 : ℚ)) + (q := (5825236662951187 / 20000000000000000 : ℚ)) + (U := (-(3083831613937107456921 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_8 : Uω (aρ 8) (bρ 8) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -955,25 +847,21 @@ lemma U_366_8 : have hlg : Real.log (5151334192303659 / 20000000000000000 : ℝ) ≤ (-(1356476525443648126067 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5151334192303659 / 20000000000000000 : ℝ) = - (5151334192303659 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5151334192303659 / 5000000000000000 : ℚ)) - (U := (29817835156351873933 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5151334192303659 / 5000000000000000 : ℝ) ≤ - (29817835156351873933 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2477735619681159 / 10000000000000000 : ℝ)) (q := - (5151334192303659 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5151334192303659 / 20000000000000000 : ℚ)) + (r' := (5151334192303659 / 5000000000000000 : ℚ)) + (U := (-(1356476525443648126067 / 1000000000000000000000 : ℚ))) + (U' := (29817835156351873933 / 1000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (2477735619681159 / 10000000000000000 : ℚ)) + (q := (5151334192303659 / 20000000000000000 : ℚ)) + (U := (-(1356476525443648126067 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_9 : Uω (aρ 9) (bρ 9) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -981,25 +869,21 @@ lemma U_366_9 : have hlg : Real.log (4237814704640477 / 20000000000000000 : ℝ) ≤ (-(969802835152118119703 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4237814704640477 / 20000000000000000 : ℝ) = - (4237814704640477 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4237814704640477 / 2500000000000000 : ℚ)) - (U := (329848127910381880297 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4237814704640477 / 2500000000000000 : ℝ) ≤ - (329848127910381880297 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1905181760377977 / 10000000000000000 : ℝ)) (q := - (4237814704640477 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4237814704640477 / 20000000000000000 : ℚ)) + (r' := (4237814704640477 / 2500000000000000 : ℚ)) + (U := (-(969802835152118119703 / 625000000000000000000 : ℚ))) + (U' := (329848127910381880297 / 625000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (1905181760377977 / 10000000000000000 : ℚ)) + (q := (4237814704640477 / 20000000000000000 : ℚ)) + (U := (-(969802835152118119703 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_10 : Uω (aρ 10) (bρ 10) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -1007,26 +891,21 @@ lemma U_366_10 : have hlg : Real.log (1410773245971509 / 10000000000000000 : ℝ) ≤ (-(4896117841857481864347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1410773245971509 / 10000000000000000 : ℝ) = - (1410773245971509 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1410773245971509 / 1250000000000000 : ℚ)) - (U := (302486010392518135653 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1410773245971509 / 1250000000000000 : ℝ) ≤ - (302486010392518135653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (438736290587759 / 5000000000000000 : ℝ)) (q := - (1410773245971509 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1410773245971509 / 10000000000000000 : ℚ)) + (r' := (1410773245971509 / 1250000000000000 : ℚ)) + (U := (-(4896117841857481864347 / 2500000000000000000000 : ℚ))) + (U' := (302486010392518135653 / 2500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1472075366883 / 4000000000000 : ℚ)) + (s := (438736290587759 / 5000000000000000 : ℚ)) + (q := (1410773245971509 / 10000000000000000 : ℚ)) + (U := (-(4896117841857481864347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_366_11 : Uω (aρ 11) (bρ 11) (1472075366883 / 4000000000000 : ℝ) ≤ @@ -1147,25 +1026,21 @@ lemma U_367_1 : have hlg : Real.log (57954991501027651 / 160000000000000000 : ℝ) ≤ (-(10155071140210231970999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57954991501027651 / 160000000000000000 : ℝ) = - (57954991501027651 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57954991501027651 / 40000000000000000 : ℚ)) - (U := (3707872465789768029001 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (57954991501027651 / 40000000000000000 : ℝ) ≤ - (3707872465789768029001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (905535584035493 / 2500000000000000 : ℝ)) (q := - (57954991501027651 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57954991501027651 / 160000000000000000 : ℚ)) + (r' := (57954991501027651 / 40000000000000000 : ℚ)) + (U := (-(10155071140210231970999 / 10000000000000000000000 : ℚ))) + (U' := (3707872465789768029001 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (905535584035493 / 2500000000000000 : ℚ)) + (q := (57954991501027651 / 160000000000000000 : ℚ)) + (U := (-(10155071140210231970999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_2 : Uω (aρ 2) (bρ 2) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1173,25 +1048,21 @@ lemma U_367_2 : have hlg : Real.log (57570683791531163 / 160000000000000000 : ℝ) ≤ (-(5110801692648868227249 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57570683791531163 / 160000000000000000 : ℝ) = - (57570683791531163 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57570683791531163 / 40000000000000000 : ℚ)) - (U := (1820670110351131772751 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57570683791531163 / 40000000000000000 : ℝ) ≤ - (1820670110351131772751 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3597872884964911 / 10000000000000000 : ℝ)) (q := - (57570683791531163 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57570683791531163 / 160000000000000000 : ℚ)) + (r' := (57570683791531163 / 40000000000000000 : ℚ)) + (U := (-(5110801692648868227249 / 5000000000000000000000 : ℚ))) + (U' := (1820670110351131772751 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (3597872884964911 / 10000000000000000 : ℚ)) + (q := (57570683791531163 / 160000000000000000 : ℚ)) + (U := (-(5110801692648868227249 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_3 : Uω (aρ 3) (bρ 3) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1199,25 +1070,21 @@ lemma U_367_3 : have hlg : Real.log (11360078421341719 / 32000000000000000 : ℝ) ≤ (-(10356305857235350616427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11360078421341719 / 32000000000000000 : ℝ) = - (11360078421341719 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11360078421341719 / 8000000000000000 : ℚ)) - (U := (3506637748764649383573 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (11360078421341719 / 8000000000000000 : ℝ) ≤ - (3506637748764649383573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (354898253071209 / 1000000000000000 : ℝ)) (q := - (11360078421341719 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11360078421341719 / 32000000000000000 : ℚ)) + (r' := (11360078421341719 / 8000000000000000 : ℚ)) + (U := (-(10356305857235350616427 / 10000000000000000000000 : ℚ))) + (U' := (3506637748764649383573 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (354898253071209 / 1000000000000000 : ℚ)) + (q := (11360078421341719 / 32000000000000000 : ℚ)) + (U := (-(10356305857235350616427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_4 : Uω (aρ 4) (bρ 4) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1225,25 +1092,21 @@ lemma U_367_4 : have hlg : Real.log (2220633741887267 / 6400000000000000 : ℝ) ≤ (-(5292526826907858834617 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2220633741887267 / 6400000000000000 : ℝ) = - (2220633741887267 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2220633741887267 / 1600000000000000 : ℚ)) - (U := (1638944976092141165383 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2220633741887267 / 1600000000000000 : ℝ) ≤ - (1638944976092141165383 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138668325673449 / 400000000000000 : ℝ)) (q := - (2220633741887267 / 6400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2220633741887267 / 6400000000000000 : ℚ)) + (r' := (2220633741887267 / 1600000000000000 : ℚ)) + (U := (-(5292526826907858834617 / 5000000000000000000000 : ℚ))) + (U' := (1638944976092141165383 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (138668325673449 / 400000000000000 : ℚ)) + (q := (2220633741887267 / 6400000000000000 : ℚ)) + (U := (-(5292526826907858834617 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_5 : Uω (aρ 5) (bρ 5) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1251,25 +1114,21 @@ lemma U_367_5 : have hlg : Real.log (53546009270215219 / 160000000000000000 : ℝ) ≤ (-(10946325440292095100241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (53546009270215219 / 160000000000000000 : ℝ) = - (53546009270215219 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53546009270215219 / 40000000000000000 : ℚ)) - (U := (2916618165707904899759 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53546009270215219 / 40000000000000000 : ℝ) ≤ - (2916618165707904899759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1669334388275209 / 5000000000000000 : ℝ)) (q := - (53546009270215219 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53546009270215219 / 160000000000000000 : ℚ)) + (r' := (53546009270215219 / 40000000000000000 : ℚ)) + (U := (-(10946325440292095100241 / 10000000000000000000000 : ℚ))) + (U' := (2916618165707904899759 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (1669334388275209 / 5000000000000000 : ℚ)) + (q := (53546009270215219 / 160000000000000000 : ℚ)) + (U := (-(10946325440292095100241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_6 : Uω (aρ 6) (bρ 6) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1277,25 +1136,21 @@ lemma U_367_6 : have hlg : Real.log (50687564767897259 / 160000000000000000 : ℝ) ≤ (-(11494932050507656954393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (50687564767897259 / 160000000000000000 : ℝ) = - (50687564767897259 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50687564767897259 / 40000000000000000 : ℚ)) - (U := (2368011555492343045607 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50687564767897259 / 40000000000000000 : ℝ) ≤ - (2368011555492343045607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3148603588900673 / 10000000000000000 : ℝ)) (q := - (50687564767897259 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50687564767897259 / 160000000000000000 : ℚ)) + (r' := (50687564767897259 / 40000000000000000 : ℚ)) + (U := (-(11494932050507656954393 / 10000000000000000000000 : ℚ))) + (U' := (2368011555492343045607 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (3148603588900673 / 10000000000000000 : ℚ)) + (q := (50687564767897259 / 160000000000000000 : ℚ)) + (U := (-(11494932050507656954393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_7 : Uω (aρ 7) (bρ 7) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1303,25 +1158,21 @@ lemma U_367_7 : have hlg : Real.log (46708160430774691 / 160000000000000000 : ℝ) ≤ (-(12312549237462678980321 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46708160430774691 / 160000000000000000 : ℝ) = - (46708160430774691 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46708160430774691 / 40000000000000000 : ℚ)) - (U := (1550394368537321019679 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46708160430774691 / 40000000000000000 : ℝ) ≤ - (1550394368537321019679 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89838732110011 / 312500000000000 : ℝ)) (q := - (46708160430774691 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46708160430774691 / 160000000000000000 : ℚ)) + (r' := (46708160430774691 / 40000000000000000 : ℚ)) + (U := (-(12312549237462678980321 / 10000000000000000000000 : ℚ))) + (U' := (1550394368537321019679 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (89838732110011 / 312500000000000 : ℚ)) + (q := (46708160430774691 / 160000000000000000 : ℚ)) + (U := (-(12312549237462678980321 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_8 : Uω (aρ 8) (bρ 8) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1329,25 +1180,21 @@ lemma U_367_8 : have hlg : Real.log (1652777790648547 / 6400000000000000 : ℝ) ≤ (-(3384601519907263353979 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1652777790648547 / 6400000000000000 : ℝ) = - (1652777790648547 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1652777790648547 / 1600000000000000 : ℚ)) - (U := (81134381592736646021 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1652777790648547 / 1600000000000000 : ℝ) ≤ - (81134381592736646021 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99391664831609 / 400000000000000 : ℝ)) (q := - (1652777790648547 / 6400000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1652777790648547 / 6400000000000000 : ℚ)) + (r' := (1652777790648547 / 1600000000000000 : ℚ)) + (U := (-(3384601519907263353979 / 2500000000000000000000 : ℚ))) + (U' := (81134381592736646021 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (99391664831609 / 400000000000000 : ℚ)) + (q := (1652777790648547 / 6400000000000000 : ℚ)) + (U := (-(3384601519907263353979 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_9 : Uω (aρ 9) (bρ 9) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1355,25 +1202,21 @@ lemma U_367_9 : have hlg : Real.log (34018858804644867 / 160000000000000000 : ℝ) ≤ (-(7741293864429637342667 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34018858804644867 / 160000000000000000 : ℝ) = - (34018858804644867 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34018858804644867 / 20000000000000000 : ℚ)) - (U := (2655913840070362657333 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34018858804644867 / 20000000000000000 : ℝ) ≤ - (2655913840070362657333 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (478296000988531 / 2500000000000000 : ℝ)) (q := - (34018858804644867 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34018858804644867 / 160000000000000000 : ℚ)) + (r' := (34018858804644867 / 20000000000000000 : ℚ)) + (U := (-(7741293864429637342667 / 5000000000000000000000 : ℚ))) + (U' := (2655913840070362657333 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (478296000988531 / 2500000000000000 : ℚ)) + (q := (34018858804644867 / 160000000000000000 : ℚ)) + (U := (-(7741293864429637342667 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_10 : Uω (aρ 10) (bρ 10) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1381,26 +1224,21 @@ lemma U_367_10 : have hlg : Real.log (22739869400635267 / 160000000000000000 : ℝ) ≤ (-(19510540693039739543589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (22739869400635267 / 160000000000000000 : ℝ) = - (22739869400635267 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22739869400635267 / 20000000000000000 : ℚ)) - (U := (1283874715960260456411 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22739869400635267 / 20000000000000000 : ℝ) ≤ - (1283874715960260456411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (222967340486981 / 2500000000000000 : ℝ)) (q := - (22739869400635267 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22739869400635267 / 160000000000000000 : ℚ)) + (r' := (22739869400635267 / 20000000000000000 : ℚ)) + (U := (-(19510540693039739543589 / 10000000000000000000000 : ℚ))) + (U' := (1283874715960260456411 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9438025778103 / 25600000000000 : ℚ)) + (s := (222967340486981 / 2500000000000000 : ℚ)) + (q := (22739869400635267 / 160000000000000000 : ℚ)) + (U := (-(19510540693039739543589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_367_11 : Uω (aρ 11) (bρ 11) (9438025778103 / 25600000000000 : ℝ) ≤ @@ -1523,25 +1361,21 @@ lemma U_368_1 : have hlg : Real.log (29029819612999467 / 80000000000000000 : ℝ) ≤ (-(5068515349750366186051 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29029819612999467 / 80000000000000000 : ℝ) = - (29029819612999467 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29029819612999467 / 20000000000000000 : ℚ)) - (U := (1862956453249633813949 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29029819612999467 / 20000000000000000 : ℝ) ≤ - (1862956453249633813949 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1814341449699699 / 5000000000000000 : ℝ)) (q := - (29029819612999467 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29029819612999467 / 80000000000000000 : ℚ)) + (r' := (29029819612999467 / 20000000000000000 : ℚ)) + (U := (-(5068515349750366186051 / 5000000000000000000000 : ℚ))) + (U' := (1862956453249633813949 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (1814341449699699 / 5000000000000000 : ℚ)) + (q := (29029819612999467 / 80000000000000000 : ℚ)) + (U := (-(5068515349750366186051 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_2 : Uω (aρ 2) (bρ 2) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1549,25 +1383,21 @@ lemma U_368_2 : have hlg : Real.log (28837669394875791 / 80000000000000000 : ℝ) ≤ (-(10203441365534420333661 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28837669394875791 / 80000000000000000 : ℝ) = - (28837669394875791 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28837669394875791 / 20000000000000000 : ℚ)) - (U := (3659502240465579666339 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28837669394875791 / 20000000000000000 : ℝ) ≤ - (3659502240465579666339 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3604414357378479 / 10000000000000000 : ℝ)) (q := - (28837669394875791 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28837669394875791 / 80000000000000000 : ℚ)) + (r' := (28837669394875791 / 20000000000000000 : ℚ)) + (U := (-(10203441365534420333661 / 10000000000000000000000 : ℚ))) + (U' := (3659502240465579666339 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (3604414357378479 / 10000000000000000 : ℚ)) + (q := (28837669394875791 / 80000000000000000 : ℚ)) + (U := (-(10203441365534420333661 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_3 : Uω (aρ 3) (bρ 3) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1575,25 +1405,21 @@ lemma U_368_3 : have hlg : Real.log (28452534606018127 / 80000000000000000 : ℝ) ≤ (-(10337893877074504726461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28452534606018127 / 80000000000000000 : ℝ) = - (28452534606018127 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28452534606018127 / 20000000000000000 : ℚ)) - (U := (3525049728925495273539 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28452534606018127 / 20000000000000000 : ℝ) ≤ - (3525049728925495273539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3555526766514063 / 10000000000000000 : ℝ)) (q := - (28452534606018127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28452534606018127 / 80000000000000000 : ℚ)) + (r' := (28452534606018127 / 20000000000000000 : ℚ)) + (U := (-(10337893877074504726461 / 10000000000000000000000 : ℚ))) + (U' := (3525049728925495273539 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (3555526766514063 / 10000000000000000 : ℚ)) + (q := (28452534606018127 / 80000000000000000 : ℚ)) + (U := (-(10337893877074504726461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_4 : Uω (aρ 4) (bρ 4) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1601,25 +1427,21 @@ lemma U_368_4 : have hlg : Real.log (5562058133920343 / 16000000000000000 : ℝ) ≤ (-(10566205139813757343053 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5562058133920343 / 16000000000000000 : ℝ) = - (5562058133920343 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5562058133920343 / 4000000000000000 : ℚ)) - (U := (3296738466186242656947 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5562058133920343 / 4000000000000000 : ℝ) ≤ - (3296738466186242656947 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (43415749543437 / 125000000000000 : ℝ)) (q := - (5562058133920343 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5562058133920343 / 16000000000000000 : ℚ)) + (r' := (5562058133920343 / 4000000000000000 : ℚ)) + (U := (-(10566205139813757343053 / 10000000000000000000000 : ℚ))) + (U' := (3296738466186242656947 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (43415749543437 / 125000000000000 : ℚ)) + (q := (5562058133920343 / 16000000000000000 : ℚ)) + (U := (-(10566205139813757343053 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_5 : Uω (aρ 5) (bρ 5) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1627,25 +1449,21 @@ lemma U_368_5 : have hlg : Real.log (26825452307701863 / 80000000000000000 : ℝ) ≤ (-(2185350968710533704413 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26825452307701863 / 80000000000000000 : ℝ) = - (26825452307701863 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26825452307701863 / 20000000000000000 : ℚ)) - (U := (587237752489466295587 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26825452307701863 / 20000000000000000 : ℝ) ≤ - (587237752489466295587 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3345240292334997 / 10000000000000000 : ℝ)) (q := - (26825452307701863 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26825452307701863 / 80000000000000000 : ℚ)) + (r' := (26825452307701863 / 20000000000000000 : ℚ)) + (U := (-(2185350968710533704413 / 2000000000000000000000 : ℚ))) + (U' := (587237752489466295587 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (3345240292334997 / 10000000000000000 : ℚ)) + (q := (26825452307701863 / 80000000000000000 : ℚ)) + (U := (-(2185350968710533704413 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_6 : Uω (aρ 6) (bρ 6) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1653,25 +1471,21 @@ lemma U_368_6 : have hlg : Real.log (25396426807367743 / 80000000000000000 : ℝ) ≤ (-(11474181469007055192813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25396426807367743 / 80000000000000000 : ℝ) = - (25396426807367743 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25396426807367743 / 20000000000000000 : ℚ)) - (U := (2388762136992944807187 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25396426807367743 / 20000000000000000 : ℝ) ≤ - (2388762136992944807187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3155224292391467 / 10000000000000000 : ℝ)) (q := - (25396426807367743 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25396426807367743 / 80000000000000000 : ℚ)) + (r' := (25396426807367743 / 20000000000000000 : ℚ)) + (U := (-(11474181469007055192813 / 10000000000000000000000 : ℚ))) + (U' := (2388762136992944807187 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (3155224292391467 / 10000000000000000 : ℚ)) + (q := (25396426807367743 / 80000000000000000 : ℚ)) + (U := (-(11474181469007055192813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_7 : Uω (aρ 7) (bρ 7) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1679,25 +1493,21 @@ lemma U_368_7 : have hlg : Real.log (4681442008695679 / 16000000000000000 : ℝ) ≤ (-(6144912688669251179439 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4681442008695679 / 16000000000000000 : ℝ) = - (4681442008695679 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4681442008695679 / 4000000000000000 : ℚ)) - (U := (786559114330748820561 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4681442008695679 / 4000000000000000 : ℝ) ≤ - (786559114330748820561 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (288158148217913 / 1000000000000000 : ℝ)) (q := - (4681442008695679 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4681442008695679 / 16000000000000000 : ℚ)) + (r' := (4681442008695679 / 4000000000000000 : ℚ)) + (U := (-(6144912688669251179439 / 5000000000000000000000 : ℚ))) + (U' := (786559114330748820561 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (288158148217913 / 1000000000000000 : ℚ)) + (q := (4681442008695679 / 16000000000000000 : ℚ)) + (U := (-(6144912688669251179439 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_8 : Uω (aρ 8) (bρ 8) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1705,25 +1515,21 @@ lemma U_368_8 : have hlg : Real.log (828563869753399 / 3200000000000000 : ℝ) ≤ (-(13512121635417570816127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (828563869753399 / 3200000000000000 : ℝ) = - (828563869753399 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (828563869753399 / 800000000000000 : ℚ)) - (U := (350821970582429183873 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (828563869753399 / 800000000000000 : ℝ) ≤ - (350821970582429183873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99673792344331 / 400000000000000 : ℝ)) (q := - (828563869753399 / 3200000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (828563869753399 / 3200000000000000 : ℚ)) + (r' := (828563869753399 / 800000000000000 : ℚ)) + (U := (-(13512121635417570816127 / 10000000000000000000000 : ℚ))) + (U' := (350821970582429183873 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (99673792344331 / 400000000000000 : ℚ)) + (q := (828563869753399 / 3200000000000000 : ℚ)) + (U := (-(13512121635417570816127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_9 : Uω (aρ 9) (bρ 9) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1731,25 +1537,21 @@ lemma U_368_9 : have hlg : Real.log (17067555723637463 / 80000000000000000 : ℝ) ≤ (-(3089694597383226710451 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17067555723637463 / 80000000000000000 : ℝ) = - (17067555723637463 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17067555723637463 / 10000000000000000 : ℚ)) - (U := (1069188484416773289549 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17067555723637463 / 10000000000000000 : ℝ) ≤ - (1069188484416773289549 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1921175181918897 / 10000000000000000 : ℝ)) (q := - (17067555723637463 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17067555723637463 / 80000000000000000 : ℚ)) + (r' := (17067555723637463 / 10000000000000000 : ℚ)) + (U := (-(3089694597383226710451 / 2000000000000000000000 : ℚ))) + (U' := (1069188484416773289549 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (1921175181918897 / 10000000000000000 : ℚ)) + (q := (17067555723637463 / 80000000000000000 : ℚ)) + (U := (-(3089694597383226710451 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_10 : Uω (aρ 10) (bρ 10) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1757,25 +1559,21 @@ lemma U_368_10 : have hlg : Real.log (458118293853527 / 3200000000000000 : ℝ) ≤ (-(19437786537202591506609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (458118293853527 / 3200000000000000 : ℝ) = - (458118293853527 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (458118293853527 / 400000000000000 : ℚ)) - (U := (1356628871797408493391 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (458118293853527 / 400000000000000 : ℝ) ≤ - (1356628871797408493391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36243384843563 / 400000000000000 : ℝ)) (q := - (458118293853527 / 3200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (458118293853527 / 3200000000000000 : ℚ)) + (r' := (458118293853527 / 400000000000000 : ℚ)) + (U := (-(19437786537202591506609 / 10000000000000000000000 : ℚ))) + (U' := (1356628871797408493391 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23636923020387 / 64000000000000 : ℚ)) + (s := (36243384843563 / 400000000000000 : ℚ)) + (q := (458118293853527 / 3200000000000000 : ℚ)) + (U := (-(19437786537202591506609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_368_11 : Uω (aρ 11) (bρ 11) (23636923020387 / 64000000000000 : ℝ) ≤ @@ -1897,25 +1695,21 @@ lemma U_369_1 : have hlg : Real.log (58164286946338561 / 160000000000000000 : ℝ) ≤ (-(5059511373369090753989 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58164286946338561 / 160000000000000000 : ℝ) = - (58164286946338561 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58164286946338561 / 40000000000000000 : ℚ)) - (U := (1871960429630909246011 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58164286946338561 / 40000000000000000 : ℝ) ≤ - (1871960429630909246011 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3635223462077867 / 10000000000000000 : ℝ)) (q := - (58164286946338561 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58164286946338561 / 160000000000000000 : ℚ)) + (r' := (58164286946338561 / 40000000000000000 : ℚ)) + (U := (-(5059511373369090753989 / 5000000000000000000000 : ℚ))) + (U' := (1871960429630909246011 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (3635223462077867 / 10000000000000000 : ℚ)) + (q := (58164286946338561 / 160000000000000000 : ℚ)) + (U := (-(5059511373369090753989 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_2 : Uω (aρ 2) (bρ 2) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -1923,25 +1717,21 @@ lemma U_369_2 : have hlg : Real.log (57779993756959153 / 160000000000000000 : ℝ) ≤ (-(5092656138621636409351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57779993756959153 / 160000000000000000 : ℝ) = - (57779993756959153 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57779993756959153 / 40000000000000000 : ℚ)) - (U := (1838815664378363590649 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57779993756959153 / 40000000000000000 : ℝ) ≤ - (1838815664378363590649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3610955825915441 / 10000000000000000 : ℝ)) (q := - (57779993756959153 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57779993756959153 / 160000000000000000 : ℚ)) + (r' := (57779993756959153 / 40000000000000000 : ℚ)) + (U := (-(5092656138621636409351 / 5000000000000000000000 : ℚ))) + (U' := (1838815664378363590649 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (3610955825915441 / 10000000000000000 : ℚ)) + (q := (57779993756959153 / 160000000000000000 : ℚ)) + (U := (-(5092656138621636409351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_3 : Uω (aρ 3) (bρ 3) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -1949,25 +1739,21 @@ lemma U_369_3 : have hlg : Real.log (57009746204712257 / 160000000000000000 : ℝ) ≤ (-(10319515754482508126191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57009746204712257 / 160000000000000000 : ℝ) = - (57009746204712257 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57009746204712257 / 40000000000000000 : ℚ)) - (U := (3543427851517491873809 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57009746204712257 / 40000000000000000 : ℝ) ≤ - (3543427851517491873809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3562070988234579 / 10000000000000000 : ℝ)) (q := - (57009746204712257 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57009746204712257 / 160000000000000000 : ℚ)) + (r' := (57009746204712257 / 40000000000000000 : ℚ)) + (U := (-(10319515754482508126191 / 10000000000000000000000 : ℚ))) + (U' := (3543427851517491873809 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (3562070988234579 / 10000000000000000 : ℚ)) + (q := (57009746204712257 / 160000000000000000 : ℚ)) + (U := (-(10319515754482508126191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_4 : Uω (aρ 4) (bρ 4) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -1975,25 +1761,21 @@ lemma U_369_4 : have hlg : Real.log (55725318787519921 / 160000000000000000 : ℝ) ≤ (-(10547392147312262476351 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55725318787519921 / 160000000000000000 : ℝ) = - (55725318787519921 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55725318787519921 / 40000000000000000 : ℚ)) - (U := (3315551458687737523649 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55725318787519921 / 40000000000000000 : ℝ) ≤ - (3315551458687737523649 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3479811742150537 / 10000000000000000 : ℝ)) (q := - (55725318787519921 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55725318787519921 / 160000000000000000 : ℚ)) + (r' := (55725318787519921 / 40000000000000000 : ℚ)) + (U := (-(10547392147312262476351 / 10000000000000000000000 : ℚ))) + (U' := (3315551458687737523649 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (3479811742150537 / 10000000000000000 : ℚ)) + (q := (55725318787519921 / 160000000000000000 : ℚ)) + (U := (-(10547392147312262476351 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_5 : Uω (aρ 5) (bρ 5) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2001,25 +1783,21 @@ lemma U_369_5 : have hlg : Real.log (53755798986894057 / 160000000000000000 : ℝ) ≤ (-(1090722265397408139433 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (53755798986894057 / 160000000000000000 : ℝ) = - (53755798986894057 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53755798986894057 / 40000000000000000 : ℚ)) - (U := (295572095202591860567 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53755798986894057 / 40000000000000000 : ℝ) ≤ - (295572095202591860567 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (418976460800913 / 1250000000000000 : ℝ)) (q := - (53755798986894057 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53755798986894057 / 160000000000000000 : ℚ)) + (r' := (53755798986894057 / 40000000000000000 : ℚ)) + (U := (-(1090722265397408139433 / 1000000000000000000000 : ℚ))) + (U' := (295572095202591860567 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (418976460800913 / 1250000000000000 : ℚ)) + (q := (53755798986894057 / 160000000000000000 : ℚ)) + (U := (-(1090722265397408139433 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_6 : Uω (aρ 6) (bρ 6) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2027,25 +1805,21 @@ lemma U_369_6 : have hlg : Real.log (50898139787561073 / 160000000000000000 : ℝ) ≤ (-(1431684297798292659107 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (50898139787561073 / 160000000000000000 : ℝ) = - (50898139787561073 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50898139787561073 / 40000000000000000 : ℚ)) - (U := (301183652951707340893 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50898139787561073 / 40000000000000000 : ℝ) ≤ - (301183652951707340893 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3161844661630681 / 10000000000000000 : ℝ)) (q := - (50898139787561073 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50898139787561073 / 160000000000000000 : ℚ)) + (r' := (50898139787561073 / 40000000000000000 : ℚ)) + (U := (-(1431684297798292659107 / 1250000000000000000000 : ℚ))) + (U' := (301183652951707340893 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (3161844661630681 / 10000000000000000 : ℚ)) + (q := (50898139787561073 / 160000000000000000 : ℚ)) + (U := (-(1431684297798292659107 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_7 : Uω (aρ 7) (bρ 7) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2053,25 +1827,21 @@ lemma U_369_7 : have hlg : Real.log (46920672324473113 / 160000000000000000 : ℝ) ≤ (-(12267154618652294812397 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46920672324473113 / 160000000000000000 : ℝ) = - (46920672324473113 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46920672324473113 / 40000000000000000 : ℚ)) - (U := (1595788987347705187603 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46920672324473113 / 40000000000000000 : ℝ) ≤ - (1595788987347705187603 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1444161304752343 / 5000000000000000 : ℝ)) (q := - (46920672324473113 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46920672324473113 / 160000000000000000 : ℚ)) + (r' := (46920672324473113 / 40000000000000000 : ℚ)) + (U := (-(12267154618652294812397 / 10000000000000000000000 : ℚ))) + (U' := (1595788987347705187603 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (1444161304752343 / 5000000000000000 : ℚ)) + (q := (46920672324473113 / 160000000000000000 : ℚ)) + (U := (-(12267154618652294812397 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_8 : Uω (aρ 8) (bρ 8) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2079,25 +1849,21 @@ lemma U_369_8 : have hlg : Real.log (41536919893371961 / 160000000000000000 : ℝ) ≤ (-(6742955734919824914827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41536919893371961 / 160000000000000000 : ℝ) = - (41536919893371961 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41536919893371961 / 40000000000000000 : ℚ)) - (U := (188516068080175085173 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41536919893371961 / 40000000000000000 : ℝ) ≤ - (188516068080175085173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1249447603478521 / 5000000000000000 : ℝ)) (q := - (41536919893371961 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41536919893371961 / 160000000000000000 : ℚ)) + (r' := (41536919893371961 / 40000000000000000 : ℚ)) + (U := (-(6742955734919824914827 / 5000000000000000000000 : ℚ))) + (U' := (188516068080175085173 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (1249447603478521 / 5000000000000000 : ℚ)) + (q := (41536919893371961 / 160000000000000000 : ℚ)) + (U := (-(6742955734919824914827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_9 : Uω (aρ 9) (bρ 9) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2105,25 +1871,21 @@ lemma U_369_9 : have hlg : Real.log (6850255333021829 / 32000000000000000 : ℝ) ≤ (-(3082899951093501236787 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6850255333021829 / 32000000000000000 : ℝ) = - (6850255333021829 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6850255333021829 / 4000000000000000 : ℚ)) - (U := (1075983130706498763213 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6850255333021829 / 4000000000000000 : ℝ) ≤ - (1075983130706498763213 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (192915543178419 / 1000000000000000 : ℝ)) (q := - (6850255333021829 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6850255333021829 / 32000000000000000 : ℚ)) + (r' := (6850255333021829 / 4000000000000000 : ℚ)) + (U := (-(3082899951093501236787 / 2000000000000000000000 : ℚ))) + (U' := (1075983130706498763213 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (192915543178419 / 1000000000000000 : ℚ)) + (q := (6850255333021829 / 32000000000000000 : ℚ)) + (U := (-(3082899951093501236787 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_10 : Uω (aρ 10) (bρ 10) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2131,26 +1893,21 @@ lemma U_369_10 : have hlg : Real.log (4614115023376829 / 32000000000000000 : ℝ) ≤ (-(19366158133686468909589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4614115023376829 / 32000000000000000 : ℝ) = - (4614115023376829 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4614115023376829 / 4000000000000000 : ℚ)) - (U := (1428257275313531090411 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4614115023376829 / 4000000000000000 : ℝ) ≤ - (1428257275313531090411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (184025354350213 / 2000000000000000 : ℝ)) (q := - (4614115023376829 / 32000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4614115023376829 / 32000000000000000 : ℚ)) + (r' := (4614115023376829 / 4000000000000000 : ℚ)) + (U := (-(19366158133686468909589 / 10000000000000000000000 : ℚ))) + (U' := (1428257275313531090411 / 10000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47357563191033 / 128000000000000 : ℚ)) + (s := (184025354350213 / 2000000000000000 : ℚ)) + (q := (4614115023376829 / 32000000000000000 : ℚ)) + (U := (-(19366158133686468909589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_369_11 : Uω (aρ 11) (bρ 11) (47357563191033 / 128000000000000 : ℝ) ≤ @@ -2273,25 +2030,21 @@ lemma U_370_1 : have hlg : Real.log (14567233665517871 / 40000000000000000 : ℝ) ≤ (-(10101047165118847851507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14567233665517871 / 40000000000000000 : ℝ) = - (14567233665517871 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14567233665517871 / 10000000000000000 : ℚ)) - (U := (3761896440881152148493 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14567233665517871 / 10000000000000000 : ℝ) ≤ - (3761896440881152148493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1820882012090249 / 5000000000000000 : ℝ)) (q := - (14567233665517871 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14567233665517871 / 40000000000000000 : ℚ)) + (r' := (14567233665517871 / 10000000000000000 : ℚ)) + (U := (-(10101047165118847851507 / 10000000000000000000000 : ℚ))) + (U' := (3761896440881152148493 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (1820882012090249 / 5000000000000000 : ℚ)) + (q := (14567233665517871 / 40000000000000000 : ℚ)) + (U := (-(10101047165118847851507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_2 : Uω (aρ 2) (bρ 2) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2299,25 +2052,21 @@ lemma U_370_2 : have hlg : Real.log (14471162173330529 / 40000000000000000 : ℝ) ≤ (-(317725500037437652139 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14471162173330529 / 40000000000000000 : ℝ) = - (14471162173330529 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14471162173330529 / 10000000000000000 : ℚ)) - (U := (115491487650062347861 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14471162173330529 / 10000000000000000 : ℝ) ≤ - (115491487650062347861 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3617497290596827 / 10000000000000000 : ℝ)) (q := - (14471162173330529 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14471162173330529 / 40000000000000000 : ℚ)) + (r' := (14471162173330529 / 10000000000000000 : ℚ)) + (U := (-(317725500037437652139 / 312500000000000000000 : ℚ))) + (U' := (115491487650062347861 / 312500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (3617497290596827 / 10000000000000000 : ℚ)) + (q := (14471162173330529 / 40000000000000000 : ℚ)) + (U := (-(317725500037437652139 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_3 : Uω (aρ 3) (bρ 3) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2325,25 +2074,21 @@ lemma U_370_3 : have hlg : Real.log (14278605771339089 / 40000000000000000 : ℝ) ≤ (-(10301171365095080003113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14278605771339089 / 40000000000000000 : ℝ) = - (14278605771339089 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14278605771339089 / 10000000000000000 : ℚ)) - (U := (3561772240904919996887 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14278605771339089 / 10000000000000000 : ℝ) ≤ - (3561772240904919996887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3568615195951107 / 10000000000000000 : ℝ)) (q := - (14278605771339089 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14278605771339089 / 40000000000000000 : ℚ)) + (r' := (14278605771339089 / 10000000000000000 : ℚ)) + (U := (-(10301171365095080003113 / 10000000000000000000000 : ℚ))) + (U' := (3561772240904919996887 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (3568615195951107 / 10000000000000000 : ℚ)) + (q := (14278605771339089 / 40000000000000000 : ℚ)) + (U := (-(10301171365095080003113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_4 : Uω (aρ 4) (bρ 4) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2351,25 +2096,21 @@ lemma U_370_4 : have hlg : Real.log (13957513973517219 / 40000000000000000 : ℝ) ≤ (-(2632153635611494003493 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13957513973517219 / 40000000000000000 : ℝ) = - (13957513973517219 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13957513973517219 / 10000000000000000 : ℚ)) - (U := (833582265888505996507 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13957513973517219 / 10000000000000000 : ℝ) ≤ - (833582265888505996507 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (871590869526293 / 2500000000000000 : ℝ)) (q := - (13957513973517219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13957513973517219 / 40000000000000000 : ℚ)) + (r' := (13957513973517219 / 10000000000000000 : ℚ)) + (U := (-(2632153635611494003493 / 2500000000000000000000 : ℚ))) + (U' := (833582265888505996507 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (871590869526293 / 2500000000000000 : ℚ)) + (q := (13957513973517219 / 40000000000000000 : ℚ)) + (U := (-(2632153635611494003493 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_5 : Uω (aρ 5) (bρ 5) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2377,25 +2118,21 @@ lemma U_370_5 : have hlg : Real.log (13465173097600487 / 40000000000000000 : ℝ) ≤ (-(5443864360199435669073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13465173097600487 / 40000000000000000 : ℝ) = - (13465173097600487 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13465173097600487 / 10000000000000000 : ℚ)) - (U := (1487607442800564330927 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13465173097600487 / 10000000000000000 : ℝ) ≤ - (1487607442800564330927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1679191479740903 / 5000000000000000 : ℝ)) (q := - (13465173097600487 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13465173097600487 / 40000000000000000 : ℚ)) + (r' := (13465173097600487 / 10000000000000000 : ℚ)) + (U := (-(5443864360199435669073 / 5000000000000000000000 : ℚ))) + (U' := (1487607442800564330927 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (1679191479740903 / 5000000000000000 : ℚ)) + (q := (13465173097600487 / 40000000000000000 : ℚ)) + (U := (-(5443864360199435669073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_6 : Uω (aρ 6) (bρ 6) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2403,25 +2140,21 @@ lemma U_370_6 : have hlg : Real.log (12750855825783927 / 40000000000000000 : ℝ) ≤ (-(11432810606514017181871 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12750855825783927 / 40000000000000000 : ℝ) = - (12750855825783927 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12750855825783927 / 10000000000000000 : ℚ)) - (U := (2430132999485982818129 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12750855825783927 / 10000000000000000 : ℝ) ≤ - (2430132999485982818129 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1584232349356763 / 5000000000000000 : ℝ)) (q := - (12750855825783927 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12750855825783927 / 40000000000000000 : ℚ)) + (r' := (12750855825783927 / 10000000000000000 : ℚ)) + (U := (-(11432810606514017181871 / 10000000000000000000000 : ℚ))) + (U' := (2430132999485982818129 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (1584232349356763 / 5000000000000000 : ℚ)) + (q := (12750855825783927 / 40000000000000000 : ℚ)) + (U := (-(11432810606514017181871 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_7 : Uω (aρ 7) (bρ 7) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2429,25 +2162,21 @@ lemma U_370_7 : have hlg : Real.log (11756729298786639 / 40000000000000000 : ℝ) ≤ (-(15305670883222720007 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11756729298786639 / 40000000000000000 : ℝ) = - (11756729298786639 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11756729298786639 / 10000000000000000 : ℚ)) - (U := (2023008624277279993 / 12500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11756729298786639 / 10000000000000000 : ℝ) ≤ - (2023008624277279993 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1447531407987441 / 5000000000000000 : ℝ)) (q := - (11756729298786639 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11756729298786639 / 40000000000000000 : ℚ)) + (r' := (11756729298786639 / 10000000000000000 : ℚ)) + (U := (-(15305670883222720007 / 12500000000000000000 : ℚ))) + (U' := (2023008624277279993 / 12500000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (1447531407987441 / 5000000000000000 : ℚ)) + (q := (11756729298786639 / 40000000000000000 : ℚ)) + (U := (-(15305670883222720007 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_8 : Uω (aρ 8) (bρ 8) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2455,25 +2184,21 @@ lemma U_370_8 : have hlg : Real.log (416456241716739 / 1600000000000000 : ℝ) ≤ (-(13459775135250613273287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (416456241716739 / 1600000000000000 : ℝ) = - (416456241716739 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (416456241716739 / 400000000000000 : ℚ)) - (U := (403168470749386726713 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (416456241716739 / 400000000000000 : ℝ) ≤ - (403168470749386726713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1566214274613 / 6250000000000 : ℝ)) (q := - (416456241716739 / 1600000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (416456241716739 / 1600000000000000 : ℚ)) + (r' := (416456241716739 / 400000000000000 : ℚ)) + (U := (-(13459775135250613273287 / 10000000000000000000000 : ℚ))) + (U' := (403168470749386726713 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (1566214274613 / 6250000000000 : ℚ)) + (q := (416456241716739 / 1600000000000000 : ℚ)) + (U := (-(13459775135250613273287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_9 : Uω (aρ 9) (bρ 9) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2481,25 +2206,21 @@ lemma U_370_9 : have hlg : Real.log (8591838884655659 / 40000000000000000 : ℝ) ≤ (-(61522666701171816901 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8591838884655659 / 40000000000000000 : ℝ) = - (8591838884655659 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8591838884655659 / 5000000000000000 : ℚ)) - (U := (21654994934828183099 / 40000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8591838884655659 / 5000000000000000 : ℝ) ≤ - (21654994934828183099 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121070305538087 / 625000000000000 : ℝ)) (q := - (8591838884655659 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8591838884655659 / 40000000000000000 : ℚ)) + (r' := (8591838884655659 / 5000000000000000 : ℚ)) + (U := (-(61522666701171816901 / 40000000000000000000 : ℚ))) + (U' := (21654994934828183099 / 40000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (121070305538087 / 625000000000000 : ℚ)) + (q := (8591838884655659 / 40000000000000000 : ℚ)) + (U := (-(61522666701171816901 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_10 : Uω (aρ 10) (bρ 10) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2507,26 +2228,21 @@ lemma U_370_10 : have hlg : Real.log (5808478283835511 / 40000000000000000 : ℝ) ≤ (-(3859121660113755047557 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5808478283835511 / 40000000000000000 : ℝ) = - (5808478283835511 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5808478283835511 / 5000000000000000 : ℚ)) - (U := (299761421686244952443 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5808478283835511 / 5000000000000000 : ℝ) ≤ - (299761421686244952443 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (467001810847159 / 5000000000000000 : ℝ)) (q := - (5808478283835511 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5808478283835511 / 40000000000000000 : ℚ)) + (r' := (5808478283835511 / 5000000000000000 : ℚ)) + (U := (-(3859121660113755047557 / 2000000000000000000000 : ℚ))) + (U' := (299761421686244952443 / 2000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11860320085323 / 32000000000000 : ℚ)) + (s := (467001810847159 / 5000000000000000 : ℚ)) + (q := (5808478283835511 / 40000000000000000 : ℚ)) + (U := (-(3859121660113755047557 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_370_11 : Uω (aρ 11) (bρ 11) (11860320085323 / 32000000000000 : ℝ) ≤ @@ -2648,25 +2364,21 @@ lemma U_371_1 : have hlg : Real.log (58373582373222463 / 160000000000000000 : ℝ) ≤ (-(10083103838467802937571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58373582373222463 / 160000000000000000 : ℝ) = - (58373582373222463 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58373582373222463 / 40000000000000000 : ℚ)) - (U := (3779839767532197062429 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58373582373222463 / 40000000000000000 : ℝ) ≤ - (3779839767532197062429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1824152292855193 / 5000000000000000 : ℝ)) (q := - (58373582373222463 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58373582373222463 / 160000000000000000 : ℚ)) + (r' := (58373582373222463 / 40000000000000000 : ℚ)) + (U := (-(10083103838467802937571 / 10000000000000000000000 : ℚ))) + (U' := (3779839767532197062429 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (1824152292855193 / 5000000000000000 : ℚ)) + (q := (58373582373222463 / 160000000000000000 : ℚ)) + (U := (-(10083103838467802937571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_2 : Uω (aρ 2) (bρ 2) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2674,25 +2386,21 @@ lemma U_371_2 : have hlg : Real.log (57989303599007487 / 160000000000000000 : ℝ) ≤ (-(10149152418818740405747 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57989303599007487 / 160000000000000000 : ℝ) = - (57989303599007487 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57989303599007487 / 40000000000000000 : ℚ)) - (U := (3713791187181259594253 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (57989303599007487 / 40000000000000000 : ℝ) ≤ - (3713791187181259594253 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1812019375721757 / 5000000000000000 : ℝ)) (q := - (57989303599007487 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57989303599007487 / 160000000000000000 : ℚ)) + (r' := (57989303599007487 / 40000000000000000 : ℚ)) + (U := (-(10149152418818740405747 / 10000000000000000000000 : ℚ))) + (U' := (3713791187181259594253 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (1812019375721757 / 5000000000000000 : ℚ)) + (q := (57989303599007487 / 160000000000000000 : ℚ)) + (U := (-(10149152418818740405747 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_3 : Uω (aρ 3) (bρ 3) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2700,25 +2408,21 @@ lemma U_371_3 : have hlg : Real.log (57219099854583759 / 160000000000000000 : ℝ) ≤ (-(2570715146308073706789 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57219099854583759 / 160000000000000000 : ℝ) = - (57219099854583759 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57219099854583759 / 40000000000000000 : ℚ)) - (U := (895020755191926293211 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57219099854583759 / 40000000000000000 : ℝ) ≤ - (895020755191926293211 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (893789847435137 / 2500000000000000 : ℝ)) (q := - (57219099854583759 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57219099854583759 / 160000000000000000 : ℚ)) + (r' := (57219099854583759 / 40000000000000000 : ℚ)) + (U := (-(2570715146308073706789 / 2500000000000000000000 : ℚ))) + (U' := (895020755191926293211 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (893789847435137 / 2500000000000000 : ℚ)) + (q := (57219099854583759 / 160000000000000000 : ℚ)) + (U := (-(2570715146308073706789 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_4 : Uω (aρ 4) (bρ 4) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2726,25 +2430,21 @@ lemma U_371_4 : have hlg : Real.log (55934792660773479 / 160000000000000000 : ℝ) ≤ (-(10509872192106231280577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55934792660773479 / 160000000000000000 : ℝ) = - (55934792660773479 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55934792660773479 / 40000000000000000 : ℚ)) - (U := (3353071413893768719423 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55934792660773479 / 40000000000000000 : ℝ) ≤ - (3353071413893768719423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3492915171579263 / 10000000000000000 : ℝ)) (q := - (55934792660773479 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55934792660773479 / 160000000000000000 : ℚ)) + (r' := (55934792660773479 / 40000000000000000 : ℚ)) + (U := (-(10509872192106231280577 / 10000000000000000000000 : ℚ))) + (U' := (3353071413893768719423 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (3492915171579263 / 10000000000000000 : ℚ)) + (q := (55934792660773479 / 160000000000000000 : ℚ)) + (U := (-(10509872192106231280577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_5 : Uω (aρ 5) (bρ 5) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2752,25 +2452,21 @@ lemma U_371_5 : have hlg : Real.log (53965584831598407 / 160000000000000000 : ℝ) ≤ (-(2173654578512854934223 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (53965584831598407 / 160000000000000000 : ℝ) = - (53965584831598407 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53965584831598407 / 40000000000000000 : ℚ)) - (U := (598934142687145065777 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (53965584831598407 / 40000000000000000 : ℝ) ≤ - (598934142687145065777 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3364954112267379 / 10000000000000000 : ℝ)) (q := - (53965584831598407 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53965584831598407 / 160000000000000000 : ℚ)) + (r' := (53965584831598407 / 40000000000000000 : ℚ)) + (U := (-(2173654578512854934223 / 2000000000000000000000 : ℚ))) + (U' := (598934142687145065777 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (3364954112267379 / 10000000000000000 : ℚ)) + (q := (53965584831598407 / 160000000000000000 : ℚ)) + (U := (-(2173654578512854934223 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_6 : Uω (aρ 6) (bρ 6) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2778,25 +2474,21 @@ lemma U_371_6 : have hlg : Real.log (51108704178080479 / 160000000000000000 : ℝ) ≤ (-(1426523744804845731913 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51108704178080479 / 160000000000000000 : ℝ) = - (51108704178080479 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51108704178080479 / 40000000000000000 : ℚ)) - (U := (306344205945154268087 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51108704178080479 / 40000000000000000 : ℝ) ≤ - (306344205945154268087 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1587542202858819 / 5000000000000000 : ℝ)) (q := - (51108704178080479 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51108704178080479 / 160000000000000000 : ℚ)) + (r' := (51108704178080479 / 40000000000000000 : ℚ)) + (U := (-(1426523744804845731913 / 1250000000000000000000 : ℚ))) + (U' := (306344205945154268087 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (1587542202858819 / 5000000000000000 : ℚ)) + (q := (51108704178080479 / 160000000000000000 : ℚ)) + (U := (-(1426523744804845731913 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_7 : Uω (aρ 7) (bρ 7) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2804,25 +2496,21 @@ lemma U_371_7 : have hlg : Real.log (47133154750311471 / 160000000000000000 : ℝ) ≤ (-(381936605880278124109 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47133154750311471 / 160000000000000000 : ℝ) = - (47133154750311471 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47133154750311471 / 40000000000000000 : ℚ)) - (U := (51280381807221875891 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47133154750311471 / 40000000000000000 : ℝ) ≤ - (51280381807221875891 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (181362631750407 / 625000000000000 : ℝ)) (q := - (47133154750311471 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47133154750311471 / 160000000000000000 : ℚ)) + (r' := (47133154750311471 / 40000000000000000 : ℚ)) + (U := (-(381936605880278124109 / 312500000000000000000 : ℚ))) + (U' := (51280381807221875891 / 312500000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (181362631750407 / 625000000000000 : ℚ)) + (q := (47133154750311471 / 160000000000000000 : ℚ)) + (U := (-(381936605880278124109 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_8 : Uω (aρ 8) (bρ 8) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2830,25 +2518,21 @@ lemma U_371_8 : have hlg : Real.log (41754306508743559 / 160000000000000000 : ℝ) ≤ (-(13433712188266326115151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41754306508743559 / 160000000000000000 : ℝ) = - (41754306508743559 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41754306508743559 / 40000000000000000 : ℚ)) - (U := (429231417733673884849 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41754306508743559 / 40000000000000000 : ℝ) ≤ - (429231417733673884849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2512987729150523 / 10000000000000000 : ℝ)) (q := - (41754306508743559 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41754306508743559 / 160000000000000000 : ℚ)) + (r' := (41754306508743559 / 40000000000000000 : ℚ)) + (U := (-(13433712188266326115151 / 10000000000000000000000 : ℚ))) + (U' := (429231417733673884849 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (2512987729150523 / 10000000000000000 : ℚ)) + (q := (41754306508743559 / 160000000000000000 : ℚ)) + (U := (-(13433712188266326115151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_9 : Uω (aρ 9) (bρ 9) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2856,25 +2540,21 @@ lemma U_371_9 : have hlg : Real.log (34483349129133271 / 160000000000000000 : ℝ) ≤ (-(191837155107511234621 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34483349129133271 / 160000000000000000 : ℝ) = - (34483349129133271 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34483349129133271 / 20000000000000000 : ℚ)) - (U := (68093037504988765379 / 125000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34483349129133271 / 20000000000000000 : ℝ) ≤ - (68093037504988765379 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1945083685059237 / 10000000000000000 : ℝ)) (q := - (34483349129133271 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34483349129133271 / 160000000000000000 : ℚ)) + (r' := (34483349129133271 / 20000000000000000 : ℚ)) + (U := (-(191837155107511234621 / 125000000000000000000 : ℚ))) + (U' := (68093037504988765379 / 125000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (1945083685059237 / 10000000000000000 : ℚ)) + (q := (34483349129133271 / 160000000000000000 : ℚ)) + (U := (-(191837155107511234621 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_10 : Uω (aρ 10) (bρ 10) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -2882,26 +2562,21 @@ lemma U_371_10 : have hlg : Real.log (23395986837515407 / 160000000000000000 : ℝ) ≤ (-(9613046547344408264177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23395986837515407 / 160000000000000000 : ℝ) = - (23395986837515407 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23395986837515407 / 20000000000000000 : ℚ)) - (U := (784161157155591735823 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23395986837515407 / 20000000000000000 : ℝ) ≤ - (784161157155591735823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (236930608025501 / 2500000000000000 : ℝ)) (q := - (23395986837515407 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23395986837515407 / 160000000000000000 : ℚ)) + (r' := (23395986837515407 / 20000000000000000 : ℚ)) + (U := (-(9613046547344408264177 / 5000000000000000000000 : ℚ))) + (U' := (784161157155591735823 / 5000000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47524997491551 / 128000000000000 : ℚ)) + (s := (236930608025501 / 2500000000000000 : ℚ)) + (q := (23395986837515407 / 160000000000000000 : ℚ)) + (U := (-(9613046547344408264177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_371_11 : Uω (aρ 11) (bρ 11) (47524997491551 / 128000000000000 : ℝ) ≤ @@ -3025,25 +2700,21 @@ lemma U_372_1 : have hlg : Real.log (29239115039908057 / 80000000000000000 : ℝ) ≤ (-(5032596325617203968613 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29239115039908057 / 80000000000000000 : ℝ) = - (29239115039908057 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29239115039908057 / 20000000000000000 : ℚ)) - (U := (1898875477382796031387 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29239115039908057 / 20000000000000000 : ℝ) ≤ - (1898875477382796031387 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228427821666913 / 625000000000000 : ℝ)) (q := - (29239115039908057 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29239115039908057 / 80000000000000000 : ℚ)) + (r' := (29239115039908057 / 20000000000000000 : ℚ)) + (U := (-(5032596325617203968613 / 5000000000000000000000 : ℚ))) + (U' := (1898875477382796031387 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (228427821666913 / 625000000000000 : ℚ)) + (q := (29239115039908057 / 80000000000000000 : ℚ)) + (U := (-(5032596325617203968613 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_2 : Uω (aρ 2) (bρ 2) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3051,25 +2722,21 @@ lemma U_372_2 : have hlg : Real.log (29046979237090549 / 80000000000000000 : ℝ) ≤ (-(10131121412167346282789 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29046979237090549 / 80000000000000000 : ℝ) = - (29046979237090549 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29046979237090549 / 20000000000000000 : ℚ)) - (U := (3731822193832653717211 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29046979237090549 / 20000000000000000 : ℝ) ≤ - (3731822193832653717211 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3630580208476231 / 10000000000000000 : ℝ)) (q := - (29046979237090549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29046979237090549 / 80000000000000000 : ℚ)) + (r' := (29046979237090549 / 20000000000000000 : ℚ)) + (U := (-(10131121412167346282789 / 10000000000000000000000 : ℚ))) + (U' := (3731822193832653717211 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (3630580208476231 / 10000000000000000 : ℚ)) + (q := (29046979237090549 / 80000000000000000 : ℚ)) + (U := (-(10131121412167346282789 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_3 : Uω (aρ 3) (bρ 3) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3077,25 +2744,21 @@ lemma U_372_3 : have hlg : Real.log (28661888256502593 / 80000000000000000 : ℝ) ≤ (-(641536455743347809409 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28661888256502593 / 80000000000000000 : ℝ) = - (28661888256502593 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28661888256502593 / 20000000000000000 : ℚ)) - (U := (224897519631652190591 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28661888256502593 / 20000000000000000 : ℝ) ≤ - (224897519631652190591 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1790851784839621 / 5000000000000000 : ℝ)) (q := - (28661888256502593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28661888256502593 / 80000000000000000 : ℚ)) + (r' := (28661888256502593 / 20000000000000000 : ℚ)) + (U := (-(641536455743347809409 / 625000000000000000000 : ℚ))) + (U' := (224897519631652190591 / 625000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (1790851784839621 / 5000000000000000 : ℚ)) + (q := (28661888256502593 / 80000000000000000 : ℚ)) + (U := (-(641536455743347809409 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_4 : Uω (aρ 4) (bρ 4) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3103,25 +2766,21 @@ lemma U_372_4 : have hlg : Real.log (28019764544771253 / 80000000000000000 : ℝ) ≤ (-(10491164963935251592369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28019764544771253 / 80000000000000000 : ℝ) = - (28019764544771253 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28019764544771253 / 20000000000000000 : ℚ)) - (U := (3371778642064748407631 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28019764544771253 / 20000000000000000 : ℝ) ≤ - (3371778642064748407631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3499466822811407 / 10000000000000000 : ℝ)) (q := - (28019764544771253 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28019764544771253 / 80000000000000000 : ℚ)) + (r' := (28019764544771253 / 20000000000000000 : ℚ)) + (U := (-(10491164963935251592369 / 10000000000000000000000 : ℚ))) + (U' := (3371778642064748407631 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (3499466822811407 / 10000000000000000 : ℚ)) + (q := (28019764544771253 / 80000000000000000 : ℚ)) + (U := (-(10491164963935251592369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_5 : Uω (aρ 5) (bρ 5) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3129,25 +2788,21 @@ lemma U_372_5 : have hlg : Real.log (27035238158055049 / 80000000000000000 : ℝ) ≤ (-(10848855021095157620113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27035238158055049 / 80000000000000000 : ℝ) = - (27035238158055049 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27035238158055049 / 20000000000000000 : ℚ)) - (U := (3014088584904842379887 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27035238158055049 / 20000000000000000 : ℝ) ≤ - (3014088584904842379887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (842881286366839 / 2500000000000000 : ℝ)) (q := - (27035238158055049 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27035238158055049 / 80000000000000000 : ℚ)) + (r' := (27035238158055049 / 20000000000000000 : ℚ)) + (U := (-(10848855021095157620113 / 10000000000000000000000 : ℚ))) + (U' := (3014088584904842379887 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (842881286366839 / 2500000000000000 : ℚ)) + (q := (27035238158055049 / 80000000000000000 : ℚ)) + (U := (-(10848855021095157620113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_6 : Uω (aρ 6) (bρ 6) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3155,25 +2810,21 @@ lemma U_372_6 : have hlg : Real.log (25606991214438649 / 80000000000000000 : ℝ) ≤ (-(2847903064094822168529 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25606991214438649 / 80000000000000000 : ℝ) = - (25606991214438649 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25606991214438649 / 20000000000000000 : ℚ)) - (U := (617832837405177831471 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25606991214438649 / 20000000000000000 : ℝ) ≤ - (617832837405177831471 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397712973087907 / 1250000000000000 : ℝ)) (q := - (25606991214438649 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25606991214438649 / 80000000000000000 : ℚ)) + (r' := (25606991214438649 / 20000000000000000 : ℚ)) + (U := (-(2847903064094822168529 / 2500000000000000000000 : ℚ))) + (U' := (617832837405177831471 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (397712973087907 / 1250000000000000 : ℚ)) + (q := (25606991214438649 / 80000000000000000 : ℚ)) + (U := (-(2847903064094822168529 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_7 : Uω (aρ 7) (bρ 7) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3181,25 +2832,21 @@ lemma U_372_7 : have hlg : Real.log (23619692520409741 / 80000000000000000 : ℝ) ≤ (-(12199458412337004357933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23619692520409741 / 80000000000000000 : ℝ) = - (23619692520409741 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23619692520409741 / 20000000000000000 : ℚ)) - (U := (1663485193662995642067 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23619692520409741 / 20000000000000000 : ℝ) ≤ - (1663485193662995642067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2908540491956029 / 10000000000000000 : ℝ)) (q := - (23619692520409741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23619692520409741 / 80000000000000000 : ℚ)) + (r' := (23619692520409741 / 20000000000000000 : ℚ)) + (U := (-(12199458412337004357933 / 10000000000000000000000 : ℚ))) + (U' := (1663485193662995642067 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (2908540491956029 / 10000000000000000 : ℚ)) + (q := (23619692520409741 / 80000000000000000 : ℚ)) + (U := (-(12199458412337004357933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_8 : Uω (aρ 8) (bρ 8) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3207,25 +2854,21 @@ lemma U_372_8 : have hlg : Real.log (20931483544297449 / 80000000000000000 : ℝ) ≤ (-(3351930547426756303613 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20931483544297449 / 80000000000000000 : ℝ) = - (20931483544297449 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20931483544297449 / 20000000000000000 : ℚ)) - (U := (113805354073243696387 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20931483544297449 / 20000000000000000 : ℝ) ≤ - (113805354073243696387 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (630007474816989 / 2500000000000000 : ℝ)) (q := - (20931483544297449 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20931483544297449 / 80000000000000000 : ℚ)) + (r' := (20931483544297449 / 20000000000000000 : ℚ)) + (U := (-(3351930547426756303613 / 2500000000000000000000 : ℚ))) + (U' := (113805354073243696387 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (630007474816989 / 2500000000000000 : ℚ)) + (q := (20931483544297449 / 80000000000000000 : ℚ)) + (U := (-(3351930547426756303613 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_9 : Uω (aρ 9) (bρ 9) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3233,25 +2876,21 @@ lemma U_372_9 : have hlg : Real.log (17299629239625421 / 80000000000000000 : ℝ) ≤ (-(7656707819277447128447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17299629239625421 / 80000000000000000 : ℝ) = - (17299629239625421 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17299629239625421 / 10000000000000000 : ℚ)) - (U := (2740499885222552871553 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17299629239625421 / 10000000000000000 : ℝ) ≤ - (2740499885222552871553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1953031951459949 / 10000000000000000 : ℝ)) (q := - (17299629239625421 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17299629239625421 / 80000000000000000 : ℚ)) + (r' := (17299629239625421 / 10000000000000000 : ℚ)) + (U := (-(7656707819277447128447 / 5000000000000000000000 : ℚ))) + (U' := (2740499885222552871553 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (1953031951459949 / 10000000000000000 : ℚ)) + (q := (17299629239625421 / 80000000000000000 : ℚ)) + (U := (-(7656707819277447128447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_10 : Uω (aρ 10) (bρ 10) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3259,26 +2898,21 @@ lemma U_372_10 : have hlg : Real.log (2355685035371973 / 16000000000000000 : ℝ) ≤ (-(19157571507822823325749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2355685035371973 / 16000000000000000 : ℝ) = - (2355685035371973 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2355685035371973 / 2000000000000000 : ℚ)) - (U := (1636843901177176674251 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2355685035371973 / 2000000000000000 : ℝ) ≤ - (1636843901177176674251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24032249231589 / 250000000000000 : ℝ)) (q := - (2355685035371973 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2355685035371973 / 16000000000000000 : ℚ)) + (r' := (2355685035371973 / 2000000000000000 : ℚ)) + (U := (-(19157571507822823325749 / 10000000000000000000000 : ℚ))) + (U' := (1636843901177176674251 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4760871464181 / 12800000000000 : ℚ)) + (s := (24032249231589 / 250000000000000 : ℚ)) + (q := (2355685035371973 / 16000000000000000 : ℚ)) + (U := (-(19157571507822823325749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_372_11 : Uω (aρ 11) (bρ 11) (4760871464181 / 12800000000000 : ℝ) ≤ @@ -3400,25 +3034,21 @@ lemma U_373_1 : have hlg : Real.log (58582877781876861 / 160000000000000000 : ℝ) ≤ (-(2009462697697571396643 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58582877781876861 / 160000000000000000 : ℝ) = - (58582877781876861 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58582877781876861 / 40000000000000000 : ℚ)) - (U := (763126023502428603357 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58582877781876861 / 40000000000000000 : ℝ) ≤ - (763126023502428603357 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3661385707064217 / 10000000000000000 : ℝ)) (q := - (58582877781876861 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58582877781876861 / 160000000000000000 : ℚ)) + (r' := (58582877781876861 / 40000000000000000 : ℚ)) + (U := (-(2009462697697571396643 / 2000000000000000000000 : ℚ))) + (U' := (763126023502428603357 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (3661385707064217 / 10000000000000000 : ℚ)) + (q := (58582877781876861 / 160000000000000000 : ℚ)) + (U := (-(2009462697697571396643 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_2 : Uω (aρ 2) (bρ 2) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3426,25 +3056,21 @@ lemma U_373_2 : have hlg : Real.log (58198613319007573 / 160000000000000000 : ℝ) ≤ (-(252828071598570374709 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58198613319007573 / 160000000000000000 : ℝ) = - (58198613319007573 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58198613319007573 / 40000000000000000 : ℚ)) - (U := (93745518551429625291 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58198613319007573 / 40000000000000000 : ℝ) ≤ - (93745518551429625291 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (909280415428889 / 2500000000000000 : ℝ)) (q := - (58198613319007573 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58198613319007573 / 160000000000000000 : ℚ)) + (r' := (58198613319007573 / 40000000000000000 : ℚ)) + (U := (-(252828071598570374709 / 250000000000000000000 : ℚ))) + (U' := (93745518551429625291 / 250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (909280415428889 / 2500000000000000 : ℚ)) + (q := (58198613319007573 / 160000000000000000 : ℚ)) + (U := (-(252828071598570374709 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_3 : Uω (aρ 3) (bρ 3) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3452,25 +3078,21 @@ lemma U_373_3 : have hlg : Real.log (57428453061226893 / 160000000000000000 : ℝ) ≤ (-(512316968137633730297 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57428453061226893 / 160000000000000000 : ℝ) = - (57428453061226893 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57428453061226893 / 40000000000000000 : ℚ)) - (U := (180830212162366269703 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57428453061226893 / 40000000000000000 : ℝ) ≤ - (180830212162366269703 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3588247735842971 / 10000000000000000 : ℝ)) (q := - (57428453061226893 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57428453061226893 / 160000000000000000 : ℚ)) + (r' := (57428453061226893 / 40000000000000000 : ℚ)) + (U := (-(512316968137633730297 / 500000000000000000000 : ℚ))) + (U' := (180830212162366269703 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (3588247735842971 / 10000000000000000 : ℚ)) + (q := (57428453061226893 / 160000000000000000 : ℚ)) + (U := (-(512316968137633730297 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_4 : Uω (aρ 4) (bρ 4) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3478,25 +3100,21 @@ lemma U_373_4 : have hlg : Real.log (56144265182270437 / 160000000000000000 : ℝ) ≤ (-(5236246363160253772561 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56144265182270437 / 160000000000000000 : ℝ) = - (56144265182270437 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56144265182270437 / 40000000000000000 : ℚ)) - (U := (1695225439839746227439 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56144265182270437 / 40000000000000000 : ℝ) ≤ - (1695225439839746227439 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1753009216019207 / 5000000000000000 : ℝ)) (q := - (56144265182270437 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56144265182270437 / 160000000000000000 : ℚ)) + (r' := (56144265182270437 / 40000000000000000 : ℚ)) + (U := (-(5236246363160253772561 / 5000000000000000000000 : ℚ))) + (U' := (1695225439839746227439 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (1753009216019207 / 5000000000000000 : ℚ)) + (q := (56144265182270437 / 160000000000000000 : ℚ)) + (U := (-(5236246363160253772561 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_5 : Uω (aρ 5) (bρ 5) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3504,25 +3122,21 @@ lemma U_373_5 : have hlg : Real.log (54175366849519829 / 160000000000000000 : ℝ) ≤ (-(5414737478748498833533 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54175366849519829 / 160000000000000000 : ℝ) = - (54175366849519829 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54175366849519829 / 40000000000000000 : ℚ)) - (U := (1516734324251501166467 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54175366849519829 / 40000000000000000 : ℝ) ≤ - (1516734324251501166467 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (844524014944897 / 2500000000000000 : ℝ)) (q := - (54175366849519829 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54175366849519829 / 160000000000000000 : ℚ)) + (r' := (54175366849519829 / 40000000000000000 : ℚ)) + (U := (-(5414737478748498833533 / 5000000000000000000000 : ℚ))) + (U' := (1516734324251501166467 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (844524014944897 / 2500000000000000 : ℚ)) + (q := (54175366849519829 / 160000000000000000 : ℚ)) + (U := (-(5414737478748498833533 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_6 : Uω (aρ 6) (bρ 6) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3530,25 +3144,21 @@ lemma U_373_6 : have hlg : Real.log (51319258071870397 / 160000000000000000 : ℝ) ≤ (-(2274215463942847126499 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51319258071870397 / 160000000000000000 : ℝ) = - (51319258071870397 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51319258071870397 / 40000000000000000 : ℚ)) - (U := (498373257257152873501 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51319258071870397 / 40000000000000000 : ℝ) ≤ - (498373257257152873501 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3188322837713409 / 10000000000000000 : ℝ)) (q := - (51319258071870397 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51319258071870397 / 160000000000000000 : ℚ)) + (r' := (51319258071870397 / 40000000000000000 : ℚ)) + (U := (-(2274215463942847126499 / 2000000000000000000000 : ℚ))) + (U' := (498373257257152873501 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (3188322837713409 / 10000000000000000 : ℚ)) + (q := (51319258071870397 / 160000000000000000 : ℚ)) + (U := (-(2274215463942847126499 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_7 : Uω (aρ 7) (bρ 7) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3556,25 +3166,21 @@ lemma U_373_7 : have hlg : Real.log (47345608117045269 / 160000000000000000 : ℝ) ≤ (-(1522124691229523665977 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47345608117045269 / 160000000000000000 : ℝ) = - (47345608117045269 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47345608117045269 / 40000000000000000 : ℚ)) - (U := (210743259520476334023 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47345608117045269 / 40000000000000000 : ℝ) ≤ - (210743259520476334023 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (728819493530067 / 2500000000000000 : ℝ)) (q := - (47345608117045269 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47345608117045269 / 160000000000000000 : ℚ)) + (r' := (47345608117045269 / 40000000000000000 : ℚ)) + (U := (-(1522124691229523665977 / 1250000000000000000000 : ℚ))) + (U' := (210743259520476334023 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (728819493530067 / 2500000000000000 : ℚ)) + (q := (47345608117045269 / 160000000000000000 : ℚ)) + (U := (-(1522124691229523665977 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_8 : Uω (aρ 8) (bρ 8) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3582,25 +3188,21 @@ lemma U_373_8 : have hlg : Real.log (41971606093120077 / 160000000000000000 : ℝ) ≤ (-(3345451176135521414619 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (41971606093120077 / 160000000000000000 : ℝ) = - (41971606093120077 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41971606093120077 / 40000000000000000 : ℚ)) - (U := (120284725364478585381 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41971606093120077 / 40000000000000000 : ℝ) ≤ - (120284725364478585381 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2527069372469619 / 10000000000000000 : ℝ)) (q := - (41971606093120077 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41971606093120077 / 160000000000000000 : ℚ)) + (r' := (41971606093120077 / 40000000000000000 : ℚ)) + (U := (-(3345451176135521414619 / 2500000000000000000000 : ℚ))) + (U' := (120284725364478585381 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (2527069372469619 / 10000000000000000 : ℚ)) + (q := (41971606093120077 / 160000000000000000 : ℚ)) + (U := (-(3345451176135521414619 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_9 : Uω (aρ 9) (bρ 9) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3608,25 +3210,21 @@ lemma U_373_9 : have hlg : Real.log (34715084613313061 / 160000000000000000 : ℝ) ≤ (-(15279995068813354745051 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34715084613313061 / 160000000000000000 : ℝ) = - (34715084613313061 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34715084613313061 / 20000000000000000 : ℚ)) - (U := (5514420340186645254949 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34715084613313061 / 20000000000000000 : ℝ) ≤ - (5514420340186645254949 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (980484907926871 / 5000000000000000 : ℝ)) (q := - (34715084613313061 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34715084613313061 / 160000000000000000 : ℚ)) + (r' := (34715084613313061 / 20000000000000000 : ℚ)) + (U := (-(15279995068813354745051 / 10000000000000000000000 : ℚ))) + (U' := (5514420340186645254949 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (980484907926871 / 5000000000000000 : ℚ)) + (q := (34715084613313061 / 160000000000000000 : ℚ)) + (U := (-(15279995068813354745051 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_10 : Uω (aρ 10) (bρ 10) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3634,26 +3232,21 @@ lemma U_373_10 : have hlg : Real.log (23716554219765741 / 160000000000000000 : ℝ) ≤ (-(4772501299645587367841 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (23716554219765741 / 160000000000000000 : ℝ) = - (23716554219765741 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23716554219765741 / 20000000000000000 : ℚ)) - (U := (426102552604412632159 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23716554219765741 / 20000000000000000 : ℝ) ≤ - (426102552604412632159 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (974712550155327 / 10000000000000000 : ℝ)) (q := - (23716554219765741 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23716554219765741 / 160000000000000000 : ℚ)) + (r' := (23716554219765741 / 20000000000000000 : ℚ)) + (U := (-(4772501299645587367841 / 2500000000000000000000 : ℚ))) + (U' := (426102552604412632159 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47692431792069 / 128000000000000 : ℚ)) + (s := (974712550155327 / 10000000000000000 : ℚ)) + (q := (23716554219765741 / 160000000000000000 : ℚ)) + (U := (-(4772501299645587367841 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_373_11 : Uω (aρ 11) (bρ 11) (47692431792069 / 128000000000000 : ℝ) ≤ @@ -3776,25 +3369,21 @@ lemma U_374_1 : have hlg : Real.log (7335940684928617 / 20000000000000000 : ℝ) ≤ (-(10029466235912752073139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7335940684928617 / 20000000000000000 : ℝ) = - (7335940684928617 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7335940684928617 / 5000000000000000 : ℚ)) - (U := (3833477370087247926861 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7335940684928617 / 5000000000000000 : ℝ) ≤ - (3833477370087247926861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1833963133447121 / 5000000000000000 : ℝ)) (q := - (7335940684928617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7335940684928617 / 20000000000000000 : ℚ)) + (r' := (7335940684928617 / 5000000000000000 : ℚ)) + (U := (-(10029466235912752073139 / 10000000000000000000000 : ℚ))) + (U' := (3833477370087247926861 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (1833963133447121 / 5000000000000000 : ℚ)) + (q := (7335940684928617 / 20000000000000000 : ℚ)) + (U := (-(10029466235912752073139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_2 : Uω (aρ 2) (bρ 2) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3802,25 +3391,21 @@ lemma U_374_2 : have hlg : Real.log (3643954258353147 / 10000000000000000 : ℝ) ≤ (-(2523789164369170187899 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3643954258353147 / 10000000000000000 : ℝ) = - (3643954258353147 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3643954258353147 / 2500000000000000 : ℚ)) - (U := (941946737130829812101 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3643954258353147 / 2500000000000000 : ℝ) ≤ - (941946737130829812101 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3643663111181919 / 10000000000000000 : ℝ)) (q := - (3643954258353147 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3643954258353147 / 10000000000000000 : ℚ)) + (r' := (3643954258353147 / 2500000000000000 : ℚ)) + (U := (-(2523789164369170187899 / 2500000000000000000000 : ℚ))) + (U' := (941946737130829812101 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (3643663111181919 / 10000000000000000 : ℚ)) + (q := (3643954258353147 / 10000000000000000 : ℚ)) + (U := (-(2523789164369170187899 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_3 : Uω (aρ 3) (bρ 3) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3828,25 +3413,21 @@ lemma U_374_3 : have hlg : Real.log (359582059374067 / 1000000000000000 : ℝ) ≤ (-(10228128676152854997047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (359582059374067 / 1000000000000000 : ℝ) = - (359582059374067 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (359582059374067 / 250000000000000 : ℚ)) - (U := (3634814929847145002953 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (359582059374067 / 250000000000000 : ℝ) ≤ - (3634814929847145002953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (718958377661393 / 2000000000000000 : ℝ)) (q := - (359582059374067 / 1000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (359582059374067 / 1000000000000000 : ℚ)) + (r' := (359582059374067 / 250000000000000 : ℚ)) + (U := (-(10228128676152854997047 / 10000000000000000000000 : ℚ))) + (U' := (3634814929847145002953 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (718958377661393 / 2000000000000000 : ℚ)) + (q := (359582059374067 / 1000000000000000 : ℚ)) + (U := (-(10228128676152854997047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_4 : Uω (aρ 4) (bρ 4) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3854,25 +3435,21 @@ lemma U_374_4 : have hlg : Real.log (3515562558802351 / 10000000000000000 : ℝ) ≤ (-(10453855348389118523381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3515562558802351 / 10000000000000000 : ℝ) = - (3515562558802351 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3515562558802351 / 2500000000000000 : ℚ)) - (U := (3409088257610881476619 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3515562558802351 / 2500000000000000 : ℝ) ≤ - (3409088257610881476619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3512569999495327 / 10000000000000000 : ℝ)) (q := - (3515562558802351 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3515562558802351 / 10000000000000000 : ℚ)) + (r' := (3515562558802351 / 2500000000000000 : ℚ)) + (U := (-(10453855348389118523381 / 10000000000000000000000 : ℚ))) + (U' := (3409088257610881476619 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (3512569999495327 / 10000000000000000 : ℚ)) + (q := (3515562558802351 / 10000000000000000 : ℚ)) + (U := (-(10453855348389118523381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_5 : Uω (aρ 5) (bρ 5) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3880,25 +3457,21 @@ lemma U_374_5 : have hlg : Real.log (6785032054670867 / 20000000000000000 : ℝ) ≤ (-(10810132554148952355511 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6785032054670867 / 20000000000000000 : ℝ) = - (6785032054670867 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6785032054670867 / 5000000000000000 : ℚ)) - (U := (3052811051851047644489 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6785032054670867 / 5000000000000000 : ℝ) ≤ - (3052811051851047644489 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (846166713974123 / 2500000000000000 : ℝ)) (q := - (6785032054670867 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6785032054670867 / 20000000000000000 : ℚ)) + (r' := (6785032054670867 / 5000000000000000 : ℚ)) + (U := (-(10810132554148952355511 / 10000000000000000000000 : ℚ))) + (U' := (3052811051851047644489 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (846166713974123 / 2500000000000000 : ℚ)) + (q := (6785032054670867 / 20000000000000000 : ℚ)) + (U := (-(10810132554148952355511 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_6 : Uω (aρ 6) (bρ 6) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3906,25 +3479,21 @@ lemma U_374_6 : have hlg : Real.log (642806639040847 / 2000000000000000 : ℝ) ≤ (-(11350584968972253481687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (642806639040847 / 2000000000000000 : ℝ) = - (642806639040847 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (642806639040847 / 500000000000000 : ℚ)) - (U := (2512358637027746518313 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (642806639040847 / 500000000000000 : ℝ) ≤ - (2512358637027746518313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (638988313354819 / 2000000000000000 : ℝ)) (q := - (642806639040847 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (642806639040847 / 2000000000000000 : ℚ)) + (r' := (642806639040847 / 500000000000000 : ℚ)) + (U := (-(11350584968972253481687 / 10000000000000000000000 : ℚ))) + (U' := (2512358637027746518313 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (638988313354819 / 2000000000000000 : ℚ)) + (q := (642806639040847 / 2000000000000000 : ℚ)) + (U := (-(11350584968972253481687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_7 : Uω (aρ 7) (bρ 7) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3932,23 +3501,21 @@ lemma U_374_7 : have hlg : Real.log (9267934380643 / 31250000000000 : ℝ) ≤ (-(3038647123310739096387 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (9267934380643 / 31250000000000 : ℝ) = (9267934380643 / 7812500000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9267934380643 / 7812500000000 : ℚ)) - (U := (427088778189260903613 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9267934380643 / 7812500000000 : ℝ) ≤ - (427088778189260903613 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (584402912147429 / 2000000000000000 : ℝ)) (q := - (9267934380643 / 31250000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9267934380643 / 31250000000000 : ℚ)) + (r' := (9267934380643 / 7812500000000 : ℚ)) + (U := (-(3038647123310739096387 / 2500000000000000000000 : ℚ))) + (U' := (427088778189260903613 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (584402912147429 / 2000000000000000 : ℚ)) + (q := (9267934380643 / 31250000000000 : ℚ)) + (U := (-(3038647123310739096387 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_8 : Uω (aρ 8) (bρ 8) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3956,25 +3523,21 @@ lemma U_374_8 : have hlg : Real.log (1315006990691277 / 5000000000000000 : ℝ) ≤ (-(534238372073429131109 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1315006990691277 / 5000000000000000 : ℝ) = - (1315006990691277 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1315006990691277 / 1250000000000000 : ℚ)) - (U := (20279372166570868891 / 400000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1315006990691277 / 1250000000000000 : ℝ) ≤ - (20279372166570868891 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2534106171230733 / 10000000000000000 : ℝ)) (q := - (1315006990691277 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1315006990691277 / 5000000000000000 : ℚ)) + (r' := (1315006990691277 / 1250000000000000 : ℚ)) + (U := (-(534238372073429131109 / 400000000000000000000 : ℚ))) + (U' := (20279372166570868891 / 400000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (2534106171230733 / 10000000000000000 : ℚ)) + (q := (1315006990691277 / 5000000000000000 : ℚ)) + (U := (-(534238372073429131109 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_9 : Uω (aρ 9) (bρ 9) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -3982,25 +3545,21 @@ lemma U_374_9 : have hlg : Real.log (4353853567226101 / 20000000000000000 : ℝ) ≤ (-(15246709423082283256313 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4353853567226101 / 20000000000000000 : ℝ) = - (4353853567226101 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4353853567226101 / 2500000000000000 : ℚ)) - (U := (5547705985917716743687 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4353853567226101 / 2500000000000000 : ℝ) ≤ - (5547705985917716743687 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (984448702025863 / 5000000000000000 : ℝ)) (q := - (4353853567226101 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4353853567226101 / 20000000000000000 : ℚ)) + (r' := (4353853567226101 / 2500000000000000 : ℚ)) + (U := (-(15246709423082283256313 / 10000000000000000000000 : ℚ))) + (U' := (5547705985917716743687 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (984448702025863 / 5000000000000000 : ℚ)) + (q := (4353853567226101 / 20000000000000000 : ℚ)) + (U := (-(15246709423082283256313 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_10 : Uω (aρ 10) (bρ 10) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -4008,26 +3567,21 @@ lemma U_374_10 : have hlg : Real.log (1492196606227513 / 10000000000000000 : ℝ) ≤ (-(760934330201234651191 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1492196606227513 / 10000000000000000 : ℝ) = - (1492196606227513 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1492196606227513 / 1250000000000000 : ℚ)) - (U := (70842286158765348809 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1492196606227513 / 1250000000000000 : ℝ) ≤ - (70842286158765348809 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (987996082775651 / 10000000000000000 : ℝ)) (q := - (1492196606227513 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1492196606227513 / 10000000000000000 : ℚ)) + (r' := (1492196606227513 / 1250000000000000 : ℚ)) + (U := (-(760934330201234651191 / 400000000000000000000 : ℚ))) + (U' := (70842286158765348809 / 400000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5972018617791 / 16000000000000 : ℚ)) + (s := (987996082775651 / 10000000000000000 : ℚ)) + (q := (1492196606227513 / 10000000000000000 : ℚ)) + (U := (-(760934330201234651191 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_374_11 : Uω (aρ 11) (bρ 11) (5972018617791 / 16000000000000 : ℝ) ≤ @@ -4149,25 +3703,21 @@ lemma U_375_1 : have hlg : Real.log (11758434634499287 / 32000000000000000 : ℝ) ≤ (-(10011650779804707866637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11758434634499287 / 32000000000000000 : ℝ) = - (11758434634499287 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11758434634499287 / 8000000000000000 : ℚ)) - (U := (3851292826195292133363 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (11758434634499287 / 8000000000000000 : ℝ) ≤ - (3851292826195292133363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (734893365232739 / 2000000000000000 : ℝ)) (q := - (11758434634499287 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11758434634499287 / 32000000000000000 : ℚ)) + (r' := (11758434634499287 / 8000000000000000 : ℚ)) + (U := (-(10011650779804707866637 / 10000000000000000000000 : ℚ))) + (U' := (3851292826195292133363 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (734893365232739 / 2000000000000000 : ℚ)) + (q := (11758434634499287 / 32000000000000000 : ℚ)) + (U := (-(10011650779804707866637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_2 : Uω (aρ 2) (bρ 2) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4175,25 +3725,21 @@ lemma U_375_2 : have hlg : Real.log (58407922918271723 / 160000000000000000 : ℝ) ≤ (-(10077222676728475367993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58407922918271723 / 160000000000000000 : ℝ) = - (58407922918271723 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58407922918271723 / 40000000000000000 : ℚ)) - (U := (3785720929271524632007 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58407922918271723 / 40000000000000000 : ℝ) ≤ - (3785720929271524632007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1825102278447803 / 5000000000000000 : ℝ)) (q := - (58407922918271723 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58407922918271723 / 160000000000000000 : ℚ)) + (r' := (58407922918271723 / 40000000000000000 : ℚ)) + (U := (-(10077222676728475367993 / 10000000000000000000000 : ℚ))) + (U' := (3785720929271524632007 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (1825102278447803 / 5000000000000000 : ℚ)) + (q := (58407922918271723 / 160000000000000000 : ℚ)) + (U := (-(10077222676728475367993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_3 : Uω (aρ 3) (bρ 3) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4201,25 +3747,21 @@ lemma U_375_3 : have hlg : Real.log (57637805829474139 / 160000000000000000 : ℝ) ≤ (-(1020995111110190420443 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57637805829474139 / 160000000000000000 : ℝ) = - (57637805829474139 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57637805829474139 / 40000000000000000 : ℚ)) - (U := (365299249489809579557 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57637805829474139 / 40000000000000000 : ℝ) ≤ - (365299249489809579557 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (900334006786477 / 2500000000000000 : ℝ)) (q := - (57637805829474139 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57637805829474139 / 160000000000000000 : ℚ)) + (r' := (57637805829474139 / 40000000000000000 : ℚ)) + (U := (-(1020995111110190420443 / 1000000000000000000000 : ℚ))) + (U' := (365299249489809579557 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (900334006786477 / 2500000000000000 : ℚ)) + (q := (57637805829474139 / 160000000000000000 : ℚ)) + (U := (-(1020995111110190420443 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_4 : Uω (aρ 4) (bρ 4) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4227,25 +3769,21 @@ lemma U_375_4 : have hlg : Real.log (56353736367110363 / 160000000000000000 : ℝ) ≤ (-(521762635000115749317 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56353736367110363 / 160000000000000000 : ℝ) = - (56353736367110363 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56353736367110363 / 40000000000000000 : ℚ)) - (U := (171384545299884250683 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56353736367110363 / 40000000000000000 : ℝ) ≤ - (171384545299884250683 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (879780381353859 / 2500000000000000 : ℝ)) (q := - (56353736367110363 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56353736367110363 / 160000000000000000 : ℚ)) + (r' := (56353736367110363 / 40000000000000000 : ℚ)) + (U := (-(521762635000115749317 / 500000000000000000000 : ℚ))) + (U' := (171384545299884250683 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (879780381353859 / 2500000000000000 : ℚ)) + (q := (56353736367110363 / 160000000000000000 : ℚ)) + (U := (-(521762635000115749317 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_5 : Uω (aρ 5) (bρ 5) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4253,25 +3791,21 @@ lemma U_375_5 : have hlg : Real.log (54385145085147731 / 160000000000000000 : ℝ) ≤ (-(10790827664296983932529 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54385145085147731 / 160000000000000000 : ℝ) = - (54385145085147731 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54385145085147731 / 40000000000000000 : ℚ)) - (U := (3072115941703016067471 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54385145085147731 / 40000000000000000 : ℝ) ≤ - (3072115941703016067471 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3391237534505107 / 10000000000000000 : ℝ)) (q := - (54385145085147731 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54385145085147731 / 160000000000000000 : ℚ)) + (r' := (54385145085147731 / 40000000000000000 : ℚ)) + (U := (-(10790827664296983932529 / 10000000000000000000000 : ℚ))) + (U' := (3072115941703016067471 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (3391237534505107 / 10000000000000000 : ℚ)) + (q := (54385145085147731 / 160000000000000000 : ℚ)) + (U := (-(10790827664296983932529 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_6 : Uω (aρ 6) (bρ 6) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4279,25 +3813,21 @@ lemma U_375_6 : have hlg : Real.log (51529801599142563 / 160000000000000000 : ℝ) ≤ (-(1133013502582213637493 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51529801599142563 / 160000000000000000 : ℝ) = - (51529801599142563 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51529801599142563 / 40000000000000000 : ℚ)) - (U := (253280858017786362507 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51529801599142563 / 40000000000000000 : ℝ) ≤ - (253280858017786362507 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3201559973894461 / 10000000000000000 : ℝ)) (q := - (51529801599142563 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51529801599142563 / 160000000000000000 : ℚ)) + (r' := (51529801599142563 / 40000000000000000 : ℚ)) + (U := (-(1133013502582213637493 / 1000000000000000000000 : ℚ))) + (U' := (253280858017786362507 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (3201559973894461 / 10000000000000000 : ℚ)) + (q := (51529801599142563 / 160000000000000000 : ℚ)) + (U := (-(1133013502582213637493 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_7 : Uω (aρ 7) (bρ 7) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4305,25 +3835,21 @@ lemma U_375_7 : have hlg : Real.log (47558032825797763 / 160000000000000000 : ℝ) ≤ (-(6066115528469227373073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47558032825797763 / 160000000000000000 : ℝ) = - (47558032825797763 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47558032825797763 / 40000000000000000 : ℚ)) - (U := (865356274530772626927 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47558032825797763 / 40000000000000000 : ℝ) ≤ - (865356274530772626927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2928750257986361 / 10000000000000000 : ℝ)) (q := - (47558032825797763 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47558032825797763 / 160000000000000000 : ℚ)) + (r' := (47558032825797763 / 40000000000000000 : ℚ)) + (U := (-(6066115528469227373073 / 5000000000000000000000 : ℚ))) + (U' := (865356274530772626927 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (2928750257986361 / 10000000000000000 : ℚ)) + (q := (47558032825797763 / 160000000000000000 : ℚ)) + (U := (-(6066115528469227373073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_8 : Uω (aρ 8) (bρ 8) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4331,25 +3857,21 @@ lemma U_375_8 : have hlg : Real.log (42188820093339523 / 160000000000000000 : ℝ) ≤ (-(6665092777346813657789 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42188820093339523 / 160000000000000000 : ℝ) = - (42188820093339523 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42188820093339523 / 40000000000000000 : ℚ)) - (U := (266379025653186342211 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42188820093339523 / 40000000000000000 : ℝ) ≤ - (266379025653186342211 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2541140317769081 / 10000000000000000 : ℝ)) (q := - (42188820093339523 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42188820093339523 / 160000000000000000 : ℚ)) + (r' := (42188820093339523 / 40000000000000000 : ℚ)) + (U := (-(6665092777346813657789 / 5000000000000000000000 : ℚ))) + (U' := (266379025653186342211 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (2541140317769081 / 10000000000000000 : ℚ)) + (q := (42188820093339523 / 160000000000000000 : ℚ)) + (U := (-(6665092777346813657789 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_9 : Uω (aρ 9) (bρ 9) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4357,25 +3879,21 @@ lemma U_375_9 : have hlg : Real.log (34946491241789147 / 160000000000000000 : ℝ) ≤ (-(15213557444680535887109 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (34946491241789147 / 160000000000000000 : ℝ) = - (34946491241789147 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34946491241789147 / 20000000000000000 : ℚ)) - (U := (5580857964319464112891 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34946491241789147 / 20000000000000000 : ℝ) ≤ - (5580857964319464112891 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (494203709921321 / 2500000000000000 : ℝ)) (q := - (34946491241789147 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34946491241789147 / 160000000000000000 : ℚ)) + (r' := (34946491241789147 / 20000000000000000 : ℚ)) + (U := (-(15213557444680535887109 / 10000000000000000000000 : ℚ))) + (U' := (5580857964319464112891 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (494203709921321 / 2500000000000000 : ℚ)) + (q := (34946491241789147 / 160000000000000000 : ℚ)) + (U := (-(15213557444680535887109 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_10 : Uω (aρ 10) (bρ 10) (47859866092587 / 128000000000000 : ℝ) ≤ @@ -4383,26 +3901,21 @@ lemma U_375_10 : have hlg : Real.log (4806533814394367 / 32000000000000000 : ℝ) ≤ (-(18957596983821605453081 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4806533814394367 / 32000000000000000 : ℝ) = - (4806533814394367 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4806533814394367 / 4000000000000000 : ℚ)) - (U := (1836818425178394546919 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4806533814394367 / 4000000000000000 : ℝ) ≤ - (1836818425178394546919 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6257163137207 / 62500000000000 : ℝ)) (q := - (4806533814394367 / 32000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4806533814394367 / 32000000000000000 : ℚ)) + (r' := (4806533814394367 / 4000000000000000 : ℚ)) + (U := (-(18957596983821605453081 / 10000000000000000000000 : ℚ))) + (U' := (1836818425178394546919 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47859866092587 / 128000000000000 : ℚ)) + (s := (6257163137207 / 62500000000000 : ℚ)) + (q := (4806533814394367 / 32000000000000000 : ℚ)) + (U := (-(18957596983821605453081 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_375_11 : Uω (aρ 11) (bρ 11) (47859866092587 / 128000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U31.lean b/LeanPool/Zeta5Irrational/Table/U31.lean index 67180ab892..7372f0d2e4 100644 --- a/LeanPool/Zeta5Irrational/Table/U31.lean +++ b/LeanPool/Zeta5Irrational/Table/U31.lean @@ -24,25 +24,21 @@ lemma U_376_1 : have hlg : Real.log (29448410430551627 / 80000000000000000 : ℝ) ≤ (-(9993867007066015957191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29448410430551627 / 80000000000000000 : ℝ) = - (29448410430551627 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29448410430551627 / 20000000000000000 : ℚ)) - (U := (3869076598933984042809 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29448410430551627 / 20000000000000000 : ℝ) ≤ - (3869076598933984042809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3681007384875563 / 10000000000000000 : ℝ)) (q := - (29448410430551627 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29448410430551627 / 80000000000000000 : ℚ)) + (r' := (29448410430551627 / 20000000000000000 : ℚ)) + (U := (-(9993867007066015957191 / 10000000000000000000000 : ℚ))) + (U' := (3869076598933984042809 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (3681007384875563 / 10000000000000000 : ℚ)) + (q := (29448410430551627 / 80000000000000000 : ℚ)) + (U := (-(9993867007066015957191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_2 : Uω (aρ 2) (bρ 2) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_376_2 : have hlg : Real.log (5851257767303279 / 16000000000000000 : ℝ) ≤ (-(10059320806281235657447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5851257767303279 / 16000000000000000 : ℝ) = - (5851257767303279 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5851257767303279 / 4000000000000000 : ℚ)) - (U := (3803622799718764342553 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5851257767303279 / 4000000000000000 : ℝ) ≤ - (3803622799718764342553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (731349199775351 / 2000000000000000 : ℝ)) (q := - (5851257767303279 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5851257767303279 / 16000000000000000 : ℚ)) + (r' := (5851257767303279 / 4000000000000000 : ℚ)) + (U := (-(10059320806281235657447 / 10000000000000000000000 : ℚ))) + (U' := (3803622799718764342553 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (731349199775351 / 2000000000000000 : ℚ)) + (q := (5851257767303279 / 16000000000000000 : ℚ)) + (U := (-(10059320806281235657447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_3 : Uω (aρ 3) (bρ 3) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_376_3 : have hlg : Real.log (5774248205069027 / 16000000000000000 : ℝ) ≤ (-(2038361309453471391991 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5774248205069027 / 16000000000000000 : ℝ) = - (5774248205069027 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5774248205069027 / 4000000000000000 : ℚ)) - (U := (734227411746528608009 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5774248205069027 / 4000000000000000 : ℝ) ≤ - (734227411746528608009 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180394007621697 / 500000000000000 : ℝ)) (q := - (5774248205069027 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5774248205069027 / 16000000000000000 : ℚ)) + (r' := (5774248205069027 / 4000000000000000 : ℚ)) + (U := (-(2038361309453471391991 / 2000000000000000000000 : ℚ))) + (U' := (734227411746528608009 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (180394007621697 / 500000000000000 : ℚ)) + (q := (5774248205069027 / 16000000000000000 : ℚ)) + (U := (-(2038361309453471391991 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_4 : Uω (aρ 4) (bρ 4) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_376_4 : have hlg : Real.log (28229235731470567 / 80000000000000000 : ℝ) ≤ (-(5208342325874971915933 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28229235731470567 / 80000000000000000 : ℝ) = - (28229235731470567 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28229235731470567 / 20000000000000000 : ℚ)) - (U := (1723129477125028084067 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28229235731470567 / 20000000000000000 : ℝ) ≤ - (1723129477125028084067 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1762836505015149 / 5000000000000000 : ℝ)) (q := - (28229235731470567 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28229235731470567 / 80000000000000000 : ℚ)) + (r' := (28229235731470567 / 20000000000000000 : ℚ)) + (U := (-(5208342325874971915933 / 5000000000000000000000 : ℚ))) + (U' := (1723129477125028084067 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (1762836505015149 / 5000000000000000 : ℚ)) + (q := (28229235731470567 / 80000000000000000 : ℚ)) + (U := (-(5208342325874971915933 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_5 : Uω (aρ 5) (bρ 5) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_376_5 : have hlg : Real.log (5449003279831591 / 16000000000000000 : ℝ) ≤ (-(2692890035511764538969 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5449003279831591 / 16000000000000000 : ℝ) = - (5449003279831591 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5449003279831591 / 4000000000000000 : ℚ)) - (U := (772845865988235461031 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5449003279831591 / 4000000000000000 : ℝ) ≤ - (772845865988235461031 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (679561619257429 / 2000000000000000 : ℝ)) (q := - (5449003279831591 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5449003279831591 / 16000000000000000 : ℚ)) + (r' := (5449003279831591 / 4000000000000000 : ℚ)) + (U := (-(2692890035511764538969 / 2500000000000000000000 : ℚ))) + (U' := (772845865988235461031 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (679561619257429 / 2000000000000000 : ℚ)) + (q := (5449003279831591 / 16000000000000000 : ℚ)) + (U := (-(2692890035511764538969 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_6 : Uω (aρ 6) (bρ 6) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_376_6 : have hlg : Real.log (25817534757717279 / 80000000000000000 : ℝ) ≤ (-(11309727313063090127271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25817534757717279 / 80000000000000000 : ℝ) = - (25817534757717279 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25817534757717279 / 20000000000000000 : ℚ)) - (U := (2553216292936909872729 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25817534757717279 / 20000000000000000 : ℝ) ≤ - (2553216292936909872729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100255564408343 / 312500000000000 : ℝ)) (q := - (25817534757717279 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25817534757717279 / 80000000000000000 : ℚ)) + (r' := (25817534757717279 / 20000000000000000 : ℚ)) + (U := (-(11309727313063090127271 / 10000000000000000000000 : ℚ))) + (U' := (2553216292936909872729 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (100255564408343 / 312500000000000 : ℚ)) + (q := (25817534757717279 / 80000000000000000 : ℚ)) + (U := (-(11309727313063090127271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_7 : Uω (aρ 7) (bρ 7) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_376_7 : have hlg : Real.log (23832117278369707 / 80000000000000000 : ℝ) ≤ (-(12109924977090579279271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23832117278369707 / 80000000000000000 : ℝ) = - (23832117278369707 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23832117278369707 / 20000000000000000 : ℚ)) - (U := (1753018628909420720729 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23832117278369707 / 20000000000000000 : ℝ) ≤ - (1753018628909420720729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2935485071990083 / 10000000000000000 : ℝ)) (q := - (23832117278369707 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23832117278369707 / 80000000000000000 : ℚ)) + (r' := (23832117278369707 / 20000000000000000 : ℚ)) + (U := (-(12109924977090579279271 / 10000000000000000000000 : ℚ))) + (U' := (1753018628909420720729 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (2935485071990083 / 10000000000000000 : ℚ)) + (q := (23832117278369707 / 80000000000000000 : ℚ)) + (U := (-(12109924977090579279271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_8 : Uω (aρ 8) (bρ 8) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_376_8 : have hlg : Real.log (21148697721244531 / 80000000000000000 : ℝ) ≤ (-(13304483040210431015309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21148697721244531 / 80000000000000000 : ℝ) = - (21148697721244531 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21148697721244531 / 20000000000000000 : ℚ)) - (U := (558460565789568984691 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21148697721244531 / 20000000000000000 : ℝ) ≤ - (558460565789568984691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2548171834048789 / 10000000000000000 : ℝ)) (q := - (21148697721244531 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21148697721244531 / 80000000000000000 : ℚ)) + (r' := (21148697721244531 / 20000000000000000 : ℚ)) + (U := (-(13304483040210431015309 / 10000000000000000000000 : ℚ))) + (U' := (558460565789568984691 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (2548171834048789 / 10000000000000000 : ℚ)) + (q := (21148697721244531 / 80000000000000000 : ℚ)) + (U := (-(13304483040210431015309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_9 : Uω (aρ 9) (bρ 9) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_376_9 : have hlg : Real.log (3506207369726651 / 16000000000000000 : ℝ) ≤ (-(15180537896117200035529 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3506207369726651 / 16000000000000000 : ℝ) = - (3506207369726651 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3506207369726651 / 2000000000000000 : ℚ)) - (U := (5613877512882799964471 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3506207369726651 / 2000000000000000 : ℝ) ≤ - (5613877512882799964471 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (198472224425597 / 1000000000000000 : ℝ)) (q := - (3506207369726651 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3506207369726651 / 16000000000000000 : ℚ)) + (r' := (3506207369726651 / 2000000000000000 : ℚ)) + (U := (-(15180537896117200035529 / 10000000000000000000000 : ℚ))) + (U' := (5613877512882799964471 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (198472224425597 / 1000000000000000 : ℚ)) + (q := (3506207369726651 / 16000000000000000 : ℚ)) + (U := (-(15180537896117200035529 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_10 : Uω (aρ 10) (bρ 10) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_376_10 : have hlg : Real.log (12094582942561791 / 80000000000000000 : ℝ) ≤ (-(18892689722321229897263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12094582942561791 / 80000000000000000 : ℝ) = - (12094582942561791 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12094582942561791 / 10000000000000000 : ℚ)) - (U := (1901725686678770102737 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12094582942561791 / 10000000000000000 : ℝ) ≤ - (1901725686678770102737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63385487577069 / 625000000000000 : ℝ)) (q := - (12094582942561791 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12094582942561791 / 80000000000000000 : ℚ)) + (r' := (12094582942561791 / 10000000000000000 : ℚ)) + (U := (-(18892689722321229897263 / 10000000000000000000000 : ℚ))) + (U' := (1901725686678770102737 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23971791621423 / 64000000000000 : ℚ)) + (s := (63385487577069 / 625000000000000 : ℚ)) + (q := (12094582942561791 / 80000000000000000 : ℚ)) + (U := (-(18892689722321229897263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_376_11 : Uω (aρ 11) (bρ 11) (23971791621423 / 64000000000000 : ℝ) ≤ @@ -399,25 +358,21 @@ lemma U_377_1 : have hlg : Real.log (59001468545273121 / 160000000000000000 : ℝ) ≤ (-(9976114805201331339663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59001468545273121 / 160000000000000000 : ℝ) = - (59001468545273121 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59001468545273121 / 40000000000000000 : ℚ)) - (U := (3886828800798668660337 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59001468545273121 / 40000000000000000 : ℝ) ≤ - (3886828800798668660337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (921886985758203 / 2500000000000000 : ℝ)) (q := - (59001468545273121 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59001468545273121 / 160000000000000000 : ℚ)) + (r' := (59001468545273121 / 40000000000000000 : ℚ)) + (U := (-(9976114805201331339663 / 10000000000000000000000 : ℚ))) + (U' := (3886828800798668660337 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (921886985758203 / 2500000000000000 : ℚ)) + (q := (59001468545273121 / 160000000000000000 : ℚ)) + (U := (-(9976114805201331339663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_2 : Uω (aρ 2) (bρ 2) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -425,25 +380,21 @@ lemma U_377_2 : have hlg : Real.log (58617232398093521 / 160000000000000000 : ℝ) ≤ (-(2510362732834259353731 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58617232398093521 / 160000000000000000 : ℝ) = - (58617232398093521 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58617232398093521 / 40000000000000000 : ℚ)) - (U := (955373168665740646269 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58617232398093521 / 40000000000000000 : ℝ) ≤ - (955373168665740646269 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1831643718572681 / 5000000000000000 : ℝ)) (q := - (58617232398093521 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58617232398093521 / 160000000000000000 : ℚ)) + (r' := (58617232398093521 / 40000000000000000 : ℚ)) + (U := (-(2510362732834259353731 / 2500000000000000000000 : ℚ))) + (U' := (955373168665740646269 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (1831643718572681 / 5000000000000000 : ℚ)) + (q := (58617232398093521 / 160000000000000000 : ℚ)) + (U := (-(2510362732834259353731 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_3 : Uω (aρ 3) (bρ 3) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -451,25 +402,21 @@ lemma U_377_3 : have hlg : Real.log (57847158164087953 / 160000000000000000 : ℝ) ≤ (-(10173694864971688524833 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57847158164087953 / 160000000000000000 : ℝ) = - (57847158164087953 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57847158164087953 / 40000000000000000 : ℚ)) - (U := (3689248741028311475167 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57847158164087953 / 40000000000000000 : ℝ) ≤ - (3689248741028311475167 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1807212132122333 / 5000000000000000 : ℝ)) (q := - (57847158164087953 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57847158164087953 / 160000000000000000 : ℚ)) + (r' := (57847158164087953 / 40000000000000000 : ℚ)) + (U := (-(10173694864971688524833 / 10000000000000000000000 : ℚ))) + (U' := (3689248741028311475167 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (1807212132122333 / 5000000000000000 : ℚ)) + (q := (57847158164087953 / 160000000000000000 : ℚ)) + (U := (-(10173694864971688524833 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_4 : Uω (aρ 4) (bρ 4) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -477,25 +424,21 @@ lemma U_377_4 : have hlg : Real.log (56563206230168601 / 160000000000000000 : ℝ) ≤ (-(5199075537472519501479 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56563206230168601 / 160000000000000000 : ℝ) = - (56563206230168601 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56563206230168601 / 40000000000000000 : ℚ)) - (U := (1732396265527480498521 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56563206230168601 / 40000000000000000 : ℝ) ≤ - (1732396265527480498521 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3532224453569747 / 10000000000000000 : ℝ)) (q := - (56563206230168601 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56563206230168601 / 160000000000000000 : ℚ)) + (r' := (56563206230168601 / 40000000000000000 : ℚ)) + (U := (-(5199075537472519501479 / 5000000000000000000000 : ℚ))) + (U' := (1732396265527480498521 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (3532224453569747 / 10000000000000000 : ℚ)) + (q := (56563206230168601 / 160000000000000000 : ℚ)) + (U := (-(5199075537472519501479 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_5 : Uω (aρ 5) (bρ 5) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -503,25 +446,21 @@ lemma U_377_5 : have hlg : Real.log (54594919582282977 / 160000000000000000 : ℝ) ≤ (-(10752329842358406152703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54594919582282977 / 160000000000000000 : ℝ) = - (54594919582282977 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54594919582282977 / 40000000000000000 : ℚ)) - (U := (3110613763641593847297 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54594919582282977 / 40000000000000000 : ℝ) ≤ - (3110613763641593847297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (851094635479761 / 2500000000000000 : ℝ)) (q := - (54594919582282977 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54594919582282977 / 160000000000000000 : ℚ)) + (r' := (54594919582282977 / 40000000000000000 : ℚ)) + (U := (-(10752329842358406152703 / 10000000000000000000000 : ℚ))) + (U' := (3110613763641593847297 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (851094635479761 / 2500000000000000 : ℚ)) + (q := (54594919582282977 / 160000000000000000 : ℚ)) + (U := (-(10752329842358406152703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_6 : Uω (aρ 6) (bρ 6) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -529,25 +468,21 @@ lemma U_377_6 : have hlg : Real.log (51740334887951473 / 160000000000000000 : ℝ) ≤ (-(11289361654615094735919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51740334887951473 / 160000000000000000 : ℝ) = - (51740334887951473 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51740334887951473 / 40000000000000000 : ℚ)) - (U := (2573581951384905264081 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51740334887951473 / 40000000000000000 : ℝ) ≤ - (2573581951384905264081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1607397915133803 / 5000000000000000 : ℝ)) (q := - (51740334887951473 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51740334887951473 / 160000000000000000 : ℚ)) + (r' := (51740334887951473 / 40000000000000000 : ℚ)) + (U := (-(11289361654615094735919 / 10000000000000000000000 : ℚ))) + (U' := (2573581951384905264081 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (1607397915133803 / 5000000000000000 : ℚ)) + (q := (51740334887951473 / 160000000000000000 : ℚ)) + (U := (-(11289361654615094735919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_7 : Uω (aρ 7) (bρ 7) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -555,25 +490,21 @@ lemma U_377_7 : have hlg : Real.log (47770429270239633 / 160000000000000000 : ℝ) ≤ (-(12087670011636276249273 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47770429270239633 / 160000000000000000 : ℝ) = - (47770429270239633 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47770429270239633 / 40000000000000000 : ℚ)) - (U := (1775273594363723750727 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47770429270239633 / 40000000000000000 : ℝ) ≤ - (1775273594363723750727 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1471109504406813 / 5000000000000000 : ℝ)) (q := - (47770429270239633 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47770429270239633 / 160000000000000000 : ℚ)) + (r' := (47770429270239633 / 40000000000000000 : ℚ)) + (U := (-(12087670011636276249273 / 10000000000000000000000 : ℚ))) + (U' := (1775273594363723750727 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (1471109504406813 / 5000000000000000 : ℚ)) + (q := (47770429270239633 / 160000000000000000 : ℚ)) + (U := (-(12087670011636276249273 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_8 : Uω (aρ 8) (bρ 8) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -581,25 +512,21 @@ lemma U_377_8 : have hlg : Real.log (1696237996931321 / 6400000000000000 : ℝ) ≤ (-(13278851339418135968547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1696237996931321 / 6400000000000000 : ℝ) = - (1696237996931321 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1696237996931321 / 1600000000000000 : ℚ)) - (U := (584092266581864031453 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1696237996931321 / 1600000000000000 : ℝ) ≤ - (584092266581864031453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (51104014835681 / 200000000000000 : ℝ)) (q := - (1696237996931321 / 6400000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1696237996931321 / 6400000000000000 : ℚ)) + (r' := (1696237996931321 / 1600000000000000 : ℚ)) + (U := (-(13278851339418135968547 / 10000000000000000000000 : ℚ))) + (U' := (584092266581864031453 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (51104014835681 / 200000000000000 : ℚ)) + (q := (1696237996931321 / 6400000000000000 : ℚ)) + (U := (-(13278851339418135968547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_9 : Uω (aρ 9) (bρ 9) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -607,25 +534,21 @@ lemma U_377_9 : have hlg : Real.log (35177576859602393 / 160000000000000000 : ℝ) ≤ (-(3029529911736138818707 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35177576859602393 / 160000000000000000 : ℝ) = - (35177576859602393 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35177576859602393 / 20000000000000000 : ℚ)) - (U := (1129353170063861181293 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35177576859602393 / 20000000000000000 : ℝ) ≤ - (1129353170063861181293 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1992619737183971 / 10000000000000000 : ℝ)) (q := - (35177576859602393 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35177576859602393 / 160000000000000000 : ℚ)) + (r' := (35177576859602393 / 20000000000000000 : ℚ)) + (U := (-(3029529911736138818707 / 2000000000000000000000 : ℚ))) + (U' := (1129353170063861181293 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (1992619737183971 / 10000000000000000 : ℚ)) + (q := (35177576859602393 / 160000000000000000 : ℚ)) + (U := (-(3029529911736138818707 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_10 : Uω (aρ 10) (bρ 10) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -633,26 +556,21 @@ lemma U_377_10 : have hlg : Real.log (24344675185006513 / 160000000000000000 : ℝ) ≤ (-(18828606670727822522699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24344675185006513 / 160000000000000000 : ℝ) = - (24344675185006513 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24344675185006513 / 20000000000000000 : ℚ)) - (U := (1965808738272177477301 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24344675185006513 / 20000000000000000 : ℝ) ≤ - (1965808738272177477301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (513533030677243 / 5000000000000000 : ℝ)) (q := - (24344675185006513 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24344675185006513 / 160000000000000000 : ℚ)) + (r' := (24344675185006513 / 20000000000000000 : ℚ)) + (U := (-(18828606670727822522699 / 10000000000000000000000 : ℚ))) + (U' := (1965808738272177477301 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9605460078621 / 25600000000000 : ℚ)) + (s := (513533030677243 / 5000000000000000 : ℚ)) + (q := (24344675185006513 / 160000000000000000 : ℚ)) + (U := (-(18828606670727822522699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_377_11 : Uω (aρ 11) (bρ 11) (9605460078621 / 25600000000000 : ℝ) ≤ @@ -774,25 +692,21 @@ lemma U_378_1 : have hlg : Real.log (2955305811251481 / 8000000000000000 : ℝ) ≤ (-(9958394062313398461891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2955305811251481 / 8000000000000000 : ℝ) = - (2955305811251481 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2955305811251481 / 2000000000000000 : ℚ)) - (U := (3904549543686601538109 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2955305811251481 / 2000000000000000 : ℝ) ≤ - (3904549543686601538109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (369408850063839 / 1000000000000000 : ℝ)) (q := - (2955305811251481 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2955305811251481 / 8000000000000000 : ℚ)) + (r' := (2955305811251481 / 2000000000000000 : ℚ)) + (U := (-(9958394062313398461891 / 10000000000000000000000 : ℚ))) + (U' := (3904549543686601538109 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (369408850063839 / 1000000000000000 : ℚ)) + (q := (2955305811251481 / 8000000000000000 : ℚ)) + (U := (-(9958394062313398461891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_2 : Uω (aρ 2) (bρ 2) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -800,25 +714,21 @@ lemma U_378_2 : have hlg : Real.log (14680471773403183 / 40000000000000000 : ℝ) ≤ (-(10023612937712580116809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14680471773403183 / 40000000000000000 : ℝ) = - (14680471773403183 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14680471773403183 / 10000000000000000 : ℚ)) - (U := (3839330668287419883191 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14680471773403183 / 10000000000000000 : ℝ) ≤ - (3839330668287419883191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3669828871721279 / 10000000000000000 : ℝ)) (q := - (14680471773403183 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14680471773403183 / 40000000000000000 : ℚ)) + (r' := (14680471773403183 / 10000000000000000 : ℚ)) + (U := (-(10023612937712580116809 / 10000000000000000000000 : ℚ))) + (U' := (3839330668287419883191 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (3669828871721279 / 10000000000000000 : ℚ)) + (q := (14680471773403183 / 40000000000000000 : ℚ)) + (U := (-(10023612937712580116809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_3 : Uω (aρ 3) (bρ 3) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -826,25 +736,21 @@ lemma U_378_3 : have hlg : Real.log (14487958542562941 / 40000000000000000 : ℝ) ≤ (-(10155615945187571679447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14487958542562941 / 40000000000000000 : ℝ) = - (14487958542562941 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14487958542562941 / 10000000000000000 : ℚ)) - (U := (3707327660812428320553 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14487958542562941 / 10000000000000000 : ℝ) ≤ - (3707327660812428320553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1810484181325579 / 5000000000000000 : ℝ)) (q := - (14487958542562941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14487958542562941 / 40000000000000000 : ℚ)) + (r' := (14487958542562941 / 10000000000000000 : ℚ)) + (U := (-(10155615945187571679447 / 10000000000000000000000 : ℚ))) + (U' := (3707327660812428320553 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (1810484181325579 / 5000000000000000 : ℚ)) + (q := (14487958542562941 / 40000000000000000 : ℚ)) + (U := (-(10155615945187571679447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_4 : Uω (aρ 4) (bρ 4) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -852,25 +758,21 @@ lemma U_378_4 : have hlg : Real.log (14166985167654459 / 40000000000000000 : ℝ) ≤ (-(518982592080921205731 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14166985167654459 / 40000000000000000 : ℝ) = - (14166985167654459 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14166985167654459 / 10000000000000000 : ℚ)) - (U := (174164588219078794269 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14166985167654459 / 10000000000000000 : ℝ) ≤ - (174164588219078794269 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3538775856261917 / 10000000000000000 : ℝ)) (q := - (14166985167654459 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14166985167654459 / 40000000000000000 : ℚ)) + (r' := (14166985167654459 / 10000000000000000 : ℚ)) + (U := (-(518982592080921205731 / 500000000000000000000 : ℚ))) + (U' := (174164588219078794269 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (3538775856261917 / 10000000000000000 : ℚ)) + (q := (14166985167654459 / 40000000000000000 : ℚ)) + (U := (-(518982592080921205731 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_5 : Uω (aρ 5) (bρ 5) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -878,25 +780,21 @@ lemma U_378_5 : have hlg : Real.log (13674951360604657 / 40000000000000000 : ℝ) ≤ (-(10733136621036858840227 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13674951360604657 / 40000000000000000 : ℝ) = - (13674951360604657 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13674951360604657 / 10000000000000000 : ℚ)) - (U := (3129806984963141159773 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13674951360604657 / 10000000000000000 : ℝ) ≤ - (3129806984963141159773 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (213184304504501 / 625000000000000 : ℝ)) (q := - (13674951360604657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13674951360604657 / 40000000000000000 : ℚ)) + (r' := (13674951360604657 / 10000000000000000 : ℚ)) + (U := (-(10733136621036858840227 / 10000000000000000000000 : ℚ))) + (U' := (3129806984963141159773 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (213184304504501 / 625000000000000 : ℚ)) + (q := (13674951360604657 / 40000000000000000 : ℚ)) + (U := (-(10733136621036858840227 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_6 : Uω (aρ 6) (bρ 6) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -904,25 +802,21 @@ lemma U_378_6 : have hlg : Real.log (12961399433092597 / 40000000000000000 : ℝ) ≤ (-(11269037875509371656561 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12961399433092597 / 40000000000000000 : ℝ) = - (12961399433092597 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12961399433092597 / 10000000000000000 : ℚ)) - (U := (2593905730490628343439 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12961399433092597 / 10000000000000000 : ℝ) ≤ - (2593905730490628343439 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1610706641727993 / 5000000000000000 : ℝ)) (q := - (12961399433092597 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12961399433092597 / 40000000000000000 : ℚ)) + (r' := (12961399433092597 / 10000000000000000 : ℚ)) + (U := (-(11269037875509371656561 / 10000000000000000000000 : ℚ))) + (U' := (2593905730490628343439 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (1610706641727993 / 5000000000000000 : ℚ)) + (q := (12961399433092597 / 40000000000000000 : ℚ)) + (U := (-(11269037875509371656561 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_7 : Uω (aρ 7) (bρ 7) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -930,25 +824,21 @@ lemma U_378_7 : have hlg : Real.log (11969154253592859 / 40000000000000000 : ℝ) ≤ (-(2413093184052817137671 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11969154253592859 / 40000000000000000 : ℝ) = - (11969154253592859 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11969154253592859 / 10000000000000000 : ℚ)) - (U := (359495537147182862329 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11969154253592859 / 10000000000000000 : ℝ) ≤ - (359495537147182862329 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2948952074466117 / 10000000000000000 : ℝ)) (q := - (11969154253592859 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11969154253592859 / 40000000000000000 : ℚ)) + (r' := (11969154253592859 / 10000000000000000 : ℚ)) + (U := (-(2413093184052817137671 / 2000000000000000000000 : ℚ))) + (U' := (359495537147182862329 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (2948952074466117 / 10000000000000000 : ℚ)) + (q := (11969154253592859 / 40000000000000000 : ℚ)) + (U := (-(2413093184052817137671 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_8 : Uω (aρ 8) (bρ 8) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -956,25 +846,21 @@ lemma U_378_8 : have hlg : Real.log (10628620926866167 / 40000000000000000 : ℝ) ≤ (-(13253290037235338137851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10628620926866167 / 40000000000000000 : ℝ) = - (10628620926866167 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10628620926866167 / 10000000000000000 : ℚ)) - (U := (609653568764661862149 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10628620926866167 / 10000000000000000 : ℝ) ≤ - (609653568764661862149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2562227062442771 / 10000000000000000 : ℝ)) (q := - (10628620926866167 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10628620926866167 / 40000000000000000 : ℚ)) + (r' := (10628620926866167 / 10000000000000000 : ℚ)) + (U := (-(13253290037235338137851 / 10000000000000000000000 : ℚ))) + (U' := (609653568764661862149 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (2562227062442771 / 10000000000000000 : ℚ)) + (q := (10628620926866167 / 40000000000000000 : ℚ)) + (U := (-(13253290037235338137851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_9 : Uω (aρ 9) (bρ 9) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -982,25 +868,21 @@ lemma U_378_9 : have hlg : Real.log (352930016678841 / 1600000000000000 : ℝ) ≤ (-(7557445616019576398087 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (352930016678841 / 1600000000000000 : ℝ) = - (352930016678841 / 200000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (352930016678841 / 200000000000000 : ℚ)) - (U := (2839762088480423601913 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (352930016678841 / 200000000000000 : ℝ) ≤ - (2839762088480423601913 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2500634294819 / 12500000000000 : ℝ)) (q := - (352930016678841 / 1600000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (352930016678841 / 1600000000000000 : ℚ)) + (r' := (352930016678841 / 200000000000000 : ℚ)) + (U := (-(7557445616019576398087 / 5000000000000000000000 : ℚ))) + (U' := (2839762088480423601913 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (2500634294819 / 12500000000000 : ℚ)) + (q := (352930016678841 / 1600000000000000 : ℚ)) + (U := (-(7557445616019576398087 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_10 : Uω (aρ 10) (bρ 10) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -1008,26 +890,21 @@ lemma U_378_10 : have hlg : Real.log (6124808429773381 / 40000000000000000 : ℝ) ≤ (-(18765319741641310131049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6124808429773381 / 40000000000000000 : ℝ) = - (6124808429773381 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6124808429773381 / 5000000000000000 : ℚ)) - (U := (2029095667358689868951 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6124808429773381 / 5000000000000000 : ℝ) ≤ - (2029095667358689868951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (519922737875689 / 5000000000000000 : ℝ)) (q := - (6124808429773381 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6124808429773381 / 40000000000000000 : ℚ)) + (r' := (6124808429773381 / 5000000000000000 : ℚ)) + (U := (-(18765319741641310131049 / 10000000000000000000000 : ℚ))) + (U' := (2029095667358689868951 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (12027754385841 / 32000000000000 : ℚ)) + (s := (519922737875689 / 5000000000000000 : ℚ)) + (q := (6124808429773381 / 40000000000000000 : ℚ)) + (U := (-(18765319741641310131049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_378_11 : Uω (aρ 11) (bρ 11) (12027754385841 / 32000000000000 : ℝ) ≤ @@ -1148,25 +1025,21 @@ lemma U_379_1 : have hlg : Real.log (11842152780079227 / 32000000000000000 : ℝ) ≤ (-(9940704667098828597671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11842152780079227 / 32000000000000000 : ℝ) = - (11842152780079227 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11842152780079227 / 8000000000000000 : ℚ)) - (U := (3922238938901171402329 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (11842152780079227 / 8000000000000000 : ℝ) ≤ - (3922238938901171402329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (185031452884761 / 500000000000000 : ℝ)) (q := - (11842152780079227 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11842152780079227 / 32000000000000000 : ℚ)) + (r' := (11842152780079227 / 8000000000000000 : ℚ)) + (U := (-(9940704667098828597671 / 10000000000000000000000 : ℚ))) + (U' := (3922238938901171402329 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (185031452884761 / 500000000000000 : ℚ)) + (q := (11842152780079227 / 32000000000000000 : ℚ)) + (U := (-(9940704667098828597671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_2 : Uω (aρ 2) (bρ 2) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1174,25 +1047,21 @@ lemma U_379_2 : have hlg : Real.log (58826541759748119 / 160000000000000000 : ℝ) ≤ (-(2501451677958700695517 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58826541759748119 / 160000000000000000 : ℝ) = - (58826541759748119 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58826541759748119 / 40000000000000000 : ℚ)) - (U := (964284223541299304483 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58826541759748119 / 40000000000000000 : ℝ) ≤ - (964284223541299304483 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1838185151312109 / 5000000000000000 : ℝ)) (q := - (58826541759748119 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58826541759748119 / 160000000000000000 : ℚ)) + (r' := (58826541759748119 / 40000000000000000 : ℚ)) + (U := (-(2501451677958700695517 / 2500000000000000000000 : ℚ))) + (U' := (964284223541299304483 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (1838185151312109 / 5000000000000000 : ℚ)) + (q := (58826541759748119 / 160000000000000000 : ℚ)) + (U := (-(2501451677958700695517 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_3 : Uω (aρ 3) (bρ 3) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1200,25 +1069,21 @@ lemma U_379_3 : have hlg : Real.log (58056510069762047 / 160000000000000000 : ℝ) ≤ (-(5068784834766586812851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58056510069762047 / 160000000000000000 : ℝ) = - (58056510069762047 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58056510069762047 / 40000000000000000 : ℚ)) - (U := (1862686968233413187149 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58056510069762047 / 40000000000000000 : ℝ) ≤ - (1862686968233413187149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3627512447725959 / 10000000000000000 : ℝ)) (q := - (58056510069762047 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58056510069762047 / 160000000000000000 : ℚ)) + (r' := (58056510069762047 / 40000000000000000 : ℚ)) + (U := (-(5068784834766586812851 / 5000000000000000000000 : ℚ))) + (U' := (1862686968233413187149 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (3627512447725959 / 10000000000000000 : ℚ)) + (q := (58056510069762047 / 160000000000000000 : ℚ)) + (U := (-(5068784834766586812851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_4 : Uω (aρ 4) (bρ 4) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1226,25 +1091,21 @@ lemma U_379_4 : have hlg : Real.log (56772674786100383 / 160000000000000000 : ℝ) ≤ (-(414447472980535392993 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56772674786100383 / 160000000000000000 : ℝ) = - (56772674786100383 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56772674786100383 / 40000000000000000 : ℚ)) - (U := (140070271259464607007 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56772674786100383 / 40000000000000000 : ℝ) ≤ - (140070271259464607007 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3545327218333251 / 10000000000000000 : ℝ)) (q := - (56772674786100383 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56772674786100383 / 160000000000000000 : ℚ)) + (r' := (56772674786100383 / 40000000000000000 : ℚ)) + (U := (-(414447472980535392993 / 400000000000000000000 : ℚ))) + (U' := (140070271259464607007 / 400000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (3545327218333251 / 10000000000000000 : ℚ)) + (q := (56772674786100383 / 160000000000000000 : ℚ)) + (U := (-(414447472980535392993 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_5 : Uω (aρ 5) (bρ 5) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1252,25 +1113,21 @@ lemma U_379_5 : have hlg : Real.log (54804690384051199 / 160000000000000000 : ℝ) ≤ (-(10713980334728234077113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54804690384051199 / 160000000000000000 : ℝ) = - (54804690384051199 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54804690384051199 / 40000000000000000 : ℚ)) - (U := (3148963271271765922887 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54804690384051199 / 40000000000000000 : ℝ) ≤ - (3148963271271765922887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3417519087412103 / 10000000000000000 : ℝ)) (q := - (54804690384051199 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54804690384051199 / 160000000000000000 : ℚ)) + (r' := (54804690384051199 / 40000000000000000 : ℚ)) + (U := (-(10713980334728234077113 / 10000000000000000000000 : ℚ))) + (U' := (3148963271271765922887 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (3417519087412103 / 10000000000000000 : ℚ)) + (q := (54804690384051199 / 160000000000000000 : ℚ)) + (U := (-(10713980334728234077113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_6 : Uω (aρ 6) (bρ 6) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1278,25 +1135,21 @@ lemma U_379_6 : have hlg : Real.log (51950858064239079 / 160000000000000000 : ℝ) ≤ (-(11248755801878956064031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51950858064239079 / 160000000000000000 : ℝ) = - (51950858064239079 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51950858064239079 / 40000000000000000 : ℚ)) - (U := (2614187804121043935969 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51950858064239079 / 40000000000000000 : ℝ) ≤ - (2614187804121043935969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (807007605643897 / 2500000000000000 : ℝ)) (q := - (51950858064239079 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51950858064239079 / 160000000000000000 : ℚ)) + (r' := (51950858064239079 / 40000000000000000 : ℚ)) + (U := (-(11248755801878956064031 / 10000000000000000000000 : ℚ))) + (U' := (2614187804121043935969 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (807007605643897 / 2500000000000000 : ℚ)) + (q := (51950858064239079 / 160000000000000000 : ℚ)) + (U := (-(11248755801878956064031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_7 : Uω (aρ 7) (bρ 7) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1304,25 +1157,21 @@ lemma U_379_7 : have hlg : Real.log (47982797836763607 / 160000000000000000 : ℝ) ≤ (-(602165623219844768649 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (47982797836763607 / 160000000000000000 : ℝ) = - (47982797836763607 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47982797836763607 / 40000000000000000 : ℚ)) - (U := (90981557080155231351 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47982797836763607 / 40000000000000000 : ℝ) ≤ - (90981557080155231351 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1477842137450577 / 5000000000000000 : ℝ)) (q := - (47982797836763607 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47982797836763607 / 160000000000000000 : ℚ)) + (r' := (47982797836763607 / 40000000000000000 : ℚ)) + (U := (-(602165623219844768649 / 500000000000000000000 : ℚ))) + (U' := (90981557080155231351 / 500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (1477842137450577 / 5000000000000000 : ℚ)) + (q := (47982797836763607 / 160000000000000000 : ℚ)) + (U := (-(602165623219844768649 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_8 : Uω (aρ 8) (bρ 8) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1330,25 +1179,21 @@ lemma U_379_8 : have hlg : Real.log (42622996964835687 / 160000000000000000 : ℝ) ≤ (-(6613899361208653044927 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42622996964835687 / 160000000000000000 : ℝ) = - (42622996964835687 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42622996964835687 / 40000000000000000 : ℚ)) - (U := (317572441791346955073 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42622996964835687 / 40000000000000000 : ℝ) ≤ - (317572441791346955073 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (642312704312541 / 2500000000000000 : ℝ)) (q := - (42622996964835687 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42622996964835687 / 160000000000000000 : ℚ)) + (r' := (42622996964835687 / 40000000000000000 : ℚ)) + (U := (-(6613899361208653044927 / 5000000000000000000000 : ℚ))) + (U' := (317572441791346955073 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (642312704312541 / 2500000000000000 : ℚ)) + (q := (42622996964835687 / 160000000000000000 : ℚ)) + (U := (-(6613899361208653044927 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_9 : Uω (aρ 9) (bρ 9) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1356,25 +1201,21 @@ lemma U_379_9 : have hlg : Real.log (1416333961811631 / 6400000000000000 : ℝ) ≤ (-(3770565433462939589999 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1416333961811631 / 6400000000000000 : ℝ) = - (1416333961811631 / 800000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1416333961811631 / 800000000000000 : ℚ)) - (U := (1428038418787060410001 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1416333961811631 / 800000000000000 : ℝ) ≤ - (1428038418787060410001 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40167709113341 / 200000000000000 : ℝ)) (q := - (1416333961811631 / 6400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1416333961811631 / 6400000000000000 : ℚ)) + (r' := (1416333961811631 / 800000000000000 : ℚ)) + (U := (-(3770565433462939589999 / 2500000000000000000000 : ℚ))) + (U' := (1428038418787060410001 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (40167709113341 / 200000000000000 : ℚ)) + (q := (1416333961811631 / 6400000000000000 : ℚ)) + (U := (-(3770565433462939589999 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_10 : Uω (aρ 10) (bρ 10) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1382,26 +1223,21 @@ lemma U_379_10 : have hlg : Real.log (24652876119599351 / 160000000000000000 : ℝ) ≤ (-(3740560484983560820433 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24652876119599351 / 160000000000000000 : ℝ) = - (24652876119599351 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24652876119599351 / 20000000000000000 : ℚ)) - (U := (418322596816439179567 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24652876119599351 / 20000000000000000 : ℝ) ≤ - (418322596816439179567 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (526255186725311 / 5000000000000000 : ℝ)) (q := - (24652876119599351 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24652876119599351 / 160000000000000000 : ℚ)) + (r' := (24652876119599351 / 20000000000000000 : ℚ)) + (U := (-(3740560484983560820433 / 2000000000000000000000 : ℚ))) + (U' := (418322596816439179567 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (48194734693623 / 128000000000000 : ℚ)) + (s := (526255186725311 / 5000000000000000 : ℚ)) + (q := (24652876119599351 / 160000000000000000 : ℚ)) + (U := (-(3740560484983560820433 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_379_11 : Uω (aρ 11) (bρ 11) (48194734693623 / 128000000000000 : ℝ) ≤ @@ -1523,25 +1359,21 @@ lemma U_380_1 : have hlg : Real.log (29657705785697957 / 80000000000000000 : ℝ) ≤ (-(4961523254421947127759 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29657705785697957 / 80000000000000000 : ℝ) = - (29657705785697957 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29657705785697957 / 20000000000000000 : ℚ)) - (U := (1969948548578052872241 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29657705785697957 / 20000000000000000 : ℝ) ≤ - (1969948548578052872241 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (14481131305493 / 39062500000000 : ℝ)) (q := - (29657705785697957 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29657705785697957 / 80000000000000000 : ℚ)) + (r' := (29657705785697957 / 20000000000000000 : ℚ)) + (U := (-(4961523254421947127759 / 5000000000000000000000 : ℚ))) + (U' := (1969948548578052872241 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (14481131305493 / 39062500000000 : ℚ)) + (q := (29657705785697957 / 80000000000000000 : ℚ)) + (U := (-(4961523254421947127759 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_2 : Uω (aρ 2) (bρ 2) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1549,25 +1381,21 @@ lemma U_380_2 : have hlg : Real.log (29465598198328121 / 80000000000000000 : ℝ) ≤ (-(1248504017592068370069 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29465598198328121 / 80000000000000000 : ℝ) = - (29465598198328121 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29465598198328121 / 20000000000000000 : ℚ)) - (U := (484363933157931629931 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29465598198328121 / 20000000000000000 : ℝ) ≤ - (484363933157931629931 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3682911729873749 / 10000000000000000 : ℝ)) (q := - (29465598198328121 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29465598198328121 / 80000000000000000 : ℚ)) + (r' := (29465598198328121 / 20000000000000000 : ℚ)) + (U := (-(1248504017592068370069 / 1250000000000000000000 : ℚ))) + (U' := (484363933157931629931 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (3682911729873749 / 10000000000000000 : ℚ)) + (q := (29465598198328121 / 80000000000000000 : ℚ)) + (U := (-(1248504017592068370069 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_3 : Uω (aρ 3) (bρ 3) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1575,25 +1403,21 @@ lemma U_380_3 : have hlg : Real.log (29080592931597497 / 80000000000000000 : ℝ) ≤ (-(10119555920267487374541 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29080592931597497 / 80000000000000000 : ℝ) = - (29080592931597497 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29080592931597497 / 20000000000000000 : ℚ)) - (U := (3743387685732512625459 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29080592931597497 / 20000000000000000 : ℝ) ≤ - (3743387685732512625459 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3634056519541093 / 10000000000000000 : ℝ)) (q := - (29080592931597497 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29080592931597497 / 80000000000000000 : ℚ)) + (r' := (29080592931597497 / 20000000000000000 : ℚ)) + (U := (-(10119555920267487374541 / 10000000000000000000000 : ℚ))) + (U' := (3743387685732512625459 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (3634056519541093 / 10000000000000000 : ℚ)) + (q := (29080592931597497 / 80000000000000000 : ℚ)) + (U := (-(10119555920267487374541 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_4 : Uω (aρ 4) (bρ 4) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1601,25 +1425,21 @@ lemma U_380_4 : have hlg : Real.log (28438704289207221 / 80000000000000000 : ℝ) ≤ (-(10342755897080370757173 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28438704289207221 / 80000000000000000 : ℝ) = - (28438704289207221 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28438704289207221 / 20000000000000000 : ℚ)) - (U := (3520187708919629242827 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28438704289207221 / 20000000000000000 : ℝ) ≤ - (3520187708919629242827 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (887969635002131 / 2500000000000000 : ℝ)) (q := - (28438704289207221 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28438704289207221 / 80000000000000000 : ℚ)) + (r' := (28438704289207221 / 20000000000000000 : ℚ)) + (U := (-(10342755897080370757173 / 10000000000000000000000 : ℚ))) + (U' := (3520187708919629242827 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (887969635002131 / 2500000000000000 : ℚ)) + (q := (28438704289207221 / 80000000000000000 : ℚ)) + (U := (-(10342755897080370757173 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_5 : Uω (aρ 5) (bρ 5) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1627,25 +1447,21 @@ lemma U_380_5 : have hlg : Real.log (5490957441246801 / 16000000000000000 : ℝ) ≤ (-(10694860840911806552079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5490957441246801 / 16000000000000000 : ℝ) = - (5490957441246801 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5490957441246801 / 4000000000000000 : ℚ)) - (U := (3168082765088193447921 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5490957441246801 / 4000000000000000 : ℝ) ≤ - (3168082765088193447921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (171204459430011 / 500000000000000 : ℝ)) (q := - (5490957441246801 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5490957441246801 / 16000000000000000 : ℚ)) + (r' := (5490957441246801 / 4000000000000000 : ℚ)) + (U := (-(10694860840911806552079 / 10000000000000000000000 : ℚ))) + (U' := (3168082765088193447921 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (171204459430011 / 500000000000000 : ℚ)) + (q := (5490957441246801 / 16000000000000000 : ℚ)) + (U := (-(10694860840911806552079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_6 : Uω (aρ 6) (bρ 6) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1653,25 +1469,21 @@ lemma U_380_6 : have hlg : Real.log (26028057949488689 / 80000000000000000 : ℝ) ≤ (-(5614257630474681781133 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26028057949488689 / 80000000000000000 : ℝ) = - (26028057949488689 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26028057949488689 / 20000000000000000 : ℚ)) - (U := (1317214172525318218867 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26028057949488689 / 20000000000000000 : ℝ) ≤ - (1317214172525318218867 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3234647249553891 / 10000000000000000 : ℝ)) (q := - (26028057949488689 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26028057949488689 / 80000000000000000 : ℚ)) + (r' := (26028057949488689 / 20000000000000000 : ℚ)) + (U := (-(5614257630474681781133 / 5000000000000000000000 : ℚ))) + (U' := (1317214172525318218867 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (3234647249553891 / 10000000000000000 : ℚ)) + (q := (26028057949488689 / 80000000000000000 : ℚ)) + (U := (-(5614257630474681781133 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_7 : Uω (aρ 7) (bρ 7) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1679,25 +1491,21 @@ lemma U_380_7 : have hlg : Real.log (24044485892302941 / 80000000000000000 : ℝ) ≤ (-(3005302351793728355003 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24044485892302941 / 80000000000000000 : ℝ) = - (24044485892302941 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24044485892302941 / 20000000000000000 : ℚ)) - (U := (460433549706271644997 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24044485892302941 / 20000000000000000 : ℝ) ≤ - (460433549706271644997 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1481207808008727 / 5000000000000000 : ℝ)) (q := - (24044485892302941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24044485892302941 / 80000000000000000 : ℚ)) + (r' := (24044485892302941 / 20000000000000000 : ℚ)) + (U := (-(3005302351793728355003 / 2500000000000000000000 : ℚ))) + (U' := (460433549706271644997 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (1481207808008727 / 5000000000000000 : ℚ)) + (q := (24044485892302941 / 80000000000000000 : ℚ)) + (U := (-(3005302351793728355003 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_8 : Uω (aρ 8) (bρ 8) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1705,25 +1513,21 @@ lemma U_380_8 : have hlg : Real.log (21365744931642169 / 80000000000000000 : ℝ) ≤ (-(6601188493753449905703 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21365744931642169 / 80000000000000000 : ℝ) = - (21365744931642169 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21365744931642169 / 20000000000000000 : ℚ)) - (U := (330283309246550094297 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21365744931642169 / 20000000000000000 : ℝ) ≤ - (330283309246550094297 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2576272027192261 / 10000000000000000 : ℝ)) (q := - (21365744931642169 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21365744931642169 / 80000000000000000 : ℚ)) + (r' := (21365744931642169 / 20000000000000000 : ℚ)) + (U := (-(6601188493753449905703 / 5000000000000000000000 : ℚ))) + (U' := (330283309246550094297 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (2576272027192261 / 10000000000000000 : ℚ)) + (q := (21365744931642169 / 80000000000000000 : ℚ)) + (U := (-(6601188493753449905703 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_9 : Uω (aρ 9) (bρ 9) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1731,25 +1535,21 @@ lemma U_380_9 : have hlg : Real.log (17761809949724573 / 80000000000000000 : ℝ) ≤ (-(601990395975625400427 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17761809949724573 / 80000000000000000 : ℝ) = - (17761809949724573 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17761809949724573 / 10000000000000000 : ℚ)) - (U := (229786220384374599573 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17761809949724573 / 10000000000000000 : ℝ) ≤ - (229786220384374599573 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1008126955036431 / 5000000000000000 : ℝ)) (q := - (17761809949724573 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17761809949724573 / 80000000000000000 : ℚ)) + (r' := (17761809949724573 / 10000000000000000 : ℚ)) + (U := (-(601990395975625400427 / 400000000000000000000 : ℚ))) + (U' := (229786220384374599573 / 400000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (1008126955036431 / 5000000000000000 : ℚ)) + (q := (17761809949724573 / 80000000000000000 : ℚ)) + (U := (-(601990395975625400427 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_10 : Uω (aρ 10) (bρ 10) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1757,26 +1557,21 @@ lemma U_380_10 : have hlg : Real.log (12402817534183093 / 80000000000000000 : ℝ) ≤ (-(4660257416487714340737 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12402817534183093 / 80000000000000000 : ℝ) = - (12402817534183093 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12402817534183093 / 10000000000000000 : ℚ)) - (U := (538346435762285659263 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12402817534183093 / 10000000000000000 : ℝ) ≤ - (538346435762285659263 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (266266209920623 / 2500000000000000 : ℝ)) (q := - (12402817534183093 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12402817534183093 / 80000000000000000 : ℚ)) + (r' := (12402817534183093 / 10000000000000000 : ℚ)) + (U := (-(4660257416487714340737 / 2500000000000000000000 : ℚ))) + (U' := (538346435762285659263 / 2500000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (24139225921941 / 64000000000000 : ℚ)) + (s := (266266209920623 / 2500000000000000 : ℚ)) + (q := (12402817534183093 / 80000000000000000 : ℚ)) + (U := (-(4660257416487714340737 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_380_11 : Uω (aρ 11) (bρ 11) (24139225921941 / 64000000000000 : ℝ) ≤ @@ -1898,25 +1693,21 @@ lemma U_381_1 : have hlg : Real.log (59420059238052021 / 160000000000000000 : ℝ) ≤ (-(9905419477420379522699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59420059238052021 / 160000000000000000 : ℝ) = - (59420059238052021 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59420059238052021 / 40000000000000000 : ℚ)) - (U := (3957524128579620477301 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59420059238052021 / 40000000000000000 : ℝ) ≤ - (3957524128579620477301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3713710170174237 / 10000000000000000 : ℝ)) (q := - (59420059238052021 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59420059238052021 / 160000000000000000 : ℚ)) + (r' := (59420059238052021 / 40000000000000000 : ℚ)) + (U := (-(9905419477420379522699 / 10000000000000000000000 : ℚ))) + (U' := (3957524128579620477301 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (3713710170174237 / 10000000000000000 : ℚ)) + (q := (59420059238052021 / 160000000000000000 : ℚ)) + (U := (-(9905419477420379522699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_2 : Uω (aρ 2) (bρ 2) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -1924,25 +1715,21 @@ lemma U_381_2 : have hlg : Real.log (59035851004492581 / 160000000000000000 : ℝ) ≤ (-(997028911205224600551 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59035851004492581 / 160000000000000000 : ℝ) = - (59035851004492581 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59035851004492581 / 40000000000000000 : ℚ)) - (U := (389265449394775399449 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59035851004492581 / 40000000000000000 : ℝ) ≤ - (389265449394775399449 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3689453153489307 / 10000000000000000 : ℝ)) (q := - (59035851004492581 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59035851004492581 / 160000000000000000 : ℚ)) + (r' := (59035851004492581 / 40000000000000000 : ℚ)) + (U := (-(997028911205224600551 / 1000000000000000000000 : ℚ))) + (U' := (389265449394775399449 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (3689453153489307 / 10000000000000000 : ℚ)) + (q := (59035851004492581 / 160000000000000000 : ℚ)) + (U := (-(997028911205224600551 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_3 : Uω (aρ 3) (bρ 3) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -1950,25 +1737,21 @@ lemma U_381_3 : have hlg : Real.log (58265861551122629 / 160000000000000000 : ℝ) ≤ (-(10101574580285721318899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58265861551122629 / 160000000000000000 : ℝ) = - (58265861551122629 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58265861551122629 / 40000000000000000 : ℚ)) - (U := (3761369025714278681101 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58265861551122629 / 40000000000000000 : ℝ) ≤ - (3761369025714278681101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3640600578168063 / 10000000000000000 : ℝ)) (q := - (58265861551122629 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58265861551122629 / 160000000000000000 : ℚ)) + (r' := (58265861551122629 / 40000000000000000 : ℚ)) + (U := (-(10101574580285721318899 / 10000000000000000000000 : ℚ))) + (U' := (3761369025714278681101 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (3640600578168063 / 10000000000000000 : ℚ)) + (q := (58265861551122629 / 160000000000000000 : ℚ)) + (U := (-(10101574580285721318899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_4 : Uω (aρ 4) (bρ 4) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -1976,25 +1759,21 @@ lemma U_381_4 : have hlg : Real.log (56982142049344933 / 160000000000000000 : ℝ) ≤ (-(10324358933471767397939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56982142049344933 / 160000000000000000 : ℝ) = - (56982142049344933 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56982142049344933 / 40000000000000000 : ℚ)) - (U := (3538584672528232602061 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56982142049344933 / 40000000000000000 : ℝ) ≤ - (3538584672528232602061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3558429821510851 / 10000000000000000 : ℝ)) (q := - (56982142049344933 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56982142049344933 / 160000000000000000 : ℚ)) + (r' := (56982142049344933 / 40000000000000000 : ℚ)) + (U := (-(10324358933471767397939 / 10000000000000000000000 : ℚ))) + (U' := (3538584672528232602061 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (3558429821510851 / 10000000000000000 : ℚ)) + (q := (56982142049344933 / 160000000000000000 : ℚ)) + (U := (-(10324358933471767397939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_5 : Uω (aρ 5) (bρ 5) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2002,25 +1781,21 @@ lemma U_381_5 : have hlg : Real.log (55014457532915797 / 160000000000000000 : ℝ) ≤ (-(2135155599578764903971 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55014457532915797 / 160000000000000000 : ℝ) = - (55014457532915797 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55014457532915797 / 40000000000000000 : ℚ)) - (U := (637433121621235096029 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55014457532915797 / 40000000000000000 : ℝ) ≤ - (637433121621235096029 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3430659176292209 / 10000000000000000 : ℝ)) (q := - (55014457532915797 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55014457532915797 / 160000000000000000 : ℚ)) + (r' := (55014457532915797 / 40000000000000000 : ℚ)) + (U := (-(2135155599578764903971 / 2000000000000000000000 : ℚ))) + (U' := (637433121621235096029 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (3430659176292209 / 10000000000000000 : ℚ)) + (q := (55014457532915797 / 160000000000000000 : ℚ)) + (U := (-(2135155599578764903971 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_6 : Uω (aρ 6) (bρ 6) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2028,25 +1803,21 @@ lemma U_381_6 : have hlg : Real.log (52161371251878461 / 160000000000000000 : ℝ) ≤ (-(2802079020257341762367 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52161371251878461 / 160000000000000000 : ℝ) = - (52161371251878461 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52161371251878461 / 40000000000000000 : ℚ)) - (U := (663656881242658237633 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52161371251878461 / 40000000000000000 : ℝ) ≤ - (663656881242658237633 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1620631883151271 / 5000000000000000 : ℝ)) (q := - (52161371251878461 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52161371251878461 / 160000000000000000 : ℚ)) + (r' := (52161371251878461 / 40000000000000000 : ℚ)) + (U := (-(2802079020257341762367 / 2500000000000000000000 : ℚ))) + (U' := (663656881242658237633 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (1620631883151271 / 5000000000000000 : ℚ)) + (q := (52161371251878461 / 160000000000000000 : ℚ)) + (U := (-(2802079020257341762367 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_7 : Uω (aρ 7) (bρ 7) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2054,25 +1825,21 @@ lemma U_381_7 : have hlg : Real.log (48195138904654069 / 160000000000000000 : ℝ) ≤ (-(11999156513438851452341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (48195138904654069 / 160000000000000000 : ℝ) = - (48195138904654069 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48195138904654069 / 40000000000000000 : ℚ)) - (U := (1863787092561148547659 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48195138904654069 / 40000000000000000 : ℝ) ≤ - (1863787092561148547659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2969146103659493 / 10000000000000000 : ℝ)) (q := - (48195138904654069 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48195138904654069 / 160000000000000000 : ℚ)) + (r' := (48195138904654069 / 40000000000000000 : ℚ)) + (U := (-(11999156513438851452341 / 10000000000000000000000 : ℚ))) + (U' := (1863787092561148547659 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (2969146103659493 / 10000000000000000 : ℚ)) + (q := (48195138904654069 / 160000000000000000 : ℚ)) + (U := (-(11999156513438851452341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_8 : Uω (aρ 8) (bρ 8) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2080,25 +1847,21 @@ lemma U_381_8 : have hlg : Real.log (8567992513762633 / 32000000000000000 : ℝ) ≤ (-(329425610719656756109 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8567992513762633 / 32000000000000000 : ℝ) = - (8567992513762633 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8567992513762633 / 8000000000000000 : ℚ)) - (U := (17147979430343243891 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8567992513762633 / 8000000000000000 : ℝ) ≤ - (17147979430343243891 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (129164535650969 / 500000000000000 : ℝ)) (q := - (8567992513762633 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8567992513762633 / 32000000000000000 : ℚ)) + (r' := (8567992513762633 / 8000000000000000 : ℚ)) + (U := (-(329425610719656756109 / 250000000000000000000 : ℚ))) + (U' := (17147979430343243891 / 250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (129164535650969 / 500000000000000 : ℚ)) + (q := (8567992513762633 / 32000000000000000 : ℚ)) + (U := (-(329425610719656756109 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_9 : Uω (aρ 9) (bρ 9) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2106,25 +1869,21 @@ lemma U_381_9 : have hlg : Real.log (35638815122779349 / 160000000000000000 : ℝ) ≤ (-(15017384581172952189737 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35638815122779349 / 160000000000000000 : ℝ) = - (35638815122779349 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35638815122779349 / 20000000000000000 : ℚ)) - (U := (5777030827827047810263 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35638815122779349 / 20000000000000000 : ℝ) ≤ - (5777030827827047810263 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2024112910625153 / 10000000000000000 : ℝ)) (q := - (35638815122779349 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35638815122779349 / 160000000000000000 : ℚ)) + (r' := (35638815122779349 / 20000000000000000 : ℚ)) + (U := (-(15017384581172952189737 / 10000000000000000000000 : ℚ))) + (U' := (5777030827827047810263 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (2024112910625153 / 10000000000000000 : ℚ)) + (q := (35638815122779349 / 160000000000000000 : ℚ)) + (U := (-(15017384581172952189737 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_10 : Uω (aρ 10) (bρ 10) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2132,26 +1891,21 @@ lemma U_381_10 : have hlg : Real.log (24957541445636653 / 160000000000000000 : ℝ) ≤ (-(18579977755783579673383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (24957541445636653 / 160000000000000000 : ℝ) = - (24957541445636653 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24957541445636653 / 20000000000000000 : ℚ)) - (U := (2214437653216420326617 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24957541445636653 / 20000000000000000 : ℝ) ≤ - (2214437653216420326617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (269378183619329 / 2500000000000000 : ℝ)) (q := - (24957541445636653 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24957541445636653 / 160000000000000000 : ℚ)) + (r' := (24957541445636653 / 20000000000000000 : ℚ)) + (U := (-(18579977755783579673383 / 10000000000000000000000 : ℚ))) + (U' := (2214437653216420326617 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (48362168994141 / 128000000000000 : ℚ)) + (s := (269378183619329 / 2500000000000000 : ℚ)) + (q := (24957541445636653 / 160000000000000000 : ℚ)) + (U := (-(18579977755783579673383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_381_11 : Uω (aρ 11) (bρ 11) (48362168994141 / 128000000000000 : ℝ) ≤ @@ -2274,25 +2028,21 @@ lemma U_382_1 : have hlg : Real.log (3720294181274211 / 10000000000000000 : ℝ) ≤ (-(395512938531258084853 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3720294181274211 / 10000000000000000 : ℝ) = - (3720294181274211 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3720294181274211 / 2500000000000000 : ℚ)) - (U := (159004805708741915147 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3720294181274211 / 2500000000000000 : ℝ) ≤ - (159004805708741915147 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (930062681400543 / 2500000000000000 : ℝ)) (q := - (3720294181274211 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3720294181274211 / 10000000000000000 : ℚ)) + (r' := (3720294181274211 / 2500000000000000 : ℚ)) + (U := (-(395512938531258084853 / 400000000000000000000 : ℚ))) + (U' := (159004805708741915147 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (121114715361 / 320000000000 : ℚ)) + (s := (930062681400543 / 2500000000000000 : ℚ)) + (q := (3720294181274211 / 10000000000000000 : ℚ)) + (U := (-(395512938531258084853 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_2 : Uω (aρ 2) (bρ 2) (121114715361 / 320000000000 : ℝ) ≤ @@ -2300,25 +2050,21 @@ lemma U_382_2 : have hlg : Real.log (1478512639585287 / 4000000000000000 : ℝ) ≤ (-(398103100560546859391 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1478512639585287 / 4000000000000000 : ℝ) = - (1478512639585287 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1478512639585287 / 1000000000000000 : ℚ)) - (U := (156414643679453140609 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1478512639585287 / 1000000000000000 : ℝ) ≤ - (156414643679453140609 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (739198914698037 / 2000000000000000 : ℝ)) (q := - (1478512639585287 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1478512639585287 / 4000000000000000 : ℚ)) + (r' := (1478512639585287 / 1000000000000000 : ℚ)) + (U := (-(398103100560546859391 / 400000000000000000000 : ℚ))) + (U' := (156414643679453140609 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (121114715361 / 320000000000 : ℚ)) + (s := (739198914698037 / 2000000000000000 : ℚ)) + (q := (1478512639585287 / 4000000000000000 : ℚ)) + (U := (-(398103100560546859391 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_3 : Uω (aρ 3) (bρ 3) (121114715361 / 320000000000 : ℝ) ≤ @@ -2326,25 +2072,21 @@ lemma U_382_3 : have hlg : Real.log (1824079285441027 / 5000000000000000 : ℝ) ≤ (-(2520906383278679509249 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1824079285441027 / 5000000000000000 : ℝ) = - (1824079285441027 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1824079285441027 / 1250000000000000 : ℚ)) - (U := (944829518221320490751 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1824079285441027 / 1250000000000000 : ℝ) ≤ - (944829518221320490751 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1823572311838929 / 5000000000000000 : ℝ)) (q := - (1824079285441027 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1824079285441027 / 5000000000000000 : ℚ)) + (r' := (1824079285441027 / 1250000000000000 : ℚ)) + (U := (-(2520906383278679509249 / 2500000000000000000000 : ℚ))) + (U' := (944829518221320490751 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (121114715361 / 320000000000 : ℚ)) + (s := (1823572311838929 / 5000000000000000 : ℚ)) + (q := (1824079285441027 / 5000000000000000 : ℚ)) + (U := (-(2520906383278679509249 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_4 : Uω (aρ 4) (bρ 4) (121114715361 / 320000000000 : ℝ) ≤ @@ -2352,25 +2094,21 @@ lemma U_382_4 : have hlg : Real.log (1783964850020739 / 5000000000000000 : ℝ) ≤ (-(25764989521341751801 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1783964850020739 / 5000000000000000 : ℝ) = - (1783964850020739 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1783964850020739 / 1250000000000000 : ℚ)) - (U := (8892369493658248199 / 25000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1783964850020739 / 1250000000000000 : ℝ) ≤ - (8892369493658248199 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1782490531530853 / 5000000000000000 : ℝ)) (q := - (1783964850020739 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1783964850020739 / 5000000000000000 : ℚ)) + (r' := (1783964850020739 / 1250000000000000 : ℚ)) + (U := (-(25764989521341751801 / 25000000000000000000 : ℚ))) + (U' := (8892369493658248199 / 25000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (121114715361 / 320000000000 : ℚ)) + (s := (1782490531530853 / 5000000000000000 : ℚ)) + (q := (1783964850020739 / 5000000000000000 : ℚ)) + (U := (-(25764989521341751801 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_5 : Uω (aρ 5) (bρ 5) (121114715361 / 320000000000 : ℝ) ≤ @@ -2378,25 +2116,21 @@ lemma U_382_5 : have hlg : Real.log (430619841801571 / 1250000000000000 : ℝ) ≤ (-(10656731664801098998343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (430619841801571 / 1250000000000000 : ℝ) = - (430619841801571 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (430619841801571 / 312500000000000 : ℚ)) - (U := (3206211941198901001657 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (430619841801571 / 312500000000000 : ℝ) ≤ - (3206211941198901001657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1718614525569443 / 5000000000000000 : ℝ)) (q := - (430619841801571 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (430619841801571 / 1250000000000000 : ℚ)) + (r' := (430619841801571 / 312500000000000 : ℚ)) + (U := (-(10656731664801098998343 / 10000000000000000000000 : ℚ))) + (U' := (3206211941198901001657 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (121114715361 / 320000000000 : ℚ)) + (s := (1718614525569443 / 5000000000000000 : ℚ)) + (q := (430619841801571 / 1250000000000000 : ℚ)) + (U := (-(10656731664801098998343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_6 : Uω (aρ 6) (bρ 6) (121114715361 / 320000000000 : ℝ) ≤ @@ -2404,25 +2138,21 @@ lemma U_382_6 : have hlg : Real.log (1633332004315943 / 5000000000000000 : ℝ) ≤ (-(11188158091501860923951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1633332004315943 / 5000000000000000 : ℝ) = - (1633332004315943 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1633332004315943 / 1250000000000000 : ℚ)) - (U := (2674785514498139076049 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1633332004315943 / 1250000000000000 : ℝ) ≤ - (2674785514498139076049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1623939987358761 / 5000000000000000 : ℝ)) (q := - (1633332004315943 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1633332004315943 / 5000000000000000 : ℚ)) + (r' := (1633332004315943 / 1250000000000000 : ℚ)) + (U := (-(11188158091501860923951 / 10000000000000000000000 : ℚ))) + (U' := (2674785514498139076049 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (121114715361 / 320000000000 : ℚ)) + (s := (1623939987358761 / 5000000000000000 : ℚ)) + (q := (1633332004315943 / 5000000000000000 : ℚ)) + (U := (-(11188158091501860923951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_7 : Uω (aρ 7) (bρ 7) (121114715361 / 320000000000 : ℝ) ≤ @@ -2430,25 +2160,21 @@ lemma U_382_7 : have hlg : Real.log (3018831202702193 / 10000000000000000 : ℝ) ≤ (-(5988576774856659351441 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3018831202702193 / 10000000000000000 : ℝ) = - (3018831202702193 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3018831202702193 / 2500000000000000 : ℚ)) - (U := (942895028143340648559 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3018831202702193 / 2500000000000000 : ℝ) ≤ - (942895028143340648559 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (371984467952267 / 1250000000000000 : ℝ)) (q := - (3018831202702193 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3018831202702193 / 10000000000000000 : ℚ)) + (r' := (3018831202702193 / 2500000000000000 : ℚ)) + (U := (-(5988576774856659351441 / 5000000000000000000000 : ℚ))) + (U' := (942895028143340648559 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (121114715361 / 320000000000 : ℚ)) + (s := (371984467952267 / 1250000000000000 : ℚ)) + (q := (3018831202702193 / 10000000000000000 : ℚ)) + (U := (-(5988576774856659351441 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_8 : Uω (aρ 8) (bρ 8) (121114715361 / 320000000000 : ℝ) ≤ @@ -2456,25 +2182,21 @@ lemma U_382_8 : have hlg : Real.log (5368551905695767 / 20000000000000000 : ℝ) ≤ (-(13151740646229372841851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5368551905695767 / 20000000000000000 : ℝ) = - (5368551905695767 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5368551905695767 / 5000000000000000 : ℚ)) - (U := (711202959770627158149 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5368551905695767 / 5000000000000000 : ℝ) ≤ - (711202959770627158149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2590306895249517 / 10000000000000000 : ℝ)) (q := - (5368551905695767 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5368551905695767 / 20000000000000000 : ℚ)) + (r' := (5368551905695767 / 5000000000000000 : ℚ)) + (U := (-(13151740646229372841851 / 10000000000000000000000 : ℚ))) + (U' := (711202959770627158149 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (121114715361 / 320000000000 : ℚ)) + (s := (2590306895249517 / 10000000000000000 : ℚ)) + (q := (5368551905695767 / 20000000000000000 : ℚ)) + (U := (-(13151740646229372841851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_9 : Uω (aρ 9) (bρ 9) (121114715361 / 320000000000 : ℝ) ≤ @@ -2482,25 +2204,21 @@ lemma U_382_9 : have hlg : Real.log (4469241949103891 / 20000000000000000 : ℝ) ≤ (-(14985134648602909743777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4469241949103891 / 20000000000000000 : ℝ) = - (4469241949103891 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4469241949103891 / 2500000000000000 : ℚ)) - (U := (5809280760397090256223 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4469241949103891 / 2500000000000000 : ℝ) ≤ - (5809280760397090256223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2031962567017641 / 10000000000000000 : ℝ)) (q := - (4469241949103891 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4469241949103891 / 20000000000000000 : ℚ)) + (r' := (4469241949103891 / 2500000000000000 : ℚ)) + (U := (-(14985134648602909743777 / 10000000000000000000000 : ℚ))) + (U' := (5809280760397090256223 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (121114715361 / 320000000000 : ℚ)) + (s := (2031962567017641 / 10000000000000000 : ℚ)) + (q := (4469241949103891 / 20000000000000000 : ℚ)) + (U := (-(14985134648602909743777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_10 : Uω (aρ 10) (bρ 10) (121114715361 / 320000000000 : ℝ) ≤ @@ -2508,26 +2226,21 @@ lemma U_382_10 : have hlg : Real.log (3138578058074391 / 20000000000000000 : ℝ) ≤ (-(72342282154980825373 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3138578058074391 / 20000000000000000 : ℝ) = - (3138578058074391 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3138578058074391 / 2500000000000000 : ℚ)) - (U := (8885903036425424627 / 39062500000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3138578058074391 / 2500000000000000 : ℝ) ≤ - (8885903036425424627 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1089857709483141 / 10000000000000000 : ℝ)) (q := - (3138578058074391 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3138578058074391 / 20000000000000000 : ℚ)) + (r' := (3138578058074391 / 2500000000000000 : ℚ)) + (U := (-(72342282154980825373 / 39062500000000000000 : ℚ))) + (U' := (8885903036425424627 / 39062500000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (121114715361 / 320000000000 : ℚ)) + (s := (1089857709483141 / 10000000000000000 : ℚ)) + (q := (3138578058074391 / 20000000000000000 : ℚ)) + (U := (-(72342282154980825373 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_382_11 : Uω (aρ 11) (bρ 11) (121114715361 / 320000000000 : ℝ) ≤ @@ -2647,25 +2360,21 @@ lemma U_383_1 : have hlg : Real.log (11925870911684943 / 32000000000000000 : ℝ) ≤ (-(38555696708818691983 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11925870911684943 / 32000000000000000 : ℝ) = - (11925870911684943 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11925870911684943 / 8000000000000000 : ℚ)) - (U := (15596426752118808017 / 39062500000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (11925870911684943 / 8000000000000000 : ℝ) ≤ - (15596426752118808017 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (745358256098571 / 2000000000000000 : ℝ)) (q := - (11925870911684943 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11925870911684943 / 32000000000000000 : ℚ)) + (r' := (11925870911684943 / 8000000000000000 : ℚ)) + (U := (-(38555696708818691983 / 39062500000000000000 : ℚ))) + (U' := (15596426752118808017 / 39062500000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (745358256098571 / 2000000000000000 : ℚ)) + (q := (11925870911684943 / 32000000000000000 : ℚ)) + (U := (-(38555696708818691983 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_2 : Uω (aρ 2) (bρ 2) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2673,25 +2382,21 @@ lemma U_383_2 : have hlg : Real.log (59245160133566219 / 160000000000000000 : ℝ) ≤ (-(993489723544569558129 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59245160133566219 / 160000000000000000 : ℝ) = - (59245160133566219 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59245160133566219 / 40000000000000000 : ℚ)) - (U := (392804637055430441871 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59245160133566219 / 40000000000000000 : ℝ) ≤ - (392804637055430441871 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3702535989895543 / 10000000000000000 : ℝ)) (q := - (59245160133566219 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59245160133566219 / 160000000000000000 : ℚ)) + (r' := (59245160133566219 / 40000000000000000 : ℚ)) + (U := (-(993489723544569558129 / 1000000000000000000000 : ℚ))) + (U' := (392804637055430441871 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (3702535989895543 / 10000000000000000 : ℚ)) + (q := (59245160133566219 / 160000000000000000 : ℚ)) + (U := (-(993489723544569558129 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_3 : Uω (aρ 3) (bρ 3) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2699,25 +2404,21 @@ lemma U_383_3 : have hlg : Real.log (58475212612729563 / 160000000000000000 : ℝ) ≤ (-(2516427165727103197089 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58475212612729563 / 160000000000000000 : ℝ) = - (58475212612729563 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58475212612729563 / 40000000000000000 : ℚ)) - (U := (949308735772896802911 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58475212612729563 / 40000000000000000 : ℝ) ≤ - (949308735772896802911 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3653688656140961 / 10000000000000000 : ℝ)) (q := - (58475212612729563 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58475212612729563 / 160000000000000000 : ℚ)) + (r' := (58475212612729563 / 40000000000000000 : ℚ)) + (U := (-(2516427165727103197089 / 2500000000000000000000 : ℚ))) + (U' := (949308735772896802911 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (3653688656140961 / 10000000000000000 : ℚ)) + (q := (58475212612729563 / 160000000000000000 : ℚ)) + (U := (-(2516427165727103197089 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_4 : Uω (aρ 4) (bρ 4) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2725,25 +2426,21 @@ lemma U_383_4 : have hlg : Real.log (57191608034129379 / 160000000000000000 : ℝ) ≤ (-(10287666397815893786367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57191608034129379 / 160000000000000000 : ℝ) = - (57191608034129379 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57191608034129379 / 40000000000000000 : ℚ)) - (U := (3575277208184106213633 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57191608034129379 / 40000000000000000 : ℝ) ≤ - (3575277208184106213633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1785766132440469 / 5000000000000000 : ℝ)) (q := - (57191608034129379 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57191608034129379 / 160000000000000000 : ℚ)) + (r' := (57191608034129379 / 40000000000000000 : ℚ)) + (U := (-(10287666397815893786367 / 10000000000000000000000 : ℚ))) + (U' := (3575277208184106213633 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (1785766132440469 / 5000000000000000 : ℚ)) + (q := (57191608034129379 / 160000000000000000 : ℚ)) + (U := (-(10287666397815893786367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_5 : Uω (aρ 5) (bρ 5) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2751,25 +2448,21 @@ lemma U_383_5 : have hlg : Real.log (55224221070690603 / 160000000000000000 : ℝ) ≤ (-(5318860850787325044227 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55224221070690603 / 160000000000000000 : ℝ) = - (55224221070690603 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55224221070690603 / 40000000000000000 : ℚ)) - (U := (1612610952212674955773 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55224221070690603 / 40000000000000000 : ℝ) ≤ - (1612610952212674955773 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3443798813786091 / 10000000000000000 : ℝ)) (q := - (55224221070690603 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55224221070690603 / 160000000000000000 : ℚ)) + (r' := (55224221070690603 / 40000000000000000 : ℚ)) + (U := (-(5318860850787325044227 / 5000000000000000000000 : ℚ))) + (U' := (1612610952212674955773 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (3443798813786091 / 10000000000000000 : ℚ)) + (q := (55224221070690603 / 160000000000000000 : ℚ)) + (U := (-(5318860850787325044227 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_6 : Uω (aρ 6) (bρ 6) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2777,25 +2470,21 @@ lemma U_383_6 : have hlg : Real.log (52371874572716323 / 160000000000000000 : ℝ) ≤ (-(11168041122814828369441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52371874572716323 / 160000000000000000 : ℝ) = - (52371874572716323 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52371874572716323 / 40000000000000000 : ℚ)) - (U := (2694902483185171630559 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52371874572716323 / 40000000000000000 : ℝ) ≤ - (2694902483185171630559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1627247938339653 / 5000000000000000 : ℝ)) (q := - (52371874572716323 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52371874572716323 / 160000000000000000 : ℚ)) + (r' := (52371874572716323 / 40000000000000000 : ℚ)) + (U := (-(11168041122814828369441 / 10000000000000000000000 : ℚ))) + (U' := (2694902483185171630559 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (1627247938339653 / 5000000000000000 : ℚ)) + (q := (52371874572716323 / 160000000000000000 : ℚ)) + (U := (-(11168041122814828369441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_7 : Uω (aρ 7) (bρ 7) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2803,25 +2492,21 @@ lemma U_383_7 : have hlg : Real.log (48407452846251931 / 160000000000000000 : ℝ) ≤ (-(11955200284190424110453 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (48407452846251931 / 160000000000000000 : ℝ) = - (48407452846251931 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48407452846251931 / 40000000000000000 : ℚ)) - (U := (1907743321809575889547 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48407452846251931 / 40000000000000000 : ℝ) ≤ - (1907743321809575889547 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2982604541631257 / 10000000000000000 : ℝ)) (q := - (48407452846251931 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48407452846251931 / 160000000000000000 : ℚ)) + (r' := (48407452846251931 / 40000000000000000 : ℚ)) + (U := (-(11955200284190424110453 / 10000000000000000000000 : ℚ))) + (U' := (1907743321809575889547 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (2982604541631257 / 10000000000000000 : ℚ)) + (q := (48407452846251931 / 160000000000000000 : ℚ)) + (U := (-(11955200284190424110453 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_8 : Uω (aρ 8) (bρ 8) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2829,25 +2514,21 @@ lemma U_383_8 : have hlg : Real.log (43056848055855387 / 160000000000000000 : ℝ) ≤ (-(3281631310863808718577 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (43056848055855387 / 160000000000000000 : ℝ) = - (43056848055855387 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43056848055855387 / 40000000000000000 : ℚ)) - (U := (184104590636191281423 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43056848055855387 / 40000000000000000 : ℝ) ≤ - (184104590636191281423 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2597320594171689 / 10000000000000000 : ℝ)) (q := - (43056848055855387 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43056848055855387 / 160000000000000000 : ℚ)) + (r' := (43056848055855387 / 40000000000000000 : ℚ)) + (U := (-(3281631310863808718577 / 2500000000000000000000 : ℚ))) + (U' := (184104590636191281423 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (2597320594171689 / 10000000000000000 : ℚ)) + (q := (43056848055855387 / 160000000000000000 : ℚ)) + (U := (-(3281631310863808718577 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_9 : Uω (aρ 9) (bρ 9) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2855,25 +2536,21 @@ lemma U_383_9 : have hlg : Real.log (35868982172610707 / 160000000000000000 : ℝ) ≤ (-(934563061726455595199 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35868982172610707 / 160000000000000000 : ℝ) = - (35868982172610707 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35868982172610707 / 20000000000000000 : ℚ)) - (U := (365087901336044404801 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35868982172610707 / 20000000000000000 : ℝ) ≤ - (365087901336044404801 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (254975373390763 / 1250000000000000 : ℝ)) (q := - (35868982172610707 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35868982172610707 / 160000000000000000 : ℚ)) + (r' := (35868982172610707 / 20000000000000000 : ℚ)) + (U := (-(934563061726455595199 / 625000000000000000000 : ℚ))) + (U' := (365087901336044404801 / 625000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (254975373390763 / 1250000000000000 : ℚ)) + (q := (35868982172610707 / 160000000000000000 : ℚ)) + (U := (-(934563061726455595199 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_10 : Uω (aρ 10) (bρ 10) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -2881,26 +2558,21 @@ lemma U_383_10 : have hlg : Real.log (25258911793304411 / 160000000000000000 : ℝ) ≤ (-(9229973893465110443607 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25258911793304411 / 160000000000000000 : ℝ) = - (25258911793304411 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25258911793304411 / 20000000000000000 : ℚ)) - (U := (1167233811034889556393 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25258911793304411 / 20000000000000000 : ℝ) ≤ - (1167233811034889556393 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1102103223207817 / 10000000000000000 : ℝ)) (q := - (25258911793304411 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25258911793304411 / 160000000000000000 : ℚ)) + (r' := (25258911793304411 / 20000000000000000 : ℚ)) + (U := (-(9229973893465110443607 / 5000000000000000000000 : ℚ))) + (U' := (1167233811034889556393 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (48529603294659 / 128000000000000 : ℚ)) + (s := (1102103223207817 / 10000000000000000 : ℚ)) + (q := (25258911793304411 / 160000000000000000 : ℚ)) + (U := (-(9229973893465110443607 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_383_11 : Uω (aρ 11) (bρ 11) (48529603294659 / 128000000000000 : ℝ) ≤ @@ -3023,25 +2695,21 @@ lemma U_384_1 : have hlg : Real.log (29867001106093319 / 80000000000000000 : ℝ) ≤ (-(9852724051552499823691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29867001106093319 / 80000000000000000 : ℝ) = - (29867001106093319 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29867001106093319 / 20000000000000000 : ℚ)) - (U := (4010219554447500176309 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29867001106093319 / 20000000000000000 : ℝ) ≤ - (4010219554447500176309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3733331834849111 / 10000000000000000 : ℝ)) (q := - (29867001106093319 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29867001106093319 / 80000000000000000 : ℚ)) + (r' := (29867001106093319 / 20000000000000000 : ℚ)) + (U := (-(9852724051552499823691 / 10000000000000000000000 : ℚ))) + (U' := (4010219554447500176309 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (3733331834849111 / 10000000000000000 : ℚ)) + (q := (29867001106093319 / 80000000000000000 : ℚ)) + (U := (-(9852724051552499823691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_2 : Uω (aρ 2) (bρ 2) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3049,25 +2717,21 @@ lemma U_384_2 : have hlg : Real.log (29674907327554487 / 80000000000000000 : ℝ) ≤ (-(9917248165762109789853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29674907327554487 / 80000000000000000 : ℝ) = - (29674907327554487 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29674907327554487 / 20000000000000000 : ℚ)) - (U := (3945695440237890210147 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29674907327554487 / 20000000000000000 : ℝ) ≤ - (3945695440237890210147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3709077402724403 / 10000000000000000 : ℝ)) (q := - (29674907327554487 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29674907327554487 / 80000000000000000 : ℚ)) + (r' := (29674907327554487 / 20000000000000000 : ℚ)) + (U := (-(9917248165762109789853 / 10000000000000000000000 : ℚ))) + (U' := (3945695440237890210147 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (3709077402724403 / 10000000000000000 : ℚ)) + (q := (29674907327554487 / 80000000000000000 : ℚ)) + (U := (-(9917248165762109789853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_3 : Uω (aρ 3) (bρ 3) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3075,25 +2739,21 @@ lemma U_384_3 : have hlg : Real.log (1171597759750651 / 3200000000000000 : ℝ) ≤ (-(5023911927221671117419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1171597759750651 / 3200000000000000 : ℝ) = - (1171597759750651 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1171597759750651 / 800000000000000 : ℚ)) - (U := (1907559875778328882581 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1171597759750651 / 800000000000000 : ℝ) ≤ - (1907559875778328882581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73204653512547 / 200000000000000 : ℝ)) (q := - (1171597759750651 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1171597759750651 / 3200000000000000 : ℚ)) + (r' := (1171597759750651 / 800000000000000 : ℚ)) + (U := (-(5023911927221671117419 / 5000000000000000000000 : ℚ))) + (U' := (1907559875778328882581 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (73204653512547 / 200000000000000 : ℚ)) + (q := (1171597759750651 / 3200000000000000 : ℚ)) + (U := (-(5023911927221671117419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_4 : Uω (aρ 4) (bρ 4) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3101,25 +2761,21 @@ lemma U_384_4 : have hlg : Real.log (28648170275744011 / 80000000000000000 : ℝ) ≤ (-(10269370577536574744851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28648170275744011 / 80000000000000000 : ℝ) = - (28648170275744011 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28648170275744011 / 20000000000000000 : ℚ)) - (U := (3593573028463425255149 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28648170275744011 / 20000000000000000 : ℝ) ≤ - (3593573028463425255149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (111815107099587 / 312500000000000 : ℝ)) (q := - (28648170275744011 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28648170275744011 / 80000000000000000 : ℚ)) + (r' := (28648170275744011 / 20000000000000000 : ℚ)) + (U := (-(10269370577536574744851 / 10000000000000000000000 : ℚ))) + (U' := (3593573028463425255149 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (111815107099587 / 312500000000000 : ℚ)) + (q := (28648170275744011 / 80000000000000000 : ℚ)) + (U := (-(10269370577536574744851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_5 : Uω (aρ 5) (bρ 5) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3127,25 +2783,21 @@ lemma U_384_5 : have hlg : Real.log (27664550749155799 / 80000000000000000 : ℝ) ≤ (-(2654686992240856056823 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27664550749155799 / 80000000000000000 : ℝ) = - (27664550749155799 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27664550749155799 / 20000000000000000 : ℚ)) - (U := (811048909259143943177 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27664550749155799 / 20000000000000000 : ℝ) ≤ - (811048909259143943177 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3450368464874731 / 10000000000000000 : ℝ)) (q := - (27664550749155799 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27664550749155799 / 80000000000000000 : ℚ)) + (r' := (27664550749155799 / 20000000000000000 : ℚ)) + (U := (-(2654686992240856056823 / 2500000000000000000000 : ℚ))) + (U' := (811048909259143943177 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (3450368464874731 / 10000000000000000 : ℚ)) + (q := (27664550749155799 / 80000000000000000 : ℚ)) + (U := (-(2654686992240856056823 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_6 : Uω (aρ 6) (bρ 6) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3153,25 +2805,21 @@ lemma U_384_6 : have hlg : Real.log (26238561285308971 / 80000000000000000 : ℝ) ≤ (-(11147965006472399763539 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26238561285308971 / 80000000000000000 : ℝ) = - (26238561285308971 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26238561285308971 / 20000000000000000 : ℚ)) - (U := (2714978599527600236461 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26238561285308971 / 20000000000000000 : ℝ) ≤ - (2714978599527600236461 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101909733564157 / 312500000000000 : ℝ)) (q := - (26238561285308971 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26238561285308971 / 80000000000000000 : ℚ)) + (r' := (26238561285308971 / 20000000000000000 : ℚ)) + (U := (-(11147965006472399763539 / 10000000000000000000000 : ℚ))) + (U' := (2714978599527600236461 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (101909733564157 / 312500000000000 : ℚ)) + (q := (26238561285308971 / 80000000000000000 : ℚ)) + (U := (-(11147965006472399763539 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_7 : Uω (aρ 7) (bρ 7) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3179,25 +2827,21 @@ lemma U_384_7 : have hlg : Real.log (4851359975918859 / 16000000000000000 : ℝ) ≤ (-(5966648243356786807413 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4851359975918859 / 16000000000000000 : ℝ) = - (4851359975918859 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4851359975918859 / 4000000000000000 : ℚ)) - (U := (964823559643213192587 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4851359975918859 / 4000000000000000 : ℝ) ≤ - (964823559643213192587 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (597866500676871 / 2000000000000000 : ℝ)) (q := - (4851359975918859 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4851359975918859 / 16000000000000000 : ℚ)) + (r' := (4851359975918859 / 4000000000000000 : ℚ)) + (U := (-(5966648243356786807413 / 5000000000000000000000 : ℚ))) + (U' := (964823559643213192587 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (597866500676871 / 2000000000000000 : ℚ)) + (q := (4851359975918859 / 16000000000000000 : ℚ)) + (U := (-(5966648243356786807413 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_8 : Uω (aρ 8) (bρ 8) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3205,25 +2849,21 @@ lemma U_384_8 : have hlg : Real.log (21582630580093707 / 80000000000000000 : ℝ) ≤ (-(1310137782768200082229 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21582630580093707 / 80000000000000000 : ℝ) = - (21582630580093707 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21582630580093707 / 20000000000000000 : ℚ)) - (U := (76156577831799917771 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21582630580093707 / 20000000000000000 : ℝ) ≤ - (76156577831799917771 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325541478731151 / 1250000000000000 : ℝ)) (q := - (21582630580093707 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21582630580093707 / 80000000000000000 : ℚ)) + (r' := (21582630580093707 / 20000000000000000 : ℚ)) + (U := (-(1310137782768200082229 / 1000000000000000000000 : ℚ))) + (U' := (76156577831799917771 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (325541478731151 / 1250000000000000 : ℚ)) + (q := (21582630580093707 / 80000000000000000 : ℚ)) + (U := (-(1310137782768200082229 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_9 : Uω (aρ 9) (bρ 9) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3231,25 +2871,21 @@ lemma U_384_9 : have hlg : Real.log (17991977855449379 / 80000000000000000 : ℝ) ≤ (-(14921006500376229850049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17991977855449379 / 80000000000000000 : ℝ) = - (17991977855449379 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17991977855449379 / 10000000000000000 : ℚ)) - (U := (5873408908623770149951 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17991977855449379 / 10000000000000000 : ℝ) ≤ - (5873408908623770149951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1023817138524063 / 5000000000000000 : ℝ)) (q := - (17991977855449379 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17991977855449379 / 80000000000000000 : ℚ)) + (r' := (17991977855449379 / 10000000000000000 : ℚ)) + (U := (-(14921006500376229850049 / 10000000000000000000000 : ℚ))) + (U' := (5873408908623770149951 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (1023817138524063 / 5000000000000000 : ℚ)) + (q := (17991977855449379 / 80000000000000000 : ℚ)) + (U := (-(14921006500376229850049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_10 : Uω (aρ 10) (bρ 10) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3257,26 +2893,21 @@ lemma U_384_10 : have hlg : Real.log (12704214832724787 / 80000000000000000 : ℝ) ≤ (-(18400928188958520139997 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12704214832724787 / 80000000000000000 : ℝ) = - (12704214832724787 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12704214832724787 / 10000000000000000 : ℚ)) - (U := (2393487220041479860003 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12704214832724787 / 10000000000000000 : ℝ) ≤ - (2393487220041479860003 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (557126277430989 / 5000000000000000 : ℝ)) (q := - (12704214832724787 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12704214832724787 / 80000000000000000 : ℚ)) + (r' := (12704214832724787 / 10000000000000000 : ℚ)) + (U := (-(18400928188958520139997 / 10000000000000000000000 : ℚ))) + (U' := (2393487220041479860003 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (24306660222459 / 64000000000000 : ℚ)) + (s := (557126277430989 / 5000000000000000 : ℚ)) + (q := (12704214832724787 / 80000000000000000 : ℚ)) + (U := (-(18400928188958520139997 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_384_11 : Uω (aρ 11) (bρ 11) (24306660222459 / 64000000000000 : ℝ) ≤ @@ -3398,25 +3029,21 @@ lemma U_385_1 : have hlg : Real.log (59838649861695569 / 160000000000000000 : ℝ) ≤ (-(9835220437739158478671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59838649861695569 / 160000000000000000 : ℝ) = - (59838649861695569 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59838649861695569 / 40000000000000000 : ℚ)) - (U := (4027723168260841521329 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59838649861695569 / 40000000000000000 : ℝ) ≤ - (4027723168260841521329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3739872388673743 / 10000000000000000 : ℝ)) (q := - (59838649861695569 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59838649861695569 / 160000000000000000 : ℚ)) + (r' := (59838649861695569 / 40000000000000000 : ℚ)) + (U := (-(9835220437739158478671 / 10000000000000000000000 : ℚ))) + (U' := (4027723168260841521329 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (3739872388673743 / 10000000000000000 : ℚ)) + (q := (59838649861695569 / 160000000000000000 : ℚ)) + (U := (-(9835220437739158478671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_2 : Uω (aρ 2) (bρ 2) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3424,25 +3051,21 @@ lemma U_385_2 : have hlg : Real.log (11890893829638173 / 32000000000000000 : ℝ) ≤ (-(4949815097480732821211 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11890893829638173 / 32000000000000000 : ℝ) = - (11890893829638173 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11890893829638173 / 8000000000000000 : ℚ)) - (U := (1981656705519267178789 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (11890893829638173 / 8000000000000000 : ℝ) ≤ - (1981656705519267178789 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (743123762399131 / 2000000000000000 : ℝ)) (q := - (11890893829638173 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11890893829638173 / 32000000000000000 : ℚ)) + (r' := (11890893829638173 / 8000000000000000 : ℚ)) + (U := (-(4949815097480732821211 / 5000000000000000000000 : ℚ))) + (U' := (1981656705519267178789 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (743123762399131 / 2000000000000000 : ℚ)) + (q := (11890893829638173 / 32000000000000000 : ℚ)) + (U := (-(4949815097480732821211 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_3 : Uω (aρ 3) (bρ 3) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3450,25 +3073,21 @@ lemma U_385_3 : have hlg : Real.log (58684563259077641 / 160000000000000000 : ℝ) ≤ (-(5014985496557094599463 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58684563259077641 / 160000000000000000 : ℝ) = - (58684563259077641 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58684563259077641 / 40000000000000000 : ℚ)) - (U := (1916486306442905400537 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58684563259077641 / 40000000000000000 : ℝ) ≤ - (1916486306442905400537 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1833388341103251 / 5000000000000000 : ℝ)) (q := - (58684563259077641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58684563259077641 / 160000000000000000 : ℚ)) + (r' := (58684563259077641 / 40000000000000000 : ℚ)) + (U := (-(5014985496557094599463 / 5000000000000000000000 : ℚ))) + (U' := (1916486306442905400537 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (1833388341103251 / 5000000000000000 : ℚ)) + (q := (58684563259077641 / 160000000000000000 : ℚ)) + (U := (-(5014985496557094599463 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_4 : Uω (aρ 4) (bρ 4) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3476,25 +3095,21 @@ lemma U_385_4 : have hlg : Real.log (57401072754472689 / 160000000000000000 : ℝ) ≤ (-(5125554112303715040283 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57401072754472689 / 160000000000000000 : ℝ) = - (57401072754472689 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57401072754472689 / 40000000000000000 : ℚ)) - (U := (1805917690696284959717 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57401072754472689 / 40000000000000000 : ℝ) ≤ - (1805917690696284959717 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3584634550195883 / 10000000000000000 : ℝ)) (q := - (57401072754472689 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57401072754472689 / 160000000000000000 : ℚ)) + (r' := (57401072754472689 / 40000000000000000 : ℚ)) + (U := (-(5125554112303715040283 / 5000000000000000000000 : ℚ))) + (U' := (1805917690696284959717 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (3584634550195883 / 10000000000000000 : ℚ)) + (q := (57401072754472689 / 160000000000000000 : ℚ)) + (U := (-(5125554112303715040283 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_5 : Uω (aρ 5) (bρ 5) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3502,25 +3117,21 @@ lemma U_385_5 : have hlg : Real.log (55433981038552289 / 160000000000000000 : ℝ) ≤ (-(2119962065703611401969 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55433981038552289 / 160000000000000000 : ℝ) = - (55433981038552289 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55433981038552289 / 40000000000000000 : ℚ)) - (U := (652626655496388598031 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55433981038552289 / 40000000000000000 : ℝ) ≤ - (652626655496388598031 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3456938005040833 / 10000000000000000 : ℝ)) (q := - (55433981038552289 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55433981038552289 / 160000000000000000 : ℚ)) + (r' := (55433981038552289 / 40000000000000000 : ℚ)) + (U := (-(2119962065703611401969 / 2000000000000000000000 : ℚ))) + (U' := (652626655496388598031 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (3456938005040833 / 10000000000000000 : ℚ)) + (q := (55433981038552289 / 160000000000000000 : ℚ)) + (U := (-(2119962065703611401969 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_6 : Uω (aρ 6) (bρ 6) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3528,25 +3139,21 @@ lemma U_385_6 : have hlg : Real.log (10516473629322909 / 32000000000000000 : ℝ) ≤ (-(445117183001040530557 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10516473629322909 / 32000000000000000 : ℝ) = - (10516473629322909 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10516473629322909 / 8000000000000000 : ℚ)) - (U := (109400561238959469443 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10516473629322909 / 8000000000000000 : ℝ) ≤ - (109400561238959469443 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (653545353737723 / 2000000000000000 : ℝ)) (q := - (10516473629322909 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10516473629322909 / 32000000000000000 : ℚ)) + (r' := (10516473629322909 / 8000000000000000 : ℚ)) + (U := (-(445117183001040530557 / 400000000000000000000 : ℚ))) + (U' := (109400561238959469443 / 400000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (653545353737723 / 2000000000000000 : ℚ)) + (q := (10516473629322909 / 32000000000000000 : ℚ)) + (U := (-(445117183001040530557 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_7 : Uω (aρ 7) (bρ 7) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3554,25 +3161,21 @@ lemma U_385_7 : have hlg : Real.log (9723948005422973 / 32000000000000000 : ℝ) ≤ (-(1488930241095184756289 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9723948005422973 / 32000000000000000 : ℝ) = - (9723948005422973 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9723948005422973 / 8000000000000000 : ℚ)) - (U := (243937709654815243711 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9723948005422973 / 8000000000000000 : ℝ) ≤ - (243937709654815243711 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (599211926902231 / 2000000000000000 : ℝ)) (q := - (9723948005422973 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9723948005422973 / 32000000000000000 : ℚ)) + (r' := (9723948005422973 / 8000000000000000 : ℚ)) + (U := (-(1488930241095184756289 / 1250000000000000000000 : ℚ))) + (U' := (243937709654815243711 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (599211926902231 / 2000000000000000 : ℚ)) + (q := (9723948005422973 / 32000000000000000 : ℚ)) + (U := (-(1488930241095184756289 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_8 : Uω (aρ 8) (bρ 8) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3580,25 +3183,21 @@ lemma U_385_8 : have hlg : Real.log (8654730943457773 / 32000000000000000 : ℝ) ≤ (-(6538149004840853801523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8654730943457773 / 32000000000000000 : ℝ) = - (8654730943457773 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8654730943457773 / 8000000000000000 : ℚ)) - (U := (393322798159146198477 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8654730943457773 / 8000000000000000 : ℝ) ≤ - (393322798159146198477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (522268124424581 / 2000000000000000 : ℝ)) (q := - (8654730943457773 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8654730943457773 / 32000000000000000 : ℚ)) + (r' := (8654730943457773 / 8000000000000000 : ℚ)) + (U := (-(6538149004840853801523 / 5000000000000000000000 : ℚ))) + (U' := (393322798159146198477 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (522268124424581 / 2000000000000000 : ℚ)) + (q := (8654730943457773 / 32000000000000000 : ℚ)) + (U := (-(6538149004840853801523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_9 : Uω (aρ 9) (bρ 9) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3606,25 +3205,21 @@ lemma U_385_9 : have hlg : Real.log (36098857042559593 / 160000000000000000 : ℝ) ≤ (-(14889126104872971111557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (36098857042559593 / 160000000000000000 : ℝ) = - (36098857042559593 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36098857042559593 / 20000000000000000 : ℚ)) - (U := (5905289304127028888443 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36098857042559593 / 20000000000000000 : ℝ) ≤ - (5905289304127028888443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1027728270570873 / 5000000000000000 : ℝ)) (q := - (36098857042559593 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36098857042559593 / 160000000000000000 : ℚ)) + (r' := (36098857042559593 / 20000000000000000 : ℚ)) + (U := (-(14889126104872971111557 / 10000000000000000000000 : ℚ))) + (U' := (5905289304127028888443 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (1027728270570873 / 5000000000000000 : ℚ)) + (q := (36098857042559593 / 160000000000000000 : ℚ)) + (U := (-(14889126104872971111557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_10 : Uω (aρ 10) (bρ 10) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3632,26 +3227,21 @@ lemma U_385_10 : have hlg : Real.log (25557202981117793 / 160000000000000000 : ℝ) ≤ (-(18342546204662378687801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25557202981117793 / 160000000000000000 : ℝ) = - (25557202981117793 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25557202981117793 / 20000000000000000 : ℚ)) - (U := (2451869204337621312199 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25557202981117793 / 20000000000000000 : ℝ) ≤ - (2451869204337621312199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1126308816956521 / 10000000000000000 : ℝ)) (q := - (25557202981117793 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25557202981117793 / 160000000000000000 : ℚ)) + (r' := (25557202981117793 / 20000000000000000 : ℚ)) + (U := (-(18342546204662378687801 / 10000000000000000000000 : ℚ))) + (U' := (2451869204337621312199 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (48697037595177 / 128000000000000 : ℚ)) + (s := (1126308816956521 / 10000000000000000 : ℚ)) + (q := (25557202981117793 / 160000000000000000 : ℚ)) + (U := (-(18342546204662378687801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_385_11 : Uω (aρ 11) (bρ 11) (48697037595177 / 128000000000000 : ℝ) ≤ @@ -3774,25 +3364,21 @@ lemma U_386_1 : have hlg : Real.log (14985824376743447 / 40000000000000000 : ℝ) ≤ (-(9817747408755780516049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14985824376743447 / 40000000000000000 : ℝ) = - (14985824376743447 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14985824376743447 / 10000000000000000 : ℚ)) - (U := (4045196197244219483951 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14985824376743447 / 10000000000000000 : ℝ) ≤ - (4045196197244219483951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29268851109137 / 78125000000000 : ℝ)) (q := - (14985824376743447 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14985824376743447 / 40000000000000000 : ℚ)) + (r' := (14985824376743447 / 10000000000000000 : ℚ)) + (U := (-(9817747408755780516049 / 10000000000000000000000 : ℚ))) + (U' := (4045196197244219483951 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (29268851109137 / 78125000000000 : ℚ)) + (q := (14985824376743447 / 40000000000000000 : ℚ)) + (U := (-(9817747408755780516049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_2 : Uω (aρ 2) (bρ 2) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3800,25 +3386,21 @@ lemma U_386_2 : have hlg : Real.log (14889780903240487 / 40000000000000000 : ℝ) ≤ (-(4941021606811480716549 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14889780903240487 / 40000000000000000 : ℝ) = - (14889780903240487 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14889780903240487 / 10000000000000000 : ℚ)) - (U := (1990450196188519283451 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14889780903240487 / 10000000000000000 : ℝ) ≤ - (1990450196188519283451 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (465270027216007 / 1250000000000000 : ℝ)) (q := - (14889780903240487 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14889780903240487 / 40000000000000000 : ℚ)) + (r' := (14889780903240487 / 10000000000000000 : ℚ)) + (U := (-(4941021606811480716549 / 5000000000000000000000 : ℚ))) + (U' := (1990450196188519283451 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (465270027216007 / 1250000000000000 : ℚ)) + (q := (14889780903240487 / 40000000000000000 : ℚ)) + (U := (-(4941021606811480716549 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_3 : Uω (aρ 3) (bρ 3) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3826,25 +3408,21 @@ lemma U_386_3 : have hlg : Real.log (14697309606979173 / 40000000000000000 : ℝ) ≤ (-(625759372808085277601 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14697309606979173 / 40000000000000000 : ℝ) = - (14697309606979173 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14697309606979173 / 10000000000000000 : ℚ)) - (U := (240674602566914722399 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14697309606979173 / 10000000000000000 : ℝ) ≤ - (240674602566914722399 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3673320675947399 / 10000000000000000 : ℝ)) (q := - (14697309606979173 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14697309606979173 / 40000000000000000 : ℚ)) + (r' := (14697309606979173 / 10000000000000000 : ℚ)) + (U := (-(625759372808085277601 / 625000000000000000000 : ℚ))) + (U' := (240674602566914722399 / 625000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (3673320675947399 / 10000000000000000 : ℚ)) + (q := (14697309606979173 / 40000000000000000 : ℚ)) + (U := (-(625759372808085277601 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_4 : Uω (aρ 4) (bρ 4) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3852,25 +3430,21 @@ lemma U_386_4 : have hlg : Real.log (2875290232240193 / 8000000000000000 : ℝ) ≤ (-(10232879216613597053591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2875290232240193 / 8000000000000000 : ℝ) = - (2875290232240193 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2875290232240193 / 2000000000000000 : ℚ)) - (U := (3630064389386402946409 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2875290232240193 / 2000000000000000 : ℝ) ≤ - (3630064389386402946409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (718237126824659 / 2000000000000000 : ℝ)) (q := - (2875290232240193 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2875290232240193 / 8000000000000000 : ℚ)) + (r' := (2875290232240193 / 2000000000000000 : ℚ)) + (U := (-(10232879216613597053591 / 10000000000000000000000 : ℚ))) + (U' := (3630064389386402946409 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (718237126824659 / 2000000000000000 : ℚ)) + (q := (2875290232240193 / 8000000000000000 : ℚ)) + (U := (-(10232879216613597053591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_5 : Uω (aρ 5) (bρ 5) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3878,25 +3452,21 @@ lemma U_386_5 : have hlg : Real.log (13884714924115549 / 40000000000000000 : ℝ) ≤ (-(10580908642584709892287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13884714924115549 / 40000000000000000 : ℝ) = - (13884714924115549 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13884714924115549 / 10000000000000000 : ℚ)) - (U := (3282034963415290107713 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13884714924115549 / 10000000000000000 : ℝ) ≤ - (3282034963415290107713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3463507434915587 / 10000000000000000 : ℝ)) (q := - (13884714924115549 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13884714924115549 / 40000000000000000 : ℚ)) + (r' := (13884714924115549 / 10000000000000000 : ℚ)) + (U := (-(10580908642584709892287 / 10000000000000000000000 : ℚ))) + (U' := (3282034963415290107713 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (3463507434915587 / 10000000000000000 : ℚ)) + (q := (13884714924115549 / 40000000000000000 : ℚ)) + (U := (-(10580908642584709892287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_6 : Uω (aρ 6) (bρ 6) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3904,25 +3474,21 @@ lemma U_386_6 : have hlg : Real.log (13171902828846341 / 40000000000000000 : ℝ) ≤ (-(11107934662065662635813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13171902828846341 / 40000000000000000 : ℝ) = - (13171902828846341 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13171902828846341 / 10000000000000000 : ℚ)) - (U := (2755008943934337364187 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13171902828846341 / 10000000000000000 : ℝ) ≤ - (2755008943934337364187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3274341762420983 / 10000000000000000 : ℝ)) (q := - (13171902828846341 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13171902828846341 / 40000000000000000 : ℚ)) + (r' := (13171902828846341 / 10000000000000000 : ℚ)) + (U := (-(11107934662065662635813 / 10000000000000000000000 : ℚ))) + (U' := (2755008943934337364187 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (3274341762420983 / 10000000000000000 : ℚ)) + (q := (13171902828846341 / 40000000000000000 : ℚ)) + (U := (-(11107934662065662635813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_7 : Uω (aρ 7) (bρ 7) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3930,25 +3496,21 @@ lemma U_386_7 : have hlg : Real.log (12181468423672783 / 40000000000000000 : ℝ) ≤ (-(2377927276686470457359 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12181468423672783 / 40000000000000000 : ℝ) = - (12181468423672783 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12181468423672783 / 10000000000000000 : ℚ)) - (U := (394661444513529542641 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12181468423672783 / 10000000000000000 : ℝ) ≤ - (394661444513529542641 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (750696485148551 / 2500000000000000 : ℝ)) (q := - (12181468423672783 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12181468423672783 / 40000000000000000 : ℚ)) + (r' := (12181468423672783 / 10000000000000000 : ℚ)) + (U := (-(2377927276686470457359 / 2000000000000000000000 : ℚ))) + (U' := (394661444513529542641 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (750696485148551 / 2500000000000000 : ℚ)) + (q := (12181468423672783 / 40000000000000000 : ℚ)) + (U := (-(2377927276686470457359 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_8 : Uω (aρ 8) (bρ 8) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3956,25 +3518,21 @@ lemma U_386_8 : have hlg : Real.log (10845507221032959 / 40000000000000000 : ℝ) ≤ (-(13051285403735799505811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10845507221032959 / 40000000000000000 : ℝ) = - (10845507221032959 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10845507221032959 / 10000000000000000 : ℚ)) - (U := (811658202264200494189 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10845507221032959 / 10000000000000000 : ℝ) ≤ - (811658202264200494189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (654586747653573 / 2500000000000000 : ℝ)) (q := - (10845507221032959 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10845507221032959 / 40000000000000000 : ℚ)) + (r' := (10845507221032959 / 10000000000000000 : ℚ)) + (U := (-(13051285403735799505811 / 10000000000000000000000 : ℚ))) + (U' := (811658202264200494189 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (654586747653573 / 2500000000000000 : ℚ)) + (q := (10845507221032959 / 40000000000000000 : ℚ)) + (U := (-(13051285403735799505811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_9 : Uω (aρ 9) (bρ 9) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -3982,25 +3540,21 @@ lemma U_386_9 : have hlg : Real.log (9053421747210509 / 40000000000000000 : ℝ) ≤ (-(7428683367336118564909 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9053421747210509 / 40000000000000000 : ℝ) = - (9053421747210509 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9053421747210509 / 5000000000000000 : ℚ)) - (U := (2968524337163881435091 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9053421747210509 / 5000000000000000 : ℝ) ≤ - (2968524337163881435091 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2063269882063067 / 10000000000000000 : ℝ)) (q := - (9053421747210509 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9053421747210509 / 40000000000000000 : ℚ)) + (r' := (9053421747210509 / 5000000000000000 : ℚ)) + (U := (-(7428683367336118564909 / 5000000000000000000000 : ℚ))) + (U' := (2968524337163881435091 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (2063269882063067 / 10000000000000000 : ℚ)) + (q := (9053421747210509 / 40000000000000000 : ℚ)) + (U := (-(7428683367336118564909 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_10 : Uω (aρ 10) (bρ 10) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -4008,26 +3562,21 @@ lemma U_386_10 : have hlg : Real.log (6426313849671687 / 40000000000000000 : ℝ) ≤ (-(18284783532368180351299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6426313849671687 / 40000000000000000 : ℝ) = - (6426313849671687 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6426313849671687 / 5000000000000000 : ℚ)) - (U := (2509631876631819648701 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6426313849671687 / 5000000000000000 : ℝ) ≤ - (2509631876631819648701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (71142185424291 / 625000000000000 : ℝ)) (q := - (6426313849671687 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6426313849671687 / 40000000000000000 : ℚ)) + (r' := (6426313849671687 / 5000000000000000 : ℚ)) + (U := (-(18284783532368180351299 / 10000000000000000000000 : ℚ))) + (U' := (2509631876631819648701 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (12195188686359 / 32000000000000 : ℚ)) + (s := (71142185424291 / 625000000000000 : ℚ)) + (q := (6426313849671687 / 40000000000000000 : ℚ)) + (U := (-(18284783532368180351299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_386_11 : Uω (aρ 11) (bρ 11) (12195188686359 / 32000000000000 : ℝ) ≤ @@ -4149,25 +3698,21 @@ lemma U_387_1 : have hlg : Real.log (12009589029608683 / 32000000000000000 : ℝ) ≤ (-(9800304857901901130603 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12009589029608683 / 32000000000000000 : ℝ) = - (12009589029608683 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12009589029608683 / 8000000000000000 : ℚ)) - (U := (4062638748098098869397 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (12009589029608683 / 8000000000000000 : ℝ) ≤ - (4062638748098098869397 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (750590698947851 / 2000000000000000 : ℝ)) (q := - (12009589029608683 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12009589029608683 / 32000000000000000 : ℚ)) + (r' := (12009589029608683 / 8000000000000000 : ℚ)) + (U := (-(9800304857901901130603 / 10000000000000000000000 : ℚ))) + (U' := (4062638748098098869397 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (750590698947851 / 2000000000000000 : ℚ)) + (q := (12009589029608683 / 32000000000000000 : ℚ)) + (U := (-(9800304857901901130603 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_2 : Uω (aρ 2) (bρ 2) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4175,25 +3720,21 @@ lemma U_387_2 : have hlg : Real.log (59663778049571223 / 160000000000000000 : ℝ) ≤ (-(4932243556451181186989 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59663778049571223 / 160000000000000000 : ℝ) = - (59663778049571223 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59663778049571223 / 40000000000000000 : ℚ)) - (U := (1999228246548818813011 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59663778049571223 / 40000000000000000 : ℝ) ≤ - (1999228246548818813011 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3728701619940231 / 10000000000000000 : ℝ)) (q := - (59663778049571223 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59663778049571223 / 160000000000000000 : ℚ)) + (r' := (59663778049571223 / 40000000000000000 : ℚ)) + (U := (-(4932243556451181186989 / 5000000000000000000000 : ℚ))) + (U' := (1999228246548818813011 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (3728701619940231 / 10000000000000000 : ℚ)) + (q := (59663778049571223 / 160000000000000000 : ℚ)) + (U := (-(4932243556451181186989 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_3 : Uω (aρ 3) (bρ 3) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4201,25 +3742,21 @@ lemma U_387_3 : have hlg : Real.log (58893913494597647 / 160000000000000000 : ℝ) ≤ (-(499718032825331389293 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58893913494597647 / 160000000000000000 : ℝ) = - (58893913494597647 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58893913494597647 / 40000000000000000 : ℚ)) - (U := (193429147474668610707 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58893913494597647 / 40000000000000000 : ℝ) ≤ - (193429147474668610707 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1839932328459267 / 5000000000000000 : ℝ)) (q := - (58893913494597647 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58893913494597647 / 160000000000000000 : ℚ)) + (r' := (58893913494597647 / 40000000000000000 : ℚ)) + (U := (-(499718032825331389293 / 500000000000000000000 : ℚ))) + (U' := (193429147474668610707 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (1839932328459267 / 5000000000000000 : ℚ)) + (q := (58893913494597647 / 160000000000000000 : ℚ)) + (U := (-(499718032825331389293 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_4 : Uω (aρ 4) (bρ 4) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4227,25 +3764,21 @@ lemma U_387_4 : have hlg : Real.log (57610536224189447 / 160000000000000000 : ℝ) ≤ (-(10214683431811717131443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57610536224189447 / 160000000000000000 : ℝ) = - (57610536224189447 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57610536224189447 / 40000000000000000 : ℚ)) - (U := (3648260174188282868557 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57610536224189447 / 40000000000000000 : ℝ) ≤ - (3648260174188282868557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3597736679182509 / 10000000000000000 : ℝ)) (q := - (57610536224189447 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57610536224189447 / 160000000000000000 : ℚ)) + (r' := (57610536224189447 / 40000000000000000 : ℚ)) + (U := (-(10214683431811717131443 / 10000000000000000000000 : ℚ))) + (U' := (3648260174188282868557 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (3597736679182509 / 10000000000000000 : ℚ)) + (q := (57610536224189447 / 160000000000000000 : ℚ)) + (U := (-(10214683431811717131443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_5 : Uω (aρ 5) (bρ 5) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4253,25 +3786,21 @@ lemma U_387_5 : have hlg : Real.log (55643737477052503 / 160000000000000000 : ℝ) ≤ (-(10562042774298962654907 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55643737477052503 / 160000000000000000 : ℝ) = - (55643737477052503 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55643737477052503 / 40000000000000000 : ℚ)) - (U := (3300900831701037345093 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55643737477052503 / 40000000000000000 : ℝ) ≤ - (3300900831701037345093 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3470076755125391 / 10000000000000000 : ℝ)) (q := - (55643737477052503 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55643737477052503 / 160000000000000000 : ℚ)) + (r' := (55643737477052503 / 40000000000000000 : ℚ)) + (U := (-(10562042774298962654907 / 10000000000000000000000 : ℚ))) + (U' := (3300900831701037345093 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (3470076755125391 / 10000000000000000 : ℚ)) + (q := (55643737477052503 / 160000000000000000 : ℚ)) + (U := (-(10562042774298962654907 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_6 : Uω (aρ 6) (bρ 6) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4279,25 +3808,21 @@ lemma U_387_6 : have hlg : Real.log (52792852091490599 / 160000000000000000 : ℝ) ≤ (-(11087980102211234289417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52792852091490599 / 160000000000000000 : ℝ) = - (52792852091490599 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52792852091490599 / 40000000000000000 : ℚ)) - (U := (2774963503788765710583 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52792852091490599 / 40000000000000000 : ℝ) ≤ - (2774963503788765710583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3280956457070153 / 10000000000000000 : ℝ)) (q := - (52792852091490599 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52792852091490599 / 160000000000000000 : ℚ)) + (r' := (52792852091490599 / 40000000000000000 : ℚ)) + (U := (-(11087980102211234289417 / 10000000000000000000000 : ℚ))) + (U' := (2774963503788765710583 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (3280956457070153 / 10000000000000000 : ℚ)) + (q := (52792852091490599 / 160000000000000000 : ℚ)) + (U := (-(11087980102211234289417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_7 : Uω (aρ 7) (bρ 7) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4305,25 +3830,21 @@ lemma U_387_7 : have hlg : Real.log (48832000806173063 / 160000000000000000 : ℝ) ≤ (-(11867879625428304621113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (48832000806173063 / 160000000000000000 : ℝ) = - (48832000806173063 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48832000806173063 / 40000000000000000 : ℚ)) - (U := (1995063980571695378887 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48832000806173063 / 40000000000000000 : ℝ) ≤ - (1995063980571695378887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3009511427165461 / 10000000000000000 : ℝ)) (q := - (48832000806173063 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48832000806173063 / 160000000000000000 : ℚ)) + (r' := (48832000806173063 / 40000000000000000 : ℚ)) + (U := (-(11867879625428304621113 / 10000000000000000000000 : ℚ))) + (U' := (1995063980571695378887 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (3009511427165461 / 10000000000000000 : ℚ)) + (q := (48832000806173063 / 160000000000000000 : ℚ)) + (U := (-(11867879625428304621113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_8 : Uω (aρ 8) (bρ 8) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4331,25 +3852,21 @@ lemma U_387_8 : have hlg : Real.log (1739615352638351 / 6400000000000000 : ℝ) ≤ (-(3256584906897836630917 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1739615352638351 / 6400000000000000 : ℝ) = - (1739615352638351 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1739615352638351 / 1600000000000000 : ℚ)) - (U := (209150994602163369083 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1739615352638351 / 1600000000000000 : ℝ) ≤ - (209150994602163369083 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105014038189147 / 400000000000000 : ℝ)) (q := - (1739615352638351 / 6400000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1739615352638351 / 6400000000000000 : ℚ)) + (r' := (1739615352638351 / 1600000000000000 : ℚ)) + (U := (-(3256584906897836630917 / 2500000000000000000000 : ℚ))) + (U' := (209150994602163369083 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (105014038189147 / 400000000000000 : ℚ)) + (q := (1739615352638351 / 6400000000000000 : ℚ)) + (U := (-(3256584906897836630917 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_9 : Uω (aρ 9) (bρ 9) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4357,25 +3874,21 @@ lemma U_387_9 : have hlg : Real.log (7265689271534427 / 32000000000000000 : ℝ) ≤ (-(593029093542680300733 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7265689271534427 / 32000000000000000 : ℝ) = - (7265689271534427 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7265689271534427 / 4000000000000000 : ℚ)) - (U := (238747522817319699267 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7265689271534427 / 4000000000000000 : ℝ) ≤ - (238747522817319699267 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (414214880160569 / 2000000000000000 : ℝ)) (q := - (7265689271534427 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7265689271534427 / 32000000000000000 : ℚ)) + (r' := (7265689271534427 / 4000000000000000 : ℚ)) + (U := (-(593029093542680300733 / 400000000000000000000 : ℚ))) + (U' := (238747522817319699267 / 400000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (414214880160569 / 2000000000000000 : ℚ)) + (q := (7265689271534427 / 32000000000000000 : ℚ)) + (U := (-(593029093542680300733 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_10 : Uω (aρ 10) (bρ 10) (9772894379139 / 25600000000000 : ℝ) ≤ @@ -4383,26 +3896,21 @@ lemma U_387_10 : have hlg : Real.log (25852609418760503 / 160000000000000000 : ℝ) ≤ (-(18227622739612179984223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (25852609418760503 / 160000000000000000 : ℝ) = - (25852609418760503 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25852609418760503 / 20000000000000000 : ℚ)) - (U := (2566792669387820015777 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25852609418760503 / 20000000000000000 : ℝ) ≤ - (2566792669387820015777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1150153816933891 / 10000000000000000 : ℝ)) (q := - (25852609418760503 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25852609418760503 / 160000000000000000 : ℚ)) + (r' := (25852609418760503 / 20000000000000000 : ℚ)) + (U := (-(18227622739612179984223 / 10000000000000000000000 : ℚ))) + (U' := (2566792669387820015777 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9772894379139 / 25600000000000 : ℚ)) + (s := (1150153816933891 / 10000000000000000 : ℚ)) + (q := (25852609418760503 / 160000000000000000 : ℚ)) + (U := (-(18227622739612179984223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_387_11 : Uω (aρ 11) (bρ 11) (9772894379139 / 25600000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U32.lean b/LeanPool/Zeta5Irrational/Table/U32.lean index 996e520fc7..90e38b002e 100644 --- a/LeanPool/Zeta5Irrational/Table/U32.lean +++ b/LeanPool/Zeta5Irrational/Table/U32.lean @@ -24,25 +24,21 @@ lemma U_388_1 : have hlg : Real.log (30076296392463209 / 80000000000000000 : ℝ) ≤ (-(9782892679034460345389 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30076296392463209 / 80000000000000000 : ℝ) = - (30076296392463209 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30076296392463209 / 20000000000000000 : ℚ)) - (U := (4080050926965539654611 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30076296392463209 / 20000000000000000 : ℝ) ≤ - (4080050926965539654611 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1879747023492823 / 5000000000000000 : ℝ)) (q := - (30076296392463209 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30076296392463209 / 80000000000000000 : ℚ)) + (r' := (30076296392463209 / 20000000000000000 : ℚ)) + (U := (-(9782892679034460345389 / 10000000000000000000000 : ℚ))) + (U' := (4080050926965539654611 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1879747023492823 / 5000000000000000 : ℚ)) + (q := (30076296392463209 / 80000000000000000 : ℚ)) + (U := (-(9782892679034460345389 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_2 : Uω (aρ 2) (bρ 2) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_388_2 : have hlg : Real.log (29884216229083321 / 80000000000000000 : ℝ) ≤ (-(9846961784527956511941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29884216229083321 / 80000000000000000 : ℝ) = - (29884216229083321 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29884216229083321 / 20000000000000000 : ℚ)) - (U := (4015981821472043488059 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29884216229083321 / 20000000000000000 : ℝ) ≤ - (4015981821472043488059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1867621509325337 / 5000000000000000 : ℝ)) (q := - (29884216229083321 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29884216229083321 / 80000000000000000 : ℚ)) + (r' := (29884216229083321 / 20000000000000000 : ℚ)) + (U := (-(9846961784527956511941 / 10000000000000000000000 : ℚ))) + (U' := (4015981821472043488059 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1867621509325337 / 5000000000000000 : ℚ)) + (q := (29884216229083321 / 80000000000000000 : ℚ)) + (U := (-(9846961784527956511941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_3 : Uω (aρ 3) (bρ 3) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_388_3 : have hlg : Real.log (29499294229832269 / 80000000000000000 : ℝ) ≤ (-(9976602955068756301647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29499294229832269 / 80000000000000000 : ℝ) = - (29499294229832269 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29499294229832269 / 20000000000000000 : ℚ)) - (U := (3886340650931243698353 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29499294229832269 / 20000000000000000 : ℝ) ≤ - (3886340650931243698353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3686408625187911 / 10000000000000000 : ℝ)) (q := - (29499294229832269 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29499294229832269 / 80000000000000000 : ℚ)) + (r' := (29499294229832269 / 20000000000000000 : ℚ)) + (U := (-(9976602955068756301647 / 10000000000000000000000 : ℚ))) + (U' := (3886340650931243698353 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (3686408625187911 / 10000000000000000 : ℚ)) + (q := (29499294229832269 / 80000000000000000 : ℚ)) + (U := (-(9976602955068756301647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_4 : Uω (aρ 4) (bρ 4) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_388_4 : have hlg : Real.log (28857633747162473 / 80000000000000000 : ℝ) ≤ (-(5098260374562509612519 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28857633747162473 / 80000000000000000 : ℝ) = - (28857633747162473 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28857633747162473 / 20000000000000000 : ℚ)) - (U := (1833211428437490387481 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28857633747162473 / 20000000000000000 : ℝ) ≤ - (1833211428437490387481 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1802143842792731 / 5000000000000000 : ℝ)) (q := - (28857633747162473 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28857633747162473 / 80000000000000000 : ℚ)) + (r' := (28857633747162473 / 20000000000000000 : ℚ)) + (U := (-(5098260374562509612519 / 5000000000000000000000 : ℚ))) + (U' := (1833211428437490387481 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1802143842792731 / 5000000000000000 : ℚ)) + (q := (28857633747162473 / 80000000000000000 : ℚ)) + (U := (-(5098260374562509612519 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_5 : Uω (aρ 5) (bρ 5) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_388_5 : have hlg : Real.log (27874307192648233 / 80000000000000000 : ℝ) ≤ (-(10543212587579755254357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27874307192648233 / 80000000000000000 : ℝ) = - (27874307192648233 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27874307192648233 / 20000000000000000 : ℚ)) - (U := (3319731018420244745643 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27874307192648233 / 20000000000000000 : ℝ) ≤ - (3319731018420244745643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1738322983145951 / 5000000000000000 : ℝ)) (q := - (27874307192648233 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27874307192648233 / 80000000000000000 : ℚ)) + (r' := (27874307192648233 / 20000000000000000 : ℚ)) + (U := (-(10543212587579755254357 / 10000000000000000000000 : ℚ))) + (U' := (3319731018420244745643 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1738322983145951 / 5000000000000000 : ℚ)) + (q := (27874307192648233 / 80000000000000000 : ℚ)) + (U := (-(10543212587579755254357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_6 : Uω (aρ 6) (bρ 6) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_388_6 : have hlg : Real.log (26449045244686297 / 80000000000000000 : ℝ) ≤ (-(11068065731103946049403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26449045244686297 / 80000000000000000 : ℝ) = - (26449045244686297 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26449045244686297 / 20000000000000000 : ℚ)) - (U := (2794877874896053950597 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26449045244686297 / 20000000000000000 : ℝ) ≤ - (2794877874896053950597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1643785427220709 / 5000000000000000 : ℝ)) (q := - (26449045244686297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26449045244686297 / 80000000000000000 : ℚ)) + (r' := (26449045244686297 / 20000000000000000 : ℚ)) + (U := (-(11068065731103946049403 / 10000000000000000000000 : ℚ))) + (U' := (2794877874896053950597 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1643785427220709 / 5000000000000000 : ℚ)) + (q := (26449045244686297 / 80000000000000000 : ℚ)) + (U := (-(11068065731103946049403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_7 : Uω (aρ 7) (bρ 7) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_388_7 : have hlg : Real.log (24469060702708113 / 80000000000000000 : ℝ) ≤ (-(1480771428879991064171 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24469060702708113 / 80000000000000000 : ℝ) = - (24469060702708113 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24469060702708113 / 20000000000000000 : ℚ)) - (U := (252096521870008935829 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24469060702708113 / 20000000000000000 : ℝ) ≤ - (252096521870008935829 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (377029512463359 / 1250000000000000 : ℝ)) (q := - (24469060702708113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24469060702708113 / 80000000000000000 : ℚ)) + (r' := (24469060702708113 / 20000000000000000 : ℚ)) + (U := (-(1480771428879991064171 / 1250000000000000000000 : ℚ))) + (U' := (252096521870008935829 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (377029512463359 / 1250000000000000 : ℚ)) + (q := (24469060702708113 / 80000000000000000 : ℚ)) + (U := (-(1480771428879991064171 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_8 : Uω (aρ 8) (bρ 8) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_388_8 : have hlg : Real.log (21799359833153453 / 80000000000000000 : ℝ) ≤ (-(13001460302417974526679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21799359833153453 / 80000000000000000 : ℝ) = - (21799359833153453 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21799359833153453 / 20000000000000000 : ℚ)) - (U := (861483303582025473321 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21799359833153453 / 20000000000000000 : ℝ) ≤ - (861483303582025473321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2632352533658207 / 10000000000000000 : ℝ)) (q := - (21799359833153453 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21799359833153453 / 80000000000000000 : ℚ)) + (r' := (21799359833153453 / 20000000000000000 : ℚ)) + (U := (-(13001460302417974526679 / 10000000000000000000000 : ℚ))) + (U' := (861483303582025473321 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (2632352533658207 / 10000000000000000 : ℚ)) + (q := (21799359833153453 / 80000000000000000 : ℚ)) + (U := (-(13001460302417974526679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_9 : Uω (aρ 9) (bρ 9) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_388_9 : have hlg : Real.log (18221567971968993 / 80000000000000000 : ℝ) ≤ (-(7397103440139706118931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18221567971968993 / 80000000000000000 : ℝ) = - (18221567971968993 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18221567971968993 / 10000000000000000 : ℚ)) - (U := (3000104264360293881069 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18221567971968993 / 10000000000000000 : ℝ) ≤ - (3000104264360293881069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (519717549180523 / 2500000000000000 : ℝ)) (q := - (18221567971968993 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18221567971968993 / 80000000000000000 : ℚ)) + (r' := (18221567971968993 / 10000000000000000 : ℚ)) + (U := (-(7397103440139706118931 / 5000000000000000000000 : ℚ))) + (U' := (3000104264360293881069 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (519717549180523 / 2500000000000000 : ℚ)) + (q := (18221567971968993 / 80000000000000000 : ℚ)) + (U := (-(7397103440139706118931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_10 : Uω (aρ 10) (bρ 10) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_388_10 : have hlg : Real.log (12999643230488421 / 80000000000000000 : ℝ) ≤ (-(3634209441235360305123 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (12999643230488421 / 80000000000000000 : ℝ) = - (12999643230488421 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12999643230488421 / 10000000000000000 : ℚ)) - (U := (524673640564639694877 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12999643230488421 / 10000000000000000 : ℝ) ≤ - (524673640564639694877 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1161948044846949 / 10000000000000000 : ℝ)) (q := - (12999643230488421 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12999643230488421 / 80000000000000000 : ℚ)) + (r' := (12999643230488421 / 10000000000000000 : ℚ)) + (U := (-(3634209441235360305123 / 2000000000000000000000 : ℚ))) + (U' := (524673640564639694877 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (24474094522977 / 64000000000000 : ℚ)) + (s := (1161948044846949 / 10000000000000000 : ℚ)) + (q := (12999643230488421 / 80000000000000000 : ℚ)) + (U := (-(3634209441235360305123 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_388_11 : Uω (aρ 11) (bρ 11) (24474094522977 / 64000000000000 : ℝ) ≤ @@ -399,25 +358,21 @@ lemma U_389_1 : have hlg : Real.log (7545236005777453 / 20000000000000000 : ℝ) ≤ (-(4874079507725232605329 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7545236005777453 / 20000000000000000 : ℝ) = - (7545236005777453 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7545236005777453 / 5000000000000000 : ℚ)) - (U := (2057392295274767394671 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7545236005777453 / 5000000000000000 : ℝ) ≤ - (2057392295274767394671 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117892973434979 / 312500000000000 : ℝ)) (q := - (7545236005777453 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7545236005777453 / 20000000000000000 : ℚ)) + (r' := (7545236005777453 / 5000000000000000 : ℚ)) + (U := (-(4874079507725232605329 / 5000000000000000000000 : ℚ))) + (U' := (2057392295274767394671 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (117892973434979 / 312500000000000 : ℚ)) + (q := (7545236005777453 / 20000000000000000 : ℚ)) + (U := (-(4874079507725232605329 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_2 : Uω (aρ 2) (bρ 2) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -425,25 +380,21 @@ lemma U_389_2 : have hlg : Real.log (7497217648987823 / 20000000000000000 : ℝ) ≤ (-(9812003014569464231753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7497217648987823 / 20000000000000000 : ℝ) = - (7497217648987823 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7497217648987823 / 5000000000000000 : ℚ)) - (U := (4050940591430535768247 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7497217648987823 / 5000000000000000 : ℝ) ≤ - (4050940591430535768247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1874162902819849 / 5000000000000000 : ℝ)) (q := - (7497217648987823 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7497217648987823 / 20000000000000000 : ℚ)) + (r' := (7497217648987823 / 5000000000000000 : ℚ)) + (U := (-(9812003014569464231753 / 10000000000000000000000 : ℚ))) + (U' := (4050940591430535768247 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (1874162902819849 / 5000000000000000 : ℚ)) + (q := (7497217648987823 / 20000000000000000 : ℚ)) + (U := (-(9812003014569464231753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_3 : Uω (aρ 3) (bρ 3) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -451,25 +402,21 @@ lemma U_389_3 : have hlg : Real.log (3700496130444567 / 10000000000000000 : ℝ) ≤ (-(310661935157438047953 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3700496130444567 / 10000000000000000 : ℝ) = - (3700496130444567 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3700496130444567 / 2500000000000000 : ℚ)) - (U := (122555052530061952047 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3700496130444567 / 2500000000000000 : ℝ) ≤ - (122555052530061952047 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3699496523891009 / 10000000000000000 : ℝ)) (q := - (3700496130444567 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3700496130444567 / 10000000000000000 : ℚ)) + (r' := (3700496130444567 / 2500000000000000 : ℚ)) + (U := (-(310661935157438047953 / 312500000000000000000 : ℚ))) + (U' := (122555052530061952047 / 312500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (3699496523891009 / 10000000000000000 : ℚ)) + (q := (3700496130444567 / 10000000000000000 : ℚ)) + (U := (-(310661935157438047953 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_4 : Uω (aρ 4) (bρ 4) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -477,25 +424,21 @@ lemma U_389_4 : have hlg : Real.log (7240591139195777 / 20000000000000000 : ℝ) ≤ (-(10160294209093882698789 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7240591139195777 / 20000000000000000 : ℝ) = - (7240591139195777 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7240591139195777 / 5000000000000000 : ℚ)) - (U := (3702649396906117301211 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7240591139195777 / 5000000000000000 : ℝ) ≤ - (3702649396906117301211 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (904347395815663 / 2500000000000000 : ℝ)) (q := - (7240591139195777 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7240591139195777 / 20000000000000000 : ℚ)) + (r' := (7240591139195777 / 5000000000000000 : ℚ)) + (U := (-(10160294209093882698789 / 10000000000000000000000 : ℚ))) + (U' := (3702649396906117301211 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (904347395815663 / 2500000000000000 : ℚ)) + (q := (7240591139195777 / 20000000000000000 : ℚ)) + (U := (-(10160294209093882698789 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_5 : Uω (aρ 5) (bρ 5) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -503,25 +446,21 @@ lemma U_389_5 : have hlg : Real.log (3497397850278163 / 10000000000000000 : ℝ) ≤ (-(10505658718397677553489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3497397850278163 / 10000000000000000 : ℝ) = - (3497397850278163 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3497397850278163 / 2500000000000000 : ℚ)) - (U := (3357284887602322446511 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3497397850278163 / 2500000000000000 : ℝ) ≤ - (3357284887602322446511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3489784063958201 / 10000000000000000 : ℝ)) (q := - (3497397850278163 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3497397850278163 / 10000000000000000 : ℚ)) + (r' := (3497397850278163 / 2500000000000000 : ℚ)) + (U := (-(10505658718397677553489 / 10000000000000000000000 : ℚ))) + (U' := (3357284887602322446511 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (3489784063958201 / 10000000000000000 : ℚ)) + (q := (3497397850278163 / 10000000000000000 : ℚ)) + (U := (-(10505658718397677553489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_6 : Uω (aρ 6) (bρ 6) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -529,25 +468,21 @@ lemma U_389_6 : have hlg : Real.log (6638570025956783 / 20000000000000000 : ℝ) ≤ (-(11028356902751511319297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6638570025956783 / 20000000000000000 : ℝ) = - (6638570025956783 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6638570025956783 / 5000000000000000 : ℚ)) - (U := (2834586703248488680703 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6638570025956783 / 5000000000000000 : ℝ) ≤ - (2834586703248488680703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1650399382249329 / 5000000000000000 : ℝ)) (q := - (6638570025956783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6638570025956783 / 20000000000000000 : ℚ)) + (r' := (6638570025956783 / 5000000000000000 : ℚ)) + (U := (-(11028356902751511319297 / 10000000000000000000000 : ℚ))) + (U' := (2834586703248488680703 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (1650399382249329 / 5000000000000000 : ℚ)) + (q := (6638570025956783 / 20000000000000000 : ℚ)) + (U := (-(11028356902751511319297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_7 : Uω (aρ 7) (bρ 7) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -555,25 +490,21 @@ lemma U_389_7 : have hlg : Real.log (6143792905079437 / 20000000000000000 : ℝ) ≤ (-(11802899846123785371143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6143792905079437 / 20000000000000000 : ℝ) = - (6143792905079437 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6143792905079437 / 5000000000000000 : ℚ)) - (U := (2060043759876214628857 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6143792905079437 / 5000000000000000 : ℝ) ≤ - (2060043759876214628857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23669398627979 / 78125000000000 : ℝ)) (q := - (6143792905079437 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6143792905079437 / 20000000000000000 : ℚ)) + (r' := (6143792905079437 / 5000000000000000 : ℚ)) + (U := (-(11802899846123785371143 / 10000000000000000000000 : ℚ))) + (U' := (2060043759876214628857 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (23669398627979 / 78125000000000 : ℚ)) + (q := (6143792905079437 / 20000000000000000 : ℚ)) + (U := (-(11802899846123785371143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_8 : Uω (aρ 8) (bρ 8) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -581,25 +512,21 @@ lemma U_389_8 : have hlg : Real.log (2738458420520823 / 10000000000000000 : ℝ) ≤ (-(12951899506522119733701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2738458420520823 / 10000000000000000 : ℝ) = - (2738458420520823 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2738458420520823 / 2500000000000000 : ℚ)) - (U := (911044099477880266299 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2738458420520823 / 2500000000000000 : ℝ) ≤ - (911044099477880266299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2646348611683521 / 10000000000000000 : ℝ)) (q := - (2738458420520823 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2738458420520823 / 10000000000000000 : ℚ)) + (r' := (2738458420520823 / 2500000000000000 : ℚ)) + (U := (-(12951899506522119733701 / 10000000000000000000000 : ℚ))) + (U' := (911044099477880266299 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (2646348611683521 / 10000000000000000 : ℚ)) + (q := (2738458420520823 / 10000000000000000 : ℚ)) + (U := (-(12951899506522119733701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_9 : Uω (aρ 9) (bρ 9) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -607,25 +534,21 @@ lemma U_389_9 : have hlg : Real.log (4584038610599473 / 20000000000000000 : ℝ) ≤ (-(14731518704915448957371 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4584038610599473 / 20000000000000000 : ℝ) = - (4584038610599473 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4584038610599473 / 2500000000000000 : ℚ)) - (U := (6062896704084551042629 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4584038610599473 / 2500000000000000 : ℝ) ≤ - (6062896704084551042629 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (523609002400337 / 2500000000000000 : ℝ)) (q := - (4584038610599473 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4584038610599473 / 20000000000000000 : ℚ)) + (r' := (4584038610599473 / 2500000000000000 : ℚ)) + (U := (-(14731518704915448957371 / 10000000000000000000000 : ℚ))) + (U' := (6062896704084551042629 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (523609002400337 / 2500000000000000 : ℚ)) + (q := (4584038610599473 / 20000000000000000 : ℚ)) + (U := (-(14731518704915448957371 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_10 : Uω (aρ 10) (bρ 10) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -633,23 +556,21 @@ lemma U_389_10 : have hlg : Real.log (3286336287777 / 20000000000000 : ℝ) ≤ (-(9029794594203179324451 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show (3286336287777 / 20000000000000 : ℝ) = (3286336287777 / 2500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3286336287777 / 2500000000000 : ℚ)) - (U := (1367413110296820675549 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3286336287777 / 2500000000000 : ℝ) ≤ - (1367413110296820675549 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9482341762191 / 80000000000000 : ℝ)) (q := - (3286336287777 / 20000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3286336287777 / 20000000000000 : ℚ)) + (r' := (3286336287777 / 2500000000000 : ℚ)) + (U := (-(9029794594203179324451 / 5000000000000000000000 : ℚ))) + (U' := (1367413110296820675549 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (6139452918309 / 16000000000000 : ℚ)) + (s := (9482341762191 / 80000000000000 : ℚ)) + (q := (3286336287777 / 20000000000000 : ℚ)) + (U := (-(9029794594203179324451 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_389_11 : Uω (aρ 11) (bρ 11) (6139452918309 / 16000000000000 : ℝ) ≤ @@ -771,25 +692,21 @@ lemma U_390_1 : have hlg : Real.log (30285591645513059 / 80000000000000000 : ℝ) ≤ (-(9713545579860973935019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30285591645513059 / 80000000000000000 : ℝ) = - (30285591645513059 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30285591645513059 / 20000000000000000 : ℚ)) - (U := (4149398026139026064981 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30285591645513059 / 20000000000000000 : ℝ) ≤ - (4149398026139026064981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3785656250792171 / 10000000000000000 : ℝ)) (q := - (30285591645513059 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30285591645513059 / 80000000000000000 : ℚ)) + (r' := (30285591645513059 / 20000000000000000 : ℚ)) + (U := (-(9713545579860973935019 / 10000000000000000000000 : ℚ))) + (U' := (4149398026139026064981 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (3785656250792171 / 10000000000000000 : ℚ)) + (q := (30285591645513059 / 80000000000000000 : ℚ)) + (U := (-(9713545579860973935019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_2 : Uω (aρ 2) (bρ 2) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -797,25 +714,21 @@ lemma U_390_2 : have hlg : Real.log (30093524907666447 / 80000000000000000 : ℝ) ≤ (-(1955433209774552219883 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30093524907666447 / 80000000000000000 : ℝ) = - (30093524907666447 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30093524907666447 / 20000000000000000 : ℚ)) - (U := (817155511425447780117 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30093524907666447 / 20000000000000000 : ℝ) ≤ - (817155511425447780117 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1880704289420259 / 5000000000000000 : ℝ)) (q := - (30093524907666447 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30093524907666447 / 80000000000000000 : ℚ)) + (r' := (30093524907666447 / 20000000000000000 : ℚ)) + (U := (-(1955433209774552219883 / 2000000000000000000000 : ℚ))) + (U' := (817155511425447780117 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (1880704289420259 / 5000000000000000 : ℚ)) + (q := (30093524907666447 / 80000000000000000 : ℚ)) + (U := (-(1955433209774552219883 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_3 : Uω (aρ 3) (bρ 3) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -823,25 +736,21 @@ lemma U_390_3 : have hlg : Real.log (29708643657269043 / 80000000000000000 : ℝ) ≤ (-(9905885984557209782699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29708643657269043 / 80000000000000000 : ℝ) = - (29708643657269043 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29708643657269043 / 20000000000000000 : ℚ)) - (U := (3957057621442790217301 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29708643657269043 / 20000000000000000 : ℝ) ≤ - (3957057621442790217301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3712584372591167 / 10000000000000000 : ℝ)) (q := - (29708643657269043 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29708643657269043 / 80000000000000000 : ℚ)) + (r' := (29708643657269043 / 20000000000000000 : ℚ)) + (U := (-(9905885984557209782699 / 10000000000000000000000 : ℚ))) + (U' := (3957057621442790217301 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (3712584372591167 / 10000000000000000 : ℚ)) + (q := (29708643657269043 / 80000000000000000 : ℚ)) + (U := (-(9905885984557209782699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_4 : Uω (aρ 4) (bρ 4) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -849,25 +758,21 @@ lemma U_390_4 : have hlg : Real.log (1162683790316947 / 3200000000000000 : ℝ) ≤ (-(10124198641054031683193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1162683790316947 / 3200000000000000 : ℝ) = - (1162683790316947 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1162683790316947 / 800000000000000 : ℚ)) - (U := (3738744964945968316807 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1162683790316947 / 800000000000000 : ℝ) ≤ - (3738744964945968316807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (145219653152793 / 400000000000000 : ℝ)) (q := - (1162683790316947 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1162683790316947 / 3200000000000000 : ℚ)) + (r' := (1162683790316947 / 800000000000000 : ℚ)) + (U := (-(10124198641054031683193 / 10000000000000000000000 : ℚ))) + (U' := (3738744964945968316807 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (145219653152793 / 400000000000000 : ℚ)) + (q := (1162683790316947 / 3200000000000000 : ℚ)) + (U := (-(10124198641054031683193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_5 : Uω (aρ 5) (bρ 5) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -875,25 +780,21 @@ lemma U_390_5 : have hlg : Real.log (28084056696482443 / 80000000000000000 : ℝ) ≤ (-(10468245961831071935927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28084056696482443 / 80000000000000000 : ℝ) = - (28084056696482443 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28084056696482443 / 20000000000000000 : ℚ)) - (U := (3394697644168928064073 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28084056696482443 / 20000000000000000 : ℝ) ≤ - (3394697644168928064073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3502921732794517 / 10000000000000000 : ℝ)) (q := - (28084056696482443 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28084056696482443 / 80000000000000000 : ℚ)) + (r' := (28084056696482443 / 20000000000000000 : ℚ)) + (U := (-(10468245961831071935927 / 10000000000000000000000 : ℚ))) + (U' := (3394697644168928064073 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (3502921732794517 / 10000000000000000 : ℚ)) + (q := (28084056696482443 / 80000000000000000 : ℚ)) + (U := (-(10468245961831071935927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_6 : Uω (aρ 6) (bρ 6) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -901,25 +802,21 @@ lemma U_390_6 : have hlg : Real.log (26659510291728759 / 80000000000000000 : ℝ) ≤ (-(1098880688224468762929 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26659510291728759 / 80000000000000000 : ℝ) = - (26659510291728759 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26659510291728759 / 20000000000000000 : ℚ)) - (U := (287413672375531237071 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26659510291728759 / 20000000000000000 : ℝ) ≤ - (287413672375531237071 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207126594171631 / 625000000000000 : ℝ)) (q := - (26659510291728759 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26659510291728759 / 80000000000000000 : ℚ)) + (r' := (26659510291728759 / 20000000000000000 : ℚ)) + (U := (-(1098880688224468762929 / 1000000000000000000000 : ℚ))) + (U' := (287413672375531237071 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (207126594171631 / 625000000000000 : ℚ)) + (q := (26659510291728759 / 80000000000000000 : ℚ)) + (U := (-(1098880688224468762929 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_7 : Uω (aρ 7) (bρ 7) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -927,25 +824,21 @@ lemma U_390_7 : have hlg : Real.log (24681269771681939 / 80000000000000000 : ℝ) ≤ (-(5879909935102141370187 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24681269771681939 / 80000000000000000 : ℝ) = - (24681269771681939 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24681269771681939 / 20000000000000000 : ℚ)) - (U := (1051561867897858629813 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24681269771681939 / 20000000000000000 : ℝ) ≤ - (1051561867897858629813 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3043126757494391 / 10000000000000000 : ℝ)) (q := - (24681269771681939 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24681269771681939 / 80000000000000000 : ℚ)) + (r' := (24681269771681939 / 20000000000000000 : ℚ)) + (U := (-(5879909935102141370187 / 5000000000000000000000 : ℚ))) + (U' := (1051561867897858629813 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (3043126757494391 / 10000000000000000 : ℚ)) + (q := (24681269771681939 / 80000000000000000 : ℚ)) + (U := (-(5879909935102141370187 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_8 : Uω (aρ 8) (bρ 8) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -953,25 +846,21 @@ lemma U_390_8 : have hlg : Real.log (22015937632653179 / 80000000000000000 : ℝ) ≤ (-(12902600052262391086187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22015937632653179 / 80000000000000000 : ℝ) = - (22015937632653179 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22015937632653179 / 20000000000000000 : ℚ)) - (U := (960343553737608913813 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22015937632653179 / 20000000000000000 : ℝ) ≤ - (960343553737608913813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2660335374077201 / 10000000000000000 : ℝ)) (q := - (22015937632653179 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22015937632653179 / 80000000000000000 : ℚ)) + (r' := (22015937632653179 / 20000000000000000 : ℚ)) + (U := (-(12902600052262391086187 / 10000000000000000000000 : ℚ))) + (U' := (960343553737608913813 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (2660335374077201 / 10000000000000000 : ℚ)) + (q := (22015937632653179 / 80000000000000000 : ℚ)) + (U := (-(12902600052262391086187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_9 : Uω (aρ 9) (bρ 9) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -979,25 +868,21 @@ lemma U_390_9 : have hlg : Real.log (18450605960057299 / 80000000000000000 : ℝ) ≤ (-(7334647102916508509139 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18450605960057299 / 80000000000000000 : ℝ) = - (18450605960057299 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18450605960057299 / 10000000000000000 : ℚ)) - (U := (3062560601583491490861 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18450605960057299 / 10000000000000000 : ℝ) ≤ - (3062560601583491490861 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2109968084288231 / 10000000000000000 : ℝ)) (q := - (18450605960057299 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18450605960057299 / 80000000000000000 : ℚ)) + (r' := (18450605960057299 / 10000000000000000 : ℚ)) + (U := (-(7334647102916508509139 / 5000000000000000000000 : ℚ))) + (U' := (3062560601583491490861 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (2109968084288231 / 10000000000000000 : ℚ)) + (q := (18450605960057299 / 80000000000000000 : ℚ)) + (U := (-(7334647102916508509139 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_10 : Uω (aρ 10) (bρ 10) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -1005,26 +890,21 @@ lemma U_390_10 : have hlg : Real.log (2657961919588723 / 16000000000000000 : ℝ) ≤ (-(17950290879875761555441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2657961919588723 / 16000000000000000 : ℝ) = - (2657961919588723 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2657961919588723 / 2000000000000000 : ℚ)) - (U := (2844124529124238444559 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2657961919588723 / 2000000000000000 : ℝ) ≤ - (2844124529124238444559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (120832802725481 / 1000000000000000 : ℝ)) (q := - (2657961919588723 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2657961919588723 / 16000000000000000 : ℚ)) + (r' := (2657961919588723 / 2000000000000000 : ℚ)) + (U := (-(17950290879875761555441 / 10000000000000000000000 : ℚ))) + (U' := (2844124529124238444559 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4928305764699 / 12800000000000 : ℚ)) + (s := (120832802725481 / 1000000000000000 : ℚ)) + (q := (2657961919588723 / 16000000000000000 : ℚ)) + (U := (-(17950290879875761555441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_390_11 : Uω (aρ 11) (bρ 11) (4928305764699 / 12800000000000 : ℝ) ≤ @@ -1146,25 +1026,21 @@ lemma U_391_1 : have hlg : Real.log (15195119629879051 / 40000000000000000 : ℝ) ≤ (-(9679051542797064085659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15195119629879051 / 40000000000000000 : ℝ) = - (15195119629879051 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15195119629879051 / 10000000000000000 : ℚ)) - (U := (4183892063202935914341 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15195119629879051 / 10000000000000000 : ℝ) ≤ - (4183892063202935914341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3798737349625463 / 10000000000000000 : ℝ)) (q := - (15195119629879051 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15195119629879051 / 40000000000000000 : ℚ)) + (r' := (15195119629879051 / 10000000000000000 : ℚ)) + (U := (-(9679051542797064085659 / 10000000000000000000000 : ℚ))) + (U' := (4183892063202935914341 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (3798737349625463 / 10000000000000000 : ℚ)) + (q := (15195119629879051 / 40000000000000000 : ℚ)) + (U := (-(9679051542797064085659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_2 : Uω (aρ 2) (bρ 2) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1172,25 +1048,21 @@ lemma U_391_2 : have hlg : Real.log (15099089582401141 / 40000000000000000 : ℝ) ≤ (-(608903127591907559467 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15099089582401141 / 40000000000000000 : ℝ) = - (15099089582401141 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15099089582401141 / 10000000000000000 : ℚ)) - (U := (257530847783092440533 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15099089582401141 / 10000000000000000 : ℝ) ≤ - (257530847783092440533 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (943622834599127 / 2500000000000000 : ℝ)) (q := - (15099089582401141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15099089582401141 / 40000000000000000 : ℚ)) + (r' := (15099089582401141 / 10000000000000000 : ℚ)) + (U := (-(608903127591907559467 / 625000000000000000000 : ℚ))) + (U' := (257530847783092440533 / 625000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (943622834599127 / 2500000000000000 : ℚ)) + (q := (15099089582401141 / 40000000000000000 : ℚ)) + (U := (-(608903127591907559467 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_3 : Uω (aρ 3) (bρ 3) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1198,25 +1070,21 @@ lemma U_391_3 : have hlg : Real.log (596266361461553 / 1600000000000000 : ℝ) ≤ (-(4935357126377696842237 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (596266361461553 / 1600000000000000 : ℝ) = - (596266361461553 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (596266361461553 / 400000000000000 : ℚ)) - (U := (1996114676622303157763 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (596266361461553 / 400000000000000 : ℝ) ≤ - (1996114676622303157763 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (74513443436307 / 200000000000000 : ℝ)) (q := - (596266361461553 / 1600000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (596266361461553 / 1600000000000000 : ℚ)) + (r' := (596266361461553 / 400000000000000 : ℚ)) + (U := (-(4935357126377696842237 / 5000000000000000000000 : ℚ))) + (U' := (1996114676622303157763 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (74513443436307 / 200000000000000 : ℚ)) + (q := (596266361461553 / 1600000000000000 : ℚ)) + (U := (-(4935357126377696842237 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_4 : Uω (aρ 4) (bρ 4) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1224,25 +1092,21 @@ lemma U_391_4 : have hlg : Real.log (14585912178574077 / 40000000000000000 : ℝ) ≤ (-(10088233099897932006419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14585912178574077 / 40000000000000000 : ℝ) = - (14585912178574077 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14585912178574077 / 10000000000000000 : ℚ)) - (U := (3774710506102067993581 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14585912178574077 / 10000000000000000 : ℝ) ≤ - (3774710506102067993581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (455449115487247 / 1250000000000000 : ℝ)) (q := - (14585912178574077 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14585912178574077 / 40000000000000000 : ℚ)) + (r' := (14585912178574077 / 10000000000000000 : ℚ)) + (U := (-(10088233099897932006419 / 10000000000000000000000 : ℚ))) + (U' := (3774710506102067993581 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (455449115487247 / 1250000000000000 : ℚ)) + (q := (14585912178574077 / 40000000000000000 : ℚ)) + (U := (-(10088233099897932006419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_5 : Uω (aρ 5) (bρ 5) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1250,25 +1114,21 @@ lemma U_391_5 : have hlg : Real.log (14094464447323703 / 40000000000000000 : ℝ) ≤ (-(10430973256828805279317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14094464447323703 / 40000000000000000 : ℝ) = - (14094464447323703 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14094464447323703 / 10000000000000000 : ℚ)) - (U := (3431970349171194720683 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14094464447323703 / 10000000000000000 : ℝ) ≤ - (3431970349171194720683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3516058977607789 / 10000000000000000 : ℝ)) (q := - (14094464447323703 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14094464447323703 / 40000000000000000 : ℚ)) + (r' := (14094464447323703 / 10000000000000000 : ℚ)) + (U := (-(10430973256828805279317 / 10000000000000000000000 : ℚ))) + (U' := (3431970349171194720683 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (3516058977607789 / 10000000000000000 : ℚ)) + (q := (14094464447323703 / 40000000000000000 : ℚ)) + (U := (-(10430973256828805279317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_6 : Uω (aρ 6) (bρ 6) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1276,25 +1136,21 @@ lemma U_391_6 : have hlg : Real.log (13382367932049789 / 40000000000000000 : ℝ) ≤ (-(1094941439062756986717 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13382367932049789 / 40000000000000000 : ℝ) = - (13382367932049789 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13382367932049789 / 10000000000000000 : ℚ)) - (U := (291352921537243013283 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13382367932049789 / 10000000000000000 : ℝ) ≤ - (291352921537243013283 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207953193444427 / 625000000000000 : ℝ)) (q := - (13382367932049789 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13382367932049789 / 40000000000000000 : ℚ)) + (r' := (13382367932049789 / 10000000000000000 : ℚ)) + (U := (-(1094941439062756986717 / 1000000000000000000000 : ℚ))) + (U' := (291352921537243013283 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (207953193444427 / 625000000000000 : ℚ)) + (q := (13382367932049789 / 40000000000000000 : ℚ)) + (U := (-(1094941439062756986717 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_7 : Uω (aρ 7) (bρ 7) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1302,25 +1158,21 @@ lemma U_391_7 : have hlg : Real.log (12393677662625217 / 40000000000000000 : ℝ) ≤ (-(11716929769262015717329 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12393677662625217 / 40000000000000000 : ℝ) = - (12393677662625217 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12393677662625217 / 10000000000000000 : ℚ)) - (U := (2146013836737984282671 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12393677662625217 / 10000000000000000 : ℝ) ≤ - (2146013836737984282671 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1528283670579273 / 5000000000000000 : ℝ)) (q := - (12393677662625217 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12393677662625217 / 40000000000000000 : ℚ)) + (r' := (12393677662625217 / 10000000000000000 : ℚ)) + (U := (-(11716929769262015717329 / 10000000000000000000000 : ℚ))) + (U' := (2146013836737984282671 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (1528283670579273 / 5000000000000000 : ℚ)) + (q := (12393677662625217 / 40000000000000000 : ℚ)) + (U := (-(11716929769262015717329 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_8 : Uω (aρ 8) (bρ 8) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1328,25 +1180,21 @@ lemma U_391_8 : have hlg : Real.log (2212417122326671 / 8000000000000000 : ℝ) ≤ (-(12853559027970004128109 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2212417122326671 / 8000000000000000 : ℝ) = - (2212417122326671 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2212417122326671 / 2000000000000000 : ℚ)) - (U := (1009384578029995871891 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2212417122326671 / 2000000000000000 : ℝ) ≤ - (1009384578029995871891 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (534862593400523 / 2000000000000000 : ℝ)) (q := - (2212417122326671 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2212417122326671 / 8000000000000000 : ℚ)) + (r' := (2212417122326671 / 2000000000000000 : ℚ)) + (U := (-(12853559027970004128109 / 10000000000000000000000 : ℚ))) + (U' := (1009384578029995871891 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (534862593400523 / 2000000000000000 : ℚ)) + (q := (2212417122326671 / 8000000000000000 : ℚ)) + (U := (-(12853559027970004128109 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_9 : Uω (aρ 9) (bρ 9) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1354,25 +1202,21 @@ lemma U_391_9 : have hlg : Real.log (9282462741746189 / 40000000000000000 : ℝ) ≤ (-(14607525600897892519987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9282462741746189 / 40000000000000000 : ℝ) = - (9282462741746189 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9282462741746189 / 5000000000000000 : ℚ)) - (U := (6186889808102107480013 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9282462741746189 / 5000000000000000 : ℝ) ≤ - (6186889808102107480013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (265683395052379 / 1250000000000000 : ℝ)) (q := - (9282462741746189 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9282462741746189 / 40000000000000000 : ℚ)) + (r' := (9282462741746189 / 5000000000000000 : ℚ)) + (U := (-(14607525600897892519987 / 10000000000000000000000 : ℚ))) + (U' := (6186889808102107480013 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (265683395052379 / 1250000000000000 : ℚ)) + (q := (9282462741746189 / 40000000000000000 : ℚ)) + (U := (-(14607525600897892519987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_10 : Uω (aρ 10) (bρ 10) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1380,26 +1224,21 @@ lemma U_391_10 : have hlg : Real.log (1343310603680641 / 8000000000000000 : ℝ) ≤ (-(17843043740896604037687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1343310603680641 / 8000000000000000 : ℝ) = - (1343310603680641 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1343310603680641 / 1000000000000000 : ℚ)) - (U := (2951371668103395962313 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1343310603680641 / 1000000000000000 : ℝ) ≤ - (2951371668103395962313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61553566612127 / 500000000000000 : ℝ)) (q := - (1343310603680641 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1343310603680641 / 8000000000000000 : ℚ)) + (r' := (1343310603680641 / 1000000000000000 : ℚ)) + (U := (-(17843043740896604037687 / 10000000000000000000000 : ℚ))) + (U' := (2951371668103395962313 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (12362622986877 / 32000000000000 : ℚ)) + (s := (61553566612127 / 500000000000000 : ℚ)) + (q := (1343310603680641 / 8000000000000000 : ℚ)) + (U := (-(17843043740896604037687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_391_11 : Uω (aρ 11) (bρ 11) (12362622986877 / 32000000000000 : ℝ) ≤ @@ -1521,25 +1360,21 @@ lemma U_392_1 : have hlg : Real.log (30494886865928941 / 80000000000000000 : ℝ) ≤ (-(9644676083344422677201 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30494886865928941 / 80000000000000000 : ℝ) = - (30494886865928941 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30494886865928941 / 20000000000000000 : ℚ)) - (U := (4218267522655577322799 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30494886865928941 / 20000000000000000 : ℝ) ≤ - (4218267522655577322799 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (952954611610051 / 2500000000000000 : ℝ)) (q := - (30494886865928941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30494886865928941 / 80000000000000000 : ℚ)) + (r' := (30494886865928941 / 20000000000000000 : ℚ)) + (U := (-(9644676083344422677201 / 10000000000000000000000 : ℚ))) + (U' := (4218267522655577322799 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (952954611610051 / 2500000000000000 : ℚ)) + (q := (30494886865928941 / 80000000000000000 : ℚ)) + (U := (-(9644676083344422677201 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_2 : Uω (aρ 2) (bρ 2) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1547,25 +1382,21 @@ lemma U_392_2 : have hlg : Real.log (30302833367924369 / 80000000000000000 : ℝ) ≤ (-(4853927077589738354537 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30302833367924369 / 80000000000000000 : ℝ) = - (30302833367924369 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30302833367924369 / 20000000000000000 : ℚ)) - (U := (2077544725410261645463 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30302833367924369 / 20000000000000000 : ℝ) ≤ - (2077544725410261645463 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3787574084449061 / 10000000000000000 : ℝ)) (q := - (30302833367924369 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30302833367924369 / 80000000000000000 : ℚ)) + (r' := (30302833367924369 / 20000000000000000 : ℚ)) + (U := (-(4853927077589738354537 / 5000000000000000000000 : ℚ))) + (U' := (2077544725410261645463 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (3787574084449061 / 10000000000000000 : ℚ)) + (q := (30302833367924369 / 80000000000000000 : ℚ)) + (U := (-(4853927077589738354537 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_3 : Uω (aρ 3) (bρ 3) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1573,25 +1404,21 @@ lemma U_392_3 : have hlg : Real.log (5983598458612137 / 16000000000000000 : ℝ) ≤ (-(983566585803844534669 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5983598458612137 / 16000000000000000 : ℝ) = - (5983598458612137 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5983598458612137 / 4000000000000000 : ℚ)) - (U := (402727774796155465331 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5983598458612137 / 4000000000000000 : ℝ) ≤ - (402727774796155465331 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (186937996104157 / 500000000000000 : ℝ)) (q := - (5983598458612137 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5983598458612137 / 16000000000000000 : ℚ)) + (r' := (5983598458612137 / 4000000000000000 : ℚ)) + (U := (-(983566585803844534669 / 1000000000000000000000 : ℚ))) + (U' := (402727774796155465331 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (186937996104157 / 500000000000000 : ℚ)) + (q := (5983598458612137 / 16000000000000000 : ℚ)) + (U := (-(983566585803844534669 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_4 : Uω (aρ 4) (bρ 4) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1599,25 +1426,21 @@ lemma U_392_4 : have hlg : Real.log (29276553360926369 / 80000000000000000 : ℝ) ≤ (-(10052396650727247046407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29276553360926369 / 80000000000000000 : ℝ) = - (29276553360926369 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29276553360926369 / 20000000000000000 : ℚ)) - (U := (3810546955272752953593 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29276553360926369 / 20000000000000000 : ℝ) ≤ - (3810546955272752953593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3656694370114561 / 10000000000000000 : ℝ)) (q := - (29276553360926369 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29276553360926369 / 80000000000000000 : ℚ)) + (r' := (29276553360926369 / 20000000000000000 : ℚ)) + (U := (-(10052396650727247046407 / 10000000000000000000000 : ℚ))) + (U' := (3810546955272752953593 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (3656694370114561 / 10000000000000000 : ℚ)) + (q := (29276553360926369 / 80000000000000000 : ℚ)) + (U := (-(10052396650727247046407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_5 : Uω (aρ 5) (bρ 5) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1625,25 +1448,21 @@ lemma U_392_5 : have hlg : Real.log (28293799415661033 / 80000000000000000 : ℝ) ≤ (-(10393839554312362094071 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28293799415661033 / 80000000000000000 : ℝ) = - (28293799415661033 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28293799415661033 / 20000000000000000 : ℚ)) - (U := (3469104051687637905929 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28293799415661033 / 20000000000000000 : ℝ) ≤ - (3469104051687637905929 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3529195803133227 / 10000000000000000 : ℝ)) (q := - (28293799415661033 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28293799415661033 / 80000000000000000 : ℚ)) + (r' := (28293799415661033 / 20000000000000000 : ℚ)) + (U := (-(10393839554312362094071 / 10000000000000000000000 : ℚ))) + (U' := (3469104051687637905929 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (3529195803133227 / 10000000000000000 : ℚ)) + (q := (28293799415661033 / 80000000000000000 : ℚ)) + (U := (-(10393839554312362094071 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_6 : Uω (aρ 6) (bρ 6) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1651,25 +1470,21 @@ lemma U_392_6 : have hlg : Real.log (1074798275030437 / 3200000000000000 : ℝ) ≤ (-(5455089082246591798157 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1074798275030437 / 3200000000000000 : ℝ) = - (1074798275030437 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1074798275030437 / 800000000000000 : ℚ)) - (U := (1476382720753408201843 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1074798275030437 / 800000000000000 : ℝ) ≤ - (1476382720753408201843 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16702377716491 / 50000000000000 : ℝ)) (q := - (1074798275030437 / 3200000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1074798275030437 / 3200000000000000 : ℚ)) + (r' := (1074798275030437 / 800000000000000 : ℚ)) + (U := (-(5455089082246591798157 / 5000000000000000000000 : ℚ))) + (U' := (1476382720753408201843 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (16702377716491 / 50000000000000 : ℚ)) + (q := (1074798275030437 / 3200000000000000 : ℚ)) + (U := (-(5455089082246591798157 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_7 : Uω (aρ 7) (bρ 7) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1677,25 +1492,21 @@ lemma U_392_7 : have hlg : Real.log (24893428446483941 / 80000000000000000 : ℝ) ≤ (-(11674227833276534326773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24893428446483941 / 80000000000000000 : ℝ) = - (24893428446483941 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24893428446483941 / 20000000000000000 : ℚ)) - (U := (2188715772723465673227 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24893428446483941 / 20000000000000000 : ℝ) ≤ - (2188715772723465673227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1535002408369477 / 5000000000000000 : ℝ)) (q := - (24893428446483941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24893428446483941 / 80000000000000000 : ℚ)) + (r' := (24893428446483941 / 20000000000000000 : ℚ)) + (U := (-(11674227833276534326773 / 10000000000000000000000 : ℚ))) + (U' := (2188715772723465673227 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (1535002408369477 / 5000000000000000 : ℚ)) + (q := (24893428446483941 / 80000000000000000 : ℚ)) + (U := (-(11674227833276534326773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_8 : Uω (aρ 8) (bρ 8) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1703,25 +1514,21 @@ lemma U_392_8 : have hlg : Real.log (22232368708121793 / 80000000000000000 : ℝ) ≤ (-(12804773572830401849953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22232368708121793 / 80000000000000000 : ℝ) = - (22232368708121793 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22232368708121793 / 20000000000000000 : ℚ)) - (U := (1058170033169598150047 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22232368708121793 / 20000000000000000 : ℝ) ≤ - (1058170033169598150047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2688281533488417 / 10000000000000000 : ℝ)) (q := - (22232368708121793 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22232368708121793 / 80000000000000000 : ℚ)) + (r' := (22232368708121793 / 20000000000000000 : ℚ)) + (U := (-(12804773572830401849953 / 10000000000000000000000 : ℚ))) + (U' := (1058170033169598150047 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (2688281533488417 / 10000000000000000 : ℚ)) + (q := (22232368708121793 / 80000000000000000 : ℚ)) + (U := (-(12804773572830401849953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_9 : Uω (aρ 9) (bρ 9) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1729,25 +1536,21 @@ lemma U_392_9 : have hlg : Real.log (18679115879380353 / 80000000000000000 : ℝ) ≤ (-(14546205320110649728969 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18679115879380353 / 80000000000000000 : ℝ) = - (18679115879380353 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18679115879380353 / 10000000000000000 : ℚ)) - (U := (6248210088889350271031 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18679115879380353 / 10000000000000000 : ℝ) ≤ - (6248210088889350271031 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2140933954663057 / 10000000000000000 : ℝ)) (q := - (18679115879380353 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18679115879380353 / 80000000000000000 : ℚ)) + (r' := (18679115879380353 / 10000000000000000 : ℚ)) + (U := (-(14546205320110649728969 / 10000000000000000000000 : ℚ))) + (U' := (6248210088889350271031 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (2140933954663057 / 10000000000000000 : ℚ)) + (q := (18679115879380353 / 80000000000000000 : ℚ)) + (U := (-(14546205320110649728969 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_10 : Uω (aρ 10) (bρ 10) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1755,26 +1558,21 @@ lemma U_392_10 : have hlg : Real.log (13575298042598981 / 80000000000000000 : ℝ) ≤ (-(8868874065295747246851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13575298042598981 / 80000000000000000 : ℝ) = - (13575298042598981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13575298042598981 / 10000000000000000 : ℚ)) - (U := (1528333639204252753149 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13575298042598981 / 10000000000000000 : ℝ) ≤ - (1528333639204252753149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626769264481357 / 5000000000000000 : ℝ)) (q := - (13575298042598981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13575298042598981 / 80000000000000000 : ℚ)) + (r' := (13575298042598981 / 10000000000000000 : ℚ)) + (U := (-(8868874065295747246851 / 5000000000000000000000 : ℚ))) + (U' := (1528333639204252753149 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (24808963124013 / 64000000000000 : ℚ)) + (s := (626769264481357 / 5000000000000000 : ℚ)) + (q := (13575298042598981 / 80000000000000000 : ℚ)) + (U := (-(8868874065295747246851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_392_11 : Uω (aρ 11) (bρ 11) (24808963124013 / 64000000000000 : ℝ) ≤ @@ -1896,25 +1694,21 @@ lemma U_393_1 : have hlg : Real.log (3824941808013551 / 10000000000000000 : ℝ) ≤ (-(9610418389026122523323 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3824941808013551 / 10000000000000000 : ℝ) = - (3824941808013551 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3824941808013551 / 2500000000000000 : ℚ)) - (U := (4252525216973877476677 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3824941808013551 / 2500000000000000 : ℝ) ≤ - (4252525216973877476677 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1912449770628551 / 5000000000000000 : ℝ)) (q := - (3824941808013551 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3824941808013551 / 10000000000000000 : ℚ)) + (r' := (3824941808013551 / 2500000000000000 : ℚ)) + (U := (-(9610418389026122523323 / 10000000000000000000000 : ℚ))) + (U' := (4252525216973877476677 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (1912449770628551 / 5000000000000000 : ℚ)) + (q := (3824941808013551 / 10000000000000000 : ℚ)) + (U := (-(9610418389026122523323 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_2 : Uω (aρ 2) (bρ 2) (777896258571 / 2000000000000 : ℝ) ≤ @@ -1922,25 +1716,21 @@ lemma U_393_2 : have hlg : Real.log (3800935939698811 / 10000000000000000 : ℝ) ≤ (-(9673377561479211552663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3800935939698811 / 10000000000000000 : ℝ) = - (3800935939698811 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3800935939698811 / 2500000000000000 : ℚ)) - (U := (4189566044520788447337 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3800935939698811 / 2500000000000000 : ℝ) ≤ - (4189566044520788447337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1900328408568811 / 5000000000000000 : ℝ)) (q := - (3800935939698811 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3800935939698811 / 10000000000000000 : ℚ)) + (r' := (3800935939698811 / 2500000000000000 : ℚ)) + (U := (-(9673377561479211552663 / 10000000000000000000000 : ℚ))) + (U' := (4189566044520788447337 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (1900328408568811 / 5000000000000000 : ℚ)) + (q := (3800935939698811 / 10000000000000000 : ℚ)) + (U := (-(9673377561479211552663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_3 : Uω (aρ 3) (bρ 3) (777896258571 / 2000000000000 : ℝ) ≤ @@ -1948,25 +1738,21 @@ lemma U_393_3 : have hlg : Real.log (7505666579816867 / 20000000000000000 : ℝ) ≤ (-(4900369968979588461839 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7505666579816867 / 20000000000000000 : ℝ) = - (7505666579816867 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7505666579816867 / 5000000000000000 : ℚ)) - (U := (2031101834020411538161 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7505666579816867 / 5000000000000000 : ℝ) ≤ - (2031101834020411538161 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3751847623906867 / 10000000000000000 : ℝ)) (q := - (7505666579816867 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7505666579816867 / 20000000000000000 : ℚ)) + (r' := (7505666579816867 / 5000000000000000 : ℚ)) + (U := (-(4900369968979588461839 / 5000000000000000000000 : ℚ))) + (U' := (2031101834020411538161 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (3751847623906867 / 10000000000000000 : ℚ)) + (q := (7505666579816867 / 20000000000000000 : ℚ)) + (U := (-(4900369968979588461839 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_4 : Uω (aρ 4) (bρ 4) (777896258571 / 2000000000000 : ℝ) ≤ @@ -1974,25 +1760,21 @@ lemma U_393_4 : have hlg : Real.log (7345320443908921 / 20000000000000000 : ℝ) ≤ (-(10016688368706092780689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7345320443908921 / 20000000000000000 : ℝ) = - (7345320443908921 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7345320443908921 / 5000000000000000 : ℚ)) - (U := (3846255237293907219311 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7345320443908921 / 5000000000000000 : ℝ) ≤ - (3846255237293907219311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3669795669063921 / 10000000000000000 : ℝ)) (q := - (7345320443908921 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7345320443908921 / 20000000000000000 : ℚ)) + (r' := (7345320443908921 / 5000000000000000 : ℚ)) + (U := (-(10016688368706092780689 / 10000000000000000000000 : ℚ))) + (U' := (3846255237293907219311 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (3669795669063921 / 10000000000000000 : ℚ)) + (q := (7345320443908921 / 20000000000000000 : ℚ)) + (U := (-(10016688368706092780689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_5 : Uω (aρ 5) (bρ 5) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2000,25 +1782,21 @@ lemma U_393_5 : have hlg : Real.log (7099667069545649 / 20000000000000000 : ℝ) ≤ (-(1294605477124456972273 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7099667069545649 / 20000000000000000 : ℝ) = - (7099667069545649 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7099667069545649 / 5000000000000000 : ℚ)) - (U := (438262473625543027727 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7099667069545649 / 5000000000000000 : ℝ) ≤ - (438262473625543027727 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3542332214035649 / 10000000000000000 : ℝ)) (q := - (7099667069545649 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7099667069545649 / 20000000000000000 : ℚ)) + (r' := (7099667069545649 / 5000000000000000 : ℚ)) + (U := (-(1294605477124456972273 / 1250000000000000000000 : ℚ))) + (U' := (438262473625543027727 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (3542332214035649 / 10000000000000000 : ℚ)) + (q := (7099667069545649 / 20000000000000000 : ℚ)) + (U := (-(1294605477124456972273 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_6 : Uω (aρ 6) (bρ 6) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2026,25 +1804,21 @@ lemma U_393_6 : have hlg : Real.log (1685948336291547 / 5000000000000000 : ℝ) ≤ (-(10871096955729972325563 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1685948336291547 / 5000000000000000 : ℝ) = - (1685948336291547 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1685948336291547 / 1250000000000000 : ℚ)) - (U := (2991846650270027674437 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1685948336291547 / 1250000000000000 : ℝ) ≤ - (2991846650270027674437 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (838424716199047 / 2500000000000000 : ℝ)) (q := - (1685948336291547 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1685948336291547 / 5000000000000000 : ℚ)) + (r' := (1685948336291547 / 1250000000000000 : ℚ)) + (U := (-(10871096955729972325563 / 10000000000000000000000 : ℚ))) + (U' := (2991846650270027674437 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (838424716199047 / 2500000000000000 : ℚ)) + (q := (1685948336291547 / 5000000000000000 : ℚ)) + (U := (-(10871096955729972325563 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_7 : Uω (aρ 7) (bρ 7) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2052,25 +1826,21 @@ lemma U_393_7 : have hlg : Real.log (3124936162240121 / 10000000000000000 : ℝ) ≤ (-(5815856187888038278651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3124936162240121 / 10000000000000000 : ℝ) = - (3124936162240121 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3124936162240121 / 2500000000000000 : ℚ)) - (U := (1115615615111961721349 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3124936162240121 / 2500000000000000 : ℝ) ≤ - (1115615615111961721349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1541719612435121 / 5000000000000000 : ℝ)) (q := - (3124936162240121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3124936162240121 / 10000000000000000 : ℚ)) + (r' := (3124936162240121 / 2500000000000000 : ℚ)) + (U := (-(5815856187888038278651 / 5000000000000000000000 : ℚ))) + (U' := (1115615615111961721349 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (1541719612435121 / 5000000000000000 : ℚ)) + (q := (3124936162240121 / 10000000000000000 : ℚ)) + (U := (-(5815856187888038278651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_8 : Uω (aρ 8) (bρ 8) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2078,25 +1848,21 @@ lemma U_393_8 : have hlg : Real.log (5585132661784443 / 20000000000000000 : ℝ) ≤ (-(6378120437829771179201 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5585132661784443 / 20000000000000000 : ℝ) = - (5585132661784443 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5585132661784443 / 5000000000000000 : ℚ)) - (U := (553351365170228820799 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5585132661784443 / 5000000000000000 : ℝ) ≤ - (553351365170228820799 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2702241213514443 / 10000000000000000 : ℝ)) (q := - (5585132661784443 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5585132661784443 / 20000000000000000 : ℚ)) + (r' := (5585132661784443 / 5000000000000000 : ℚ)) + (U := (-(6378120437829771179201 / 5000000000000000000000 : ℚ))) + (U' := (553351365170228820799 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (2702241213514443 / 10000000000000000 : ℚ)) + (q := (5585132661784443 / 20000000000000000 : ℚ)) + (U := (-(6378120437829771179201 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_9 : Uω (aρ 9) (bρ 9) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2104,25 +1870,21 @@ lemma U_393_9 : have hlg : Real.log (4698294981566537 / 20000000000000000 : ℝ) ≤ (-(7242662998772565864273 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4698294981566537 / 20000000000000000 : ℝ) = - (4698294981566537 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4698294981566537 / 2500000000000000 : ℚ)) - (U := (3154544705727434135727 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4698294981566537 / 2500000000000000 : ℝ) ≤ - (3154544705727434135727 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2156369161656537 / 10000000000000000 : ℝ)) (q := - (4698294981566537 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4698294981566537 / 20000000000000000 : ℚ)) + (r' := (4698294981566537 / 2500000000000000 : ℚ)) + (U := (-(7242662998772565864273 / 5000000000000000000000 : ℚ))) + (U' := (3154544705727434135727 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (2156369161656537 / 10000000000000000 : ℚ)) + (q := (4698294981566537 / 20000000000000000 : ℚ)) + (U := (-(7242662998772565864273 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_10 : Uω (aρ 10) (bρ 10) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2130,26 +1892,21 @@ lemma U_393_10 : have hlg : Real.log (3429110991584379 / 20000000000000000 : ℝ) ≤ (-(17634312313178388895607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3429110991584379 / 20000000000000000 : ℝ) = - (3429110991584379 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3429110991584379 / 2500000000000000 : ℚ)) - (U := (3160103095821611104393 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3429110991584379 / 2500000000000000 : ℝ) ≤ - (3160103095821611104393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1275744205169379 / 10000000000000000 : ℝ)) (q := - (3429110991584379 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3429110991584379 / 20000000000000000 : ℚ)) + (r' := (3429110991584379 / 2500000000000000 : ℚ)) + (U := (-(17634312313178388895607 / 10000000000000000000000 : ℚ))) + (U' := (3160103095821611104393 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (777896258571 / 2000000000000 : ℚ)) + (s := (1275744205169379 / 10000000000000000 : ℚ)) + (q := (3429110991584379 / 20000000000000000 : ℚ)) + (U := (-(17634312313178388895607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_393_11 : Uω (aρ 11) (bρ 11) (777896258571 / 2000000000000 : ℝ) ≤ @@ -2271,25 +2028,21 @@ lemma U_394_1 : have hlg : Real.log (30704182054378223 / 80000000000000000 : ℝ) ≤ (-(478813882784368812437 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30704182054378223 / 80000000000000000 : ℝ) = - (30704182054378223 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30704182054378223 / 20000000000000000 : ℚ)) - (U := (214333297515631187563 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30704182054378223 / 20000000000000000 : ℝ) ≤ - (214333297515631187563 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3837980634096587 / 10000000000000000 : ℝ)) (q := - (30704182054378223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30704182054378223 / 80000000000000000 : ℚ)) + (r' := (30704182054378223 / 20000000000000000 : ℚ)) + (U := (-(478813882784368812437 / 500000000000000000000 : ℚ))) + (U' := (214333297515631187563 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (3837980634096587 / 10000000000000000 : ℚ)) + (q := (30704182054378223 / 80000000000000000 : ℚ)) + (U := (-(478813882784368812437 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_2 : Uω (aρ 2) (bρ 2) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2297,25 +2050,21 @@ lemma U_394_2 : have hlg : Real.log (1220485664574031 / 3200000000000000 : ℝ) ≤ (-(4819509720196513865331 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1220485664574031 / 3200000000000000 : ℝ) = - (1220485664574031 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1220485664574031 / 800000000000000 : ℚ)) - (U := (2111962082803486134669 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1220485664574031 / 800000000000000 : ℝ) ≤ - (2111962082803486134669 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152549581463989 / 400000000000000 : ℝ)) (q := - (1220485664574031 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1220485664574031 / 3200000000000000 : ℚ)) + (r' := (1220485664574031 / 800000000000000 : ℚ)) + (U := (-(4819509720196513865331 / 5000000000000000000000 : ℚ))) + (U' := (2111962082803486134669 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (152549581463989 / 400000000000000 : ℚ)) + (q := (1220485664574031 / 3200000000000000 : ℚ)) + (U := (-(4819509720196513865331 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_3 : Uω (aρ 3) (bρ 3) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2323,25 +2072,21 @@ lemma U_394_3 : have hlg : Real.log (30127340153718827 / 80000000000000000 : ℝ) ≤ (-(152592744360776913309 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30127340153718827 / 80000000000000000 : ℝ) = - (30127340153718827 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30127340153718827 / 20000000000000000 : ℚ)) - (U := (64015749482973086691 / 156250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30127340153718827 / 20000000000000000 : ℝ) ≤ - (64015749482973086691 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1882467638895869 / 5000000000000000 : ℝ)) (q := - (30127340153718827 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30127340153718827 / 80000000000000000 : ℚ)) + (r' := (30127340153718827 / 20000000000000000 : ℚ)) + (U := (-(152592744360776913309 / 156250000000000000000 : ℚ))) + (U' := (64015749482973086691 / 156250000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (1882467638895869 / 5000000000000000 : ℚ)) + (q := (30127340153718827 / 80000000000000000 : ℚ)) + (U := (-(152592744360776913309 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_4 : Uω (aρ 4) (bρ 4) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2349,25 +2094,21 @@ lemma U_394_4 : have hlg : Real.log (29486009607562647 / 80000000000000000 : ℝ) ≤ (-(1247638417364616165651 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29486009607562647 / 80000000000000000 : ℝ) = - (29486009607562647 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29486009607562647 / 20000000000000000 : ℚ)) - (U := (485229533385383834349 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29486009607562647 / 20000000000000000 : ℝ) ≤ - (485229533385383834349 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3682896822317693 / 10000000000000000 : ℝ)) (q := - (29486009607562647 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29486009607562647 / 80000000000000000 : ℚ)) + (r' := (29486009607562647 / 20000000000000000 : ℚ)) + (U := (-(1247638417364616165651 / 1250000000000000000000 : ℚ))) + (U' := (485229533385383834349 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (3682896822317693 / 10000000000000000 : ℚ)) + (q := (29486009607562647 / 80000000000000000 : ℚ)) + (U := (-(1247638417364616165651 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_5 : Uω (aρ 5) (bρ 5) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2375,25 +2116,21 @@ lemma U_394_5 : have hlg : Real.log (28503535500595011 / 80000000000000000 : ℝ) ≤ (-(10319985019208236224207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28503535500595011 / 80000000000000000 : ℝ) = - (28503535500595011 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28503535500595011 / 20000000000000000 : ℚ)) - (U := (3542958586791763775793 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28503535500595011 / 20000000000000000 : ℝ) ≤ - (3542958586791763775793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55554190857981 / 156250000000000 : ℝ)) (q := - (28503535500595011 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28503535500595011 / 80000000000000000 : ℚ)) + (r' := (28503535500595011 / 20000000000000000 : ℚ)) + (U := (-(10319985019208236224207 / 10000000000000000000000 : ℚ))) + (U' := (3542958586791763775793 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (55554190857981 / 156250000000000 : ℚ)) + (q := (28503535500595011 / 80000000000000000 : ℚ)) + (U := (-(10319985019208236224207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_6 : Uω (aρ 6) (bρ 6) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2401,25 +2138,21 @@ lemma U_394_6 : have hlg : Real.log (27080385431910887 / 80000000000000000 : ℝ) ≤ (-(2708042382818369174677 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27080385431910887 / 80000000000000000 : ℝ) = - (27080385431910887 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27080385431910887 / 20000000000000000 : ℚ)) - (U := (757693518681630825323 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27080385431910887 / 20000000000000000 : ℝ) ≤ - (757693518681630825323 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3366921072879753 / 10000000000000000 : ℝ)) (q := - (27080385431910887 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27080385431910887 / 80000000000000000 : ℚ)) + (r' := (27080385431910887 / 20000000000000000 : ℚ)) + (U := (-(2708042382818369174677 / 2500000000000000000000 : ℚ))) + (U' := (757693518681630825323 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (3366921072879753 / 10000000000000000 : ℚ)) + (q := (27080385431910887 / 80000000000000000 : ℚ)) + (U := (-(2708042382818369174677 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_7 : Uω (aρ 7) (bρ 7) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2427,25 +2160,21 @@ lemma U_394_7 : have hlg : Real.log (25105538039242823 / 80000000000000000 : ℝ) ≤ (-(11589381733398019179671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25105538039242823 / 80000000000000000 : ℝ) = - (25105538039242823 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25105538039242823 / 20000000000000000 : ℚ)) - (U := (2273561872601980820329 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25105538039242823 / 20000000000000000 : ℝ) ≤ - (2273561872601980820329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3096870605472737 / 10000000000000000 : ℝ)) (q := - (25105538039242823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25105538039242823 / 80000000000000000 : ℚ)) + (r' := (25105538039242823 / 20000000000000000 : ℚ)) + (U := (-(11589381733398019179671 / 10000000000000000000000 : ℚ))) + (U' := (2273561872601980820329 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (3096870605472737 / 10000000000000000 : ℚ)) + (q := (25105538039242823 / 80000000000000000 : ℚ)) + (U := (-(11589381733398019179671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_8 : Uω (aρ 8) (bρ 8) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2453,25 +2182,21 @@ lemma U_394_8 : have hlg : Real.log (22448657588370731 / 80000000000000000 : ℝ) ≤ (-(12707958173717871882943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22448657588370731 / 80000000000000000 : ℝ) = - (22448657588370731 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22448657588370731 / 20000000000000000 : ℚ)) - (U := (1154985432282128117057 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22448657588370731 / 20000000000000000 : ℝ) ≤ - (1154985432282128117057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1358096072047357 / 5000000000000000 : ℝ)) (q := - (22448657588370731 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22448657588370731 / 80000000000000000 : ℚ)) + (r' := (22448657588370731 / 20000000000000000 : ℚ)) + (U := (-(12707958173717871882943 / 10000000000000000000000 : ℚ))) + (U' := (1154985432282128117057 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (1358096072047357 / 5000000000000000 : ℚ)) + (q := (22448657588370731 / 80000000000000000 : ℚ)) + (U := (-(12707958173717871882943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_9 : Uω (aρ 9) (bρ 9) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2479,25 +2204,21 @@ lemma U_394_9 : have hlg : Real.log (18907120318109339 / 80000000000000000 : ℝ) ≤ (-(14424880463678895676333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18907120318109339 / 80000000000000000 : ℝ) = - (18907120318109339 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18907120318109339 / 10000000000000000 : ℚ)) - (U := (6369534945321104323667 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18907120318109339 / 10000000000000000 : ℝ) ≤ - (6369534945321104323667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1085886727444683 / 5000000000000000 : ℝ)) (q := - (18907120318109339 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18907120318109339 / 80000000000000000 : ℚ)) + (r' := (18907120318109339 / 10000000000000000 : ℚ)) + (U := (-(14424880463678895676333 / 10000000000000000000000 : ℚ))) + (U' := (6369534945321104323667 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (1085886727444683 / 5000000000000000 : ℚ)) + (q := (18907120318109339 / 80000000000000000 : ℚ)) + (U := (-(14424880463678895676333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_10 : Uω (aρ 10) (bρ 10) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2505,26 +2226,21 @@ lemma U_394_10 : have hlg : Real.log (13856597508524971 / 80000000000000000 : ℝ) ≤ (-(2191581450344132072969 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13856597508524971 / 80000000000000000 : ℝ) = - (13856597508524971 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13856597508524971 / 10000000000000000 : ℚ)) - (U := (407720475780867927031 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13856597508524971 / 10000000000000000 : ℝ) ≤ - (407720475780867927031 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (648850892994137 / 5000000000000000 : ℝ)) (q := - (13856597508524971 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13856597508524971 / 80000000000000000 : ℚ)) + (r' := (13856597508524971 / 10000000000000000 : ℚ)) + (U := (-(2191581450344132072969 / 1250000000000000000000 : ℚ))) + (U' := (407720475780867927031 / 1250000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (24976397424531 / 64000000000000 : ℚ)) + (s := (648850892994137 / 5000000000000000 : ℚ)) + (q := (13856597508524971 / 80000000000000000 : ℚ)) + (U := (-(2191581450344132072969 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_394_11 : Uω (aρ 11) (bρ 11) (24976397424531 / 64000000000000 : ℝ) ≤ @@ -2646,25 +2362,21 @@ lemma U_395_1 : have hlg : Real.log (15404414818409489 / 40000000000000000 : ℝ) ≤ (-(1908450617476454881111 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15404414818409489 / 40000000000000000 : ℝ) = - (15404414818409489 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15404414818409489 / 10000000000000000 : ℚ)) - (U := (864138103723545118889 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15404414818409489 / 10000000000000000 : ℝ) ≤ - (864138103723545118889 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3851061724978807 / 10000000000000000 : ℝ)) (q := - (15404414818409489 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15404414818409489 / 40000000000000000 : ℚ)) + (r' := (15404414818409489 / 10000000000000000 : ℚ)) + (U := (-(1908450617476454881111 / 2000000000000000000000 : ℚ))) + (U' := (864138103723545118889 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (3851061724978807 / 10000000000000000 : ℚ)) + (q := (15404414818409489 / 40000000000000000 : ℚ)) + (U := (-(1908450617476454881111 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_2 : Uω (aρ 2) (bρ 2) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2672,25 +2384,21 @@ lemma U_395_2 : have hlg : Real.log (15308397829373917 / 40000000000000000 : ℝ) ≤ (-(9604778980370867307719 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15308397829373917 / 40000000000000000 : ℝ) = - (15308397829373917 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15308397829373917 / 10000000000000000 : ℚ)) - (U := (4258164625629132692281 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15308397829373917 / 10000000000000000 : ℝ) ≤ - (4258164625629132692281 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3826822242971021 / 10000000000000000 : ℝ)) (q := - (15308397829373917 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15308397829373917 / 40000000000000000 : ℚ)) + (r' := (15308397829373917 / 10000000000000000 : ℚ)) + (U := (-(9604778980370867307719 / 10000000000000000000000 : ℚ))) + (U' := (4258164625629132692281 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (3826822242971021 / 10000000000000000 : ℚ)) + (q := (15308397829373917 / 40000000000000000 : ℚ)) + (U := (-(9604778980370867307719 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_3 : Uω (aρ 3) (bρ 3) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2698,25 +2406,21 @@ lemma U_395_3 : have hlg : Real.log (15116006899203783 / 40000000000000000 : ℝ) ≤ (-(4865626058448077485459 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15116006899203783 / 40000000000000000 : ℝ) = - (15116006899203783 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15116006899203783 / 10000000000000000 : ℚ)) - (U := (2065845744551922514541 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15116006899203783 / 10000000000000000 : ℝ) ≤ - (2065845744551922514541 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1889011442117977 / 5000000000000000 : ℝ)) (q := - (15116006899203783 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15116006899203783 / 40000000000000000 : ℚ)) + (r' := (15116006899203783 / 10000000000000000 : ℚ)) + (U := (-(4865626058448077485459 / 5000000000000000000000 : ℚ))) + (U' := (2065845744551922514541 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (1889011442117977 / 5000000000000000 : ℚ)) + (q := (15116006899203783 / 40000000000000000 : ℚ)) + (U := (-(4865626058448077485459 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_4 : Uω (aρ 4) (bρ 4) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2724,25 +2428,21 @@ lemma U_395_4 : have hlg : Real.log (14795368431452299 / 40000000000000000 : ℝ) ≤ (-(9945652656219027259689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14795368431452299 / 40000000000000000 : ℝ) = - (14795368431452299 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14795368431452299 / 10000000000000000 : ℚ)) - (U := (3917290949780972740311 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14795368431452299 / 10000000000000000 : ℝ) ≤ - (3917290949780972740311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (923999457856303 / 2500000000000000 : ℝ)) (q := - (14795368431452299 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14795368431452299 / 40000000000000000 : ℚ)) + (r' := (14795368431452299 / 10000000000000000 : ℚ)) + (U := (-(9945652656219027259689 / 10000000000000000000000 : ℚ))) + (U' := (3917290949780972740311 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (923999457856303 / 2500000000000000 : ℚ)) + (q := (14795368431452299 / 40000000000000000 : ℚ)) + (U := (-(9945652656219027259689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_5 : Uω (aρ 5) (bρ 5) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2750,25 +2450,21 @@ lemma U_395_5 : have hlg : Real.log (2860840110100997 / 8000000000000000 : ℝ) ≤ (-(2570815536680449644243 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2860840110100997 / 8000000000000000 : ℝ) = - (2860840110100997 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2860840110100997 / 2000000000000000 : ℚ)) - (U := (894920364819550355757 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2860840110100997 / 2000000000000000 : ℝ) ≤ - (894920364819550355757 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (713720762057311 / 2000000000000000 : ℝ)) (q := - (2860840110100997 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2860840110100997 / 8000000000000000 : ℚ)) + (r' := (2860840110100997 / 2000000000000000 : ℚ)) + (U := (-(2570815536680449644243 / 2500000000000000000000 : ℚ))) + (U' := (894920364819550355757 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (713720762057311 / 2000000000000000 : ℚ)) + (q := (2860840110100997 / 8000000000000000 : ℚ)) + (U := (-(2570815536680449644243 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_6 : Uω (aρ 6) (bρ 6) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2776,25 +2472,21 @@ lemma U_395_6 : have hlg : Real.log (13592796540881929 / 40000000000000000 : ℝ) ≤ (-(2698348668215771873327 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13592796540881929 / 40000000000000000 : ℝ) = - (13592796540881929 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13592796540881929 / 10000000000000000 : ℚ)) - (U := (767387233284228126673 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13592796540881929 / 10000000000000000 : ℝ) ≤ - (767387233284228126673 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3380142180615027 / 10000000000000000 : ℝ)) (q := - (13592796540881929 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13592796540881929 / 40000000000000000 : ℚ)) + (r' := (13592796540881929 / 10000000000000000 : ℚ)) + (U := (-(2698348668215771873327 / 2500000000000000000000 : ℚ))) + (U' := (767387233284228126673 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (3380142180615027 / 10000000000000000 : ℚ)) + (q := (13592796540881929 / 40000000000000000 : ℚ)) + (U := (-(2698348668215771873327 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_7 : Uω (aρ 7) (bρ 7) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2802,25 +2494,21 @@ lemma U_395_7 : have hlg : Real.log (12605787413668453 / 40000000000000000 : ℝ) ≤ (-(11547234265459707690501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12605787413668453 / 40000000000000000 : ℝ) = - (12605787413668453 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12605787413668453 / 10000000000000000 : ℚ)) - (U := (2315709340540292309499 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12605787413668453 / 10000000000000000 : ℝ) ≤ - (2315709340540292309499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3110298997768289 / 10000000000000000 : ℝ)) (q := - (12605787413668453 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12605787413668453 / 40000000000000000 : ℚ)) + (r' := (12605787413668453 / 10000000000000000 : ℚ)) + (U := (-(11547234265459707690501 / 10000000000000000000000 : ℚ))) + (U' := (2315709340540292309499 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (3110298997768289 / 10000000000000000 : ℚ)) + (q := (12605787413668453 / 40000000000000000 : ℚ)) + (U := (-(11547234265459707690501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_8 : Uω (aρ 8) (bρ 8) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2828,25 +2516,21 @@ lemma U_395_8 : have hlg : Real.log (2255675006833453 / 8000000000000000 : ℝ) ≤ (-(6329961375780254349371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2255675006833453 / 8000000000000000 : ℝ) = - (2255675006833453 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2255675006833453 / 2000000000000000 : ℚ)) - (U := (601510427219745650629 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2255675006833453 / 2000000000000000 : ℝ) ≤ - (601510427219745650629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (546026891871539 / 2000000000000000 : ℝ)) (q := - (2255675006833453 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2255675006833453 / 8000000000000000 : ℚ)) + (r' := (2255675006833453 / 2000000000000000 : ℚ)) + (U := (-(6329961375780254349371 / 5000000000000000000000 : ℚ))) + (U' := (601510427219745650629 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (546026891871539 / 2000000000000000 : ℚ)) + (q := (2255675006833453 / 8000000000000000 : ℚ)) + (U := (-(6329961375780254349371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_9 : Uω (aρ 9) (bρ 9) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2854,25 +2538,21 @@ lemma U_395_9 : have hlg : Real.log (1902093966765393 / 8000000000000000 : ℝ) ≤ (-(14364861738092443484433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1902093966765393 / 8000000000000000 : ℝ) = - (1902093966765393 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1902093966765393 / 1000000000000000 : ℚ)) - (U := (6429553670907556515567 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1902093966765393 / 1000000000000000 : ℝ) ≤ - (6429553670907556515567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (437429497509509 / 2000000000000000 : ℝ)) (q := - (1902093966765393 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1902093966765393 / 8000000000000000 : ℚ)) + (r' := (1902093966765393 / 1000000000000000 : ℚ)) + (U := (-(14364861738092443484433 / 10000000000000000000000 : ℚ))) + (U' := (6429553670907556515567 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (437429497509509 / 2000000000000000 : ℚ)) + (q := (1902093966765393 / 8000000000000000 : ℚ)) + (U := (-(14364861738092443484433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_10 : Uω (aρ 10) (bρ 10) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -2880,26 +2560,21 @@ lemma U_395_10 : have hlg : Real.log (1399580821443121 / 8000000000000000 : ℝ) ≤ (-(4358171905916996388157 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1399580821443121 / 8000000000000000 : ℝ) = - (1399580821443121 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1399580821443121 / 1000000000000000 : ℚ)) - (U := (840431946333003611843 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1399580821443121 / 1000000000000000 : ℝ) ≤ - (840431946333003611843 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263884731547373 / 2000000000000000 : ℝ)) (q := - (1399580821443121 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1399580821443121 / 8000000000000000 : ℚ)) + (r' := (1399580821443121 / 1000000000000000 : ℚ)) + (U := (-(4358171905916996388157 / 2500000000000000000000 : ℚ))) + (U' := (840431946333003611843 / 2500000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2506011457479 / 6400000000000 : ℚ)) + (s := (263884731547373 / 2000000000000000 : ℚ)) + (q := (1399580821443121 / 8000000000000000 : ℚ)) + (U := (-(4358171905916996388157 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_395_11 : Uω (aρ 11) (bρ 11) (2506011457479 / 6400000000000 : ℝ) ≤ @@ -3021,25 +2696,21 @@ lemma U_396_1 : have hlg : Real.log (30913477211510189 / 80000000000000000 : ℝ) ≤ (-(9508343896262421957543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30913477211510189 / 80000000000000000 : ℝ) = - (30913477211510189 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30913477211510189 / 20000000000000000 : ℚ)) - (U := (4354599709737578042457 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30913477211510189 / 20000000000000000 : ℝ) ≤ - (4354599709737578042457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3864142813923641 / 10000000000000000 : ℝ)) (q := - (30913477211510189 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30913477211510189 / 80000000000000000 : ℚ)) + (r' := (30913477211510189 / 20000000000000000 : ℚ)) + (U := (-(9508343896262421957543 / 10000000000000000000000 : ℚ))) + (U' := (4354599709737578042457 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (3864142813923641 / 10000000000000000 : ℚ)) + (q := (30913477211510189 / 80000000000000000 : ℚ)) + (U := (-(9508343896262421957543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_2 : Uω (aρ 2) (bρ 2) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3047,25 +2718,21 @@ lemma U_396_2 : have hlg : Real.log (30721449651316873 / 80000000000000000 : ℝ) ≤ (-(4785327689087111628957 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30721449651316873 / 80000000000000000 : ℝ) = - (30721449651316873 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30721449651316873 / 20000000000000000 : ℚ)) - (U := (2146144113912888371043 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30721449651316873 / 20000000000000000 : ℝ) ≤ - (2146144113912888371043 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (119997029262041 / 312500000000000 : ℝ)) (q := - (30721449651316873 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30721449651316873 / 80000000000000000 : ℚ)) + (r' := (30721449651316873 / 20000000000000000 : ℚ)) + (U := (-(4785327689087111628957 / 5000000000000000000000 : ℚ))) + (U' := (2146144113912888371043 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (119997029262041 / 312500000000000 : ℚ)) + (q := (30721449651316873 / 80000000000000000 : ℚ)) + (U := (-(4785327689087111628957 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_3 : Uω (aρ 3) (bρ 3) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3073,25 +2740,21 @@ lemma U_396_3 : have hlg : Real.log (30336687255298973 / 80000000000000000 : ℝ) ≤ (-(9696688535615259549621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30336687255298973 / 80000000000000000 : ℝ) = - (30336687255298973 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30336687255298973 / 20000000000000000 : ℚ)) - (U := (4166255070384740450379 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30336687255298973 / 20000000000000000 : ℝ) ≤ - (4166255070384740450379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3791110443730837 / 10000000000000000 : ℝ)) (q := - (30336687255298973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30336687255298973 / 80000000000000000 : ℚ)) + (r' := (30336687255298973 / 20000000000000000 : ℚ)) + (U := (-(9696688535615259549621 / 10000000000000000000000 : ℚ))) + (U' := (4166255070384740450379 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (3791110443730837 / 10000000000000000 : ℚ)) + (q := (30336687255298973 / 80000000000000000 : ℚ)) + (U := (-(9696688535615259549621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_4 : Uω (aρ 4) (bρ 4) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3099,25 +2762,21 @@ lemma U_396_4 : have hlg : Real.log (29695463547771257 / 80000000000000000 : ℝ) ≤ (-(9910323425109448560787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29695463547771257 / 80000000000000000 : ℝ) = - (29695463547771257 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29695463547771257 / 20000000000000000 : ℚ)) - (U := (3952620180890551439213 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29695463547771257 / 20000000000000000 : ℝ) ≤ - (3952620180890551439213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (927274674478477 / 2500000000000000 : ℝ)) (q := - (29695463547771257 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29695463547771257 / 80000000000000000 : ℚ)) + (r' := (29695463547771257 / 20000000000000000 : ℚ)) + (U := (-(9910323425109448560787 / 10000000000000000000000 : ℚ))) + (U' := (3952620180890551439213 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (927274674478477 / 2500000000000000 : ℚ)) + (q := (29695463547771257 / 80000000000000000 : ℚ)) + (U := (-(9910323425109448560787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_5 : Uω (aρ 5) (bρ 5) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3125,25 +2784,21 @@ lemma U_396_5 : have hlg : Real.log (28713265097272909 / 80000000000000000 : ℝ) ≤ (-(10246674196579949227919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28713265097272909 / 80000000000000000 : ℝ) = - (28713265097272909 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28713265097272909 / 20000000000000000 : ℚ)) - (U := (3616269409420050772081 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28713265097272909 / 20000000000000000 : ℝ) ≤ - (3616269409420050772081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3581739004624321 / 10000000000000000 : ℝ)) (q := - (28713265097272909 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28713265097272909 / 80000000000000000 : ℚ)) + (r' := (28713265097272909 / 20000000000000000 : ℚ)) + (U := (-(10246674196579949227919 / 10000000000000000000000 : ℚ))) + (U' := (3616269409420050772081 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (3581739004624321 / 10000000000000000 : ℚ)) + (q := (28713265097272909 / 80000000000000000 : ℚ)) + (U := (-(10246674196579949227919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_6 : Uω (aρ 6) (bρ 6) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3151,25 +2806,21 @@ lemma U_396_6 : have hlg : Real.log (5458159276333873 / 16000000000000000 : ℝ) ≤ (-(5377385588401860750483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5458159276333873 / 16000000000000000 : ℝ) = - (5458159276333873 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5458159276333873 / 4000000000000000 : ℚ)) - (U := (1554086214598139249517 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5458159276333873 / 4000000000000000 : ℝ) ≤ - (1554086214598139249517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (678672440172687 / 2000000000000000 : ℝ)) (q := - (5458159276333873 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5458159276333873 / 16000000000000000 : ℚ)) + (r' := (5458159276333873 / 4000000000000000 : ℚ)) + (U := (-(5377385588401860750483 / 5000000000000000000000 : ℚ))) + (U' := (1554086214598139249517 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (678672440172687 / 2000000000000000 : ℚ)) + (q := (5458159276333873 / 16000000000000000 : ℚ)) + (U := (-(5377385588401860750483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_7 : Uω (aρ 7) (bρ 7) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3177,25 +2828,21 @@ lemma U_396_7 : have hlg : Real.log (25317599816358261 / 80000000000000000 : ℝ) ≤ (-(2876317088384850507541 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25317599816358261 / 80000000000000000 : ℝ) = - (25317599816358261 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25317599816358261 / 20000000000000000 : ℚ)) - (U := (589418813115149492459 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25317599816358261 / 20000000000000000 : ℝ) ≤ - (589418813115149492459 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3123724440295659 / 10000000000000000 : ℝ)) (q := - (25317599816358261 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25317599816358261 / 80000000000000000 : ℚ)) + (r' := (25317599816358261 / 20000000000000000 : ℚ)) + (U := (-(2876317088384850507541 / 2500000000000000000000 : ℚ))) + (U' := (589418813115149492459 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (3123724440295659 / 10000000000000000 : ℚ)) + (q := (25317599816358261 / 80000000000000000 : ℚ)) + (U := (-(2876317088384850507541 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_8 : Uω (aρ 8) (bρ 8) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3203,25 +2850,21 @@ lemma U_396_8 : have hlg : Real.log (22664808612311169 / 80000000000000000 : ℝ) ≤ (-(12612131939922347998239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22664808612311169 / 80000000000000000 : ℝ) = - (22664808612311169 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22664808612311169 / 20000000000000000 : ℚ)) - (U := (1250811666077652001761 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22664808612311169 / 20000000000000000 : ℝ) ≤ - (1250811666077652001761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1372034145311943 / 5000000000000000 : ℝ)) (q := - (22664808612311169 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22664808612311169 / 80000000000000000 : ℚ)) + (r' := (22664808612311169 / 20000000000000000 : ℚ)) + (U := (-(12612131939922347998239 / 10000000000000000000000 : ℚ))) + (U' := (1250811666077652001761 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (1372034145311943 / 5000000000000000 : ℚ)) + (q := (22664808612311169 / 80000000000000000 : ℚ)) + (U := (-(12612131939922347998239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_9 : Uω (aρ 9) (bρ 9) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3229,25 +2872,21 @@ lemma U_396_9 : have hlg : Real.log (19134640509631401 / 80000000000000000 : ℝ) ≤ (-(7152631511257893339269 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19134640509631401 / 80000000000000000 : ℝ) = - (19134640509631401 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19134640509631401 / 10000000000000000 : ℚ)) - (U := (3244576193242106660731 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19134640509631401 / 10000000000000000 : ℝ) ≤ - (3244576193242106660731 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (275311486664243 / 1250000000000000 : ℝ)) (q := - (19134640509631401 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19134640509631401 / 80000000000000000 : ℚ)) + (r' := (19134640509631401 / 10000000000000000 : ℚ)) + (U := (-(7152631511257893339269 / 5000000000000000000000 : ℚ))) + (U' := (3244576193242106660731 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (275311486664243 / 1250000000000000 : ℚ)) + (q := (19134640509631401 / 80000000000000000 : ℚ)) + (U := (-(7152631511257893339269 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_10 : Uω (aρ 10) (bρ 10) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3255,26 +2894,21 @@ lemma U_396_10 : have hlg : Real.log (14134121903874213 / 80000000000000000 : ℝ) ≤ (-(17334347667952915807461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14134121903874213 / 80000000000000000 : ℝ) = - (14134121903874213 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14134121903874213 / 10000000000000000 : ℚ)) - (U := (3460067741047084192539 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14134121903874213 / 10000000000000000 : ℝ) ≤ - (3460067741047084192539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1340921275369647 / 10000000000000000 : ℝ)) (q := - (14134121903874213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14134121903874213 / 80000000000000000 : ℚ)) + (r' := (14134121903874213 / 10000000000000000 : ℚ)) + (U := (-(17334347667952915807461 / 10000000000000000000000 : ℚ))) + (U' := (3460067741047084192539 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (25143831725049 / 64000000000000 : ℚ)) + (s := (1340921275369647 / 10000000000000000 : ℚ)) + (q := (14134121903874213 / 80000000000000000 : ℚ)) + (U := (-(17334347667952915807461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_396_11 : Uω (aρ 11) (bρ 11) (25143831725049 / 64000000000000 : ℝ) ≤ @@ -3396,25 +3030,21 @@ lemma U_397_1 : have hlg : Real.log (7754531194632573 / 20000000000000000 : ℝ) ≤ (-(9474549302467474731171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7754531194632573 / 20000000000000000 : ℝ) = - (7754531194632573 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7754531194632573 / 5000000000000000 : ℚ)) - (U := (4388394303532525268829 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7754531194632573 / 5000000000000000 : ℝ) ≤ - (4388394303532525268829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1938611950475349 / 5000000000000000 : ℝ)) (q := - (7754531194632573 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7754531194632573 / 20000000000000000 : ℚ)) + (r' := (7754531194632573 / 5000000000000000 : ℚ)) + (U := (-(9474549302467474731171 / 10000000000000000000000 : ℚ))) + (U' := (4388394303532525268829 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (1938611950475349 / 5000000000000000 : ℚ)) + (q := (7754531194632573 / 20000000000000000 : ℚ)) + (U := (-(9474549302467474731171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_2 : Uω (aρ 2) (bρ 2) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3422,25 +3052,21 @@ lemma U_397_2 : have hlg : Real.log (3853262949073229 / 10000000000000000 : ℝ) ≤ (-(2384161959690752671551 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3853262949073229 / 10000000000000000 : ℝ) = - (3853262949073229 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3853262949073229 / 2500000000000000 : ℚ)) - (U := (1081573941809247328449 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3853262949073229 / 2500000000000000 : ℝ) ≤ - (1081573941809247328449 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3852987616974583 / 10000000000000000 : ℝ)) (q := - (3853262949073229 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3853262949073229 / 10000000000000000 : ℚ)) + (r' := (3853262949073229 / 2500000000000000 : ℚ)) + (U := (-(2384161959690752671551 / 2500000000000000000000 : ℚ))) + (U' := (1081573941809247328449 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (3852987616974583 / 10000000000000000 : ℚ)) + (q := (3853262949073229 / 10000000000000000 : ℚ)) + (U := (-(2384161959690752671551 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_3 : Uω (aρ 3) (bρ 3) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3448,25 +3074,21 @@ lemma U_397_3 : have hlg : Real.log (7610340131582821 / 20000000000000000 : ℝ) ≤ (-(483112203406672262523 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7610340131582821 / 20000000000000000 : ℝ) = - (7610340131582821 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7610340131582821 / 5000000000000000 : ℚ)) - (U := (210034976893327737477 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7610340131582821 / 5000000000000000 : ℝ) ≤ - (210034976893327737477 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1902098978380473 / 5000000000000000 : ℝ)) (q := - (7610340131582821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7610340131582821 / 20000000000000000 : ℚ)) + (r' := (7610340131582821 / 5000000000000000 : ℚ)) + (U := (-(483112203406672262523 / 500000000000000000000 : ℚ))) + (U' := (210034976893327737477 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (1902098978380473 / 5000000000000000 : ℚ)) + (q := (7610340131582821 / 20000000000000000 : ℚ)) + (U := (-(483112203406672262523 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_4 : Uω (aρ 4) (bρ 4) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3474,25 +3096,21 @@ lemma U_397_4 : have hlg : Real.log (3725023708523281 / 10000000000000000 : ℝ) ≤ (-(395004750383460144211 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3725023708523281 / 10000000000000000 : ℝ) = - (3725023708523281 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3725023708523281 / 2500000000000000 : ℚ)) - (U := (159512993856539855789 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3725023708523281 / 2500000000000000 : ℝ) ≤ - (159512993856539855789 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3722199423289687 / 10000000000000000 : ℝ)) (q := - (3725023708523281 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3725023708523281 / 10000000000000000 : ℚ)) + (r' := (3725023708523281 / 2500000000000000 : ℚ)) + (U := (-(395004750383460144211 / 400000000000000000000 : ℚ))) + (U' := (159512993856539855789 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (3722199423289687 / 10000000000000000 : ℚ)) + (q := (3725023708523281 / 10000000000000000 : ℚ)) + (U := (-(395004750383460144211 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_5 : Uω (aρ 5) (bρ 5) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3500,25 +3118,21 @@ lemma U_397_5 : have hlg : Real.log (7204531876741977 / 20000000000000000 : ℝ) ≤ (-(10210220176931123704729 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7204531876741977 / 20000000000000000 : ℝ) = - (7204531876741977 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7204531876741977 / 5000000000000000 : ℚ)) - (U := (3652723429068876295271 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7204531876741977 / 5000000000000000 : ℝ) ≤ - (3652723429068876295271 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1797436901160051 / 5000000000000000 : ℝ)) (q := - (7204531876741977 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7204531876741977 / 20000000000000000 : ℚ)) + (r' := (7204531876741977 / 5000000000000000 : ℚ)) + (U := (-(10210220176931123704729 / 10000000000000000000000 : ℚ))) + (U' := (3652723429068876295271 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (1797436901160051 / 5000000000000000 : ℚ)) + (q := (7204531876741977 / 20000000000000000 : ℚ)) + (U := (-(10210220176931123704729 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_6 : Uω (aρ 6) (bρ 6) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3526,25 +3140,21 @@ lemma U_397_6 : have hlg : Real.log (6848998845567579 / 20000000000000000 : ℝ) ≤ (-(1071629785373233403567 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6848998845567579 / 20000000000000000 : ℝ) = - (6848998845567579 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6848998845567579 / 5000000000000000 : ℚ)) - (U := (314664575226766596433 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6848998845567579 / 5000000000000000 : ℝ) ≤ - (314664575226766596433 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (425822643285713 / 1250000000000000 : ℝ)) (q := - (6848998845567579 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6848998845567579 / 20000000000000000 : ℚ)) + (r' := (6848998845567579 / 5000000000000000 : ℚ)) + (U := (-(1071629785373233403567 / 1000000000000000000000 : ℚ))) + (U' := (314664575226766596433 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (425822643285713 / 1250000000000000 : ℚ)) + (q := (6848998845567579 / 20000000000000000 : ℚ)) + (U := (-(1071629785373233403567 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_7 : Uω (aρ 7) (bρ 7) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3552,25 +3162,21 @@ lemma U_397_7 : have hlg : Real.log (794487911180923 / 2500000000000000 : ℝ) ≤ (-(1146348240106701236677 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (794487911180923 / 2500000000000000 : ℝ) = - (794487911180923 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (794487911180923 / 625000000000000 : ℚ)) - (U := (239946120493298763323 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (794487911180923 / 625000000000000 : ℝ) ≤ - (239946120493298763323 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3137146970925509 / 10000000000000000 : ℝ)) (q := - (794487911180923 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (794487911180923 / 2500000000000000 : ℚ)) + (r' := (794487911180923 / 625000000000000 : ℚ)) + (U := (-(1146348240106701236677 / 1000000000000000000000 : ℚ))) + (U' := (239946120493298763323 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (3137146970925509 / 10000000000000000 : ℚ)) + (q := (794487911180923 / 2500000000000000 : ℚ)) + (U := (-(1146348240106701236677 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_8 : Uω (aρ 8) (bρ 8) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3578,25 +3184,21 @@ lemma U_397_8 : have hlg : Real.log (5693208433662741 / 20000000000000000 : ℝ) ≤ (-(785286444664797924013 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5693208433662741 / 20000000000000000 : ℝ) = - (5693208433662741 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5693208433662741 / 5000000000000000 : ℚ)) - (U := (81147530710202075987 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5693208433662741 / 5000000000000000 : ℝ) ≤ - (81147530710202075987 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1378996883240433 / 5000000000000000 : ℝ)) (q := - (5693208433662741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5693208433662741 / 20000000000000000 : ℚ)) + (r' := (5693208433662741 / 5000000000000000 : ℚ)) + (U := (-(785286444664797924013 / 625000000000000000000 : ℚ))) + (U' := (81147530710202075987 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (1378996883240433 / 5000000000000000 : ℚ)) + (q := (5693208433662741 / 20000000000000000 : ℚ)) + (U := (-(785286444664797924013 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_9 : Uω (aρ 9) (bρ 9) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3604,25 +3206,21 @@ lemma U_397_9 : have hlg : Real.log (2406028162975879 / 10000000000000000 : ℝ) ≤ (-(14246077694202213291207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2406028162975879 / 10000000000000000 : ℝ) = - (2406028162975879 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2406028162975879 / 1250000000000000 : ℚ)) - (U := (6548337714797786708793 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2406028162975879 / 1250000000000000 : ℝ) ≤ - (6548337714797786708793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2217807287129883 / 10000000000000000 : ℝ)) (q := - (2406028162975879 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2406028162975879 / 10000000000000000 : ℚ)) + (r' := (2406028162975879 / 1250000000000000 : ℚ)) + (U := (-(14246077694202213291207 / 10000000000000000000000 : ℚ))) + (U' := (6548337714797786708793 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (2217807287129883 / 10000000000000000 : ℚ)) + (q := (2406028162975879 / 10000000000000000 : ℚ)) + (U := (-(14246077694202213291207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_10 : Uω (aρ 10) (bρ 10) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3630,24 +3228,21 @@ lemma U_397_10 : have hlg : Real.log (35678952614417 / 200000000000000 : ℝ) ≤ (-(17237564134643599097387 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (35678952614417 / 200000000000000 : ℝ) = (35678952614417 / 25000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35678952614417 / 25000000000000 : ℚ)) - (U := (3556851274356400902613 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (35678952614417 / 25000000000000 : ℝ) ≤ - (3556851274356400902613 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (54488210244593 / 400000000000000 : ℝ)) (q := - (35678952614417 / 200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35678952614417 / 200000000000000 : ℚ)) + (r' := (35678952614417 / 25000000000000 : ℚ)) + (U := (-(17237564134643599097387 / 10000000000000000000000 : ℚ))) + (U' := (3556851274356400902613 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (6306887218827 / 16000000000000 : ℚ)) + (s := (54488210244593 / 400000000000000 : ℚ)) + (q := (35678952614417 / 200000000000000 : ℚ)) + (U := (-(17237564134643599097387 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_397_11 : Uω (aρ 11) (bρ 11) (6306887218827 / 16000000000000 : ℝ) ≤ @@ -3768,25 +3363,21 @@ lemma U_398_1 : have hlg : Real.log (15613709944932829 / 40000000000000000 : ℝ) ≤ (-(4703650413353603050421 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15613709944932829 / 40000000000000000 : ℝ) = - (15613709944932829 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15613709944932829 / 10000000000000000 : ℚ)) - (U := (2227821389646396949579 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15613709944932829 / 10000000000000000 : ℝ) ≤ - (2227821389646396949579 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1951693034664301 / 5000000000000000 : ℝ)) (q := - (15613709944932829 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15613709944932829 / 40000000000000000 : ℚ)) + (r' := (15613709944932829 / 10000000000000000 : ℚ)) + (U := (-(4703650413353603050421 / 5000000000000000000000 : ℚ))) + (U' := (2227821389646396949579 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (1951693034664301 / 5000000000000000 : ℚ)) + (q := (15613709944932829 / 40000000000000000 : ℚ)) + (U := (-(4703650413353603050421 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_2 : Uω (aρ 2) (bρ 2) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3794,25 +3385,21 @@ lemma U_398_2 : have hlg : Real.log (3103541132329967 / 8000000000000000 : ℝ) ≤ (-(9468977808463272198431 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3103541132329967 / 8000000000000000 : ℝ) = - (3103541132329967 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3103541132329967 / 2000000000000000 : ℚ)) - (U := (4393965797536727801569 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3103541132329967 / 2000000000000000 : ℝ) ≤ - (4393965797536727801569 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (775830588039421 / 2000000000000000 : ℝ)) (q := - (3103541132329967 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3103541132329967 / 8000000000000000 : ℚ)) + (r' := (3103541132329967 / 2000000000000000 : ℚ)) + (U := (-(9468977808463272198431 / 10000000000000000000000 : ℚ))) + (U' := (4393965797536727801569 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (775830588039421 / 2000000000000000 : ℚ)) + (q := (3103541132329967 / 8000000000000000 : ℚ)) + (U := (-(9468977808463272198431 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_3 : Uω (aρ 3) (bρ 3) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3820,25 +3407,21 @@ lemma U_398_3 : have hlg : Real.log (15325353259219533 / 40000000000000000 : ℝ) ≤ (-(1199213651081101815863 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15325353259219533 / 40000000000000000 : ℝ) = - (15325353259219533 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15325353259219533 / 10000000000000000 : ℚ)) - (U := (533654299668898184137 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15325353259219533 / 10000000000000000 : ℝ) ≤ - (533654299668898184137 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1915186422665977 / 5000000000000000 : ℝ)) (q := - (15325353259219533 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15325353259219533 / 40000000000000000 : ℚ)) + (r' := (15325353259219533 / 10000000000000000 : ℚ)) + (U := (-(1199213651081101815863 / 1250000000000000000000 : ℚ))) + (U' := (533654299668898184137 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (1915186422665977 / 5000000000000000 : ℚ)) + (q := (15325353259219533 / 40000000000000000 : ℚ)) + (U := (-(1199213651081101815863 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_4 : Uω (aρ 4) (bρ 4) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3846,25 +3429,21 @@ lemma U_398_4 : have hlg : Real.log (15004820119667203 / 40000000000000000 : ℝ) ≤ (-(9805079627997499469213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15004820119667203 / 40000000000000000 : ℝ) = - (15004820119667203 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15004820119667203 / 10000000000000000 : ℚ)) - (U := (4057863978002500530787 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15004820119667203 / 10000000000000000 : ℝ) ≤ - (4057863978002500530787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3748400456620789 / 10000000000000000 : ℝ)) (q := - (15004820119667203 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15004820119667203 / 40000000000000000 : ℚ)) + (r' := (15004820119667203 / 10000000000000000 : ℚ)) + (U := (-(9805079627997499469213 / 10000000000000000000000 : ℚ))) + (U' := (4057863978002500530787 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (3748400456620789 / 10000000000000000 : ℚ)) + (q := (15004820119667203 / 40000000000000000 : ℚ)) + (U := (-(9805079627997499469213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_5 : Uω (aρ 5) (bρ 5) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3872,25 +3451,21 @@ lemma U_398_5 : have hlg : Real.log (14513923817856079 / 40000000000000000 : ℝ) ≤ (-(10137710016249584730821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14513923817856079 / 40000000000000000 : ℝ) = - (14513923817856079 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14513923817856079 / 10000000000000000 : ℚ)) - (U := (3725233589750415269179 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14513923817856079 / 10000000000000000 : ℝ) ≤ - (3725233589750415269179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3621142225050227 / 10000000000000000 : ℝ)) (q := - (14513923817856079 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14513923817856079 / 40000000000000000 : ℚ)) + (r' := (14513923817856079 / 10000000000000000 : ℚ)) + (U := (-(10137710016249584730821 / 10000000000000000000000 : ℚ))) + (U' := (3725233589750415269179 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (3621142225050227 / 10000000000000000 : ℚ)) + (q := (14513923817856079 / 40000000000000000 : ℚ)) + (U := (-(10137710016249584730821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_6 : Uω (aρ 6) (bρ 6) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3898,25 +3473,21 @@ lemma U_398_6 : have hlg : Real.log (13803190342104979 / 40000000000000000 : ℝ) ≤ (-(10639797039393326246521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13803190342104979 / 40000000000000000 : ℝ) = - (13803190342104979 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13803190342104979 / 10000000000000000 : ℚ)) - (U := (3223146566606673753479 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13803190342104979 / 10000000000000000 : ℝ) ≤ - (3223146566606673753479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3433015862314677 / 10000000000000000 : ℝ)) (q := - (13803190342104979 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13803190342104979 / 40000000000000000 : ℚ)) + (r' := (13803190342104979 / 10000000000000000 : ℚ)) + (U := (-(10639797039393326246521 / 10000000000000000000000 : ℚ))) + (U' := (3223146566606673753479 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (3433015862314677 / 10000000000000000 : ℚ)) + (q := (13803190342104979 / 40000000000000000 : ℚ)) + (U := (-(10639797039393326246521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_7 : Uω (aρ 7) (bρ 7) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3924,25 +3495,21 @@ lemma U_398_7 : have hlg : Real.log (12817802745399477 / 40000000000000000 : ℝ) ≤ (-(11380444095054808415279 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12817802745399477 / 40000000000000000 : ℝ) = - (12817802745399477 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12817802745399477 / 10000000000000000 : ℚ)) - (U := (2482499510945191584721 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12817802745399477 / 10000000000000000 : ℝ) ≤ - (2482499510945191584721 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1581991722360963 / 5000000000000000 : ℝ)) (q := - (12817802745399477 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12817802745399477 / 40000000000000000 : ℚ)) + (r' := (12817802745399477 / 10000000000000000 : ℚ)) + (U := (-(11380444095054808415279 / 10000000000000000000000 : ℚ))) + (U' := (2482499510945191584721 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (1581991722360963 / 5000000000000000 : ℚ)) + (q := (12817802745399477 / 40000000000000000 : ℚ)) + (U := (-(11380444095054808415279 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_8 : Uω (aρ 8) (bρ 8) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3950,25 +3517,21 @@ lemma U_398_8 : have hlg : Real.log (11494392859447927 / 40000000000000000 : ℝ) ≤ (-(12470201145686833426751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11494392859447927 / 40000000000000000 : ℝ) = - (11494392859447927 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11494392859447927 / 10000000000000000 : ℚ)) - (U := (1392742460313166573249 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11494392859447927 / 10000000000000000 : ℝ) ≤ - (1392742460313166573249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2785820153086151 / 10000000000000000 : ℝ)) (q := - (11494392859447927 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11494392859447927 / 40000000000000000 : ℚ)) + (r' := (11494392859447927 / 10000000000000000 : ℚ)) + (U := (-(12470201145686833426751 / 10000000000000000000000 : ℚ))) + (U' := (1392742460313166573249 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (2785820153086151 / 10000000000000000 : ℚ)) + (q := (11494392859447927 / 40000000000000000 : ℚ)) + (U := (-(12470201145686833426751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_9 : Uω (aρ 9) (bρ 9) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -3976,25 +3539,21 @@ lemma U_398_9 : have hlg : Real.log (9737528115117821 / 40000000000000000 : ℝ) ≤ (-(3532230387094757563699 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9737528115117821 / 40000000000000000 : ℝ) = - (9737528115117821 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9737528115117821 / 5000000000000000 : ℚ)) - (U := (1666373465155242436301 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9737528115117821 / 5000000000000000 : ℝ) ≤ - (1666373465155242436301 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1124176704640549 / 5000000000000000 : ℝ)) (q := - (9737528115117821 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9737528115117821 / 40000000000000000 : ℚ)) + (r' := (9737528115117821 / 5000000000000000 : ℚ)) + (U := (-(3532230387094757563699 / 2500000000000000000000 : ℚ))) + (U' := (1666373465155242436301 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (1124176704640549 / 5000000000000000 : ℚ)) + (q := (9737528115117821 / 40000000000000000 : ℚ)) + (U := (-(3532230387094757563699 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_10 : Uω (aρ 10) (bρ 10) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -4002,26 +3561,21 @@ lemma U_398_10 : have hlg : Real.log (7272045367266537 / 40000000000000000 : ℝ) ≤ (-(17048418578553716535903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7272045367266537 / 40000000000000000 : ℝ) = - (7272045367266537 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7272045367266537 / 5000000000000000 : ℚ)) - (U := (3745996830446283464097 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7272045367266537 / 5000000000000000 : ℝ) ≤ - (3745996830446283464097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (175521383606307 / 1250000000000000 : ℝ)) (q := - (7272045367266537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7272045367266537 / 40000000000000000 : ℚ)) + (r' := (7272045367266537 / 5000000000000000 : ℚ)) + (U := (-(17048418578553716535903 / 10000000000000000000000 : ℚ))) + (U' := (3745996830446283464097 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (12697491587913 / 32000000000000 : ℚ)) + (s := (175521383606307 / 1250000000000000 : ℚ)) + (q := (7272045367266537 / 40000000000000000 : ℚ)) + (U := (-(17048418578553716535903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_398_11 : Uω (aρ 11) (bρ 11) (12697491587913 / 32000000000000 : ℝ) ≤ @@ -4143,25 +3697,21 @@ lemma U_399_1 : have hlg : Real.log (7859178742857949 / 20000000000000000 : ℝ) ≤ (-(4670250788467362062751 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7859178742857949 / 20000000000000000 : ℝ) = - (7859178742857949 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7859178742857949 / 5000000000000000 : ℚ)) - (U := (2261221014532637937249 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7859178742857949 / 5000000000000000 : ℝ) ≤ - (2261221014532637937249 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3929548230264199 / 10000000000000000 : ℝ)) (q := - (7859178742857949 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7859178742857949 / 20000000000000000 : ℚ)) + (r' := (7859178742857949 / 5000000000000000 : ℚ)) + (U := (-(4670250788467362062751 / 5000000000000000000000 : ℚ))) + (U' := (2261221014532637937249 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (3929548230264199 / 10000000000000000 : ℚ)) + (q := (7859178742857949 / 20000000000000000 : ℚ)) + (U := (-(4670250788467362062751 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_2 : Uω (aρ 2) (bρ 2) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4169,25 +3719,21 @@ lemma U_399_2 : have hlg : Real.log (312447188549721 / 800000000000000 : ℝ) ≤ (-(376070507557605859629 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (312447188549721 / 800000000000000 : ℝ) = - (312447188549721 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (312447188549721 / 200000000000000 : ℚ)) - (U := (178447236682394140371 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (312447188549721 / 200000000000000 : ℝ) ≤ - (178447236682394140371 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156212728546371 / 400000000000000 : ℝ)) (q := - (312447188549721 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (312447188549721 / 800000000000000 : ℚ)) + (r' := (312447188549721 / 200000000000000 : ℚ)) + (U := (-(376070507557605859629 / 400000000000000000000 : ℚ))) + (U' := (178447236682394140371 / 400000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (156212728546371 / 400000000000000 : ℚ)) + (q := (312447188549721 / 800000000000000 : ℚ)) + (U := (-(376070507557605859629 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_3 : Uω (aρ 3) (bρ 3) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4195,25 +3741,21 @@ lemma U_399_3 : have hlg : Real.log (1543002589485657 / 4000000000000000 : ℝ) ≤ (-(1905128218010882884229 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1543002589485657 / 4000000000000000 : ℝ) = - (1543002589485657 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1543002589485657 / 1000000000000000 : ℚ)) - (U := (867460503189117115771 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1543002589485657 / 1000000000000000 : ℝ) ≤ - (867460503189117115771 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (771309510738907 / 2000000000000000 : ℝ)) (q := - (1543002589485657 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1543002589485657 / 4000000000000000 : ℚ)) + (r' := (1543002589485657 / 1000000000000000 : ℚ)) + (U := (-(1905128218010882884229 / 2000000000000000000000 : ℚ))) + (U' := (867460503189117115771 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (771309510738907 / 2000000000000000 : ℚ)) + (q := (1543002589485657 / 4000000000000000 : ℚ)) + (U := (-(1905128218010882884229 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_4 : Uω (aρ 4) (bρ 4) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4221,25 +3763,21 @@ lemma U_399_4 : have hlg : Real.log (7554772155718287 / 20000000000000000 : ℝ) ≤ (-(243388208960620545919 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7554772155718287 / 20000000000000000 : ℝ) = - (7554772155718287 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7554772155718287 / 5000000000000000 : ℚ)) - (U := (103185381189379454081 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7554772155718287 / 5000000000000000 : ℝ) ≤ - (103185381189379454081 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3774600943049537 / 10000000000000000 : ℝ)) (q := - (7554772155718287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7554772155718287 / 20000000000000000 : ℚ)) + (r' := (7554772155718287 / 5000000000000000 : ℚ)) + (U := (-(243388208960620545919 / 250000000000000000000 : ℚ))) + (U' := (103185381189379454081 / 250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (3774600943049537 / 10000000000000000 : ℚ)) + (q := (7554772155718287 / 20000000000000000 : ℚ)) + (U := (-(243388208960620545919 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_5 : Uω (aρ 5) (bρ 5) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4247,25 +3785,21 @@ lemma U_399_5 : have hlg : Real.log (228418450178649 / 625000000000000 : ℝ) ≤ (-(5032861972902583863707 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (228418450178649 / 625000000000000 : ℝ) = - (228418450178649 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (228418450178649 / 156250000000000 : ℚ)) - (U := (1898609830097416136293 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (228418450178649 / 156250000000000 : ℝ) ≤ - (1898609830097416136293 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1823704556191509 / 5000000000000000 : ℝ)) (q := - (228418450178649 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (228418450178649 / 625000000000000 : ℚ)) + (r' := (228418450178649 / 156250000000000 : ℚ)) + (U := (-(5032861972902583863707 / 5000000000000000000000 : ℚ))) + (U' := (1898609830097416136293 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (1823704556191509 / 5000000000000000 : ℚ)) + (q := (228418450178649 / 625000000000000 : ℚ)) + (U := (-(5032861972902583863707 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_6 : Uω (aρ 6) (bρ 6) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4273,25 +3807,21 @@ lemma U_399_6 : have hlg : Real.log (1390837468862847 / 4000000000000000 : ℝ) ≤ (-(5281941496501066055649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1390837468862847 / 4000000000000000 : ℝ) = - (1390837468862847 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1390837468862847 / 1000000000000000 : ℚ)) - (U := (1649530306498933944351 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1390837468862847 / 1000000000000000 : ℝ) ≤ - (1649530306498933944351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (691889285224097 / 2000000000000000 : ℝ)) (q := - (1390837468862847 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1390837468862847 / 4000000000000000 : ℚ)) + (r' := (1390837468862847 / 1000000000000000 : ℚ)) + (U := (-(5281941496501066055649 / 5000000000000000000000 : ℚ))) + (U' := (1649530306498933944351 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (691889285224097 / 2000000000000000 : ℚ)) + (q := (1390837468862847 / 4000000000000000 : ℚ)) + (U := (-(5281941496501066055649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_7 : Uω (aρ 7) (bρ 7) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4299,25 +3829,21 @@ lemma U_399_7 : have hlg : Real.log (6461888246739339 / 20000000000000000 : ℝ) ≤ (-(1412263374616923864879 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6461888246739339 / 20000000000000000 : ℝ) = - (6461888246739339 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6461888246739339 / 5000000000000000 : ℚ)) - (U := (320604576133076135121 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6461888246739339 / 5000000000000000 : ℝ) ≤ - (320604576133076135121 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3190808709305589 / 10000000000000000 : ℝ)) (q := - (6461888246739339 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6461888246739339 / 20000000000000000 : ℚ)) + (r' := (6461888246739339 / 5000000000000000 : ℚ)) + (U := (-(1412263374616923864879 / 1250000000000000000000 : ℚ))) + (U' := (320604576133076135121 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (3190808709305589 / 10000000000000000 : ℚ)) + (q := (6461888246739339 / 20000000000000000 : ℚ)) + (U := (-(1412263374616923864879 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_8 : Uω (aρ 8) (bρ 8) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4325,25 +3851,21 @@ lemma U_399_8 : have hlg : Real.log (2900576241005023 / 10000000000000000 : ℝ) ≤ (-(3094189178564688703663 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2900576241005023 / 10000000000000000 : ℝ) = - (2900576241005023 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2900576241005023 / 2500000000000000 : ℚ)) - (U := (371546722935311296337 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2900576241005023 / 2500000000000000 : ℝ) ≤ - (371546722935311296337 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (351701824489537 / 1250000000000000 : ℝ)) (q := - (2900576241005023 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2900576241005023 / 10000000000000000 : ℚ)) + (r' := (2900576241005023 / 2500000000000000 : ℚ)) + (U := (-(3094189178564688703663 / 2500000000000000000000 : ℚ))) + (U' := (371546722935311296337 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (351701824489537 / 1250000000000000 : ℚ)) + (q := (2900576241005023 / 10000000000000000 : ℚ)) + (U := (-(3094189178564688703663 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_9 : Uω (aρ 9) (bρ 9) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4351,25 +3873,21 @@ lemma U_399_9 : have hlg : Real.log (2462681341559129 / 10000000000000000 : ℝ) ≤ (-(14013343596192001386277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2462681341559129 / 10000000000000000 : ℝ) = - (2462681341559129 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2462681341559129 / 1250000000000000 : ℚ)) - (U := (6781071812807998613723 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2462681341559129 / 1250000000000000 : ℝ) ≤ - (6781071812807998613723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (569697606346127 / 2500000000000000 : ℝ)) (q := - (2462681341559129 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2462681341559129 / 10000000000000000 : ℚ)) + (r' := (2462681341559129 / 1250000000000000 : ℚ)) + (U := (-(14013343596192001386277 / 10000000000000000000000 : ℚ))) + (U' := (6781071812807998613723 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (569697606346127 / 2500000000000000 : ℚ)) + (q := (2462681341559129 / 10000000000000000 : ℚ)) + (U := (-(14013343596192001386277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_10 : Uω (aρ 10) (bρ 10) (3195302184543 / 8000000000000 : ℝ) ≤ @@ -4377,25 +3895,21 @@ lemma U_399_10 : have hlg : Real.log (148136215159719 / 800000000000000 : ℝ) ≤ (-(843239751853213725649 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (148136215159719 / 800000000000000 : ℝ) = - (148136215159719 / 100000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (148136215159719 / 100000000000000 : ℚ)) - (U := (196481018596786274351 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (148136215159719 / 100000000000000 : ℝ) ≤ - (196481018596786274351 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57815686190169 / 400000000000000 : ℝ)) (q := - (148136215159719 / 800000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (148136215159719 / 800000000000000 : ℚ)) + (r' := (148136215159719 / 100000000000000 : ℚ)) + (U := (-(843239751853213725649 / 500000000000000000000 : ℚ))) + (U' := (196481018596786274351 / 500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (3195302184543 / 8000000000000 : ℚ)) + (s := (57815686190169 / 400000000000000 : ℚ)) + (q := (148136215159719 / 800000000000000 : ℚ)) + (U := (-(843239751853213725649 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_399_11 : Uω (aρ 11) (bρ 11) (3195302184543 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U33.lean b/LeanPool/Zeta5Irrational/Table/U33.lean index d555238a05..d5d210d2ba 100644 --- a/LeanPool/Zeta5Irrational/Table/U33.lean +++ b/LeanPool/Zeta5Irrational/Table/U33.lean @@ -24,25 +24,21 @@ lemma U_400_1 : have hlg : Real.log (15823005011909681 / 40000000000000000 : ℝ) ≤ (-(9274145591088656349597 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15823005011909681 / 40000000000000000 : ℝ) = - (15823005011909681 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15823005011909681 / 10000000000000000 : ℚ)) - (U := (4588798014911343650403 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15823005011909681 / 10000000000000000 : ℝ) ≤ - (4588798014911343650403 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3955710383905153 / 10000000000000000 : ℝ)) (q := - (15823005011909681 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15823005011909681 / 40000000000000000 : ℚ)) + (r' := (15823005011909681 / 10000000000000000 : ℚ)) + (U := (-(9274145591088656349597 / 10000000000000000000000 : ℚ))) + (U' := (4588798014911343650403 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (3955710383905153 / 10000000000000000 : ℚ)) + (q := (15823005011909681 / 40000000000000000 : ℚ)) + (U := (-(9274145591088656349597 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_2 : Uω (aρ 2) (bρ 2) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_400_2 : have hlg : Real.log (15727013095788583 / 40000000000000000 : ℝ) ≤ (-(145859318811119573189 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15727013095788583 / 40000000000000000 : ℝ) = - (15727013095788583 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15727013095788583 / 10000000000000000 : ℚ)) - (U := (70749175032630426811 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15727013095788583 / 10000000000000000 : ℝ) ≤ - (70749175032630426811 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (982870859588651 / 2500000000000000 : ℝ)) (q := - (15727013095788583 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15727013095788583 / 40000000000000000 : ℚ)) + (r' := (15727013095788583 / 10000000000000000 : ℚ)) + (U := (-(145859318811119573189 / 156250000000000000000 : ℚ))) + (U' := (70749175032630426811 / 156250000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (982870859588651 / 2500000000000000 : ℚ)) + (q := (15727013095788583 / 40000000000000000 : ℚ)) + (U := (-(145859318811119573189 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_3 : Uω (aρ 3) (bρ 3) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_400_3 : have hlg : Real.log (621387927094633 / 1600000000000000 : ℝ) ≤ (-(9458033394948477753999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (621387927094633 / 1600000000000000 : ℝ) = - (621387927094633 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (621387927094633 / 400000000000000 : ℚ)) - (U := (4404910211051522246001 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (621387927094633 / 400000000000000 : ℝ) ≤ - (4404910211051522246001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (155308883419729 / 400000000000000 : ℝ)) (q := - (621387927094633 / 1600000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (621387927094633 / 1600000000000000 : ℚ)) + (r' := (621387927094633 / 400000000000000 : ℚ)) + (U := (-(9458033394948477753999 / 10000000000000000000000 : ℚ))) + (U' := (4404910211051522246001 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (155308883419729 / 400000000000000 : ℚ)) + (q := (621387927094633 / 1600000000000000 : ℚ)) + (U := (-(9458033394948477753999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_4 : Uω (aρ 4) (bρ 4) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_400_4 : have hlg : Real.log (15214267432021373 / 40000000000000000 : ℝ) ≤ (-(4833229095758892645243 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15214267432021373 / 40000000000000000 : ℝ) = - (15214267432021373 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15214267432021373 / 10000000000000000 : ℚ)) - (U := (2098242707241107354757 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15214267432021373 / 10000000000000000 : ℝ) ≤ - (2098242707241107354757 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3800800893885999 / 10000000000000000 : ℝ)) (q := - (15214267432021373 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15214267432021373 / 40000000000000000 : ℚ)) + (r' := (15214267432021373 / 10000000000000000 : ℚ)) + (U := (-(4833229095758892645243 / 5000000000000000000000 : ℚ))) + (U' := (2098242707241107354757 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (3800800893885999 / 10000000000000000 : ℚ)) + (q := (15214267432021373 / 40000000000000000 : ℚ)) + (U := (-(4833229095758892645243 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_5 : Uω (aρ 5) (bρ 5) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_400_5 : have hlg : Real.log (14723634800085159 / 40000000000000000 : ℝ) ≤ (-(9994254414217391606101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14723634800085159 / 40000000000000000 : ℝ) = - (14723634800085159 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14723634800085159 / 10000000000000000 : ℚ)) - (U := (3868689191782608393899 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14723634800085159 / 10000000000000000 : ℝ) ≤ - (3868689191782608393899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (918418624313223 / 2500000000000000 : ℝ)) (q := - (14723634800085159 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14723634800085159 / 40000000000000000 : ℚ)) + (r' := (14723634800085159 / 10000000000000000 : ℚ)) + (U := (-(9994254414217391606101 / 10000000000000000000000 : ℚ))) + (U' := (3868689191782608393899 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (918418624313223 / 2500000000000000 : ℚ)) + (q := (14723634800085159 / 40000000000000000 : ℚ)) + (U := (-(9994254414217391606101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_6 : Uω (aρ 6) (bρ 6) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_400_6 : have hlg : Real.log (14013550919603397 / 40000000000000000 : ℝ) ≤ (-(10488546692852194258217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14013550919603397 / 40000000000000000 : ℝ) = - (14013550919603397 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14013550919603397 / 10000000000000000 : ℚ)) - (U := (3374396913147805741783 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14013550919603397 / 10000000000000000 : ℝ) ≤ - (3374396913147805741783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3485872932152011 / 10000000000000000 : ℝ)) (q := - (14013550919603397 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14013550919603397 / 40000000000000000 : ℚ)) + (r' := (14013550919603397 / 10000000000000000 : ℚ)) + (U := (-(10488546692852194258217 / 10000000000000000000000 : ℚ))) + (U' := (3374396913147805741783 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (3485872932152011 / 10000000000000000 : ℚ)) + (q := (14013550919603397 / 40000000000000000 : ℚ)) + (U := (-(10488546692852194258217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_7 : Uω (aρ 7) (bρ 7) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_400_7 : have hlg : Real.log (13029728383838411 / 40000000000000000 : ℝ) ≤ (-(2804114770301443257797 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13029728383838411 / 40000000000000000 : ℝ) = - (13029728383838411 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13029728383838411 / 10000000000000000 : ℚ)) - (U := (661621131198556742203 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13029728383838411 / 10000000000000000 : ℝ) ≤ - (661621131198556742203 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1608811522514759 / 5000000000000000 : ℝ)) (q := - (13029728383838411 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13029728383838411 / 40000000000000000 : ℚ)) + (r' := (13029728383838411 / 10000000000000000 : ℚ)) + (U := (-(2804114770301443257797 / 2500000000000000000000 : ℚ))) + (U' := (661621131198556742203 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (1608811522514759 / 5000000000000000 : ℚ)) + (q := (13029728383838411 / 40000000000000000 : ℚ)) + (U := (-(2804114770301443257797 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_8 : Uω (aρ 8) (bρ 8) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_400_8 : have hlg : Real.log (11710155055891933 / 40000000000000000 : ℝ) ≤ (-(12284230347491191553647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11710155055891933 / 40000000000000000 : ℝ) = - (11710155055891933 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11710155055891933 / 10000000000000000 : ℚ)) - (U := (1578713258508808446353 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11710155055891933 / 10000000000000000 : ℝ) ≤ - (1578713258508808446353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2841378032396279 / 10000000000000000 : ℝ)) (q := - (11710155055891933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11710155055891933 / 40000000000000000 : ℚ)) + (r' := (11710155055891933 / 10000000000000000 : ℚ)) + (U := (-(12284230347491191553647 / 10000000000000000000000 : ℚ))) + (U' := (1578713258508808446353 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (2841378032396279 / 10000000000000000 : ℚ)) + (q := (11710155055891933 / 40000000000000000 : ℚ)) + (U := (-(12284230347491191553647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_9 : Uω (aρ 9) (bρ 9) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_400_9 : have hlg : Real.log (9963713034161937 / 40000000000000000 : ℝ) ≤ (-(6949648283068307006159 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9963713034161937 / 40000000000000000 : ℝ) = - (9963713034161937 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9963713034161937 / 5000000000000000 : ℚ)) - (U := (3447559421431692993841 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9963713034161937 / 5000000000000000 : ℝ) ≤ - (3447559421431692993841 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2309122649891281 / 10000000000000000 : ℝ)) (q := - (9963713034161937 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9963713034161937 / 40000000000000000 : ℚ)) + (r' := (9963713034161937 / 5000000000000000 : ℚ)) + (U := (-(6949648283068307006159 / 5000000000000000000000 : ℚ))) + (U' := (3447559421431692993841 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (2309122649891281 / 10000000000000000 : ℚ)) + (q := (9963713034161937 / 40000000000000000 : ℚ)) + (U := (-(6949648283068307006159 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_10 : Uω (aρ 10) (bρ 10) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_400_10 : have hlg : Real.log (7540210654092581 / 40000000000000000 : ℝ) ≤ (-(16686293334959350296841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7540210654092581 / 40000000000000000 : ℝ) = - (7540210654092581 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7540210654092581 / 5000000000000000 : ℚ)) - (U := (4108122074040649703159 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7540210654092581 / 5000000000000000 : ℝ) ≤ - (4108122074040649703159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1485930493351603 / 10000000000000000 : ℝ)) (q := - (7540210654092581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7540210654092581 / 40000000000000000 : ℚ)) + (r' := (7540210654092581 / 5000000000000000 : ℚ)) + (U := (-(16686293334959350296841 / 10000000000000000000000 : ℚ))) + (U' := (4108122074040649703159 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (12864925888431 / 32000000000000 : ℚ)) + (s := (1485930493351603 / 10000000000000000 : ℚ)) + (q := (7540210654092581 / 40000000000000000 : ℚ)) + (U := (-(16686293334959350296841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_400_11 : Uω (aρ 11) (bρ 11) (12864925888431 / 32000000000000 : ℝ) ≤ @@ -399,25 +358,21 @@ lemma U_401_1 : have hlg : Real.log (995478282737609 / 2500000000000000 : ℝ) ≤ (-(2302056756254861910491 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (995478282737609 / 2500000000000000 : ℝ) = - (995478282737609 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (995478282737609 / 625000000000000 : ℚ)) - (U := (1163679145245138089509 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (995478282737609 / 625000000000000 : ℝ) ≤ - (1163679145245138089509 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3981872530395247 / 10000000000000000 : ℝ)) (q := - (995478282737609 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (995478282737609 / 2500000000000000 : ℚ)) + (r' := (995478282737609 / 625000000000000 : ℚ)) + (U := (-(2302056756254861910491 / 2500000000000000000000 : ℚ))) + (U' := (1163679145245138089509 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (3981872530395247 / 10000000000000000 : ℚ)) + (q := (995478282737609 / 2500000000000000 : ℚ)) + (U := (-(2302056756254861910491 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_2 : Uω (aρ 2) (bρ 2) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -425,25 +380,21 @@ lemma U_401_2 : have hlg : Real.log (1978958333561489 / 5000000000000000 : ℝ) ≤ (-(1853734599609437634619 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1978958333561489 / 5000000000000000 : ℝ) = - (1978958333561489 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1978958333561489 / 1250000000000000 : ℚ)) - (U := (918854121590562365381 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1978958333561489 / 1250000000000000 : ℝ) ≤ - (918854121590562365381 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3957648615250331 / 10000000000000000 : ℝ)) (q := - (1978958333561489 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1978958333561489 / 5000000000000000 : ℚ)) + (r' := (1978958333561489 / 1250000000000000 : ℚ)) + (U := (-(1853734599609437634619 / 2000000000000000000000 : ℚ))) + (U' := (918854121590562365381 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (3957648615250331 / 10000000000000000 : ℚ)) + (q := (1978958333561489 / 5000000000000000 : ℚ)) + (U := (-(1853734599609437634619 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_3 : Uω (aρ 3) (bρ 3) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -451,25 +402,21 @@ lemma U_401_3 : have hlg : Real.log (3909842528460269 / 10000000000000000 : ℝ) ≤ (-(4695439966694920649199 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3909842528460269 / 10000000000000000 : ℝ) = - (3909842528460269 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3909842528460269 / 2500000000000000 : ℚ)) - (U := (2236031836305079350801 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3909842528460269 / 2500000000000000 : ℝ) ≤ - (2236031836305079350801 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3908896444274913 / 10000000000000000 : ℝ)) (q := - (3909842528460269 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3909842528460269 / 10000000000000000 : ℚ)) + (r' := (3909842528460269 / 2500000000000000 : ℚ)) + (U := (-(4695439966694920649199 / 5000000000000000000000 : ℚ))) + (U' := (2236031836305079350801 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (3908896444274913 / 10000000000000000 : ℚ)) + (q := (3909842528460269 / 10000000000000000 : ℚ)) + (U := (-(4695439966694920649199 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_4 : Uω (aρ 4) (bρ 4) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -477,25 +424,21 @@ lemma U_401_4 : have hlg : Real.log (306379790068437 / 800000000000000 : ℝ) ≤ (-(9597862507636789230839 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (306379790068437 / 800000000000000 : ℝ) = - (306379790068437 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (306379790068437 / 200000000000000 : ℚ)) - (U := (4265081098363210769161 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (306379790068437 / 200000000000000 : ℝ) ≤ - (4265081098363210769161 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38270003201303 / 100000000000000 : ℝ)) (q := - (306379790068437 / 800000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (306379790068437 / 800000000000000 : ℚ)) + (r' := (306379790068437 / 200000000000000 : ℚ)) + (U := (-(9597862507636789230839 / 10000000000000000000000 : ℚ))) + (U' := (4265081098363210769161 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (38270003201303 / 100000000000000 : ℚ)) + (q := (306379790068437 / 800000000000000 : ℚ)) + (U := (-(9597862507636789230839 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_5 : Uω (aρ 5) (bρ 5) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -503,25 +446,21 @@ lemma U_401_5 : have hlg : Real.log (3707121461951423 / 10000000000000000 : ℝ) ≤ (-(1240411754096010472283 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3707121461951423 / 10000000000000000 : ℝ) = - (3707121461951423 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3707121461951423 / 2500000000000000 : ℚ)) - (U := (492456196653989527717 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3707121461951423 / 2500000000000000 : ℝ) ≤ - (492456196653989527717 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3699938411657221 / 10000000000000000 : ℝ)) (q := - (3707121461951423 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3707121461951423 / 10000000000000000 : ℚ)) + (r' := (3707121461951423 / 2500000000000000 : ℚ)) + (U := (-(1240411754096010472283 / 1250000000000000000000 : ℚ))) + (U' := (492456196653989527717 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (3699938411657221 / 10000000000000000 : ℚ)) + (q := (3707121461951423 / 10000000000000000 : ℚ)) + (U := (-(1240411754096010472283 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_6 : Uω (aρ 6) (bρ 6) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -529,25 +468,21 @@ lemma U_401_6 : have hlg : Real.log (1411871921821389 / 4000000000000000 : ℝ) ≤ (-(1301722415710541881821 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1411871921821389 / 4000000000000000 : ℝ) = - (1411871921821389 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1411871921821389 / 1000000000000000 : ℚ)) - (U := (431145535039458118179 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1411871921821389 / 1000000000000000 : ℝ) ≤ - (431145535039458118179 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (87807386800033 / 250000000000000 : ℝ)) (q := - (1411871921821389 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1411871921821389 / 4000000000000000 : ℚ)) + (r' := (1411871921821389 / 1000000000000000 : ℚ)) + (U := (-(1301722415710541881821 / 1250000000000000000000 : ℚ))) + (U' := (431145535039458118179 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (87807386800033 / 250000000000000 : ℚ)) + (q := (1411871921821389 / 4000000000000000 : ℚ)) + (U := (-(1301722415710541881821 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_7 : Uω (aρ 7) (bρ 7) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -555,25 +490,21 @@ lemma U_401_7 : have hlg : Real.log (410489342450739 / 1250000000000000 : ℝ) ≤ (-(5567744317910864751661 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (410489342450739 / 1250000000000000 : ℝ) = - (410489342450739 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (410489342450739 / 312500000000000 : ℚ)) - (U := (1363727485089135248339 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (410489342450739 / 312500000000000 : ℝ) ≤ - (1363727485089135248339 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3244426722866199 / 10000000000000000 : ℝ)) (q := - (410489342450739 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (410489342450739 / 1250000000000000 : ℚ)) + (r' := (410489342450739 / 312500000000000 : ℚ)) + (U := (-(5567744317910864751661 / 5000000000000000000000 : ℚ))) + (U' := (1363727485089135248339 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (3244426722866199 / 10000000000000000 : ℚ)) + (q := (410489342450739 / 1250000000000000 : ℚ)) + (U := (-(5567744317910864751661 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_8 : Uω (aρ 8) (bρ 8) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -581,25 +512,21 @@ lemma U_401_8 : have hlg : Real.log (2954486233823141 / 10000000000000000 : ℝ) ≤ (-(12192603200744992393569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2954486233823141 / 10000000000000000 : ℝ) = - (2954486233823141 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2954486233823141 / 2500000000000000 : ℚ)) - (U := (1670340405255007606431 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2954486233823141 / 2500000000000000 : ℝ) ≤ - (1670340405255007606431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2869111362640657 / 10000000000000000 : ℝ)) (q := - (2954486233823141 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2954486233823141 / 10000000000000000 : ℚ)) + (r' := (2954486233823141 / 2500000000000000 : ℚ)) + (U := (-(12192603200744992393569 / 10000000000000000000000 : ℚ))) + (U' := (1670340405255007606431 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (2869111362640657 / 10000000000000000 : ℚ)) + (q := (2954486233823141 / 10000000000000000 : ℚ)) + (U := (-(12192603200744992393569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_9 : Uω (aρ 9) (bρ 9) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -607,25 +534,21 @@ lemma U_401_9 : have hlg : Real.log (629781204456927 / 2500000000000000 : ℝ) ≤ (-(13786735457843431653397 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (629781204456927 / 2500000000000000 : ℝ) = - (629781204456927 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (629781204456927 / 625000000000000 : ℚ)) - (U := (76208148156568346603 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (629781204456927 / 625000000000000 : ℝ) ≤ - (76208148156568346603 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2339354159009791 / 10000000000000000 : ℝ)) (q := - (629781204456927 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (629781204456927 / 2500000000000000 : ℚ)) + (r' := (629781204456927 / 625000000000000 : ℚ)) + (U := (-(13786735457843431653397 / 10000000000000000000000 : ℚ))) + (U' := (76208148156568346603 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (2339354159009791 / 10000000000000000 : ℚ)) + (q := (629781204456927 / 2500000000000000 : ℚ)) + (U := (-(13786735457843431653397 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_10 : Uω (aρ 10) (bρ 10) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -633,25 +556,21 @@ lemma U_401_10 : have hlg : Real.log (767235389239469 / 4000000000000000 : ℝ) ≤ (-(16512559890281452104139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (767235389239469 / 4000000000000000 : ℝ) = - (767235389239469 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (767235389239469 / 500000000000000 : ℚ)) - (U := (4281855518718547895861 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (767235389239469 / 500000000000000 : ℝ) ≤ - (4281855518718547895861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4768251572021 / 31250000000000 : ℝ)) (q := - (767235389239469 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (767235389239469 / 4000000000000000 : ℚ)) + (r' := (767235389239469 / 500000000000000 : ℚ)) + (U := (-(16512559890281452104139 / 10000000000000000000000 : ℚ))) + (U' := (4281855518718547895861 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1294864303869 / 3200000000000 : ℚ)) + (s := (4768251572021 / 31250000000000 : ℚ)) + (q := (767235389239469 / 4000000000000000 : ℚ)) + (U := (-(16512559890281452104139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_401_11 : Uω (aρ 11) (bρ 11) (1294864303869 / 3200000000000 : ℝ) ≤ @@ -773,25 +692,21 @@ lemma U_402_1 : have hlg : Real.log (16032300021672153 / 40000000000000000 : ℝ) ≤ (-(2285685037350096200439 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16032300021672153 / 40000000000000000 : ℝ) = - (16032300021672153 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16032300021672153 / 10000000000000000 : ℚ)) - (U := (1180050864149903799561 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16032300021672153 / 10000000000000000 : ℝ) ≤ - (1180050864149903799561 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2004017334937257 / 5000000000000000 : ℝ)) (q := - (16032300021672153 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16032300021672153 / 40000000000000000 : ℚ)) + (r' := (16032300021672153 / 10000000000000000 : ℚ)) + (U := (-(2285685037350096200439 / 2500000000000000000000 : ℚ))) + (U' := (1180050864149903799561 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (2004017334937257 / 5000000000000000 : ℚ)) + (q := (16032300021672153 / 40000000000000000 : ℚ)) + (U := (-(2285685037350096200439 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_2 : Uω (aρ 2) (bρ 2) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -799,25 +714,21 @@ lemma U_402_2 : have hlg : Real.log (3187264029495937 / 8000000000000000 : ℝ) ≤ (-(4601393316889063213119 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3187264029495937 / 8000000000000000 : ℝ) = - (3187264029495937 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3187264029495937 / 2000000000000000 : ℚ)) - (U := (2330078486110936786881 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3187264029495937 / 2000000000000000 : ℝ) ≤ - (2330078486110936786881 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (99595343632207 / 250000000000000 : ℝ)) (q := - (3187264029495937 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3187264029495937 / 8000000000000000 : ℚ)) + (r' := (3187264029495937 / 2000000000000000 : ℚ)) + (U := (-(4601393316889063213119 / 5000000000000000000000 : ℚ))) + (U' := (2330078486110936786881 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (99595343632207 / 250000000000000 : ℚ)) + (q := (3187264029495937 / 8000000000000000 : ℚ)) + (U := (-(4601393316889063213119 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_3 : Uω (aρ 3) (bρ 3) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -825,25 +736,21 @@ lemma U_402_3 : have hlg : Real.log (15744041711187323 / 40000000000000000 : ℝ) ≤ (-(4662087319745159335967 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15744041711187323 / 40000000000000000 : ℝ) = - (15744041711187323 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15744041711187323 / 10000000000000000 : ℚ)) - (U := (2269384483254840664033 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15744041711187323 / 10000000000000000 : ℝ) ≤ - (2269384483254840664033 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3935070633492099 / 10000000000000000 : ℝ)) (q := - (15744041711187323 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15744041711187323 / 40000000000000000 : ℚ)) + (r' := (15744041711187323 / 10000000000000000 : ℚ)) + (U := (-(4662087319745159335967 / 5000000000000000000000 : ℚ))) + (U' := (2269384483254840664033 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (3935070633492099 / 10000000000000000 : ℚ)) + (q := (15744041711187323 / 40000000000000000 : ℚ)) + (U := (-(4662087319745159335967 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_4 : Uω (aρ 4) (bρ 4) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -851,25 +758,21 @@ lemma U_402_4 : have hlg : Real.log (15423710547039463 / 40000000000000000 : ℝ) ≤ (-(1191216852877995912977 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15423710547039463 / 40000000000000000 : ℝ) = - (15423710547039463 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15423710547039463 / 10000000000000000 : ℚ)) - (U := (541651097872004087023 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15423710547039463 / 10000000000000000 : ℝ) ≤ - (541651097872004087023 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3853199232483169 / 10000000000000000 : ℝ)) (q := - (15423710547039463 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15423710547039463 / 40000000000000000 : ℚ)) + (r' := (15423710547039463 / 10000000000000000 : ℚ)) + (U := (-(1191216852877995912977 / 1250000000000000000000 : ℚ))) + (U' := (541651097872004087023 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (3853199232483169 / 10000000000000000 : ℚ)) + (q := (15423710547039463 / 40000000000000000 : ℚ)) + (U := (-(1191216852877995912977 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_5 : Uω (aρ 5) (bρ 5) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -877,25 +780,21 @@ lemma U_402_5 : have hlg : Real.log (14933334016782087 / 40000000000000000 : ℝ) ≤ (-(9852835570745593329249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14933334016782087 / 40000000000000000 : ℝ) = - (14933334016782087 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14933334016782087 / 10000000000000000 : ℚ)) - (U := (4010108035254406670751 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14933334016782087 / 10000000000000000 : ℝ) ≤ - (4010108035254406670751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3726200886689481 / 10000000000000000 : ℝ)) (q := - (14933334016782087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14933334016782087 / 40000000000000000 : ℚ)) + (r' := (14933334016782087 / 10000000000000000 : ℚ)) + (U := (-(9852835570745593329249 / 10000000000000000000000 : ℚ))) + (U' := (4010108035254406670751 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (3726200886689481 / 10000000000000000 : ℚ)) + (q := (14933334016782087 / 40000000000000000 : ℚ)) + (U := (-(9852835570745593329249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_6 : Uω (aρ 6) (bρ 6) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -903,25 +802,21 @@ lemma U_402_6 : have hlg : Real.log (14223879762145861 / 40000000000000000 : ℝ) ≤ (-(10339572280256983547971 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14223879762145861 / 40000000000000000 : ℝ) = - (14223879762145861 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14223879762145861 / 10000000000000000 : ℚ)) - (U := (3523371325743016452029 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14223879762145861 / 10000000000000000 : ℝ) ≤ - (3523371325743016452029 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (442339266813921 / 1250000000000000 : ℝ)) (q := - (14223879762145861 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14223879762145861 / 40000000000000000 : ℚ)) + (r' := (14223879762145861 / 10000000000000000 : ℚ)) + (U := (-(10339572280256983547971 / 10000000000000000000000 : ℚ))) + (U' := (3523371325743016452029 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (442339266813921 / 1250000000000000 : ℚ)) + (q := (14223879762145861 / 40000000000000000 : ℚ)) + (U := (-(10339572280256983547971 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_7 : Uω (aρ 7) (bρ 7) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -929,25 +824,21 @@ lemma U_402_7 : have hlg : Real.log (13241568741205117 / 40000000000000000 : ℝ) ≤ (-(690949015699183907021 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13241568741205117 / 40000000000000000 : ℝ) = - (13241568741205117 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13241568741205117 / 10000000000000000 : ℚ)) - (U := (175484959675816092979 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13241568741205117 / 10000000000000000 : ℝ) ≤ - (175484959675816092979 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (817805001200249 / 2500000000000000 : ℝ)) (q := - (13241568741205117 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13241568741205117 / 40000000000000000 : ℚ)) + (r' := (13241568741205117 / 10000000000000000 : ℚ)) + (U := (-(690949015699183907021 / 625000000000000000000 : ℚ))) + (U' := (175484959675816092979 / 625000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (817805001200249 / 2500000000000000 : ℚ)) + (q := (13241568741205117 / 40000000000000000 : ℚ)) + (U := (-(690949015699183907021 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_8 : Uω (aρ 8) (bρ 8) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -955,25 +846,21 @@ lemma U_402_8 : have hlg : Real.log (11925676331596149 / 40000000000000000 : ℝ) ≤ (-(12101857029900682044303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11925676331596149 / 40000000000000000 : ℝ) = - (11925676331596149 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11925676331596149 / 10000000000000000 : ℚ)) - (U := (1761086576099317955697 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11925676331596149 / 10000000000000000 : ℝ) ≤ - (1761086576099317955697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45262741427133 / 156250000000000 : ℝ)) (q := - (11925676331596149 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11925676331596149 / 40000000000000000 : ℚ)) + (r' := (11925676331596149 / 10000000000000000 : ℚ)) + (U := (-(12101857029900682044303 / 10000000000000000000000 : ℚ))) + (U' := (1761086576099317955697 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (45262741427133 / 156250000000000 : ℚ)) + (q := (11925676331596149 / 40000000000000000 : ℚ)) + (U := (-(12101857029900682044303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_9 : Uω (aρ 9) (bρ 9) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -981,25 +868,21 @@ lemma U_402_9 : have hlg : Real.log (10189091787651641 / 40000000000000000 : ℝ) ≤ (-(6837808690690216867231 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10189091787651641 / 40000000000000000 : ℝ) = - (10189091787651641 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10189091787651641 / 10000000000000000 : ℚ)) - (U := (93663112309783132769 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10189091787651641 / 10000000000000000 : ℝ) ≤ - (93663112309783132769 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1184744403862129 / 5000000000000000 : ℝ)) (q := - (10189091787651641 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10189091787651641 / 40000000000000000 : ℚ)) + (r' := (10189091787651641 / 10000000000000000 : ℚ)) + (U := (-(6837808690690216867231 / 5000000000000000000000 : ℚ))) + (U' := (93663112309783132769 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (1184744403862129 / 5000000000000000 : ℚ)) + (q := (10189091787651641 / 40000000000000000 : ℚ)) + (U := (-(6837808690690216867231 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_10 : Uω (aρ 10) (bρ 10) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -1007,26 +890,21 @@ lemma U_402_10 : have hlg : Real.log (7803336604278519 / 40000000000000000 : ℝ) ≤ (-(2042910051658331651807 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7803336604278519 / 40000000000000000 : ℝ) = - (7803336604278519 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7803336604278519 / 5000000000000000 : ℚ)) - (U := (556391874466668348193 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7803336604278519 / 5000000000000000 : ℝ) ≤ - (556391874466668348193 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1565170249532697 / 10000000000000000 : ℝ)) (q := - (7803336604278519 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7803336604278519 / 40000000000000000 : ℚ)) + (r' := (7803336604278519 / 5000000000000000 : ℚ)) + (U := (-(2042910051658331651807 / 1250000000000000000000 : ℚ))) + (U' := (556391874466668348193 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (13032360188949 / 32000000000000 : ℚ)) + (s := (1565170249532697 / 10000000000000000 : ℚ)) + (q := (7803336604278519 / 40000000000000000 : ℚ)) + (U := (-(2042910051658331651807 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_402_11 : Uω (aρ 11) (bρ 11) (13032360188949 / 32000000000000 : ℝ) ≤ @@ -1148,25 +1026,21 @@ lemma U_403_1 : have hlg : Real.log (8068473752896849 / 20000000000000000 : ℝ) ≤ (-(9077679346739136303621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8068473752896849 / 20000000000000000 : ℝ) = - (8068473752896849 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8068473752896849 / 5000000000000000 : ℚ)) - (U := (4785264259260863696379 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8068473752896849 / 5000000000000000 : ℝ) ≤ - (4785264259260863696379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4034196802479349 / 10000000000000000 : ℝ)) (q := - (8068473752896849 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8068473752896849 / 20000000000000000 : ℚ)) + (r' := (8068473752896849 / 5000000000000000 : ℚ)) + (U := (-(9077679346739136303621 / 10000000000000000000000 : ℚ))) + (U' := (4785264259260863696379 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (4034196802479349 / 10000000000000000 : ℚ)) + (q := (8068473752896849 / 20000000000000000 : ℚ)) + (U := (-(9077679346739136303621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_2 : Uω (aρ 2) (bρ 2) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1174,25 +1048,21 @@ lemma U_403_2 : have hlg : Real.log (8020486767293193 / 20000000000000000 : ℝ) ≤ (-(2284332897053214077443 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8020486767293193 / 20000000000000000 : ℝ) = - (8020486767293193 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8020486767293193 / 5000000000000000 : ℚ)) - (U := (1181403004446785922557 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8020486767293193 / 5000000000000000 : ℝ) ≤ - (1181403004446785922557 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4009978829385693 / 10000000000000000 : ℝ)) (q := - (8020486767293193 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8020486767293193 / 20000000000000000 : ℚ)) + (r' := (8020486767293193 / 5000000000000000 : ℚ)) + (U := (-(2284332897053214077443 / 2500000000000000000000 : ℚ))) + (U' := (1181403004446785922557 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (4009978829385693 / 10000000000000000 : ℚ)) + (q := (8020486767293193 / 20000000000000000 : ℚ)) + (U := (-(2284332897053214077443 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_3 : Uω (aρ 3) (bρ 3) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1200,25 +1070,21 @@ lemma U_403_3 : have hlg : Real.log (7924356488063509 / 20000000000000000 : ℝ) ≤ (-(4628955784060132778483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7924356488063509 / 20000000000000000 : ℝ) = - (7924356488063509 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7924356488063509 / 5000000000000000 : ℚ)) - (U := (2302516018939867221517 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7924356488063509 / 5000000000000000 : ℝ) ≤ - (2302516018939867221517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3961244656506009 / 10000000000000000 : ℝ)) (q := - (7924356488063509 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7924356488063509 / 20000000000000000 : ℚ)) + (r' := (7924356488063509 / 5000000000000000 : ℚ)) + (U := (-(4628955784060132778483 / 5000000000000000000000 : ℚ))) + (U' := (2302516018939867221517 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (3961244656506009 / 10000000000000000 : ℚ)) + (q := (7924356488063509 / 20000000000000000 : ℚ)) + (U := (-(4628955784060132778483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_4 : Uω (aρ 4) (bρ 4) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1226,25 +1092,21 @@ lemma U_403_4 : have hlg : Real.log (1941053822962141 / 5000000000000000 : ℝ) ≤ (-(9462068786104314284357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1941053822962141 / 5000000000000000 : ℝ) = - (1941053822962141 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1941053822962141 / 1250000000000000 : ℚ)) - (U := (4400874819895685715643 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1941053822962141 / 1250000000000000 : ℝ) ≤ - (4400874819895685715643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121231176292377 / 312500000000000 : ℝ)) (q := - (1941053822962141 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1941053822962141 / 5000000000000000 : ℚ)) + (r' := (1941053822962141 / 1250000000000000 : ℚ)) + (U := (-(9462068786104314284357 / 10000000000000000000000 : ℚ))) + (U' := (4400874819895685715643 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (121231176292377 / 312500000000000 : ℚ)) + (q := (1941053822962141 / 5000000000000000 : ℚ)) + (U := (-(9462068786104314284357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_5 : Uω (aρ 5) (bρ 5) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1252,25 +1114,21 @@ lemma U_403_5 : have hlg : Real.log (7519089683728511 / 20000000000000000 : ℝ) ≤ (-(4891435975477487785923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7519089683728511 / 20000000000000000 : ℝ) = - (7519089683728511 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7519089683728511 / 5000000000000000 : ℚ)) - (U := (2040035827522512214077 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7519089683728511 / 5000000000000000 : ℝ) ≤ - (2040035827522512214077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3752461952571011 / 10000000000000000 : ℝ)) (q := - (7519089683728511 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7519089683728511 / 20000000000000000 : ℚ)) + (r' := (7519089683728511 / 5000000000000000 : ℚ)) + (U := (-(4891435975477487785923 / 5000000000000000000000 : ℚ))) + (U' := (2040035827522512214077 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (3752461952571011 / 10000000000000000 : ℚ)) + (q := (7519089683728511 / 20000000000000000 : ℚ)) + (U := (-(4891435975477487785923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_6 : Uω (aρ 6) (bρ 6) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1278,25 +1136,21 @@ lemma U_403_6 : have hlg : Real.log (1432903272379271 / 4000000000000000 : ℝ) ≤ (-(10265917141164475357851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1432903272379271 / 4000000000000000 : ℝ) = - (1432903272379271 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1432903272379271 / 1000000000000000 : ℚ)) - (U := (3597026464835524642149 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1432903272379271 / 1000000000000000 : ℝ) ≤ - (3597026464835524642149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (713025801175771 / 2000000000000000 : ℝ)) (q := - (1432903272379271 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1432903272379271 / 4000000000000000 : ℚ)) + (r' := (1432903272379271 / 1000000000000000 : ℚ)) + (U := (-(10265917141164475357851 / 10000000000000000000000 : ℚ))) + (U' := (3597026464835524642149 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (713025801175771 / 2000000000000000 : ℚ)) + (q := (1432903272379271 / 4000000000000000 : ℚ)) + (U := (-(10265917141164475357851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_7 : Uω (aρ 7) (bρ 7) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1304,25 +1158,21 @@ lemma U_403_7 : have hlg : Real.log (3336864559731609 / 10000000000000000 : ℝ) ≤ (-(1371941851203687294137 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3336864559731609 / 10000000000000000 : ℝ) = - (3336864559731609 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3336864559731609 / 2500000000000000 : ℚ)) - (U := (360926099546312705863 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3336864559731609 / 2500000000000000 : ℝ) ≤ - (360926099546312705863 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1649001572102859 / 5000000000000000 : ℝ)) (q := - (3336864559731609 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3336864559731609 / 10000000000000000 : ℚ)) + (r' := (3336864559731609 / 2500000000000000 : ℚ)) + (U := (-(1371941851203687294137 / 1250000000000000000000 : ℚ))) + (U' := (360926099546312705863 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (1649001572102859 / 5000000000000000 : ℚ)) + (q := (3336864559731609 / 10000000000000000 : ℚ)) + (U := (-(1371941851203687294137 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_8 : Uω (aρ 8) (bρ 8) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1330,25 +1180,21 @@ lemma U_403_8 : have hlg : Real.log (6016675453428553 / 20000000000000000 : ℝ) ≤ (-(12011974165207489099981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6016675453428553 / 20000000000000000 : ℝ) = - (6016675453428553 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6016675453428553 / 5000000000000000 : ℚ)) - (U := (1850969440792510900019 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6016675453428553 / 5000000000000000 : ℝ) ≤ - (1850969440792510900019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2924491129511053 / 10000000000000000 : ℝ)) (q := - (6016675453428553 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6016675453428553 / 20000000000000000 : ℚ)) + (r' := (6016675453428553 / 5000000000000000 : ℚ)) + (U := (-(12011974165207489099981 / 10000000000000000000000 : ℚ))) + (U' := (1850969440792510900019 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (2924491129511053 / 10000000000000000 : ℚ)) + (q := (6016675453428553 / 20000000000000000 : ℚ)) + (U := (-(12011974165207489099981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_9 : Uω (aρ 9) (bρ 9) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1356,25 +1202,21 @@ lemma U_403_9 : have hlg : Real.log (103014978817541 / 400000000000000 : ℝ) ≤ (-(1695737679398358110773 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (103014978817541 / 400000000000000 : ℝ) = - (103014978817541 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (103014978817541 / 100000000000000 : ℚ)) - (U := (37130271351641889227 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (103014978817541 / 100000000000000 : ℝ) ≤ - (37130271351641889227 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (47990604906391 / 200000000000000 : ℝ)) (q := - (103014978817541 / 400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (103014978817541 / 400000000000000 : ℚ)) + (r' := (103014978817541 / 100000000000000 : ℚ)) + (U := (-(1695737679398358110773 / 1250000000000000000000 : ℚ))) + (U' := (37130271351641889227 / 1250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (47990604906391 / 200000000000000 : ℚ)) + (q := (103014978817541 / 400000000000000 : ℚ)) + (U := (-(1695737679398358110773 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_10 : Uω (aρ 10) (bρ 10) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1382,26 +1224,21 @@ lemma U_403_10 : have hlg : Real.log (3966622080239831 / 20000000000000000 : ℝ) ≤ (-(647126960665450513509 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3966622080239831 / 20000000000000000 : ℝ) = - (3966622080239831 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3966622080239831 / 2500000000000000 : ℚ)) - (U := (184649655694549486491 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3966622080239831 / 2500000000000000 : ℝ) ≤ - (184649655694549486491 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1603962418177331 / 10000000000000000 : ℝ)) (q := - (3966622080239831 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3966622080239831 / 20000000000000000 : ℚ)) + (r' := (3966622080239831 / 2500000000000000 : ℚ)) + (U := (-(647126960665450513509 / 400000000000000000000 : ℚ))) + (U' := (184649655694549486491 / 400000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1639509667401 / 4000000000000 : ℚ)) + (s := (1603962418177331 / 10000000000000000 : ℚ)) + (q := (3966622080239831 / 20000000000000000 : ℚ)) + (U := (-(647126960665450513509 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_403_11 : Uω (aρ 11) (bρ 11) (1639509667401 / 4000000000000 : ℝ) ≤ @@ -1522,25 +1359,21 @@ lemma U_404_1 : have hlg : Real.log (8173121216923227 / 20000000000000000 : ℝ) ≤ (-(8948814032234249353119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8173121216923227 / 20000000000000000 : ℝ) = - (8173121216923227 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8173121216923227 / 5000000000000000 : ℚ)) - (U := (4914129573765750646881 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8173121216923227 / 5000000000000000 : ℝ) ≤ - (4914129573765750646881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1021630261898463 / 2500000000000000 : ℝ)) (q := - (8173121216923227 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8173121216923227 / 20000000000000000 : ℚ)) + (r' := (8173121216923227 / 5000000000000000 : ℚ)) + (U := (-(8948814032234249353119 / 10000000000000000000000 : ℚ))) + (U' := (4914129573765750646881 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (1021630261898463 / 2500000000000000 : ℚ)) + (q := (8173121216923227 / 20000000000000000 : ℚ)) + (U := (-(8948814032234249353119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_2 : Uω (aρ 2) (bρ 2) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1548,24 +1381,21 @@ lemma U_404_2 : have hlg : Real.log (126955312814517 / 312500000000000 : ℝ) ≤ (-(1125961639650166118421 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (126955312814517 / 312500000000000 : ℝ) = (126955312814517 / 78125000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (126955312814517 / 78125000000000 : ℚ)) - (U := (606906311099833881579 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (126955312814517 / 78125000000000 : ℝ) ≤ - (606906311099833881579 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4062308863309713 / 10000000000000000 : ℝ)) (q := - (126955312814517 / 312500000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (126955312814517 / 312500000000000 : ℚ)) + (r' := (126955312814517 / 78125000000000 : ℚ)) + (U := (-(1125961639650166118421 / 1250000000000000000000 : ℚ))) + (U' := (606906311099833881579 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (4062308863309713 / 10000000000000000 : ℚ)) + (q := (126955312814517 / 312500000000000 : ℚ)) + (U := (-(1125961639650166118421 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_3 : Uω (aρ 3) (bρ 3) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1573,25 +1403,21 @@ lemma U_404_3 : have hlg : Real.log (1003628408424973 / 2500000000000000 : ℝ) ≤ (-(456334444861630339123 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1003628408424973 / 2500000000000000 : ℝ) = - (1003628408424973 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1003628408424973 / 625000000000000 : ℚ)) - (U := (236812735438369660877 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1003628408424973 / 625000000000000 : ℝ) ≤ - (236812735438369660877 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4013592216930409 / 10000000000000000 : ℝ)) (q := - (1003628408424973 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1003628408424973 / 2500000000000000 : ℚ)) + (r' := (1003628408424973 / 625000000000000 : ℚ)) + (U := (-(456334444861630339123 / 500000000000000000000 : ℚ))) + (U' := (236812735438369660877 / 500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (4013592216930409 / 10000000000000000 : ℚ)) + (q := (1003628408424973 / 2500000000000000 : ℚ)) + (U := (-(456334444861630339123 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_4 : Uω (aρ 4) (bρ 4) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1599,24 +1425,21 @@ lemma U_404_4 : have hlg : Real.log (78689338583237 / 200000000000000 : ℝ) ≤ (-(9328096888636753907783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (78689338583237 / 200000000000000 : ℝ) = (78689338583237 / 50000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78689338583237 / 50000000000000 : ℚ)) - (U := (4534846717363246092217 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (78689338583237 / 50000000000000 : ℝ) ≤ - (4534846717363246092217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (157271719556773 / 400000000000000 : ℝ)) (q := - (78689338583237 / 200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78689338583237 / 200000000000000 : ℚ)) + (r' := (78689338583237 / 50000000000000 : ℚ)) + (U := (-(9328096888636753907783 / 10000000000000000000000 : ℚ))) + (U' := (4534846717363246092217 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (157271719556773 / 400000000000000 : ℚ)) + (q := (78689338583237 / 200000000000000 : ℚ)) + (U := (-(9328096888636753907783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_5 : Uω (aρ 5) (bρ 5) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1624,25 +1447,21 @@ lemma U_404_5 : have hlg : Real.log (1905982730914291 / 5000000000000000 : ℝ) ≤ (-(2411100417759986548877 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1905982730914291 / 5000000000000000 : ℝ) = - (1905982730914291 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1905982730914291 / 1250000000000000 : ℚ)) - (U := (1054635483740013451123 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1905982730914291 / 1250000000000000 : ℝ) ≤ - (1054635483740013451123 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3804979973587789 / 10000000000000000 : ℝ)) (q := - (1905982730914291 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1905982730914291 / 5000000000000000 : ℚ)) + (r' := (1905982730914291 / 1250000000000000 : ℚ)) + (U := (-(2411100417759986548877 / 2500000000000000000000 : ℚ))) + (U' := (1054635483740013451123 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (3804979973587789 / 10000000000000000 : ℚ)) + (q := (1905982730914291 / 5000000000000000 : ℚ)) + (U := (-(2411100417759986548877 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_6 : Uω (aρ 6) (bρ 6) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1650,25 +1469,21 @@ lemma U_404_6 : have hlg : Real.log (7269658282256159 / 20000000000000000 : ℝ) ≤ (-(5060114932047977894949 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7269658282256159 / 20000000000000000 : ℝ) = - (7269658282256159 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7269658282256159 / 5000000000000000 : ℚ)) - (U := (1871356870952022105051 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7269658282256159 / 5000000000000000 : ℝ) ≤ - (1871356870952022105051 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56530432926981 / 156250000000000 : ℝ)) (q := - (7269658282256159 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7269658282256159 / 20000000000000000 : ℚ)) + (r' := (7269658282256159 / 5000000000000000 : ℚ)) + (U := (-(5060114932047977894949 / 5000000000000000000000 : ℚ))) + (U' := (1871356870952022105051 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (56530432926981 / 156250000000000 : ℚ)) + (q := (7269658282256159 / 20000000000000000 : ℚ)) + (U := (-(5060114932047977894949 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_7 : Uω (aρ 7) (bρ 7) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1676,25 +1491,21 @@ lemma U_404_7 : have hlg : Real.log (423724322632849 / 1250000000000000 : ℝ) ≤ (-(10818157684744796127839 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (423724322632849 / 1250000000000000 : ℝ) = - (423724322632849 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (423724322632849 / 312500000000000 : ℚ)) - (U := (3044785921255203872161 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (423724322632849 / 312500000000000 : ℝ) ≤ - (3044785921255203872161 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3351539967956209 / 10000000000000000 : ℝ)) (q := - (423724322632849 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (423724322632849 / 1250000000000000 : ℚ)) + (r' := (423724322632849 / 312500000000000 : ℚ)) + (U := (-(10818157684744796127839 / 10000000000000000000000 : ℚ))) + (U' := (3044785921255203872161 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (3351539967956209 / 10000000000000000 : ℚ)) + (q := (423724322632849 / 1250000000000000 : ℚ)) + (U := (-(10818157684744796127839 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_8 : Uω (aρ 8) (bρ 8) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1702,25 +1513,21 @@ lemma U_404_8 : have hlg : Real.log (3062133981399583 / 10000000000000000 : ℝ) ≤ (-(5917365200118181528387 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3062133981399583 / 10000000000000000 : ℝ) = - (3062133981399583 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3062133981399583 / 2500000000000000 : ℚ)) - (U := (1014106602881818471613 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3062133981399583 / 2500000000000000 : ℝ) ≤ - (1014106602881818471613 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2979760419969791 / 10000000000000000 : ℝ)) (q := - (3062133981399583 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3062133981399583 / 10000000000000000 : ℚ)) + (r' := (3062133981399583 / 2500000000000000 : ℚ)) + (U := (-(5917365200118181528387 / 5000000000000000000000 : ℚ))) + (U' := (1014106602881818471613 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (2979760419969791 / 10000000000000000 : ℚ)) + (q := (3062133981399583 / 10000000000000000 : ℚ)) + (U := (-(5917365200118181528387 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_9 : Uω (aρ 9) (bρ 9) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1728,24 +1535,21 @@ lemma U_404_9 : have hlg : Real.log (13157222635451 / 50000000000000 : ℝ) ≤ (-(3337630368056965153349 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13157222635451 / 50000000000000 : ℝ) = (13157222635451 / 12500000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13157222635451 / 12500000000000 : ℚ)) - (U := (128105533443034846651 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (13157222635451 / 12500000000000 : ℝ) ≤ - (128105533443034846651 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98373885588441 / 400000000000000 : ℝ)) (q := - (13157222635451 / 50000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13157222635451 / 50000000000000 : ℚ)) + (r' := (13157222635451 / 12500000000000 : ℚ)) + (U := (-(3337630368056965153349 / 2500000000000000000000 : ℚ))) + (U' := (128105533443034846651 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (98373885588441 / 400000000000000 : ℚ)) + (q := (13157222635451 / 50000000000000 : ℚ)) + (U := (-(3337630368056965153349 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_10 : Uω (aρ 10) (bρ 10) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1753,26 +1557,21 @@ lemma U_404_10 : have hlg : Real.log (4095065341923027 / 20000000000000000 : ℝ) ≤ (-(15859495990828664169851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4095065341923027 / 20000000000000000 : ℝ) = - (4095065341923027 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4095065341923027 / 2500000000000000 : ℚ)) - (U := (4934919418171335830149 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4095065341923027 / 2500000000000000 : ℝ) ≤ - (4934919418171335830149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (420020615237163 / 2500000000000000 : ℝ)) (q := - (4095065341923027 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4095065341923027 / 20000000000000000 : ℚ)) + (r' := (4095065341923027 / 2500000000000000 : ℚ)) + (U := (-(15859495990828664169851 / 10000000000000000000000 : ℚ))) + (U' := (4934919418171335830149 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (6641755819863 / 16000000000000 : ℚ)) + (s := (420020615237163 / 2500000000000000 : ℚ)) + (q := (4095065341923027 / 20000000000000000 : ℚ)) + (U := (-(15859495990828664169851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_404_11 : Uω (aρ 11) (bρ 11) (6641755819863 / 16000000000000 : ℝ) ≤ @@ -1894,24 +1693,21 @@ lemma U_405_1 : have hlg : Real.log (66222149240023 / 160000000000000 : ℝ) ≤ (-(2205397067664007022223 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (66222149240023 / 160000000000000 : ℝ) = (66222149240023 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (66222149240023 / 40000000000000 : ℚ)) - (U := (1260338833835992977777 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (66222149240023 / 40000000000000 : ℝ) ≤ - (1260338833835992977777 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33110762134093 / 80000000000000 : ℝ)) (q := - (66222149240023 / 160000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (66222149240023 / 160000000000000 : ℚ)) + (r' := (66222149240023 / 40000000000000 : ℚ)) + (U := (-(2205397067664007022223 / 2500000000000000000000 : ℚ))) + (U' := (1260338833835992977777 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (33110762134093 / 80000000000000 : ℚ)) + (q := (66222149240023 / 160000000000000 : ℚ)) + (U := (-(2205397067664007022223 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_2 : Uω (aρ 2) (bρ 2) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -1919,25 +1715,21 @@ lemma U_405_2 : have hlg : Real.log (822979309962943 / 2000000000000000 : ℝ) ≤ (-(4439856992194217320277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (822979309962943 / 2000000000000000 : ℝ) = - (822979309962943 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (822979309962943 / 500000000000000 : ℚ)) - (U := (2491614810805782679723 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (822979309962943 / 500000000000000 : ℝ) ≤ - (2491614810805782679723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (205731936194909 / 500000000000000 : ℝ)) (q := - (822979309962943 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (822979309962943 / 2000000000000000 : ℚ)) + (r' := (822979309962943 / 500000000000000 : ℚ)) + (U := (-(4439856992194217320277 / 5000000000000000000000 : ℚ))) + (U' := (2491614810805782679723 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (205731936194909 / 500000000000000 : ℚ)) + (q := (822979309962943 / 2000000000000000 : ℚ)) + (U := (-(4439856992194217320277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_3 : Uω (aρ 3) (bρ 3) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -1945,25 +1737,21 @@ lemma U_405_3 : have hlg : Real.log (4066848710052361 / 10000000000000000 : ℝ) ≤ (-(2249291664094980362187 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4066848710052361 / 10000000000000000 : ℝ) = - (4066848710052361 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4066848710052361 / 2500000000000000 : ℚ)) - (U := (1216444237405019637813 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4066848710052361 / 2500000000000000 : ℝ) ≤ - (1216444237405019637813 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (254121196920217 / 625000000000000 : ℝ)) (q := - (4066848710052361 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4066848710052361 / 10000000000000000 : ℚ)) + (r' := (4066848710052361 / 2500000000000000 : ℚ)) + (U := (-(2249291664094980362187 / 2500000000000000000000 : ℚ))) + (U' := (1216444237405019637813 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (254121196920217 / 625000000000000 : ℚ)) + (q := (4066848710052361 / 10000000000000000 : ℚ)) + (U := (-(2249291664094980362187 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_4 : Uω (aρ 4) (bρ 4) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -1971,25 +1759,21 @@ lemma U_405_4 : have hlg : Real.log (7973650529002219 / 20000000000000000 : ℝ) ≤ (-(143685914272745119657 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7973650529002219 / 20000000000000000 : ℝ) = - (7973650529002219 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7973650529002219 / 5000000000000000 : ℚ)) - (U := (72922579571004880343 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7973650529002219 / 5000000000000000 : ℝ) ≤ - (72922579571004880343 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3984186440685969 / 10000000000000000 : ℝ)) (q := - (7973650529002219 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7973650529002219 / 20000000000000000 : ℚ)) + (r' := (7973650529002219 / 5000000000000000 : ℚ)) + (U := (-(143685914272745119657 / 156250000000000000000 : ℚ))) + (U' := (72922579571004880343 / 156250000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (3984186440685969 / 10000000000000000 : ℚ)) + (q := (7973650529002219 / 20000000000000000 : ℚ)) + (U := (-(143685914272745119657 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_5 : Uω (aρ 5) (bρ 5) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -1997,25 +1781,21 @@ lemma U_405_5 : have hlg : Real.log (3864383434570763 / 10000000000000000 : ℝ) ≤ (-(4753914742488689626759 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3864383434570763 / 10000000000000000 : ℝ) = - (3864383434570763 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3864383434570763 / 2500000000000000 : ℚ)) - (U := (2177557060511310373241 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3864383434570763 / 2500000000000000 : ℝ) ≤ - (2177557060511310373241 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (964373175040069 / 2500000000000000 : ℝ)) (q := - (3864383434570763 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3864383434570763 / 10000000000000000 : ℚ)) + (r' := (3864383434570763 / 2500000000000000 : ℚ)) + (U := (-(4753914742488689626759 / 5000000000000000000000 : ℚ))) + (U' := (2177557060511310373241 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (964373175040069 / 2500000000000000 : ℚ)) + (q := (3864383434570763 / 10000000000000000 : ℚ)) + (U := (-(4753914742488689626759 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_6 : Uω (aρ 6) (bρ 6) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2023,25 +1803,21 @@ lemma U_405_6 : have hlg : Real.log (1474957202092181 / 4000000000000000 : ℝ) ≤ (-(2494163466899750630607 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1474957202092181 / 4000000000000000 : ℝ) = - (1474957202092181 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1474957202092181 / 1000000000000000 : ℚ)) - (U := (971572434600249369393 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1474957202092181 / 1000000000000000 : ℝ) ≤ - (971572434600249369393 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (734150443323931 / 2000000000000000 : ℝ)) (q := - (1474957202092181 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1474957202092181 / 4000000000000000 : ℚ)) + (r' := (1474957202092181 / 1000000000000000 : ℚ)) + (U := (-(2494163466899750630607 / 2500000000000000000000 : ℚ))) + (U' := (971572434600249369393 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (734150443323931 / 2000000000000000 : ℚ)) + (q := (1474957202092181 / 4000000000000000 : ℚ)) + (U := (-(2494163466899750630607 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_7 : Uω (aρ 7) (bρ 7) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2049,25 +1825,21 @@ lemma U_405_7 : have hlg : Real.log (1721352868739247 / 5000000000000000 : ℝ) ≤ (-(2665818446664646446537 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1721352868739247 / 5000000000000000 : ℝ) = - (1721352868739247 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1721352868739247 / 1250000000000000 : ℚ)) - (U := (799917454835353553463 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1721352868739247 / 1250000000000000 : ℝ) ≤ - (799917454835353553463 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1702519530937869 / 5000000000000000 : ℝ)) (q := - (1721352868739247 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1721352868739247 / 5000000000000000 : ℚ)) + (r' := (1721352868739247 / 1250000000000000 : ℚ)) + (U := (-(2665818446664646446537 / 2500000000000000000000 : ℚ))) + (U' := (799917454835353553463 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (1702519530937869 / 5000000000000000 : ℚ)) + (q := (1721352868739247 / 5000000000000000 : ℚ)) + (U := (-(2665818446664646446537 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_8 : Uω (aρ 8) (bρ 8) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2075,25 +1847,21 @@ lemma U_405_8 : have hlg : Real.log (6231756031451009 / 20000000000000000 : ℝ) ≤ (-(11660741129451976871839 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6231756031451009 / 20000000000000000 : ℝ) = - (6231756031451009 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6231756031451009 / 5000000000000000 : ℚ)) - (U := (2202202476548023128161 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6231756031451009 / 5000000000000000 : ℝ) ≤ - (2202202476548023128161 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3034925269709759 / 10000000000000000 : ℝ)) (q := - (6231756031451009 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6231756031451009 / 20000000000000000 : ℚ)) + (r' := (6231756031451009 / 5000000000000000 : ℚ)) + (U := (-(11660741129451976871839 / 10000000000000000000000 : ℚ))) + (U' := (2202202476548023128161 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (3034925269709759 / 10000000000000000 : ℚ)) + (q := (6231756031451009 / 20000000000000000 : ℚ)) + (U := (-(11660741129451976871839 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_9 : Uω (aρ 9) (bρ 9) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2101,25 +1869,21 @@ lemma U_405_9 : have hlg : Real.log (5374695565840111 / 20000000000000000 : ℝ) ≤ (-(13140303395378854275257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5374695565840111 / 20000000000000000 : ℝ) = - (5374695565840111 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5374695565840111 / 5000000000000000 : ℚ)) - (U := (722640210621145724743 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5374695565840111 / 5000000000000000 : ℝ) ≤ - (722640210621145724743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2518830432458861 / 10000000000000000 : ℝ)) (q := - (5374695565840111 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5374695565840111 / 20000000000000000 : ℚ)) + (r' := (5374695565840111 / 5000000000000000 : ℚ)) + (U := (-(13140303395378854275257 / 10000000000000000000000 : ℚ))) + (U' := (722640210621145724743 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (2518830432458861 / 10000000000000000 : ℚ)) + (q := (5374695565840111 / 20000000000000000 : ℚ)) + (U := (-(13140303395378854275257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_10 : Uω (aρ 10) (bρ 10) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2127,25 +1891,21 @@ lemma U_405_10 : have hlg : Real.log (844353462736983 / 4000000000000000 : ℝ) ≤ (-(1555478437684198579321 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (844353462736983 / 4000000000000000 : ℝ) = - (844353462736983 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (844353462736983 / 500000000000000 : ℚ)) - (U := (523963103215801420679 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (844353462736983 / 500000000000000 : ℝ) ≤ - (523963103215801420679 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (350892242759733 / 2000000000000000 : ℝ)) (q := - (844353462736983 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (844353462736983 / 4000000000000000 : ℚ)) + (r' := (844353462736983 / 500000000000000 : ℚ)) + (U := (-(1555478437684198579321 / 1000000000000000000000 : ℚ))) + (U' := (523963103215801420679 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (3362736485061 / 8000000000000 : ℚ)) + (s := (350892242759733 / 2000000000000000 : ℚ)) + (q := (844353462736983 / 4000000000000000 : ℚ)) + (U := (-(1555478437684198579321 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_405_11 : Uω (aρ 11) (bρ 11) (3362736485061 / 8000000000000 : ℝ) ≤ @@ -2266,25 +2026,21 @@ lemma U_406_1 : have hlg : Real.log (8382416068107581 / 20000000000000000 : ℝ) ≤ (-(8695960864778360946079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8382416068107581 / 20000000000000000 : ℝ) = - (8382416068107581 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8382416068107581 / 5000000000000000 : ℚ)) - (U := (5166982741221639053921 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8382416068107581 / 5000000000000000 : ℝ) ≤ - (5166982741221639053921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (523896182619307 / 1250000000000000 : ℝ)) (q := - (8382416068107581 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8382416068107581 / 20000000000000000 : ℚ)) + (r' := (8382416068107581 / 5000000000000000 : ℚ)) + (U := (-(8695960864778360946079 / 10000000000000000000000 : ℚ))) + (U' := (5166982741221639053921 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (523896182619307 / 1250000000000000 : ℚ)) + (q := (8382416068107581 / 20000000000000000 : ℚ)) + (U := (-(8695960864778360946079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_2 : Uω (aρ 2) (bρ 2) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2292,25 +2048,21 @@ lemma U_406_2 : have hlg : Real.log (4167223006162299 / 10000000000000000 : ℝ) ≤ (-(4376676121341284168073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4167223006162299 / 10000000000000000 : ℝ) = - (4167223006162299 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4167223006162299 / 2500000000000000 : ℚ)) - (U := (2554795681658715831927 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4167223006162299 / 2500000000000000 : ℝ) ≤ - (2554795681658715831927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4166968417681473 / 10000000000000000 : ℝ)) (q := - (4167223006162299 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4167223006162299 / 10000000000000000 : ℚ)) + (r' := (4167223006162299 / 2500000000000000 : ℚ)) + (U := (-(4376676121341284168073 / 5000000000000000000000 : ℚ))) + (U' := (2554795681658715831927 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (4166968417681473 / 10000000000000000 : ℚ)) + (q := (4167223006162299 / 10000000000000000 : ℚ)) + (U := (-(4376676121341284168073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_3 : Uω (aρ 3) (bρ 3) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2318,25 +2070,21 @@ lemma U_406_3 : have hlg : Real.log (1029795871259173 / 2500000000000000 : ℝ) ≤ (-(2217325329992838613491 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1029795871259173 / 2500000000000000 : ℝ) = - (1029795871259173 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1029795871259173 / 625000000000000 : ℚ)) - (U := (1248410571507161386509 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1029795871259173 / 625000000000000 : ℝ) ≤ - (1248410571507161386509 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4118285481780259 / 10000000000000000 : ℝ)) (q := - (1029795871259173 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1029795871259173 / 2500000000000000 : ℚ)) + (r' := (1029795871259173 / 625000000000000 : ℚ)) + (U := (-(2217325329992838613491 / 2500000000000000000000 : ℚ))) + (U' := (1248410571507161386509 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (4118285481780259 / 10000000000000000 : ℚ)) + (q := (1029795871259173 / 2500000000000000 : ℚ)) + (U := (-(2217325329992838613491 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_4 : Uω (aρ 4) (bρ 4) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2344,25 +2092,21 @@ lemma U_406_4 : have hlg : Real.log (1615673075540913 / 4000000000000000 : ℝ) ≤ (-(9065427257069945571199 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1615673075540913 / 4000000000000000 : ℝ) = - (1615673075540913 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1615673075540913 / 1000000000000000 : ℚ)) - (U := (4797516348930054428801 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1615673075540913 / 1000000000000000 : ℝ) ≤ - (4797516348930054428801 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100914451761911 / 250000000000000 : ℝ)) (q := - (1615673075540913 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1615673075540913 / 4000000000000000 : ℚ)) + (r' := (1615673075540913 / 1000000000000000 : ℚ)) + (U := (-(9065427257069945571199 / 10000000000000000000000 : ℚ))) + (U' := (4797516348930054428801 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (100914451761911 / 250000000000000 : ℚ)) + (q := (1615673075540913 / 4000000000000000 : ℚ)) + (U := (-(9065427257069945571199 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_5 : Uω (aρ 5) (bρ 5) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2370,25 +2114,21 @@ lemma U_406_5 : have hlg : Real.log (391679886675027 / 1000000000000000 : ℝ) ≤ (-(4686551939544443826109 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (391679886675027 / 1000000000000000 : ℝ) = - (391679886675027 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (391679886675027 / 250000000000000 : ℚ)) - (U := (2244919863455556173891 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (391679886675027 / 250000000000000 : ℝ) ≤ - (2244919863455556173891 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (782000069121483 / 2000000000000000 : ℝ)) (q := - (391679886675027 / 1000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (391679886675027 / 1000000000000000 : ℚ)) + (r' := (391679886675027 / 250000000000000 : ℚ)) + (U := (-(4686551939544443826109 / 5000000000000000000000 : ℚ))) + (U' := (2244919863455556173891 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (782000069121483 / 2000000000000000 : ℚ)) + (q := (391679886675027 / 1000000000000000 : ℚ)) + (U := (-(4686551939544443826109 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_6 : Uω (aρ 6) (bρ 6) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2396,25 +2136,21 @@ lemma U_406_6 : have hlg : Real.log (7479900150298289 / 20000000000000000 : ℝ) ≤ (-(9835128300274148067791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7479900150298289 / 20000000000000000 : ℝ) = - (7479900150298289 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7479900150298289 / 5000000000000000 : ℚ)) - (U := (4027815305725851932209 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7479900150298289 / 5000000000000000 : ℝ) ≤ - (4027815305725851932209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (930885784386291 / 2500000000000000 : ℝ)) (q := - (7479900150298289 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7479900150298289 / 20000000000000000 : ℚ)) + (r' := (7479900150298289 / 5000000000000000 : ℚ)) + (U := (-(9835128300274148067791 / 10000000000000000000000 : ℚ))) + (U' := (4027815305725851932209 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (930885784386291 / 2500000000000000 : ℚ)) + (q := (7479900150298289 / 20000000000000000 : ℚ)) + (U := (-(9835128300274148067791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_7 : Uω (aρ 7) (bρ 7) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2422,25 +2158,21 @@ lemma U_406_7 : have hlg : Real.log (6991197808870553 / 20000000000000000 : ℝ) ≤ (-(5132228374587151913 / 4882812500000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6991197808870553 / 20000000000000000 : ℝ) = - (6991197808870553 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6991197808870553 / 5000000000000000 : ℚ)) - (U := (1636787058030035587 / 4882812500000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6991197808870553 / 5000000000000000 : ℝ) ≤ - (1636787058030035587 / 4882812500000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (864625544219357 / 2500000000000000 : ℝ)) (q := - (6991197808870553 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6991197808870553 / 20000000000000000 : ℚ)) + (r' := (6991197808870553 / 5000000000000000 : ℚ)) + (U := (-(5132228374587151913 / 4882812500000000000 : ℚ))) + (U' := (1636787058030035587 / 4882812500000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (864625544219357 / 2500000000000000 : ℚ)) + (q := (6991197808870553 / 20000000000000000 : ℚ)) + (U := (-(5132228374587151913 / 4882812500000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_8 : Uω (aρ 8) (bρ 8) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2448,25 +2180,21 @@ lemma U_406_8 : have hlg : Real.log (6339145253052087 / 20000000000000000 : ℝ) ≤ (-(11489883318043325304749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6339145253052087 / 20000000000000000 : ℝ) = - (6339145253052087 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6339145253052087 / 5000000000000000 : ℚ)) - (U := (2373060287956674695251 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6339145253052087 / 5000000000000000 : ℝ) ≤ - (2373060287956674695251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1544995636199481 / 5000000000000000 : ℝ)) (q := - (6339145253052087 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6339145253052087 / 20000000000000000 : ℚ)) + (r' := (6339145253052087 / 5000000000000000 : ℚ)) + (U := (-(11489883318043325304749 / 10000000000000000000000 : ℚ))) + (U' := (2373060287956674695251 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (1544995636199481 / 5000000000000000 : ℚ)) + (q := (6339145253052087 / 20000000000000000 : ℚ)) + (U := (-(11489883318043325304749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_9 : Uω (aρ 9) (bρ 9) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2474,24 +2202,21 @@ lemma U_406_9 : have hlg : Real.log (68577394599119 / 250000000000000 : ℝ) ≤ (-(404218113034351628443 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (68577394599119 / 250000000000000 : ℝ) = (68577394599119 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (68577394599119 / 62500000000000 : ℚ)) - (U := (28998874653148371557 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (68577394599119 / 62500000000000 : ℝ) ≤ - (28998874653148371557 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (515600643127279 / 2000000000000000 : ℝ)) (q := - (68577394599119 / 250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (68577394599119 / 250000000000000 : ℚ)) + (r' := (68577394599119 / 62500000000000 : ℚ)) + (U := (-(404218113034351628443 / 312500000000000000000 : ℚ))) + (U' := (28998874653148371557 / 312500000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (515600643127279 / 2000000000000000 : ℚ)) + (q := (68577394599119 / 250000000000000 : ℚ)) + (U := (-(404218113034351628443 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_10 : Uω (aρ 10) (bρ 10) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2499,26 +2224,21 @@ lemma U_406_10 : have hlg : Real.log (2173470319964777 / 10000000000000000 : ℝ) ≤ (-(7631299881357333164523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2173470319964777 / 10000000000000000 : ℝ) = - (2173470319964777 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2173470319964777 / 1250000000000000 : ℚ)) - (U := (2765907823142666835477 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2173470319964777 / 1250000000000000 : ℝ) ≤ - (2765907823142666835477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1827311321131429 / 10000000000000000 : ℝ)) (q := - (2173470319964777 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2173470319964777 / 10000000000000000 : ℚ)) + (r' := (2173470319964777 / 1250000000000000 : ℚ)) + (U := (-(7631299881357333164523 / 5000000000000000000000 : ℚ))) + (U' := (2765907823142666835477 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (6809190120381 / 16000000000000 : ℚ)) + (s := (1827311321131429 / 10000000000000000 : ℚ)) + (q := (2173470319964777 / 10000000000000000 : ℚ)) + (U := (-(7631299881357333164523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_406_11 : Uω (aρ 11) (bρ 11) (6809190120381 / 16000000000000 : ℝ) ≤ @@ -2639,24 +2359,21 @@ lemma U_407_1 : have hlg : Real.log (21217658642903 / 50000000000000 : ℝ) ≤ (-(342875686036299859671 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21217658642903 / 50000000000000 : ℝ) = (21217658642903 / 12500000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21217658642903 / 12500000000000 : ℚ)) - (U := (211642058203700140329 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (21217658642903 / 12500000000000 : ℝ) ≤ - (211642058203700140329 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21217468155481 / 50000000000000 : ℝ)) (q := - (21217658642903 / 50000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21217658642903 / 50000000000000 : ℚ)) + (r' := (21217658642903 / 12500000000000 : ℚ)) + (U := (-(342875686036299859671 / 400000000000000000000 : ℚ))) + (U' := (211642058203700140329 / 400000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (86161340883 / 200000000000 : ℚ)) + (s := (21217468155481 / 50000000000000 : ℚ)) + (q := (21217658642903 / 50000000000000 : ℚ)) + (U := (-(342875686036299859671 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_2 : Uω (aρ 2) (bρ 2) (86161340883 / 200000000000 : ℝ) ≤ @@ -2664,25 +2381,21 @@ lemma U_407_2 : have hlg : Real.log (527443672776311 / 1250000000000000 : ℝ) ≤ (-(1725713503188980663307 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (527443672776311 / 1250000000000000 : ℝ) = - (527443672776311 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (527443672776311 / 312500000000000 : ℚ)) - (U := (1046875218011019336693 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (527443672776311 / 312500000000000 : ℝ) ≤ - (1046875218011019336693 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (527412243858247 / 1250000000000000 : ℝ)) (q := - (527443672776311 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (527443672776311 / 1250000000000000 : ℚ)) + (r' := (527443672776311 / 312500000000000 : ℚ)) + (U := (-(1725713503188980663307 / 2000000000000000000000 : ℚ))) + (U' := (1046875218011019336693 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (86161340883 / 200000000000 : ℚ)) + (s := (527412243858247 / 1250000000000000 : ℚ)) + (q := (527443672776311 / 1250000000000000 : ℚ)) + (U := (-(1725713503188980663307 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_3 : Uω (aρ 3) (bρ 3) (86161340883 / 200000000000 : ℝ) ≤ @@ -2690,25 +2403,21 @@ lemma U_407_3 : have hlg : Real.log (8343035940000919 / 20000000000000000 : ℝ) ≤ (-(8743051013203827149901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8343035940000919 / 20000000000000000 : ℝ) = - (8343035940000919 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8343035940000919 / 5000000000000000 : ℚ)) - (U := (5119892592796172850099 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8343035940000919 / 5000000000000000 : ℝ) ≤ - (5119892592796172850099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4170631232795919 / 10000000000000000 : ℝ)) (q := - (8343035940000919 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8343035940000919 / 20000000000000000 : ℚ)) + (r' := (8343035940000919 / 5000000000000000 : ℚ)) + (U := (-(8743051013203827149901 / 10000000000000000000000 : ℚ))) + (U' := (5119892592796172850099 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (86161340883 / 200000000000 : ℚ)) + (s := (4170631232795919 / 10000000000000000 : ℚ)) + (q := (8343035940000919 / 20000000000000000 : ℚ)) + (U := (-(8743051013203827149901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_4 : Uω (aρ 4) (bρ 4) (86161340883 / 200000000000 : ℝ) ≤ @@ -2716,25 +2425,21 @@ lemma U_407_4 : have hlg : Real.log (4091539237232629 / 10000000000000000 : ℝ) ≤ (-(2234159628991301625199 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4091539237232629 / 10000000000000000 : ℝ) = - (4091539237232629 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4091539237232629 / 2500000000000000 : ℚ)) - (U := (1231576272508698374801 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4091539237232629 / 2500000000000000 : ℝ) ≤ - (1231576272508698374801 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2044483974162629 / 5000000000000000 : ℝ)) (q := - (4091539237232629 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4091539237232629 / 10000000000000000 : ℚ)) + (r' := (4091539237232629 / 2500000000000000 : ℚ)) + (U := (-(2234159628991301625199 / 2500000000000000000000 : ℚ))) + (U' := (1231576272508698374801 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (86161340883 / 200000000000 : ℚ)) + (s := (2044483974162629 / 5000000000000000 : ℚ)) + (q := (4091539237232629 / 10000000000000000 : ℚ)) + (U := (-(2234159628991301625199 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_5 : Uω (aρ 5) (bρ 5) (86161340883 / 200000000000 : ℝ) ≤ @@ -2742,25 +2447,21 @@ lemma U_407_5 : have hlg : Real.log (3969211859363087 / 10000000000000000 : ℝ) ≤ (-(1848035083146948254919 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3969211859363087 / 10000000000000000 : ℝ) = - (3969211859363087 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3969211859363087 / 2500000000000000 : ℚ)) - (U := (924553638053051745081 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3969211859363087 / 2500000000000000 : ℝ) ≤ - (924553638053051745081 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1981251555960587 / 5000000000000000 : ℝ)) (q := - (3969211859363087 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3969211859363087 / 10000000000000000 : ℚ)) + (r' := (3969211859363087 / 2500000000000000 : ℚ)) + (U := (-(1848035083146948254919 / 2000000000000000000000 : ℚ))) + (U' := (924553638053051745081 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (86161340883 / 200000000000 : ℚ)) + (s := (1981251555960587 / 5000000000000000 : ℚ)) + (q := (3969211859363087 / 10000000000000000 : ℚ)) + (U := (-(1848035083146948254919 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_6 : Uω (aρ 6) (bρ 6) (86161340883 / 200000000000 : ℝ) ≤ @@ -2768,25 +2469,21 @@ lemma U_407_6 : have hlg : Real.log (7585001271642383 / 20000000000000000 : ℝ) ≤ (-(1939118985162720111611 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7585001271642383 / 20000000000000000 : ℝ) = - (7585001271642383 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7585001271642383 / 5000000000000000 : ℚ)) - (U := (833469736037279888389 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7585001271642383 / 5000000000000000 : ℝ) ≤ - (833469736037279888389 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3776321039977383 / 10000000000000000 : ℝ)) (q := - (7585001271642383 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7585001271642383 / 20000000000000000 : ℚ)) + (r' := (7585001271642383 / 5000000000000000 : ℚ)) + (U := (-(1939118985162720111611 / 2000000000000000000000 : ℚ))) + (U' := (833469736037279888389 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (86161340883 / 200000000000 : ℚ)) + (s := (3776321039977383 / 10000000000000000 : ℚ)) + (q := (7585001271642383 / 20000000000000000 : ℚ)) + (U := (-(1939118985162720111611 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_7 : Uω (aρ 7) (bρ 7) (86161340883 / 200000000000 : ℝ) ≤ @@ -2794,25 +2491,21 @@ lemma U_407_7 : have hlg : Real.log (7096949807018291 / 20000000000000000 : ℝ) ≤ (-(10360671859386552173789 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7096949807018291 / 20000000000000000 : ℝ) = - (7096949807018291 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7096949807018291 / 5000000000000000 : ℚ)) - (U := (3502271746613447826211 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7096949807018291 / 5000000000000000 : ℝ) ≤ - (3502271746613447826211 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3511930956113291 / 10000000000000000 : ℝ)) (q := - (7096949807018291 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7096949807018291 / 20000000000000000 : ℚ)) + (r' := (7096949807018291 / 5000000000000000 : ℚ)) + (U := (-(10360671859386552173789 / 10000000000000000000000 : ℚ))) + (U' := (3502271746613447826211 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (86161340883 / 200000000000 : ℚ)) + (s := (3511930956113291 / 10000000000000000 : ℚ)) + (q := (7096949807018291 / 20000000000000000 : ℚ)) + (U := (-(10360671859386552173789 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_8 : Uω (aρ 8) (bρ 8) (86161340883 / 200000000000 : ℝ) ≤ @@ -2820,25 +2513,21 @@ lemma U_407_8 : have hlg : Real.log (805805102478053 / 2500000000000000 : ℝ) ≤ (-(2264408210820016486429 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (805805102478053 / 2500000000000000 : ℝ) = - (805805102478053 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (805805102478053 / 625000000000000 : ℚ)) - (U := (508180510379983513571 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (805805102478053 / 625000000000000 : ℝ) ≤ - (508180510379983513571 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98280113133107 / 312500000000000 : ℝ)) (q := - (805805102478053 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (805805102478053 / 2500000000000000 : ℚ)) + (r' := (805805102478053 / 625000000000000 : ℚ)) + (U := (-(2264408210820016486429 / 2000000000000000000000 : ℚ))) + (U' := (508180510379983513571 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (86161340883 / 200000000000 : ℚ)) + (s := (98280113133107 / 312500000000000 : ℚ)) + (q := (805805102478053 / 2500000000000000 : ℚ)) + (U := (-(2264408210820016486429 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_9 : Uω (aρ 9) (bρ 9) (86161340883 / 200000000000 : ℝ) ≤ @@ -2846,25 +2535,21 @@ lemma U_407_9 : have hlg : Real.log (699674745550947 / 2500000000000000 : ℝ) ≤ (-(12734304324888259626497 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (699674745550947 / 2500000000000000 : ℝ) = - (699674745550947 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (699674745550947 / 625000000000000 : ℚ)) - (U := (1128639281111740373503 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (699674745550947 / 625000000000000 : ℝ) ≤ - (1128639281111740373503 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (164805399575161 / 625000000000000 : ℝ)) (q := - (699674745550947 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (699674745550947 / 2500000000000000 : ℚ)) + (r' := (699674745550947 / 625000000000000 : ℚ)) + (U := (-(12734304324888259626497 / 10000000000000000000000 : ℚ))) + (U' := (1128639281111740373503 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (86161340883 / 200000000000 : ℚ)) + (s := (164805399575161 / 625000000000000 : ℚ)) + (q := (699674745550947 / 2500000000000000 : ℚ)) + (U := (-(12734304324888259626497 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_10 : Uω (aρ 10) (bρ 10) (86161340883 / 200000000000 : ℝ) ≤ @@ -2872,25 +2557,21 @@ lemma U_407_10 : have hlg : Real.log (558845159230569 / 2500000000000000 : ℝ) ≤ (-(3745433928253882754121 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (558845159230569 / 2500000000000000 : ℝ) = - (558845159230569 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (558845159230569 / 312500000000000 : ℚ)) - (U := (1453169923996117245879 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (558845159230569 / 312500000000000 : ℝ) ≤ - (1453169923996117245879 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (237351092016819 / 1250000000000000 : ℝ)) (q := - (558845159230569 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (558845159230569 / 2500000000000000 : ℚ)) + (r' := (558845159230569 / 312500000000000 : ℚ)) + (U := (-(3745433928253882754121 / 2500000000000000000000 : ℚ))) + (U' := (1453169923996117245879 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (86161340883 / 200000000000 : ℚ)) + (s := (237351092016819 / 1250000000000000 : ℚ)) + (q := (558845159230569 / 2500000000000000 : ℚ)) + (U := (-(3745433928253882754121 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_407_11 : Uω (aρ 11) (bρ 11) (86161340883 / 200000000000 : ℝ) ≤ @@ -3012,25 +2693,21 @@ lemma U_408_1 : have hlg : Real.log (4270017962423161 / 10000000000000000 : ℝ) ≤ (-(1701934117171983693411 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4270017962423161 / 10000000000000000 : ℝ) = - (4270017962423161 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4270017962423161 / 2500000000000000 : ℚ)) - (U := (1070654604028016306589 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4270017962423161 / 2500000000000000 : ℝ) ≤ - (1070654604028016306589 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2134990050625661 / 5000000000000000 : ℝ)) (q := - (4270017962423161 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4270017962423161 / 10000000000000000 : ℚ)) + (r' := (4270017962423161 / 2500000000000000 : ℚ)) + (U := (-(1701934117171983693411 / 2000000000000000000000 : ℚ))) + (U' := (1070654604028016306589 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (54181913021 / 125000000000 : ℚ)) + (s := (2134990050625661 / 5000000000000000 : ℚ)) + (q := (4270017962423161 / 10000000000000000 : ℚ)) + (U := (-(1701934117171983693411 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_2 : Uω (aρ 2) (bρ 2) (54181913021 / 125000000000 : ℝ) ≤ @@ -3038,25 +2715,21 @@ lemma U_408_2 : have hlg : Real.log (4246036948215849 / 10000000000000000 : ℝ) ≤ (-(535374392089433119633 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4246036948215849 / 10000000000000000 : ℝ) = - (4246036948215849 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4246036948215849 / 2500000000000000 : ℚ)) - (U := (331059583285566880367 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4246036948215849 / 2500000000000000 : ℝ) ≤ - (331059583285566880367 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2122893542673349 / 5000000000000000 : ℝ)) (q := - (4246036948215849 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4246036948215849 / 10000000000000000 : ℚ)) + (r' := (4246036948215849 / 2500000000000000 : ℚ)) + (U := (-(535374392089433119633 / 625000000000000000000 : ℚ))) + (U' := (331059583285566880367 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (54181913021 / 125000000000 : ℚ)) + (s := (2122893542673349 / 5000000000000000 : ℚ)) + (q := (4246036948215849 / 10000000000000000 : ℚ)) + (U := (-(535374392089433119633 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_3 : Uω (aρ 3) (bρ 3) (54181913021 / 125000000000 : ℝ) ≤ @@ -3064,25 +2737,21 @@ lemma U_408_3 : have hlg : Real.log (524751195412123 / 1250000000000000 : ℝ) ≤ (-(867974593018045612053 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (524751195412123 / 1250000000000000 : ℝ) = - (524751195412123 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (524751195412123 / 312500000000000 : ℚ)) - (U := (518319767581954387947 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (524751195412123 / 312500000000000 : ℝ) ≤ - (518319767581954387947 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (524641052732371 / 1250000000000000 : ℝ)) (q := - (524751195412123 / 1250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (524751195412123 / 1250000000000000 : ℚ)) + (r' := (524751195412123 / 312500000000000 : ℚ)) + (U := (-(867974593018045612053 / 1000000000000000000000 : ℚ))) + (U' := (518319767581954387947 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (54181913021 / 125000000000 : ℚ)) + (s := (524641052732371 / 1250000000000000 : ℚ)) + (q := (524751195412123 / 1250000000000000 : ℚ)) + (U := (-(867974593018045612053 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_4 : Uω (aρ 4) (bρ 4) (54181913021 / 125000000000 : ℝ) ≤ @@ -3090,25 +2759,21 @@ lemma U_408_4 : have hlg : Real.log (2059020891423341 / 5000000000000000 : ℝ) ≤ (-(8872073375269568597809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2059020891423341 / 5000000000000000 : ℝ) = - (2059020891423341 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2059020891423341 / 1250000000000000 : ℚ)) - (U := (4990870230730431402191 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2059020891423341 / 1250000000000000 : ℝ) ≤ - (4990870230730431402191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1028871760505841 / 2500000000000000 : ℝ)) (q := - (2059020891423341 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2059020891423341 / 5000000000000000 : ℚ)) + (r' := (2059020891423341 / 1250000000000000 : ℚ)) + (U := (-(8872073375269568597809 / 10000000000000000000000 : ℚ))) + (U' := (4990870230730431402191 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (54181913021 / 125000000000 : ℚ)) + (s := (1028871760505841 / 2500000000000000 : ℚ)) + (q := (2059020891423341 / 5000000000000000 : ℚ)) + (U := (-(8872073375269568597809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_5 : Uω (aρ 5) (bρ 5) (54181913021 / 125000000000 : ℝ) ≤ @@ -3116,25 +2781,21 @@ lemma U_408_5 : have hlg : Real.log (499467800122701 / 1250000000000000 : ℝ) ≤ (-(917355697984571850539 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (499467800122701 / 1250000000000000 : ℝ) = - (499467800122701 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (499467800122701 / 312500000000000 : ℚ)) - (U := (468938662615428149461 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (499467800122701 / 312500000000000 : ℝ) ≤ - (468938662615428149461 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (498634774703527 / 1250000000000000 : ℝ)) (q := - (499467800122701 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (499467800122701 / 1250000000000000 : ℚ)) + (r' := (499467800122701 / 312500000000000 : ℚ)) + (U := (-(917355697984571850539 / 1000000000000000000000 : ℚ))) + (U' := (468938662615428149461 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (54181913021 / 125000000000 : ℚ)) + (s := (498634774703527 / 1250000000000000 : ℚ)) + (q := (499467800122701 / 1250000000000000 : ℚ)) + (U := (-(917355697984571850539 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_6 : Uω (aρ 6) (bρ 6) (54181913021 / 125000000000 : ℝ) ≤ @@ -3142,25 +2803,21 @@ lemma U_408_6 : have hlg : Real.log (238693707408891 / 625000000000000 : ℝ) ≤ (-(1925140956285161018611 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (238693707408891 / 625000000000000 : ℝ) = - (238693707408891 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (238693707408891 / 156250000000000 : ℚ)) - (U := (847447764914838981389 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (238693707408891 / 156250000000000 : ℝ) ≤ - (847447764914838981389 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (475379050986189 / 1250000000000000 : ℝ)) (q := - (238693707408891 / 625000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (238693707408891 / 625000000000000 : ℚ)) + (r' := (238693707408891 / 156250000000000 : ℚ)) + (U := (-(1925140956285161018611 / 2000000000000000000000 : ℚ))) + (U' := (847447764914838981389 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (54181913021 / 125000000000 : ℚ)) + (s := (475379050986189 / 1250000000000000 : ℚ)) + (q := (238693707408891 / 625000000000000 : ℚ)) + (U := (-(1925140956285161018611 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_7 : Uω (aρ 7) (bρ 7) (54181913021 / 125000000000 : ℝ) ≤ @@ -3168,25 +2825,21 @@ lemma U_408_7 : have hlg : Real.log (7150468842237723 / 20000000000000000 : ℝ) ≤ (-(10285543461370157781439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7150468842237723 / 20000000000000000 : ℝ) = - (7150468842237723 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7150468842237723 / 5000000000000000 : ℚ)) - (U := (3577400144629842218561 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7150468842237723 / 5000000000000000 : ℝ) ≤ - (3577400144629842218561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3538963993802723 / 10000000000000000 : ℝ)) (q := - (7150468842237723 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7150468842237723 / 20000000000000000 : ℚ)) + (r' := (7150468842237723 / 5000000000000000 : ℚ)) + (U := (-(10285543461370157781439 / 10000000000000000000000 : ℚ))) + (U' := (3577400144629842218561 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (54181913021 / 125000000000 : ℚ)) + (s := (3538963993802723 / 10000000000000000 : ℚ)) + (q := (7150468842237723 / 20000000000000000 : ℚ)) + (U := (-(10285543461370157781439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_8 : Uω (aρ 8) (bρ 8) (54181913021 / 125000000000 : ℝ) ≤ @@ -3194,25 +2847,21 @@ lemma U_408_8 : have hlg : Real.log (162517991270787 / 500000000000000 : ℝ) ≤ (-(112381938674848357789 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (162517991270787 / 500000000000000 : ℝ) = - (162517991270787 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (162517991270787 / 125000000000000 : ℚ)) - (U := (26247497385151642211 / 100000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (162517991270787 / 125000000000000 : ℝ) ≤ - (26247497385151642211 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19829727835853 / 62500000000000 : ℝ)) (q := - (162517991270787 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (162517991270787 / 500000000000000 : ℚ)) + (r' := (162517991270787 / 125000000000000 : ℚ)) + (U := (-(112381938674848357789 / 100000000000000000000 : ℚ))) + (U' := (26247497385151642211 / 100000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (54181913021 / 125000000000 : ℚ)) + (s := (19829727835853 / 62500000000000 : ℚ)) + (q := (162517991270787 / 500000000000000 : ℚ)) + (U := (-(112381938674848357789 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_9 : Uω (aρ 9) (bρ 9) (54181913021 / 125000000000 : ℝ) ≤ @@ -3220,25 +2869,21 @@ lemma U_408_9 : have hlg : Real.log (2826793159500669 / 10000000000000000 : ℝ) ≤ (-(12634421825163466454341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2826793159500669 / 10000000000000000 : ℝ) = - (2826793159500669 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2826793159500669 / 2500000000000000 : ℚ)) - (U := (1228521780836533545659 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2826793159500669 / 2500000000000000 : ℝ) ≤ - (1228521780836533545659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1333294375133169 / 5000000000000000 : ℝ)) (q := - (2826793159500669 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2826793159500669 / 10000000000000000 : ℚ)) + (r' := (2826793159500669 / 2500000000000000 : ℚ)) + (U := (-(12634421825163466454341 / 10000000000000000000000 : ℚ))) + (U' := (1228521780836533545659 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (54181913021 / 125000000000 : ℚ)) + (s := (1333294375133169 / 5000000000000000 : ℚ)) + (q := (2826793159500669 / 10000000000000000 : ℚ)) + (U := (-(12634421825163466454341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_10 : Uω (aρ 10) (bρ 10) (54181913021 / 125000000000 : ℝ) ≤ @@ -3246,26 +2891,21 @@ lemma U_408_10 : have hlg : Real.log (4532971445688459 / 20000000000000000 : ℝ) ≤ (-(7421773000218264526129 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4532971445688459 / 20000000000000000 : ℝ) = - (4532971445688459 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4532971445688459 / 2500000000000000 : ℚ)) - (U := (2975434704281735473871 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4532971445688459 / 2500000000000000 : ℝ) ≤ - (2975434704281735473871 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1934532910448459 / 10000000000000000 : ℝ)) (q := - (4532971445688459 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4532971445688459 / 20000000000000000 : ℚ)) + (r' := (4532971445688459 / 2500000000000000 : ℚ)) + (U := (-(7421773000218264526129 / 5000000000000000000000 : ℚ))) + (U' := (2975434704281735473871 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (54181913021 / 125000000000 : ℚ)) + (s := (1934532910448459 / 10000000000000000 : ℚ)) + (q := (4532971445688459 / 20000000000000000 : ℚ)) + (U := (-(7421773000218264526129 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_11 : Uω (aρ 11) (bρ 11) (54181913021 / 125000000000 : ℝ) ≤ @@ -3273,26 +2913,21 @@ lemma U_408_11 : have hlg : Real.log (2518747126261537 / 20000000000000000 : ℝ) ≤ (-(10359853335001487342957 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2518747126261537 / 20000000000000000 : ℝ) = - (2518747126261537 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2518747126261537 / 2500000000000000 : ℚ)) - (U := (37354369498512657043 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2518747126261537 / 2500000000000000 : ℝ) ≤ - (37354369498512657043 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (338785217226537 / 10000000000000000 : ℝ)) (q := - (2518747126261537 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2518747126261537 / 20000000000000000 : ℚ)) + (r' := (2518747126261537 / 2500000000000000 : ℚ)) + (U := (-(10359853335001487342957 / 5000000000000000000000 : ℚ))) + (U' := (37354369498512657043 / 5000000000000000000000 : ℚ)) + 3 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (54181913021 / 125000000000 : ℚ)) + (s := (338785217226537 / 10000000000000000 : ℚ)) + (q := (2518747126261537 / 20000000000000000 : ℚ)) + (U := (-(10359853335001487342957 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_408_12 : Uω (aρ 12) (bρ 12) (54181913021 / 125000000000 : ℝ) ≤ @@ -3408,25 +3043,21 @@ lemma U_409_1 : have hlg : Real.log (8593008386704303 / 20000000000000000 : ℝ) ≤ (-(8447833787109033449899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8593008386704303 / 20000000000000000 : ℝ) = - (8593008386704303 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8593008386704303 / 5000000000000000 : ℚ)) - (U := (5415109818890966550101 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8593008386704303 / 5000000000000000 : ℝ) ≤ - (5415109818890966550101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4296466565579303 / 10000000000000000 : ℝ)) (q := - (8593008386704303 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8593008386704303 / 20000000000000000 : ℚ)) + (r' := (8593008386704303 / 5000000000000000 : ℚ)) + (U := (-(8447833787109033449899 / 10000000000000000000000 : ℚ))) + (U' := (5415109818890966550101 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (4296466565579303 / 10000000000000000 : ℚ)) + (q := (8593008386704303 / 20000000000000000 : ℚ)) + (U := (-(8447833787109033449899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_2 : Uω (aρ 2) (bρ 2) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3434,25 +3065,21 @@ lemma U_409_2 : have hlg : Real.log (1068131123693129 / 2500000000000000 : ℝ) ≤ (-(531487639599329723427 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1068131123693129 / 2500000000000000 : ℝ) = - (1068131123693129 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1068131123693129 / 625000000000000 : ℚ)) - (U := (334946335775670276573 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1068131123693129 / 625000000000000 : ℝ) ≤ - (334946335775670276573 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (267017261308127 / 625000000000000 : ℝ)) (q := - (1068131123693129 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1068131123693129 / 2500000000000000 : ℚ)) + (r' := (1068131123693129 / 625000000000000 : ℚ)) + (U := (-(531487639599329723427 / 625000000000000000000 : ℚ))) + (U' := (334946335775670276573 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (267017261308127 / 625000000000000 : ℚ)) + (q := (1068131123693129 / 2500000000000000 : ℚ)) + (U := (-(531487639599329723427 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_3 : Uω (aρ 3) (bρ 3) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3460,25 +3087,21 @@ lemma U_409_3 : have hlg : Real.log (8449002172795053 / 20000000000000000 : ℝ) ≤ (-(4308419623487413080987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8449002172795053 / 20000000000000000 : ℝ) = - (8449002172795053 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8449002172795053 / 5000000000000000 : ℚ)) - (U := (2623052179512586919013 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8449002172795053 / 5000000000000000 : ℝ) ≤ - (2623052179512586919013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4223625470530053 / 10000000000000000 : ℝ)) (q := - (8449002172795053 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8449002172795053 / 20000000000000000 : ℚ)) + (r' := (8449002172795053 / 5000000000000000 : ℚ)) + (U := (-(4308419623487413080987 / 5000000000000000000000 : ℚ))) + (U' := (2623052179512586919013 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (4223625470530053 / 10000000000000000 : ℚ)) + (q := (8449002172795053 / 20000000000000000 : ℚ)) + (U := (-(4308419623487413080987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_4 : Uω (aρ 4) (bρ 4) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3486,25 +3109,21 @@ lemma U_409_4 : have hlg : Real.log (8289088233391073 / 20000000000000000 : ℝ) ≤ (-(352316917537988224177 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8289088233391073 / 20000000000000000 : ℝ) = - (8289088233391073 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8289088233391073 / 5000000000000000 : ℚ)) - (U := (202200826702011775823 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8289088233391073 / 5000000000000000 : ℝ) ≤ - (202200826702011775823 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4142005712191073 / 10000000000000000 : ℝ)) (q := - (8289088233391073 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8289088233391073 / 20000000000000000 : ℚ)) + (r' := (8289088233391073 / 5000000000000000 : ℚ)) + (U := (-(352316917537988224177 / 400000000000000000000 : ℚ))) + (U' := (202200826702011775823 / 400000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (4142005712191073 / 10000000000000000 : ℚ)) + (q := (8289088233391073 / 20000000000000000 : ℚ)) + (U := (-(352316917537988224177 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_5 : Uω (aρ 5) (bρ 5) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3512,25 +3131,21 @@ lemma U_409_5 : have hlg : Real.log (8044544708027943 / 20000000000000000 : ℝ) ≤ (-(9107380873511893660103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8044544708027943 / 20000000000000000 : ℝ) = - (8044544708027943 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8044544708027943 / 5000000000000000 : ℚ)) - (U := (4755562732488106339897 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8044544708027943 / 5000000000000000 : ℝ) ≤ - (4755562732488106339897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4015652106162943 / 10000000000000000 : ℝ)) (q := - (8044544708027943 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8044544708027943 / 20000000000000000 : ℚ)) + (r' := (8044544708027943 / 5000000000000000 : ℚ)) + (U := (-(9107380873511893660103 / 10000000000000000000000 : ℚ))) + (U' := (4755562732488106339897 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (4015652106162943 / 10000000000000000 : ℚ)) + (q := (8044544708027943 / 20000000000000000 : ℚ)) + (U := (-(9107380873511893660103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_6 : Uω (aρ 6) (bρ 6) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3538,25 +3153,21 @@ lemma U_409_6 : have hlg : Real.log (3845696435999927 / 10000000000000000 : ℝ) ≤ (-(9556303782198983042833 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3845696435999927 / 10000000000000000 : ℝ) = - (3845696435999927 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3845696435999927 / 2500000000000000 : ℚ)) - (U := (4306639823801016957167 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3845696435999927 / 2500000000000000 : ℝ) ≤ - (4306639823801016957167 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1914870322637427 / 5000000000000000 : ℝ)) (q := - (3845696435999927 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3845696435999927 / 10000000000000000 : ℚ)) + (r' := (3845696435999927 / 2500000000000000 : ℚ)) + (U := (-(9556303782198983042833 / 10000000000000000000000 : ℚ))) + (U' := (4306639823801016957167 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (1914870322637427 / 5000000000000000 : ℚ)) + (q := (3845696435999927 / 10000000000000000 : ℚ)) + (U := (-(9556303782198983042833 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_7 : Uω (aρ 7) (bρ 7) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3564,25 +3175,21 @@ lemma U_409_7 : have hlg : Real.log (7203979667384347 / 20000000000000000 : ℝ) ≤ (-(10210986681307664216749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7203979667384347 / 20000000000000000 : ℝ) = - (7203979667384347 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7203979667384347 / 5000000000000000 : ℚ)) - (U := (3651956924692335783251 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7203979667384347 / 5000000000000000 : ℝ) ≤ - (3651956924692335783251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3565988821419347 / 10000000000000000 : ℝ)) (q := - (7203979667384347 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7203979667384347 / 20000000000000000 : ℚ)) + (r' := (7203979667384347 / 5000000000000000 : ℚ)) + (U := (-(10210986681307664216749 / 10000000000000000000000 : ℚ))) + (U' := (3651956924692335783251 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (3565988821419347 / 10000000000000000 : ℚ)) + (q := (7203979667384347 / 20000000000000000 : ℚ)) + (U := (-(10210986681307664216749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_8 : Uω (aρ 8) (bρ 8) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3590,25 +3197,21 @@ lemma U_409_8 : have hlg : Real.log (6554976318838763 / 20000000000000000 : ℝ) ≤ (-(11155077685116505444933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6554976318838763 / 20000000000000000 : ℝ) = - (6554976318838763 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6554976318838763 / 5000000000000000 : ℚ)) - (U := (2707865920883494555067 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6554976318838763 / 5000000000000000 : ℝ) ≤ - (2707865920883494555067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3200527124213763 / 10000000000000000 : ℝ)) (q := - (6554976318838763 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6554976318838763 / 20000000000000000 : ℚ)) + (r' := (6554976318838763 / 5000000000000000 : ℚ)) + (U := (-(11155077685116505444933 / 10000000000000000000000 : ℚ))) + (U' := (2707865920883494555067 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (3200527124213763 / 10000000000000000 : ℚ)) + (q := (6554976318838763 / 20000000000000000 : ℚ)) + (U := (-(11155077685116505444933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_9 : Uω (aρ 9) (bρ 9) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3616,25 +3219,21 @@ lemma U_409_9 : have hlg : Real.log (5709707646635067 / 20000000000000000 : ℝ) ≤ (-(12535644509160010633761 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5709707646635067 / 20000000000000000 : ℝ) = - (5709707646635067 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5709707646635067 / 5000000000000000 : ℚ)) - (U := (1327299096839989366239 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5709707646635067 / 5000000000000000 : ℝ) ≤ - (1327299096839989366239 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2696224080370067 / 10000000000000000 : ℝ)) (q := - (5709707646635067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5709707646635067 / 20000000000000000 : ℚ)) + (r' := (5709707646635067 / 5000000000000000 : ℚ)) + (U := (-(12535644509160010633761 / 10000000000000000000000 : ℚ))) + (U' := (1327299096839989366239 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (2696224080370067 / 10000000000000000 : ℚ)) + (q := (5709707646635067 / 20000000000000000 : ℚ)) + (U := (-(12535644509160010633761 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_10 : Uω (aρ 10) (bρ 10) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3642,25 +3241,21 @@ lemma U_409_10 : have hlg : Real.log (918977980753321 / 4000000000000000 : ℝ) ≤ (-(14707874772608179319249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (918977980753321 / 4000000000000000 : ℝ) = - (918977980753321 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (918977980753321 / 500000000000000 : ℚ)) - (U := (6086540636391820680751 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (918977980753321 / 500000000000000 : ℝ) ≤ - (6086540636391820680751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (393993074199321 / 2000000000000000 : ℝ)) (q := - (918977980753321 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (918977980753321 / 4000000000000000 : ℚ)) + (r' := (918977980753321 / 500000000000000 : ℚ)) + (U := (-(14707874772608179319249 / 10000000000000000000000 : ℚ))) + (U' := (6086540636391820680751 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (393993074199321 / 2000000000000000 : ℚ)) + (q := (918977980753321 / 4000000000000000 : ℚ)) + (U := (-(14707874772608179319249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_11 : Uω (aρ 11) (bρ 11) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3668,25 +3263,21 @@ lemma U_409_11 : have hlg : Real.log (671756125206833 / 5000000000000000 : ℝ) ≤ (-(10036489124495165724449 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (671756125206833 / 5000000000000000 : ℝ) = - (671756125206833 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (671756125206833 / 625000000000000 : ℚ)) - (U := (360718580004834275551 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (671756125206833 / 625000000000000 : ℝ) ≤ - (360718580004834275551 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (120144148565583 / 2500000000000000 : ℝ)) (q := - (671756125206833 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (671756125206833 / 5000000000000000 : ℚ)) + (r' := (671756125206833 / 625000000000000 : ℚ)) + (U := (-(10036489124495165724449 / 5000000000000000000000 : ℚ))) + (U' := (360718580004834275551 / 5000000000000000000000 : ℚ)) + 3 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (436103903921 / 1000000000000 : ℚ)) + (s := (120144148565583 / 2500000000000000 : ℚ)) + (q := (671756125206833 / 5000000000000000 : ℚ)) + (U := (-(10036489124495165724449 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_409_12 : Uω (aρ 12) (bρ 12) (436103903921 / 1000000000000 : ℝ) ≤ @@ -3802,24 +3393,21 @@ lemma U_410_1 : have hlg : Real.log (34583923371369 / 80000000000000 : ℝ) ≤ (-(2096594256290114153041 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34583923371369 / 80000000000000 : ℝ) = (34583923371369 / 20000000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34583923371369 / 20000000000000 : ℚ)) - (U := (1369141645209885846959 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34583923371369 / 20000000000000 : ℝ) ≤ - (1369141645209885846959 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17291812096749 / 40000000000000 : ℝ)) (q := - (34583923371369 / 80000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34583923371369 / 80000000000000 : ℚ)) + (r' := (34583923371369 / 20000000000000 : ℚ)) + (U := (-(2096594256290114153041 / 2500000000000000000000 : ℚ))) + (U' := (1369141645209885846959 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (219376251837 / 500000000000 : ℚ)) + (s := (17291812096749 / 40000000000000 : ℚ)) + (q := (34583923371369 / 80000000000000 : ℚ)) + (U := (-(2096594256290114153041 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_2 : Uω (aρ 2) (bρ 2) (219376251837 / 500000000000 : ℝ) ≤ @@ -3827,25 +3415,21 @@ lemma U_410_2 : have hlg : Real.log (8598024044480041 / 20000000000000000 : ℝ) ≤ (-(1055249823054743877783 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8598024044480041 / 20000000000000000 : ℝ) = - (8598024044480041 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8598024044480041 / 5000000000000000 : ℚ)) - (U := (677618127695256122217 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8598024044480041 / 5000000000000000 : ℝ) ≤ - (677618127695256122217 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4298765238335041 / 10000000000000000 : ℝ)) (q := - (8598024044480041 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8598024044480041 / 20000000000000000 : ℚ)) + (r' := (8598024044480041 / 5000000000000000 : ℚ)) + (U := (-(1055249823054743877783 / 1250000000000000000000 : ℚ))) + (U' := (677618127695256122217 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (219376251837 / 500000000000 : ℚ)) + (s := (4298765238335041 / 10000000000000000 : ℚ)) + (q := (8598024044480041 / 20000000000000000 : ℚ)) + (U := (-(1055249823054743877783 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_3 : Uω (aρ 3) (bρ 3) (219376251837 / 500000000000 : ℝ) ≤ @@ -3853,25 +3437,21 @@ lemma U_410_3 : have hlg : Real.log (4250992540614981 / 10000000000000000 : ℝ) ≤ (-(4277162989177892952323 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4250992540614981 / 10000000000000000 : ℝ) = - (4250992540614981 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4250992540614981 / 2500000000000000 : ℚ)) - (U := (2654308813822107047677 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4250992540614981 / 2500000000000000 : ℝ) ≤ - (2654308813822107047677 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2125061190717481 / 5000000000000000 : ℝ)) (q := - (4250992540614981 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4250992540614981 / 10000000000000000 : ℚ)) + (r' := (4250992540614981 / 2500000000000000 : ℚ)) + (U := (-(4277162989177892952323 / 5000000000000000000000 : ℚ))) + (U' := (2654308813822107047677 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (219376251837 / 500000000000 : ℚ)) + (s := (2125061190717481 / 5000000000000000 : ℚ)) + (q := (4250992540614981 / 10000000000000000 : ℚ)) + (U := (-(4277162989177892952323 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_4 : Uω (aρ 4) (bρ 4) (219376251837 / 500000000000 : ℝ) ≤ @@ -3879,25 +3459,21 @@ lemma U_410_4 : have hlg : Real.log (2085523121410359 / 5000000000000000 : ℝ) ≤ (-(4372090952870243498743 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2085523121410359 / 5000000000000000 : ℝ) = - (2085523121410359 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2085523121410359 / 1250000000000000 : ℚ)) - (U := (2559380850129756501257 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2085523121410359 / 1250000000000000 : ℝ) ≤ - (2559380850129756501257 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1042130991727859 / 2500000000000000 : ℝ)) (q := - (2085523121410359 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2085523121410359 / 5000000000000000 : ℚ)) + (r' := (2085523121410359 / 1250000000000000 : ℚ)) + (U := (-(4372090952870243498743 / 5000000000000000000000 : ℚ))) + (U' := (2559380850129756501257 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (219376251837 / 500000000000 : ℚ)) + (s := (1042130991727859 / 2500000000000000 : ℚ)) + (q := (2085523121410359 / 5000000000000000 : ℚ)) + (U := (-(4372090952870243498743 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_5 : Uω (aρ 5) (bρ 5) (219376251837 / 500000000000 : ℝ) ≤ @@ -3905,25 +3481,21 @@ lemma U_410_5 : have hlg : Real.log (8097603460136829 / 20000000000000000 : ℝ) ≤ (-(904164124252520286273 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8097603460136829 / 20000000000000000 : ℝ) = - (8097603460136829 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8097603460136829 / 5000000000000000 : ℚ)) - (U := (482130236347479713727 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8097603460136829 / 5000000000000000 : ℝ) ≤ - (482130236347479713727 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4042224860741829 / 10000000000000000 : ℝ)) (q := - (8097603460136829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8097603460136829 / 20000000000000000 : ℚ)) + (r' := (8097603460136829 / 5000000000000000 : ℚ)) + (U := (-(904164124252520286273 / 1000000000000000000000 : ℚ))) + (U' := (482130236347479713727 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (219376251837 / 500000000000 : ℚ)) + (s := (4042224860741829 / 10000000000000000 : ℚ)) + (q := (8097603460136829 / 20000000000000000 : ℚ)) + (U := (-(904164124252520286273 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_6 : Uω (aρ 6) (bρ 6) (219376251837 / 500000000000 : ℝ) ≤ @@ -3931,25 +3503,21 @@ lemma U_410_6 : have hlg : Real.log (7744584041430827 / 20000000000000000 : ℝ) ≤ (-(9487385073304664494243 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7744584041430827 / 20000000000000000 : ℝ) = - (7744584041430827 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7744584041430827 / 5000000000000000 : ℚ)) - (U := (4375558532695335505757 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7744584041430827 / 5000000000000000 : ℝ) ≤ - (4375558532695335505757 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3856445817175827 / 10000000000000000 : ℝ)) (q := - (7744584041430827 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7744584041430827 / 20000000000000000 : ℚ)) + (r' := (7744584041430827 / 5000000000000000 : ℚ)) + (U := (-(9487385073304664494243 / 10000000000000000000000 : ℚ))) + (U' := (4375558532695335505757 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (219376251837 / 500000000000 : ℚ)) + (s := (3856445817175827 / 10000000000000000 : ℚ)) + (q := (7744584041430827 / 20000000000000000 : ℚ)) + (U := (-(9487385073304664494243 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_7 : Uω (aρ 7) (bρ 7) (219376251837 / 500000000000 : ℝ) ≤ @@ -3957,25 +3525,21 @@ lemma U_410_7 : have hlg : Real.log (7257482467714601 / 20000000000000000 : ℝ) ≤ (-(5068496359337917405659 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7257482467714601 / 20000000000000000 : ℝ) = - (7257482467714601 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7257482467714601 / 5000000000000000 : ℚ)) - (U := (1862975443662082594341 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7257482467714601 / 5000000000000000 : ℝ) ≤ - (1862975443662082594341 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3593005624219601 / 10000000000000000 : ℝ)) (q := - (7257482467714601 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7257482467714601 / 20000000000000000 : ℚ)) + (r' := (7257482467714601 / 5000000000000000 : ℚ)) + (U := (-(5068496359337917405659 / 5000000000000000000000 : ℚ))) + (U' := (1862975443662082594341 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (219376251837 / 500000000000 : ℚ)) + (s := (3593005624219601 / 10000000000000000 : ℚ)) + (q := (7257482467714601 / 20000000000000000 : ℚ)) + (U := (-(5068496359337917405659 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_8 : Uω (aρ 8) (bρ 8) (219376251837 / 500000000000 : ℝ) ≤ @@ -3983,25 +3547,21 @@ lemma U_410_8 : have hlg : Real.log (6609211395806087 / 20000000000000000 : ℝ) ≤ (-(11072679310070797156689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6609211395806087 / 20000000000000000 : ℝ) = - (6609211395806087 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6609211395806087 / 5000000000000000 : ℚ)) - (U := (2790264295929202843311 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6609211395806087 / 5000000000000000 : ℝ) ≤ - (2790264295929202843311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3228276203651087 / 10000000000000000 : ℝ)) (q := - (6609211395806087 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6609211395806087 / 20000000000000000 : ℚ)) + (r' := (6609211395806087 / 5000000000000000 : ℚ)) + (U := (-(11072679310070797156689 / 10000000000000000000000 : ℚ))) + (U' := (2790264295929202843311 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (219376251837 / 500000000000 : ℚ)) + (s := (3228276203651087 / 10000000000000000 : ℚ)) + (q := (6609211395806087 / 20000000000000000 : ℚ)) + (U := (-(11072679310070797156689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_9 : Uω (aρ 9) (bρ 9) (219376251837 / 500000000000 : ℝ) ≤ @@ -4009,25 +3569,21 @@ lemma U_410_9 : have hlg : Real.log (1441441033374307 / 5000000000000000 : ℝ) ≤ (-(6218972905446657801553 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1441441033374307 / 5000000000000000 : ℝ) = - (1441441033374307 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1441441033374307 / 1250000000000000 : ℚ)) - (U := (712498897553342198447 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1441441033374307 / 1250000000000000 : ℝ) ≤ - (712498897553342198447 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (681448642425557 / 2500000000000000 : ℝ)) (q := - (1441441033374307 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1441441033374307 / 5000000000000000 : ℚ)) + (r' := (1441441033374307 / 1250000000000000 : ℚ)) + (U := (-(6218972905446657801553 / 5000000000000000000000 : ℚ))) + (U' := (712498897553342198447 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (219376251837 / 500000000000 : ℚ)) + (s := (681448642425557 / 2500000000000000 : ℚ)) + (q := (1441441033374307 / 5000000000000000 : ℚ)) + (U := (-(6218972905446657801553 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_10 : Uω (aρ 10) (bρ 10) (219376251837 / 500000000000 : ℝ) ≤ @@ -4035,25 +3591,21 @@ lemma U_410_10 : have hlg : Real.log (582066514092719 / 2500000000000000 : ℝ) ≤ (-(14574612834924164906609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (582066514092719 / 2500000000000000 : ℝ) = - (582066514092719 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (582066514092719 / 312500000000000 : ℚ)) - (U := (6219802574075835093391 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (582066514092719 / 312500000000000 : ℝ) ≤ - (6219802574075835093391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (250640197805219 / 1250000000000000 : ℝ)) (q := - (582066514092719 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (582066514092719 / 2500000000000000 : ℚ)) + (r' := (582066514092719 / 312500000000000 : ℚ)) + (U := (-(14574612834924164906609 / 10000000000000000000000 : ℚ))) + (U' := (6219802574075835093391 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (219376251837 / 500000000000 : ℚ)) + (s := (250640197805219 / 1250000000000000 : ℚ)) + (q := (582066514092719 / 2500000000000000 : ℚ)) + (U := (-(14574612834924164906609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_11 : Uω (aρ 11) (bρ 11) (219376251837 / 500000000000 : ℝ) ≤ @@ -4061,26 +3613,21 @@ lemma U_410_11 : have hlg : Real.log (1411651351459397 / 10000000000000000 : ℝ) ≤ (-(611820281831991679449 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1411651351459397 / 10000000000000000 : ℝ) = - (1411651351459397 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1411651351459397 / 1250000000000000 : ℚ)) - (U := (38005199699258320551 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1411651351459397 / 1250000000000000 : ℝ) ≤ - (38005199699258320551 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (295184399411897 / 5000000000000000 : ℝ)) (q := - (1411651351459397 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1411651351459397 / 10000000000000000 : ℚ)) + (r' := (1411651351459397 / 1250000000000000 : ℚ)) + (U := (-(611820281831991679449 / 312500000000000000000 : ℚ))) + (U' := (38005199699258320551 / 312500000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (219376251837 / 500000000000 : ℚ)) + (s := (295184399411897 / 5000000000000000 : ℚ)) + (q := (1411651351459397 / 10000000000000000 : ℚ)) + (U := (-(611820281831991679449 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_410_12 : Uω (aρ 12) (bρ 12) (219376251837 / 500000000000 : ℝ) ≤ @@ -4195,25 +3742,21 @@ lemma U_411_1 : have hlg : Real.log (4336233534399483 / 10000000000000000 : ℝ) ≤ (-(8355789703777010327123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4336233534399483 / 10000000000000000 : ℝ) = - (4336233534399483 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4336233534399483 / 2500000000000000 : ℚ)) - (U := (5507153902222989672877 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4336233534399483 / 2500000000000000 : ℝ) ≤ - (5507153902222989672877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2168098125689483 / 5000000000000000 : ℝ)) (q := - (4336233534399483 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4336233534399483 / 10000000000000000 : ℚ)) + (r' := (4336233534399483 / 2500000000000000 : ℚ)) + (U := (-(8355789703777010327123 / 10000000000000000000000 : ℚ))) + (U' := (5507153902222989672877 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (2168098125689483 / 5000000000000000 : ℚ)) + (q := (4336233534399483 / 10000000000000000 : ℚ)) + (U := (-(8355789703777010327123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_2 : Uω (aρ 2) (bρ 2) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4221,25 +3764,21 @@ lemma U_411_2 : have hlg : Real.log (8624511557850547 / 20000000000000000 : ℝ) ≤ (-(1682247885388241367499 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8624511557850547 / 20000000000000000 : ℝ) = - (8624511557850547 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8624511557850547 / 5000000000000000 : ℚ)) - (U := (1090340835811758632501 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8624511557850547 / 5000000000000000 : ℝ) ≤ - (1090340835811758632501 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4312009752940547 / 10000000000000000 : ℝ)) (q := - (8624511557850547 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8624511557850547 / 20000000000000000 : ℚ)) + (r' := (8624511557850547 / 5000000000000000 : ℚ)) + (U := (-(1682247885388241367499 / 2000000000000000000000 : ℚ))) + (U' := (1090340835811758632501 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (4312009752940547 / 10000000000000000 : ℚ)) + (q := (8624511557850547 / 20000000000000000 : ℚ)) + (U := (-(1682247885388241367499 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_3 : Uω (aρ 3) (bρ 3) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4247,25 +3786,21 @@ lemma U_411_3 : have hlg : Real.log (4264238242293903 / 10000000000000000 : ℝ) ≤ (-(4261607671066074145483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4264238242293903 / 10000000000000000 : ℝ) = - (4264238242293903 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4264238242293903 / 2500000000000000 : ℚ)) - (U := (2669864131933925854517 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4264238242293903 / 2500000000000000 : ℝ) ≤ - (2669864131933925854517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2131685393013903 / 5000000000000000 : ℝ)) (q := - (4264238242293903 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4264238242293903 / 10000000000000000 : ℚ)) + (r' := (4264238242293903 / 2500000000000000 : ℚ)) + (U := (-(4261607671066074145483 / 5000000000000000000000 : ℚ))) + (U' := (2669864131933925854517 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (2131685393013903 / 5000000000000000 : ℚ)) + (q := (4264238242293903 / 10000000000000000 : ℚ)) + (U := (-(4261607671066074145483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_4 : Uω (aρ 4) (bρ 4) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4273,25 +3808,21 @@ lemma U_411_4 : have hlg : Real.log (4184297229221859 / 10000000000000000 : ℝ) ≤ (-(2178115821864365629041 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4184297229221859 / 10000000000000000 : ℝ) = - (4184297229221859 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4184297229221859 / 2500000000000000 : ℚ)) - (U := (1287620079635634370959 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4184297229221859 / 2500000000000000 : ℝ) ≤ - (1287620079635634370959 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2090891470474359 / 5000000000000000 : ℝ)) (q := - (4184297229221859 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4184297229221859 / 10000000000000000 : ℚ)) + (r' := (4184297229221859 / 2500000000000000 : ℚ)) + (U := (-(2178115821864365629041 / 2500000000000000000000 : ℚ))) + (U' := (1287620079635634370959 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (2090891470474359 / 5000000000000000 : ℚ)) + (q := (4184297229221859 / 10000000000000000 : ℚ)) + (U := (-(2178115821864365629041 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_5 : Uω (aρ 5) (bρ 5) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4299,25 +3830,21 @@ lemma U_411_5 : have hlg : Real.log (2031033102636581 / 5000000000000000 : ℝ) ≤ (-(9008933307601673657931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2031033102636581 / 5000000000000000 : ℝ) = - (2031033102636581 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2031033102636581 / 1250000000000000 : ℚ)) - (U := (4854010298398326342069 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2031033102636581 / 1250000000000000 : ℝ) ≤ - (4854010298398326342069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1013877703096581 / 2500000000000000 : ℝ)) (q := - (2031033102636581 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2031033102636581 / 5000000000000000 : ℚ)) + (r' := (2031033102636581 / 1250000000000000 : ℚ)) + (U := (-(9008933307601673657931 / 10000000000000000000000 : ℚ))) + (U' := (4854010298398326342069 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (1013877703096581 / 2500000000000000 : ℚ)) + (q := (2031033102636581 / 5000000000000000 : ℚ)) + (U := (-(9008933307601673657931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_6 : Uω (aρ 6) (bρ 6) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4325,25 +3852,21 @@ lemma U_411_6 : have hlg : Real.log (7771178496422463 / 20000000000000000 : ℝ) ≤ (-(4726552237572163998887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7771178496422463 / 20000000000000000 : ℝ) = - (7771178496422463 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7771178496422463 / 5000000000000000 : ℚ)) - (U := (2204919565427836001113 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7771178496422463 / 5000000000000000 : ℝ) ≤ - (2204919565427836001113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3869797273402463 / 10000000000000000 : ℝ)) (q := - (7771178496422463 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7771178496422463 / 20000000000000000 : ℚ)) + (r' := (7771178496422463 / 5000000000000000 : ℚ)) + (U := (-(4726552237572163998887 / 5000000000000000000000 : ℚ))) + (U' := (2204919565427836001113 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (3869797273402463 / 10000000000000000 : ℚ)) + (q := (7771178496422463 / 20000000000000000 : ℚ)) + (U := (-(4726552237572163998887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_7 : Uω (aρ 7) (bρ 7) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4351,25 +3874,21 @@ lemma U_411_7 : have hlg : Real.log (7284230914933357 / 20000000000000000 : ℝ) ≤ (-(404008164002188548969 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7284230914933357 / 20000000000000000 : ℝ) = - (7284230914933357 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7284230914933357 / 5000000000000000 : ℚ)) - (U := (150509580237811451031 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7284230914933357 / 5000000000000000 : ℝ) ≤ - (150509580237811451031 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3606511072673357 / 10000000000000000 : ℝ)) (q := - (7284230914933357 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7284230914933357 / 20000000000000000 : ℚ)) + (r' := (7284230914933357 / 5000000000000000 : ℚ)) + (U := (-(404008164002188548969 / 400000000000000000000 : ℚ))) + (U' := (150509580237811451031 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (3606511072673357 / 10000000000000000 : ℚ)) + (q := (7284230914933357 / 20000000000000000 : ℚ)) + (U := (-(404008164002188548969 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_8 : Uω (aρ 8) (bρ 8) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4377,25 +3896,21 @@ lemma U_411_8 : have hlg : Real.log (1327264202182369 / 4000000000000000 : ℝ) ≤ (-(5515872638589955285107 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1327264202182369 / 4000000000000000 : ℝ) = - (1327264202182369 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1327264202182369 / 1000000000000000 : ℚ)) - (U := (1415599164410044714893 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1327264202182369 / 1000000000000000 : ℝ) ≤ - (1415599164410044714893 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (648428563998369 / 2000000000000000 : ℝ)) (q := - (1327264202182369 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1327264202182369 / 4000000000000000 : ℚ)) + (r' := (1327264202182369 / 1000000000000000 : ℚ)) + (U := (-(5515872638589955285107 / 5000000000000000000000 : ℚ))) + (U' := (1415599164410044714893 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (648428563998369 / 2000000000000000 : ℚ)) + (q := (1327264202182369 / 4000000000000000 : ℚ)) + (U := (-(5515872638589955285107 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_9 : Uω (aρ 9) (bρ 9) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4403,25 +3918,21 @@ lemma U_411_9 : have hlg : Real.log (5793768717721283 / 20000000000000000 : ℝ) ≤ (-(12389492920326356581651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5793768717721283 / 20000000000000000 : ℝ) = - (5793768717721283 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5793768717721283 / 5000000000000000 : ℚ)) - (U := (1473450685673643418349 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5793768717721283 / 5000000000000000 : ℝ) ≤ - (1473450685673643418349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2740556155161283 / 10000000000000000 : ℝ)) (q := - (5793768717721283 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5793768717721283 / 20000000000000000 : ℚ)) + (r' := (5793768717721283 / 5000000000000000 : ℚ)) + (U := (-(12389492920326356581651 / 10000000000000000000000 : ℚ))) + (U' := (1473450685673643418349 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (2740556155161283 / 10000000000000000 : ℚ)) + (q := (5793768717721283 / 20000000000000000 : ℚ)) + (U := (-(12389492920326356581651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_10 : Uω (aρ 10) (bρ 10) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4429,26 +3940,21 @@ lemma U_411_10 : have hlg : Real.log (4687254129813093 / 20000000000000000 : ℝ) ≤ (-(56675208404681107481 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4687254129813093 / 20000000000000000 : ℝ) = - (4687254129813093 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4687254129813093 / 2500000000000000 : ℚ)) - (U := (24552976786725142519 / 39062500000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4687254129813093 / 2500000000000000 : ℝ) ≤ - (24552976786725142519 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2022600600748093 / 10000000000000000 : ℝ)) (q := - (4687254129813093 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4687254129813093 / 20000000000000000 : ℚ)) + (r' := (4687254129813093 / 2500000000000000 : ℚ)) + (U := (-(56675208404681107481 / 39062500000000000000 : ℚ))) + (U' := (24552976786725142519 / 39062500000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (2022600600748093 / 10000000000000000 : ℚ)) + (q := (4687254129813093 / 20000000000000000 : ℚ)) + (U := (-(56675208404681107481 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_11 : Uω (aρ 11) (bρ 11) (880153607101 / 2000000000000 : ℝ) ≤ @@ -4456,26 +3962,21 @@ lemma U_411_11 : have hlg : Real.log (2884809956741063 / 20000000000000000 : ℝ) ≤ (-(968136623931926557471 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2884809956741063 / 20000000000000000 : ℝ) = - (2884809956741063 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2884809956741063 / 2500000000000000 : ℚ)) - (U := (71584146518073442529 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2884809956741063 / 2500000000000000 : ℝ) ≤ - (71584146518073442529 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (638633053881063 / 10000000000000000 : ℝ)) (q := - (2884809956741063 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2884809956741063 / 20000000000000000 : ℚ)) + (r' := (2884809956741063 / 2500000000000000 : ℚ)) + (U := (-(968136623931926557471 / 500000000000000000000 : ℚ))) + (U' := (71584146518073442529 / 500000000000000000000 : ℚ)) + 3 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (880153607101 / 2000000000000 : ℚ)) + (s := (638633053881063 / 10000000000000000 : ℚ)) + (q := (2884809956741063 / 20000000000000000 : ℚ)) + (U := (-(968136623931926557471 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_411_12 : Uω (aρ 12) (bρ 12) (880153607101 / 2000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U34.lean b/LeanPool/Zeta5Irrational/Table/U34.lean index 775c173e9b..196b0c8804 100644 --- a/LeanPool/Zeta5Irrational/Table/U34.lean +++ b/LeanPool/Zeta5Irrational/Table/U34.lean @@ -24,25 +24,21 @@ lemma U_412_1 : have hlg : Real.log (8698953293364661 / 20000000000000000 : ℝ) ≤ (-(8325295657190344060219 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8698953293364661 / 20000000000000000 : ℝ) = - (8698953293364661 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8698953293364661 / 5000000000000000 : ℚ)) - (U := (5537647948809655939781 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8698953293364661 / 5000000000000000 : ℝ) ≤ - (5537647948809655939781 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4349439477179661 / 10000000000000000 : ℝ)) (q := - (8698953293364661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8698953293364661 / 20000000000000000 : ℚ)) + (r' := (8698953293364661 / 5000000000000000 : ℚ)) + (U := (-(8325295657190344060219 / 10000000000000000000000 : ℚ))) + (U' := (5537647948809655939781 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (4349439477179661 / 10000000000000000 : ℚ)) + (q := (8698953293364661 / 20000000000000000 : ℚ)) + (U := (-(8325295657190344060219 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_2 : Uω (aρ 2) (bρ 2) (441401103427 / 1000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_412_2 : have hlg : Real.log (4325499530969083 / 10000000000000000 : ℝ) ≤ (-(335222984107915235267 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4325499530969083 / 10000000000000000 : ℝ) = - (4325499530969083 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4325499530969083 / 2500000000000000 : ℚ)) - (U := (219294760132084764733 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4325499530969083 / 2500000000000000 : ℝ) ≤ - (219294760132084764733 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2162627129131583 / 5000000000000000 : ℝ)) (q := - (4325499530969083 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4325499530969083 / 10000000000000000 : ℚ)) + (r' := (4325499530969083 / 2500000000000000 : ℚ)) + (U := (-(335222984107915235267 / 400000000000000000000 : ℚ))) + (U' := (219294760132084764733 / 400000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (2162627129131583 / 5000000000000000 : ℚ)) + (q := (4325499530969083 / 10000000000000000 : ℚ)) + (U := (-(335222984107915235267 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_3 : Uω (aρ 3) (bρ 3) (441401103427 / 1000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_412_3 : have hlg : Real.log (8554967854459393 / 20000000000000000 : ℝ) ≤ (-(8492201232119775677881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8554967854459393 / 20000000000000000 : ℝ) = - (8554967854459393 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8554967854459393 / 5000000000000000 : ℚ)) - (U := (5370742373880224322119 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8554967854459393 / 5000000000000000 : ℝ) ≤ - (5370742373880224322119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4276619157134393 / 10000000000000000 : ℝ)) (q := - (8554967854459393 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8554967854459393 / 20000000000000000 : ℚ)) + (r' := (8554967854459393 / 5000000000000000 : ℚ)) + (U := (-(8492201232119775677881 / 10000000000000000000000 : ℚ))) + (U' := (5370742373880224322119 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (4276619157134393 / 10000000000000000 : ℚ)) + (q := (8554967854459393 / 20000000000000000 : ℚ)) + (U := (-(8492201232119775677881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_4 : Uω (aρ 4) (bρ 4) (441401103427 / 1000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_412_4 : have hlg : Real.log (2098774082580749 / 5000000000000000 : ℝ) ≤ (-(4340422539223208551097 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2098774082580749 / 5000000000000000 : ℝ) = - (2098774082580749 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2098774082580749 / 1250000000000000 : ℚ)) - (U := (2591049263776791448903 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2098774082580749 / 1250000000000000 : ℝ) ≤ - (2591049263776791448903 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1048760453515749 / 2500000000000000 : ℝ)) (q := - (2098774082580749 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2098774082580749 / 5000000000000000 : ℚ)) + (r' := (2098774082580749 / 1250000000000000 : ℚ)) + (U := (-(4340422539223208551097 / 5000000000000000000000 : ℚ))) + (U' := (2591049263776791448903 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (1048760453515749 / 2500000000000000 : ℚ)) + (q := (2098774082580749 / 5000000000000000 : ℚ)) + (U := (-(4340422539223208551097 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_5 : Uω (aρ 5) (bρ 5) (441401103427 / 1000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_412_5 : have hlg : Real.log (407533054044943 / 1000000000000000 : ℝ) ≤ (-(4488166174250952639887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (407533054044943 / 1000000000000000 : ℝ) = - (407533054044943 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (407533054044943 / 250000000000000 : ℚ)) - (U := (2443305628749047360113 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (407533054044943 / 250000000000000 : ℝ) ≤ - (2443305628749047360113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203439824198693 / 500000000000000 : ℝ)) (q := - (407533054044943 / 1000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (407533054044943 / 1000000000000000 : ℚ)) + (r' := (407533054044943 / 250000000000000 : ℚ)) + (U := (-(4488166174250952639887 / 5000000000000000000000 : ℚ))) + (U' := (2443305628749047360113 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (203439824198693 / 500000000000000 : ℚ)) + (q := (407533054044943 / 1000000000000000 : ℚ)) + (U := (-(4488166174250952639887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_6 : Uω (aρ 6) (bρ 6) (441401103427 / 1000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_412_6 : have hlg : Real.log (3898886104311623 / 10000000000000000 : ℝ) ≤ (-(470947097206575796623 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3898886104311623 / 10000000000000000 : ℝ) = - (3898886104311623 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3898886104311623 / 2500000000000000 : ℚ)) - (U := (222200083093424203377 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3898886104311623 / 2500000000000000 : ℝ) ≤ - (222200083093424203377 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1941573993419123 / 5000000000000000 : ℝ)) (q := - (3898886104311623 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3898886104311623 / 10000000000000000 : ℚ)) + (r' := (3898886104311623 / 2500000000000000 : ℚ)) + (U := (-(470947097206575796623 / 500000000000000000000 : ℚ))) + (U' := (222200083093424203377 / 500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (1941573993419123 / 5000000000000000 : ℚ)) + (q := (3898886104311623 / 10000000000000000 : ℚ)) + (U := (-(470947097206575796623 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_7 : Uω (aρ 7) (bρ 7) (441401103427 / 1000000000000 : ℝ) ≤ @@ -180,24 +156,21 @@ lemma U_412_7 : have hlg : Real.log (45693608893127 / 125000000000000 : ℝ) ≤ (-(10063552978277690335471 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45693608893127 / 125000000000000 : ℝ) = (45693608893127 / 31250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45693608893127 / 31250000000000 : ℚ)) - (U := (3799390627722309664529 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (45693608893127 / 31250000000000 : ℝ) ≤ - (3799390627722309664529 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90500364546883 / 250000000000000 : ℝ)) (q := - (45693608893127 / 125000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45693608893127 / 125000000000000 : ℚ)) + (r' := (45693608893127 / 31250000000000 : ℚ)) + (U := (-(10063552978277690335471 / 10000000000000000000000 : ℚ))) + (U' := (3799390627722309664529 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (90500364546883 / 250000000000000 : ℚ)) + (q := (45693608893127 / 125000000000000 : ℚ)) + (U := (-(10063552978277690335471 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_8 : Uω (aρ 8) (bρ 8) (441401103427 / 1000000000000 : ℝ) ≤ @@ -205,25 +178,21 @@ lemma U_412_8 : have hlg : Real.log (3331712716879051 / 10000000000000000 : ℝ) ≤ (-(274774647827680332549 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3331712716879051 / 10000000000000000 : ℝ) = - (3331712716879051 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3331712716879051 / 2500000000000000 : ℚ)) - (U := (71798942322319667451 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3331712716879051 / 2500000000000000 : ℝ) ≤ - (71798942322319667451 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1628002122036551 / 5000000000000000 : ℝ)) (q := - (3331712716879051 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3331712716879051 / 10000000000000000 : ℚ)) + (r' := (3331712716879051 / 2500000000000000 : ℚ)) + (U := (-(274774647827680332549 / 250000000000000000000 : ℚ))) + (U' := (71798942322319667451 / 250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (1628002122036551 / 5000000000000000 : ℚ)) + (q := (3331712716879051 / 10000000000000000 : ℚ)) + (U := (-(274774647827680332549 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_9 : Uω (aρ 9) (bρ 9) (441401103427 / 1000000000000 : ℝ) ≤ @@ -231,25 +200,21 @@ lemma U_412_9 : have hlg : Real.log (5821757867243393 / 20000000000000000 : ℝ) ≤ (-(1234130017850107135807 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5821757867243393 / 20000000000000000 : ℝ) = - (5821757867243393 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5821757867243393 / 5000000000000000 : ℚ)) - (U := (152164342749892864193 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5821757867243393 / 5000000000000000 : ℝ) ≤ - (152164342749892864193 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2755302305918393 / 10000000000000000 : ℝ)) (q := - (5821757867243393 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5821757867243393 / 20000000000000000 : ℚ)) + (r' := (5821757867243393 / 5000000000000000 : ℚ)) + (U := (-(1234130017850107135807 / 1000000000000000000000 : ℚ))) + (U' := (152164342749892864193 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (2755302305918393 / 10000000000000000 : ℚ)) + (q := (5821757867243393 / 20000000000000000 : ℚ)) + (U := (-(1234130017850107135807 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_10 : Uω (aρ 10) (bρ 10) (441401103427 / 1000000000000 : ℝ) ≤ @@ -257,26 +222,21 @@ lemma U_412_10 : have hlg : Real.log (2358956177358807 / 10000000000000000 : ℝ) ≤ (-(14443658687485022068619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2358956177358807 / 10000000000000000 : ℝ) = - (2358956177358807 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2358956177358807 / 1250000000000000 : ℚ)) - (U := (6350756721514977931381 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2358956177358807 / 1250000000000000 : ℝ) ≤ - (6350756721514977931381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1020007913443807 / 5000000000000000 : ℝ)) (q := - (2358956177358807 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2358956177358807 / 10000000000000000 : ℚ)) + (r' := (2358956177358807 / 1250000000000000 : ℚ)) + (U := (-(14443658687485022068619 / 10000000000000000000000 : ℚ))) + (U' := (6350756721514977931381 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (1020007913443807 / 5000000000000000 : ℚ)) + (q := (2358956177358807 / 10000000000000000 : ℚ)) + (U := (-(14443658687485022068619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_11 : Uω (aρ 11) (bρ 11) (441401103427 / 1000000000000 : ℝ) ≤ @@ -284,25 +244,21 @@ lemma U_412_11 : have hlg : Real.log (735793522556029 / 5000000000000000 : ℝ) ≤ (-(19162436512716292548947 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (735793522556029 / 5000000000000000 : ℝ) = - (735793522556029 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (735793522556029 / 625000000000000 : ℚ)) - (U := (1631978896283707451053 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (735793522556029 / 625000000000000 : ℝ) ≤ - (1631978896283707451053 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (170938547149779 / 2500000000000000 : ℝ)) (q := - (735793522556029 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (735793522556029 / 5000000000000000 : ℚ)) + (r' := (735793522556029 / 625000000000000 : ℚ)) + (U := (-(19162436512716292548947 / 10000000000000000000000 : ℚ))) + (U' := (1631978896283707451053 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (441401103427 / 1000000000000 : ℚ)) + (s := (170938547149779 / 2500000000000000 : ℚ)) + (q := (735793522556029 / 5000000000000000 : ℚ)) + (U := (-(19162436512716292548947 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_412_12 : Uω (aρ 12) (bρ 12) (441401103427 / 1000000000000 : ℝ) ≤ @@ -419,25 +375,21 @@ lemma U_413_1 : have hlg : Real.log (8725439516552003 / 20000000000000000 : ℝ) ≤ (-(829489431824442098373 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8725439516552003 / 20000000000000000 : ℝ) = - (8725439516552003 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8725439516552003 / 5000000000000000 : ℚ)) - (U := (556804928775557901627 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8725439516552003 / 5000000000000000 : ℝ) ≤ - (556804928775557901627 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4362682701602003 / 10000000000000000 : ℝ)) (q := - (8725439516552003 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8725439516552003 / 20000000000000000 : ℚ)) + (r' := (8725439516552003 / 5000000000000000 : ℚ)) + (U := (-(829489431824442098373 / 1000000000000000000000 : ℚ))) + (U' := (556804928775557901627 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (4362682701602003 / 10000000000000000 : ℚ)) + (q := (8725439516552003 / 20000000000000000 : ℚ)) + (U := (-(829489431824442098373 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_2 : Uω (aρ 2) (bρ 2) (885450806607 / 2000000000000 : ℝ) ≤ @@ -445,25 +397,21 @@ lemma U_413_2 : have hlg : Real.log (1735497311365583 / 4000000000000000 : ℝ) ≤ (-(417500176740119125927 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1735497311365583 / 4000000000000000 : ℝ) = - (1735497311365583 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1735497311365583 / 1000000000000000 : ℚ)) - (U := (275647003559880874073 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1735497311365583 / 1000000000000000 : ℝ) ≤ - (275647003559880874073 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (867699750877583 / 2000000000000000 : ℝ)) (q := - (1735497311365583 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1735497311365583 / 4000000000000000 : ℚ)) + (r' := (1735497311365583 / 1000000000000000 : ℚ)) + (U := (-(417500176740119125927 / 500000000000000000000 : ℚ))) + (U' := (275647003559880874073 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (867699750877583 / 2000000000000000 : ℚ)) + (q := (1735497311365583 / 4000000000000000 : ℚ)) + (U := (-(417500176740119125927 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_3 : Uω (aρ 3) (bρ 3) (885450806607 / 2000000000000 : ℝ) ≤ @@ -471,25 +419,21 @@ lemma U_413_3 : have hlg : Real.log (8581459191154971 / 20000000000000000 : ℝ) ≤ (-(1692256610190248951243 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8581459191154971 / 20000000000000000 : ℝ) = - (8581459191154971 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8581459191154971 / 5000000000000000 : ℚ)) - (U := (1080332111009751048757 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8581459191154971 / 5000000000000000 : ℝ) ≤ - (1080332111009751048757 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4289867495064971 / 10000000000000000 : ℝ)) (q := - (8581459191154971 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8581459191154971 / 20000000000000000 : ℚ)) + (r' := (8581459191154971 / 5000000000000000 : ℚ)) + (U := (-(1692256610190248951243 / 2000000000000000000000 : ℚ))) + (U' := (1080332111009751048757 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (4289867495064971 / 10000000000000000 : ℚ)) + (q := (8581459191154971 / 20000000000000000 : ℚ)) + (U := (-(1692256610190248951243 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_4 : Uω (aρ 4) (bρ 4) (885450806607 / 2000000000000 : ℝ) ≤ @@ -497,25 +441,21 @@ lemma U_413_4 : have hlg : Real.log (4210799051116593 / 10000000000000000 : ℝ) ≤ (-(1729865328848618984599 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4210799051116593 / 10000000000000000 : ℝ) = - (4210799051116593 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4210799051116593 / 2500000000000000 : ℚ)) - (U := (1042723392351381015401 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4210799051116593 / 2500000000000000 : ℝ) ≤ - (1042723392351381015401 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2104150293604093 / 5000000000000000 : ℝ)) (q := - (4210799051116593 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4210799051116593 / 10000000000000000 : ℚ)) + (r' := (4210799051116593 / 2500000000000000 : ℚ)) + (U := (-(1729865328848618984599 / 2000000000000000000000 : ℚ))) + (U' := (1042723392351381015401 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (2104150293604093 / 5000000000000000 : ℚ)) + (q := (4210799051116593 / 10000000000000000 : ℚ)) + (U := (-(1729865328848618984599 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_5 : Uω (aρ 5) (bρ 5) (885450806607 / 2000000000000 : ℝ) ≤ @@ -523,25 +463,21 @@ lemma U_413_5 : have hlg : Real.log (8177189473928883 / 20000000000000000 : ℝ) ≤ (-(8943837665525954089233 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8177189473928883 / 20000000000000000 : ℝ) = - (8177189473928883 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8177189473928883 / 5000000000000000 : ℚ)) - (U := (4919105940474045910767 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8177189473928883 / 5000000000000000 : ℝ) ≤ - (4919105940474045910767 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4082081878238883 / 10000000000000000 : ℝ)) (q := - (8177189473928883 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8177189473928883 / 20000000000000000 : ℚ)) + (r' := (8177189473928883 / 5000000000000000 : ℚ)) + (U := (-(8943837665525954089233 / 10000000000000000000000 : ℚ))) + (U' := (4919105940474045910767 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (4082081878238883 / 10000000000000000 : ℚ)) + (q := (8177189473928883 / 20000000000000000 : ℚ)) + (U := (-(8943837665525954089233 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_6 : Uω (aρ 6) (bρ 6) (885450806607 / 2000000000000 : ℝ) ≤ @@ -549,25 +485,21 @@ lemma U_413_6 : have hlg : Real.log (782436518566833 / 2000000000000000 : ℝ) ≤ (-(9384896663309727471479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (782436518566833 / 2000000000000000 : ℝ) = - (782436518566833 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (782436518566833 / 500000000000000 : ℚ)) - (U := (4478046942690272528521 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (782436518566833 / 500000000000000 : ℝ) ≤ - (4478046942690272528521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (389649796511833 / 1000000000000000 : ℝ)) (q := - (782436518566833 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (782436518566833 / 2000000000000000 : ℚ)) + (r' := (782436518566833 / 500000000000000 : ℚ)) + (U := (-(9384896663309727471479 / 10000000000000000000000 : ℚ))) + (U' := (4478046942690272528521 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (389649796511833 / 1000000000000000 : ℚ)) + (q := (782436518566833 / 2000000000000000 : ℚ)) + (U := (-(9384896663309727471479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_7 : Uω (aρ 7) (bρ 7) (885450806607 / 2000000000000 : ℝ) ≤ @@ -575,25 +507,21 @@ lemma U_413_7 : have hlg : Real.log (1834430503309113 / 5000000000000000 : ℝ) ≤ (-(10027038309970569596151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1834430503309113 / 5000000000000000 : ℝ) = - (1834430503309113 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1834430503309113 / 1250000000000000 : ℚ)) - (U := (3835905296029430403849 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1834430503309113 / 1250000000000000 : ℝ) ≤ - (3835905296029430403849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (908379043361613 / 2500000000000000 : ℝ)) (q := - (1834430503309113 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1834430503309113 / 5000000000000000 : ℚ)) + (r' := (1834430503309113 / 1250000000000000 : ℚ)) + (U := (-(10027038309970569596151 / 10000000000000000000000 : ℚ))) + (U' := (3835905296029430403849 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (908379043361613 / 2500000000000000 : ℚ)) + (q := (1834430503309113 / 5000000000000000 : ℚ)) + (U := (-(10027038309970569596151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_8 : Uω (aρ 8) (bρ 8) (885450806607 / 2000000000000 : ℝ) ≤ @@ -601,25 +529,21 @@ lemma U_413_8 : have hlg : Real.log (3345262365188567 / 10000000000000000 : ℝ) ≤ (-(10950399669358784600239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3345262365188567 / 10000000000000000 : ℝ) = - (3345262365188567 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3345262365188567 / 2500000000000000 : ℚ)) - (U := (2912543936641215399761 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3345262365188567 / 2500000000000000 : ℝ) ≤ - (2912543936641215399761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1634930270963567 / 5000000000000000 : ℝ)) (q := - (3345262365188567 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3345262365188567 / 10000000000000000 : ℚ)) + (r' := (3345262365188567 / 2500000000000000 : ℚ)) + (U := (-(10950399669358784600239 / 10000000000000000000000 : ℚ))) + (U' := (2912543936641215399761 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (1634930270963567 / 5000000000000000 : ℚ)) + (q := (3345262365188567 / 10000000000000000 : ℚ)) + (U := (-(10950399669358784600239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_9 : Uω (aρ 9) (bρ 9) (885450806607 / 2000000000000 : ℝ) ≤ @@ -627,25 +551,21 @@ lemma U_413_9 : have hlg : Real.log (5849731828561447 / 20000000000000000 : ℝ) ≤ (-(6146682270563129851507 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5849731828561447 / 20000000000000000 : ℝ) = - (5849731828561447 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5849731828561447 / 5000000000000000 : ℚ)) - (U := (784789532436870148493 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5849731828561447 / 5000000000000000 : ℝ) ≤ - (784789532436870148493 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2770033268471447 / 10000000000000000 : ℝ)) (q := - (5849731828561447 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5849731828561447 / 20000000000000000 : ℚ)) + (r' := (5849731828561447 / 5000000000000000 : ℚ)) + (U := (-(6146682270563129851507 / 5000000000000000000000 : ℚ))) + (U' := (784789532436870148493 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (2770033268471447 / 10000000000000000 : ℚ)) + (q := (5849731828561447 / 20000000000000000 : ℚ)) + (U := (-(6146682270563129851507 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_10 : Uω (aρ 10) (bρ 10) (885450806607 / 2000000000000 : ℝ) ≤ @@ -653,26 +573,21 @@ lemma U_413_10 : have hlg : Real.log (4748508407420689 / 20000000000000000 : ℝ) ≤ (-(3594754308831076809627 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4748508407420689 / 20000000000000000 : ℝ) = - (4748508407420689 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4748508407420689 / 2500000000000000 : ℚ)) - (U := (1603849543418923190373 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4748508407420689 / 2500000000000000 : ℝ) ≤ - (1603849543418923190373 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2057368880825689 / 10000000000000000 : ℝ)) (q := - (4748508407420689 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4748508407420689 / 20000000000000000 : ℚ)) + (r' := (4748508407420689 / 2500000000000000 : ℚ)) + (U := (-(3594754308831076809627 / 2500000000000000000000 : ℚ))) + (U' := (1603849543418923190373 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (2057368880825689 / 10000000000000000 : ℚ)) + (q := (4748508407420689 / 20000000000000000 : ℚ)) + (U := (-(3594754308831076809627 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_11 : Uω (aρ 11) (bρ 11) (885450806607 / 2000000000000 : ℝ) ≤ @@ -680,26 +595,21 @@ lemma U_413_11 : have hlg : Real.log (2998981120853179 / 20000000000000000 : ℝ) ≤ (-(18974596681744203262247 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2998981120853179 / 20000000000000000 : ℝ) = - (2998981120853179 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2998981120853179 / 2500000000000000 : ℚ)) - (U := (1819818727255796737753 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2998981120853179 / 2500000000000000 : ℝ) ≤ - (1819818727255796737753 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (726318220463179 / 10000000000000000 : ℝ)) (q := - (2998981120853179 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2998981120853179 / 20000000000000000 : ℚ)) + (r' := (2998981120853179 / 2500000000000000 : ℚ)) + (U := (-(18974596681744203262247 / 10000000000000000000000 : ℚ))) + (U' := (1819818727255796737753 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (885450806607 / 2000000000000 : ℚ)) + (s := (726318220463179 / 10000000000000000 : ℚ)) + (q := (2998981120853179 / 20000000000000000 : ℚ)) + (U := (-(18974596681744203262247 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_413_12 : Uω (aρ 12) (bρ 12) (885450806607 / 2000000000000 : ℝ) ≤ @@ -816,25 +726,21 @@ lemma U_414_1 : have hlg : Real.log (1750385147674701 / 4000000000000000 : ℝ) ≤ (-(8264585124940494284273 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1750385147674701 / 4000000000000000 : ℝ) = - (1750385147674701 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1750385147674701 / 1000000000000000 : ℚ)) - (U := (5598358481059505715727 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1750385147674701 / 1000000000000000 : ℝ) ≤ - (5598358481059505715727 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (875185184931701 / 2000000000000000 : ℝ)) (q := - (1750385147674701 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1750385147674701 / 4000000000000000 : ℚ)) + (r' := (1750385147674701 / 1000000000000000 : ℚ)) + (U := (-(8264585124940494284273 / 10000000000000000000000 : ℚ))) + (U' := (5598358481059505715727 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22202485159 / 50000000000 : ℚ)) + (s := (875185184931701 / 2000000000000000 : ℚ)) + (q := (1750385147674701 / 4000000000000000 : ℚ)) + (U := (-(8264585124940494284273 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_2 : Uω (aρ 2) (bρ 2) (22202485159 / 50000000000 : ℝ) ≤ @@ -842,25 +748,21 @@ lemma U_414_2 : have hlg : Real.log (4351987021301887 / 10000000000000000 : ℝ) ≤ (-(8319525651625783148213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4351987021301887 / 10000000000000000 : ℝ) = - (4351987021301887 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4351987021301887 / 2500000000000000 : ℚ)) - (U := (5543417954374216851787 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4351987021301887 / 2500000000000000 : ℝ) ≤ - (5543417954374216851787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2175871620699387 / 5000000000000000 : ℝ)) (q := - (4351987021301887 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4351987021301887 / 10000000000000000 : ℚ)) + (r' := (4351987021301887 / 2500000000000000 : ℚ)) + (U := (-(8319525651625783148213 / 10000000000000000000000 : ℚ))) + (U' := (5543417954374216851787 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22202485159 / 50000000000 : ℚ)) + (s := (2175871620699387 / 5000000000000000 : ℚ)) + (q := (4351987021301887 / 10000000000000000 : ℚ)) + (U := (-(8319525651625783148213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_3 : Uω (aρ 3) (bρ 3) (22202485159 / 50000000000 : ℝ) ≤ @@ -868,25 +770,21 @@ lemma U_414_3 : have hlg : Real.log (8607950494980963 / 20000000000000000 : ℝ) ≤ (-(4215230103394798454407 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8607950494980963 / 20000000000000000 : ℝ) = - (8607950494980963 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8607950494980963 / 5000000000000000 : ℚ)) - (U := (2716241699605201545593 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8607950494980963 / 5000000000000000 : ℝ) ≤ - (2716241699605201545593 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4303115800125963 / 10000000000000000 : ℝ)) (q := - (8607950494980963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8607950494980963 / 20000000000000000 : ℚ)) + (r' := (8607950494980963 / 5000000000000000 : ℚ)) + (U := (-(4215230103394798454407 / 5000000000000000000000 : ℚ))) + (U' := (2716241699605201545593 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22202485159 / 50000000000 : ℚ)) + (s := (4303115800125963 / 10000000000000000 : ℚ)) + (q := (8607950494980963 / 20000000000000000 : ℚ)) + (U := (-(4215230103394798454407 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_4 : Uω (aρ 4) (bρ 4) (22202485159 / 50000000000 : ℝ) ≤ @@ -894,25 +792,21 @@ lemma U_414_4 : have hlg : Real.log (4224049887558109 / 10000000000000000 : ℝ) ≤ (-(8617907356384918787213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4224049887558109 / 10000000000000000 : ℝ) = - (4224049887558109 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4224049887558109 / 2500000000000000 : ℚ)) - (U := (5245036249615081212787 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4224049887558109 / 2500000000000000 : ℝ) ≤ - (5245036249615081212787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2110779630663109 / 5000000000000000 : ℝ)) (q := - (4224049887558109 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4224049887558109 / 10000000000000000 : ℚ)) + (r' := (4224049887558109 / 2500000000000000 : ℚ)) + (U := (-(8617907356384918787213 / 10000000000000000000000 : ℚ))) + (U' := (5245036249615081212787 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22202485159 / 50000000000 : ℚ)) + (s := (2110779630663109 / 5000000000000000 : ℚ)) + (q := (4224049887558109 / 10000000000000000 : ℚ)) + (U := (-(8617907356384918787213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_5 : Uω (aρ 5) (bρ 5) (22202485159 / 50000000000 : ℝ) ≤ @@ -920,24 +814,21 @@ lemma U_414_5 : have hlg : Real.log (82037175923353 / 200000000000000 : ℝ) ≤ (-(8911448565837778337919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (82037175923353 / 200000000000000 : ℝ) = (82037175923353 / 50000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82037175923353 / 50000000000000 : ℚ)) - (U := (4951495040162221662081 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (82037175923353 / 50000000000000 : ℝ) ≤ - (4951495040162221662081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (40953669978803 / 100000000000000 : ℝ)) (q := - (82037175923353 / 200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82037175923353 / 200000000000000 : ℚ)) + (r' := (82037175923353 / 50000000000000 : ℚ)) + (U := (-(8911448565837778337919 / 10000000000000000000000 : ℚ))) + (U' := (4951495040162221662081 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22202485159 / 50000000000 : ℚ)) + (s := (40953669978803 / 100000000000000 : ℚ)) + (q := (82037175923353 / 200000000000000 : ℚ)) + (U := (-(8911448565837778337919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_6 : Uω (aρ 6) (bρ 6) (22202485159 / 50000000000 : ℝ) ≤ @@ -945,25 +836,21 @@ lemma U_414_6 : have hlg : Real.log (7850957435088173 / 20000000000000000 : ℝ) ≤ (-(9350967824237916076221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7850957435088173 / 20000000000000000 : ℝ) = - (7850957435088173 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7850957435088173 / 5000000000000000 : ℚ)) - (U := (4511975781762083923779 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7850957435088173 / 5000000000000000 : ℝ) ≤ - (4511975781762083923779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3909847215773173 / 10000000000000000 : ℝ)) (q := - (7850957435088173 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7850957435088173 / 20000000000000000 : ℚ)) + (r' := (7850957435088173 / 5000000000000000 : ℚ)) + (U := (-(9350967824237916076221 / 10000000000000000000000 : ℚ))) + (U' := (4511975781762083923779 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22202485159 / 50000000000 : ℚ)) + (s := (3909847215773173 / 10000000000000000 : ℚ)) + (q := (7850957435088173 / 20000000000000000 : ℚ)) + (U := (-(9350967824237916076221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_7 : Uω (aρ 7) (bρ 7) (22202485159 / 50000000000 : ℝ) ≤ @@ -971,25 +858,21 @@ lemma U_414_7 : have hlg : Real.log (1472892941447899 / 4000000000000000 : ℝ) ≤ (-(4995329531900420707149 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1472892941447899 / 4000000000000000 : ℝ) = - (1472892941447899 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1472892941447899 / 1000000000000000 : ℚ)) - (U := (1936142271099579292851 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1472892941447899 / 1000000000000000 : ℝ) ≤ - (1936142271099579292851 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (729403173736899 / 2000000000000000 : ℝ)) (q := - (1472892941447899 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1472892941447899 / 4000000000000000 : ℚ)) + (r' := (1472892941447899 / 1000000000000000 : ℚ)) + (U := (-(4995329531900420707149 / 5000000000000000000000 : ℚ))) + (U' := (1936142271099579292851 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22202485159 / 50000000000 : ℚ)) + (s := (729403173736899 / 2000000000000000 : ℚ)) + (q := (1472892941447899 / 4000000000000000 : ℚ)) + (U := (-(4995329531900420707149 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_8 : Uω (aρ 8) (bρ 8) (22202485159 / 50000000000 : ℝ) ≤ @@ -997,25 +880,21 @@ lemma U_414_8 : have hlg : Real.log (3358809482831227 / 10000000000000000 : ℝ) ≤ (-(10909985018713567947419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3358809482831227 / 10000000000000000 : ℝ) = - (3358809482831227 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3358809482831227 / 2500000000000000 : ℚ)) - (U := (2952958587286432052581 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3358809482831227 / 2500000000000000 : ℝ) ≤ - (2952958587286432052581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1641855889223727 / 5000000000000000 : ℝ)) (q := - (3358809482831227 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3358809482831227 / 10000000000000000 : ℚ)) + (r' := (3358809482831227 / 2500000000000000 : ℚ)) + (U := (-(10909985018713567947419 / 10000000000000000000000 : ℚ))) + (U' := (2952958587286432052581 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22202485159 / 50000000000 : ℚ)) + (s := (1641855889223727 / 5000000000000000 : ℚ)) + (q := (3358809482831227 / 10000000000000000 : ℚ)) + (U := (-(10909985018713567947419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_9 : Uω (aρ 9) (bρ 9) (22202485159 / 50000000000 : ℝ) ≤ @@ -1023,25 +902,21 @@ lemma U_414_9 : have hlg : Real.log (5877690842706347 / 20000000000000000 : ℝ) ≤ (-(191338797200200775319 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5877690842706347 / 20000000000000000 : ℝ) = - (5877690842706347 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5877690842706347 / 5000000000000000 : ℚ)) - (U := (25269696643549224681 / 156250000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5877690842706347 / 5000000000000000 : ℝ) ≤ - (25269696643549224681 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2784749283851347 / 10000000000000000 : ℝ)) (q := - (5877690842706347 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5877690842706347 / 20000000000000000 : ℚ)) + (r' := (5877690842706347 / 5000000000000000 : ℚ)) + (U := (-(191338797200200775319 / 156250000000000000000 : ℚ))) + (U' := (25269696643549224681 / 156250000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22202485159 / 50000000000 : ℚ)) + (s := (2784749283851347 / 10000000000000000 : ℚ)) + (q := (5877690842706347 / 20000000000000000 : ℚ)) + (U := (-(191338797200200775319 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_10 : Uω (aρ 10) (bρ 10) (22202485159 / 50000000000 : ℝ) ≤ @@ -1049,26 +924,21 @@ lemma U_414_10 : have hlg : Real.log (2389521924000261 / 10000000000000000 : ℝ) ≤ (-(286298355615774617203 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2389521924000261 / 10000000000000000 : ℝ) = - (2389521924000261 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2389521924000261 / 1250000000000000 : ℚ)) - (U := (129589952564225382797 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2389521924000261 / 1250000000000000 : ℝ) ≤ - (129589952564225382797 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1037330661320261 / 5000000000000000 : ℝ)) (q := - (2389521924000261 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2389521924000261 / 10000000000000000 : ℚ)) + (r' := (2389521924000261 / 1250000000000000 : ℚ)) + (U := (-(286298355615774617203 / 200000000000000000000 : ℚ))) + (U' := (129589952564225382797 / 200000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22202485159 / 50000000000 : ℚ)) + (s := (1037330661320261 / 5000000000000000 : ℚ)) + (q := (2389521924000261 / 10000000000000000 : ℚ)) + (U := (-(286298355615774617203 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_11 : Uω (aρ 11) (bρ 11) (22202485159 / 50000000000 : ℝ) ≤ @@ -1076,26 +946,21 @@ lemma U_414_11 : have hlg : Real.log (3052657018071263 / 20000000000000000 : ℝ) ≤ (-(3759439815845592521937 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3052657018071263 / 20000000000000000 : ℝ) = - (3052657018071263 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3052657018071263 / 2500000000000000 : ℚ)) - (U := (399443265954407478063 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3052657018071263 / 2500000000000000 : ℝ) ≤ - (399443265954407478063 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (766751118916263 / 10000000000000000 : ℝ)) (q := - (3052657018071263 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3052657018071263 / 20000000000000000 : ℚ)) + (r' := (3052657018071263 / 2500000000000000 : ℚ)) + (U := (-(3759439815845592521937 / 2000000000000000000000 : ℚ))) + (U' := (399443265954407478063 / 2000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22202485159 / 50000000000 : ℚ)) + (s := (766751118916263 / 10000000000000000 : ℚ)) + (q := (3052657018071263 / 20000000000000000 : ℚ)) + (U := (-(3759439815845592521937 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_414_12 : Uω (aρ 12) (bρ 12) (22202485159 / 50000000000 : ℝ) ≤ @@ -1211,25 +1076,21 @@ lemma U_415_1 : have hlg : Real.log (2194602989710383 / 5000000000000000 : ℝ) ≤ (-(2058591880093690254427 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2194602989710383 / 5000000000000000 : ℝ) = - (2194602989710383 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2194602989710383 / 1250000000000000 : ℚ)) - (U := (1407144021406309745573 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2194602989710383 / 1250000000000000 : ℝ) ≤ - (1407144021406309745573 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1097292286590383 / 2500000000000000 : ℝ)) (q := - (2194602989710383 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2194602989710383 / 5000000000000000 : ℚ)) + (r' := (2194602989710383 / 1250000000000000 : ℚ)) + (U := (-(2058591880093690254427 / 2500000000000000000000 : ℚ))) + (U' := (1407144021406309745573 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (1097292286590383 / 2500000000000000 : ℚ)) + (q := (2194602989710383 / 5000000000000000 : ℚ)) + (U := (-(2058591880093690254427 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_2 : Uω (aρ 2) (bρ 2) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1237,25 +1098,21 @@ lemma U_415_2 : have hlg : Real.log (272826922479647 / 625000000000000 : ℝ) ≤ (-(4144570193375825698037 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (272826922479647 / 625000000000000 : ℝ) = - (272826922479647 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (272826922479647 / 156250000000000 : ℚ)) - (U := (2786901609624174301963 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (272826922479647 / 156250000000000 : ℝ) ≤ - (2786901609624174301963 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (272811732461169 / 625000000000000 : ℝ)) (q := - (272826922479647 / 625000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (272826922479647 / 625000000000000 : ℚ)) + (r' := (272826922479647 / 156250000000000 : ℚ)) + (U := (-(4144570193375825698037 / 5000000000000000000000 : ℚ))) + (U' := (2786901609624174301963 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (272811732461169 / 625000000000000 : ℚ)) + (q := (272826922479647 / 625000000000000 : ℚ)) + (U := (-(4144570193375825698037 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_3 : Uω (aρ 3) (bρ 3) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1263,25 +1120,21 @@ lemma U_415_3 : have hlg : Real.log (8634441766240031 / 20000000000000000 : ℝ) ≤ (-(4199866056630123266719 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8634441766240031 / 20000000000000000 : ℝ) = - (8634441766240031 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8634441766240031 / 5000000000000000 : ℚ)) - (U := (2731605746369876733281 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8634441766240031 / 5000000000000000 : ℝ) ≤ - (2731605746369876733281 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4316364072620031 / 10000000000000000 : ℝ)) (q := - (8634441766240031 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8634441766240031 / 20000000000000000 : ℚ)) + (r' := (8634441766240031 / 5000000000000000 : ℚ)) + (U := (-(4199866056630123266719 / 5000000000000000000000 : ℚ))) + (U' := (2731605746369876733281 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (4316364072620031 / 10000000000000000 : ℚ)) + (q := (8634441766240031 / 20000000000000000 : ℚ)) + (U := (-(4199866056630123266719 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_4 : Uω (aρ 4) (bρ 4) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1289,25 +1142,21 @@ lemma U_415_4 : have hlg : Real.log (1694920269980443 / 4000000000000000 : ℝ) ≤ (-(8586586592335453971777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1694920269980443 / 4000000000000000 : ℝ) = - (1694920269980443 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1694920269980443 / 1000000000000000 : ℚ)) - (U := (5276357013664546028223 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1694920269980443 / 1000000000000000 : ℝ) ≤ - (5276357013664546028223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (846963567469443 / 2000000000000000 : ℝ)) (q := - (1694920269980443 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1694920269980443 / 4000000000000000 : ℚ)) + (r' := (1694920269980443 / 1000000000000000 : ℚ)) + (U := (-(8586586592335453971777 / 10000000000000000000000 : ℚ))) + (U' := (5276357013664546028223 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (846963567469443 / 2000000000000000 : ℚ)) + (q := (1694920269980443 / 4000000000000000 : ℚ)) + (U := (-(8586586592335453971777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_5 : Uω (aρ 5) (bρ 5) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1315,25 +1164,21 @@ lemma U_415_5 : have hlg : Real.log (4115122719391029 / 10000000000000000 : ℝ) ≤ (-(34684235794435448991 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4115122719391029 / 10000000000000000 : ℝ) = - (4115122719391029 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4115122719391029 / 2500000000000000 : ℚ)) - (U := (19467887666502051009 / 39062500000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4115122719391029 / 2500000000000000 : ℝ) ≤ - (19467887666502051009 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2054325922781029 / 5000000000000000 : ℝ)) (q := - (4115122719391029 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4115122719391029 / 10000000000000000 : ℚ)) + (r' := (4115122719391029 / 2500000000000000 : ℚ)) + (U := (-(34684235794435448991 / 39062500000000000000 : ℚ))) + (U' := (19467887666502051009 / 39062500000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (2054325922781029 / 5000000000000000 : ℚ)) + (q := (4115122719391029 / 10000000000000000 : ℚ)) + (U := (-(34684235794435448991 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_6 : Uω (aρ 6) (bρ 6) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1341,25 +1186,21 @@ lemma U_415_6 : have hlg : Real.log (787754896431033 / 2000000000000000 : ℝ) ≤ (-(4658577313435840435391 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (787754896431033 / 2000000000000000 : ℝ) = - (787754896431033 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (787754896431033 / 500000000000000 : ℚ)) - (U := (2272894489564159564609 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (787754896431033 / 500000000000000 : ℝ) ≤ - (2272894489564159564609 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (392319574623033 / 1000000000000000 : ℝ)) (q := - (787754896431033 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (787754896431033 / 2000000000000000 : ℚ)) + (r' := (787754896431033 / 500000000000000 : ℚ)) + (U := (-(4658577313435840435391 / 5000000000000000000000 : ℚ))) + (U' := (2272894489564159564609 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (392319574623033 / 1000000000000000 : ℚ)) + (q := (787754896431033 / 2000000000000000 : ℚ)) + (U := (-(4658577313435840435391 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_7 : Uω (aρ 7) (bρ 7) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1367,25 +1208,21 @@ lemma U_415_7 : have hlg : Real.log (3695602762945023 / 10000000000000000 : ℝ) ≤ (-(9954414220290087389677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3695602762945023 / 10000000000000000 : ℝ) = - (3695602762945023 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3695602762945023 / 2500000000000000 : ℚ)) - (U := (3908529385709912610323 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3695602762945023 / 2500000000000000 : ℝ) ≤ - (3908529385709912610323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1830256844285023 / 5000000000000000 : ℝ)) (q := - (3695602762945023 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3695602762945023 / 10000000000000000 : ℚ)) + (r' := (3695602762945023 / 2500000000000000 : ℚ)) + (U := (-(9954414220290087389677 / 10000000000000000000000 : ℚ))) + (U' := (3908529385709912610323 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (1830256844285023 / 5000000000000000 : ℚ)) + (q := (3695602762945023 / 10000000000000000 : ℚ)) + (U := (-(9954414220290087389677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_8 : Uω (aρ 8) (bρ 8) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1393,25 +1230,21 @@ lemma U_415_8 : have hlg : Real.log (421544262712109 / 1250000000000000 : ℝ) ≤ (-(5434870227411690620931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (421544262712109 / 1250000000000000 : ℝ) = - (421544262712109 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (421544262712109 / 312500000000000 : ℚ)) - (U := (1496601575588309379069 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (421544262712109 / 312500000000000 : ℝ) ≤ - (1496601575588309379069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (206097376088359 / 625000000000000 : ℝ)) (q := - (421544262712109 / 1250000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (421544262712109 / 1250000000000000 : ℚ)) + (r' := (421544262712109 / 312500000000000 : ℚ)) + (U := (-(5434870227411690620931 / 5000000000000000000000 : ℚ))) + (U' := (1496601575588309379069 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (206097376088359 / 625000000000000 : ℚ)) + (q := (421544262712109 / 1250000000000000 : ℚ)) + (U := (-(5434870227411690620931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_9 : Uω (aρ 9) (bρ 9) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1419,25 +1252,21 @@ lemma U_415_9 : have hlg : Real.log (2952817572699407 / 10000000000000000 : ℝ) ≤ (-(12198252685595503436989 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2952817572699407 / 10000000000000000 : ℝ) = - (2952817572699407 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2952817572699407 / 2500000000000000 : ℚ)) - (U := (1664690920404496563011 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2952817572699407 / 2500000000000000 : ℝ) ≤ - (1664690920404496563011 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1399725293889407 / 5000000000000000 : ℝ)) (q := - (2952817572699407 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2952817572699407 / 10000000000000000 : ℚ)) + (r' := (2952817572699407 / 2500000000000000 : ℚ)) + (U := (-(12198252685595503436989 / 10000000000000000000000 : ℚ))) + (U' := (1664690920404496563011 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (1399725293889407 / 5000000000000000 : ℚ)) + (q := (2952817572699407 / 10000000000000000 : ℚ)) + (U := (-(12198252685595503436989 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_10 : Uω (aρ 10) (bρ 10) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1445,25 +1274,21 @@ lemma U_415_10 : have hlg : Real.log (601190022448769 / 2500000000000000 : ℝ) ≤ (-(1781418685494105864799 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (601190022448769 / 2500000000000000 : ℝ) = - (601190022448769 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (601190022448769 / 312500000000000 : ℚ)) - (U := (817883240630894135201 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (601190022448769 / 312500000000000 : ℝ) ≤ - (817883240630894135201 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (32685853991643 / 156250000000000 : ℝ)) (q := - (601190022448769 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (601190022448769 / 2500000000000000 : ℚ)) + (r' := (601190022448769 / 312500000000000 : ℚ)) + (U := (-(1781418685494105864799 / 1250000000000000000000 : ℚ))) + (U' := (817883240630894135201 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (32685853991643 / 156250000000000 : ℚ)) + (q := (601190022448769 / 2500000000000000 : ℚ)) + (U := (-(1781418685494105864799 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_11 : Uω (aρ 11) (bρ 11) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1471,24 +1296,21 @@ lemma U_415_11 : have hlg : Real.log (31045228193841 / 200000000000000 : ℝ) ≤ (-(9314361252783403192807 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (31045228193841 / 200000000000000 : ℝ) = (31045228193841 / 25000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31045228193841 / 25000000000000 : ℚ)) - (U := (1082846451716596807193 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (31045228193841 / 25000000000000 : ℝ) ≤ - (1082846451716596807193 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8053739214641 / 100000000000000 : ℝ)) (q := - (31045228193841 / 200000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31045228193841 / 200000000000000 : ℚ)) + (r' := (31045228193841 / 25000000000000 : ℚ)) + (U := (-(9314361252783403192807 / 5000000000000000000000 : ℚ))) + (U' := (1082846451716596807193 / 5000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (890748006113 / 2000000000000 : ℚ)) + (s := (8053739214641 / 100000000000000 : ℚ)) + (q := (31045228193841 / 200000000000000 : ℚ)) + (U := (-(9314361252783403192807 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_415_12 : Uω (aρ 12) (bρ 12) (890748006113 / 2000000000000 : ℝ) ≤ @@ -1604,25 +1426,21 @@ lemma U_416_1 : have hlg : Real.log (4402449088984149 / 10000000000000000 : ℝ) ≤ (-(8204240952676966510493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4402449088984149 / 10000000000000000 : ℝ) = - (4402449088984149 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4402449088984149 / 2500000000000000 : ℚ)) - (U := (5658702653323033489507 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4402449088984149 / 2500000000000000 : ℝ) ≤ - (5658702653323033489507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2201206183361649 / 5000000000000000 : ℝ)) (q := - (4402449088984149 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4402449088984149 / 10000000000000000 : ℚ)) + (r' := (4402449088984149 / 2500000000000000 : ℚ)) + (U := (-(8204240952676966510493 / 10000000000000000000000 : ℚ))) + (U' := (5658702653323033489507 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (2201206183361649 / 5000000000000000 : ℚ)) + (q := (4402449088984149 / 10000000000000000 : ℚ)) + (U := (-(8204240952676966510493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_2 : Uω (aρ 2) (bρ 2) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1630,25 +1448,21 @@ lemma U_416_2 : have hlg : Real.log (1094618623393083 / 2500000000000000 : ℝ) ≤ (-(1032355897364107694117 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1094618623393083 / 2500000000000000 : ℝ) = - (1094618623393083 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1094618623393083 / 625000000000000 : ℚ)) - (U := (700512053385892305883 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1094618623393083 / 625000000000000 : ℝ) ≤ - (700512053385892305883 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68409877943901 / 156250000000000 : ℝ)) (q := - (1094618623393083 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1094618623393083 / 2500000000000000 : ℚ)) + (r' := (1094618623393083 / 625000000000000 : ℚ)) + (U := (-(1032355897364107694117 / 1250000000000000000000 : ℚ))) + (U' := (700512053385892305883 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (68409877943901 / 156250000000000 : ℚ)) + (q := (1094618623393083 / 2500000000000000 : ℚ)) + (U := (-(1032355897364107694117 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_3 : Uω (aρ 3) (bρ 3) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1656,25 +1470,21 @@ lemma U_416_3 : have hlg : Real.log (8660933005231133 / 20000000000000000 : ℝ) ≤ (-(8369098189383941263791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8660933005231133 / 20000000000000000 : ℝ) = - (8660933005231133 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8660933005231133 / 5000000000000000 : ℚ)) - (U := (5493845416616058736209 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8660933005231133 / 5000000000000000 : ℝ) ≤ - (5493845416616058736209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4329612312846133 / 10000000000000000 : ℝ)) (q := - (8660933005231133 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8660933005231133 / 20000000000000000 : ℚ)) + (r' := (8660933005231133 / 5000000000000000 : ℚ)) + (U := (-(8369098189383941263791 / 10000000000000000000000 : ℚ))) + (U' := (5493845416616058736209 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (4329612312846133 / 10000000000000000 : ℚ)) + (q := (8660933005231133 / 20000000000000000 : ℚ)) + (U := (-(8369098189383941263791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_4 : Uω (aρ 4) (bρ 4) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1682,25 +1492,21 @@ lemma U_416_4 : have hlg : Real.log (4250551413754841 / 10000000000000000 : ℝ) ≤ (-(8555363735410042263653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4250551413754841 / 10000000000000000 : ℝ) = - (4250551413754841 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4250551413754841 / 2500000000000000 : ℚ)) - (U := (5307579870589957736347 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4250551413754841 / 2500000000000000 : ℝ) ≤ - (5307579870589957736347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2124038158094841 / 5000000000000000 : ℝ)) (q := - (4250551413754841 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4250551413754841 / 10000000000000000 : ℚ)) + (r' := (4250551413754841 / 2500000000000000 : ℚ)) + (U := (-(8555363735410042263653 / 10000000000000000000000 : ℚ))) + (U' := (5307579870589957736347 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (2124038158094841 / 5000000000000000 : ℚ)) + (q := (4250551413754841 / 10000000000000000 : ℚ)) + (U := (-(8555363735410042263653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_5 : Uω (aρ 5) (bρ 5) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1708,25 +1514,21 @@ lemma U_416_5 : have hlg : Real.log (4128386507949351 / 10000000000000000 : ℝ) ≤ (-(884698437876299503827 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4128386507949351 / 10000000000000000 : ℝ) = - (4128386507949351 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4128386507949351 / 2500000000000000 : ℚ)) - (U := (501595922723700496173 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4128386507949351 / 2500000000000000 : ℝ) ≤ - (501595922723700496173 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2060968211956851 / 5000000000000000 : ℝ)) (q := - (4128386507949351 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4128386507949351 / 10000000000000000 : ℚ)) + (r' := (4128386507949351 / 2500000000000000 : ℚ)) + (U := (-(884698437876299503827 / 1000000000000000000000 : ℚ))) + (U' := (501595922723700496173 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (2060968211956851 / 5000000000000000 : ℚ)) + (q := (4128386507949351 / 10000000000000000 : ℚ)) + (U := (-(884698437876299503827 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_6 : Uω (aρ 6) (bρ 6) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1734,25 +1536,21 @@ lemma U_416_6 : have hlg : Real.log (3952069890330607 / 10000000000000000 : ℝ) ≤ (-(9283456279446531117199 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3952069890330607 / 10000000000000000 : ℝ) = - (3952069890330607 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3952069890330607 / 2500000000000000 : ℚ)) - (U := (4579487326553468882801 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3952069890330607 / 2500000000000000 : ℝ) ≤ - (4579487326553468882801 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1968271781908107 / 5000000000000000 : ℝ)) (q := - (3952069890330607 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3952069890330607 / 10000000000000000 : ℚ)) + (r' := (3952069890330607 / 2500000000000000 : ℚ)) + (U := (-(9283456279446531117199 / 10000000000000000000000 : ℚ))) + (U' := (4579487326553468882801 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (1968271781908107 / 5000000000000000 : ℚ)) + (q := (3952069890330607 / 10000000000000000 : ℚ)) + (U := (-(9283456279446531117199 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_7 : Uω (aρ 7) (bρ 7) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1760,25 +1558,21 @@ lemma U_416_7 : have hlg : Real.log (3708972244928743 / 10000000000000000 : ℝ) ≤ (-(2479575692907522664859 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3708972244928743 / 10000000000000000 : ℝ) = - (3708972244928743 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3708972244928743 / 2500000000000000 : ℚ)) - (U := (986160208592477335141 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3708972244928743 / 2500000000000000 : ℝ) ≤ - (986160208592477335141 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1837004826886243 / 5000000000000000 : ℝ)) (q := - (3708972244928743 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3708972244928743 / 10000000000000000 : ℚ)) + (r' := (3708972244928743 / 2500000000000000 : ℚ)) + (U := (-(2479575692907522664859 / 2500000000000000000000 : ℚ))) + (U' := (986160208592477335141 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (1837004826886243 / 5000000000000000 : ℚ)) + (q := (3708972244928743 / 10000000000000000 : ℚ)) + (U := (-(2479575692907522664859 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_8 : Uω (aρ 8) (bρ 8) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1786,25 +1580,21 @@ lemma U_416_8 : have hlg : Real.log (677179250626111 / 2000000000000000 : ℝ) ≤ (-(2165932898364507387119 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (677179250626111 / 2000000000000000 : ℝ) = - (677179250626111 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (677179250626111 / 500000000000000 : ℚ)) - (U := (606655822835492612881 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (677179250626111 / 500000000000000 : ℝ) ≤ - (606655822835492612881 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (331139932151611 / 1000000000000000 : ℝ)) (q := - (677179250626111 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (677179250626111 / 2000000000000000 : ℚ)) + (r' := (677179250626111 / 500000000000000 : ℚ)) + (U := (-(2165932898364507387119 / 2000000000000000000000 : ℚ))) + (U' := (606655822835492612881 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (331139932151611 / 1000000000000000 : ℚ)) + (q := (677179250626111 / 2000000000000000 : ℚ)) + (U := (-(2165932898364507387119 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_9 : Uω (aρ 9) (bρ 9) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1812,25 +1602,21 @@ lemma U_416_9 : have hlg : Real.log (5933564967200663 / 20000000000000000 : ℝ) ≤ (-(12151070657503466858303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5933564967200663 / 20000000000000000 : ℝ) = - (5933564967200663 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5933564967200663 / 5000000000000000 : ℚ)) - (U := (1711872948496533141697 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5933564967200663 / 5000000000000000 : ℝ) ≤ - (1711872948496533141697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2814137410815663 / 10000000000000000 : ℝ)) (q := - (5933564967200663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5933564967200663 / 20000000000000000 : ℚ)) + (r' := (5933564967200663 / 5000000000000000 : ℚ)) + (U := (-(12151070657503466858303 / 10000000000000000000000 : ℚ))) + (U' := (1711872948496533141697 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (2814137410815663 / 10000000000000000 : ℚ)) + (q := (5933564967200663 / 20000000000000000 : ℚ)) + (U := (-(12151070657503466858303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_10 : Uω (aρ 10) (bρ 10) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1838,25 +1624,21 @@ lemma U_416_10 : have hlg : Real.log (604992356392347 / 2500000000000000 : ℝ) ≤ (-(3547075465469153810511 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (604992356392347 / 2500000000000000 : ℝ) = - (604992356392347 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (604992356392347 / 312500000000000 : ℚ)) - (U := (1651528386780846189489 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (604992356392347 / 312500000000000 : ℝ) ≤ - (1651528386780846189489 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263633791031097 / 1250000000000000 : ℝ)) (q := - (604992356392347 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (604992356392347 / 2500000000000000 : ℚ)) + (r' := (604992356392347 / 312500000000000 : ℚ)) + (U := (-(3547075465469153810511 / 2500000000000000000000 : ℚ))) + (U' := (1651528386780846189489 / 2500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (263633791031097 / 1250000000000000 : ℚ)) + (q := (604992356392347 / 2500000000000000 : ℚ)) + (U := (-(3547075465469153810511 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_11 : Uω (aρ 11) (bρ 11) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1864,26 +1646,21 @@ lemma U_416_11 : have hlg : Real.log (1577413760887911 / 10000000000000000 : ℝ) ≤ (-(738719378596878066367 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1577413760887911 / 10000000000000000 : ℝ) = - (1577413760887911 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1577413760887911 / 1250000000000000 : ℚ)) - (U := (93057237763121933633 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1577413760887911 / 1250000000000000 : ℝ) ≤ - (93057237763121933633 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421217812545411 / 5000000000000000 : ℝ)) (q := - (1577413760887911 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1577413760887911 / 10000000000000000 : ℚ)) + (r' := (1577413760887911 / 1250000000000000 : ℚ)) + (U := (-(738719378596878066367 / 400000000000000000000 : ℚ))) + (U' := (93057237763121933633 / 400000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (446698302933 / 1000000000000 : ℚ)) + (s := (421217812545411 / 5000000000000000 : ℚ)) + (q := (1577413760887911 / 10000000000000000 : ℚ)) + (U := (-(738719378596878066367 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_416_12 : Uω (aρ 12) (bρ 12) (446698302933 / 1000000000000 : ℝ) ≤ @@ -1998,25 +1775,21 @@ lemma U_417_1 : have hlg : Real.log (883138439576587 / 2000000000000000 : ℝ) ≤ (-(2043551218737480737427 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (883138439576587 / 2000000000000000 : ℝ) = - (883138439576587 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (883138439576587 / 500000000000000 : ℚ)) - (U := (1422184682762519262573 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (883138439576587 / 500000000000000 : ℝ) ≤ - (1422184682762519262573 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (441565558575587 / 1000000000000000 : ℝ)) (q := - (883138439576587 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (883138439576587 / 2000000000000000 : ℚ)) + (r' := (883138439576587 / 500000000000000 : ℚ)) + (U := (-(2043551218737480737427 / 2500000000000000000000 : ℚ))) + (U' := (1422184682762519262573 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (441565558575587 / 1000000000000000 : ℚ)) + (q := (883138439576587 / 2000000000000000 : ℚ)) + (U := (-(2043551218737480737427 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_2 : Uω (aρ 2) (bρ 2) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2024,25 +1797,21 @@ lemma U_417_2 : have hlg : Real.log (4391718223036311 / 10000000000000000 : ℝ) ≤ (-(2057161367982340828791 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4391718223036311 / 10000000000000000 : ℝ) = - (4391718223036311 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4391718223036311 / 2500000000000000 : ℚ)) - (U := (1408574533517659171209 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4391718223036311 / 2500000000000000 : ℝ) ≤ - (1408574533517659171209 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2195738324286311 / 5000000000000000 : ℝ)) (q := - (4391718223036311 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4391718223036311 / 10000000000000000 : ℚ)) + (r' := (4391718223036311 / 2500000000000000 : ℚ)) + (U := (-(2057161367982340828791 / 2500000000000000000000 : ℚ))) + (U' := (1408574533517659171209 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (2195738324286311 / 5000000000000000 : ℚ)) + (q := (4391718223036311 / 10000000000000000 : ℚ)) + (U := (-(2057161367982340828791 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_3 : Uω (aρ 3) (bρ 3) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2050,25 +1819,21 @@ lemma U_417_3 : have hlg : Real.log (1085928026531197 / 2500000000000000 : ℝ) ≤ (-(833855785951075132007 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1085928026531197 / 2500000000000000 : ℝ) = - (1085928026531197 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1085928026531197 / 625000000000000 : ℚ)) - (U := (552438574648924867993 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1085928026531197 / 625000000000000 : ℝ) ≤ - (552438574648924867993 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (542857565137447 / 1250000000000000 : ℝ)) (q := - (1085928026531197 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1085928026531197 / 2500000000000000 : ℚ)) + (r' := (1085928026531197 / 625000000000000 : ℚ)) + (U := (-(833855785951075132007 / 1000000000000000000000 : ℚ))) + (U' := (552438574648924867993 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (542857565137447 / 1250000000000000 : ℚ)) + (q := (1085928026531197 / 2500000000000000 : ℚ)) + (U := (-(833855785951075132007 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_4 : Uω (aρ 4) (bρ 4) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2076,25 +1841,21 @@ lemma U_417_4 : have hlg : Real.log (8527604208845687 / 20000000000000000 : ℝ) ≤ (-(1704847634940521090967 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8527604208845687 / 20000000000000000 : ℝ) = - (8527604208845687 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8527604208845687 / 5000000000000000 : ℚ)) - (U := (1067741086259478909033 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8527604208845687 / 5000000000000000 : ℝ) ≤ - (1067741086259478909033 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4261334698760687 / 10000000000000000 : ℝ)) (q := - (8527604208845687 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8527604208845687 / 20000000000000000 : ℚ)) + (r' := (8527604208845687 / 5000000000000000 : ℚ)) + (U := (-(1704847634940521090967 / 2000000000000000000000 : ℚ))) + (U' := (1067741086259478909033 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (4261334698760687 / 10000000000000000 : ℚ)) + (q := (8527604208845687 / 20000000000000000 : ℚ)) + (U := (-(1704847634940521090967 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_5 : Uω (aρ 5) (bρ 5) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2102,25 +1863,21 @@ lemma U_417_5 : have hlg : Real.log (8283300326280939 / 20000000000000000 : ℝ) ≤ (-(1101863492402909633239 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8283300326280939 / 20000000000000000 : ℝ) = - (8283300326280939 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8283300326280939 / 5000000000000000 : ℚ)) - (U := (631004458347090366761 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8283300326280939 / 5000000000000000 : ℝ) ≤ - (631004458347090366761 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4135220735530939 / 10000000000000000 : ℝ)) (q := - (8283300326280939 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8283300326280939 / 20000000000000000 : ℚ)) + (r' := (8283300326280939 / 5000000000000000 : ℚ)) + (U := (-(1101863492402909633239 / 1250000000000000000000 : ℚ))) + (U' := (631004458347090366761 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (4135220735530939 / 10000000000000000 : ℚ)) + (q := (8283300326280939 / 20000000000000000 : ℚ)) + (U := (-(1101863492402909633239 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_6 : Uω (aρ 6) (bρ 6) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2128,25 +1885,21 @@ lemma U_417_6 : have hlg : Real.log (7930729891367817 / 20000000000000000 : ℝ) ≤ (-(9249871998363191376847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7930729891367817 / 20000000000000000 : ℝ) = - (7930729891367817 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7930729891367817 / 5000000000000000 : ℚ)) - (U := (4613071607636808623153 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7930729891367817 / 5000000000000000 : ℝ) ≤ - (4613071607636808623153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3949890675757817 / 10000000000000000 : ℝ)) (q := - (7930729891367817 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7930729891367817 / 20000000000000000 : ℚ)) + (r' := (7930729891367817 / 5000000000000000 : ℚ)) + (U := (-(9249871998363191376847 / 10000000000000000000000 : ℚ))) + (U' := (4613071607636808623153 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (3949890675757817 / 10000000000000000 : ℚ)) + (q := (7930729891367817 / 20000000000000000 : ℚ)) + (U := (-(9249871998363191376847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_7 : Uω (aρ 7) (bρ 7) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2154,25 +1907,21 @@ lemma U_417_7 : have hlg : Real.log (1488936323901157 / 4000000000000000 : ℝ) ≤ (-(494116186075126798691 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1488936323901157 / 4000000000000000 : ℝ) = - (1488936323901157 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1488936323901157 / 1000000000000000 : ℚ)) - (U := (199030994224873201309 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1488936323901157 / 1000000000000000 : ℝ) ≤ - (199030994224873201309 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (737500756931157 / 2000000000000000 : ℝ)) (q := - (1488936323901157 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1488936323901157 / 4000000000000000 : ℚ)) + (r' := (1488936323901157 / 1000000000000000 : ℚ)) + (U := (-(494116186075126798691 / 500000000000000000000 : ℚ))) + (U' := (199030994224873201309 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (737500756931157 / 2000000000000000 : ℚ)) + (q := (1488936323901157 / 4000000000000000 : ℚ)) + (U := (-(494116186075126798691 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_8 : Uω (aρ 8) (bρ 8) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2180,25 +1929,21 @@ lemma U_417_8 : have hlg : Real.log (3399435967944357 / 10000000000000000 : ℝ) ≤ (-(10789755663946743181419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3399435967944357 / 10000000000000000 : ℝ) = - (3399435967944357 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3399435967944357 / 2500000000000000 : ℚ)) - (U := (3073187942053256818581 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3399435967944357 / 2500000000000000 : ℝ) ≤ - (3073187942053256818581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1662617876189357 / 5000000000000000 : ℝ)) (q := - (3399435967944357 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3399435967944357 / 10000000000000000 : ℚ)) + (r' := (3399435967944357 / 2500000000000000 : ℚ)) + (U := (-(10789755663946743181419 / 10000000000000000000000 : ℚ))) + (U' := (3073187942053256818581 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (1662617876189357 / 5000000000000000 : ℚ)) + (q := (3399435967944357 / 10000000000000000 : ℚ)) + (U := (-(10789755663946743181419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_9 : Uω (aρ 9) (bρ 9) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2206,25 +1951,21 @@ lemma U_417_9 : have hlg : Real.log (372592533353797 / 1250000000000000 : ℝ) ≤ (-(756508381948669364161 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (372592533353797 / 1250000000000000 : ℝ) = - (372592533353797 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (372592533353797 / 312500000000000 : ℚ)) - (U := (109925593426330635839 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (372592533353797 / 312500000000000 : ℝ) ≤ - (109925593426330635839 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (88400311828461 / 312500000000000 : ℝ)) (q := - (372592533353797 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (372592533353797 / 1250000000000000 : ℚ)) + (r' := (372592533353797 / 312500000000000 : ℚ)) + (U := (-(756508381948669364161 / 625000000000000000000 : ℚ))) + (U' := (109925593426330635839 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (88400311828461 / 312500000000000 : ℚ)) + (q := (372592533353797 / 1250000000000000 : ℚ)) + (U := (-(756508381948669364161 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_10 : Uω (aρ 10) (bρ 10) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2232,26 +1973,21 @@ lemma U_417_10 : have hlg : Real.log (2435150630002837 / 10000000000000000 : ℝ) ≤ (-(2825152954444311047283 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2435150630002837 / 10000000000000000 : ℝ) = - (2435150630002837 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2435150630002837 / 1250000000000000 : ℚ)) - (U := (1333730127355688952717 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2435150630002837 / 1250000000000000 : ℝ) ≤ - (1333730127355688952717 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1063094869175337 / 5000000000000000 : ℝ)) (q := - (2435150630002837 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2435150630002837 / 10000000000000000 : ℚ)) + (r' := (2435150630002837 / 1250000000000000 : ℚ)) + (U := (-(2825152954444311047283 / 2000000000000000000000 : ℚ))) + (U' := (1333730127355688952717 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (1063094869175337 / 5000000000000000 : ℚ)) + (q := (2435150630002837 / 10000000000000000 : ℚ)) + (U := (-(2825152954444311047283 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_11 : Uω (aρ 11) (bρ 11) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2259,26 +1995,21 @@ lemma U_417_11 : have hlg : Real.log (3203768806367033 / 20000000000000000 : ℝ) ≤ (-(3662808807969156807193 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3203768806367033 / 20000000000000000 : ℝ) = - (3203768806367033 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3203768806367033 / 2500000000000000 : ℚ)) - (U := (496074273830843192807 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3203768806367033 / 2500000000000000 : ℝ) ≤ - (496074273830843192807 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (878133910917033 / 10000000000000000 : ℝ)) (q := - (3203768806367033 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3203768806367033 / 20000000000000000 : ℚ)) + (r' := (3203768806367033 / 2500000000000000 : ℚ)) + (U := (-(3662808807969156807193 / 2000000000000000000000 : ℚ))) + (U' := (496074273830843192807 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (896045205619 / 2000000000000 : ℚ)) + (s := (878133910917033 / 10000000000000000 : ℚ)) + (q := (3203768806367033 / 20000000000000000 : ℚ)) + (U := (-(3662808807969156807193 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_417_12 : Uω (aρ 12) (bρ 12) (896045205619 / 2000000000000 : ℝ) ≤ @@ -2395,25 +2126,21 @@ lemma U_418_1 : have hlg : Real.log (442231375208497 / 1000000000000000 : ℝ) ≤ (-(326368824010608195853 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (442231375208497 / 1000000000000000 : ℝ) = - (442231375208497 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (442231375208497 / 250000000000000 : ℚ)) - (U := (228148920229391804147 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (442231375208497 / 250000000000000 : ℝ) ≤ - (228148920229391804147 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27639232467359 / 62500000000000 : ℝ)) (q := - (442231375208497 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (442231375208497 / 1000000000000000 : ℚ)) + (r' := (442231375208497 / 250000000000000 : ℚ)) + (U := (-(326368824010608195853 / 400000000000000000000 : ℚ))) + (U' := (228148920229391804147 / 400000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (27639232467359 / 62500000000000 : ℚ)) + (q := (442231375208497 / 1000000000000000 : ℚ)) + (U := (-(326368824010608195853 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_2 : Uω (aρ 2) (bρ 2) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2421,25 +2148,21 @@ lemma U_418_2 : have hlg : Real.log (8796680172236137 / 20000000000000000 : ℝ) ≤ (-(4106789379413987168301 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8796680172236137 / 20000000000000000 : ℝ) = - (8796680172236137 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8796680172236137 / 5000000000000000 : ℚ)) - (U := (2824682423586012831699 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8796680172236137 / 5000000000000000 : ℝ) ≤ - (2824682423586012831699 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4398098875353637 / 10000000000000000 : ℝ)) (q := - (8796680172236137 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8796680172236137 / 20000000000000000 : ℚ)) + (r' := (8796680172236137 / 5000000000000000 : ℚ)) + (U := (-(4106789379413987168301 / 5000000000000000000000 : ℚ))) + (U' := (2824682423586012831699 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (4398098875353637 / 10000000000000000 : ℚ)) + (q := (8796680172236137 / 20000000000000000 : ℚ)) + (U := (-(4106789379413987168301 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_3 : Uω (aρ 3) (bρ 3) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2447,25 +2170,21 @@ lemma U_418_3 : have hlg : Real.log (174013396077207 / 400000000000000 : ℝ) ≤ (-(8323322613875938862681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (174013396077207 / 400000000000000 : ℝ) = - (174013396077207 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (174013396077207 / 100000000000000 : ℚ)) - (U := (5539620992124061137319 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (174013396077207 / 100000000000000 : ℝ) ≤ - (5539620992124061137319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (86989692266557 / 200000000000000 : ℝ)) (q := - (174013396077207 / 400000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (174013396077207 / 400000000000000 : ℚ)) + (r' := (174013396077207 / 100000000000000 : ℚ)) + (U := (-(8323322613875938862681 / 10000000000000000000000 : ℚ))) + (U' := (5539620992124061137319 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (86989692266557 / 200000000000000 : ℚ)) + (q := (174013396077207 / 400000000000000 : ℚ)) + (U := (-(8323322613875938862681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_4 : Uω (aρ 4) (bρ 4) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2473,25 +2192,21 @@ lemma U_418_4 : have hlg : Real.log (4270427431846133 / 10000000000000000 : ℝ) ≤ (-(8508711691084804030819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4270427431846133 / 10000000000000000 : ℝ) = - (4270427431846133 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4270427431846133 / 2500000000000000 : ℚ)) - (U := (5354231914915195969181 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4270427431846133 / 2500000000000000 : ℝ) ≤ - (5354231914915195969181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2133981927112383 / 5000000000000000 : ℝ)) (q := - (4270427431846133 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4270427431846133 / 10000000000000000 : ℚ)) + (r' := (4270427431846133 / 2500000000000000 : ℚ)) + (U := (-(8508711691084804030819 / 10000000000000000000000 : ℚ))) + (U' := (5354231914915195969181 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (2133981927112383 / 5000000000000000 : ℚ)) + (q := (4270427431846133 / 10000000000000000 : ℚ)) + (U := (-(8508711691084804030819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_5 : Uω (aρ 5) (bρ 5) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2499,25 +2214,21 @@ lemma U_418_5 : have hlg : Real.log (2074140970562173 / 5000000000000000 : ℝ) ≤ (-(2199727085099057476111 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2074140970562173 / 5000000000000000 : ℝ) = - (2074140970562173 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2074140970562173 / 1250000000000000 : ℚ)) - (U := (1266008816400942523889 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2074140970562173 / 1250000000000000 : ℝ) ≤ - (1266008816400942523889 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (129433212253631 / 312500000000000 : ℝ)) (q := - (2074140970562173 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2074140970562173 / 5000000000000000 : ℚ)) + (r' := (2074140970562173 / 1250000000000000 : ℚ)) + (U := (-(2199727085099057476111 / 2500000000000000000000 : ℚ))) + (U' := (1266008816400942523889 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (129433212253631 / 312500000000000 : ℚ)) + (q := (2074140970562173 / 5000000000000000 : ℚ)) + (U := (-(2199727085099057476111 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_6 : Uω (aρ 6) (bρ 6) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2525,25 +2236,21 @@ lemma U_418_6 : have hlg : Real.log (3972012342168089 / 10000000000000000 : ℝ) ≤ (-(4616561195014913821701 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3972012342168089 / 10000000000000000 : ℝ) = - (3972012342168089 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3972012342168089 / 2500000000000000 : ℚ)) - (U := (2314910607985086178299 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3972012342168089 / 2500000000000000 : ℝ) ≤ - (2314910607985086178299 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1978281984671839 / 5000000000000000 : ℝ)) (q := - (3972012342168089 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3972012342168089 / 10000000000000000 : ℚ)) + (r' := (3972012342168089 / 2500000000000000 : ℚ)) + (U := (-(4616561195014913821701 / 5000000000000000000000 : ℚ))) + (U' := (2314910607985086178299 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (1978281984671839 / 5000000000000000 : ℚ)) + (q := (3972012342168089 / 10000000000000000 : ℚ)) + (U := (-(4616561195014913821701 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_7 : Uω (aρ 7) (bρ 7) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2551,25 +2258,21 @@ lemma U_418_7 : have hlg : Real.log (1491609900548377 / 4000000000000000 : ℝ) ≤ (-(4932191768818572964023 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1491609900548377 / 4000000000000000 : ℝ) = - (1491609900548377 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1491609900548377 / 1000000000000000 : ℚ)) - (U := (1999280034181427035977 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1491609900548377 / 1000000000000000 : ℝ) ≤ - (1999280034181427035977 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (738850033701877 / 2000000000000000 : ℝ)) (q := - (1491609900548377 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1491609900548377 / 4000000000000000 : ℚ)) + (r' := (1491609900548377 / 1000000000000000 : ℚ)) + (U := (-(4932191768818572964023 / 5000000000000000000000 : ℚ))) + (U' := (1999280034181427035977 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (738850033701877 / 2000000000000000 : ℚ)) + (q := (1491609900548377 / 4000000000000000 : ℚ)) + (U := (-(4932191768818572964023 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_8 : Uω (aρ 8) (bρ 8) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2577,25 +2280,21 @@ lemma U_418_8 : have hlg : Real.log (1703102460552339 / 5000000000000000 : ℝ) ≤ (-(2153972694606828066529 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1703102460552339 / 5000000000000000 : ℝ) = - (1703102460552339 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1703102460552339 / 1250000000000000 : ℚ)) - (U := (618616026593171933471 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1703102460552339 / 1250000000000000 : ℝ) ≤ - (618616026593171933471 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (416519019914607 / 1250000000000000 : ℝ)) (q := - (1703102460552339 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1703102460552339 / 5000000000000000 : ℚ)) + (r' := (1703102460552339 / 1250000000000000 : ℚ)) + (U := (-(2153972694606828066529 / 2000000000000000000000 : ℚ))) + (U' := (618616026593171933471 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (416519019914607 / 1250000000000000 : ℚ)) + (q := (1703102460552339 / 5000000000000000 : ℚ)) + (U := (-(2153972694606828066529 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_9 : Uω (aρ 9) (bρ 9) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2603,25 +2302,21 @@ lemma U_418_9 : have hlg : Real.log (597543304028569 / 2000000000000000 : ℝ) ≤ (-(12080757024811163845657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (597543304028569 / 2000000000000000 : ℝ) = - (597543304028569 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (597543304028569 / 500000000000000 : ℚ)) - (U := (1782186581188836154343 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (597543304028569 / 500000000000000 : ℝ) ≤ - (1782186581188836154343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (283614098575319 / 1000000000000000 : ℝ)) (q := - (597543304028569 / 2000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (597543304028569 / 2000000000000000 : ℚ)) + (r' := (597543304028569 / 500000000000000 : ℚ)) + (U := (-(12080757024811163845657 / 10000000000000000000000 : ℚ))) + (U' := (1782186581188836154343 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (283614098575319 / 1000000000000000 : ℚ)) + (q := (597543304028569 / 2000000000000000 : ℚ)) + (U := (-(12080757024811163845657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_10 : Uω (aρ 10) (bρ 10) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2629,26 +2324,21 @@ lemma U_418_10 : have hlg : Real.log (1221365447276197 / 5000000000000000 : ℝ) ≤ (-(14094684596889839880361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1221365447276197 / 5000000000000000 : ℝ) = - (1221365447276197 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1221365447276197 / 625000000000000 : ℚ)) - (U := (6699730812110160119639 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1221365447276197 / 625000000000000 : ℝ) ≤ - (6699730812110160119639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (266841096008411 / 1250000000000000 : ℝ)) (q := - (1221365447276197 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1221365447276197 / 5000000000000000 : ℚ)) + (r' := (1221365447276197 / 625000000000000 : ℚ)) + (U := (-(14094684596889839880361 / 10000000000000000000000 : ℚ))) + (U' := (6699730812110160119639 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (266841096008411 / 1250000000000000 : ℚ)) + (q := (1221365447276197 / 5000000000000000 : ℚ)) + (U := (-(14094684596889839880361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_11 : Uω (aρ 11) (bρ 11) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2656,25 +2346,21 @@ lemma U_418_11 : have hlg : Real.log (322777936483651 / 2000000000000000 : ℝ) ≤ (-(18239378751248439378963 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (322777936483651 / 2000000000000000 : ℝ) = - (322777936483651 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (322777936483651 / 250000000000000 : ℚ)) - (U := (2555036657751560621037 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (322777936483651 / 250000000000000 : ℝ) ≤ - (2555036657751560621037 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89552297000401 / 1000000000000000 : ℝ)) (q := - (322777936483651 / 2000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (322777936483651 / 2000000000000000 : ℚ)) + (r' := (322777936483651 / 250000000000000 : ℚ)) + (U := (-(18239378751248439378963 / 10000000000000000000000 : ℚ))) + (U' := (2555036657751560621037 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1794739010991 / 4000000000000 : ℚ)) + (s := (89552297000401 / 1000000000000000 : ℚ)) + (q := (322777936483651 / 2000000000000000 : ℚ)) + (U := (-(18239378751248439378963 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_418_12 : Uω (aρ 12) (bρ 12) (1794739010991 / 4000000000000 : ℝ) ≤ @@ -2791,25 +2477,21 @@ lemma U_419_1 : have hlg : Real.log (2214467653061543 / 5000000000000000 : ℝ) ≤ (-(2036064686302483332461 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2214467653061543 / 5000000000000000 : ℝ) = - (2214467653061543 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2214467653061543 / 1250000000000000 : ℚ)) - (U := (1429671215197516667539 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2214467653061543 / 1250000000000000 : ℝ) ≤ - (1429671215197516667539 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1107224700867793 / 2500000000000000 : ℝ)) (q := - (2214467653061543 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2214467653061543 / 5000000000000000 : ℚ)) + (r' := (2214467653061543 / 1250000000000000 : ℚ)) + (U := (-(2036064686302483332461 / 2500000000000000000000 : ℚ))) + (U' := (1429671215197516667539 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (224673451343 / 500000000000 : ℚ)) + (s := (1107224700867793 / 2500000000000000 : ℚ)) + (q := (2214467653061543 / 5000000000000000 : ℚ)) + (U := (-(2036064686302483332461 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_2 : Uω (aρ 2) (bρ 2) (224673451343 / 500000000000 : ℝ) ≤ @@ -2817,25 +2499,21 @@ lemma U_419_2 : have hlg : Real.log (4404961948106287 / 10000000000000000 : ℝ) ≤ (-(8198534714646879541903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4404961948106287 / 10000000000000000 : ℝ) = - (4404961948106287 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4404961948106287 / 2500000000000000 : ℚ)) - (U := (5664408891353120458097 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4404961948106287 / 2500000000000000 : ℝ) ≤ - (5664408891353120458097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2202360549973787 / 5000000000000000 : ℝ)) (q := - (4404961948106287 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4404961948106287 / 10000000000000000 : ℚ)) + (r' := (4404961948106287 / 2500000000000000 : ℚ)) + (U := (-(8198534714646879541903 / 10000000000000000000000 : ℚ))) + (U' := (5664408891353120458097 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (224673451343 / 500000000000 : ℚ)) + (s := (2202360549973787 / 5000000000000000 : ℚ)) + (q := (4404961948106287 / 10000000000000000 : ℚ)) + (U := (-(8198534714646879541903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_3 : Uω (aρ 3) (bρ 3) (224673451343 / 500000000000 : ℝ) ≤ @@ -2843,25 +2521,21 @@ lemma U_419_3 : have hlg : Real.log (4356957693793537 / 10000000000000000 : ℝ) ≤ (-(4154055276627529415703 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4356957693793537 / 10000000000000000 : ℝ) = - (4356957693793537 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4356957693793537 / 2500000000000000 : ℚ)) - (U := (2777416526372470584297 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4356957693793537 / 2500000000000000 : ℝ) ≤ - (2777416526372470584297 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2178054348836037 / 5000000000000000 : ℝ)) (q := - (4356957693793537 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4356957693793537 / 10000000000000000 : ℚ)) + (r' := (4356957693793537 / 2500000000000000 : ℚ)) + (U := (-(4154055276627529415703 / 5000000000000000000000 : ℚ))) + (U' := (2777416526372470584297 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (224673451343 / 500000000000 : ℚ)) + (s := (2178054348836037 / 5000000000000000 : ℚ)) + (q := (4356957693793537 / 10000000000000000 : ℚ)) + (U := (-(4154055276627529415703 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_4 : Uω (aρ 4) (bρ 4) (224673451343 / 500000000000 : ℝ) ≤ @@ -2869,25 +2543,21 @@ lemma U_419_4 : have hlg : Real.log (8554105494806037 / 20000000000000000 : ℝ) ≤ (-(53082558156334955823 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8554105494806037 / 20000000000000000 : ℝ) = - (8554105494806037 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8554105494806037 / 5000000000000000 : ℚ)) - (U := (33560839381165044177 / 62500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8554105494806037 / 5000000000000000 : ℝ) ≤ - (33560839381165044177 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4274592985956037 / 10000000000000000 : ℝ)) (q := - (8554105494806037 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8554105494806037 / 20000000000000000 : ℚ)) + (r' := (8554105494806037 / 5000000000000000 : ℚ)) + (U := (-(53082558156334955823 / 62500000000000000000 : ℚ))) + (U' := (33560839381165044177 / 62500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (224673451343 / 500000000000 : ℚ)) + (s := (4274592985956037 / 10000000000000000 : ℚ)) + (q := (8554105494806037 / 20000000000000000 : ℚ)) + (U := (-(53082558156334955823 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_5 : Uω (aρ 5) (bρ 5) (224673451343 / 500000000000 : ℝ) ≤ @@ -2895,25 +2565,21 @@ lemma U_419_5 : have hlg : Real.log (2077456843122793 / 5000000000000000 : ℝ) ≤ (-(2195733594623203264179 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2077456843122793 / 5000000000000000 : ℝ) = - (2077456843122793 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2077456843122793 / 1250000000000000 : ℚ)) - (U := (1270002306876796735821 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2077456843122793 / 1250000000000000 : ℝ) ≤ - (1270002306876796735821 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1037126195744043 / 2500000000000000 : ℝ)) (q := - (2077456843122793 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2077456843122793 / 5000000000000000 : ℚ)) + (r' := (2077456843122793 / 1250000000000000 : ℚ)) + (U := (-(2195733594623203264179 / 2500000000000000000000 : ℚ))) + (U' := (1270002306876796735821 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (224673451343 / 500000000000 : ℚ)) + (s := (1037126195744043 / 2500000000000000 : ℚ)) + (q := (2077456843122793 / 5000000000000000 : ℚ)) + (U := (-(2195733594623203264179 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_6 : Uω (aρ 6) (bρ 6) (224673451343 / 500000000000 : ℝ) ≤ @@ -2921,25 +2587,21 @@ lemma U_419_6 : have hlg : Real.log (7957319303559397 / 20000000000000000 : ℝ) ≤ (-(92164010080748980551 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7957319303559397 / 20000000000000000 : ℝ) = - (7957319303559397 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7957319303559397 / 5000000000000000 : ℚ)) - (U := (46465425979251019449 / 100000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7957319303559397 / 5000000000000000 : ℝ) ≤ - (46465425979251019449 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3963237089184397 / 10000000000000000 : ℝ)) (q := - (7957319303559397 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7957319303559397 / 20000000000000000 : ℚ)) + (r' := (7957319303559397 / 5000000000000000 : ℚ)) + (U := (-(92164010080748980551 / 100000000000000000000 : ℚ))) + (U' := (46465425979251019449 / 100000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (224673451343 / 500000000000 : ℚ)) + (s := (3963237089184397 / 10000000000000000 : ℚ)) + (q := (7957319303559397 / 20000000000000000 : ℚ)) + (U := (-(92164010080748980551 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_7 : Uω (aρ 7) (bρ 7) (224673451343 / 500000000000 : ℝ) ≤ @@ -2947,25 +2609,21 @@ lemma U_419_7 : have hlg : Real.log (1867854233724793 / 5000000000000000 : ℝ) ≤ (-(9846476084902234316057 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1867854233724793 / 5000000000000000 : ℝ) = - (1867854233724793 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1867854233724793 / 1250000000000000 : ℚ)) - (U := (4016467521097765683943 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1867854233724793 / 1250000000000000 : ℝ) ≤ - (4016467521097765683943 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (925249025321043 / 2500000000000000 : ℝ)) (q := - (1867854233724793 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1867854233724793 / 5000000000000000 : ℚ)) + (r' := (1867854233724793 / 1250000000000000 : ℚ)) + (U := (-(9846476084902234316057 / 10000000000000000000000 : ℚ))) + (U' := (4016467521097765683943 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (224673451343 / 500000000000 : ℚ)) + (s := (925249025321043 / 2500000000000000 : ℚ)) + (q := (1867854233724793 / 5000000000000000 : ℚ)) + (U := (-(9846476084902234316057 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_8 : Uω (aρ 8) (bρ 8) (224673451343 / 500000000000 : ℝ) ≤ @@ -2973,25 +2631,21 @@ lemma U_419_8 : have hlg : Real.log (6825946552857763 / 20000000000000000 : ℝ) ≤ (-(2687503131290268703811 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6825946552857763 / 20000000000000000 : ℝ) = - (6825946552857763 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6825946552857763 / 5000000000000000 : ℚ)) - (U := (778232770209731296189 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6825946552857763 / 5000000000000000 : ℝ) ≤ - (778232770209731296189 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3339067370582763 / 10000000000000000 : ℝ)) (q := - (6825946552857763 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6825946552857763 / 20000000000000000 : ℚ)) + (r' := (6825946552857763 / 5000000000000000 : ℚ)) + (U := (-(2687503131290268703811 / 2500000000000000000000 : ℚ))) + (U' := (778232770209731296189 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (224673451343 / 500000000000 : ℚ)) + (s := (3339067370582763 / 10000000000000000 : ℚ)) + (q := (6825946552857763 / 20000000000000000 : ℚ)) + (U := (-(2687503131290268703811 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_9 : Uω (aρ 9) (bρ 9) (224673451343 / 500000000000 : ℝ) ≤ @@ -2999,25 +2653,21 @@ lemma U_419_9 : have hlg : Real.log (5989382065455843 / 20000000000000000 : ℝ) ≤ (-(1507180034067428396347 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5989382065455843 / 20000000000000000 : ℝ) = - (5989382065455843 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5989382065455843 / 5000000000000000 : ℚ)) - (U := (225687916682571603653 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5989382065455843 / 5000000000000000 : ℝ) ≤ - (225687916682571603653 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2843468511540843 / 10000000000000000 : ℝ)) (q := - (5989382065455843 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5989382065455843 / 20000000000000000 : ℚ)) + (r' := (5989382065455843 / 5000000000000000 : ℚ)) + (U := (-(1507180034067428396347 / 1250000000000000000000 : ℚ))) + (U' := (225687916682571603653 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (224673451343 / 500000000000 : ℚ)) + (s := (2843468511540843 / 10000000000000000 : ℚ)) + (q := (5989382065455843 / 20000000000000000 : ℚ)) + (U := (-(1507180034067428396347 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_10 : Uω (aρ 10) (bρ 10) (224673451343 / 500000000000 : ℝ) ≤ @@ -3025,26 +2675,21 @@ lemma U_419_10 : have hlg : Real.log (4900608754398927 / 20000000000000000 : ℝ) ≤ (-(7031864198912791906271 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4900608754398927 / 20000000000000000 : ℝ) = - (4900608754398927 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4900608754398927 / 2500000000000000 : ℚ)) - (U := (3365343505587208093729 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4900608754398927 / 2500000000000000 : ℝ) ≤ - (3365343505587208093729 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2143254233978927 / 10000000000000000 : ℝ)) (q := - (4900608754398927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4900608754398927 / 20000000000000000 : ℚ)) + (r' := (4900608754398927 / 2500000000000000 : ℚ)) + (U := (-(7031864198912791906271 / 5000000000000000000000 : ℚ))) + (U' := (3365343505587208093729 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (224673451343 / 500000000000 : ℚ)) + (s := (2143254233978927 / 10000000000000000 : ℚ)) + (q := (4900608754398927 / 20000000000000000 : ℚ)) + (U := (-(7031864198912791906271 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_11 : Uω (aρ 11) (bρ 11) (224673451343 / 500000000000 : ℝ) ≤ @@ -3052,26 +2697,21 @@ lemma U_419_11 : have hlg : Real.log (3251506681080341 / 20000000000000000 : ℝ) ≤ (-(9083068948402617052851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3251506681080341 / 20000000000000000 : ℝ) = - (3251506681080341 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3251506681080341 / 2500000000000000 : ℚ)) - (U := (1314138756097382947149 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3251506681080341 / 2500000000000000 : ℝ) ≤ - (1314138756097382947149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (912628786865341 / 10000000000000000 : ℝ)) (q := - (3251506681080341 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3251506681080341 / 20000000000000000 : ℚ)) + (r' := (3251506681080341 / 2500000000000000 : ℚ)) + (U := (-(9083068948402617052851 / 5000000000000000000000 : ℚ))) + (U' := (1314138756097382947149 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (224673451343 / 500000000000 : ℚ)) + (s := (912628786865341 / 10000000000000000 : ℚ)) + (q := (3251506681080341 / 20000000000000000 : ℚ)) + (U := (-(9083068948402617052851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_419_12 : Uω (aρ 12) (bρ 12) (224673451343 / 500000000000 : ℝ) ≤ @@ -3186,25 +2826,21 @@ lemma U_420_1 : have hlg : Real.log (4435556859998017 / 10000000000000000 : ℝ) ≤ (-(4064659621397125910963 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4435556859998017 / 10000000000000000 : ℝ) = - (4435556859998017 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4435556859998017 / 2500000000000000 : ℚ)) - (U := (2866812181602874089037 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4435556859998017 / 2500000000000000 : ℝ) ≤ - (2866812181602874089037 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2217760205919267 / 5000000000000000 : ℝ)) (q := - (4435556859998017 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4435556859998017 / 10000000000000000 : ℚ)) + (r' := (4435556859998017 / 2500000000000000 : ℚ)) + (U := (-(4064659621397125910963 / 5000000000000000000000 : ℚ))) + (U' := (2866812181602874089037 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (2217760205919267 / 5000000000000000 : ℚ)) + (q := (4435556859998017 / 10000000000000000 : ℚ)) + (U := (-(4064659621397125910963 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_2 : Uω (aρ 2) (bρ 2) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3212,25 +2848,21 @@ lemma U_420_2 : have hlg : Real.log (8823167618011783 / 20000000000000000 : ℝ) ≤ (-(4091756635633582914549 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8823167618011783 / 20000000000000000 : ℝ) = - (8823167618011783 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8823167618011783 / 5000000000000000 : ℚ)) - (U := (2839715167366417085451 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8823167618011783 / 5000000000000000 : ℝ) ≤ - (2839715167366417085451 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4411343322364283 / 10000000000000000 : ℝ)) (q := - (8823167618011783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8823167618011783 / 20000000000000000 : ℚ)) + (r' := (8823167618011783 / 5000000000000000 : ℚ)) + (U := (-(4091756635633582914549 / 5000000000000000000000 : ℚ))) + (U' := (2839715167366417085451 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (4411343322364283 / 10000000000000000 : ℚ)) + (q := (8823167618011783 / 20000000000000000 : ℚ)) + (U := (-(4091756635633582914549 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_3 : Uω (aρ 3) (bρ 3) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3238,25 +2870,21 @@ lemma U_420_3 : have hlg : Real.log (8727160963465661 / 20000000000000000 : ℝ) ≤ (-(8292921607161953238429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8727160963465661 / 20000000000000000 : ℝ) = - (8727160963465661 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8727160963465661 / 5000000000000000 : ℚ)) - (U := (5570021998838046761571 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8727160963465661 / 5000000000000000 : ℝ) ≤ - (5570021998838046761571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4362732774168161 / 10000000000000000 : ℝ)) (q := - (8727160963465661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8727160963465661 / 20000000000000000 : ℚ)) + (r' := (8727160963465661 / 5000000000000000 : ℚ)) + (U := (-(8292921607161953238429 / 10000000000000000000000 : ℚ))) + (U' := (5570021998838046761571 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (4362732774168161 / 10000000000000000 : ℚ)) + (q := (8727160963465661 / 20000000000000000 : ℚ)) + (U := (-(8292921607161953238429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_4 : Uω (aρ 4) (bρ 4) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3264,25 +2892,21 @@ lemma U_420_4 : have hlg : Real.log (1713471220459449 / 4000000000000000 : ℝ) ≤ (-(1059716367714879467071 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1713471220459449 / 4000000000000000 : ℝ) = - (1713471220459449 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1713471220459449 / 1000000000000000 : ℚ)) - (U := (673151583035120532929 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1713471220459449 / 1000000000000000 : ℝ) ≤ - (673151583035120532929 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (856244418812949 / 2000000000000000 : ℝ)) (q := - (1713471220459449 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1713471220459449 / 4000000000000000 : ℚ)) + (r' := (1713471220459449 / 1000000000000000 : ℚ)) + (U := (-(1059716367714879467071 / 1250000000000000000000 : ℚ))) + (U' := (673151583035120532929 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (856244418812949 / 2000000000000000 : ℚ)) + (q := (1713471220459449 / 4000000000000000 : ℚ)) + (U := (-(1059716367714879467071 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_5 : Uω (aρ 5) (bρ 5) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3290,25 +2914,21 @@ lemma U_420_5 : have hlg : Real.log (1664618159464713 / 4000000000000000 : ℝ) ≤ (-(1753397194246807411647 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1664618159464713 / 4000000000000000 : ℝ) = - (1664618159464713 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1664618159464713 / 1000000000000000 : ℚ)) - (U := (1019191526953192588353 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1664618159464713 / 1000000000000000 : ℝ) ≤ - (1019191526953192588353 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (831029341685213 / 2000000000000000 : ℝ)) (q := - (1664618159464713 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1664618159464713 / 4000000000000000 : ℚ)) + (r' := (1664618159464713 / 1000000000000000 : ℚ)) + (U := (-(1753397194246807411647 / 2000000000000000000000 : ℚ))) + (U' := (1019191526953192588353 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (831029341685213 / 2000000000000000 : ℚ)) + (q := (1664618159464713 / 4000000000000000 : ℚ)) + (U := (-(1753397194246807411647 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_6 : Uω (aρ 6) (bρ 6) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3316,25 +2936,21 @@ lemma U_420_6 : have hlg : Real.log (7970613749913629 / 20000000000000000 : ℝ) ≤ (-(183994155135901900949 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7970613749913629 / 20000000000000000 : ℝ) = - (7970613749913629 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7970613749913629 / 5000000000000000 : ℚ)) - (U := (93264716984098099051 / 200000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7970613749913629 / 5000000000000000 : ℝ) ≤ - (93264716984098099051 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3969910036156129 / 10000000000000000 : ℝ)) (q := - (7970613749913629 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7970613749913629 / 20000000000000000 : ℚ)) + (r' := (7970613749913629 / 5000000000000000 : ℚ)) + (U := (-(183994155135901900949 / 200000000000000000000 : ℚ))) + (U' := (93264716984098099051 / 200000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (3969910036156129 / 10000000000000000 : ℚ)) + (q := (7970613749913629 / 20000000000000000 : ℚ)) + (U := (-(183994155135901900949 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_7 : Uω (aρ 7) (bρ 7) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3342,25 +2958,21 @@ lemma U_420_7 : have hlg : Real.log (7484783918439749 / 20000000000000000 : ℝ) ≤ (-(9828601241911390730523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7484783918439749 / 20000000000000000 : ℝ) = - (7484783918439749 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7484783918439749 / 5000000000000000 : ℚ)) - (U := (4034342364088609269477 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7484783918439749 / 5000000000000000 : ℝ) ≤ - (4034342364088609269477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3707741585442249 / 10000000000000000 : ℝ)) (q := - (7484783918439749 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7484783918439749 / 20000000000000000 : ℚ)) + (r' := (7484783918439749 / 5000000000000000 : ℚ)) + (U := (-(9828601241911390730523 / 10000000000000000000000 : ℚ))) + (U' := (4034342364088609269477 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (3707741585442249 / 10000000000000000 : ℚ)) + (q := (7484783918439749 / 20000000000000000 : ℚ)) + (U := (-(9828601241911390730523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_8 : Uω (aρ 8) (bρ 8) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3368,25 +2980,21 @@ lemma U_420_8 : have hlg : Real.log (3419741037623649 / 10000000000000000 : ℝ) ≤ (-(1073020264259629767199 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3419741037623649 / 10000000000000000 : ℝ) = - (3419741037623649 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3419741037623649 / 2500000000000000 : ℚ)) - (U := (313274096340370232801 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3419741037623649 / 2500000000000000 : ℝ) ≤ - (313274096340370232801 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1672990696794899 / 5000000000000000 : ℝ)) (q := - (3419741037623649 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3419741037623649 / 10000000000000000 : ℚ)) + (r' := (3419741037623649 / 2500000000000000 : ℚ)) + (U := (-(1073020264259629767199 / 1000000000000000000000 : ℚ))) + (U' := (313274096340370232801 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (1672990696794899 / 5000000000000000 : ℚ)) + (q := (3419741037623649 / 10000000000000000 : ℚ)) + (U := (-(1073020264259629767199 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_9 : Uω (aρ 9) (bρ 9) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3394,25 +3002,21 @@ lemma U_420_9 : have hlg : Real.log (120066552720337 / 400000000000000 : ℝ) ≤ (-(12034183515403065078679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (120066552720337 / 400000000000000 : ℝ) = - (120066552720337 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (120066552720337 / 100000000000000 : ℚ)) - (U := (1828760090596934921321 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (120066552720337 / 100000000000000 : ℝ) ≤ - (1828760090596934921321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57015851654387 / 200000000000000 : ℝ)) (q := - (120066552720337 / 400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (120066552720337 / 400000000000000 : ℚ)) + (r' := (120066552720337 / 100000000000000 : ℚ)) + (U := (-(12034183515403065078679 / 10000000000000000000000 : ℚ))) + (U' := (1828760090596934921321 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (57015851654387 / 200000000000000 : ℚ)) + (q := (120066552720337 / 400000000000000 : ℚ)) + (U := (-(12034183515403065078679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_10 : Uω (aρ 10) (bρ 10) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3420,26 +3024,21 @@ lemma U_420_10 : have hlg : Real.log (4915742317110657 / 20000000000000000 : ℝ) ≤ (-(561315799852319578607 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4915742317110657 / 20000000000000000 : ℝ) = - (4915742317110657 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4915742317110657 / 2500000000000000 : ℚ)) - (U := (270460816507680421393 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4915742317110657 / 2500000000000000 : ℝ) ≤ - (270460816507680421393 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2151766297308157 / 10000000000000000 : ℝ)) (q := - (4915742317110657 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4915742317110657 / 20000000000000000 : ℚ)) + (r' := (4915742317110657 / 2500000000000000 : ℚ)) + (U := (-(561315799852319578607 / 400000000000000000000 : ℚ))) + (U' := (270460816507680421393 / 400000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (2151766297308157 / 10000000000000000 : ℚ)) + (q := (4915742317110657 / 20000000000000000 : ℚ)) + (U := (-(561315799852319578607 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_11 : Uω (aρ 11) (bρ 11) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3447,26 +3046,21 @@ lemma U_420_11 : have hlg : Real.log (3274966393514093 / 20000000000000000 : ℝ) ≤ (-(18094246652620039559979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3274966393514093 / 20000000000000000 : ℝ) = - (3274966393514093 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3274966393514093 / 2500000000000000 : ℚ)) - (U := (2700168756379960440021 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3274966393514093 / 2500000000000000 : ℝ) ≤ - (2700168756379960440021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (929466999916593 / 10000000000000000 : ℝ)) (q := - (3274966393514093 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3274966393514093 / 20000000000000000 : ℚ)) + (r' := (3274966393514093 / 2500000000000000 : ℚ)) + (U := (-(18094246652620039559979 / 10000000000000000000000 : ℚ))) + (U' := (2700168756379960440021 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1800036210497 / 4000000000000 : ℚ)) + (s := (929466999916593 / 10000000000000000 : ℚ)) + (q := (3274966393514093 / 20000000000000000 : ℚ)) + (U := (-(18094246652620039559979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_420_12 : Uω (aρ 12) (bρ 12) (1800036210497 / 4000000000000 : ℝ) ≤ @@ -3582,25 +3176,21 @@ lemma U_421_1 : have hlg : Real.log (1776871365484197 / 4000000000000000 : ℝ) ≤ (-(8114402026328109846991 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1776871365484197 / 4000000000000000 : ℝ) = - (1776871365484197 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1776871365484197 / 1000000000000000 : ℚ)) - (U := (5748541579671890153009 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1776871365484197 / 1000000000000000 : ℝ) ≤ - (5748541579671890153009 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (888428403976197 / 2000000000000000 : ℝ)) (q := - (1776871365484197 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1776871365484197 / 4000000000000000 : ℚ)) + (r' := (1776871365484197 / 1000000000000000 : ℚ)) + (U := (-(8114402026328109846991 / 10000000000000000000000 : ℚ))) + (U' := (5748541579671890153009 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7210739241 / 16000000000 : ℚ)) + (s := (888428403976197 / 2000000000000000 : ℚ)) + (q := (1776871365484197 / 4000000000000000 : ℚ)) + (U := (-(8114402026328109846991 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_2 : Uω (aρ 2) (bρ 2) (7210739241 / 16000000000 : ℝ) ≤ @@ -3608,25 +3198,21 @@ lemma U_421_2 : have hlg : Real.log (4418205668821777 / 10000000000000000 : ℝ) ≤ (-(4084257180438267317039 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4418205668821777 / 10000000000000000 : ℝ) = - (4418205668821777 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4418205668821777 / 2500000000000000 : ℚ)) - (U := (2847214622561732682961 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4418205668821777 / 2500000000000000 : ℝ) ≤ - (2847214622561732682961 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2208982771306777 / 5000000000000000 : ℝ)) (q := - (4418205668821777 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4418205668821777 / 10000000000000000 : ℚ)) + (r' := (4418205668821777 / 2500000000000000 : ℚ)) + (U := (-(4084257180438267317039 / 5000000000000000000000 : ℚ))) + (U' := (2847214622561732682961 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7210739241 / 16000000000 : ℚ)) + (s := (2208982771306777 / 5000000000000000 : ℚ)) + (q := (4418205668821777 / 10000000000000000 : ℚ)) + (U := (-(4084257180438267317039 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_3 : Uω (aρ 3) (bρ 3) (7210739241 / 16000000000 : ℝ) ≤ @@ -3634,25 +3220,21 @@ lemma U_421_3 : have hlg : Real.log (1748081306306361 / 4000000000000000 : ℝ) ≤ (-(8277755705431535785367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1748081306306361 / 4000000000000000 : ℝ) = - (1748081306306361 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1748081306306361 / 1000000000000000 : ℚ)) - (U := (5585187900568464214633 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1748081306306361 / 1000000000000000 : ℝ) ≤ - (5585187900568464214633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (873871368570361 / 2000000000000000 : ℝ)) (q := - (1748081306306361 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1748081306306361 / 4000000000000000 : ℚ)) + (r' := (1748081306306361 / 1000000000000000 : ℚ)) + (U := (-(8277755705431535785367 / 10000000000000000000000 : ℚ))) + (U' := (5585187900568464214633 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7210739241 / 16000000000 : ℚ)) + (s := (873871368570361 / 2000000000000000 : ℚ)) + (q := (1748081306306361 / 4000000000000000 : ℚ)) + (U := (-(8277755705431535785367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_4 : Uω (aρ 4) (bρ 4) (7210739241 / 16000000000 : ℝ) ≤ @@ -3660,25 +3242,21 @@ lemma U_421_4 : have hlg : Real.log (4290303343137727 / 10000000000000000 : ℝ) ≤ (-(67698212214232369843 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4290303343137727 / 10000000000000000 : ℝ) = - (4290303343137727 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4290303343137727 / 2500000000000000 : ℚ)) - (U := (43205336633767630157 / 80000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4290303343137727 / 2500000000000000 : ℝ) ≤ - (43205336633767630157 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2143925589330227 / 5000000000000000 : ℝ)) (q := - (4290303343137727 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4290303343137727 / 10000000000000000 : ℚ)) + (r' := (4290303343137727 / 2500000000000000 : ℚ)) + (U := (-(67698212214232369843 / 80000000000000000000 : ℚ))) + (U' := (43205336633767630157 / 80000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7210739241 / 16000000000 : ℚ)) + (s := (2143925589330227 / 5000000000000000 : ℚ)) + (q := (4290303343137727 / 10000000000000000 : ℚ)) + (U := (-(67698212214232369843 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_5 : Uω (aρ 5) (bρ 5) (7210739241 / 16000000000 : ℝ) ≤ @@ -3686,24 +3264,21 @@ lemma U_421_5 : have hlg : Real.log (52102213481619 / 125000000000000 : ℝ) ≤ (-(8751063036737577972069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52102213481619 / 125000000000000 : ℝ) = (52102213481619 / 31250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52102213481619 / 31250000000000 : ℚ)) - (U := (5111880569262422027931 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (52102213481619 / 31250000000000 : ℝ) ≤ - (5111880569262422027931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26011178554869 / 62500000000000 : ℝ)) (q := - (52102213481619 / 125000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52102213481619 / 125000000000000 : ℚ)) + (r' := (52102213481619 / 31250000000000 : ℚ)) + (U := (-(8751063036737577972069 / 10000000000000000000000 : ℚ))) + (U' := (5111880569262422027931 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7210739241 / 16000000000 : ℚ)) + (s := (26011178554869 / 62500000000000 : ℚ)) + (q := (52102213481619 / 125000000000000 : ℚ)) + (U := (-(8751063036737577972069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_6 : Uω (aρ 6) (bρ 6) (7210739241 / 16000000000 : ℝ) ≤ @@ -3711,25 +3286,21 @@ lemma U_421_6 : have hlg : Real.log (798390802426913 / 2000000000000000 : ℝ) ≤ (-(2295760635244161997167 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (798390802426913 / 2000000000000000 : ℝ) = - (798390802426913 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (798390802426913 / 500000000000000 : ℚ)) - (U := (1169975266255838002833 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (798390802426913 / 500000000000000 : ℝ) ≤ - (1169975266255838002833 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397658281112913 / 1000000000000000 : ℝ)) (q := - (798390802426913 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (798390802426913 / 2000000000000000 : ℚ)) + (r' := (798390802426913 / 500000000000000 : ℚ)) + (U := (-(2295760635244161997167 / 2500000000000000000000 : ℚ))) + (U' := (1169975266255838002833 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7210739241 / 16000000000 : ℚ)) + (s := (397658281112913 / 1000000000000000 : ℚ)) + (q := (798390802426913 / 2000000000000000 : ℚ)) + (U := (-(2295760635244161997167 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_7 : Uω (aρ 7) (bρ 7) (7210739241 / 16000000000 : ℝ) ≤ @@ -3737,25 +3308,21 @@ lemma U_421_7 : have hlg : Real.log (7498150455807673 / 20000000000000000 : ℝ) ≤ (-(306586215248868418239 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7498150455807673 / 20000000000000000 : ℝ) = - (7498150455807673 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7498150455807673 / 5000000000000000 : ℚ)) - (U := (126630772438631581761 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7498150455807673 / 5000000000000000 : ℝ) ≤ - (126630772438631581761 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3714486623427673 / 10000000000000000 : ℝ)) (q := - (7498150455807673 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7498150455807673 / 20000000000000000 : ℚ)) + (r' := (7498150455807673 / 5000000000000000 : ℚ)) + (U := (-(306586215248868418239 / 312500000000000000000 : ℚ))) + (U' := (126630772438631581761 / 312500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7210739241 / 16000000000 : ℚ)) + (s := (3714486623427673 / 10000000000000000 : ℚ)) + (q := (7498150455807673 / 20000000000000000 : ℚ)) + (U := (-(306586215248868418239 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_8 : Uω (aρ 8) (bρ 8) (7210739241 / 16000000000 : ℝ) ≤ @@ -3763,25 +3330,21 @@ lemma U_421_8 : have hlg : Real.log (685301641672891 / 2000000000000000 : ℝ) ≤ (-(1338804206099587571027 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (685301641672891 / 2000000000000000 : ℝ) = - (685301641672891 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (685301641672891 / 500000000000000 : ℚ)) - (U := (394063744650412428973 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (685301641672891 / 500000000000000 : ℝ) ≤ - (394063744650412428973 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (335289423568891 / 1000000000000000 : ℝ)) (q := - (685301641672891 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (685301641672891 / 2000000000000000 : ℚ)) + (r' := (685301641672891 / 500000000000000 : ℚ)) + (U := (-(1338804206099587571027 / 1250000000000000000000 : ℚ))) + (U' := (394063744650412428973 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7210739241 / 16000000000 : ℚ)) + (s := (335289423568891 / 1000000000000000 : ℚ)) + (q := (685301641672891 / 2000000000000000 : ℚ)) + (U := (-(1338804206099587571027 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_9 : Uω (aρ 9) (bρ 9) (7210739241 / 16000000000 : ℝ) ≤ @@ -3789,25 +3352,21 @@ lemma U_421_9 : have hlg : Real.log (1203453955705317 / 4000000000000000 : ℝ) ≤ (-(12010986417487087268443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1203453955705317 / 4000000000000000 : ℝ) = - (1203453955705317 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1203453955705317 / 1000000000000000 : ℚ)) - (U := (1851957188512912731557 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1203453955705317 / 1000000000000000 : ℝ) ≤ - (1851957188512912731557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (571622645169317 / 2000000000000000 : ℝ)) (q := - (1203453955705317 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1203453955705317 / 4000000000000000 : ℚ)) + (r' := (1203453955705317 / 1000000000000000 : ℚ)) + (U := (-(12010986417487087268443 / 10000000000000000000000 : ℚ))) + (U' := (1851957188512912731557 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (7210739241 / 16000000000 : ℚ)) + (s := (571622645169317 / 2000000000000000 : ℚ)) + (q := (1203453955705317 / 4000000000000000 : ℚ)) + (U := (-(12010986417487087268443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_10 : Uω (aρ 10) (bρ 10) (7210739241 / 16000000000 : ℝ) ≤ @@ -3815,26 +3374,21 @@ lemma U_421_10 : have hlg : Real.log (2465431317835013 / 10000000000000000 : ℝ) ≤ (-(350054580804219201741 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2465431317835013 / 10000000000000000 : ℝ) = - (2465431317835013 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2465431317835013 / 1250000000000000 : ℚ)) - (U := (169805804420780798259 / 250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2465431317835013 / 1250000000000000 : ℝ) ≤ - (169805804420780798259 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1080132558242513 / 5000000000000000 : ℝ)) (q := - (2465431317835013 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2465431317835013 / 10000000000000000 : ℚ)) + (r' := (2465431317835013 / 1250000000000000 : ℚ)) + (U := (-(350054580804219201741 / 250000000000000000000 : ℚ))) + (U' := (169805804420780798259 / 250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (7210739241 / 16000000000 : ℚ)) + (s := (1080132558242513 / 5000000000000000 : ℚ)) + (q := (2465431317835013 / 10000000000000000 : ℚ)) + (U := (-(350054580804219201741 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_11 : Uω (aρ 11) (bρ 11) (7210739241 / 16000000000 : ℝ) ≤ @@ -3842,25 +3396,21 @@ lemma U_421_11 : have hlg : Real.log (659634558201427 / 4000000000000000 : ℝ) ≤ (-(4505909143362031622123 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (659634558201427 / 4000000000000000 : ℝ) = - (659634558201427 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (659634558201427 / 500000000000000 : ℚ)) - (U := (692694708887968377877 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (659634558201427 / 500000000000000 : ℝ) ≤ - (692694708887968377877 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (189210379605427 / 2000000000000000 : ℝ)) (q := - (659634558201427 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (659634558201427 / 4000000000000000 : ℚ)) + (r' := (659634558201427 / 500000000000000 : ℚ)) + (U := (-(4505909143362031622123 / 2500000000000000000000 : ℚ))) + (U' := (692694708887968377877 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (7210739241 / 16000000000 : ℚ)) + (s := (189210379605427 / 2000000000000000 : ℚ)) + (q := (659634558201427 / 4000000000000000 : ℚ)) + (U := (-(4505909143362031622123 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_421_12 : Uω (aρ 12) (bρ 12) (7210739241 / 16000000000 : ℝ) ≤ @@ -3975,25 +3525,21 @@ lemma U_422_1 : have hlg : Real.log (8897599934522477 / 20000000000000000 : ℝ) ≤ (-(2024876757354868561347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8897599934522477 / 20000000000000000 : ℝ) = - (8897599934522477 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8897599934522477 / 5000000000000000 : ℚ)) - (U := (1440859144145131438653 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8897599934522477 / 5000000000000000 : ℝ) ≤ - (1440859144145131438653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4448763627599977 / 10000000000000000 : ℝ)) (q := - (8897599934522477 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8897599934522477 / 20000000000000000 : ℚ)) + (r' := (8897599934522477 / 5000000000000000 : ℚ)) + (U := (-(2024876757354868561347 / 2500000000000000000000 : ℚ))) + (U' := (1440859144145131438653 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (4448763627599977 / 10000000000000000 : ℚ)) + (q := (8897599934522477 / 20000000000000000 : ℚ)) + (U := (-(2024876757354868561347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_2 : Uω (aρ 2) (bρ 2) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4001,25 +3547,21 @@ lemma U_422_2 : have hlg : Real.log (442482752755881 / 1000000000000000 : ℝ) ≤ (-(1630707583193492241937 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (442482752755881 / 1000000000000000 : ℝ) = - (442482752755881 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (442482752755881 / 250000000000000 : ℚ)) - (U := (1141881138006507758063 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (442482752755881 / 250000000000000 : ℝ) ≤ - (1141881138006507758063 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27653673504407 / 62500000000000 : ℝ)) (q := - (442482752755881 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (442482752755881 / 1000000000000000 : ℚ)) + (r' := (442482752755881 / 250000000000000 : ℚ)) + (U := (-(1630707583193492241937 / 2000000000000000000000 : ℚ))) + (U' := (1141881138006507758063 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (27653673504407 / 62500000000000 : ℚ)) + (q := (442482752755881 / 1000000000000000 : ℚ)) + (U := (-(1630707583193492241937 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_3 : Uω (aρ 3) (bρ 3) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4027,25 +3569,21 @@ lemma U_422_3 : have hlg : Real.log (4376826045910491 / 10000000000000000 : ℝ) ≤ (-(4131306389108922398569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4376826045910491 / 10000000000000000 : ℝ) = - (4376826045910491 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4376826045910491 / 2500000000000000 : ℚ)) - (U := (2800165413891077601431 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4376826045910491 / 2500000000000000 : ℝ) ≤ - (2800165413891077601431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2187990451879241 / 5000000000000000 : ℝ)) (q := - (4376826045910491 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4376826045910491 / 10000000000000000 : ℚ)) + (r' := (4376826045910491 / 2500000000000000 : ℚ)) + (U := (-(4131306389108922398569 / 5000000000000000000000 : ℚ))) + (U' := (2800165413891077601431 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (2187990451879241 / 5000000000000000 : ℚ)) + (q := (4376826045910491 / 10000000000000000 : ℚ)) + (U := (-(4131306389108922398569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_4 : Uω (aρ 4) (bρ 4) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4053,25 +3591,21 @@ lemma U_422_4 : have hlg : Real.log (2148464311712387 / 5000000000000000 : ℝ) ≤ (-(8446845986117236546949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2148464311712387 / 5000000000000000 : ℝ) = - (2148464311712387 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2148464311712387 / 1250000000000000 : ℚ)) - (U := (5416097619882763453051 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2148464311712387 / 1250000000000000 : ℝ) ≤ - (5416097619882763453051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268405014990753 / 625000000000000 : ℝ)) (q := - (2148464311712387 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2148464311712387 / 5000000000000000 : ℚ)) + (r' := (2148464311712387 / 1250000000000000 : ℚ)) + (U := (-(8446845986117236546949 / 10000000000000000000000 : ℚ))) + (U' := (5416097619882763453051 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (268405014990753 / 625000000000000 : ℚ)) + (q := (2148464311712387 / 5000000000000000 : ℚ)) + (U := (-(8446845986117236546949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_5 : Uω (aρ 5) (bρ 5) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4079,25 +3613,21 @@ lemma U_422_5 : have hlg : Real.log (8349617452008769 / 20000000000000000 : ℝ) ≤ (-(8735165493515219476671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8349617452008769 / 20000000000000000 : ℝ) = - (8349617452008769 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8349617452008769 / 5000000000000000 : ℚ)) - (U := (5127778112484780523329 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8349617452008769 / 5000000000000000 : ℝ) ≤ - (5127778112484780523329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4168430364346269 / 10000000000000000 : ℝ)) (q := - (8349617452008769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8349617452008769 / 20000000000000000 : ℚ)) + (r' := (8349617452008769 / 5000000000000000 : ℚ)) + (U := (-(8735165493515219476671 / 10000000000000000000000 : ℚ))) + (U' := (5127778112484780523329 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (4168430364346269 / 10000000000000000 : ℚ)) + (q := (8349617452008769 / 20000000000000000 : ℚ)) + (U := (-(8735165493515219476671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_6 : Uω (aρ 6) (bρ 6) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4105,25 +3635,21 @@ lemma U_422_6 : have hlg : Real.log (7997202127490299 / 20000000000000000 : ℝ) ≤ (-(9166405265891975863527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7997202127490299 / 20000000000000000 : ℝ) = - (7997202127490299 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7997202127490299 / 5000000000000000 : ℚ)) - (U := (4696538340108024136473 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7997202127490299 / 5000000000000000 : ℝ) ≤ - (4696538340108024136473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3983255414967799 / 10000000000000000 : ℝ)) (q := - (7997202127490299 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7997202127490299 / 20000000000000000 : ℚ)) + (r' := (7997202127490299 / 5000000000000000 : ℚ)) + (U := (-(9166405265891975863527 / 10000000000000000000000 : ℚ))) + (U' := (4696538340108024136473 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (3983255414967799 / 10000000000000000 : ℚ)) + (q := (7997202127490299 / 20000000000000000 : ℚ)) + (U := (-(9166405265891975863527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_7 : Uω (aρ 7) (bρ 7) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4131,25 +3657,21 @@ lemma U_422_7 : have hlg : Real.log (7511516549429117 / 20000000000000000 : ℝ) ≤ (-(4896474451519480225219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7511516549429117 / 20000000000000000 : ℝ) = - (7511516549429117 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7511516549429117 / 5000000000000000 : ℚ)) - (U := (2034997351480519774781 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7511516549429117 / 5000000000000000 : ℝ) ≤ - (2034997351480519774781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3721231217666617 / 10000000000000000 : ℝ)) (q := - (7511516549429117 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7511516549429117 / 20000000000000000 : ℚ)) + (r' := (7511516549429117 / 5000000000000000 : ℚ)) + (U := (-(4896474451519480225219 / 5000000000000000000000 : ℚ))) + (U' := (2034997351480519774781 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (3721231217666617 / 10000000000000000 : ℚ)) + (q := (7511516549429117 / 20000000000000000 : ℚ)) + (U := (-(4896474451519480225219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_8 : Uω (aρ 8) (bρ 8) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4157,25 +3679,21 @@ lemma U_422_8 : have hlg : Real.log (1373309916918359 / 4000000000000000 : ℝ) ≤ (-(10690705368396436709341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1373309916918359 / 4000000000000000 : ℝ) = - (1373309916918359 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1373309916918359 / 1000000000000000 : ℚ)) - (U := (3172238237603563290659 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1373309916918359 / 1000000000000000 : ℝ) ≤ - (3172238237603563290659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (671961180833859 / 2000000000000000 : ℝ)) (q := - (1373309916918359 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1373309916918359 / 4000000000000000 : ℚ)) + (r' := (1373309916918359 / 1000000000000000 : ℚ)) + (U := (-(10690705368396436709341 / 10000000000000000000000 : ℚ))) + (U' := (3172238237603563290659 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (671961180833859 / 2000000000000000 : ℚ)) + (q := (1373309916918359 / 4000000000000000 : ℚ)) + (U := (-(10690705368396436709341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_9 : Uω (aρ 9) (bρ 9) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4183,25 +3701,21 @@ lemma U_422_9 : have hlg : Real.log (6031208519259153 / 20000000000000000 : ℝ) ≤ (-(5993924322941902594337 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6031208519259153 / 20000000000000000 : ℝ) = - (6031208519259153 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6031208519259153 / 5000000000000000 : ℚ)) - (U := (937547480058097405663 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6031208519259153 / 5000000000000000 : ℝ) ≤ - (937547480058097405663 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2865430467196653 / 10000000000000000 : ℝ)) (q := - (6031208519259153 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6031208519259153 / 20000000000000000 : ℚ)) + (r' := (6031208519259153 / 5000000000000000 : ℚ)) + (U := (-(5993924322941902594337 / 5000000000000000000000 : ℚ))) + (U' := (937547480058097405663 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (2865430467196653 / 10000000000000000 : ℚ)) + (q := (6031208519259153 / 20000000000000000 : ℚ)) + (U := (-(5993924322941902594337 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_10 : Uω (aρ 10) (bρ 10) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4209,25 +3723,21 @@ lemma U_422_10 : have hlg : Real.log (618246233222387 / 2500000000000000 : ℝ) ≤ (-(2794318392676469736287 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (618246233222387 / 2500000000000000 : ℝ) = - (618246233222387 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (618246233222387 / 312500000000000 : ℚ)) - (U := (1364564689123530263713 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (618246233222387 / 312500000000000 : ℝ) ≤ - (1364564689123530263713 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (542187711802899 / 2500000000000000 : ℝ)) (q := - (618246233222387 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (618246233222387 / 2500000000000000 : ℚ)) + (r' := (618246233222387 / 312500000000000 : ℚ)) + (U := (-(2794318392676469736287 / 2000000000000000000000 : ℚ))) + (U' := (1364564689123530263713 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (542187711802899 / 2500000000000000 : ℚ)) + (q := (618246233222387 / 2500000000000000 : ℚ)) + (U := (-(2794318392676469736287 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_11 : Uω (aρ 11) (bρ 11) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4235,26 +3745,21 @@ lemma U_422_11 : have hlg : Real.log (3321138969712857 / 20000000000000000 : ℝ) ≤ (-(3590848971023895272907 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3321138969712857 / 20000000000000000 : ℝ) = - (3321138969712857 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3321138969712857 / 2500000000000000 : ℚ)) - (U := (568034110776104727093 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3321138969712857 / 2500000000000000 : ℝ) ≤ - (568034110776104727093 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (962396577350357 / 10000000000000000 : ℝ)) (q := - (3321138969712857 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3321138969712857 / 20000000000000000 : ℚ)) + (r' := (3321138969712857 / 2500000000000000 : ℚ)) + (U := (-(3590848971023895272907 / 2000000000000000000000 : ℚ))) + (U' := (568034110776104727093 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1805333410003 / 4000000000000 : ℚ)) + (s := (962396577350357 / 10000000000000000 : ℚ)) + (q := (3321138969712857 / 20000000000000000 : ℚ)) + (U := (-(3590848971023895272907 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_422_12 : Uω (aρ 12) (bρ 12) (1805333410003 / 4000000000000 : ℝ) ≤ @@ -4371,24 +3876,21 @@ lemma U_423_1 : have hlg : Real.log (139231922520343 / 312500000000000 : ℝ) ≤ (-(4042317092986279800841 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (139231922520343 / 312500000000000 : ℝ) = (139231922520343 / 78125000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (139231922520343 / 78125000000000 : ℚ)) - (U := (2889154710013720199159 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (139231922520343 / 78125000000000 : ℝ) ≤ - (2889154710013720199159 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (556923154374619 / 1250000000000000 : ℝ)) (q := - (139231922520343 / 312500000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (139231922520343 / 312500000000000 : ℚ)) + (r' := (139231922520343 / 78125000000000 : ℚ)) + (U := (-(4042317092986279800841 / 5000000000000000000000 : ℚ))) + (U' := (2889154710013720199159 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (556923154374619 / 1250000000000000 : ℚ)) + (q := (139231922520343 / 312500000000000 : ℚ)) + (U := (-(4042317092986279800841 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_2 : Uω (aρ 2) (bρ 2) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4396,25 +3898,21 @@ lemma U_423_2 : have hlg : Real.log (1772579754088731 / 4000000000000000 : ℝ) ≤ (-(4069291934667686941101 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1772579754088731 / 4000000000000000 : ℝ) = - (1772579754088731 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1772579754088731 / 1000000000000000 : ℚ)) - (U := (2862179868332313058899 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1772579754088731 / 1000000000000000 : ℝ) ≤ - (2862179868332313058899 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (886241995329731 / 2000000000000000 : ℝ)) (q := - (1772579754088731 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1772579754088731 / 4000000000000000 : ℚ)) + (r' := (1772579754088731 / 1000000000000000 : ℚ)) + (U := (-(4069291934667686941101 / 5000000000000000000000 : ℚ))) + (U' := (2862179868332313058899 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (886241995329731 / 2000000000000000 : ℚ)) + (q := (1772579754088731 / 4000000000000000 : ℚ)) + (U := (-(4069291934667686941101 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_3 : Uω (aρ 3) (bρ 3) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4422,25 +3920,21 @@ lemma U_423_3 : have hlg : Real.log (4383448822184229 / 10000000000000000 : ℝ) ≤ (-(4123746377996051450701 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4383448822184229 / 10000000000000000 : ℝ) = - (4383448822184229 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4383448822184229 / 2500000000000000 : ℚ)) - (U := (2807725425003948549299 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4383448822184229 / 2500000000000000 : ℝ) ≤ - (2807725425003948549299 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2191302478461729 / 5000000000000000 : ℝ)) (q := - (4383448822184229 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4383448822184229 / 10000000000000000 : ℚ)) + (r' := (4383448822184229 / 2500000000000000 : ℚ)) + (U := (-(4123746377996051450701 / 5000000000000000000000 : ℚ))) + (U' := (2807725425003948549299 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (2191302478461729 / 5000000000000000 : ℚ)) + (q := (4383448822184229 / 10000000000000000 : ℚ)) + (U := (-(4123746377996051450701 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_4 : Uω (aρ 4) (bρ 4) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4448,24 +3942,21 @@ lemma U_423_4 : have hlg : Real.log (33621514781749 / 78125000000000 : ℝ) ≤ (-(4215719623000383988557 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33621514781749 / 78125000000000 : ℝ) = (33621514781749 / 19531250000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33621514781749 / 19531250000000 : ℚ)) - (U := (2715752179999616011443 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33621514781749 / 19531250000000 : ℝ) ≤ - (2715752179999616011443 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (134409664929617 / 312500000000000 : ℝ)) (q := - (33621514781749 / 78125000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33621514781749 / 78125000000000 : ℚ)) + (r' := (33621514781749 / 19531250000000 : ℚ)) + (U := (-(4215719623000383988557 / 5000000000000000000000 : ℚ))) + (U' := (2715752179999616011443 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (134409664929617 / 312500000000000 : ℚ)) + (q := (33621514781749 / 78125000000000 : ℚ)) + (U := (-(4215719623000383988557 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_5 : Uω (aρ 5) (bρ 5) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4473,25 +3964,21 @@ lemma U_423_5 : have hlg : Real.log (8362880682481939 / 20000000000000000 : ℝ) ≤ (-(1743858652094064989949 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8362880682481939 / 20000000000000000 : ℝ) = - (8362880682481939 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8362880682481939 / 5000000000000000 : ℚ)) - (U := (1028730069105935010051 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8362880682481939 / 5000000000000000 : ℝ) ≤ - (1028730069105935010051 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4175072095436939 / 10000000000000000 : ℝ)) (q := - (8362880682481939 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8362880682481939 / 20000000000000000 : ℚ)) + (r' := (8362880682481939 / 5000000000000000 : ℚ)) + (U := (-(1743858652094064989949 / 2000000000000000000000 : ℚ))) + (U' := (1028730069105935010051 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (4175072095436939 / 10000000000000000 : ℚ)) + (q := (8362880682481939 / 20000000000000000 : ℚ)) + (U := (-(1743858652094064989949 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_6 : Uω (aρ 6) (bρ 6) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4499,25 +3986,21 @@ lemma U_423_6 : have hlg : Real.log (2002624015108933 / 5000000000000000 : ℝ) ≤ (-(914979583729635317381 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2002624015108933 / 5000000000000000 : ℝ) = - (2002624015108933 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2002624015108933 / 1250000000000000 : ℚ)) - (U := (471314776870364682619 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2002624015108933 / 1250000000000000 : ℝ) ≤ - (471314776870364682619 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (997481962132683 / 2500000000000000 : ℝ)) (q := - (2002624015108933 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2002624015108933 / 5000000000000000 : ℚ)) + (r' := (2002624015108933 / 1250000000000000 : ℚ)) + (U := (-(914979583729635317381 / 1000000000000000000000 : ℚ))) + (U' := (471314776870364682619 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (997481962132683 / 2500000000000000 : ℚ)) + (q := (2002624015108933 / 5000000000000000 : ℚ)) + (U := (-(914979583729635317381 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_7 : Uω (aρ 7) (bρ 7) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4525,25 +4008,21 @@ lemma U_423_7 : have hlg : Real.log (3762441100856269 / 10000000000000000 : ℝ) ≤ (-(9775171167791601484043 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3762441100856269 / 10000000000000000 : ℝ) = - (3762441100856269 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3762441100856269 / 2500000000000000 : ℚ)) - (U := (4087772438208398515957 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3762441100856269 / 2500000000000000 : ℝ) ≤ - (4087772438208398515957 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1863987685283769 / 5000000000000000 : ℝ)) (q := - (3762441100856269 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3762441100856269 / 10000000000000000 : ℚ)) + (r' := (3762441100856269 / 2500000000000000 : ℚ)) + (U := (-(9775171167791601484043 / 10000000000000000000000 : ℚ))) + (U' := (4087772438208398515957 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (1863987685283769 / 5000000000000000 : ℚ)) + (q := (3762441100856269 / 10000000000000000 : ℚ)) + (U := (-(9775171167791601484043 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_8 : Uω (aρ 8) (bρ 8) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4551,25 +4030,21 @@ lemma U_423_8 : have hlg : Real.log (3440040793032031 / 10000000000000000 : ℝ) ≤ (-(1067101762719614924343 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3440040793032031 / 10000000000000000 : ℝ) = - (3440040793032031 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3440040793032031 / 2500000000000000 : ℚ)) - (U := (319192597880385075657 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3440040793032031 / 2500000000000000 : ℝ) ≤ - (319192597880385075657 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1683358203129531 / 5000000000000000 : ℝ)) (q := - (3440040793032031 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3440040793032031 / 10000000000000000 : ℚ)) + (r' := (3440040793032031 / 2500000000000000 : ℚ)) + (U := (-(1067101762719614924343 / 1000000000000000000000 : ℚ))) + (U' := (319192597880385075657 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (1683358203129531 / 5000000000000000 : ℚ)) + (q := (3440040793032031 / 10000000000000000 : ℚ)) + (U := (-(1067101762719614924343 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_9 : Uω (aρ 9) (bρ 9) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4577,25 +4052,21 @@ lemma U_423_9 : have hlg : Real.log (6045143884208817 / 20000000000000000 : ℝ) ≤ (-(239295397413106100289 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6045143884208817 / 20000000000000000 : ℝ) = - (6045143884208817 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6045143884208817 / 5000000000000000 : ℚ)) - (U := (37963474706893899711 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6045143884208817 / 5000000000000000 : ℝ) ≤ - (37963474706893899711 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2872744332763817 / 10000000000000000 : ℝ)) (q := - (6045143884208817 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6045143884208817 / 20000000000000000 : ℚ)) + (r' := (6045143884208817 / 5000000000000000 : ℚ)) + (U := (-(239295397413106100289 / 200000000000000000000 : ℚ))) + (U' := (37963474706893899711 / 200000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (2872744332763817 / 10000000000000000 : ℚ)) + (q := (6045143884208817 / 20000000000000000 : ℚ)) + (U := (-(239295397413106100289 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_10 : Uω (aρ 10) (bρ 10) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4603,26 +4074,21 @@ lemma U_423_10 : have hlg : Real.log (2480532080237303 / 10000000000000000 : ℝ) ≤ (-(6970560032833848866531 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2480532080237303 / 10000000000000000 : ℝ) = - (2480532080237303 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2480532080237303 / 1250000000000000 : ℚ)) - (U := (3426647671666151133469 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2480532080237303 / 1250000000000000 : ℝ) ≤ - (3426647671666151133469 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1088611821262303 / 5000000000000000 : ℝ)) (q := - (2480532080237303 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2480532080237303 / 10000000000000000 : ℚ)) + (r' := (2480532080237303 / 1250000000000000 : ℚ)) + (U := (-(6970560032833848866531 / 5000000000000000000000 : ℚ))) + (U' := (3426647671666151133469 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (1088611821262303 / 5000000000000000 : ℚ)) + (q := (2480532080237303 / 10000000000000000 : ℚ)) + (U := (-(6970560032833848866531 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_11 : Uω (aρ 11) (bρ 11) (451995502439 / 1000000000000 : ℝ) ≤ @@ -4630,25 +4096,21 @@ lemma U_423_11 : have hlg : Real.log (668775393450461 / 4000000000000000 : ℝ) ≤ (-(4471503425795417789409 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (668775393450461 / 4000000000000000 : ℝ) = - (668775393450461 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (668775393450461 / 500000000000000 : ℚ)) - (U := (727100426454582210591 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (668775393450461 / 500000000000000 : ℝ) ≤ - (727100426454582210591 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (195702615101461 / 2000000000000000 : ℝ)) (q := - (668775393450461 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (668775393450461 / 4000000000000000 : ℚ)) + (r' := (668775393450461 / 500000000000000 : ℚ)) + (U := (-(4471503425795417789409 / 2500000000000000000000 : ℚ))) + (U' := (727100426454582210591 / 2500000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (451995502439 / 1000000000000 : ℚ)) + (s := (195702615101461 / 2000000000000000 : ℚ)) + (q := (668775393450461 / 4000000000000000 : ℚ)) + (U := (-(4471503425795417789409 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_423_12 : Uω (aρ 12) (bρ 12) (451995502439 / 1000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U35.lean b/LeanPool/Zeta5Irrational/Table/U35.lean index dfffb84095..47618ccabd 100644 --- a/LeanPool/Zeta5Irrational/Table/U35.lean +++ b/LeanPool/Zeta5Irrational/Table/U35.lean @@ -24,25 +24,21 @@ lemma U_424_1 : have hlg : Real.log (8924086147760843 / 20000000000000000 : ℝ) ≤ (-(8069783430186067276137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8924086147760843 / 20000000000000000 : ℝ) = - (8924086147760843 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8924086147760843 / 5000000000000000 : ℚ)) - (U := (5793160175813932723863 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8924086147760843 / 5000000000000000 : ℝ) ≤ - (5793160175813932723863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4462006842073343 / 10000000000000000 : ℝ)) (q := - (8924086147760843 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8924086147760843 / 20000000000000000 : ℚ)) + (r' := (8924086147760843 / 5000000000000000 : ℚ)) + (U := (-(8069783430186067276137 / 10000000000000000000000 : ℚ))) + (U' := (5793160175813932723863 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (4462006842073343 / 10000000000000000 : ℚ)) + (q := (8924086147760843 / 20000000000000000 : ℚ)) + (U := (-(8069783430186067276137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_2 : Uω (aρ 2) (bρ 2) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_424_2 : have hlg : Real.log (8876142483631273 / 20000000000000000 : ℝ) ≤ (-(1624730430815369043297 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8876142483631273 / 20000000000000000 : ℝ) = - (8876142483631273 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8876142483631273 / 5000000000000000 : ℚ)) - (U := (1147858290384630956703 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8876142483631273 / 5000000000000000 : ℝ) ≤ - (1147858290384630956703 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4437832190453773 / 10000000000000000 : ℝ)) (q := - (8876142483631273 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8876142483631273 / 20000000000000000 : ℚ)) + (r' := (8876142483631273 / 5000000000000000 : ℚ)) + (U := (-(1624730430815369043297 / 2000000000000000000000 : ℚ))) + (U' := (1147858290384630956703 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (4437832190453773 / 10000000000000000 : ℚ)) + (q := (8876142483631273 / 20000000000000000 : ℚ)) + (U := (-(1624730430815369043297 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_3 : Uω (aρ 3) (bρ 3) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_424_3 : have hlg : Real.log (4390071594604641 / 10000000000000000 : ℝ) ≤ (-(4116197784770404230469 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4390071594604641 / 10000000000000000 : ℝ) = - (4390071594604641 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4390071594604641 / 2500000000000000 : ℚ)) - (U := (2815274018229595769531 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4390071594604641 / 2500000000000000 : ℝ) ≤ - (2815274018229595769531 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2194614501190891 / 5000000000000000 : ℝ)) (q := - (4390071594604641 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4390071594604641 / 10000000000000000 : ℚ)) + (r' := (4390071594604641 / 2500000000000000 : ℚ)) + (U := (-(4116197784770404230469 / 5000000000000000000000 : ℚ))) + (U' := (2815274018229595769531 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (2194614501190891 / 5000000000000000 : ℚ)) + (q := (4390071594604641 / 10000000000000000 : ℚ)) + (U := (-(4116197784770404230469 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_4 : Uω (aρ 4) (bρ 4) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_424_4 : have hlg : Real.log (8620358298217587 / 20000000000000000 : ℝ) ≤ (-(8416056233038239239309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8620358298217587 / 20000000000000000 : ℝ) = - (8620358298217587 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8620358298217587 / 5000000000000000 : ℚ)) - (U := (5446887372961760760691 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8620358298217587 / 5000000000000000 : ℝ) ≤ - (5446887372961760760691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4307738292455087 / 10000000000000000 : ℝ)) (q := - (8620358298217587 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8620358298217587 / 20000000000000000 : ℚ)) + (r' := (8620358298217587 / 5000000000000000 : ℚ)) + (U := (-(8416056233038239239309 / 10000000000000000000000 : ℚ))) + (U' := (5446887372961760760691 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (4307738292455087 / 10000000000000000 : ℚ)) + (q := (8620358298217587 / 20000000000000000 : ℚ)) + (U := (-(8416056233038239239309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_5 : Uω (aρ 5) (bρ 5) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_424_5 : have hlg : Real.log (837614384878577 / 2000000000000000 : ℝ) ≤ (-(8703446256895322532487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (837614384878577 / 2000000000000000 : ℝ) = - (837614384878577 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (837614384878577 / 500000000000000 : ℚ)) - (U := (5159497349104677467513 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (837614384878577 / 500000000000000 : ℝ) ≤ - (5159497349104677467513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (418171376235827 / 1000000000000000 : ℝ)) (q := - (837614384878577 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (837614384878577 / 2000000000000000 : ℚ)) + (r' := (837614384878577 / 500000000000000 : ℚ)) + (U := (-(8703446256895322532487 / 10000000000000000000000 : ℚ))) + (U' := (5159497349104677467513 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (418171376235827 / 1000000000000000 : ℚ)) + (q := (837614384878577 / 2000000000000000 : ℚ)) + (U := (-(8703446256895322532487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_6 : Uω (aρ 6) (bρ 6) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_424_6 : have hlg : Real.log (8023789823958269 / 20000000000000000 : ℝ) ≤ (-(2283303540356153156021 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8023789823958269 / 20000000000000000 : ℝ) = - (8023789823958269 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8023789823958269 / 5000000000000000 : ℚ)) - (U := (1182432361143846843979 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8023789823958269 / 5000000000000000 : ℝ) ≤ - (1182432361143846843979 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3996600112670769 / 10000000000000000 : ℝ)) (q := - (8023789823958269 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8023789823958269 / 20000000000000000 : ℚ)) + (r' := (8023789823958269 / 5000000000000000 : ℚ)) + (U := (-(2283303540356153156021 / 2500000000000000000000 : ℚ))) + (U' := (1182432361143846843979 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (3996600112670769 / 10000000000000000 : ℚ)) + (q := (8023789823958269 / 20000000000000000 : ℚ)) + (U := (-(2283303540356153156021 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_7 : Uω (aρ 7) (bρ 7) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_424_7 : have hlg : Real.log (188456185376221 / 500000000000000 : ℝ) ≤ (-(2439356390886610766343 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (188456185376221 / 500000000000000 : ℝ) = - (188456185376221 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (188456185376221 / 125000000000000 : ℚ)) - (U := (1026379510613389233657 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (188456185376221 / 125000000000000 : ℝ) ≤ - (1026379510613389233657 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (186735954226067 / 500000000000000 : ℝ)) (q := - (188456185376221 / 500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (188456185376221 / 500000000000000 : ℚ)) + (r' := (188456185376221 / 125000000000000 : ℚ)) + (U := (-(2439356390886610766343 / 2500000000000000000000 : ℚ))) + (U' := (1026379510613389233657 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (186735954226067 / 500000000000000 : ℚ)) + (q := (188456185376221 / 500000000000000 : ℚ)) + (U := (-(2439356390886610766343 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_8 : Uω (aρ 8) (bρ 8) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_424_8 : have hlg : Real.log (344680621415669 / 1000000000000000 : ℝ) ≤ (-(10651370252152340611 / 10000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (344680621415669 / 1000000000000000 : ℝ) = - (344680621415669 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (344680621415669 / 250000000000000 : ℚ)) - (U := (3211573353847659389 / 10000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (344680621415669 / 250000000000000 : ℝ) ≤ - (3211573353847659389 / 10000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84340643728147 / 250000000000000 : ℝ)) (q := - (344680621415669 / 1000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (344680621415669 / 1000000000000000 : ℚ)) + (r' := (344680621415669 / 250000000000000 : ℚ)) + (U := (-(10651370252152340611 / 10000000000000000000 : ℚ))) + (U' := (3211573353847659389 / 10000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (84340643728147 / 250000000000000 : ℚ)) + (q := (344680621415669 / 1000000000000000 : ℚ)) + (U := (-(10651370252152340611 / 10000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_9 : Uω (aρ 9) (bρ 9) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_424_9 : have hlg : Real.log (6059075899093861 / 20000000000000000 : ℝ) ≤ (-(1194174976479651820651 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6059075899093861 / 20000000000000000 : ℝ) = - (6059075899093861 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6059075899093861 / 5000000000000000 : ℚ)) - (U := (192119384120348179349 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6059075899093861 / 5000000000000000 : ℝ) ≤ - (192119384120348179349 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2880054848266361 / 10000000000000000 : ℝ)) (q := - (6059075899093861 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6059075899093861 / 20000000000000000 : ℚ)) + (r' := (6059075899093861 / 5000000000000000 : ℚ)) + (U := (-(1194174976479651820651 / 1000000000000000000000 : ℚ))) + (U' := (192119384120348179349 / 1000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (2880054848266361 / 10000000000000000 : ℚ)) + (q := (6059075899093861 / 20000000000000000 : ℚ)) + (U := (-(1194174976479651820651 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_10 : Uω (aρ 10) (bρ 10) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_424_10 : have hlg : Real.log (2488072835094411 / 10000000000000000 : ℝ) ≤ (-(13910766432101367482929 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2488072835094411 / 10000000000000000 : ℝ) = - (2488072835094411 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2488072835094411 / 1250000000000000 : ℚ)) - (U := (6883648976898632517071 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2488072835094411 / 1250000000000000 : ℝ) ≤ - (6883648976898632517071 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1092841826428161 / 5000000000000000 : ℝ)) (q := - (2488072835094411 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2488072835094411 / 10000000000000000 : ℚ)) + (r' := (2488072835094411 / 1250000000000000 : ℚ)) + (U := (-(13910766432101367482929 / 10000000000000000000000 : ℚ))) + (U' := (6883648976898632517071 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (1092841826428161 / 5000000000000000 : ℚ)) + (q := (2488072835094411 / 10000000000000000 : ℚ)) + (U := (-(13910766432101367482929 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_11 : Uω (aρ 11) (bρ 11) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_424_11 : have hlg : Real.log (3366397878121701 / 20000000000000000 : ℝ) ≤ (-(8909444894819806137933 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3366397878121701 / 20000000000000000 : ℝ) = - (3366397878121701 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3366397878121701 / 2500000000000000 : ℚ)) - (U := (1487762809680193862067 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3366397878121701 / 2500000000000000 : ℝ) ≤ - (1487762809680193862067 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (994412486994201 / 10000000000000000 : ℝ)) (q := - (3366397878121701 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3366397878121701 / 20000000000000000 : ℚ)) + (r' := (3366397878121701 / 2500000000000000 : ℚ)) + (U := (-(8909444894819806137933 / 5000000000000000000000 : ℚ))) + (U' := (1487762809680193862067 / 5000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1810630609509 / 4000000000000 : ℚ)) + (s := (994412486994201 / 10000000000000000 : ℚ)) + (q := (3366397878121701 / 20000000000000000 : ℚ)) + (U := (-(8909444894819806137933 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_424_12 : Uω (aρ 12) (bρ 12) (1810630609509 / 4000000000000 : ℝ) ≤ @@ -420,25 +374,21 @@ lemma U_425_1 : have hlg : Real.log (357493170156023 / 800000000000000 : ℝ) ≤ (-(4027477348275718747337 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (357493170156023 / 800000000000000 : ℝ) = - (357493170156023 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (357493170156023 / 200000000000000 : ℚ)) - (U := (2903994454724281252663 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (357493170156023 / 200000000000000 : ℝ) ≤ - (2903994454724281252663 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (178745137953223 / 400000000000000 : ℝ)) (q := - (357493170156023 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (357493170156023 / 800000000000000 : ℚ)) + (r' := (357493170156023 / 200000000000000 : ℚ)) + (U := (-(4027477348275718747337 / 5000000000000000000000 : ℚ))) + (U' := (2903994454724281252663 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (178745137953223 / 400000000000000 : ℚ)) + (q := (357493170156023 / 800000000000000 : ℚ)) + (U := (-(4027477348275718747337 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_2 : Uω (aρ 2) (bρ 2) (906639604631 / 2000000000000 : ℝ) ≤ @@ -446,25 +396,21 @@ lemma U_425_2 : have hlg : Real.log (1777877238938007 / 4000000000000000 : ℝ) ≤ (-(4054371351793893970459 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1777877238938007 / 4000000000000000 : ℝ) = - (1777877238938007 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1777877238938007 / 1000000000000000 : ℚ)) - (U := (2877100451206106029541 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1777877238938007 / 1000000000000000 : ℝ) ≤ - (2877100451206106029541 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (888890880426007 / 2000000000000000 : ℝ)) (q := - (1777877238938007 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1777877238938007 / 4000000000000000 : ℚ)) + (r' := (1777877238938007 / 1000000000000000 : ℚ)) + (U := (-(4054371351793893970459 / 5000000000000000000000 : ℚ))) + (U' := (2877100451206106029541 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (888890880426007 / 2000000000000000 : ℚ)) + (q := (1777877238938007 / 4000000000000000 : ℚ)) + (U := (-(4054371351793893970459 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_3 : Uω (aρ 3) (bρ 3) (906639604631 / 2000000000000 : ℝ) ≤ @@ -472,25 +418,21 @@ lemma U_425_3 : have hlg : Real.log (8793388726378293 / 20000000000000000 : ℝ) ≤ (-(8217321149963825466591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8793388726378293 / 20000000000000000 : ℝ) = - (8793388726378293 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8793388726378293 / 5000000000000000 : ℚ)) - (U := (5645622456036174533409 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8793388726378293 / 5000000000000000 : ℝ) ≤ - (5645622456036174533409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4395853040168293 / 10000000000000000 : ℝ)) (q := - (8793388726378293 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8793388726378293 / 20000000000000000 : ℚ)) + (r' := (8793388726378293 / 5000000000000000 : ℚ)) + (U := (-(8217321149963825466591 / 10000000000000000000000 : ℚ))) + (U' := (5645622456036174533409 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (4395853040168293 / 10000000000000000 : ℚ)) + (q := (8793388726378293 / 20000000000000000 : ℚ)) + (U := (-(8217321149963825466591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_4 : Uω (aρ 4) (bρ 4) (906639604631 / 2000000000000 : ℝ) ≤ @@ -498,25 +440,21 @@ lemma U_425_4 : have hlg : Real.log (4316804394612983 / 10000000000000000 : ℝ) ≤ (-(4200348437088783331463 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4316804394612983 / 10000000000000000 : ℝ) = - (4316804394612983 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4316804394612983 / 2500000000000000 : ℚ)) - (U := (2731123365911216668537 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4316804394612983 / 2500000000000000 : ℝ) ≤ - (2731123365911216668537 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2157183642040483 / 5000000000000000 : ℝ)) (q := - (4316804394612983 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4316804394612983 / 10000000000000000 : ℚ)) + (r' := (4316804394612983 / 2500000000000000 : ℚ)) + (U := (-(4200348437088783331463 / 5000000000000000000000 : ℚ))) + (U' := (2731123365911216668537 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (2157183642040483 / 5000000000000000 : ℚ)) + (q := (4316804394612983 / 10000000000000000 : ℚ)) + (U := (-(4200348437088783331463 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_5 : Uω (aρ 5) (bρ 5) (906639604631 / 2000000000000 : ℝ) ≤ @@ -524,25 +462,21 @@ lemma U_425_5 : have hlg : Real.log (8389406951225531 / 20000000000000000 : ℝ) ≤ (-(8687624402469212596989 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8389406951225531 / 20000000000000000 : ℝ) = - (8389406951225531 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8389406951225531 / 5000000000000000 : ℚ)) - (U := (5175319203530787403011 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8389406951225531 / 5000000000000000 : ℝ) ≤ - (5175319203530787403011 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4188355365415531 / 10000000000000000 : ℝ)) (q := - (8389406951225531 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8389406951225531 / 20000000000000000 : ℚ)) + (r' := (8389406951225531 / 5000000000000000 : ℚ)) + (U := (-(8687624402469212596989 / 10000000000000000000000 : ℚ))) + (U' := (5175319203530787403011 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (4188355365415531 / 10000000000000000 : ℚ)) + (q := (8389406951225531 / 20000000000000000 : ℚ)) + (U := (-(8687624402469212596989 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_6 : Uω (aρ 6) (bρ 6) (906639604631 / 2000000000000 : ℝ) ≤ @@ -550,25 +484,21 @@ lemma U_425_6 : have hlg : Real.log (8037083418905043 / 20000000000000000 : ℝ) ≤ (-(1139582518123484126347 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8037083418905043 / 20000000000000000 : ℝ) = - (8037083418905043 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8037083418905043 / 5000000000000000 : ℚ)) - (U := (593285432626515873653 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8037083418905043 / 5000000000000000 : ℝ) ≤ - (593285432626515873653 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4003272208235043 / 10000000000000000 : ℝ)) (q := - (8037083418905043 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8037083418905043 / 20000000000000000 : ℚ)) + (r' := (8037083418905043 / 5000000000000000 : ℚ)) + (U := (-(1139582518123484126347 / 1250000000000000000000 : ℚ))) + (U' := (593285432626515873653 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (4003272208235043 / 10000000000000000 : ℚ)) + (q := (8037083418905043 / 20000000000000000 : ℚ)) + (U := (-(1139582518123484126347 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_7 : Uω (aρ 7) (bρ 7) (906639604631 / 2000000000000 : ℝ) ≤ @@ -576,25 +506,21 @@ lemma U_425_7 : have hlg : Real.log (3775806095905767 / 10000000000000000 : ℝ) ≤ (-(1947942394458633086619 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3775806095905767 / 10000000000000000 : ℝ) = - (3775806095905767 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3775806095905767 / 2500000000000000 : ℚ)) - (U := (824646326741366913381 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3775806095905767 / 2500000000000000 : ℝ) ≤ - (824646326741366913381 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1870731180950767 / 5000000000000000 : ℝ)) (q := - (3775806095905767 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3775806095905767 / 10000000000000000 : ℚ)) + (r' := (3775806095905767 / 2500000000000000 : ℚ)) + (U := (-(1947942394458633086619 / 2000000000000000000000 : ℚ))) + (U' := (824646326741366913381 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (1870731180950767 / 5000000000000000 : ℚ)) + (q := (3775806095905767 / 10000000000000000 : ℚ)) + (U := (-(1947942394458633086619 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_8 : Uω (aρ 8) (bρ 8) (906639604631 / 2000000000000 : ℝ) ≤ @@ -602,25 +528,21 @@ lemma U_425_8 : have hlg : Real.log (6907142118447623 / 20000000000000000 : ℝ) ≤ (-(10631763071366856419741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6907142118447623 / 20000000000000000 : ℝ) = - (6907142118447623 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6907142118447623 / 5000000000000000 : ℚ)) - (U := (3231180534633143580259 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6907142118447623 / 5000000000000000 : ℝ) ≤ - (3231180534633143580259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3380533939877623 / 10000000000000000 : ℝ)) (q := - (6907142118447623 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6907142118447623 / 20000000000000000 : ℚ)) + (r' := (6907142118447623 / 5000000000000000 : ℚ)) + (U := (-(10631763071366856419741 / 10000000000000000000000 : ℚ))) + (U' := (3231180534633143580259 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (3380533939877623 / 10000000000000000 : ℚ)) + (q := (6907142118447623 / 20000000000000000 : ℚ)) + (U := (-(10631763071366856419741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_9 : Uω (aρ 9) (bρ 9) (906639604631 / 2000000000000 : ℝ) ≤ @@ -628,24 +550,21 @@ lemma U_425_9 : have hlg : Real.log (23722674177189 / 78125000000000 : ℝ) ≤ (-(11918788004198888387561 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23722674177189 / 78125000000000 : ℝ) = (23722674177189 / 19531250000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23722674177189 / 19531250000000 : ℚ)) - (U := (1944155601801111612439 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23722674177189 / 19531250000000 : ℝ) ≤ - (1944155601801111612439 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180460127446899 / 625000000000000 : ℝ)) (q := - (23722674177189 / 78125000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23722674177189 / 78125000000000 : ℚ)) + (r' := (23722674177189 / 19531250000000 : ℚ)) + (U := (-(11918788004198888387561 / 10000000000000000000000 : ℚ))) + (U' := (1944155601801111612439 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (180460127446899 / 625000000000000 : ℚ)) + (q := (23722674177189 / 78125000000000 : ℚ)) + (U := (-(11918788004198888387561 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_10 : Uω (aρ 10) (bρ 10) (906639604631 / 2000000000000 : ℝ) ≤ @@ -653,26 +572,21 @@ lemma U_425_10 : have hlg : Real.log (2495607271404321 / 10000000000000000 : ℝ) ≤ (-(3470132493185344546727 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2495607271404321 / 10000000000000000 : ℝ) = - (2495607271404321 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2495607271404321 / 1250000000000000 : ℚ)) - (U := (1728471359064655453273 / 2500000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (2495607271404321 / 1250000000000000 : ℝ) ≤ - (1728471359064655453273 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1097065513046821 / 5000000000000000 : ℝ)) (q := - (2495607271404321 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2495607271404321 / 10000000000000000 : ℚ)) + (r' := (2495607271404321 / 1250000000000000 : ℚ)) + (U := (-(3470132493185344546727 / 2500000000000000000000 : ℚ))) + (U' := (1728471359064655453273 / 2500000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (1097065513046821 / 5000000000000000 : ℚ)) + (q := (2495607271404321 / 10000000000000000 : ℚ)) + (U := (-(3470132493185344546727 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_11 : Uω (aρ 11) (bρ 11) (906639604631 / 2000000000000 : ℝ) ≤ @@ -680,26 +594,21 @@ lemma U_425_11 : have hlg : Real.log (3388711953436309 / 20000000000000000 : ℝ) ≤ (-(221910297290179888531 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3388711953436309 / 20000000000000000 : ℝ) = - (3388711953436309 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3388711953436309 / 2500000000000000 : ℚ)) - (U := (38019895322320111469 / 125000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3388711953436309 / 2500000000000000 : ℝ) ≤ - (38019895322320111469 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1010105062926309 / 10000000000000000 : ℝ)) (q := - (3388711953436309 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3388711953436309 / 20000000000000000 : ℚ)) + (r' := (3388711953436309 / 2500000000000000 : ℚ)) + (U := (-(221910297290179888531 / 125000000000000000000 : ℚ))) + (U' := (38019895322320111469 / 125000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (906639604631 / 2000000000000 : ℚ)) + (s := (1010105062926309 / 10000000000000000 : ℚ)) + (q := (3388711953436309 / 20000000000000000 : ℚ)) + (U := (-(221910297290179888531 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_425_12 : Uω (aρ 12) (bρ 12) (906639604631 / 2000000000000 : ℝ) ≤ @@ -815,25 +724,21 @@ lemma U_426_1 : have hlg : Real.log (1790114471944513 / 4000000000000000 : ℝ) ≤ (-(1608029583970223099703 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1790114471944513 / 4000000000000000 : ℝ) = - (1790114471944513 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1790114471944513 / 1000000000000000 : ℚ)) - (U := (1164559137229776900297 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1790114471944513 / 1000000000000000 : ℝ) ≤ - (1164559137229776900297 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (895050011054013 / 2000000000000000 : ℝ)) (q := - (1790114471944513 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1790114471944513 / 4000000000000000 : ℚ)) + (r' := (1790114471944513 / 1000000000000000 : ℚ)) + (U := (-(1608029583970223099703 / 2000000000000000000000 : ℚ))) + (U' := (1164559137229776900297 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (363185561803 / 800000000000 : ℚ)) + (s := (895050011054013 / 2000000000000000 : ℚ)) + (q := (1790114471944513 / 4000000000000000 : ℚ)) + (U := (-(1608029583970223099703 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_2 : Uω (aρ 2) (bρ 2) (363185561803 / 800000000000 : ℝ) ≤ @@ -841,25 +746,21 @@ lemma U_426_2 : have hlg : Real.log (8902629903629441 / 20000000000000000 : ℝ) ≤ (-(252932982861302534687 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8902629903629441 / 20000000000000000 : ℝ) = - (8902629903629441 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8902629903629441 / 5000000000000000 : ℚ)) - (U := (180284004826197465313 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8902629903629441 / 5000000000000000 : ℝ) ≤ - (180284004826197465313 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4451076611686941 / 10000000000000000 : ℝ)) (q := - (8902629903629441 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8902629903629441 / 20000000000000000 : ℚ)) + (r' := (8902629903629441 / 5000000000000000 : ℚ)) + (U := (-(252932982861302534687 / 312500000000000000000 : ℚ))) + (U' := (180284004826197465313 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (363185561803 / 800000000000 : ℚ)) + (s := (4451076611686941 / 10000000000000000 : ℚ)) + (q := (8902629903629441 / 20000000000000000 : ℚ)) + (U := (-(252932982861302534687 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_3 : Uω (aρ 3) (bρ 3) (363185561803 / 800000000000 : ℝ) ≤ @@ -867,25 +768,21 @@ lemma U_426_3 : have hlg : Real.log (220165856397753 / 500000000000000 : ℝ) ≤ (-(4101134714336247887123 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (220165856397753 / 500000000000000 : ℝ) = - (220165856397753 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (220165856397753 / 125000000000000 : ℚ)) - (U := (2830337088663752112877 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (220165856397753 / 125000000000000 : ℝ) ≤ - (2830337088663752112877 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (220123853515881 / 500000000000000 : ℝ)) (q := - (220165856397753 / 500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (220165856397753 / 500000000000000 : ℚ)) + (r' := (220165856397753 / 125000000000000 : ℚ)) + (U := (-(4101134714336247887123 / 5000000000000000000000 : ℚ))) + (U' := (2830337088663752112877 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (363185561803 / 800000000000 : ℚ)) + (s := (220123853515881 / 500000000000000 : ℚ)) + (q := (220165856397753 / 500000000000000 : ℚ)) + (U := (-(4101134714336247887123 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_4 : Uω (aρ 4) (bρ 4) (363185561803 / 800000000000 : ℝ) ≤ @@ -893,25 +790,21 @@ lemma U_426_4 : have hlg : Real.log (864685925725911 / 2000000000000000 : ℝ) ≤ (-(8385361096703903811737 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (864685925725911 / 2000000000000000 : ℝ) = - (864685925725911 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (864685925725911 / 500000000000000 : ℚ)) - (U := (5477582509296096188263 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (864685925725911 / 500000000000000 : ℝ) ≤ - (5477582509296096188263 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (432099625273161 / 1000000000000000 : ℝ)) (q := - (864685925725911 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (864685925725911 / 2000000000000000 : ℚ)) + (r' := (864685925725911 / 500000000000000 : ℚ)) + (U := (-(8385361096703903811737 / 10000000000000000000000 : ℚ))) + (U' := (5477582509296096188263 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (363185561803 / 800000000000 : ℚ)) + (s := (432099625273161 / 1000000000000000 : ℚ)) + (q := (864685925725911 / 2000000000000000 : ℚ)) + (U := (-(8385361096703903811737 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_5 : Uω (aρ 5) (bρ 5) (363185561803 / 800000000000 : ℝ) ≤ @@ -919,25 +812,21 @@ lemma U_426_5 : have hlg : Real.log (1680533998020911 / 4000000000000000 : ℝ) ≤ (-(541989226078443513091 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1680533998020911 / 4000000000000000 : ℝ) = - (1680533998020911 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1680533998020911 / 1000000000000000 : ℚ)) - (U := (324444749296556486909 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1680533998020911 / 1000000000000000 : ℝ) ≤ - (324444749296556486909 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (838999380982411 / 2000000000000000 : ℝ)) (q := - (1680533998020911 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1680533998020911 / 4000000000000000 : ℚ)) + (r' := (1680533998020911 / 1000000000000000 : ℚ)) + (U := (-(541989226078443513091 / 625000000000000000000 : ℚ))) + (U' := (324444749296556486909 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (363185561803 / 800000000000 : ℚ)) + (s := (838999380982411 / 2000000000000000 : ℚ)) + (q := (1680533998020911 / 4000000000000000 : ℚ)) + (U := (-(541989226078443513091 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_6 : Uω (aρ 6) (bρ 6) (363185561803 / 800000000000 : ℝ) ≤ @@ -945,25 +834,21 @@ lemma U_426_6 : have hlg : Real.log (8050376846117527 / 20000000000000000 : ℝ) ≤ (-(2275033423792574258343 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8050376846117527 / 20000000000000000 : ℝ) = - (8050376846117527 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8050376846117527 / 5000000000000000 : ℚ)) - (U := (1190702477707425741657 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8050376846117527 / 5000000000000000 : ℝ) ≤ - (1190702477707425741657 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4009944136065027 / 10000000000000000 : ℝ)) (q := - (8050376846117527 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8050376846117527 / 20000000000000000 : ℚ)) + (r' := (8050376846117527 / 5000000000000000 : ℚ)) + (U := (-(2275033423792574258343 / 2500000000000000000000 : ℚ))) + (U' := (1190702477707425741657 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (363185561803 / 800000000000 : ℚ)) + (s := (4009944136065027 / 10000000000000000 : ℚ)) + (q := (8050376846117527 / 20000000000000000 : ℚ)) + (U := (-(2275033423792574258343 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_7 : Uω (aρ 7) (bρ 7) (363185561803 / 800000000000 : ℝ) ≤ @@ -971,25 +856,21 @@ lemma U_426_7 : have hlg : Real.log (3782488267178449 / 10000000000000000 : ℝ) ≤ (-(1215253784585170195443 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3782488267178449 / 10000000000000000 : ℝ) = - (3782488267178449 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3782488267178449 / 2500000000000000 : ℚ)) - (U := (517614166164829804557 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3782488267178449 / 2500000000000000 : ℝ) ≤ - (517614166164829804557 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1874102602532199 / 5000000000000000 : ℝ)) (q := - (3782488267178449 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3782488267178449 / 10000000000000000 : ℚ)) + (r' := (3782488267178449 / 2500000000000000 : ℚ)) + (U := (-(1215253784585170195443 / 1250000000000000000000 : ℚ))) + (U' := (517614166164829804557 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (363185561803 / 800000000000 : ℚ)) + (s := (1874102602532199 / 5000000000000000 : ℚ)) + (q := (3782488267178449 / 10000000000000000 : ℚ)) + (U := (-(1215253784585170195443 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_8 : Uω (aρ 8) (bρ 8) (363185561803 / 800000000000 : ℝ) ≤ @@ -997,25 +878,21 @@ lemma U_426_8 : have hlg : Real.log (6920670663515501 / 20000000000000000 : ℝ) ≤ (-(2122439182815299947461 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6920670663515501 / 20000000000000000 : ℝ) = - (6920670663515501 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6920670663515501 / 5000000000000000 : ℚ)) - (U := (650149538384700052539 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6920670663515501 / 5000000000000000 : ℝ) ≤ - (650149538384700052539 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3387440985563001 / 10000000000000000 : ℝ)) (q := - (6920670663515501 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6920670663515501 / 20000000000000000 : ℚ)) + (r' := (6920670663515501 / 5000000000000000 : ℚ)) + (U := (-(2122439182815299947461 / 2000000000000000000000 : ℚ))) + (U' := (650149538384700052539 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (363185561803 / 800000000000 : ℚ)) + (s := (3387440985563001 / 10000000000000000 : ℚ)) + (q := (6920670663515501 / 20000000000000000 : ℚ)) + (U := (-(2122439182815299947461 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_9 : Uω (aρ 9) (bρ 9) (363185561803 / 800000000000 : ℝ) ≤ @@ -1023,25 +900,21 @@ lemma U_426_9 : have hlg : Real.log (1521732495046507 / 5000000000000000 : ℝ) ≤ (-(2973971066903655038759 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1521732495046507 / 5000000000000000 : ℝ) = - (1521732495046507 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1521732495046507 / 1250000000000000 : ℚ)) - (U := (491764834596344961241 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1521732495046507 / 1250000000000000 : ℝ) ≤ - (491764834596344961241 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (361833241324191 / 1250000000000000 : ℝ)) (q := - (1521732495046507 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1521732495046507 / 5000000000000000 : ℚ)) + (r' := (1521732495046507 / 1250000000000000 : ℚ)) + (U := (-(2973971066903655038759 / 2500000000000000000000 : ℚ))) + (U' := (491764834596344961241 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (363185561803 / 800000000000 : ℚ)) + (s := (361833241324191 / 1250000000000000 : ℚ)) + (q := (1521732495046507 / 5000000000000000 : ℚ)) + (U := (-(2973971066903655038759 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_10 : Uω (aρ 10) (bρ 10) (363185561803 / 800000000000 : ℝ) ≤ @@ -1049,26 +922,21 @@ lemma U_426_10 : have hlg : Real.log (5006270923733017 / 20000000000000000 : ℝ) ≤ (-(1731301202107627005709 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5006270923733017 / 20000000000000000 : ℝ) = - (5006270923733017 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5006270923733017 / 5000000000000000 : ℚ)) - (U := (1566748642372994291 / 1250000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (5006270923733017 / 5000000000000000 : ℝ) ≤ - (1566748642372994291 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2202565907635517 / 10000000000000000 : ℝ)) (q := - (5006270923733017 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5006270923733017 / 20000000000000000 : ℚ)) + (r' := (5006270923733017 / 5000000000000000 : ℚ)) + (U := (-(1731301202107627005709 / 1250000000000000000000 : ℚ))) + (U' := (1566748642372994291 / 1250000000000000000000 : ℚ)) + 2 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (363185561803 / 800000000000 : ℚ)) + (s := (2202565907635517 / 10000000000000000 : ℚ)) + (q := (5006270923733017 / 20000000000000000 : ℚ)) + (U := (-(1731301202107627005709 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_11 : Uω (aρ 11) (bρ 11) (363185561803 / 800000000000 : ℝ) ≤ @@ -1076,26 +944,21 @@ lemma U_426_11 : have hlg : Real.log (1705414343765671 / 10000000000000000 : ℝ) ≤ (-(17687769941311851423913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1705414343765671 / 10000000000000000 : ℝ) = - (1705414343765671 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1705414343765671 / 1250000000000000 : ℚ)) - (U := (3106645467688148576087 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1705414343765671 / 1250000000000000 : ℝ) ≤ - (3106645467688148576087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (512800148819421 / 5000000000000000 : ℝ)) (q := - (1705414343765671 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1705414343765671 / 10000000000000000 : ℚ)) + (r' := (1705414343765671 / 1250000000000000 : ℚ)) + (U := (-(17687769941311851423913 / 10000000000000000000000 : ℚ))) + (U' := (3106645467688148576087 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (363185561803 / 800000000000 : ℚ)) + (s := (512800148819421 / 5000000000000000 : ℚ)) + (q := (1705414343765671 / 10000000000000000 : ℚ)) + (U := (-(17687769941311851423913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_426_12 : Uω (aρ 12) (bρ 12) (363185561803 / 800000000000 : ℝ) ≤ @@ -1211,25 +1074,21 @@ lemma U_427_1 : have hlg : Real.log (8963815465228221 / 20000000000000000 : ℝ) ≤ (-(2006340758789207906781 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8963815465228221 / 20000000000000000 : ℝ) = - (8963815465228221 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8963815465228221 / 5000000000000000 : ℚ)) - (U := (1459395142710792093219 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8963815465228221 / 5000000000000000 : ℝ) ≤ - (1459395142710792093219 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4481871661393221 / 10000000000000000 : ℝ)) (q := - (8963815465228221 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8963815465228221 / 20000000000000000 : ℚ)) + (r' := (8963815465228221 / 5000000000000000 : ℚ)) + (U := (-(2006340758789207906781 / 2500000000000000000000 : ℚ))) + (U' := (1459395142710792093219 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (28415256387 / 62500000000 : ℚ)) + (s := (4481871661393221 / 10000000000000000 : ℚ)) + (q := (8963815465228221 / 20000000000000000 : ℚ)) + (U := (-(2006340758789207906781 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_2 : Uω (aρ 2) (bρ 2) (28415256387 / 62500000000 : ℝ) ≤ @@ -1237,25 +1096,21 @@ lemma U_427_2 : have hlg : Real.log (8915873610458937 / 20000000000000000 : ℝ) ≤ (-(1615798066397558523171 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8915873610458937 / 20000000000000000 : ℝ) = - (8915873610458937 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8915873610458937 / 5000000000000000 : ℚ)) - (U := (1156790654802441476829 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8915873610458937 / 5000000000000000 : ℝ) ≤ - (1156790654802441476829 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4457698819133937 / 10000000000000000 : ℝ)) (q := - (8915873610458937 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8915873610458937 / 20000000000000000 : ℚ)) + (r' := (8915873610458937 / 5000000000000000 : ℚ)) + (U := (-(1615798066397558523171 / 2000000000000000000000 : ℚ))) + (U' := (1156790654802441476829 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (28415256387 / 62500000000 : ℚ)) + (s := (4457698819133937 / 10000000000000000 : ℚ)) + (q := (8915873610458937 / 20000000000000000 : ℚ)) + (U := (-(1615798066397558523171 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_3 : Uω (aρ 3) (bρ 3) (28415256387 / 62500000000 : ℝ) ≤ @@ -1263,25 +1118,21 @@ lemma U_427_3 : have hlg : Real.log (4409939888919593 / 10000000000000000 : ℝ) ≤ (-(818724033738776100043 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4409939888919593 / 10000000000000000 : ℝ) = - (4409939888919593 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4409939888919593 / 2500000000000000 : ℚ)) - (U := (567570326861223899957 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4409939888919593 / 2500000000000000 : ℝ) ≤ - (567570326861223899957 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2204550546432093 / 5000000000000000 : ℝ)) (q := - (4409939888919593 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4409939888919593 / 10000000000000000 : ℚ)) + (r' := (4409939888919593 / 2500000000000000 : ℚ)) + (U := (-(818724033738776100043 / 1000000000000000000000 : ℚ))) + (U' := (567570326861223899957 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2204550546432093 / 5000000000000000 : ℚ)) + (q := (4409939888919593 / 10000000000000000 : ℚ)) + (U := (-(818724033738776100043 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_4 : Uω (aρ 4) (bρ 4) (28415256387 / 62500000000 : ℝ) ≤ @@ -1289,25 +1140,21 @@ lemma U_427_4 : have hlg : Real.log (4330054851211299 / 10000000000000000 : ℝ) ≤ (-(1046256103529695111109 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4330054851211299 / 10000000000000000 : ℝ) = - (4330054851211299 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4330054851211299 / 2500000000000000 : ℚ)) - (U := (686611847220304888891 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4330054851211299 / 2500000000000000 : ℝ) ≤ - (686611847220304888891 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2163812599256299 / 5000000000000000 : ℝ)) (q := - (4330054851211299 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4330054851211299 / 10000000000000000 : ℚ)) + (r' := (4330054851211299 / 2500000000000000 : ℚ)) + (U := (-(1046256103529695111109 / 1250000000000000000000 : ℚ))) + (U' := (686611847220304888891 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2163812599256299 / 5000000000000000 : ℚ)) + (q := (4330054851211299 / 10000000000000000 : ℚ)) + (U := (-(1046256103529695111109 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_5 : Uω (aρ 5) (bρ 5) (28415256387 / 62500000000 : ℝ) ≤ @@ -1315,25 +1162,21 @@ lemma U_427_5 : have hlg : Real.log (4207966482862127 / 10000000000000000 : ℝ) ≤ (-(2164013955424430799831 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4207966482862127 / 10000000000000000 : ℝ) = - (4207966482862127 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4207966482862127 / 2500000000000000 : ℚ)) - (U := (1301721946075569200169 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4207966482862127 / 2500000000000000 : ℝ) ≤ - (1301721946075569200169 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2100819190574627 / 5000000000000000 : ℝ)) (q := - (4207966482862127 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4207966482862127 / 10000000000000000 : ℚ)) + (r' := (4207966482862127 / 2500000000000000 : ℚ)) + (U := (-(2164013955424430799831 / 2500000000000000000000 : ℚ))) + (U' := (1301721946075569200169 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2100819190574627 / 5000000000000000 : ℚ)) + (q := (4207966482862127 / 10000000000000000 : ℚ)) + (U := (-(2164013955424430799831 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_6 : Uω (aρ 6) (bρ 6) (28415256387 / 62500000000 : ℝ) ≤ @@ -1341,25 +1184,21 @@ lemma U_427_6 : have hlg : Real.log (4031835053215791 / 10000000000000000 : ℝ) ≤ (-(9083634719625875003053 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4031835053215791 / 10000000000000000 : ℝ) = - (4031835053215791 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4031835053215791 / 2500000000000000 : ℚ)) - (U := (4779308886374124996947 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4031835053215791 / 2500000000000000 : ℝ) ≤ - (4779308886374124996947 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2008307948498291 / 5000000000000000 : ℝ)) (q := - (4031835053215791 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4031835053215791 / 10000000000000000 : ℚ)) + (r' := (4031835053215791 / 2500000000000000 : ℚ)) + (U := (-(9083634719625875003053 / 10000000000000000000000 : ℚ))) + (U' := (4779308886374124996947 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2008307948498291 / 5000000000000000 : ℚ)) + (q := (4031835053215791 / 10000000000000000 : ℚ)) + (U := (-(9083634719625875003053 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_7 : Uω (aρ 7) (bρ 7) (28415256387 / 62500000000 : ℝ) ≤ @@ -1367,25 +1206,21 @@ lemma U_427_7 : have hlg : Real.log (1894585111256033 / 5000000000000000 : ℝ) ≤ (-(4852190180007776394843 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1894585111256033 / 5000000000000000 : ℝ) = - (1894585111256033 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1894585111256033 / 1250000000000000 : ℚ)) - (U := (2079281622992223605157 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1894585111256033 / 1250000000000000 : ℝ) ≤ - (2079281622992223605157 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (938736904087283 / 2500000000000000 : ℝ)) (q := - (1894585111256033 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1894585111256033 / 5000000000000000 : ℚ)) + (r' := (1894585111256033 / 1250000000000000 : ℚ)) + (U := (-(4852190180007776394843 / 5000000000000000000000 : ℚ))) + (U' := (2079281622992223605157 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (28415256387 / 62500000000 : ℚ)) + (s := (938736904087283 / 2500000000000000 : ℚ)) + (q := (1894585111256033 / 5000000000000000 : ℚ)) + (U := (-(4852190180007776394843 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_8 : Uω (aρ 8) (bρ 8) (28415256387 / 62500000000 : ℝ) ≤ @@ -1393,25 +1228,21 @@ lemma U_427_8 : have hlg : Real.log (693419807050719 / 2000000000000000 : ℝ) ≤ (-(10592668610642755392833 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (693419807050719 / 2000000000000000 : ℝ) = - (693419807050719 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (693419807050719 / 500000000000000 : ℚ)) - (U := (3270274995357244607167 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (693419807050719 / 500000000000000 : ℝ) ≤ - (3270274995357244607167 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (339434689317219 / 1000000000000000 : ℝ)) (q := - (693419807050719 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (693419807050719 / 2000000000000000 : ℚ)) + (r' := (693419807050719 / 500000000000000 : ℚ)) + (U := (-(10592668610642755392833 / 10000000000000000000000 : ℚ))) + (U' := (3270274995357244607167 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (28415256387 / 62500000000 : ℚ)) + (s := (339434689317219 / 1000000000000000 : ℚ)) + (q := (693419807050719 / 2000000000000000 : ℚ)) + (U := (-(10592668610642755392833 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_9 : Uω (aρ 9) (bρ 9) (28415256387 / 62500000000 : ℝ) ≤ @@ -1419,25 +1250,21 @@ lemma U_427_9 : have hlg : Real.log (6100852096483651 / 20000000000000000 : ℝ) ≤ (-(5936519118310741301741 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6100852096483651 / 20000000000000000 : ℝ) = - (6100852096483651 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6100852096483651 / 5000000000000000 : ℚ)) - (U := (994952684689258698259 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6100852096483651 / 5000000000000000 : ℝ) ≤ - (994952684689258698259 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2901966547508651 / 10000000000000000 : ℝ)) (q := - (6100852096483651 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6100852096483651 / 20000000000000000 : ℚ)) + (r' := (6100852096483651 / 5000000000000000 : ℚ)) + (U := (-(5936519118310741301741 / 5000000000000000000000 : ℚ))) + (U' := (994952684689258698259 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2901966547508651 / 10000000000000000 : ℚ)) + (q := (6100852096483651 / 20000000000000000 : ℚ)) + (U := (-(5936519118310741301741 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_10 : Uω (aρ 10) (bρ 10) (28415256387 / 62500000000 : ℝ) ≤ @@ -1445,26 +1272,21 @@ lemma U_427_10 : have hlg : Real.log (5021314955928739 / 20000000000000000 : ℝ) ≤ (-(3455101075548872166831 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5021314955928739 / 20000000000000000 : ℝ) = - (5021314955928739 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5021314955928739 / 5000000000000000 : ℚ)) - (U := (10634825951127833169 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5021314955928739 / 5000000000000000 : ℝ) ≤ - (10634825951127833169 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2210988440448739 / 10000000000000000 : ℝ)) (q := - (5021314955928739 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5021314955928739 / 20000000000000000 : ℚ)) + (r' := (5021314955928739 / 5000000000000000 : ℚ)) + (U := (-(3455101075548872166831 / 2500000000000000000000 : ℚ))) + (U' := (10634825951127833169 / 2500000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (28415256387 / 62500000000 : ℚ)) + (s := (2210988440448739 / 10000000000000000 : ℚ)) + (q := (5021314955928739 / 20000000000000000 : ℚ)) + (U := (-(3455101075548872166831 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_11 : Uω (aρ 11) (bρ 11) (28415256387 / 62500000000 : ℝ) ≤ @@ -1472,26 +1294,21 @@ lemma U_427_11 : have hlg : Real.log (3432756893474963 / 20000000000000000 : ℝ) ≤ (-(8811842877035075998573 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3432756893474963 / 20000000000000000 : ℝ) = - (3432756893474963 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3432756893474963 / 2500000000000000 : ℚ)) - (U := (1585364827464924001427 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3432756893474963 / 2500000000000000 : ℝ) ≤ - (1585364827464924001427 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1040907004199963 / 10000000000000000 : ℝ)) (q := - (3432756893474963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3432756893474963 / 20000000000000000 : ℚ)) + (r' := (3432756893474963 / 2500000000000000 : ℚ)) + (U := (-(8811842877035075998573 / 5000000000000000000000 : ℚ))) + (U' := (1585364827464924001427 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (28415256387 / 62500000000 : ℚ)) + (s := (1040907004199963 / 10000000000000000 : ℚ)) + (q := (3432756893474963 / 20000000000000000 : ℚ)) + (U := (-(8811842877035075998573 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_427_12 : Uω (aρ 12) (bρ 12) (28415256387 / 62500000000 : ℝ) ≤ @@ -1608,25 +1425,21 @@ lemma U_428_1 : have hlg : Real.log (8977058570418943 / 20000000000000000 : ℝ) ≤ (-(8010599977827891867547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8977058570418943 / 20000000000000000 : ℝ) = - (8977058570418943 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8977058570418943 / 5000000000000000 : ℚ)) - (U := (5852343628172108132453 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8977058570418943 / 5000000000000000 : ℝ) ≤ - (5852343628172108132453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4488493267201443 / 10000000000000000 : ℝ)) (q := - (8977058570418943 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8977058570418943 / 20000000000000000 : ℚ)) + (r' := (8977058570418943 / 5000000000000000 : ℚ)) + (U := (-(8010599977827891867547 / 10000000000000000000000 : ℚ))) + (U' := (5852343628172108132453 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (4488493267201443 / 10000000000000000 : ℚ)) + (q := (8977058570418943 / 20000000000000000 : ℚ)) + (U := (-(8010599977827891867547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_2 : Uω (aρ 2) (bρ 2) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1634,25 +1447,21 @@ lemma U_428_2 : have hlg : Real.log (1116139664398489 / 2500000000000000 : ℝ) ≤ (-(1612829455829885220953 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1116139664398489 / 2500000000000000 : ℝ) = - (1116139664398489 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1116139664398489 / 625000000000000 : ℚ)) - (U := (1159759265370114779047 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1116139664398489 / 625000000000000 : ℝ) ≤ - (1159759265370114779047 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1116080256120103 / 2500000000000000 : ℝ)) (q := - (1116139664398489 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1116139664398489 / 2500000000000000 : ℚ)) + (r' := (1116139664398489 / 625000000000000 : ℚ)) + (U := (-(1612829455829885220953 / 2000000000000000000000 : ℚ))) + (U' := (1159759265370114779047 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (1116080256120103 / 2500000000000000 : ℚ)) + (q := (1116139664398489 / 2500000000000000 : ℚ)) + (U := (-(1612829455829885220953 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_3 : Uω (aρ 3) (bρ 3) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1660,25 +1469,21 @@ lemma U_428_3 : have hlg : Real.log (1104140661524963 / 2500000000000000 : ℝ) ≤ (-(2043058452034576909719 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1104140661524963 / 2500000000000000 : ℝ) = - (1104140661524963 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1104140661524963 / 625000000000000 : ℚ)) - (U := (1422677449465423090281 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1104140661524963 / 625000000000000 : ℝ) ≤ - (1422677449465423090281 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1103931276960551 / 2500000000000000 : ℝ)) (q := - (1104140661524963 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1104140661524963 / 2500000000000000 : ℚ)) + (r' := (1104140661524963 / 625000000000000 : ℚ)) + (U := (-(2043058452034576909719 / 2500000000000000000000 : ℚ))) + (U' := (1422677449465423090281 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (1103931276960551 / 2500000000000000 : ℚ)) + (q := (1104140661524963 / 2500000000000000 : ℚ)) + (U := (-(2043058452034576909719 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_4 : Uω (aρ 4) (bρ 4) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1686,25 +1491,21 @@ lemma U_428_4 : have hlg : Real.log (8673360124821363 / 20000000000000000 : ℝ) ≤ (-(4177379998365973504417 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8673360124821363 / 20000000000000000 : ℝ) = - (8673360124821363 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8673360124821363 / 5000000000000000 : ℚ)) - (U := (2754091804634026495583 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8673360124821363 / 5000000000000000 : ℝ) ≤ - (2754091804634026495583 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4334254121528863 / 10000000000000000 : ℝ)) (q := - (8673360124821363 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8673360124821363 / 20000000000000000 : ℚ)) + (r' := (8673360124821363 / 5000000000000000 : ℚ)) + (U := (-(4177379998365973504417 / 5000000000000000000000 : ℚ))) + (U' := (2754091804634026495583 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (4334254121528863 / 10000000000000000 : ℚ)) + (q := (8673360124821363 / 20000000000000000 : ℚ)) + (U := (-(4177379998365973504417 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_5 : Uω (aρ 5) (bρ 5) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1712,25 +1513,21 @@ lemma U_428_5 : have hlg : Real.log (8429195878384133 / 20000000000000000 : ℝ) ≤ (-(8640308936621060834287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8429195878384133 / 20000000000000000 : ℝ) = - (8429195878384133 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8429195878384133 / 5000000000000000 : ℚ)) - (U := (5222634669378939165713 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8429195878384133 / 5000000000000000 : ℝ) ≤ - (5222634669378939165713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4208279794426633 / 10000000000000000 : ℝ)) (q := - (8429195878384133 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8429195878384133 / 20000000000000000 : ℚ)) + (r' := (8429195878384133 / 5000000000000000 : ℚ)) + (U := (-(8640308936621060834287 / 10000000000000000000000 : ℚ))) + (U' := (5222634669378939165713 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (4208279794426633 / 10000000000000000 : ℚ)) + (q := (8429195878384133 / 20000000000000000 : ℚ)) + (U := (-(8640308936621060834287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_6 : Uω (aρ 6) (bρ 6) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1738,25 +1535,21 @@ lemma U_428_6 : have hlg : Real.log (1615392640135501 / 4000000000000000 : ℝ) ≤ (-(9067163126475235429003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1615392640135501 / 4000000000000000 : ℝ) = - (1615392640135501 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1615392640135501 / 1000000000000000 : ℚ)) - (U := (4795780479524764570997 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1615392640135501 / 1000000000000000 : ℝ) ≤ - (4795780479524764570997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (804657498372001 / 2000000000000000 : ℝ)) (q := - (1615392640135501 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1615392640135501 / 4000000000000000 : ℚ)) + (r' := (1615392640135501 / 1000000000000000 : ℚ)) + (U := (-(9067163126475235429003 / 10000000000000000000000 : ℚ))) + (U' := (4795780479524764570997 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (804657498372001 / 2000000000000000 : ℚ)) + (q := (1615392640135501 / 4000000000000000 : ℚ)) + (U := (-(9067163126475235429003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_7 : Uω (aρ 7) (bρ 7) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1764,25 +1557,21 @@ lemma U_428_7 : have hlg : Real.log (7591703926135517 / 20000000000000000 : ℝ) ≤ (-(9686762106250244520731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7591703926135517 / 20000000000000000 : ℝ) = - (7591703926135517 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7591703926135517 / 5000000000000000 : ℚ)) - (U := (4176181499749755479269 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7591703926135517 / 5000000000000000 : ℝ) ≤ - (4176181499749755479269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3761689598078017 / 10000000000000000 : ℝ)) (q := - (7591703926135517 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7591703926135517 / 20000000000000000 : ℚ)) + (r' := (7591703926135517 / 5000000000000000 : ℚ)) + (U := (-(9686762106250244520731 / 10000000000000000000000 : ℚ))) + (U' := (4176181499749755479269 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (3761689598078017 / 10000000000000000 : ℚ)) + (q := (7591703926135517 / 20000000000000000 : ℚ)) + (U := (-(9686762106250244520731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_8 : Uω (aρ 8) (bρ 8) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1790,24 +1579,21 @@ lemma U_428_8 : have hlg : Real.log (27139548227949 / 78125000000000 : ℝ) ≤ (-(10573180992541647374207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27139548227949 / 78125000000000 : ℝ) = (27139548227949 / 19531250000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27139548227949 / 19531250000000 : ℚ)) - (U := (3289762613458352625793 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27139548227949 / 19531250000000 : ℝ) ≤ - (3289762613458352625793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (850312917409361 / 2500000000000000 : ℝ)) (q := - (27139548227949 / 78125000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27139548227949 / 78125000000000 : ℚ)) + (r' := (27139548227949 / 19531250000000 : ℚ)) + (U := (-(10573180992541647374207 / 10000000000000000000000 : ℚ))) + (U' := (3289762613458352625793 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (850312917409361 / 2500000000000000 : ℚ)) + (q := (27139548227949 / 78125000000000 : ℚ)) + (U := (-(10573180992541647374207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_9 : Uω (aρ 9) (bρ 9) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1815,25 +1601,21 @@ lemma U_428_9 : have hlg : Real.log (1528692740726231 / 5000000000000000 : ℝ) ≤ (-(11850249595588193161761 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1528692740726231 / 5000000000000000 : ℝ) = - (1528692740726231 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1528692740726231 / 1250000000000000 : ℚ)) - (U := (2012694010411806838239 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1528692740726231 / 1250000000000000 : ℝ) ≤ - (2012694010411806838239 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90914497329607 / 312500000000000 : ℝ)) (q := - (1528692740726231 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1528692740726231 / 5000000000000000 : ℚ)) + (r' := (1528692740726231 / 1250000000000000 : ℚ)) + (U := (-(11850249595588193161761 / 10000000000000000000000 : ℚ))) + (U' := (2012694010411806838239 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (90914497329607 / 312500000000000 : ℚ)) + (q := (1528692740726231 / 5000000000000000 : ℚ)) + (U := (-(11850249595588193161761 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_10 : Uω (aρ 10) (bρ 10) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1841,25 +1623,21 @@ lemma U_428_10 : have hlg : Real.log (251817338999233 / 1000000000000000 : ℝ) ≤ (-(6895256495096437908121 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (251817338999233 / 1000000000000000 : ℝ) = - (251817338999233 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (251817338999233 / 250000000000000 : ℚ)) - (U := (36215307903562091879 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (251817338999233 / 250000000000000 : ℝ) ≤ - (36215307903562091879 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27742484564027 / 125000000000000 : ℝ)) (q := - (251817338999233 / 1000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (251817338999233 / 1000000000000000 : ℚ)) + (r' := (251817338999233 / 250000000000000 : ℚ)) + (U := (-(6895256495096437908121 / 5000000000000000000000 : ℚ))) + (U' := (36215307903562091879 / 5000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (27742484564027 / 125000000000000 : ℚ)) + (q := (251817338999233 / 1000000000000000 : ℚ)) + (U := (-(6895256495096437908121 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_11 : Uω (aρ 11) (bρ 11) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -1867,26 +1645,21 @@ lemma U_428_11 : have hlg : Real.log (3454504769179323 / 20000000000000000 : ℝ) ≤ (-(3512106326516641677623 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3454504769179323 / 20000000000000000 : ℝ) = - (3454504769179323 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3454504769179323 / 2500000000000000 : ℚ)) - (U := (646776755283358322377 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3454504769179323 / 2500000000000000 : ℝ) ≤ - (646776755283358322377 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1056033380521823 / 10000000000000000 : ℝ)) (q := - (3454504769179323 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3454504769179323 / 20000000000000000 : ℚ)) + (r' := (3454504769179323 / 2500000000000000 : ℚ)) + (U := (-(3512106326516641677623 / 2000000000000000000000 : ℚ))) + (U' := (646776755283358322377 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1821225008521 / 4000000000000 : ℚ)) + (s := (1056033380521823 / 10000000000000000 : ℚ)) + (q := (3454504769179323 / 20000000000000000 : ℚ)) + (U := (-(3512106326516641677623 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_428_12 : Uω (aρ 12) (bρ 12) (1821225008521 / 4000000000000 : ℝ) ≤ @@ -2003,25 +1776,21 @@ lemma U_429_1 : have hlg : Real.log (2247575418824031 / 5000000000000000 : ℝ) ≤ (-(7995858683509481005467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2247575418824031 / 5000000000000000 : ℝ) = - (2247575418824031 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2247575418824031 / 1250000000000000 : ℚ)) - (U := (5867084922490518994533 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2247575418824031 / 1250000000000000 : ℝ) ≤ - (5867084922490518994533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1123778718174031 / 2500000000000000 : ℝ)) (q := - (2247575418824031 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2247575418824031 / 5000000000000000 : ℚ)) + (r' := (2247575418824031 / 1250000000000000 : ℚ)) + (U := (-(7995858683509481005467 / 10000000000000000000000 : ℚ))) + (U' := (5867084922490518994533 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (1123778718174031 / 2500000000000000 : ℚ)) + (q := (2247575418824031 / 5000000000000000 : ℚ)) + (U := (-(7995858683509481005467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_2 : Uω (aρ 2) (bρ 2) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2029,25 +1798,21 @@ lemma U_429_2 : have hlg : Real.log (8942361017825701 / 20000000000000000 : ℝ) ≤ (-(251541444613192942879 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8942361017825701 / 20000000000000000 : ℝ) = - (8942361017825701 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8942361017825701 / 5000000000000000 : ℚ)) - (U := (181675543074307057121 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8942361017825701 / 5000000000000000 : ℝ) ≤ - (181675543074307057121 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4470943227735701 / 10000000000000000 : ℝ)) (q := - (8942361017825701 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8942361017825701 / 20000000000000000 : ℚ)) + (r' := (8942361017825701 / 5000000000000000 : ℚ)) + (U := (-(251541444613192942879 / 312500000000000000000 : ℚ))) + (U' := (181675543074307057121 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (4470943227735701 / 10000000000000000 : ℚ)) + (q := (8942361017825701 / 20000000000000000 : ℚ)) + (U := (-(251541444613192942879 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_3 : Uω (aρ 3) (bρ 3) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2055,25 +1820,21 @@ lemma U_429_3 : have hlg : Real.log (2211592699756421 / 5000000000000000 : ℝ) ≤ (-(4078624886629356679157 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2211592699756421 / 5000000000000000 : ℝ) = - (2211592699756421 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2211592699756421 / 1250000000000000 : ℚ)) - (U := (2852846916370643320843 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2211592699756421 / 1250000000000000 : ℝ) ≤ - (2852846916370643320843 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1105587278821421 / 2500000000000000 : ℝ)) (q := - (2211592699756421 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2211592699756421 / 5000000000000000 : ℚ)) + (r' := (2211592699756421 / 1250000000000000 : ℚ)) + (U := (-(4078624886629356679157 / 5000000000000000000000 : ℚ))) + (U' := (2852846916370643320843 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (1105587278821421 / 2500000000000000 : ℚ)) + (q := (2211592699756421 / 5000000000000000 : ℚ)) + (U := (-(4078624886629356679157 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_4 : Uω (aρ 4) (bρ 4) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2081,25 +1842,21 @@ lemma U_429_4 : have hlg : Real.log (8686610524559697 / 20000000000000000 : ℝ) ≤ (-(8339494530471527057847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8686610524559697 / 20000000000000000 : ℝ) = - (8686610524559697 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8686610524559697 / 5000000000000000 : ℚ)) - (U := (5523449075528472942153 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8686610524559697 / 5000000000000000 : ℝ) ≤ - (5523449075528472942153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4340883021884697 / 10000000000000000 : ℝ)) (q := - (8686610524559697 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8686610524559697 / 20000000000000000 : ℚ)) + (r' := (8686610524559697 / 5000000000000000 : ℚ)) + (U := (-(8339494530471527057847 / 10000000000000000000000 : ℚ))) + (U' := (5523449075528472942153 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (4340883021884697 / 10000000000000000 : ℚ)) + (q := (8686610524559697 / 20000000000000000 : ℚ)) + (U := (-(8339494530471527057847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_5 : Uω (aρ 5) (bρ 5) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2107,25 +1864,21 @@ lemma U_429_5 : have hlg : Real.log (844245872838181 / 2000000000000000 : ℝ) ≤ (-(8624586883225874612507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (844245872838181 / 2000000000000000 : ℝ) = - (844245872838181 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (844245872838181 / 500000000000000 : ℚ)) - (U := (5238356722774125387493 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (844245872838181 / 500000000000000 : ℝ) ≤ - (5238356722774125387493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421492114504181 / 1000000000000000 : ℝ)) (q := - (844245872838181 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (844245872838181 / 2000000000000000 : ℚ)) + (r' := (844245872838181 / 500000000000000 : ℚ)) + (U := (-(8624586883225874612507 / 10000000000000000000000 : ℚ))) + (U' := (5238356722774125387493 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (421492114504181 / 1000000000000000 : ℚ)) + (q := (844245872838181 / 2000000000000000 : ℚ)) + (U := (-(8624586883225874612507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_6 : Uω (aρ 6) (bρ 6) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2133,25 +1886,21 @@ lemma U_429_6 : have hlg : Real.log (8090256129680071 / 20000000000000000 : ℝ) ≤ (-(4525359412151244814811 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8090256129680071 / 20000000000000000 : ℝ) = - (8090256129680071 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8090256129680071 / 5000000000000000 : ℚ)) - (U := (2406112390848755185189 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8090256129680071 / 5000000000000000 : ℝ) ≤ - (2406112390848755185189 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4029958921480071 / 10000000000000000 : ℝ)) (q := - (8090256129680071 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8090256129680071 / 20000000000000000 : ℚ)) + (r' := (8090256129680071 / 5000000000000000 : ℚ)) + (U := (-(4525359412151244814811 / 5000000000000000000000 : ℚ))) + (U' := (2406112390848755185189 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (4029958921480071 / 10000000000000000 : ℚ)) + (q := (8090256129680071 / 20000000000000000 : ℚ)) + (U := (-(4525359412151244814811 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_7 : Uω (aρ 7) (bρ 7) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2159,25 +1908,21 @@ lemma U_429_7 : have hlg : Real.log (950633372499571 / 2500000000000000 : ℝ) ≤ (-(1933835079997006956291 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (950633372499571 / 2500000000000000 : ℝ) = - (950633372499571 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (950633372499571 / 625000000000000 : ℚ)) - (U := (838753641202993043709 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (950633372499571 / 625000000000000 : ℝ) ≤ - (838753641202993043709 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (471053894069571 / 1250000000000000 : ℝ)) (q := - (950633372499571 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (950633372499571 / 2500000000000000 : ℚ)) + (r' := (950633372499571 / 625000000000000 : ℚ)) + (U := (-(1933835079997006956291 / 2000000000000000000000 : ℚ))) + (U' := (838753641202993043709 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (471053894069571 / 1250000000000000 : ℚ)) + (q := (950633372499571 / 2500000000000000 : ℚ)) + (U := (-(1933835079997006956291 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_8 : Uω (aρ 8) (bρ 8) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2185,25 +1930,21 @@ lemma U_429_8 : have hlg : Real.log (6961249497933711 / 20000000000000000 : ℝ) ≤ (-(5276866446176848011757 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6961249497933711 / 20000000000000000 : ℝ) = - (6961249497933711 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6961249497933711 / 5000000000000000 : ℚ)) - (U := (1654605356823151988243 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6961249497933711 / 5000000000000000 : ℝ) ≤ - (1654605356823151988243 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3408155321833711 / 10000000000000000 : ℝ)) (q := - (6961249497933711 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6961249497933711 / 20000000000000000 : ℚ)) + (r' := (6961249497933711 / 5000000000000000 : ℚ)) + (U := (-(5276866446176848011757 / 5000000000000000000000 : ℚ))) + (U' := (1654605356823151988243 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (3408155321833711 / 10000000000000000 : ℚ)) + (q := (6961249497933711 / 20000000000000000 : ℚ)) + (U := (-(5276866446176848011757 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_9 : Uω (aρ 9) (bρ 9) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2211,25 +1952,21 @@ lemma U_429_9 : have hlg : Real.log (1225737320768777 / 4000000000000000 : ℝ) ≤ (-(5913759015820159389253 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1225737320768777 / 4000000000000000 : ℝ) = - (1225737320768777 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1225737320768777 / 1000000000000000 : ℚ)) - (U := (1017712787179840610747 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1225737320768777 / 1000000000000000 : ℝ) ≤ - (1017712787179840610747 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (583311611220777 / 2000000000000000 : ℝ)) (q := - (1225737320768777 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1225737320768777 / 4000000000000000 : ℚ)) + (r' := (1225737320768777 / 1000000000000000 : ℚ)) + (U := (-(5913759015820159389253 / 5000000000000000000000 : ℚ))) + (U' := (1017712787179840610747 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (583311611220777 / 2000000000000000 : ℚ)) + (q := (1225737320768777 / 4000000000000000 : ℚ)) + (U := (-(5913759015820159389253 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_10 : Uω (aρ 10) (bρ 10) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2237,26 +1974,21 @@ lemma U_429_10 : have hlg : Real.log (2525683267082197 / 10000000000000000 : ℝ) ≤ (-(1720091831909998787893 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2525683267082197 / 10000000000000000 : ℝ) = - (2525683267082197 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2525683267082197 / 2500000000000000 : ℚ)) - (U := (12776118840001212107 / 1250000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2525683267082197 / 2500000000000000 : ℝ) ≤ - (12776118840001212107 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1113898509959697 / 5000000000000000 : ℝ)) (q := - (2525683267082197 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2525683267082197 / 10000000000000000 : ℚ)) + (r' := (2525683267082197 / 2500000000000000 : ℚ)) + (U := (-(1720091831909998787893 / 1250000000000000000000 : ℚ))) + (U' := (12776118840001212107 / 1250000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (1113898509959697 / 5000000000000000 : ℚ)) + (q := (2525683267082197 / 10000000000000000 : ℚ)) + (U := (-(1720091831909998787893 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_11 : Uω (aρ 11) (bρ 11) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2264,25 +1996,21 @@ lemma U_429_11 : have hlg : Real.log (434509994437601 / 2500000000000000 : ℝ) ≤ (-(17498270634776701115959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (434509994437601 / 2500000000000000 : ℝ) = - (434509994437601 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (434509994437601 / 312500000000000 : ℚ)) - (U := (3296144774223298884041 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (434509994437601 / 312500000000000 : ℝ) ≤ - (3296144774223298884041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (133873383432601 / 1250000000000000 : ℝ)) (q := - (434509994437601 / 2500000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (434509994437601 / 2500000000000000 : ℚ)) + (r' := (434509994437601 / 312500000000000 : ℚ)) + (U := (-(17498270634776701115959 / 10000000000000000000000 : ℚ))) + (U' := (3296144774223298884041 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (911936804137 / 2000000000000 : ℚ)) + (s := (133873383432601 / 1250000000000000 : ℚ)) + (q := (434509994437601 / 2500000000000000 : ℚ)) + (U := (-(17498270634776701115959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_429_12 : Uω (aρ 12) (bρ 12) (911936804137 / 2000000000000 : ℝ) ≤ @@ -2399,25 +2127,21 @@ lemma U_430_1 : have hlg : Real.log (4501772389930573 / 10000000000000000 : ℝ) ≤ (-(3990569544065491910013 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4501772389930573 / 10000000000000000 : ℝ) = - (4501772389930573 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4501772389930573 / 2500000000000000 : ℚ)) - (U := (2940902258934508089987 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4501772389930573 / 2500000000000000 : ℝ) ≤ - (2940902258934508089987 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2250868238939323 / 5000000000000000 : ℝ)) (q := - (4501772389930573 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4501772389930573 / 10000000000000000 : ℚ)) + (r' := (4501772389930573 / 2500000000000000 : ℚ)) + (U := (-(3990569544065491910013 / 5000000000000000000000 : ℚ))) + (U' := (2940902258934508089987 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (2250868238939323 / 5000000000000000 : ℚ)) + (q := (4501772389930573 / 10000000000000000 : ℚ)) + (U := (-(3990569544065491910013 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_2 : Uω (aρ 2) (bρ 2) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2425,25 +2149,21 @@ lemma U_430_2 : have hlg : Real.log (8955604718381581 / 20000000000000000 : ℝ) ≤ (-(1004315889034024038327 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8955604718381581 / 20000000000000000 : ℝ) = - (8955604718381581 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8955604718381581 / 5000000000000000 : ℚ)) - (U := (728552061715975961673 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8955604718381581 / 5000000000000000 : ℝ) ≤ - (728552061715975961673 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4477565428909081 / 10000000000000000 : ℝ)) (q := - (8955604718381581 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8955604718381581 / 20000000000000000 : ℚ)) + (r' := (8955604718381581 / 5000000000000000 : ℚ)) + (U := (-(1004315889034024038327 / 1250000000000000000000 : ℚ))) + (U' := (728552061715975961673 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (4477565428909081 / 10000000000000000 : ℚ)) + (q := (8955604718381581 / 20000000000000000 : ℚ)) + (U := (-(1004315889034024038327 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_3 : Uω (aρ 3) (bρ 3) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2451,25 +2171,21 @@ lemma U_430_3 : have hlg : Real.log (2214904074587733 / 5000000000000000 : ℝ) ≤ (-(8142288165387616772923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2214904074587733 / 5000000000000000 : ℝ) = - (2214904074587733 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2214904074587733 / 1250000000000000 : ℚ)) - (U := (5720655440612383227077 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2214904074587733 / 1250000000000000 : ℝ) ≤ - (5720655440612383227077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (276810819701777 / 625000000000000 : ℝ)) (q := - (2214904074587733 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2214904074587733 / 5000000000000000 : ℚ)) + (r' := (2214904074587733 / 1250000000000000 : ℚ)) + (U := (-(8142288165387616772923 / 10000000000000000000000 : ℚ))) + (U' := (5720655440612383227077 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (276810819701777 / 625000000000000 : ℚ)) + (q := (2214904074587733 / 5000000000000000 : ℚ)) + (U := (-(8142288165387616772923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_4 : Uω (aρ 4) (bρ 4) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2477,25 +2193,21 @@ lemma U_430_4 : have hlg : Real.log (4349930450870627 / 10000000000000000 : ℝ) ≤ (-(4162126179034898229433 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4349930450870627 / 10000000000000000 : ℝ) = - (4349930450870627 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4349930450870627 / 2500000000000000 : ℚ)) - (U := (2769345623965101770567 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4349930450870627 / 2500000000000000 : ℝ) ≤ - (2769345623965101770567 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2173755949841877 / 5000000000000000 : ℝ)) (q := - (4349930450870627 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4349930450870627 / 10000000000000000 : ℚ)) + (r' := (4349930450870627 / 2500000000000000 : ℚ)) + (U := (-(4162126179034898229433 / 5000000000000000000000 : ℚ))) + (U' := (2769345623965101770567 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (2173755949841877 / 5000000000000000 : ℚ)) + (q := (4349930450870627 / 10000000000000000 : ℚ)) + (U := (-(4162126179034898229433 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_5 : Uω (aρ 5) (bρ 5) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2503,25 +2215,21 @@ lemma U_430_5 : have hlg : Real.log (4227860758006511 / 10000000000000000 : ℝ) ≤ (-(2152222395771836180129 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4227860758006511 / 10000000000000000 : ℝ) = - (4227860758006511 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4227860758006511 / 2500000000000000 : ℚ)) - (U := (1313513505728163819871 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4227860758006511 / 2500000000000000 : ℝ) ≤ - (1313513505728163819871 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2110781216645261 / 5000000000000000 : ℝ)) (q := - (4227860758006511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4227860758006511 / 10000000000000000 : ℚ)) + (r' := (4227860758006511 / 2500000000000000 : ℚ)) + (U := (-(2152222395771836180129 / 2500000000000000000000 : ℚ))) + (U' := (1313513505728163819871 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (2110781216645261 / 5000000000000000 : ℚ)) + (q := (4227860758006511 / 10000000000000000 : ℚ)) + (U := (-(2152222395771836180129 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_6 : Uω (aρ 6) (bρ 6) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2529,25 +2237,21 @@ lemma U_430_6 : have hlg : Real.log (8103548894258587 / 20000000000000000 : ℝ) ≤ (-(9034301722152087805031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8103548894258587 / 20000000000000000 : ℝ) = - (8103548894258587 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8103548894258587 / 5000000000000000 : ℚ)) - (U := (4828641883847912194969 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8103548894258587 / 5000000000000000 : ℝ) ≤ - (4828641883847912194969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4036630186676087 / 10000000000000000 : ℝ)) (q := - (8103548894258587 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8103548894258587 / 20000000000000000 : ℚ)) + (r' := (8103548894258587 / 5000000000000000 : ℚ)) + (U := (-(9034301722152087805031 / 10000000000000000000000 : ℚ))) + (U' := (4828641883847912194969 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (4036630186676087 / 10000000000000000 : ℚ)) + (q := (8103548894258587 / 20000000000000000 : ℚ)) + (U := (-(9034301722152087805031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_7 : Uω (aρ 7) (bρ 7) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2555,25 +2259,21 @@ lemma U_430_7 : have hlg : Real.log (1523685921779237 / 4000000000000000 : ℝ) ≤ (-(2412905031614942433679 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1523685921779237 / 4000000000000000 : ℝ) = - (1523685921779237 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1523685921779237 / 1000000000000000 : ℚ)) - (U := (1052830869885057566321 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1523685921779237 / 1000000000000000 : ℝ) ≤ - (1052830869885057566321 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (755034456414737 / 2000000000000000 : ℝ)) (q := - (1523685921779237 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1523685921779237 / 4000000000000000 : ℚ)) + (r' := (1523685921779237 / 1000000000000000 : ℚ)) + (U := (-(2412905031614942433679 / 2500000000000000000000 : ℚ))) + (U' := (1052830869885057566321 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (755034456414737 / 2000000000000000 : ℚ)) + (q := (1523685921779237 / 4000000000000000 : ℚ)) + (U := (-(2412905031614942433679 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_8 : Uω (aρ 8) (bρ 8) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2581,25 +2281,21 @@ lemma U_430_8 : have hlg : Real.log (6974773532061733 / 20000000000000000 : ℝ) ≤ (-(2633581035938500616407 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6974773532061733 / 20000000000000000 : ℝ) = - (6974773532061733 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6974773532061733 / 5000000000000000 : ℚ)) - (U := (832154865561499383593 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6974773532061733 / 5000000000000000 : ℝ) ≤ - (832154865561499383593 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3415057856579233 / 10000000000000000 : ℝ)) (q := - (6974773532061733 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6974773532061733 / 20000000000000000 : ℚ)) + (r' := (6974773532061733 / 5000000000000000 : ℚ)) + (U := (-(2633581035938500616407 / 2500000000000000000000 : ℚ))) + (U' := (832154865561499383593 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (3415057856579233 / 10000000000000000 : ℚ)) + (q := (6974773532061733 / 20000000000000000 : ℚ)) + (U := (-(2633581035938500616407 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_9 : Uω (aρ 9) (bρ 9) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2607,25 +2303,21 @@ lemma U_430_9 : have hlg : Real.log (191956220107513 / 625000000000000 : ℝ) ≤ (-(11804843234626741708411 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (191956220107513 / 625000000000000 : ℝ) = - (191956220107513 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (191956220107513 / 156250000000000 : ℚ)) - (U := (2058100371373258291589 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (191956220107513 / 156250000000000 : ℝ) ≤ - (2058100371373258291589 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (730962249079479 / 2500000000000000 : ℝ)) (q := - (191956220107513 / 625000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (191956220107513 / 625000000000000 : ℚ)) + (r' := (191956220107513 / 156250000000000 : ℚ)) + (U := (-(11804843234626741708411 / 10000000000000000000000 : ℚ))) + (U' := (2058100371373258291589 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (730962249079479 / 2500000000000000 : ℚ)) + (q := (191956220107513 / 625000000000000 : ℚ)) + (U := (-(11804843234626741708411 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_10 : Uω (aρ 10) (bρ 10) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2633,25 +2325,21 @@ lemma U_430_10 : have hlg : Real.log (101327487089151 / 400000000000000 : ℝ) ≤ (-(13731068287134637534901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (101327487089151 / 400000000000000 : ℝ) = - (101327487089151 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (101327487089151 / 100000000000000 : ℚ)) - (U := (131875318865362465099 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (101327487089151 / 100000000000000 : ℝ) ≤ - (131875318865362465099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44723666816601 / 200000000000000 : ℝ)) (q := - (101327487089151 / 400000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (101327487089151 / 400000000000000 : ℚ)) + (r' := (101327487089151 / 100000000000000 : ℚ)) + (U := (-(13731068287134637534901 / 10000000000000000000000 : ℚ))) + (U' := (131875318865362465099 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (44723666816601 / 200000000000000 : ℚ)) + (q := (101327487089151 / 400000000000000 : ℚ)) + (U := (-(13731068287134637534901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_11 : Uω (aρ 11) (bρ 11) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2659,26 +2347,21 @@ lemma U_430_11 : have hlg : Real.log (3497489587483911 / 20000000000000000 : ℝ) ≤ (-(17436868223522066249077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3497489587483911 / 20000000000000000 : ℝ) = - (3497489587483911 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3497489587483911 / 2500000000000000 : ℚ)) - (U := (3357547185477933750923 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3497489587483911 / 2500000000000000 : ℝ) ≤ - (3357547185477933750923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1085775200061411 / 10000000000000000 : ℝ)) (q := - (3497489587483911 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3497489587483911 / 20000000000000000 : ℚ)) + (r' := (3497489587483911 / 2500000000000000 : ℚ)) + (U := (-(17436868223522066249077 / 10000000000000000000000 : ℚ))) + (U' := (3357547185477933750923 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1826522208027 / 4000000000000 : ℚ)) + (s := (1085775200061411 / 10000000000000000 : ℚ)) + (q := (3497489587483911 / 20000000000000000 : ℚ)) + (U := (-(17436868223522066249077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_430_12 : Uω (aρ 12) (bρ 12) (1826522208027 / 4000000000000 : ℝ) ≤ @@ -2795,25 +2478,21 @@ lemma U_431_1 : have hlg : Real.log (4508393942057693 / 10000000000000000 : ℝ) ≤ (-(7966441127904307519531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4508393942057693 / 10000000000000000 : ℝ) = - (4508393942057693 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4508393942057693 / 2500000000000000 : ℚ)) - (U := (5896502478095692480469 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4508393942057693 / 2500000000000000 : ℝ) ≤ - (5896502478095692480469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2254179041375193 / 5000000000000000 : ℝ)) (q := - (4508393942057693 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4508393942057693 / 10000000000000000 : ℚ)) + (r' := (4508393942057693 / 2500000000000000 : ℚ)) + (U := (-(7966441127904307519531 / 10000000000000000000000 : ℚ))) + (U' := (5896502478095692480469 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (91458540389 / 200000000000 : ℚ)) + (s := (2254179041375193 / 5000000000000000 : ℚ)) + (q := (4508393942057693 / 10000000000000000 : ℚ)) + (U := (-(7966441127904307519531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_2 : Uω (aρ 2) (bρ 2) (91458540389 / 200000000000 : ℝ) ≤ @@ -2821,25 +2500,21 @@ lemma U_431_2 : have hlg : Real.log (1121106052108097 / 2500000000000000 : ℝ) ≤ (-(4009874934127237774067 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1121106052108097 / 2500000000000000 : ℝ) = - (1121106052108097 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1121106052108097 / 625000000000000 : ℚ)) - (U := (2921596868872762225933 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1121106052108097 / 625000000000000 : ℝ) ≤ - (2921596868872762225933 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (280261726750611 / 625000000000000 : ℝ)) (q := - (1121106052108097 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1121106052108097 / 2500000000000000 : ℚ)) + (r' := (1121106052108097 / 625000000000000 : ℚ)) + (U := (-(4009874934127237774067 / 5000000000000000000000 : ℚ))) + (U' := (2921596868872762225933 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (91458540389 / 200000000000 : ℚ)) + (s := (280261726750611 / 625000000000000 : ℚ)) + (q := (1121106052108097 / 2500000000000000 : ℚ)) + (U := (-(4009874934127237774067 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_3 : Uω (aρ 3) (bρ 3) (91458540389 / 200000000000 : ℝ) ≤ @@ -2847,25 +2522,21 @@ lemma U_431_3 : have hlg : Real.log (8872861790209053 / 20000000000000000 : ℝ) ≤ (-(4063674458732947917093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8872861790209053 / 20000000000000000 : ℝ) = - (8872861790209053 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8872861790209053 / 5000000000000000 : ℚ)) - (U := (2867797344267052082907 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8872861790209053 / 5000000000000000 : ℝ) ≤ - (2867797344267052082907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4435597107704053 / 10000000000000000 : ℝ)) (q := - (8872861790209053 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8872861790209053 / 20000000000000000 : ℚ)) + (r' := (8872861790209053 / 5000000000000000 : ℚ)) + (U := (-(4063674458732947917093 / 5000000000000000000000 : ℚ))) + (U' := (2867797344267052082907 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (91458540389 / 200000000000 : ℚ)) + (s := (4435597107704053 / 10000000000000000 : ℚ)) + (q := (8872861790209053 / 20000000000000000 : ℚ)) + (U := (-(4063674458732947917093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_4 : Uω (aρ 4) (bρ 4) (91458540389 / 200000000000 : ℝ) ≤ @@ -2873,25 +2544,21 @@ lemma U_431_4 : have hlg : Real.log (4356555628234529 / 10000000000000000 : ℝ) ≤ (-(1661806681693453128021 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4356555628234529 / 10000000000000000 : ℝ) = - (4356555628234529 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4356555628234529 / 2500000000000000 : ℚ)) - (U := (1110782039506546871979 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4356555628234529 / 2500000000000000 : ℝ) ≤ - (1110782039506546871979 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2177070377514529 / 5000000000000000 : ℝ)) (q := - (4356555628234529 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4356555628234529 / 10000000000000000 : ℚ)) + (r' := (4356555628234529 / 2500000000000000 : ℚ)) + (U := (-(1661806681693453128021 / 2000000000000000000000 : ℚ))) + (U' := (1110782039506546871979 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (91458540389 / 200000000000 : ℚ)) + (s := (2177070377514529 / 5000000000000000 : ℚ)) + (q := (4356555628234529 / 10000000000000000 : ℚ)) + (U := (-(1661806681693453128021 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_5 : Uω (aρ 5) (bρ 5) (91458540389 / 200000000000 : ℝ) ≤ @@ -2899,25 +2566,21 @@ lemma U_431_5 : have hlg : Real.log (169379684831433 / 400000000000000 : ℝ) ≤ (-(8593216958152678828791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (169379684831433 / 400000000000000 : ℝ) = - (169379684831433 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (169379684831433 / 100000000000000 : ℚ)) - (U := (5269726647847321171209 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (169379684831433 / 100000000000000 : ℝ) ≤ - (5269726647847321171209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84564073189333 / 200000000000000 : ℝ)) (q := - (169379684831433 / 400000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (169379684831433 / 400000000000000 : ℚ)) + (r' := (169379684831433 / 100000000000000 : ℚ)) + (U := (-(8593216958152678828791 / 10000000000000000000000 : ℚ))) + (U' := (5269726647847321171209 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (91458540389 / 200000000000 : ℚ)) + (s := (84564073189333 / 200000000000000 : ℚ)) + (q := (169379684831433 / 400000000000000 : ℚ)) + (U := (-(8593216958152678828791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_6 : Uω (aρ 6) (bρ 6) (91458540389 / 200000000000 : ℝ) ≤ @@ -2925,25 +2588,21 @@ lemma U_431_6 : have hlg : Real.log (8116841495226927 / 20000000000000000 : ℝ) ≤ (-(9017911729525724670809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8116841495226927 / 20000000000000000 : ℝ) = - (8116841495226927 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8116841495226927 / 5000000000000000 : ℚ)) - (U := (4845031876474275329191 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8116841495226927 / 5000000000000000 : ℝ) ≤ - (4845031876474275329191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4043301288261927 / 10000000000000000 : ℝ)) (q := - (8116841495226927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8116841495226927 / 20000000000000000 : ℚ)) + (r' := (8116841495226927 / 5000000000000000 : ℚ)) + (U := (-(9017911729525724670809 / 10000000000000000000000 : ℚ))) + (U' := (4845031876474275329191 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (91458540389 / 200000000000 : ℚ)) + (s := (4043301288261927 / 10000000000000000 : ℚ)) + (q := (8116841495226927 / 20000000000000000 : ℚ)) + (U := (-(9017911729525724670809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_7 : Uω (aρ 7) (bρ 7) (91458540389 / 200000000000 : ℝ) ≤ @@ -2951,25 +2610,21 @@ lemma U_431_7 : have hlg : Real.log (3815895907553403 / 10000000000000000 : ℝ) ≤ (-(38536384686198961727 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3815895907553403 / 10000000000000000 : ℝ) = - (3815895907553403 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3815895907553403 / 2500000000000000 : ℚ)) - (U := (16915389737801038273 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3815895907553403 / 2500000000000000 : ℝ) ≤ - (16915389737801038273 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1890956494450903 / 5000000000000000 : ℝ)) (q := - (3815895907553403 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3815895907553403 / 10000000000000000 : ℚ)) + (r' := (3815895907553403 / 2500000000000000 : ℚ)) + (U := (-(38536384686198961727 / 40000000000000000000 : ℚ))) + (U' := (16915389737801038273 / 40000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (91458540389 / 200000000000 : ℚ)) + (s := (1890956494450903 / 5000000000000000 : ℚ)) + (q := (3815895907553403 / 10000000000000000 : ℚ)) + (U := (-(38536384686198961727 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_8 : Uω (aρ 8) (bρ 8) (91458540389 / 200000000000 : ℝ) ≤ @@ -2977,25 +2632,21 @@ lemma U_431_8 : have hlg : Real.log (436768528468821 / 1250000000000000 : ℝ) ≤ (-(10514954581502450073807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (436768528468821 / 1250000000000000 : ℝ) = - (436768528468821 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (436768528468821 / 312500000000000 : ℚ)) - (U := (3347989024497549926193 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (436768528468821 / 312500000000000 : ℝ) ≤ - (3347989024497549926193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (427744910079517 / 1250000000000000 : ℝ)) (q := - (436768528468821 / 1250000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (436768528468821 / 1250000000000000 : ℚ)) + (r' := (436768528468821 / 312500000000000 : ℚ)) + (U := (-(10514954581502450073807 / 10000000000000000000000 : ℚ))) + (U' := (3347989024497549926193 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (91458540389 / 200000000000 : ℚ)) + (s := (427744910079517 / 1250000000000000 : ℚ)) + (q := (436768528468821 / 1250000000000000 : ℚ)) + (U := (-(10514954581502450073807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_9 : Uω (aρ 9) (bρ 9) (91458540389 / 200000000000 : ℝ) ≤ @@ -3003,25 +2654,21 @@ lemma U_431_9 : have hlg : Real.log (1539127076395919 / 5000000000000000 : ℝ) ≤ (-(5891112448543313736457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1539127076395919 / 5000000000000000 : ℝ) = - (1539127076395919 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1539127076395919 / 1250000000000000 : ℚ)) - (U := (1040359354456686263543 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1539127076395919 / 1250000000000000 : ℝ) ≤ - (1040359354456686263543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (732784189769669 / 2500000000000000 : ℝ)) (q := - (1539127076395919 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1539127076395919 / 5000000000000000 : ℚ)) + (r' := (1539127076395919 / 1250000000000000 : ℚ)) + (U := (-(5891112448543313736457 / 5000000000000000000000 : ℚ))) + (U' := (1040359354456686263543 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (91458540389 / 200000000000 : ℚ)) + (s := (732784189769669 / 2500000000000000 : ℚ)) + (q := (1539127076395919 / 5000000000000000 : ℚ)) + (U := (-(5891112448543313736457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_10 : Uω (aρ 10) (bρ 10) (91458540389 / 200000000000 : ℝ) ≤ @@ -3029,25 +2676,21 @@ lemma U_431_10 : have hlg : Real.log (635171296828693 / 2500000000000000 : ℝ) ≤ (-(13701512890367255710259 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (635171296828693 / 2500000000000000 : ℝ) = - (635171296828693 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (635171296828693 / 625000000000000 : ℚ)) - (U := (161430715632744289741 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (635171296828693 / 625000000000000 : ℝ) ≤ - (161430715632744289741 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (280569732702443 / 1250000000000000 : ℝ)) (q := - (635171296828693 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (635171296828693 / 2500000000000000 : ℚ)) + (r' := (635171296828693 / 625000000000000 : ℚ)) + (U := (-(13701512890367255710259 / 10000000000000000000000 : ℚ))) + (U' := (161430715632744289741 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (91458540389 / 200000000000 : ℚ)) + (s := (280569732702443 / 1250000000000000 : ℚ)) + (q := (635171296828693 / 2500000000000000 : ℚ)) + (U := (-(13701512890367255710259 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_11 : Uω (aρ 11) (bρ 11) (91458540389 / 200000000000 : ℝ) ≤ @@ -3055,24 +2698,21 @@ lemma U_431_11 : have hlg : Real.log (109960635615987 / 625000000000000 : ℝ) ≤ (-(17376292052470984479999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (109960635615987 / 625000000000000 : ℝ) = (109960635615987 / 78125000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (109960635615987 / 78125000000000 : ℚ)) - (U := (3418123356529015520001 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (109960635615987 / 78125000000000 : ℝ) ≤ - (3418123356529015520001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (137550556613323 / 1250000000000000 : ℝ)) (q := - (109960635615987 / 625000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (109960635615987 / 625000000000000 : ℚ)) + (r' := (109960635615987 / 78125000000000 : ℚ)) + (U := (-(17376292052470984479999 / 10000000000000000000000 : ℚ))) + (U' := (3418123356529015520001 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (91458540389 / 200000000000 : ℚ)) + (s := (137550556613323 / 1250000000000000 : ℚ)) + (q := (109960635615987 / 625000000000000 : ℚ)) + (U := (-(17376292052470984479999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_431_12 : Uω (aρ 12) (bρ 12) (91458540389 / 200000000000 : ℝ) ≤ @@ -3188,25 +2828,21 @@ lemma U_432_1 : have hlg : Real.log (903003098806021 / 2000000000000000 : ℝ) ≤ (-(7951764739322229786499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (903003098806021 / 2000000000000000 : ℝ) = - (903003098806021 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (903003098806021 / 500000000000000 : ℚ)) - (U := (5911178866677770213501 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (903003098806021 / 500000000000000 : ℝ) ≤ - (5911178866677770213501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (451497968731271 / 1000000000000000 : ℝ)) (q := - (903003098806021 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (903003098806021 / 2000000000000000 : ℚ)) + (r' := (903003098806021 / 500000000000000 : ℚ)) + (U := (-(7951764739322229786499 / 10000000000000000000000 : ℚ))) + (U' := (5911178866677770213501 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (451497968731271 / 1000000000000000 : ℚ)) + (q := (903003098806021 / 2000000000000000 : ℚ)) + (U := (-(7951764739322229786499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_2 : Uω (aρ 2) (bρ 2) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3214,25 +2850,21 @@ lemma U_432_2 : have hlg : Real.log (1796418422656891 / 4000000000000000 : ℝ) ≤ (-(1000624303876394457959 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1796418422656891 / 4000000000000000 : ℝ) = - (1796418422656891 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1796418422656891 / 1000000000000000 : ℚ)) - (U := (732243646873605542041 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1796418422656891 / 1000000000000000 : ℝ) ≤ - (732243646873605542041 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (898161965009391 / 2000000000000000 : ℝ)) (q := - (1796418422656891 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1796418422656891 / 4000000000000000 : ℚ)) + (r' := (1796418422656891 / 1000000000000000 : ℚ)) + (U := (-(1000624303876394457959 / 1250000000000000000000 : ℚ))) + (U' := (732243646873605542041 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (898161965009391 / 2000000000000000 : ℚ)) + (q := (1796418422656891 / 4000000000000000 : ℚ)) + (U := (-(1000624303876394457959 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_3 : Uω (aρ 3) (bρ 3) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3240,25 +2872,21 @@ lemma U_432_3 : have hlg : Real.log (8886107274633451 / 20000000000000000 : ℝ) ≤ (-(31689187354433060421 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8886107274633451 / 20000000000000000 : ℝ) = - (8886107274633451 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8886107274633451 / 5000000000000000 : ℚ)) - (U := (22462936106504439579 / 39062500000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8886107274633451 / 5000000000000000 : ℝ) ≤ - (22462936106504439579 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4442221092745951 / 10000000000000000 : ℝ)) (q := - (8886107274633451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8886107274633451 / 20000000000000000 : ℚ)) + (r' := (8886107274633451 / 5000000000000000 : ℚ)) + (U := (-(31689187354433060421 / 39062500000000000000 : ℚ))) + (U' := (22462936106504439579 / 39062500000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (4442221092745951 / 10000000000000000 : ℚ)) + (q := (8886107274633451 / 20000000000000000 : ℚ)) + (U := (-(31689187354433060421 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_4 : Uω (aρ 4) (bρ 4) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3266,25 +2894,21 @@ lemma U_432_4 : have hlg : Real.log (1745272317769101 / 4000000000000000 : ℝ) ≤ (-(8293837610929466732469 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1745272317769101 / 4000000000000000 : ℝ) = - (1745272317769101 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1745272317769101 / 1000000000000000 : ℚ)) - (U := (5569105995070533267531 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1745272317769101 / 1000000000000000 : ℝ) ≤ - (5569105995070533267531 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (872153917604601 / 2000000000000000 : ℝ)) (q := - (1745272317769101 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1745272317769101 / 4000000000000000 : ℚ)) + (r' := (1745272317769101 / 1000000000000000 : ℚ)) + (U := (-(8293837610929466732469 / 10000000000000000000000 : ℚ))) + (U' := (5569105995070533267531 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (872153917604601 / 2000000000000000 : ℚ)) + (q := (1745272317769101 / 4000000000000000 : ℚ)) + (U := (-(8293837610929466732469 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_5 : Uω (aρ 5) (bρ 5) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3292,25 +2916,21 @@ lemma U_432_5 : have hlg : Real.log (8482246905349727 / 20000000000000000 : ℝ) ≤ (-(4288784465369381867481 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8482246905349727 / 20000000000000000 : ℝ) = - (8482246905349727 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8482246905349727 / 5000000000000000 : ℚ)) - (U := (2642687337630618132519 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8482246905349727 / 5000000000000000 : ℝ) ≤ - (2642687337630618132519 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4234844823862227 / 10000000000000000 : ℝ)) (q := - (8482246905349727 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8482246905349727 / 20000000000000000 : ℚ)) + (r' := (8482246905349727 / 5000000000000000 : ℚ)) + (U := (-(4288784465369381867481 / 5000000000000000000000 : ℚ))) + (U' := (2642687337630618132519 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (4234844823862227 / 10000000000000000 : ℚ)) + (q := (8482246905349727 / 20000000000000000 : ℚ)) + (U := (-(4288784465369381867481 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_6 : Uω (aρ 6) (bρ 6) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3318,25 +2938,21 @@ lemma U_432_6 : have hlg : Real.log (2032533483348397 / 5000000000000000 : ℝ) ≤ (-(2250387189094811231179 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2032533483348397 / 5000000000000000 : ℝ) = - (2032533483348397 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2032533483348397 / 1250000000000000 : ℚ)) - (U := (1215348712405188768821 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2032533483348397 / 1250000000000000 : ℝ) ≤ - (1215348712405188768821 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (506246528380761 / 1250000000000000 : ℝ)) (q := - (2032533483348397 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2032533483348397 / 5000000000000000 : ℚ)) + (r' := (2032533483348397 / 1250000000000000 : ℚ)) + (U := (-(2250387189094811231179 / 2500000000000000000000 : ℚ))) + (U' := (1215348712405188768821 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (506246528380761 / 1250000000000000 : ℚ)) + (q := (2032533483348397 / 5000000000000000 : ℚ)) + (U := (-(2250387189094811231179 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_7 : Uω (aρ 7) (bρ 7) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3344,25 +2960,21 @@ lemma U_432_7 : have hlg : Real.log (1529030720176911 / 4000000000000000 : ℝ) ≤ (-(4808301710880464751429 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1529030720176911 / 4000000000000000 : ℝ) = - (1529030720176911 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1529030720176911 / 1000000000000000 : ℚ)) - (U := (2123170092119535248571 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1529030720176911 / 1000000000000000 : ℝ) ≤ - (2123170092119535248571 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (757730655059411 / 2000000000000000 : ℝ)) (q := - (1529030720176911 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1529030720176911 / 4000000000000000 : ℚ)) + (r' := (1529030720176911 / 1000000000000000 : ℚ)) + (U := (-(4808301710880464751429 / 5000000000000000000000 : ℚ))) + (U' := (2123170092119535248571 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (757730655059411 / 2000000000000000 : ℚ)) + (q := (1529030720176911 / 4000000000000000 : ℚ)) + (U := (-(4808301710880464751429 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_8 : Uω (aρ 8) (bρ 8) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3370,25 +2982,21 @@ lemma U_432_8 : have hlg : Real.log (1750454568739631 / 5000000000000000 : ℝ) ≤ (-(10495624041434001507059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1750454568739631 / 5000000000000000 : ℝ) = - (1750454568739631 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1750454568739631 / 1250000000000000 : ℚ)) - (U := (3367319564565998492941 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1750454568739631 / 1250000000000000 : ℝ) ≤ - (3367319564565998492941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (214303725044439 / 625000000000000 : ℝ)) (q := - (1750454568739631 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1750454568739631 / 5000000000000000 : ℚ)) + (r' := (1750454568739631 / 1250000000000000 : ℚ)) + (U := (-(10495624041434001507059 / 10000000000000000000000 : ℚ))) + (U' := (3367319564565998492941 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (214303725044439 / 625000000000000 : ℚ)) + (q := (1750454568739631 / 5000000000000000 : ℚ)) + (U := (-(10495624041434001507059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_9 : Uω (aρ 9) (bρ 9) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3396,25 +3004,21 @@ lemma U_432_9 : have hlg : Real.log (6170414413915467 / 20000000000000000 : ℝ) ≤ (-(2939915678554231113423 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6170414413915467 / 20000000000000000 : ℝ) = - (6170414413915467 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6170414413915467 / 5000000000000000 : ℚ)) - (U := (525820222945768886577 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6170414413915467 / 5000000000000000 : ℝ) ≤ - (525820222945768886577 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2938421368027967 / 10000000000000000 : ℝ)) (q := - (6170414413915467 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6170414413915467 / 20000000000000000 : ℚ)) + (r' := (6170414413915467 / 5000000000000000 : ℚ)) + (U := (-(2939915678554231113423 / 2500000000000000000000 : ℚ))) + (U' := (525820222945768886577 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (2938421368027967 / 10000000000000000 : ℚ)) + (q := (6170414413915467 / 20000000000000000 : ℚ)) + (U := (-(2939915678554231113423 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_10 : Uω (aρ 10) (bρ 10) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3422,26 +3026,21 @@ lemma U_432_10 : have hlg : Real.log (5096354726270043 / 20000000000000000 : ℝ) ≤ (-(13672067484211088375381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5096354726270043 / 20000000000000000 : ℝ) = - (5096354726270043 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5096354726270043 / 5000000000000000 : ℚ)) - (U := (190876121788911624619 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5096354726270043 / 5000000000000000 : ℝ) ≤ - (190876121788911624619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2252920713877543 / 10000000000000000 : ℝ)) (q := - (5096354726270043 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5096354726270043 / 20000000000000000 : ℚ)) + (r' := (5096354726270043 / 5000000000000000 : ℚ)) + (U := (-(13672067484211088375381 / 10000000000000000000000 : ℚ))) + (U' := (190876121788911624619 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (2252920713877543 / 10000000000000000 : ℚ)) + (q := (5096354726270043 / 20000000000000000 : ℚ)) + (U := (-(13672067484211088375381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_11 : Uω (aρ 11) (bρ 11) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3449,26 +3048,21 @@ lemma U_432_11 : have hlg : Real.log (3539838466569181 / 20000000000000000 : ℝ) ≤ (-(8658255887911272410519 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3539838466569181 / 20000000000000000 : ℝ) = - (3539838466569181 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3539838466569181 / 2500000000000000 : ℚ)) - (U := (1738951816588727589481 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3539838466569181 / 2500000000000000 : ℝ) ≤ - (1738951816588727589481 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1114881080381681 / 10000000000000000 : ℝ)) (q := - (3539838466569181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3539838466569181 / 20000000000000000 : ℚ)) + (r' := (3539838466569181 / 2500000000000000 : ℚ)) + (U := (-(8658255887911272410519 / 5000000000000000000000 : ℚ))) + (U' := (1738951816588727589481 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1831819407533 / 4000000000000 : ℚ)) + (s := (1114881080381681 / 10000000000000000 : ℚ)) + (q := (3539838466569181 / 20000000000000000 : ℚ)) + (U := (-(8658255887911272410519 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_432_12 : Uω (aρ 12) (bρ 12) (1831819407533 / 4000000000000 : ℝ) ≤ @@ -3584,25 +3178,21 @@ lemma U_433_1 : have hlg : Real.log (9043274091696977 / 20000000000000000 : ℝ) ≤ (-(1587421971831349571987 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9043274091696977 / 20000000000000000 : ℝ) = - (9043274091696977 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9043274091696977 / 5000000000000000 : ℚ)) - (U := (1185166749368650428013 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9043274091696977 / 5000000000000000 : ℝ) ≤ - (1185166749368650428013 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4521601291566977 / 10000000000000000 : ℝ)) (q := - (9043274091696977 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9043274091696977 / 20000000000000000 : ℚ)) + (r' := (9043274091696977 / 5000000000000000 : ℚ)) + (U := (-(1587421971831349571987 / 2000000000000000000000 : ℚ))) + (U' := (1185166749368650428013 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (4521601291566977 / 10000000000000000 : ℚ)) + (q := (9043274091696977 / 20000000000000000 : ℚ)) + (U := (-(1587421971831349571987 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_2 : Uω (aρ 2) (bρ 2) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3610,25 +3200,21 @@ lemma U_433_2 : have hlg : Real.log (4497667903824867 / 10000000000000000 : ℝ) ≤ (-(998782592033725802447 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4497667903824867 / 10000000000000000 : ℝ) = - (4497667903824867 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4497667903824867 / 2500000000000000 : ℚ)) - (U := (734085358716274197553 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4497667903824867 / 2500000000000000 : ℝ) ≤ - (734085358716274197553 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2248716010014867 / 5000000000000000 : ℝ)) (q := - (4497667903824867 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4497667903824867 / 10000000000000000 : ℚ)) + (r' := (4497667903824867 / 2500000000000000 : ℚ)) + (U := (-(998782592033725802447 / 1250000000000000000000 : ℚ))) + (U' := (734085358716274197553 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (2248716010014867 / 5000000000000000 : ℚ)) + (q := (4497667903824867 / 10000000000000000 : ℚ)) + (U := (-(998782592033725802447 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_3 : Uω (aρ 3) (bρ 3) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3636,25 +3222,21 @@ lemma U_433_3 : have hlg : Real.log (8899352751657329 / 20000000000000000 : ℝ) ≤ (-(8097537234734476602597 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8899352751657329 / 20000000000000000 : ℝ) = - (8899352751657329 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8899352751657329 / 5000000000000000 : ℚ)) - (U := (5765406371265523397403 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8899352751657329 / 5000000000000000 : ℝ) ≤ - (5765406371265523397403 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4448845070387329 / 10000000000000000 : ℝ)) (q := - (8899352751657329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8899352751657329 / 20000000000000000 : ℚ)) + (r' := (8899352751657329 / 5000000000000000 : ℚ)) + (U := (-(8097537234734476602597 / 10000000000000000000000 : ℚ))) + (U' := (5765406371265523397403 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (4448845070387329 / 10000000000000000 : ℚ)) + (q := (8899352751657329 / 20000000000000000 : ℚ)) + (U := (-(8097537234734476602597 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_4 : Uω (aρ 4) (bρ 4) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3662,25 +3244,21 @@ lemma U_433_4 : have hlg : Real.log (873961189897237 / 2000000000000000 : ℝ) ≤ (-(8278664895044969696437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (873961189897237 / 2000000000000000 : ℝ) = - (873961189897237 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (873961189897237 / 500000000000000 : ℚ)) - (U := (5584278710955030303563 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (873961189897237 / 500000000000000 : ℝ) ≤ - (5584278710955030303563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (436739839876737 / 1000000000000000 : ℝ)) (q := - (873961189897237 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (873961189897237 / 2000000000000000 : ℚ)) + (r' := (873961189897237 / 500000000000000 : ℚ)) + (U := (-(8278664895044969696437 / 10000000000000000000000 : ℚ))) + (U' := (5584278710955030303563 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (436739839876737 / 1000000000000000 : ℚ)) + (q := (873961189897237 / 2000000000000000 : ℚ)) + (U := (-(8278664895044969696437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_5 : Uω (aρ 5) (bρ 5) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3688,25 +3266,21 @@ lemma U_433_5 : have hlg : Real.log (4247754753818727 / 10000000000000000 : ℝ) ≤ (-(4280972711764913015427 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4247754753818727 / 10000000000000000 : ℝ) = - (4247754753818727 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4247754753818727 / 2500000000000000 : ℚ)) - (U := (2650499091235086984573 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4247754753818727 / 2500000000000000 : ℝ) ≤ - (2650499091235086984573 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2120742963383727 / 5000000000000000 : ℝ)) (q := - (4247754753818727 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4247754753818727 / 10000000000000000 : ℚ)) + (r' := (4247754753818727 / 2500000000000000 : ℚ)) + (U := (-(4280972711764913015427 / 5000000000000000000000 : ℚ))) + (U' := (2650499091235086984573 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (2120742963383727 / 5000000000000000 : ℚ)) + (q := (4247754753818727 / 10000000000000000 : ℚ)) + (U := (-(4280972711764913015427 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_6 : Uω (aρ 6) (bρ 6) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3714,25 +3288,21 @@ lemma U_433_6 : have hlg : Real.log (325737048382469 / 800000000000000 : ℝ) ≤ (-(8985212713119600161899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (325737048382469 / 800000000000000 : ℝ) = - (325737048382469 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (325737048382469 / 200000000000000 : ℚ)) - (U := (4877730892880399838101 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (325737048382469 / 200000000000000 : ℝ) ≤ - (4877730892880399838101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (162265720153269 / 400000000000000 : ℝ)) (q := - (325737048382469 / 800000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (325737048382469 / 800000000000000 : ℚ)) + (r' := (325737048382469 / 200000000000000 : ℚ)) + (U := (-(8985212713119600161899 / 10000000000000000000000 : ℚ))) + (U' := (4877730892880399838101 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (162265720153269 / 400000000000000 : ℚ)) + (q := (325737048382469 / 800000000000000 : ℚ)) + (U := (-(8985212713119600161899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_7 : Uω (aρ 7) (bρ 7) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3740,25 +3310,21 @@ lemma U_433_7 : have hlg : Real.log (3829257484234693 / 10000000000000000 : ℝ) ≤ (-(2399785441056326483251 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3829257484234693 / 10000000000000000 : ℝ) = - (3829257484234693 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3829257484234693 / 2500000000000000 : ℚ)) - (U := (1065950460443673516749 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3829257484234693 / 2500000000000000 : ℝ) ≤ - (1065950460443673516749 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1897696571749693 / 5000000000000000 : ℝ)) (q := - (3829257484234693 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3829257484234693 / 10000000000000000 : ℚ)) + (r' := (3829257484234693 / 2500000000000000 : ℚ)) + (U := (-(2399785441056326483251 / 2500000000000000000000 : ℚ))) + (U' := (1065950460443673516749 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (1897696571749693 / 5000000000000000 : ℚ)) + (q := (3829257484234693 / 10000000000000000 : ℚ)) + (U := (-(2399785441056326483251 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_8 : Uω (aρ 8) (bρ 8) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3766,25 +3332,21 @@ lemma U_433_8 : have hlg : Real.log (3507669498542777 / 10000000000000000 : ℝ) ≤ (-(1309541545056140365681 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3507669498542777 / 10000000000000000 : ℝ) = - (3507669498542777 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3507669498542777 / 2500000000000000 : ℚ)) - (U := (423326405693859634319 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3507669498542777 / 2500000000000000 : ℝ) ≤ - (423326405693859634319 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1717879411727777 / 5000000000000000 : ℝ)) (q := - (3507669498542777 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3507669498542777 / 10000000000000000 : ℚ)) + (r' := (3507669498542777 / 2500000000000000 : ℚ)) + (U := (-(1309541545056140365681 / 1250000000000000000000 : ℚ))) + (U' := (423326405693859634319 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (1717879411727777 / 5000000000000000 : ℚ)) + (q := (3507669498542777 / 10000000000000000 : ℚ)) + (U := (-(1309541545056140365681 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_9 : Uω (aρ 9) (bρ 9) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3792,25 +3354,21 @@ lemma U_433_9 : have hlg : Real.log (123686347836671 / 400000000000000 : ℝ) ≤ (-(11737156383840359370543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (123686347836671 / 400000000000000 : ℝ) = - (123686347836671 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123686347836671 / 100000000000000 : ℚ)) - (U := (2125787222159640629457 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (123686347836671 / 100000000000000 : ℝ) ≤ - (2125787222159640629457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58914056931271 / 200000000000000 : ℝ)) (q := - (123686347836671 / 400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123686347836671 / 400000000000000 : ℚ)) + (r' := (123686347836671 / 100000000000000 : ℚ)) + (U := (-(11737156383840359370543 / 10000000000000000000000 : ℚ))) + (U' := (2125787222159640629457 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (58914056931271 / 200000000000000 : ℚ)) + (q := (123686347836671 / 400000000000000 : ℚ)) + (U := (-(11737156383840359370543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_10 : Uω (aρ 10) (bρ 10) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3818,26 +3376,21 @@ lemma U_433_10 : have hlg : Real.log (2555663769420043 / 10000000000000000 : ℝ) ≤ (-(6821365551110305732887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2555663769420043 / 10000000000000000 : ℝ) = - (2555663769420043 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2555663769420043 / 2500000000000000 : ℚ)) - (U := (110106251889694267113 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2555663769420043 / 2500000000000000 : ℝ) ≤ - (110106251889694267113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1130636013532543 / 5000000000000000 : ℝ)) (q := - (2555663769420043 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2555663769420043 / 10000000000000000 : ℚ)) + (r' := (2555663769420043 / 2500000000000000 : ℚ)) + (U := (-(6821365551110305732887 / 5000000000000000000000 : ℚ))) + (U' := (110106251889694267113 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (1130636013532543 / 5000000000000000 : ℚ)) + (q := (2555663769420043 / 10000000000000000 : ℚ)) + (U := (-(6821365551110305732887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_11 : Uω (aρ 11) (bρ 11) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3845,26 +3398,21 @@ lemma U_433_11 : have hlg : Real.log (3560789838101703 / 20000000000000000 : ℝ) ≤ (-(8628749439416123003623 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3560789838101703 / 20000000000000000 : ℝ) = - (3560789838101703 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3560789838101703 / 2500000000000000 : ℚ)) - (U := (1768458265083876996377 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3560789838101703 / 2500000000000000 : ℝ) ≤ - (1768458265083876996377 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1129210952531703 / 10000000000000000 : ℝ)) (q := - (3560789838101703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3560789838101703 / 20000000000000000 : ℚ)) + (r' := (3560789838101703 / 2500000000000000 : ℚ)) + (U := (-(8628749439416123003623 / 5000000000000000000000 : ℚ))) + (U' := (1768458265083876996377 / 5000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (917234003643 / 2000000000000 : ℚ)) + (s := (1129210952531703 / 10000000000000000 : ℚ)) + (q := (3560789838101703 / 20000000000000000 : ℚ)) + (U := (-(8628749439416123003623 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_433_12 : Uω (aρ 12) (bρ 12) (917234003643 / 2000000000000 : ℝ) ≤ @@ -3981,24 +3529,21 @@ lemma U_434_1 : have hlg : Real.log (56603232468919 / 125000000000000 : ℝ) ≤ (-(3961238212228721508109 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56603232468919 / 125000000000000 : ℝ) = (56603232468919 / 31250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56603232468919 / 31250000000000 : ℚ)) - (U := (2970233590771278491891 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (56603232468919 / 31250000000000 : ℝ) ≤ - (2970233590771278491891 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (226411144775727 / 500000000000000 : ℝ)) (q := - (56603232468919 / 125000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56603232468919 / 125000000000000 : ℚ)) + (r' := (56603232468919 / 31250000000000 : ℚ)) + (U := (-(3961238212228721508109 / 5000000000000000000000 : ℚ))) + (U' := (2970233590771278491891 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (226411144775727 / 500000000000000 : ℚ)) + (q := (56603232468919 / 125000000000000 : ℚ)) + (U := (-(3961238212228721508109 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_2 : Uω (aρ 2) (bρ 2) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4006,25 +3551,21 @@ lemma U_434_2 : have hlg : Real.log (9008579499969673 / 20000000000000000 : ℝ) ≤ (-(7975548720041766875749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9008579499969673 / 20000000000000000 : ℝ) = - (9008579499969673 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9008579499969673 / 5000000000000000 : ℚ)) - (U := (5887394885958233124251 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9008579499969673 / 5000000000000000 : ℝ) ≤ - (5887394885958233124251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4504054212967173 / 10000000000000000 : ℝ)) (q := - (9008579499969673 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9008579499969673 / 20000000000000000 : ℚ)) + (r' := (9008579499969673 / 5000000000000000 : ℚ)) + (U := (-(7975548720041766875749 / 10000000000000000000000 : ℚ))) + (U' := (5887394885958233124251 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (4504054212967173 / 10000000000000000 : ℚ)) + (q := (9008579499969673 / 20000000000000000 : ℚ)) + (U := (-(7975548720041766875749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_3 : Uω (aρ 3) (bρ 3) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4032,25 +3573,21 @@ lemma U_434_3 : have hlg : Real.log (1782519644262739 / 4000000000000000 : ℝ) ≤ (-(4041332333650775896749 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1782519644262739 / 4000000000000000 : ℝ) = - (1782519644262739 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1782519644262739 / 1000000000000000 : ℚ)) - (U := (2890139469349224103251 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1782519644262739 / 1000000000000000 : ℝ) ≤ - (2890139469349224103251 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (891093808132239 / 2000000000000000 : ℝ)) (q := - (1782519644262739 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1782519644262739 / 4000000000000000 : ℚ)) + (r' := (1782519644262739 / 1000000000000000 : ℚ)) + (U := (-(4041332333650775896749 / 5000000000000000000000 : ℚ))) + (U' := (2890139469349224103251 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (891093808132239 / 2000000000000000 : ℚ)) + (q := (1782519644262739 / 4000000000000000 : ℚ)) + (U := (-(4041332333650775896749 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_4 : Uω (aρ 4) (bρ 4) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4058,25 +3595,21 @@ lemma U_434_4 : have hlg : Real.log (875286218695081 / 2000000000000000 : ℝ) ≤ (-(4131757595361709041687 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (875286218695081 / 2000000000000000 : ℝ) = - (875286218695081 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (875286218695081 / 500000000000000 : ℚ)) - (U := (2799714207638290958313 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (875286218695081 / 500000000000000 : ℝ) ≤ - (2799714207638290958313 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (437402718736331 / 1000000000000000 : ℝ)) (q := - (875286218695081 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (875286218695081 / 2000000000000000 : ℚ)) + (r' := (875286218695081 / 500000000000000 : ℚ)) + (U := (-(4131757595361709041687 / 5000000000000000000000 : ℚ))) + (U' := (2799714207638290958313 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (437402718736331 / 1000000000000000 : ℚ)) + (q := (875286218695081 / 2000000000000000 : ℚ)) + (U := (-(4131757595361709041687 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_5 : Uω (aρ 5) (bρ 5) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4084,25 +3617,21 @@ lemma U_434_5 : have hlg : Real.log (1701754409744643 / 4000000000000000 : ℝ) ≤ (-(1709269271915022459983 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1701754409744643 / 4000000000000000 : ℝ) = - (1701754409744643 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1701754409744643 / 1000000000000000 : ℚ)) - (U := (1063319449284977540017 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1701754409744643 / 1000000000000000 : ℝ) ≤ - (1063319449284977540017 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (849625393694143 / 2000000000000000 : ℝ)) (q := - (1701754409744643 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1701754409744643 / 4000000000000000 : ℚ)) + (r' := (1701754409744643 / 1000000000000000 : ℚ)) + (U := (-(1709269271915022459983 / 2000000000000000000000 : ℚ))) + (U' := (1063319449284977540017 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (849625393694143 / 2000000000000000 : ℚ)) + (q := (1701754409744643 / 4000000000000000 : ℚ)) + (U := (-(1709269271915022459983 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_6 : Uω (aρ 6) (bρ 6) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4110,25 +3639,21 @@ lemma U_434_6 : have hlg : Real.log (4078359162264601 / 10000000000000000 : ℝ) ≤ (-(8968903510601811328087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4078359162264601 / 10000000000000000 : ℝ) = - (4078359162264601 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4078359162264601 / 2500000000000000 : ℚ)) - (U := (4894040095398188671913 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4078359162264601 / 2500000000000000 : ℝ) ≤ - (4894040095398188671913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2031656809708351 / 5000000000000000 : ℝ)) (q := - (4078359162264601 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4078359162264601 / 10000000000000000 : ℚ)) + (r' := (4078359162264601 / 2500000000000000 : ℚ)) + (U := (-(8968903510601811328087 / 10000000000000000000000 : ℚ))) + (U' := (4894040095398188671913 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (2031656809708351 / 5000000000000000 : ℚ)) + (q := (4078359162264601 / 10000000000000000 : ℚ)) + (U := (-(8968903510601811328087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_7 : Uω (aρ 7) (bρ 7) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4136,25 +3661,21 @@ lemma U_434_7 : have hlg : Real.log (1534375184017047 / 4000000000000000 : ℝ) ≤ (-(4790855543348075876977 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1534375184017047 / 4000000000000000 : ℝ) = - (1534375184017047 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1534375184017047 / 1000000000000000 : ℚ)) - (U := (2140616259651924123023 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1534375184017047 / 1000000000000000 : ℝ) ≤ - (2140616259651924123023 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (760426519146547 / 2000000000000000 : ℝ)) (q := - (1534375184017047 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1534375184017047 / 4000000000000000 : ℚ)) + (r' := (1534375184017047 / 1000000000000000 : ℚ)) + (U := (-(4790855543348075876977 / 5000000000000000000000 : ℚ))) + (U' := (2140616259651924123023 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (760426519146547 / 2000000000000000 : ℚ)) + (q := (1534375184017047 / 4000000000000000 : ℚ)) + (U := (-(4790855543348075876977 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_8 : Uω (aρ 8) (bρ 8) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4162,25 +3683,21 @@ lemma U_434_8 : have hlg : Real.log (7028858628479507 / 20000000000000000 : ℝ) ≤ (-(10457079376504312439157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7028858628479507 / 20000000000000000 : ℝ) = - (7028858628479507 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7028858628479507 / 5000000000000000 : ℚ)) - (U := (3405864229495687560843 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7028858628479507 / 5000000000000000 : ℝ) ≤ - (3405864229495687560843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3442656955467007 / 10000000000000000 : ℝ)) (q := - (7028858628479507 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7028858628479507 / 20000000000000000 : ℚ)) + (r' := (7028858628479507 / 5000000000000000 : ℚ)) + (U := (-(10457079376504312439157 / 10000000000000000000000 : ℚ))) + (U' := (3405864229495687560843 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (3442656955467007 / 10000000000000000 : ℚ)) + (q := (7028858628479507 / 20000000000000000 : ℚ)) + (U := (-(10457079376504312439157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_9 : Uω (aρ 9) (bρ 9) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4188,25 +3705,21 @@ lemma U_434_9 : have hlg : Real.log (3099108631247451 / 10000000000000000 : ℝ) ≤ (-(2928676401593483871823 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3099108631247451 / 10000000000000000 : ℝ) = - (3099108631247451 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3099108631247451 / 2500000000000000 : ℚ)) - (U := (537059499906516128177 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3099108631247451 / 2500000000000000 : ℝ) ≤ - (537059499906516128177 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1476490608921201 / 5000000000000000 : ℝ)) (q := - (3099108631247451 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3099108631247451 / 10000000000000000 : ℚ)) + (r' := (3099108631247451 / 2500000000000000 : ℚ)) + (U := (-(2928676401593483871823 / 2500000000000000000000 : ℚ))) + (U' := (537059499906516128177 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (1476490608921201 / 5000000000000000 : ℚ)) + (q := (3099108631247451 / 10000000000000000 : ℚ)) + (U := (-(2928676401593483871823 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_10 : Uω (aρ 10) (bρ 10) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4214,26 +3727,21 @@ lemma U_434_10 : have hlg : Real.log (5126288939717917 / 20000000000000000 : ℝ) ≤ (-(13613502791977963723017 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5126288939717917 / 20000000000000000 : ℝ) = - (5126288939717917 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5126288939717917 / 5000000000000000 : ℚ)) - (U := (249440814022036276983 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5126288939717917 / 5000000000000000 : ℝ) ≤ - (249440814022036276983 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2269611928560417 / 10000000000000000 : ℝ)) (q := - (5126288939717917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5126288939717917 / 20000000000000000 : ℚ)) + (r' := (5126288939717917 / 5000000000000000 : ℚ)) + (U := (-(13613502791977963723017 / 10000000000000000000000 : ℚ))) + (U' := (249440814022036276983 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (2269611928560417 / 10000000000000000 : ℚ)) + (q := (5126288939717917 / 20000000000000000 : ℚ)) + (U := (-(13613502791977963723017 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_11 : Uω (aρ 11) (bρ 11) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4241,26 +3749,21 @@ lemma U_434_11 : have hlg : Real.log (1790799986019643 / 10000000000000000 : ℝ) ≤ (-(3439845305272605237621 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1790799986019643 / 10000000000000000 : ℝ) = - (1790799986019643 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1790799986019643 / 1250000000000000 : ℚ)) - (U := (719037776527394762379 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1790799986019643 / 1250000000000000 : ℝ) ≤ - (719037776527394762379 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (571699793543393 / 5000000000000000 : ℝ)) (q := - (1790799986019643 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1790799986019643 / 10000000000000000 : ℚ)) + (r' := (1790799986019643 / 1250000000000000 : ℚ)) + (U := (-(3439845305272605237621 / 2000000000000000000000 : ℚ))) + (U' := (719037776527394762379 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1837116607039 / 4000000000000 : ℚ)) + (s := (571699793543393 / 5000000000000000 : ℚ)) + (q := (1790799986019643 / 10000000000000000 : ℚ)) + (U := (-(3439845305272605237621 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_434_12 : Uω (aρ 12) (bρ 12) (1837116607039 / 4000000000000 : ℝ) ≤ @@ -4377,25 +3880,21 @@ lemma U_435_1 : have hlg : Real.log (9069760298051741 / 20000000000000000 : ℝ) ≤ (-(3953932186274931808203 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9069760298051741 / 20000000000000000 : ℝ) = - (9069760298051741 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9069760298051741 / 5000000000000000 : ℚ)) - (U := (2977539616725068191797 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9069760298051741 / 5000000000000000 : ℝ) ≤ - (2977539616725068191797 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4534844499156741 / 10000000000000000 : ℝ)) (q := - (9069760298051741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9069760298051741 / 20000000000000000 : ℚ)) + (r' := (9069760298051741 / 5000000000000000 : ℚ)) + (U := (-(3953932186274931808203 / 5000000000000000000000 : ℚ))) + (U' := (2977539616725068191797 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (229970650849 / 500000000000 : ℚ)) + (s := (4534844499156741 / 10000000000000000 : ℚ)) + (q := (9069760298051741 / 20000000000000000 : ℚ)) + (U := (-(3953932186274931808203 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_2 : Uω (aρ 2) (bρ 2) (229970650849 / 500000000000 : ℝ) ≤ @@ -4403,25 +3902,21 @@ lemma U_435_2 : have hlg : Real.log (9021823190253283 / 20000000000000000 : ℝ) ≤ (-(1592171663724093181691 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9021823190253283 / 20000000000000000 : ℝ) = - (9021823190253283 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9021823190253283 / 5000000000000000 : ℚ)) - (U := (1180417057475906818309 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9021823190253283 / 5000000000000000 : ℝ) ≤ - (1180417057475906818309 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4510676403868283 / 10000000000000000 : ℝ)) (q := - (9021823190253283 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9021823190253283 / 20000000000000000 : ℚ)) + (r' := (9021823190253283 / 5000000000000000 : ℚ)) + (U := (-(1592171663724093181691 / 2000000000000000000000 : ℚ))) + (U' := (1180417057475906818309 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (229970650849 / 500000000000 : ℚ)) + (s := (4510676403868283 / 10000000000000000 : ℚ)) + (q := (9021823190253283 / 20000000000000000 : ℚ)) + (U := (-(1592171663724093181691 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_3 : Uω (aρ 3) (bρ 3) (229970650849 / 500000000000 : ℝ) ≤ @@ -4429,25 +3924,21 @@ lemma U_435_3 : have hlg : Real.log (8925843683635361 / 20000000000000000 : ℝ) ≤ (-(1008476774321000244151 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8925843683635361 / 20000000000000000 : ℝ) = - (8925843683635361 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8925843683635361 / 5000000000000000 : ℚ)) - (U := (724391176428999755849 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8925843683635361 / 5000000000000000 : ℝ) ≤ - (724391176428999755849 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4462093003600361 / 10000000000000000 : ℝ)) (q := - (8925843683635361 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8925843683635361 / 20000000000000000 : ℚ)) + (r' := (8925843683635361 / 5000000000000000 : ℚ)) + (U := (-(1008476774321000244151 / 1250000000000000000000 : ℚ))) + (U' := (724391176428999755849 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (229970650849 / 500000000000 : ℚ)) + (s := (4462093003600361 / 10000000000000000 : ℚ)) + (q := (8925843683635361 / 20000000000000000 : ℚ)) + (U := (-(1008476774321000244151 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_4 : Uω (aρ 4) (bρ 4) (229970650849 / 500000000000 : ℝ) ≤ @@ -4455,25 +3946,21 @@ lemma U_435_4 : have hlg : Real.log (876611245288137 / 2000000000000000 : ℝ) ≤ (-(1031048553524197032573 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (876611245288137 / 2000000000000000 : ℝ) = - (876611245288137 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (876611245288137 / 500000000000000 : ℚ)) - (U := (701819397225802967427 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (876611245288137 / 500000000000000 : ℝ) ≤ - (701819397225802967427 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (438065595391137 / 1000000000000000 : ℝ)) (q := - (876611245288137 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (876611245288137 / 2000000000000000 : ℚ)) + (r' := (876611245288137 / 500000000000000 : ℚ)) + (U := (-(1031048553524197032573 / 1250000000000000000000 : ℚ))) + (U' := (701819397225802967427 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (229970650849 / 500000000000 : ℚ)) + (s := (438065595391137 / 1000000000000000 : ℚ)) + (q := (876611245288137 / 2000000000000000 : ℚ)) + (U := (-(1031048553524197032573 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_5 : Uω (aρ 5) (bρ 5) (229970650849 / 500000000000 : ℝ) ≤ @@ -4481,25 +3968,21 @@ lemma U_435_5 : have hlg : Real.log (8522034528893589 / 20000000000000000 : ℝ) ≤ (-(8530771662286591006543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8522034528893589 / 20000000000000000 : ℝ) = - (8522034528893589 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8522034528893589 / 5000000000000000 : ℚ)) - (U := (5332171943713408993457 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8522034528893589 / 5000000000000000 : ℝ) ≤ - (5332171943713408993457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4254767949258589 / 10000000000000000 : ℝ)) (q := - (8522034528893589 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8522034528893589 / 20000000000000000 : ℚ)) + (r' := (8522034528893589 / 5000000000000000 : ℚ)) + (U := (-(8530771662286591006543 / 10000000000000000000000 : ℚ))) + (U' := (5332171943713408993457 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (229970650849 / 500000000000 : ℚ)) + (s := (4254767949258589 / 10000000000000000 : ℚ)) + (q := (8522034528893589 / 20000000000000000 : ℚ)) + (U := (-(8530771662286591006543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_6 : Uω (aρ 6) (bρ 6) (229970650849 / 500000000000 : ℝ) ≤ @@ -4507,25 +3990,21 @@ lemma U_435_6 : have hlg : Real.log (1021251284886079 / 2500000000000000 : ℝ) ≤ (-(8952621060125969732773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1021251284886079 / 2500000000000000 : ℝ) = - (1021251284886079 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1021251284886079 / 625000000000000 : ℚ)) - (U := (4910322545874030267227 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1021251284886079 / 625000000000000 : ℝ) ≤ - (4910322545874030267227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (127187002331051 / 312500000000000 : ℝ)) (q := - (1021251284886079 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1021251284886079 / 2500000000000000 : ℚ)) + (r' := (1021251284886079 / 625000000000000 : ℚ)) + (U := (-(8952621060125969732773 / 10000000000000000000000 : ℚ))) + (U' := (4910322545874030267227 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (229970650849 / 500000000000 : ℚ)) + (s := (127187002331051 / 312500000000000 : ℚ)) + (q := (1021251284886079 / 2500000000000000 : ℚ)) + (U := (-(8952621060125969732773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_7 : Uω (aρ 7) (bρ 7) (229970650849 / 500000000000 : ℝ) ≤ @@ -4533,24 +4012,21 @@ lemma U_435_7 : have hlg : Real.log (24016363931063 / 62500000000000 : ℝ) ≤ (-(9564311277543446347187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24016363931063 / 62500000000000 : ℝ) = (24016363931063 / 15625000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24016363931063 / 15625000000000 : ℚ)) - (U := (4298632328456553652813 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (24016363931063 / 15625000000000 : ℝ) ≤ - (4298632328456553652813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95221790855129 / 250000000000000 : ℝ)) (q := - (24016363931063 / 62500000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24016363931063 / 62500000000000 : ℚ)) + (r' := (24016363931063 / 15625000000000 : ℚ)) + (U := (-(9564311277543446347187 / 10000000000000000000000 : ℚ))) + (U' := (4298632328456553652813 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (229970650849 / 500000000000 : ℚ)) + (s := (95221790855129 / 250000000000000 : ℚ)) + (q := (24016363931063 / 62500000000000 : ℚ)) + (U := (-(9564311277543446347187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_8 : Uω (aρ 8) (bρ 8) (229970650849 / 500000000000 : ℝ) ≤ @@ -4558,25 +4034,21 @@ lemma U_435_8 : have hlg : Real.log (3521188587841929 / 10000000000000000 : ℝ) ≤ (-(10437864928602727238181 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3521188587841929 / 10000000000000000 : ℝ) = - (3521188587841929 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3521188587841929 / 2500000000000000 : ℚ)) - (U := (3425078677397272761819 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3521188587841929 / 2500000000000000 : ℝ) ≤ - (3425078677397272761819 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1724777001644429 / 5000000000000000 : ℝ)) (q := - (3521188587841929 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3521188587841929 / 10000000000000000 : ℚ)) + (r' := (3521188587841929 / 2500000000000000 : ℚ)) + (U := (-(10437864928602727238181 / 10000000000000000000000 : ℚ))) + (U' := (3425078677397272761819 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (229970650849 / 500000000000 : ℚ)) + (s := (1724777001644429 / 5000000000000000 : ℚ)) + (q := (3521188587841929 / 10000000000000000 : ℚ)) + (U := (-(10437864928602727238181 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_9 : Uω (aρ 9) (bρ 9) (229970650849 / 500000000000 : ℝ) ≤ @@ -4584,25 +4056,21 @@ lemma U_435_9 : have hlg : Real.log (1553028512204731 / 5000000000000000 : ℝ) ≤ (-(11692310084797909684141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1553028512204731 / 5000000000000000 : ℝ) = - (1553028512204731 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1553028512204731 / 1250000000000000 : ℚ)) - (U := (2170633521202090315859 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1553028512204731 / 1250000000000000 : ℝ) ≤ - (2170633521202090315859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (740064126195981 / 2500000000000000 : ℝ)) (q := - (1553028512204731 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1553028512204731 / 5000000000000000 : ℚ)) + (r' := (1553028512204731 / 1250000000000000 : ℚ)) + (U := (-(11692310084797909684141 / 10000000000000000000000 : ℚ))) + (U' := (2170633521202090315859 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (229970650849 / 500000000000 : ℚ)) + (s := (740064126195981 / 2500000000000000 : ℚ)) + (q := (1553028512204731 / 5000000000000000 : ℚ)) + (U := (-(11692310084797909684141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_10 : Uω (aρ 10) (bρ 10) (229970650849 / 500000000000 : ℝ) ≤ @@ -4610,26 +4078,21 @@ lemma U_435_10 : have hlg : Real.log (2570619527121791 / 10000000000000000 : ℝ) ≤ (-(13584381614807102870191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2570619527121791 / 10000000000000000 : ℝ) = - (2570619527121791 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2570619527121791 / 2500000000000000 : ℚ)) - (U := (278561991192897129809 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2570619527121791 / 2500000000000000 : ℝ) ≤ - (278561991192897129809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1138970271851791 / 5000000000000000 : ℝ)) (q := - (2570619527121791 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2570619527121791 / 10000000000000000 : ℚ)) + (r' := (2570619527121791 / 2500000000000000 : ℚ)) + (U := (-(13584381614807102870191 / 10000000000000000000000 : ℚ))) + (U' := (278561991192897129809 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (229970650849 / 500000000000 : ℚ)) + (s := (1138970271851791 / 5000000000000000 : ℚ)) + (q := (2570619527121791 / 10000000000000000 : ℚ)) + (U := (-(13584381614807102870191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_11 : Uω (aρ 11) (bρ 11) (229970650849 / 500000000000 : ℝ) ≤ @@ -4637,25 +4100,21 @@ lemma U_435_11 : have hlg : Real.log (360227406247933 / 2000000000000000 : ℝ) ≤ (-(1714166942718427090193 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (360227406247933 / 2000000000000000 : ℝ) = - (360227406247933 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (360227406247933 / 250000000000000 : ℚ)) - (U := (365274598181572909807 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (360227406247933 / 250000000000000 : ℝ) ≤ - (365274598181572909807 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (115745217814433 / 1000000000000000 : ℝ)) (q := - (360227406247933 / 2000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (360227406247933 / 2000000000000000 : ℚ)) + (r' := (360227406247933 / 250000000000000 : ℚ)) + (U := (-(1714166942718427090193 / 1000000000000000000000 : ℚ))) + (U' := (365274598181572909807 / 1000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (229970650849 / 500000000000 : ℚ)) + (s := (115745217814433 / 1000000000000000 : ℚ)) + (q := (360227406247933 / 2000000000000000 : ℚ)) + (U := (-(1714166942718427090193 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_435_12 : Uω (aρ 12) (bρ 12) (229970650849 / 500000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U36.lean b/LeanPool/Zeta5Irrational/Table/U36.lean index 4f0839b183..ebe48dfbbe 100644 --- a/LeanPool/Zeta5Irrational/Table/U36.lean +++ b/LeanPool/Zeta5Irrational/Table/U36.lean @@ -24,25 +24,21 @@ lemma U_436_1 : have hlg : Real.log (9083003400772417 / 20000000000000000 : ℝ) ≤ (-(7893273641033907831537 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9083003400772417 / 20000000000000000 : ℝ) = - (9083003400772417 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9083003400772417 / 5000000000000000 : ℚ)) - (U := (5969669964966092168463 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9083003400772417 / 5000000000000000 : ℝ) ≤ - (5969669964966092168463 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4541466102494917 / 10000000000000000 : ℝ)) (q := - (9083003400772417 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9083003400772417 / 20000000000000000 : ℚ)) + (r' := (9083003400772417 / 5000000000000000 : ℚ)) + (U := (-(7893273641033907831537 / 10000000000000000000000 : ℚ))) + (U' := (5969669964966092168463 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (368482761309 / 800000000000 : ℚ)) + (s := (4541466102494917 / 10000000000000000 : ℚ)) + (q := (9083003400772417 / 20000000000000000 : ℚ)) + (U := (-(7893273641033907831537 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_2 : Uω (aρ 2) (bρ 2) (368482761309 / 800000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_436_2 : have hlg : Real.log (9035066878509517 / 20000000000000000 : ℝ) ≤ (-(3973094734289888371921 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9035066878509517 / 20000000000000000 : ℝ) = - (9035066878509517 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9035066878509517 / 5000000000000000 : ℚ)) - (U := (2958377068710111628079 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9035066878509517 / 5000000000000000 : ℝ) ≤ - (2958377068710111628079 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4517298592742017 / 10000000000000000 : ℝ)) (q := - (9035066878509517 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9035066878509517 / 20000000000000000 : ℚ)) + (r' := (9035066878509517 / 5000000000000000 : ℚ)) + (U := (-(3973094734289888371921 / 5000000000000000000000 : ℚ))) + (U' := (2958377068710111628079 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (368482761309 / 800000000000 : ℚ)) + (s := (4517298592742017 / 10000000000000000 : ℚ)) + (q := (9035066878509517 / 20000000000000000 : ℚ)) + (U := (-(3973094734289888371921 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_3 : Uω (aρ 3) (bρ 3) (368482761309 / 800000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_436_3 : have hlg : Real.log (4469544569327471 / 10000000000000000 : ℝ) ≤ (-(8052985750959086163193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4469544569327471 / 10000000000000000 : ℝ) = - (4469544569327471 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4469544569327471 / 2500000000000000 : ℚ)) - (U := (5809957855040913836807 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4469544569327471 / 2500000000000000 : ℝ) ≤ - (5809957855040913836807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2234358479618721 / 5000000000000000 : ℝ)) (q := - (4469544569327471 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4469544569327471 / 10000000000000000 : ℚ)) + (r' := (4469544569327471 / 2500000000000000 : ℚ)) + (U := (-(8052985750959086163193 / 10000000000000000000000 : ℚ))) + (U' := (5809957855040913836807 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (368482761309 / 800000000000 : ℚ)) + (s := (2234358479618721 / 5000000000000000 : ℚ)) + (q := (4469544569327471 / 10000000000000000 : ℚ)) + (U := (-(8052985750959086163193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_4 : Uω (aρ 4) (bρ 4) (368482761309 / 800000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_436_4 : have hlg : Real.log (8779362696863987 / 20000000000000000 : ℝ) ≤ (-(8233284538001393696237 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8779362696863987 / 20000000000000000 : ℝ) = - (8779362696863987 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8779362696863987 / 5000000000000000 : ℚ)) - (U := (5629659067998606303763 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8779362696863987 / 5000000000000000 : ℝ) ≤ - (5629659067998606303763 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4387284698511487 / 10000000000000000 : ℝ)) (q := - (8779362696863987 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8779362696863987 / 20000000000000000 : ℚ)) + (r' := (8779362696863987 / 5000000000000000 : ℚ)) + (U := (-(8233284538001393696237 / 10000000000000000000000 : ℚ))) + (U' := (5629659067998606303763 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (368482761309 / 800000000000 : ℚ)) + (s := (4387284698511487 / 10000000000000000 : ℚ)) + (q := (8779362696863987 / 20000000000000000 : ℚ)) + (U := (-(8233284538001393696237 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_5 : Uω (aρ 5) (bρ 5) (368482761309 / 800000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_436_5 : have hlg : Real.log (853529694843337 / 2000000000000000 : ℝ) ≤ (-(2128805313859165745199 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (853529694843337 / 2000000000000000 : ℝ) = - (853529694843337 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (853529694843337 / 500000000000000 : ℚ)) - (U := (1336930587640834254801 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (853529694843337 / 500000000000000 : ℝ) ≤ - (1336930587640834254801 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (426140886941587 / 1000000000000000 : ℝ)) (q := - (853529694843337 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (853529694843337 / 2000000000000000 : ℚ)) + (r' := (853529694843337 / 500000000000000 : ℚ)) + (U := (-(2128805313859165745199 / 2500000000000000000000 : ℚ))) + (U' := (1336930587640834254801 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (368482761309 / 800000000000 : ℚ)) + (s := (426140886941587 / 1000000000000000 : ℚ)) + (q := (853529694843337 / 2000000000000000 : ℚ)) + (U := (-(2128805313859165745199 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_6 : Uω (aρ 6) (bρ 6) (368482761309 / 800000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_436_6 : have hlg : Real.log (8183302074027421 / 20000000000000000 : ℝ) ≤ (-(4468182636717128945429 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8183302074027421 / 20000000000000000 : ℝ) = - (8183302074027421 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8183302074027421 / 5000000000000000 : ℚ)) - (U := (2463289166282871054571 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8183302074027421 / 5000000000000000 : ℝ) ≤ - (2463289166282871054571 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4076654370149921 / 10000000000000000 : ℝ)) (q := - (8183302074027421 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8183302074027421 / 20000000000000000 : ℚ)) + (r' := (8183302074027421 / 5000000000000000 : ℚ)) + (U := (-(4468182636717128945429 / 5000000000000000000000 : ℚ))) + (U' := (2463289166282871054571 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (368482761309 / 800000000000 : ℚ)) + (s := (4076654370149921 / 10000000000000000 : ℚ)) + (q := (8183302074027421 / 20000000000000000 : ℚ)) + (U := (-(4468182636717128945429 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_7 : Uω (aρ 7) (bρ 7) (368482761309 / 800000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_436_7 : have hlg : Real.log (1924649146056621 / 5000000000000000 : ℝ) ≤ (-(9546942225749288231573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1924649146056621 / 5000000000000000 : ℝ) = - (1924649146056621 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1924649146056621 / 1250000000000000 : ℚ)) - (U := (4316001380250711768427 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1924649146056621 / 1250000000000000 : ℝ) ≤ - (4316001380250711768427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (476951282638623 / 1250000000000000 : ℝ)) (q := - (1924649146056621 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1924649146056621 / 5000000000000000 : ℚ)) + (r' := (1924649146056621 / 1250000000000000 : ℚ)) + (U := (-(9546942225749288231573 / 10000000000000000000000 : ℚ))) + (U' := (4316001380250711768427 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (368482761309 / 800000000000 : ℚ)) + (s := (476951282638623 / 1250000000000000 : ℚ)) + (q := (1924649146056621 / 5000000000000000 : ℚ)) + (U := (-(9546942225749288231573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_8 : Uω (aρ 8) (bρ 8) (368482761309 / 800000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_436_8 : have hlg : Real.log (282235785807553 / 800000000000000 : ℝ) ≤ (-(2083737771356987306073 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (282235785807553 / 800000000000000 : ℝ) = - (282235785807553 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (282235785807553 / 200000000000000 : ℚ)) - (U := (688850949843012693927 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (282235785807553 / 200000000000000 : ℝ) ≤ - (688850949843012693927 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (138257998936453 / 400000000000000 : ℝ)) (q := - (282235785807553 / 800000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (282235785807553 / 800000000000000 : ℚ)) + (r' := (282235785807553 / 200000000000000 : ℚ)) + (U := (-(2083737771356987306073 / 2000000000000000000000 : ℚ))) + (U' := (688850949843012693927 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (368482761309 / 800000000000 : ℚ)) + (s := (138257998936453 / 400000000000000 : ℚ)) + (q := (282235785807553 / 800000000000000 : ℚ)) + (U := (-(2083737771356987306073 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_9 : Uω (aρ 9) (bρ 9) (368482761309 / 800000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_436_9 : have hlg : Real.log (194562742921581 / 625000000000000 : ℝ) ≤ (-(18234327382226959179 / 15625000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (194562742921581 / 625000000000000 : ℝ) = - (194562742921581 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194562742921581 / 156250000000000 : ℚ)) - (U := (3426522002148040821 / 15625000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194562742921581 / 156250000000000 : ℝ) ≤ - (3426522002148040821 / 15625000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (741882182518273 / 2500000000000000 : ℝ)) (q := - (194562742921581 / 625000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194562742921581 / 625000000000000 : ℚ)) + (r' := (194562742921581 / 156250000000000 : ℚ)) + (U := (-(18234327382226959179 / 15625000000000000000 : ℚ))) + (U' := (3426522002148040821 / 15625000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (368482761309 / 800000000000 : ℚ)) + (s := (741882182518273 / 2500000000000000 : ℚ)) + (q := (194562742921581 / 625000000000000 : ℚ)) + (U := (-(18234327382226959179 / 15625000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_10 : Uω (aρ 10) (bρ 10) (368482761309 / 800000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_436_10 : have hlg : Real.log (5156178005762329 / 20000000000000000 : ℝ) ≤ (-(6777683322747721136581 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5156178005762329 / 20000000000000000 : ℝ) = - (5156178005762329 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5156178005762329 / 5000000000000000 : ℚ)) - (U := (153788480252278863419 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5156178005762329 / 5000000000000000 : ℝ) ≤ - (153788480252278863419 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2286257995839829 / 10000000000000000 : ℝ)) (q := - (5156178005762329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5156178005762329 / 20000000000000000 : ℚ)) + (r' := (5156178005762329 / 5000000000000000 : ℚ)) + (U := (-(6777683322747721136581 / 5000000000000000000000 : ℚ))) + (U' := (153788480252278863419 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (368482761309 / 800000000000 : ℚ)) + (s := (2286257995839829 / 10000000000000000 : ℚ)) + (q := (5156178005762329 / 20000000000000000 : ℚ)) + (U := (-(6777683322747721136581 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_11 : Uω (aρ 11) (bρ 11) (368482761309 / 800000000000 : ℝ) ≤ @@ -285,25 +244,21 @@ lemma U_436_11 : have hlg : Real.log (724563401128357 / 4000000000000000 : ℝ) ≤ (-(8542401856030899137819 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (724563401128357 / 4000000000000000 : ℝ) = - (724563401128357 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (724563401128357 / 500000000000000 : ℚ)) - (U := (1854805848469100862181 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (724563401128357 / 500000000000000 : ℝ) ≤ - (1854805848469100862181 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (234274724384857 / 2000000000000000 : ℝ)) (q := - (724563401128357 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (724563401128357 / 4000000000000000 : ℚ)) + (r' := (724563401128357 / 500000000000000 : ℚ)) + (U := (-(8542401856030899137819 / 5000000000000000000000 : ℚ))) + (U' := (1854805848469100862181 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (368482761309 / 800000000000 : ℚ)) + (s := (234274724384857 / 2000000000000000 : ℚ)) + (q := (724563401128357 / 4000000000000000 : ℚ)) + (U := (-(8542401856030899137819 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_436_12 : Uω (aρ 12) (bρ 12) (368482761309 / 800000000000 : ℝ) ≤ @@ -420,25 +375,21 @@ lemma U_437_1 : have hlg : Real.log (2274061625797599 / 5000000000000000 : ℝ) ≤ (-(7878704167782229152803 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2274061625797599 / 5000000000000000 : ℝ) = - (2274061625797599 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2274061625797599 / 1250000000000000 : ℚ)) - (U := (5984239438217770847197 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2274061625797599 / 1250000000000000 : ℝ) ≤ - (5984239438217770847197 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1137021926382599 / 2500000000000000 : ℝ)) (q := - (2274061625797599 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2274061625797599 / 5000000000000000 : ℚ)) + (r' := (2274061625797599 / 1250000000000000 : ℚ)) + (U := (-(7878704167782229152803 / 10000000000000000000000 : ℚ))) + (U' := (5984239438217770847197 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (1137021926382599 / 2500000000000000 : ℚ)) + (q := (2274061625797599 / 5000000000000000 : ℚ)) + (U := (-(7878704167782229152803 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_2 : Uω (aρ 2) (bρ 2) (922531203149 / 2000000000000 : ℝ) ≤ @@ -446,25 +397,21 @@ lemma U_437_2 : have hlg : Real.log (9048310564747279 / 20000000000000000 : ℝ) ≤ (-(317261684270894545459 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9048310564747279 / 20000000000000000 : ℝ) = - (9048310564747279 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9048310564747279 / 5000000000000000 : ℚ)) - (U := (237256059969105454541 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9048310564747279 / 5000000000000000 : ℝ) ≤ - (237256059969105454541 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4523920779597279 / 10000000000000000 : ℝ)) (q := - (9048310564747279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9048310564747279 / 20000000000000000 : ℚ)) + (r' := (9048310564747279 / 5000000000000000 : ℚ)) + (U := (-(317261684270894545459 / 400000000000000000000 : ℚ))) + (U' := (237256059969105454541 / 400000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (4523920779597279 / 10000000000000000 : ℚ)) + (q := (9048310564747279 / 20000000000000000 : ℚ)) + (U := (-(317261684270894545459 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_3 : Uω (aρ 3) (bρ 3) (922531203149 / 2000000000000 : ℝ) ≤ @@ -472,25 +419,21 @@ lemma U_437_3 : have hlg : Real.log (8952334586404863 / 20000000000000000 : ℝ) ≤ (-(4019089635595831755489 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8952334586404863 / 20000000000000000 : ℝ) = - (8952334586404863 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8952334586404863 / 5000000000000000 : ℚ)) - (U := (2912382167404168244511 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8952334586404863 / 5000000000000000 : ℝ) ≤ - (2912382167404168244511 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4475340907604863 / 10000000000000000 : ℝ)) (q := - (8952334586404863 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8952334586404863 / 20000000000000000 : ℚ)) + (r' := (8952334586404863 / 5000000000000000 : ℚ)) + (U := (-(4019089635595831755489 / 5000000000000000000000 : ℚ))) + (U' := (2912382167404168244511 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (4475340907604863 / 10000000000000000 : ℚ)) + (q := (8952334586404863 / 20000000000000000 : ℚ)) + (U := (-(4019089635595831755489 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_4 : Uω (aρ 4) (bρ 4) (922531203149 / 2000000000000 : ℝ) ≤ @@ -498,25 +441,21 @@ lemma U_437_4 : have hlg : Real.log (4396306459498997 / 10000000000000000 : ℝ) ≤ (-(256818857844002620983 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4396306459498997 / 10000000000000000 : ℝ) = - (4396306459498997 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4396306459498997 / 2500000000000000 : ℚ)) - (U := (176398129843497379017 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4396306459498997 / 2500000000000000 : ℝ) ≤ - (176398129843497379017 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2196956710631497 / 5000000000000000 : ℝ)) (q := - (4396306459498997 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4396306459498997 / 10000000000000000 : ℚ)) + (r' := (4396306459498997 / 2500000000000000 : ℚ)) + (U := (-(256818857844002620983 / 312500000000000000000 : ℚ))) + (U' := (176398129843497379017 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (2196956710631497 / 5000000000000000 : ℚ)) + (q := (4396306459498997 / 10000000000000000 : ℚ)) + (U := (-(256818857844002620983 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_5 : Uω (aρ 5) (bρ 5) (922531203149 / 2000000000000 : ℝ) ≤ @@ -524,25 +463,21 @@ lemma U_437_5 : have hlg : Real.log (4274279653812787 / 10000000000000000 : ℝ) ≤ (-(8499695063155904997523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4274279653812787 / 10000000000000000 : ℝ) = - (4274279653812787 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4274279653812787 / 2500000000000000 : ℚ)) - (U := (5363248542844095002477 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4274279653812787 / 2500000000000000 : ℝ) ≤ - (5363248542844095002477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2134024864612787 / 5000000000000000 : ℝ)) (q := - (4274279653812787 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4274279653812787 / 10000000000000000 : ℚ)) + (r' := (4274279653812787 / 2500000000000000 : ℚ)) + (U := (-(8499695063155904997523 / 10000000000000000000000 : ℚ))) + (U' := (5363248542844095002477 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (2134024864612787 / 5000000000000000 : ℚ)) + (q := (4274279653812787 / 10000000000000000 : ℚ)) + (U := (-(8499695063155904997523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_6 : Uω (aρ 6) (bρ 6) (922531203149 / 2000000000000 : ℝ) ≤ @@ -550,25 +485,21 @@ lemma U_437_6 : have hlg : Real.log (2049148427531953 / 5000000000000000 : ℝ) ≤ (-(4460068031353997442141 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2049148427531953 / 5000000000000000 : ℝ) = - (2049148427531953 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2049148427531953 / 1250000000000000 : ℚ)) - (U := (2471403771646002557859 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2049148427531953 / 1250000000000000 : ℝ) ≤ - (2471403771646002557859 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1020831126716953 / 2500000000000000 : ℝ)) (q := - (2049148427531953 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2049148427531953 / 5000000000000000 : ℚ)) + (r' := (2049148427531953 / 1250000000000000 : ℚ)) + (U := (-(4460068031353997442141 / 5000000000000000000000 : ℚ))) + (U' := (2471403771646002557859 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (1020831126716953 / 2500000000000000 : ℚ)) + (q := (2049148427531953 / 5000000000000000 : ℚ)) + (U := (-(4460068031353997442141 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_7 : Uω (aρ 7) (bρ 7) (922531203149 / 2000000000000 : ℝ) ≤ @@ -576,25 +507,21 @@ lemma U_437_7 : have hlg : Real.log (3855978150560469 / 10000000000000000 : ℝ) ≤ (-(4764801910451678914299 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3855978150560469 / 10000000000000000 : ℝ) = - (3855978150560469 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3855978150560469 / 2500000000000000 : ℚ)) - (U := (2166669892548321085701 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3855978150560469 / 2500000000000000 : ℝ) ≤ - (2166669892548321085701 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1911174239310469 / 5000000000000000 : ℝ)) (q := - (3855978150560469 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3855978150560469 / 10000000000000000 : ℚ)) + (r' := (3855978150560469 / 2500000000000000 : ℚ)) + (U := (-(4764801910451678914299 / 5000000000000000000000 : ℚ))) + (U' := (2166669892548321085701 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (1911174239310469 / 5000000000000000 : ℚ)) + (q := (3855978150560469 / 10000000000000000 : ℚ)) + (U := (-(4764801910451678914299 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_8 : Uω (aρ 8) (bρ 8) (922531203149 / 2000000000000 : ℝ) ≤ @@ -602,25 +529,21 @@ lemma U_437_8 : have hlg : Real.log (7069411043431927 / 20000000000000000 : ℝ) ≤ (-(129994387526496953403 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7069411043431927 / 20000000000000000 : ℝ) = - (7069411043431927 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7069411043431927 / 5000000000000000 : ℚ)) - (U := (43292407548503046597 / 125000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7069411043431927 / 5000000000000000 : ℝ) ≤ - (43292407548503046597 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3463344872271927 / 10000000000000000 : ℝ)) (q := - (7069411043431927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7069411043431927 / 20000000000000000 : ℚ)) + (r' := (7069411043431927 / 5000000000000000 : ℚ)) + (U := (-(129994387526496953403 / 125000000000000000000 : ℚ))) + (U' := (43292407548503046597 / 125000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (3463344872271927 / 10000000000000000 : ℚ)) + (q := (7069411043431927 / 20000000000000000 : ℚ)) + (U := (-(129994387526496953403 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_9 : Uω (aρ 9) (bρ 9) (922531203149 / 2000000000000 : ℝ) ≤ @@ -628,25 +551,21 @@ lemma U_437_9 : have hlg : Real.log (3119949229481779 / 10000000000000000 : ℝ) ≤ (-(5823841816935791055419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3119949229481779 / 10000000000000000 : ℝ) = - (3119949229481779 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3119949229481779 / 2500000000000000 : ℚ)) - (U := (1107629986064208944581 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3119949229481779 / 2500000000000000 : ℝ) ≤ - (1107629986064208944581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1487398958081779 / 5000000000000000 : ℝ)) (q := - (3119949229481779 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3119949229481779 / 10000000000000000 : ℚ)) + (r' := (3119949229481779 / 2500000000000000 : ℚ)) + (U := (-(5823841816935791055419 / 5000000000000000000000 : ℚ))) + (U' := (1107629986064208944581 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (1487398958081779 / 5000000000000000 : ℚ)) + (q := (3119949229481779 / 10000000000000000 : ℚ)) + (U := (-(5823841816935791055419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_10 : Uω (aρ 10) (bρ 10) (922531203149 / 2000000000000 : ℝ) ≤ @@ -654,26 +573,21 @@ lemma U_437_10 : have hlg : Real.log (5171105915666843 / 20000000000000000 : ℝ) ≤ (-(6763228486011371335239 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5171105915666843 / 20000000000000000 : ℝ) = - (5171105915666843 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5171105915666843 / 5000000000000000 : ℚ)) - (U := (168243316988628664761 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5171105915666843 / 5000000000000000 : ℝ) ≤ - (168243316988628664761 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2294564406361843 / 10000000000000000 : ℝ)) (q := - (5171105915666843 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5171105915666843 / 20000000000000000 : ℚ)) + (r' := (5171105915666843 / 5000000000000000 : ℚ)) + (U := (-(6763228486011371335239 / 5000000000000000000000 : ℚ))) + (U' := (168243316988628664761 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (2294564406361843 / 10000000000000000 : ℚ)) + (q := (5171105915666843 / 20000000000000000 : ℚ)) + (U := (-(6763228486011371335239 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_11 : Uω (aρ 11) (bρ 11) (922531203149 / 2000000000000 : ℝ) ≤ @@ -681,26 +595,21 @@ lemma U_437_11 : have hlg : Real.log (3643233423054183 / 20000000000000000 : ℝ) ≤ (-(17028606823962924506891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3643233423054183 / 20000000000000000 : ℝ) = - (3643233423054183 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3643233423054183 / 2500000000000000 : ℚ)) - (U := (3765808585037075493109 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3643233423054183 / 2500000000000000 : ℝ) ≤ - (3765808585037075493109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1185168539954183 / 10000000000000000 : ℝ)) (q := - (3643233423054183 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3643233423054183 / 20000000000000000 : ℚ)) + (r' := (3643233423054183 / 2500000000000000 : ℚ)) + (U := (-(17028606823962924506891 / 10000000000000000000000 : ℚ))) + (U' := (3765808585037075493109 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (922531203149 / 2000000000000 : ℚ)) + (s := (1185168539954183 / 10000000000000000 : ℚ)) + (q := (3643233423054183 / 20000000000000000 : ℚ)) + (U := (-(17028606823962924506891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_437_12 : Uω (aρ 12) (bρ 12) (922531203149 / 2000000000000 : ℝ) ≤ @@ -816,25 +725,21 @@ lemma U_438_1 : have hlg : Real.log (2277372401326749 / 5000000000000000 : ℝ) ≤ (-(7864155890938650200869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2277372401326749 / 5000000000000000 : ℝ) = - (2277372401326749 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2277372401326749 / 1250000000000000 : ℚ)) - (U := (5998787715061349799131 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2277372401326749 / 1250000000000000 : ℝ) ≤ - (5998787715061349799131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (284669331766531 / 625000000000000 : ℝ)) (q := - (2277372401326749 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2277372401326749 / 5000000000000000 : ℚ)) + (r' := (2277372401326749 / 1250000000000000 : ℚ)) + (U := (-(7864155890938650200869 / 10000000000000000000000 : ℚ))) + (U' := (5998787715061349799131 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (284669331766531 / 625000000000000 : ℚ)) + (q := (2277372401326749 / 5000000000000000 : ℚ)) + (U := (-(7864155890938650200869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_2 : Uω (aρ 2) (bρ 2) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -842,25 +747,21 @@ lemma U_438_2 : have hlg : Real.log (453077712448771 / 1000000000000000 : ℝ) ≤ (-(3958458085164027500651 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (453077712448771 / 1000000000000000 : ℝ) = - (453077712448771 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (453077712448771 / 250000000000000 : ℚ)) - (U := (2973013717835972499349 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (453077712448771 / 250000000000000 : ℝ) ≤ - (2973013717835972499349 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (113263574111073 / 250000000000000 : ℝ)) (q := - (453077712448771 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (453077712448771 / 1000000000000000 : ℚ)) + (r' := (453077712448771 / 250000000000000 : ℚ)) + (U := (-(3958458085164027500651 / 5000000000000000000000 : ℚ))) + (U' := (2973013717835972499349 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (113263574111073 / 250000000000000 : ℚ)) + (q := (453077712448771 / 1000000000000000 : ℚ)) + (U := (-(3958458085164027500651 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_3 : Uω (aρ 3) (bρ 3) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -868,25 +769,21 @@ lemma U_438_3 : have hlg : Real.log (2241395006729339 / 5000000000000000 : ℝ) ≤ (-(250731084071014719003 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2241395006729339 / 5000000000000000 : ℝ) = - (2241395006729339 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2241395006729339 / 1250000000000000 : ℚ)) - (U := (182485903616485280997 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2241395006729339 / 1250000000000000 : ℝ) ≤ - (182485903616485280997 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (560245606091857 / 1250000000000000 : ℝ)) (q := - (2241395006729339 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2241395006729339 / 5000000000000000 : ℚ)) + (r' := (2241395006729339 / 1250000000000000 : ℚ)) + (U := (-(250731084071014719003 / 312500000000000000000 : ℚ))) + (U' := (182485903616485280997 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (560245606091857 / 1250000000000000 : ℚ)) + (q := (2241395006729339 / 5000000000000000 : ℚ)) + (U := (-(250731084071014719003 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_4 : Uω (aρ 4) (bρ 4) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -894,24 +791,21 @@ lemma U_438_4 : have hlg : Real.log (70446904955057 / 160000000000000 : ℝ) ≤ (-(8203145098388216551507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70446904955057 / 160000000000000 : ℝ) = (70446904955057 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70446904955057 / 40000000000000 : ℚ)) - (U := (5659798507611783448493 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70446904955057 / 40000000000000 : ℝ) ≤ - (5659798507611783448493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35204336978117 / 80000000000000 : ℝ)) (q := - (70446904955057 / 160000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70446904955057 / 160000000000000 : ℚ)) + (r' := (70446904955057 / 40000000000000 : ℚ)) + (U := (-(8203145098388216551507 / 10000000000000000000000 : ℚ))) + (U' := (5659798507611783448493 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (35204336978117 / 80000000000000 : ℚ)) + (q := (70446904955057 / 160000000000000 : ℚ)) + (U := (-(8203145098388216551507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_5 : Uω (aρ 5) (bρ 5) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -919,25 +813,21 @@ lemma U_438_5 : have hlg : Real.log (267556925210983 / 625000000000000 : ℝ) ≤ (-(265131031560338101691 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (267556925210983 / 625000000000000 : ℝ) = - (267556925210983 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (267556925210983 / 156250000000000 : ℚ)) - (U := (168085956127161898309 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (267556925210983 / 156250000000000 : ℝ) ≤ - (168085956127161898309 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1068672632242239 / 2500000000000000 : ℝ)) (q := - (267556925210983 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (267556925210983 / 625000000000000 : ℚ)) + (r' := (267556925210983 / 156250000000000 : ℚ)) + (U := (-(265131031560338101691 / 312500000000000000000 : ℚ))) + (U' := (168085956127161898309 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (1068672632242239 / 2500000000000000 : ℚ)) + (q := (267556925210983 / 625000000000000 : ℚ)) + (U := (-(265131031560338101691 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_6 : Uω (aρ 6) (bρ 6) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -945,25 +835,21 @@ lemma U_438_6 : have hlg : Real.log (4104942594083463 / 10000000000000000 : ℝ) ≤ (-(890393334056470965597 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4104942594083463 / 10000000000000000 : ℝ) = - (4104942594083463 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4104942594083463 / 2500000000000000 : ℚ)) - (U := (495901026543529034403 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4104942594083463 / 2500000000000000 : ℝ) ≤ - (495901026543529034403 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2044997242762213 / 5000000000000000 : ℝ)) (q := - (4104942594083463 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4104942594083463 / 10000000000000000 : ℚ)) + (r' := (4104942594083463 / 2500000000000000 : ℚ)) + (U := (-(890393334056470965597 / 1000000000000000000000 : ℚ))) + (U' := (495901026543529034403 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (2044997242762213 / 5000000000000000 : ℚ)) + (q := (4104942594083463 / 10000000000000000 : ℚ)) + (U := (-(890393334056470965597 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_7 : Uω (aρ 7) (bρ 7) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -971,25 +857,21 @@ lemma U_438_7 : have hlg : Real.log (3862657805392399 / 10000000000000000 : ℝ) ≤ (-(4756147976599214266163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3862657805392399 / 10000000000000000 : ℝ) = - (3862657805392399 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3862657805392399 / 2500000000000000 : ℚ)) - (U := (2175323826400785733837 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3862657805392399 / 2500000000000000 : ℝ) ≤ - (2175323826400785733837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1914543144451149 / 5000000000000000 : ℝ)) (q := - (3862657805392399 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3862657805392399 / 10000000000000000 : ℚ)) + (r' := (3862657805392399 / 2500000000000000 : ℚ)) + (U := (-(4756147976599214266163 / 5000000000000000000000 : ℚ))) + (U' := (2175323826400785733837 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (1914543144451149 / 5000000000000000 : ℚ)) + (q := (3862657805392399 / 10000000000000000 : ℚ)) + (U := (-(4756147976599214266163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_8 : Uω (aρ 8) (bρ 8) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -997,25 +879,21 @@ lemma U_438_8 : have hlg : Real.log (7082926376798527 / 20000000000000000 : ℝ) ≤ (-(1297556400836899823467 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7082926376798527 / 20000000000000000 : ℝ) = - (7082926376798527 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7082926376798527 / 5000000000000000 : ℚ)) - (U := (435311549913100176533 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7082926376798527 / 5000000000000000 : ℝ) ≤ - (435311549913100176533 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3470238706256027 / 10000000000000000 : ℝ)) (q := - (7082926376798527 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7082926376798527 / 20000000000000000 : ℚ)) + (r' := (7082926376798527 / 5000000000000000 : ℚ)) + (U := (-(1297556400836899823467 / 1250000000000000000000 : ℚ))) + (U' := (435311549913100176533 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (3470238706256027 / 10000000000000000 : ℚ)) + (q := (7082926376798527 / 20000000000000000 : ℚ)) + (U := (-(1297556400836899823467 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_9 : Uω (aρ 9) (bρ 9) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -1023,23 +901,21 @@ lemma U_438_9 : have hlg : Real.log (7817232659329 / 25000000000000 : ℝ) ≤ (-(11625452123025537848547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (7817232659329 / 25000000000000 : ℝ) = (7817232659329 / 6250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7817232659329 / 6250000000000 : ℚ)) - (U := (2237491482974462151453 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (7817232659329 / 6250000000000 : ℝ) ≤ - (2237491482974462151453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29820640852807 / 100000000000000 : ℝ)) (q := - (7817232659329 / 25000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7817232659329 / 25000000000000 : ℚ)) + (r' := (7817232659329 / 6250000000000 : ℚ)) + (U := (-(11625452123025537848547 / 10000000000000000000000 : ℚ))) + (U' := (2237491482974462151453 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (29820640852807 / 100000000000000 : ℚ)) + (q := (7817232659329 / 25000000000000 : ℚ)) + (U := (-(11625452123025537848547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_10 : Uω (aρ 10) (bρ 10) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -1047,26 +923,21 @@ lemma U_438_10 : have hlg : Real.log (5186022903438361 / 20000000000000000 : ℝ) ≤ (-(13497651695297014300729 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5186022903438361 / 20000000000000000 : ℝ) = - (5186022903438361 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5186022903438361 / 5000000000000000 : ℚ)) - (U := (365291910702985699271 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5186022903438361 / 5000000000000000 : ℝ) ≤ - (365291910702985699271 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2302859894750861 / 10000000000000000 : ℝ)) (q := - (5186022903438361 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5186022903438361 / 20000000000000000 : ℚ)) + (r' := (5186022903438361 / 5000000000000000 : ℚ)) + (U := (-(13497651695297014300729 / 10000000000000000000000 : ℚ))) + (U' := (365291910702985699271 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (2302859894750861 / 10000000000000000 : ℚ)) + (q := (5186022903438361 / 20000000000000000 : ℚ)) + (U := (-(13497651695297014300729 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_11 : Uω (aρ 11) (bρ 11) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -1074,25 +945,21 @@ lemma U_438_11 : have hlg : Real.log (183176384123639 / 1000000000000000 : ℝ) ≤ (-(1060816088683519187111 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (183176384123639 / 1000000000000000 : ℝ) = - (183176384123639 / 125000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (183176384123639 / 125000000000000 : ℚ)) - (U := (238834874378980812889 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (183176384123639 / 125000000000000 : ℝ) ≤ - (238834874378980812889 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29971032499757 / 250000000000000 : ℝ)) (q := - (183176384123639 / 1000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (183176384123639 / 1000000000000000 : ℚ)) + (r' := (183176384123639 / 125000000000000 : ℚ)) + (U := (-(1060816088683519187111 / 625000000000000000000 : ℚ))) + (U' := (238834874378980812889 / 625000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1847711006051 / 4000000000000 : ℚ)) + (s := (29971032499757 / 250000000000000 : ℚ)) + (q := (183176384123639 / 1000000000000000 : ℚ)) + (U := (-(1060816088683519187111 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_438_12 : Uω (aρ 12) (bρ 12) (1847711006051 / 4000000000000 : ℝ) ≤ @@ -1208,25 +1075,21 @@ lemma U_439_1 : have hlg : Real.log (2280683176780883 / 5000000000000000 : ℝ) ≤ (-(7665653075113846959 / 9765625000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2280683176780883 / 5000000000000000 : ℝ) = - (2280683176780883 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2280683176780883 / 1250000000000000 : ℚ)) - (U := (5872377790120528041 / 9765625000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2280683176780883 / 1250000000000000 : ℝ) ≤ - (5872377790120528041 / 9765625000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1140332727674633 / 2500000000000000 : ℝ)) (q := - (2280683176780883 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2280683176780883 / 5000000000000000 : ℚ)) + (r' := (2280683176780883 / 1250000000000000 : ℚ)) + (U := (-(7665653075113846959 / 9765625000000000000 : ℚ))) + (U' := (5872377790120528041 / 9765625000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (1140332727674633 / 2500000000000000 : ℚ)) + (q := (2280683176780883 / 5000000000000000 : ℚ)) + (U := (-(7665653075113846959 / 9765625000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_2 : Uω (aρ 2) (bρ 2) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1234,25 +1097,21 @@ lemma U_439_2 : have hlg : Real.log (453739896560137 / 1000000000000000 : ℝ) ≤ (-(7902311596652221809187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (453739896560137 / 1000000000000000 : ℝ) = - (453739896560137 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (453739896560137 / 250000000000000 : ℚ)) - (U := (5960632009347778190813 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (453739896560137 / 250000000000000 : ℝ) ≤ - (5960632009347778190813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (226858257364387 / 500000000000000 : ℝ)) (q := - (453739896560137 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (453739896560137 / 1000000000000000 : ℚ)) + (r' := (453739896560137 / 250000000000000 : ℚ)) + (U := (-(7902311596652221809187 / 10000000000000000000000 : ℚ))) + (U' := (5960632009347778190813 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (226858257364387 / 500000000000000 : ℚ)) + (q := (453739896560137 / 1000000000000000 : ℚ)) + (U := (-(7902311596652221809187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_3 : Uω (aρ 3) (bρ 3) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1260,25 +1119,21 @@ lemma U_439_3 : have hlg : Real.log (448941273011223 / 1000000000000000 : ℝ) ≤ (-(1601726388699282176059 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (448941273011223 / 1000000000000000 : ℝ) = - (448941273011223 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (448941273011223 / 250000000000000 : ℚ)) - (U := (1170862332500717823941 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (448941273011223 / 250000000000000 : ℝ) ≤ - (1170862332500717823941 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (224429439132973 / 500000000000000 : ℝ)) (q := - (448941273011223 / 1000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (448941273011223 / 1000000000000000 : ℚ)) + (r' := (448941273011223 / 250000000000000 : ℚ)) + (U := (-(1601726388699282176059 / 2000000000000000000000 : ℚ))) + (U' := (1170862332500717823941 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (224429439132973 / 500000000000000 : ℚ)) + (q := (448941273011223 / 1000000000000000 : ℚ)) + (U := (-(1601726388699282176059 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_4 : Uω (aρ 4) (bρ 4) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1286,25 +1141,21 @@ lemma U_439_4 : have hlg : Real.log (8819113298114521 / 20000000000000000 : ℝ) ≤ (-(8188109411627823297001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8819113298114521 / 20000000000000000 : ℝ) = - (8819113298114521 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8819113298114521 / 5000000000000000 : ℚ)) - (U := (5674834194372176702999 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8819113298114521 / 5000000000000000 : ℝ) ≤ - (5674834194372176702999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4407170801614521 / 10000000000000000 : ℝ)) (q := - (8819113298114521 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8819113298114521 / 20000000000000000 : ℚ)) + (r' := (8819113298114521 / 5000000000000000 : ℚ)) + (U := (-(8188109411627823297001 / 10000000000000000000000 : ℚ))) + (U' := (5674834194372176702999 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (4407170801614521 / 10000000000000000 : ℚ)) + (q := (8819113298114521 / 20000000000000000 : ℚ)) + (U := (-(8188109411627823297001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_5 : Uω (aρ 5) (bρ 5) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1312,25 +1163,21 @@ lemma U_439_5 : have hlg : Real.log (8575083846090523 / 20000000000000000 : ℝ) ≤ (-(8468715020601605035629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8575083846090523 / 20000000000000000 : ℝ) = - (8575083846090523 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8575083846090523 / 5000000000000000 : ℚ)) - (U := (5394228585398394964371 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8575083846090523 / 5000000000000000 : ℝ) ≤ - (5394228585398394964371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4281331268925523 / 10000000000000000 : ℝ)) (q := - (8575083846090523 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8575083846090523 / 20000000000000000 : ℚ)) + (r' := (8575083846090523 / 5000000000000000 : ℚ)) + (U := (-(8468715020601605035629 / 10000000000000000000000 : ℚ))) + (U' := (5394228585398394964371 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (4281331268925523 / 10000000000000000 : ℚ)) + (q := (8575083846090523 / 20000000000000000 : ℚ)) + (U := (-(8468715020601605035629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_6 : Uω (aρ 6) (bρ 6) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1338,25 +1185,21 @@ lemma U_439_6 : have hlg : Real.log (4111588254458403 / 10000000000000000 : ℝ) ≤ (-(2221939255013808664823 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4111588254458403 / 10000000000000000 : ℝ) = - (4111588254458403 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4111588254458403 / 2500000000000000 : ℚ)) - (U := (1243796646486191335177 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4111588254458403 / 2500000000000000 : ℝ) ≤ - (1243796646486191335177 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2048332153445903 / 5000000000000000 : ℝ)) (q := - (4111588254458403 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4111588254458403 / 10000000000000000 : ℚ)) + (r' := (4111588254458403 / 2500000000000000 : ℚ)) + (U := (-(2221939255013808664823 / 2500000000000000000000 : ℚ))) + (U' := (1243796646486191335177 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (2048332153445903 / 5000000000000000 : ℚ)) + (q := (4111588254458403 / 10000000000000000 : ℚ)) + (U := (-(2221939255013808664823 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_7 : Uω (aρ 7) (bρ 7) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1364,25 +1207,21 @@ lemma U_439_7 : have hlg : Real.log (309546980614561 / 800000000000000 : ℝ) ≤ (-(1186877314178239240791 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (309546980614561 / 800000000000000 : ℝ) = - (309546980614561 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (309546980614561 / 200000000000000 : ℚ)) - (U := (545990636571760759209 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (309546980614561 / 200000000000000 : ℝ) ≤ - (545990636571760759209 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (153432947763961 / 400000000000000 : ℝ)) (q := - (309546980614561 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (309546980614561 / 800000000000000 : ℚ)) + (r' := (309546980614561 / 200000000000000 : ℚ)) + (U := (-(1186877314178239240791 / 1250000000000000000000 : ℚ))) + (U' := (545990636571760759209 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (153432947763961 / 400000000000000 : ℚ)) + (q := (309546980614561 / 800000000000000 : ℚ)) + (U := (-(1186877314178239240791 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_8 : Uω (aρ 8) (bρ 8) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1390,25 +1229,21 @@ lemma U_439_8 : have hlg : Real.log (1774110162905591 / 5000000000000000 : ℝ) ≤ (-(518069465680476440557 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1774110162905591 / 5000000000000000 : ℝ) = - (1774110162905591 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1774110162905591 / 1250000000000000 : ℚ)) - (U := (175077714619523559443 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1774110162905591 / 1250000000000000 : ℝ) ≤ - (175077714619523559443 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (869282870424341 / 2500000000000000 : ℝ)) (q := - (1774110162905591 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1774110162905591 / 5000000000000000 : ℚ)) + (r' := (1774110162905591 / 1250000000000000 : ℚ)) + (U := (-(518069465680476440557 / 500000000000000000000 : ℚ))) + (U' := (175077714619523559443 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (869282870424341 / 2500000000000000 : ℚ)) + (q := (1774110162905591 / 5000000000000000 : ℚ)) + (U := (-(518069465680476440557 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_9 : Uω (aρ 9) (bρ 9) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1416,24 +1251,21 @@ lemma U_439_9 : have hlg : Real.log (50141366407917 / 160000000000000 : ℝ) ≤ (-(11603274705019627962981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (50141366407917 / 160000000000000 : ℝ) = (50141366407917 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50141366407917 / 40000000000000 : ℚ)) - (U := (2259668900980372037019 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50141366407917 / 40000000000000 : ℝ) ≤ - (2259668900980372037019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23914618075397 / 80000000000000 : ℝ)) (q := - (50141366407917 / 160000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50141366407917 / 160000000000000 : ℚ)) + (r' := (50141366407917 / 40000000000000 : ℚ)) + (U := (-(11603274705019627962981 / 10000000000000000000000 : ℚ))) + (U' := (2259668900980372037019 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (23914618075397 / 80000000000000 : ℚ)) + (q := (50141366407917 / 160000000000000 : ℚ)) + (U := (-(11603274705019627962981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_10 : Uω (aρ 10) (bρ 10) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1441,26 +1273,21 @@ lemma U_439_10 : have hlg : Real.log (5200929086686699 / 20000000000000000 : ℝ) ≤ (-(13468949928897215958101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5200929086686699 / 20000000000000000 : ℝ) = - (5200929086686699 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5200929086686699 / 5000000000000000 : ℚ)) - (U := (393993677102784041899 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5200929086686699 / 5000000000000000 : ℝ) ≤ - (393993677102784041899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2311144578616699 / 10000000000000000 : ℝ)) (q := - (5200929086686699 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5200929086686699 / 20000000000000000 : ℚ)) + (r' := (5200929086686699 / 5000000000000000 : ℚ)) + (U := (-(13468949928897215958101 / 10000000000000000000000 : ℚ))) + (U' := (393993677102784041899 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (2311144578616699 / 10000000000000000 : ℚ)) + (q := (5200929086686699 / 20000000000000000 : ℚ)) + (U := (-(13468949928897215958101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_11 : Uω (aρ 11) (bρ 11) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1468,25 +1295,21 @@ lemma U_439_11 : have hlg : Real.log (368370391680399 / 2000000000000000 : ℝ) ≤ (-(16918135276424289182913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (368370391680399 / 2000000000000000 : ℝ) = - (368370391680399 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (368370391680399 / 250000000000000 : ℚ)) - (U := (3876280132575710817087 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (368370391680399 / 250000000000000 : ℝ) ≤ - (3876280132575710817087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121239603493899 / 1000000000000000 : ℝ)) (q := - (368370391680399 / 2000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (368370391680399 / 2000000000000000 : ℚ)) + (r' := (368370391680399 / 250000000000000 : ℚ)) + (U := (-(16918135276424289182913 / 10000000000000000000000 : ℚ))) + (U' := (3876280132575710817087 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (462589901451 / 1000000000000 : ℚ)) + (s := (121239603493899 / 1000000000000000 : ℚ)) + (q := (368370391680399 / 2000000000000000 : ℚ)) + (U := (-(16918135276424289182913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_439_12 : Uω (aρ 12) (bρ 12) (462589901451 / 1000000000000 : ℝ) ≤ @@ -1603,25 +1426,21 @@ lemma U_440_1 : have hlg : Real.log (9135975808641307 / 20000000000000000 : ℝ) ≤ (-(979390335049681997199 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9135975808641307 / 20000000000000000 : ℝ) = - (9135975808641307 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9135975808641307 / 5000000000000000 : ℚ)) - (U := (753477615700318002801 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9135975808641307 / 5000000000000000 : ℝ) ≤ - (753477615700318002801 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4567952512833807 / 10000000000000000 : ℝ)) (q := - (9135975808641307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9135975808641307 / 20000000000000000 : ℚ)) + (r' := (9135975808641307 / 5000000000000000 : ℚ)) + (U := (-(979390335049681997199 / 1250000000000000000000 : ℚ))) + (U' := (753477615700318002801 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (4567952512833807 / 10000000000000000 : ℚ)) + (q := (9135975808641307 / 20000000000000000 : ℚ)) + (U := (-(979390335049681997199 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_2 : Uω (aρ 2) (bρ 2) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1629,25 +1448,21 @@ lemma U_440_2 : have hlg : Real.log (9088041611437987 / 20000000000000000 : ℝ) ≤ (-(3943864161712085556341 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9088041611437987 / 20000000000000000 : ℝ) = - (9088041611437987 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9088041611437987 / 5000000000000000 : ℚ)) - (U := (2987607641287914443659 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9088041611437987 / 5000000000000000 : ℝ) ≤ - (2987607641287914443659 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4543787328140487 / 10000000000000000 : ℝ)) (q := - (9088041611437987 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9088041611437987 / 20000000000000000 : ℚ)) + (r' := (9088041611437987 / 5000000000000000 : ℚ)) + (U := (-(3943864161712085556341 / 5000000000000000000000 : ℚ))) + (U' := (2987607641287914443659 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (4543787328140487 / 10000000000000000 : ℚ)) + (q := (9088041611437987 / 20000000000000000 : ℚ)) + (U := (-(3943864161712085556341 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_3 : Uω (aρ 3) (bρ 3) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1655,25 +1470,21 @@ lemma U_440_3 : have hlg : Real.log (899207088635803 / 2000000000000000 : ℝ) ≤ (-(7993890966444840479467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (899207088635803 / 2000000000000000 : ℝ) = - (899207088635803 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (899207088635803 / 500000000000000 : ℚ)) - (U := (5869052639555159520533 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (899207088635803 / 500000000000000 : ℝ) ≤ - (5869052639555159520533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (449521270941053 / 1000000000000000 : ℝ)) (q := - (899207088635803 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (899207088635803 / 2000000000000000 : ℚ)) + (r' := (899207088635803 / 500000000000000 : ℚ)) + (U := (-(7993890966444840479467 / 10000000000000000000000 : ℚ))) + (U' := (5869052639555159520533 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (449521270941053 / 1000000000000000 : ℚ)) + (q := (899207088635803 / 2000000000000000 : ℚ)) + (U := (-(7993890966444840479467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_4 : Uω (aρ 4) (bρ 4) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1681,25 +1492,21 @@ lemma U_440_4 : have hlg : Real.log (8832363455292731 / 20000000000000000 : ℝ) ≤ (-(4086548161261261473791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8832363455292731 / 20000000000000000 : ℝ) = - (8832363455292731 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8832363455292731 / 5000000000000000 : ℚ)) - (U := (2844923641738738526209 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8832363455292731 / 5000000000000000 : ℝ) ≤ - (2844923641738738526209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4413799459410231 / 10000000000000000 : ℝ)) (q := - (8832363455292731 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8832363455292731 / 20000000000000000 : ℚ)) + (r' := (8832363455292731 / 5000000000000000 : ℚ)) + (U := (-(4086548161261261473791 / 5000000000000000000000 : ℚ))) + (U' := (2844923641738738526209 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (4413799459410231 / 10000000000000000 : ℚ)) + (q := (8832363455292731 / 20000000000000000 : ℚ)) + (U := (-(4086548161261261473791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_5 : Uω (aρ 5) (bρ 5) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1707,25 +1514,21 @@ lemma U_440_5 : have hlg : Real.log (171766920518411 / 400000000000000 : ℝ) ≤ (-(169065220407198884057 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (171766920518411 / 400000000000000 : ℝ) = - (171766920518411 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (171766920518411 / 100000000000000 : ℚ)) - (U := (108193651712801115943 / 200000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (171766920518411 / 100000000000000 : ℝ) ≤ - (108193651712801115943 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85759438987461 / 200000000000000 : ℝ)) (q := - (171766920518411 / 400000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (171766920518411 / 400000000000000 : ℚ)) + (r' := (171766920518411 / 100000000000000 : ℚ)) + (U := (-(169065220407198884057 / 200000000000000000000 : ℚ))) + (U' := (108193651712801115943 / 200000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (85759438987461 / 200000000000000 : ℚ)) + (q := (171766920518411 / 400000000000000 : ℚ)) + (U := (-(169065220407198884057 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_6 : Uω (aρ 6) (bρ 6) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1733,25 +1536,21 @@ lemma U_440_6 : have hlg : Real.log (4118233836572227 / 10000000000000000 : ℝ) ≤ (-(8871607014660831809501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4118233836572227 / 10000000000000000 : ℝ) = - (4118233836572227 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4118233836572227 / 2500000000000000 : ℚ)) - (U := (4991336591339168190499 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4118233836572227 / 2500000000000000 : ℝ) ≤ - (4991336591339168190499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2051666985868477 / 5000000000000000 : ℝ)) (q := - (4118233836572227 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4118233836572227 / 10000000000000000 : ℚ)) + (r' := (4118233836572227 / 2500000000000000 : ℚ)) + (U := (-(8871607014660831809501 / 10000000000000000000000 : ℚ))) + (U' := (4991336591339168190499 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (2051666985868477 / 5000000000000000 : ℚ)) + (q := (4118233836572227 / 10000000000000000 : ℚ)) + (U := (-(8871607014660831809501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_7 : Uω (aρ 7) (bρ 7) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1759,25 +1558,21 @@ lemma U_440_7 : have hlg : Real.log (7752033016989401 / 20000000000000000 : ℝ) ≤ (-(9477771392971459838581 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7752033016989401 / 20000000000000000 : ℝ) = - (7752033016989401 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7752033016989401 / 5000000000000000 : ℚ)) - (U := (4385172213028540161419 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7752033016989401 / 5000000000000000 : ℝ) ≤ - (4385172213028540161419 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3842560696341901 / 10000000000000000 : ℝ)) (q := - (7752033016989401 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7752033016989401 / 20000000000000000 : ℚ)) + (r' := (7752033016989401 / 5000000000000000 : ℚ)) + (U := (-(9477771392971459838581 / 10000000000000000000000 : ℚ))) + (U' := (4385172213028540161419 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (3842560696341901 / 10000000000000000 : ℚ)) + (q := (7752033016989401 / 20000000000000000 : ℚ)) + (U := (-(9477771392971459838581 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_8 : Uω (aρ 8) (bρ 8) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1785,25 +1580,21 @@ lemma U_440_8 : have hlg : Real.log (1421990774837217 / 4000000000000000 : ℝ) ≤ (-(5171182583481206675893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1421990774837217 / 4000000000000000 : ℝ) = - (1421990774837217 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1421990774837217 / 1000000000000000 : ℚ)) - (U := (1760289219518793324107 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1421990774837217 / 1000000000000000 : ℝ) ≤ - (1760289219518793324107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (696804640975717 / 2000000000000000 : ℝ)) (q := - (1421990774837217 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1421990774837217 / 4000000000000000 : ℚ)) + (r' := (1421990774837217 / 1000000000000000 : ℚ)) + (U := (-(5171182583481206675893 / 5000000000000000000000 : ℚ))) + (U' := (1760289219518793324107 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (696804640975717 / 2000000000000000 : ℚ)) + (q := (1421990774837217 / 4000000000000000 : ℚ)) + (U := (-(5171182583481206675893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_9 : Uω (aρ 9) (bρ 9) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1811,25 +1602,21 @@ lemma U_440_9 : have hlg : Real.log (785194062665077 / 2500000000000000 : ℝ) ≤ (-(11581151095201511045311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (785194062665077 / 2500000000000000 : ℝ) = - (785194062665077 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (785194062665077 / 625000000000000 : ℚ)) - (U := (2281792510798488954689 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (785194062665077 / 625000000000000 : ℝ) ≤ - (2281792510798488954689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (749146865093279 / 2500000000000000 : ℝ)) (q := - (785194062665077 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (785194062665077 / 2500000000000000 : ℚ)) + (r' := (785194062665077 / 625000000000000 : ℚ)) + (U := (-(11581151095201511045311 / 10000000000000000000000 : ℚ))) + (U' := (2281792510798488954689 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (749146865093279 / 2500000000000000 : ℚ)) + (q := (785194062665077 / 2500000000000000 : ℚ)) + (U := (-(11581151095201511045311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_10 : Uω (aρ 10) (bρ 10) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1837,26 +1624,21 @@ lemma U_440_10 : have hlg : Real.log (1303956145297307 / 5000000000000000 : ℝ) ≤ (-(1344035079882253336513 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1303956145297307 / 5000000000000000 : ℝ) = - (1303956145297307 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1303956145297307 / 1250000000000000 : ℚ)) - (U := (42259280717746663487 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1303956145297307 / 1250000000000000 : ℝ) ≤ - (42259280717746663487 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (289927321717091 / 1250000000000000 : ℝ)) (q := - (1303956145297307 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1303956145297307 / 5000000000000000 : ℚ)) + (r' := (1303956145297307 / 1250000000000000 : ℚ)) + (U := (-(1344035079882253336513 / 1000000000000000000000 : ℚ))) + (U' := (42259280717746663487 / 1000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (289927321717091 / 1250000000000000 : ℚ)) + (q := (1303956145297307 / 5000000000000000 : ℚ)) + (U := (-(1344035079882253336513 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_11 : Uω (aρ 11) (bρ 11) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1864,26 +1646,21 @@ lemma U_440_11 : have hlg : Real.log (3703766041254587 / 20000000000000000 : ℝ) ≤ (-(16863821217932963072499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3703766041254587 / 20000000000000000 : ℝ) = - (3703766041254587 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3703766041254587 / 2500000000000000 : ℚ)) - (U := (3930594191067036927501 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3703766041254587 / 2500000000000000 : ℝ) ≤ - (3930594191067036927501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1225836660007087 / 10000000000000000 : ℝ)) (q := - (3703766041254587 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3703766041254587 / 20000000000000000 : ℚ)) + (r' := (3703766041254587 / 2500000000000000 : ℚ)) + (U := (-(16863821217932963072499 / 10000000000000000000000 : ℚ))) + (U' := (3930594191067036927501 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1853008205557 / 4000000000000 : ℚ)) + (s := (1225836660007087 / 10000000000000000 : ℚ)) + (q := (3703766041254587 / 20000000000000000 : ℚ)) + (U := (-(16863821217932963072499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_440_12 : Uω (aρ 12) (bρ 12) (1853008205557 / 4000000000000 : ℝ) ≤ @@ -1999,25 +1776,21 @@ lemma U_441_1 : have hlg : Real.log (457460945493081 / 1000000000000000 : ℝ) ≤ (-(7820637624329189336659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (457460945493081 / 1000000000000000 : ℝ) = - (457460945493081 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (457460945493081 / 250000000000000 : ℚ)) - (U := (6042305981670810663341 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (457460945493081 / 250000000000000 : ℝ) ≤ - (6042305981670810663341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228728705733581 / 500000000000000 : ℝ)) (q := - (457460945493081 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (457460945493081 / 1000000000000000 : ℚ)) + (r' := (457460945493081 / 250000000000000 : ℚ)) + (U := (-(7820637624329189336659 / 10000000000000000000000 : ℚ))) + (U' := (6042305981670810663341 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (185565680531 / 400000000000 : ℚ)) + (s := (228728705733581 / 500000000000000 : ℚ)) + (q := (457460945493081 / 1000000000000000 : ℚ)) + (U := (-(7820637624329189336659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_2 : Uω (aρ 2) (bρ 2) (185565680531 / 400000000000 : ℝ) ≤ @@ -2025,25 +1798,21 @@ lemma U_441_2 : have hlg : Real.log (9101285289689857 / 20000000000000000 : ℝ) ≤ (-(7873166288595550170051 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9101285289689857 / 20000000000000000 : ℝ) = - (9101285289689857 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9101285289689857 / 5000000000000000 : ℚ)) - (U := (5989777317404449829949 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9101285289689857 / 5000000000000000 : ℝ) ≤ - (5989777317404449829949 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4550409507009857 / 10000000000000000 : ℝ)) (q := - (9101285289689857 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9101285289689857 / 20000000000000000 : ℚ)) + (r' := (9101285289689857 / 5000000000000000 : ℚ)) + (U := (-(7873166288595550170051 / 10000000000000000000000 : ℚ))) + (U' := (5989777317404449829949 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (185565680531 / 400000000000 : ℚ)) + (s := (4550409507009857 / 10000000000000000 : ℚ)) + (q := (9101285289689857 / 20000000000000000 : ℚ)) + (U := (-(7873166288595550170051 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_3 : Uω (aρ 3) (bρ 3) (185565680531 / 400000000000 : ℝ) ≤ @@ -2051,25 +1820,21 @@ lemma U_441_3 : have hlg : Real.log (900531630534973 / 2000000000000000 : ℝ) ≤ (-(3989585847491946285049 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (900531630534973 / 2000000000000000 : ℝ) = - (900531630534973 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (900531630534973 / 500000000000000 : ℚ)) - (U := (2941885955508053714951 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (900531630534973 / 500000000000000 : ℝ) ≤ - (2941885955508053714951 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (450183662901973 / 1000000000000000 : ℝ)) (q := - (900531630534973 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (900531630534973 / 2000000000000000 : ℚ)) + (r' := (900531630534973 / 500000000000000 : ℚ)) + (U := (-(3989585847491946285049 / 5000000000000000000000 : ℚ))) + (U' := (2941885955508053714951 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (185565680531 / 400000000000 : ℚ)) + (s := (450183662901973 / 1000000000000000 : ℚ)) + (q := (900531630534973 / 2000000000000000 : ℚ)) + (U := (-(3989585847491946285049 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_4 : Uω (aρ 4) (bρ 4) (185565680531 / 400000000000 : ℝ) ≤ @@ -2077,25 +1842,21 @@ lemma U_441_4 : have hlg : Real.log (4422806795506861 / 10000000000000000 : ℝ) ≤ (-(1631621152635130144881 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4422806795506861 / 10000000000000000 : ℝ) = - (4422806795506861 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4422806795506861 / 2500000000000000 : ℚ)) - (U := (1140967568564869855119 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4422806795506861 / 2500000000000000 : ℝ) ≤ - (1140967568564869855119 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2210214047874361 / 5000000000000000 : ℝ)) (q := - (4422806795506861 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4422806795506861 / 10000000000000000 : ℚ)) + (r' := (4422806795506861 / 2500000000000000 : ℚ)) + (U := (-(1631621152635130144881 / 2000000000000000000000 : ℚ))) + (U' := (1140967568564869855119 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (185565680531 / 400000000000 : ℚ)) + (s := (2210214047874361 / 5000000000000000 : ℚ)) + (q := (4422806795506861 / 10000000000000000 : ℚ)) + (U := (-(1631621152635130144881 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_5 : Uω (aρ 5) (bρ 5) (185565680531 / 400000000000 : ℝ) ≤ @@ -2103,25 +1864,21 @@ lemma U_441_5 : have hlg : Real.log (860160814651759 / 2000000000000000 : ℝ) ≤ (-(8437830934746810842847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (860160814651759 / 2000000000000000 : ℝ) = - (860160814651759 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (860160814651759 / 500000000000000 : ℚ)) - (U := (5425112671253189157153 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (860160814651759 / 500000000000000 : ℝ) ≤ - (5425112671253189157153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (429461257058759 / 1000000000000000 : ℝ)) (q := - (860160814651759 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (860160814651759 / 2000000000000000 : ℚ)) + (r' := (860160814651759 / 500000000000000 : ℚ)) + (U := (-(8437830934746810842847 / 10000000000000000000000 : ℚ))) + (U' := (5425112671253189157153 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (185565680531 / 400000000000 : ℚ)) + (s := (429461257058759 / 1000000000000000 : ℚ)) + (q := (860160814651759 / 2000000000000000 : ℚ)) + (U := (-(8437830934746810842847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_6 : Uω (aρ 6) (bρ 6) (185565680531 / 400000000000 : ℝ) ≤ @@ -2129,25 +1886,21 @@ lemma U_441_6 : have hlg : Real.log (8249758681611879 / 20000000000000000 : ℝ) ≤ (-(2213870809572582147229 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8249758681611879 / 20000000000000000 : ℝ) = - (8249758681611879 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8249758681611879 / 5000000000000000 : ℚ)) - (U := (1251865091927417852771 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8249758681611879 / 5000000000000000 : ℝ) ≤ - (1251865091927417852771 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4110003480821879 / 10000000000000000 : ℝ)) (q := - (8249758681611879 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8249758681611879 / 20000000000000000 : ℚ)) + (r' := (8249758681611879 / 5000000000000000 : ℚ)) + (U := (-(2213870809572582147229 / 2500000000000000000000 : ℚ))) + (U' := (1251865091927417852771 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (185565680531 / 400000000000 : ℚ)) + (s := (4110003480821879 / 10000000000000000 : ℚ)) + (q := (8249758681611879 / 20000000000000000 : ℚ)) + (U := (-(2213870809572582147229 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_7 : Uω (aρ 7) (bρ 7) (185565680531 / 400000000000 : ℝ) ≤ @@ -2155,25 +1908,21 @@ lemma U_441_7 : have hlg : Real.log (7765391117776663 / 20000000000000000 : ℝ) ≤ (-(1182569310476322240769 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7765391117776663 / 20000000000000000 : ℝ) = - (7765391117776663 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7765391117776663 / 5000000000000000 : ℚ)) - (U := (550298640273677759231 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7765391117776663 / 5000000000000000 : ℝ) ≤ - (550298640273677759231 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3849297297746663 / 10000000000000000 : ℝ)) (q := - (7765391117776663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7765391117776663 / 20000000000000000 : ℚ)) + (r' := (7765391117776663 / 5000000000000000 : ℚ)) + (U := (-(1182569310476322240769 / 1250000000000000000000 : ℚ))) + (U' := (550298640273677759231 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (185565680531 / 400000000000 : ℚ)) + (s := (3849297297746663 / 10000000000000000 : ℚ)) + (q := (7765391117776663 / 20000000000000000 : ℚ)) + (U := (-(1182569310476322240769 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_8 : Uω (aρ 8) (bρ 8) (185565680531 / 400000000000 : ℝ) ≤ @@ -2181,25 +1930,21 @@ lemma U_441_8 : have hlg : Real.log (1780866512680443 / 5000000000000000 : ℝ) ≤ (-(1032337861184616429291 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1780866512680443 / 5000000000000000 : ℝ) = - (1780866512680443 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1780866512680443 / 1250000000000000 : ℚ)) - (U := (353956499415383570709 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1780866512680443 / 1250000000000000 : ℝ) ≤ - (353956499415383570709 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (872728470507943 / 2500000000000000 : ℝ)) (q := - (1780866512680443 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1780866512680443 / 5000000000000000 : ℚ)) + (r' := (1780866512680443 / 1250000000000000 : ℚ)) + (U := (-(1032337861184616429291 / 1000000000000000000000 : ℚ))) + (U' := (353956499415383570709 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (185565680531 / 400000000000 : ℚ)) + (s := (872728470507943 / 2500000000000000 : ℚ)) + (q := (1780866512680443 / 5000000000000000 : ℚ)) + (U := (-(1032337861184616429291 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_9 : Uω (aρ 9) (bρ 9) (185565680531 / 400000000000 : ℝ) ≤ @@ -2207,25 +1952,21 @@ lemma U_441_9 : have hlg : Real.log (3147715625007271 / 10000000000000000 : ℝ) ≤ (-(11559081011305702915049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3147715625007271 / 10000000000000000 : ℝ) = - (3147715625007271 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3147715625007271 / 2500000000000000 : ℚ)) - (U := (2303862594694297084951 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3147715625007271 / 2500000000000000 : ℝ) ≤ - (2303862594694297084951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1501922354842271 / 5000000000000000 : ℝ)) (q := - (3147715625007271 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3147715625007271 / 10000000000000000 : ℚ)) + (r' := (3147715625007271 / 2500000000000000 : ℚ)) + (U := (-(11559081011305702915049 / 10000000000000000000000 : ℚ))) + (U' := (2303862594694297084951 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (185565680531 / 400000000000 : ℚ)) + (s := (1501922354842271 / 5000000000000000 : ℚ)) + (q := (3147715625007271 / 10000000000000000 : ℚ)) + (U := (-(11559081011305702915049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_10 : Uω (aρ 10) (bρ 10) (185565680531 / 400000000000 : ℝ) ≤ @@ -2233,26 +1974,21 @@ lemma U_441_10 : have hlg : Real.log (5230709500928829 / 20000000000000000 : ℝ) ≤ (-(6705926721624019064597 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5230709500928829 / 20000000000000000 : ℝ) = - (5230709500928829 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5230709500928829 / 5000000000000000 : ℚ)) - (U := (225545081375980935403 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5230709500928829 / 5000000000000000 : ℝ) ≤ - (225545081375980935403 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2327681994093829 / 10000000000000000 : ℝ)) (q := - (5230709500928829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5230709500928829 / 20000000000000000 : ℚ)) + (r' := (5230709500928829 / 5000000000000000 : ℚ)) + (U := (-(6705926721624019064597 / 5000000000000000000000 : ℚ))) + (U' := (225545081375980935403 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (185565680531 / 400000000000 : ℚ)) + (s := (2327681994093829 / 10000000000000000 : ℚ)) + (q := (5230709500928829 / 20000000000000000 : ℚ)) + (U := (-(6705926721624019064597 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_11 : Uω (aρ 11) (bρ 11) (185565680531 / 400000000000 : ℝ) ≤ @@ -2260,25 +1996,21 @@ lemma U_441_11 : have hlg : Real.log (744743553781797 / 4000000000000000 : ℝ) ≤ (-(4202524258281721346399 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (744743553781797 / 4000000000000000 : ℝ) = - (744743553781797 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (744743553781797 / 500000000000000 : ℚ)) - (U := (996079593968278653601 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (744743553781797 / 500000000000000 : ℝ) ≤ - (996079593968278653601 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (247833377655797 / 2000000000000000 : ℝ)) (q := - (744743553781797 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (744743553781797 / 4000000000000000 : ℚ)) + (r' := (744743553781797 / 500000000000000 : ℚ)) + (U := (-(4202524258281721346399 / 2500000000000000000000 : ℚ))) + (U' := (996079593968278653601 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (185565680531 / 400000000000 : ℚ)) + (s := (247833377655797 / 2000000000000000 : ℚ)) + (q := (744743553781797 / 4000000000000000 : ℚ)) + (U := (-(4202524258281721346399 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_441_12 : Uω (aρ 12) (bρ 12) (185565680531 / 400000000000 : ℝ) ≤ @@ -2395,24 +2127,21 @@ lemma U_442_1 : have hlg : Real.log (57265387567411 / 125000000000000 : ℝ) ≤ (-(7806173519924622736079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (57265387567411 / 125000000000000 : ℝ) = (57265387567411 / 31250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57265387567411 / 31250000000000 : ℚ)) - (U := (6056770086075377263921 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (57265387567411 / 31250000000000 : ℝ) ≤ - (6056770086075377263921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (229059785810663 / 500000000000000 : ℝ)) (q := - (57265387567411 / 125000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57265387567411 / 125000000000000 : ℚ)) + (r' := (57265387567411 / 31250000000000 : ℚ)) + (U := (-(7806173519924622736079 / 10000000000000000000000 : ℚ))) + (U' := (6056770086075377263921 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (229059785810663 / 500000000000000 : ℚ)) + (q := (57265387567411 / 125000000000000 : ℚ)) + (U := (-(7806173519924622736079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_2 : Uω (aρ 2) (bρ 2) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2420,25 +2149,21 @@ lemma U_442_2 : have hlg : Real.log (4557264482983499 / 10000000000000000 : ℝ) ≤ (-(3929312715194378892603 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4557264482983499 / 10000000000000000 : ℝ) = - (4557264482983499 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4557264482983499 / 2500000000000000 : ℚ)) - (U := (3002159087805621107397 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4557264482983499 / 2500000000000000 : ℝ) ≤ - (3002159087805621107397 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2278515841952249 / 5000000000000000 : ℝ)) (q := - (4557264482983499 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4557264482983499 / 10000000000000000 : ℚ)) + (r' := (4557264482983499 / 2500000000000000 : ℚ)) + (U := (-(3929312715194378892603 / 5000000000000000000000 : ℚ))) + (U' := (3002159087805621107397 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (2278515841952249 / 5000000000000000 : ℚ)) + (q := (4557264482983499 / 10000000000000000 : ℚ)) + (U := (-(3929312715194378892603 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_3 : Uω (aρ 3) (bρ 3) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2446,25 +2171,21 @@ lemma U_442_3 : have hlg : Real.log (9018561717231039 / 20000000000000000 : ℝ) ≤ (-(7964474065262793540323 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9018561717231039 / 20000000000000000 : ℝ) = - (9018561717231039 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9018561717231039 / 5000000000000000 : ℚ)) - (U := (5898469540737206459677 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9018561717231039 / 5000000000000000 : ℝ) ≤ - (5898469540737206459677 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4508460541518539 / 10000000000000000 : ℝ)) (q := - (9018561717231039 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9018561717231039 / 20000000000000000 : ℚ)) + (r' := (9018561717231039 / 5000000000000000 : ℚ)) + (U := (-(7964474065262793540323 / 10000000000000000000000 : ℚ))) + (U' := (5898469540737206459677 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (4508460541518539 / 10000000000000000 : ℚ)) + (q := (9018561717231039 / 20000000000000000 : ℚ)) + (U := (-(7964474065262793540323 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_4 : Uω (aρ 4) (bρ 4) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2472,24 +2193,21 @@ lemma U_442_4 : have hlg : Real.log (70870909642991 / 160000000000000 : ℝ) ≤ (-(8143137665996417731169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70870909642991 / 160000000000000 : ℝ) = (70870909642991 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70870909642991 / 40000000000000 : ℚ)) - (U := (5719805940003582268831 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (70870909642991 / 40000000000000 : ℝ) ≤ - (5719805940003582268831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35416453685811 / 80000000000000 : ℝ)) (q := - (70870909642991 / 160000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70870909642991 / 160000000000000 : ℚ)) + (r' := (70870909642991 / 40000000000000 : ℚ)) + (U := (-(8143137665996417731169 / 10000000000000000000000 : ℚ))) + (U' := (5719805940003582268831 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (35416453685811 / 80000000000000 : ℚ)) + (q := (70870909642991 / 160000000000000 : ℚ)) + (U := (-(8143137665996417731169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_5 : Uω (aρ 5) (bρ 5) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2497,25 +2215,21 @@ lemma U_442_5 : have hlg : Real.log (2153717552038997 / 5000000000000000 : ℝ) ≤ (-(8422424689650293239287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2153717552038997 / 5000000000000000 : ℝ) = - (2153717552038997 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2153717552038997 / 1250000000000000 : ℚ)) - (U := (5440518916349706760713 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2153717552038997 / 1250000000000000 : ℝ) ≤ - (5440518916349706760713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (134414160401359 / 312500000000000 : ℝ)) (q := - (2153717552038997 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2153717552038997 / 5000000000000000 : ℚ)) + (r' := (2153717552038997 / 1250000000000000 : ℚ)) + (U := (-(8422424689650293239287 / 10000000000000000000000 : ℚ))) + (U' := (5440518916349706760713 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (134414160401359 / 312500000000000 : ℚ)) + (q := (2153717552038997 / 5000000000000000 : ℚ)) + (U := (-(8422424689650293239287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_6 : Uω (aρ 6) (bρ 6) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2523,25 +2237,21 @@ lemma U_442_6 : have hlg : Real.log (8263049535076131 / 20000000000000000 : ℝ) ≤ (-(8839385605277294481179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8263049535076131 / 20000000000000000 : ℝ) = - (8263049535076131 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8263049535076131 / 5000000000000000 : ℚ)) - (U := (5023558000722705518821 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8263049535076131 / 5000000000000000 : ℝ) ≤ - (5023558000722705518821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4116672834903631 / 10000000000000000 : ℝ)) (q := - (8263049535076131 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8263049535076131 / 20000000000000000 : ℚ)) + (r' := (8263049535076131 / 5000000000000000 : ℚ)) + (U := (-(8839385605277294481179 / 10000000000000000000000 : ℚ))) + (U' := (5023558000722705518821 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (4116672834903631 / 10000000000000000 : ℚ)) + (q := (8263049535076131 / 20000000000000000 : ℚ)) + (U := (-(8839385605277294481179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_7 : Uω (aρ 7) (bρ 7) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2549,25 +2259,21 @@ lemma U_442_7 : have hlg : Real.log (7778748819826639 / 20000000000000000 : ℝ) ≤ (-(9443367678504315809701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7778748819826639 / 20000000000000000 : ℝ) = - (7778748819826639 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7778748819826639 / 5000000000000000 : ℚ)) - (U := (4419575927495684190299 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7778748819826639 / 5000000000000000 : ℝ) ≤ - (4419575927495684190299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3856033500414139 / 10000000000000000 : ℝ)) (q := - (7778748819826639 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7778748819826639 / 20000000000000000 : ℚ)) + (r' := (7778748819826639 / 5000000000000000 : ℚ)) + (U := (-(9443367678504315809701 / 10000000000000000000000 : ℚ))) + (U' := (4419575927495684190299 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (3856033500414139 / 10000000000000000 : ℚ)) + (q := (7778748819826639 / 20000000000000000 : ℚ)) + (U := (-(9443367678504315809701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_8 : Uω (aρ 8) (bρ 8) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2575,25 +2281,21 @@ lemma U_442_8 : have hlg : Real.log (7136977187411453 / 20000000000000000 : ℝ) ≤ (-(10304429494337094953457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7136977187411453 / 20000000000000000 : ℝ) = - (7136977187411453 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7136977187411453 / 5000000000000000 : ℚ)) - (U := (3558514111662905046543 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7136977187411453 / 5000000000000000 : ℝ) ≤ - (3558514111662905046543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3497803519338953 / 10000000000000000 : ℝ)) (q := - (7136977187411453 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7136977187411453 / 20000000000000000 : ℚ)) + (r' := (7136977187411453 / 5000000000000000 : ℚ)) + (U := (-(10304429494337094953457 / 10000000000000000000000 : ℚ))) + (U' := (3558514111662905046543 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (3497803519338953 / 10000000000000000 : ℚ)) + (q := (7136977187411453 / 20000000000000000 : ℚ)) + (U := (-(10304429494337094953457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_9 : Uω (aρ 9) (bρ 9) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2601,25 +2303,21 @@ lemma U_442_9 : have hlg : Real.log (6309307068413211 / 20000000000000000 : ℝ) ≤ (-(180266627709776947529 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6309307068413211 / 20000000000000000 : ℝ) = - (6309307068413211 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6309307068413211 / 5000000000000000 : ℚ)) - (U := (36341866133973052471 / 156250000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6309307068413211 / 5000000000000000 : ℝ) ≤ - (36341866133973052471 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3011099028700711 / 10000000000000000 : ℝ)) (q := - (6309307068413211 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6309307068413211 / 20000000000000000 : ℚ)) + (r' := (6309307068413211 / 5000000000000000 : ℚ)) + (U := (-(180266627709776947529 / 156250000000000000000 : ℚ))) + (U' := (36341866133973052471 / 156250000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (3011099028700711 / 10000000000000000 : ℚ)) + (q := (6309307068413211 / 20000000000000000 : ℚ)) + (U := (-(180266627709776947529 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_10 : Uω (aρ 10) (bρ 10) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2627,25 +2325,21 @@ lemma U_442_10 : have hlg : Real.log (262279197906543 / 1000000000000000 : ℝ) ≤ (-(6691728506143263926889 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (262279197906543 / 1000000000000000 : ℝ) = - (262279197906543 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (262279197906543 / 250000000000000 : ℚ)) - (U := (239743296856736073111 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (262279197906543 / 250000000000000 : ℝ) ≤ - (239743296856736073111 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29199186898917 / 125000000000000 : ℝ)) (q := - (262279197906543 / 1000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (262279197906543 / 1000000000000000 : ℚ)) + (r' := (262279197906543 / 250000000000000 : ℚ)) + (U := (-(6691728506143263926889 / 5000000000000000000000 : ℚ))) + (U' := (239743296856736073111 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (29199186898917 / 125000000000000 : ℚ)) + (q := (262279197906543 / 1000000000000000 : ℚ)) + (U := (-(6691728506143263926889 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_11 : Uω (aρ 11) (bρ 11) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2653,26 +2347,21 @@ lemma U_442_11 : have hlg : Real.log (1871781312453091 / 10000000000000000 : ℝ) ≤ (-(3351389082507226933971 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1871781312453091 / 10000000000000000 : ℝ) = - (1871781312453091 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1871781312453091 / 1250000000000000 : ℚ)) - (U := (807493999292773066029 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1871781312453091 / 1250000000000000 : ℝ) ≤ - (807493999292773066029 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626195122446841 / 5000000000000000 : ℝ)) (q := - (1871781312453091 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1871781312453091 / 10000000000000000 : ℚ)) + (r' := (1871781312453091 / 1250000000000000 : ℚ)) + (U := (-(3351389082507226933971 / 2000000000000000000000 : ℚ))) + (U' := (807493999292773066029 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1858305405063 / 4000000000000 : ℚ)) + (s := (626195122446841 / 5000000000000000 : ℚ)) + (q := (1871781312453091 / 10000000000000000 : ℚ)) + (U := (-(3351389082507226933971 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_442_12 : Uω (aρ 12) (bρ 12) (1858305405063 / 4000000000000 : ℝ) ≤ @@ -2789,25 +2478,21 @@ lemma U_443_1 : have hlg : Real.log (917570511141501 / 2000000000000000 : ℝ) ≤ (-(7791730306659998859531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (917570511141501 / 2000000000000000 : ℝ) = - (917570511141501 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (917570511141501 / 500000000000000 : ℚ)) - (U := (6071213299340001140469 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (917570511141501 / 500000000000000 : ℝ) ≤ - (6071213299340001140469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (458781731746001 / 1000000000000000 : ℝ)) (q := - (917570511141501 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (917570511141501 / 2000000000000000 : ℚ)) + (r' := (917570511141501 / 500000000000000 : ℚ)) + (U := (-(7791730306659998859531 / 10000000000000000000000 : ℚ))) + (U' := (6071213299340001140469 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (116309625301 / 250000000000 : ℚ)) + (s := (458781731746001 / 1000000000000000 : ℚ)) + (q := (917570511141501 / 2000000000000000 : ℚ)) + (U := (-(7791730306659998859531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_2 : Uω (aρ 2) (bρ 2) (116309625301 / 250000000000 : ℝ) ≤ @@ -2815,25 +2500,21 @@ lemma U_443_2 : have hlg : Real.log (1825554528055601 / 4000000000000000 : ℝ) ≤ (-(7844105687295377049281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1825554528055601 / 4000000000000000 : ℝ) = - (1825554528055601 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1825554528055601 / 1000000000000000 : ℚ)) - (U := (6018837918704622950719 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1825554528055601 / 1000000000000000 : ℝ) ≤ - (6018837918704622950719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (912730771766601 / 2000000000000000 : ℝ)) (q := - (1825554528055601 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1825554528055601 / 4000000000000000 : ℚ)) + (r' := (1825554528055601 / 1000000000000000 : ℚ)) + (U := (-(7844105687295377049281 / 10000000000000000000000 : ℚ))) + (U' := (6018837918704622950719 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (116309625301 / 250000000000 : ℚ)) + (s := (912730771766601 / 2000000000000000 : ℚ)) + (q := (1825554528055601 / 4000000000000000 : ℚ)) + (U := (-(7844105687295377049281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_3 : Uω (aρ 3) (bρ 3) (116309625301 / 250000000000 : ℝ) ≤ @@ -2841,25 +2522,21 @@ lemma U_443_3 : have hlg : Real.log (2257951780508313 / 5000000000000000 : ℝ) ≤ (-(3974899006856099753251 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2257951780508313 / 5000000000000000 : ℝ) = - (2257951780508313 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2257951780508313 / 1250000000000000 : ℚ)) - (U := (2956572796143900246749 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2257951780508313 / 1250000000000000 : ℝ) ≤ - (2956572796143900246749 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1128771111734563 / 2500000000000000 : ℝ)) (q := - (2257951780508313 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2257951780508313 / 5000000000000000 : ℚ)) + (r' := (2257951780508313 / 1250000000000000 : ℚ)) + (U := (-(3974899006856099753251 / 5000000000000000000000 : ℚ))) + (U' := (2956572796143900246749 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (116309625301 / 250000000000 : ℚ)) + (s := (1128771111734563 / 2500000000000000 : ℚ)) + (q := (2257951780508313 / 5000000000000000 : ℚ)) + (U := (-(3974899006856099753251 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_4 : Uω (aρ 4) (bρ 4) (116309625301 / 250000000000 : ℝ) ≤ @@ -2867,25 +2544,21 @@ lemma U_443_4 : have hlg : Real.log (8872113798468999 / 20000000000000000 : ℝ) ≤ (-(254005998865564480957 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8872113798468999 / 20000000000000000 : ℝ) = - (8872113798468999 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8872113798468999 / 5000000000000000 : ℚ)) - (U := (179210988821935519043 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8872113798468999 / 5000000000000000 : ℝ) ≤ - (179210988821935519043 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4433685304438999 / 10000000000000000 : ℝ)) (q := - (8872113798468999 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8872113798468999 / 20000000000000000 : ℚ)) + (r' := (8872113798468999 / 5000000000000000 : ℚ)) + (U := (-(254005998865564480957 / 312500000000000000000 : ℚ))) + (U' := (179210988821935519043 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (116309625301 / 250000000000 : ℚ)) + (s := (4433685304438999 / 10000000000000000 : ℚ)) + (q := (8872113798468999 / 20000000000000000 : ℚ)) + (U := (-(254005998865564480957 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_5 : Uω (aρ 5) (bρ 5) (116309625301 / 250000000000 : ℝ) ≤ @@ -2893,25 +2566,21 @@ lemma U_443_5 : have hlg : Real.log (2157033052777099 / 5000000000000000 : ℝ) ≤ (-(840704221130343153201 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2157033052777099 / 5000000000000000 : ℝ) = - (2157033052777099 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2157033052777099 / 1250000000000000 : ℚ)) - (U := (545590139469656846799 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2157033052777099 / 1250000000000000 : ℝ) ≤ - (545590139469656846799 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1076973409103349 / 2500000000000000 : ℝ)) (q := - (2157033052777099 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2157033052777099 / 5000000000000000 : ℚ)) + (r' := (2157033052777099 / 1250000000000000 : ℚ)) + (U := (-(840704221130343153201 / 1000000000000000000000 : ℚ))) + (U' := (545590139469656846799 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (116309625301 / 250000000000 : ℚ)) + (s := (1076973409103349 / 2500000000000000 : ℚ)) + (q := (2157033052777099 / 5000000000000000 : ℚ)) + (U := (-(840704221130343153201 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_6 : Uω (aρ 6) (bρ 6) (116309625301 / 250000000000 : ℝ) ≤ @@ -2919,25 +2588,21 @@ lemma U_443_6 : have hlg : Real.log (4138170117144673 / 10000000000000000 : ℝ) ≤ (-(4411657015188613554371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4138170117144673 / 10000000000000000 : ℝ) = - (4138170117144673 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4138170117144673 / 2500000000000000 : ℚ)) - (U := (2519814787811386445629 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4138170117144673 / 2500000000000000 : ℝ) ≤ - (2519814787811386445629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2061671017367173 / 5000000000000000 : ℝ)) (q := - (4138170117144673 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4138170117144673 / 10000000000000000 : ℚ)) + (r' := (4138170117144673 / 2500000000000000 : ℚ)) + (U := (-(4411657015188613554371 / 5000000000000000000000 : ℚ))) + (U' := (2519814787811386445629 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (116309625301 / 250000000000 : ℚ)) + (s := (2061671017367173 / 5000000000000000 : ℚ)) + (q := (4138170117144673 / 10000000000000000 : ℚ)) + (U := (-(4411657015188613554371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_7 : Uω (aρ 7) (bρ 7) (116309625301 / 250000000000 : ℝ) ≤ @@ -2945,25 +2610,21 @@ lemma U_443_7 : have hlg : Real.log (7792106125225377 / 20000000000000000 : ℝ) ≤ (-(2356552717548743531489 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7792106125225377 / 20000000000000000 : ℝ) = - (7792106125225377 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7792106125225377 / 5000000000000000 : ℚ)) - (U := (1109183183951256468511 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7792106125225377 / 5000000000000000 : ℝ) ≤ - (1109183183951256468511 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3862769306430377 / 10000000000000000 : ℝ)) (q := - (7792106125225377 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7792106125225377 / 20000000000000000 : ℚ)) + (r' := (7792106125225377 / 5000000000000000 : ℚ)) + (U := (-(2356552717548743531489 / 2500000000000000000000 : ℚ))) + (U' := (1109183183951256468511 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (116309625301 / 250000000000 : ℚ)) + (s := (3862769306430377 / 10000000000000000 : ℚ)) + (q := (7792106125225377 / 20000000000000000 : ℚ)) + (U := (-(2356552717548743531489 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_8 : Uω (aρ 8) (bρ 8) (116309625301 / 250000000000 : ℝ) ≤ @@ -2971,25 +2632,21 @@ lemma U_443_8 : have hlg : Real.log (3575243645193809 / 10000000000000000 : ℝ) ≤ (-(2057103532297391134677 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3575243645193809 / 10000000000000000 : ℝ) = - (3575243645193809 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3575243645193809 / 2500000000000000 : ℚ)) - (U := (715485188902608865323 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3575243645193809 / 2500000000000000 : ℝ) ≤ - (715485188902608865323 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1752346061466309 / 5000000000000000 : ℝ)) (q := - (3575243645193809 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3575243645193809 / 10000000000000000 : ℚ)) + (r' := (3575243645193809 / 2500000000000000 : ℚ)) + (U := (-(2057103532297391134677 / 2000000000000000000000 : ℚ))) + (U' := (715485188902608865323 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (116309625301 / 250000000000 : ℚ)) + (s := (1752346061466309 / 5000000000000000 : ℚ)) + (q := (3575243645193809 / 10000000000000000 : ℚ)) + (U := (-(2057103532297391134677 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_9 : Uω (aρ 9) (bρ 9) (116309625301 / 250000000000 : ℝ) ≤ @@ -2997,25 +2654,21 @@ lemma U_443_9 : have hlg : Real.log (6323179977644683 / 20000000000000000 : ℝ) ≤ (-(2303020060797331947437 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6323179977644683 / 20000000000000000 : ℝ) = - (6323179977644683 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6323179977644683 / 5000000000000000 : ℚ)) - (U := (469568660402668052563 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6323179977644683 / 5000000000000000 : ℝ) ≤ - (469568660402668052563 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3018350438549683 / 10000000000000000 : ℝ)) (q := - (6323179977644683 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6323179977644683 / 20000000000000000 : ℚ)) + (r' := (6323179977644683 / 5000000000000000 : ℚ)) + (U := (-(2303020060797331947437 / 2000000000000000000000 : ℚ))) + (U' := (469568660402668052563 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (116309625301 / 250000000000 : ℚ)) + (s := (3018350438549683 / 10000000000000000 : ℚ)) + (q := (6323179977644683 / 20000000000000000 : ℚ)) + (U := (-(2303020060797331947437 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_10 : Uω (aρ 10) (bρ 10) (116309625301 / 250000000000 : ℝ) ≤ @@ -3023,25 +2676,21 @@ lemma U_443_10 : have hlg : Real.log (210417922531967 / 800000000000000 : ℝ) ≤ (-(1669395083469542458551 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (210417922531967 / 800000000000000 : ℝ) = - (210417922531967 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (210417922531967 / 200000000000000 : ℚ)) - (U := (63472867280457541449 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (210417922531967 / 200000000000000 : ℝ) ≤ - (63472867280457541449 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (93767102307967 / 400000000000000 : ℝ)) (q := - (210417922531967 / 800000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (210417922531967 / 800000000000000 : ℚ)) + (r' := (210417922531967 / 200000000000000 : ℚ)) + (U := (-(1669395083469542458551 / 1250000000000000000000 : ℚ))) + (U' := (63472867280457541449 / 1250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (116309625301 / 250000000000 : ℚ)) + (s := (93767102307967 / 400000000000000 : ℚ)) + (q := (210417922531967 / 800000000000000 : ℚ)) + (U := (-(1669395083469542458551 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_11 : Uω (aρ 11) (bρ 11) (116309625301 / 250000000000 : ℝ) ≤ @@ -3049,26 +2698,21 @@ lemma U_443_11 : have hlg : Real.log (3763303959367039 / 20000000000000000 : ℝ) ≤ (-(4176087471541592210279 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3763303959367039 / 20000000000000000 : ℝ) = - (3763303959367039 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3763303959367039 / 2500000000000000 : ℚ)) - (U := (1022516380708407789721 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3763303959367039 / 2500000000000000 : ℝ) ≤ - (1022516380708407789721 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1265510079972039 / 10000000000000000 : ℝ)) (q := - (3763303959367039 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3763303959367039 / 20000000000000000 : ℚ)) + (r' := (3763303959367039 / 2500000000000000 : ℚ)) + (U := (-(4176087471541592210279 / 2500000000000000000000 : ℚ))) + (U' := (1022516380708407789721 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (116309625301 / 250000000000 : ℚ)) + (s := (1265510079972039 / 10000000000000000 : ℚ)) + (q := (3763303959367039 / 20000000000000000 : ℚ)) + (U := (-(4176087471541592210279 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_443_12 : Uω (aρ 12) (bρ 12) (116309625301 / 250000000000 : ℝ) ≤ @@ -3183,25 +2827,21 @@ lemma U_444_1 : have hlg : Real.log (9188948211750643 / 20000000000000000 : ℝ) ≤ (-(1944326981068361120593 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9188948211750643 / 20000000000000000 : ℝ) = - (9188948211750643 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9188948211750643 / 5000000000000000 : ℚ)) - (U := (1521408920431638879407 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9188948211750643 / 5000000000000000 : ℝ) ≤ - (1521408920431638879407 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4594438918413143 / 10000000000000000 : ℝ)) (q := - (9188948211750643 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9188948211750643 / 20000000000000000 : ℚ)) + (r' := (9188948211750643 / 5000000000000000 : ℚ)) + (U := (-(1944326981068361120593 / 2500000000000000000000 : ℚ))) + (U' := (1521408920431638879407 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (4594438918413143 / 10000000000000000 : ℚ)) + (q := (9188948211750643 / 20000000000000000 : ℚ)) + (U := (-(1944326981068361120593 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_2 : Uω (aρ 2) (bρ 2) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3209,25 +2849,21 @@ lemma U_444_2 : have hlg : Real.log (4570508156315713 / 10000000000000000 : ℝ) ≤ (-(1565921399614921480789 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4570508156315713 / 10000000000000000 : ℝ) = - (4570508156315713 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4570508156315713 / 2500000000000000 : ℚ)) - (U := (1206667321585078519211 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4570508156315713 / 2500000000000000 : ℝ) ≤ - (1206667321585078519211 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2285138015901963 / 5000000000000000 : ℝ)) (q := - (4570508156315713 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4570508156315713 / 10000000000000000 : ℚ)) + (r' := (4570508156315713 / 2500000000000000 : ℚ)) + (U := (-(1565921399614921480789 / 2000000000000000000000 : ℚ))) + (U' := (1206667321585078519211 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (2285138015901963 / 5000000000000000 : ℚ)) + (q := (4570508156315713 / 10000000000000000 : ℚ)) + (U := (-(1565921399614921480789 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_3 : Uω (aρ 3) (bρ 3) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3235,25 +2871,21 @@ lemma U_444_3 : have hlg : Real.log (4522526259893739 / 10000000000000000 : ℝ) ≤ (-(7935143477042547934617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4522526259893739 / 10000000000000000 : ℝ) = - (4522526259893739 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4522526259893739 / 2500000000000000 : ℚ)) - (U := (5927800128957452065383 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4522526259893739 / 2500000000000000 : ℝ) ≤ - (5927800128957452065383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2260854172654989 / 5000000000000000 : ℝ)) (q := - (4522526259893739 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4522526259893739 / 10000000000000000 : ℚ)) + (r' := (4522526259893739 / 2500000000000000 : ℚ)) + (U := (-(7935143477042547934617 / 10000000000000000000000 : ℚ))) + (U' := (5927800128957452065383 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (2260854172654989 / 5000000000000000 : ℚ)) + (q := (4522526259893739 / 10000000000000000 : ℚ)) + (U := (-(7935143477042547934617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_4 : Uω (aρ 4) (bρ 4) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3261,25 +2893,21 @@ lemma U_444_4 : have hlg : Real.log (1110670483799291 / 2500000000000000 : ℝ) ≤ (-(507079286831002569619 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1110670483799291 / 2500000000000000 : ℝ) = - (1110670483799291 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1110670483799291 / 625000000000000 : ℚ)) - (U := (359354688543997430381 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1110670483799291 / 625000000000000 : ℝ) ≤ - (359354688543997430381 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1110078469245457 / 2500000000000000 : ℝ)) (q := - (1110670483799291 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1110670483799291 / 2500000000000000 : ℚ)) + (r' := (1110670483799291 / 625000000000000 : ℚ)) + (U := (-(507079286831002569619 / 625000000000000000000 : ℚ))) + (U' := (359354688543997430381 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (1110078469245457 / 2500000000000000 : ℚ)) + (q := (1110670483799291 / 2500000000000000 : ℚ)) + (U := (-(507079286831002569619 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_5 : Uω (aρ 5) (bρ 5) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3287,25 +2915,21 @@ lemma U_444_5 : have hlg : Real.log (8641394155645787 / 20000000000000000 : ℝ) ≤ (-(4195841713141036618307 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8641394155645787 / 20000000000000000 : ℝ) = - (8641394155645787 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8641394155645787 / 5000000000000000 : ℚ)) - (U := (2735630089858963381693 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8641394155645787 / 5000000000000000 : ℝ) ≤ - (2735630089858963381693 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4314534081568287 / 10000000000000000 : ℝ)) (q := - (8641394155645787 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8641394155645787 / 20000000000000000 : ℚ)) + (r' := (8641394155645787 / 5000000000000000 : ℚ)) + (U := (-(4195841713141036618307 / 5000000000000000000000 : ℚ))) + (U' := (2735630089858963381693 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (4314534081568287 / 10000000000000000 : ℚ)) + (q := (8641394155645787 / 20000000000000000 : ℚ)) + (U := (-(4195841713141036618307 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_6 : Uω (aρ 6) (bρ 6) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3313,25 +2937,21 @@ lemma U_444_6 : have hlg : Real.log (1657926155999757 / 4000000000000000 : ℝ) ≤ (-(880726842876476855731 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1657926155999757 / 4000000000000000 : ℝ) = - (1657926155999757 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1657926155999757 / 1000000000000000 : ℚ)) - (U := (505567517723523144269 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1657926155999757 / 1000000000000000 : ℝ) ≤ - (505567517723523144269 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (826002216212257 / 2000000000000000 : ℝ)) (q := - (1657926155999757 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1657926155999757 / 4000000000000000 : ℚ)) + (r' := (1657926155999757 / 1000000000000000 : ℚ)) + (U := (-(880726842876476855731 / 1000000000000000000000 : ℚ))) + (U' := (505567517723523144269 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (826002216212257 / 2000000000000000 : ℚ)) + (q := (1657926155999757 / 4000000000000000 : ℚ)) + (U := (-(880726842876476855731 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_7 : Uω (aρ 7) (bρ 7) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3339,25 +2959,21 @@ lemma U_444_7 : have hlg : Real.log (7805463036044279 / 20000000000000000 : ℝ) ≤ (-(9409083952601855202521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7805463036044279 / 20000000000000000 : ℝ) = - (7805463036044279 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7805463036044279 / 5000000000000000 : ℚ)) - (U := (4453859653398144797479 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7805463036044279 / 5000000000000000 : ℝ) ≤ - (4453859653398144797479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3869504717866779 / 10000000000000000 : ℝ)) (q := - (7805463036044279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7805463036044279 / 20000000000000000 : ℚ)) + (r' := (7805463036044279 / 5000000000000000 : ℚ)) + (U := (-(9409083952601855202521 / 10000000000000000000000 : ℚ))) + (U' := (4453859653398144797479 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (3869504717866779 / 10000000000000000 : ℚ)) + (q := (7805463036044279 / 20000000000000000 : ℚ)) + (U := (-(9409083952601855202521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_8 : Uω (aρ 8) (bρ 8) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3365,25 +2981,21 @@ lemma U_444_8 : have hlg : Real.log (179099909143343 / 500000000000000 : ℝ) ≤ (-(10266642961314476776443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (179099909143343 / 500000000000000 : ℝ) = - (179099909143343 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (179099909143343 / 125000000000000 : ℚ)) - (U := (3596300644685523223557 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (179099909143343 / 125000000000000 : ℝ) ≤ - (3596300644685523223557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (175578984944811 / 500000000000000 : ℝ)) (q := - (179099909143343 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (179099909143343 / 500000000000000 : ℚ)) + (r' := (179099909143343 / 125000000000000 : ℚ)) + (U := (-(10266642961314476776443 / 10000000000000000000000 : ℚ))) + (U' := (3596300644685523223557 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (175578984944811 / 500000000000000 : ℚ)) + (q := (179099909143343 / 500000000000000 : ℚ)) + (U := (-(10266642961314476776443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_9 : Uω (aρ 9) (bρ 9) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3391,25 +3003,21 @@ lemma U_444_9 : have hlg : Real.log (1584262499656509 / 5000000000000000 : ℝ) ≤ (-(5746594563859062553709 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1584262499656509 / 5000000000000000 : ℝ) = - (1584262499656509 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1584262499656509 / 1250000000000000 : ℚ)) - (U := (1184877239140937446291 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1584262499656509 / 1250000000000000 : ℝ) ≤ - (1184877239140937446291 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (378199870018567 / 1250000000000000 : ℝ)) (q := - (1584262499656509 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1584262499656509 / 5000000000000000 : ℚ)) + (r' := (1584262499656509 / 1250000000000000 : ℚ)) + (U := (-(5746594563859062553709 / 5000000000000000000000 : ℚ))) + (U' := (1184877239140937446291 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (378199870018567 / 1250000000000000 : ℚ)) + (q := (1584262499656509 / 5000000000000000 : ℚ)) + (U := (-(5746594563859062553709 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_10 : Uω (aρ 10) (bρ 10) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3417,26 +3025,21 @@ lemma U_444_10 : have hlg : Real.log (5275301925251203 / 20000000000000000 : ℝ) ≤ (-(6663481791477497625633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5275301925251203 / 20000000000000000 : ℝ) = - (5275301925251203 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5275301925251203 / 5000000000000000 : ℚ)) - (U := (267990011522502374367 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5275301925251203 / 5000000000000000 : ℝ) ≤ - (267990011522502374367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2352409920268703 / 10000000000000000 : ℝ)) (q := - (5275301925251203 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5275301925251203 / 20000000000000000 : ℚ)) + (r' := (5275301925251203 / 5000000000000000 : ℚ)) + (U := (-(6663481791477497625633 / 5000000000000000000000 : ℚ))) + (U' := (267990011522502374367 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (2352409920268703 / 10000000000000000 : ℚ)) + (q := (5275301925251203 / 20000000000000000 : ℚ)) + (U := (-(6663481791477497625633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_11 : Uω (aρ 11) (bρ 11) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3444,25 +3047,21 @@ lemma U_444_11 : have hlg : Real.log (756588991840753 / 4000000000000000 : ℝ) ≤ (-(4163073691847707252589 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (756588991840753 / 4000000000000000 : ℝ) = - (756588991840753 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (756588991840753 / 500000000000000 : ℚ)) - (U := (1035530160402292747411 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (756588991840753 / 500000000000000 : ℝ) ≤ - (1035530160402292747411 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (255705916085253 / 2000000000000000 : ℝ)) (q := - (756588991840753 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (756588991840753 / 4000000000000000 : ℚ)) + (r' := (756588991840753 / 500000000000000 : ℚ)) + (U := (-(4163073691847707252589 / 2500000000000000000000 : ℚ))) + (U' := (1035530160402292747411 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1863602604569 / 4000000000000 : ℚ)) + (s := (255705916085253 / 2000000000000000 : ℚ)) + (q := (756588991840753 / 4000000000000000 : ℚ)) + (U := (-(4163073691847707252589 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_444_12 : Uω (aρ 12) (bρ 12) (1863602604569 / 4000000000000 : ℝ) ≤ @@ -3578,25 +3177,21 @@ lemma U_445_1 : have hlg : Real.log (9202191311793929 / 20000000000000000 : ℝ) ≤ (-(7762906312763454203637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9202191311793929 / 20000000000000000 : ℝ) = - (9202191311793929 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9202191311793929 / 5000000000000000 : ℚ)) - (U := (6100037293236545796363 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9202191311793929 / 5000000000000000 : ℝ) ≤ - (6100037293236545796363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4601060519073929 / 10000000000000000 : ℝ)) (q := - (9202191311793929 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9202191311793929 / 20000000000000000 : ℚ)) + (r' := (9202191311793929 / 5000000000000000 : ℚ)) + (U := (-(7762906312763454203637 / 10000000000000000000000 : ℚ))) + (U' := (6100037293236545796363 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (4601060519073929 / 10000000000000000 : ℚ)) + (q := (9202191311793929 / 20000000000000000 : ℚ)) + (U := (-(7762906312763454203637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_2 : Uω (aρ 2) (bρ 2) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3604,25 +3199,21 @@ lemma U_445_2 : have hlg : Real.log (4577129991517879 / 10000000000000000 : ℝ) ≤ (-(1953782325437929747473 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4577129991517879 / 10000000000000000 : ℝ) = - (4577129991517879 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4577129991517879 / 2500000000000000 : ℚ)) - (U := (1511953576062070252527 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4577129991517879 / 2500000000000000 : ℝ) ≤ - (1511953576062070252527 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2288449101412879 / 5000000000000000 : ℝ)) (q := - (4577129991517879 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4577129991517879 / 10000000000000000 : ℚ)) + (r' := (4577129991517879 / 2500000000000000 : ℚ)) + (U := (-(1953782325437929747473 / 2500000000000000000000 : ℚ))) + (U' := (1511953576062070252527 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (2288449101412879 / 5000000000000000 : ℚ)) + (q := (4577129991517879 / 10000000000000000 : ℚ)) + (U := (-(1953782325437929747473 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_3 : Uω (aρ 3) (bρ 3) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3630,25 +3221,21 @@ lemma U_445_3 : have hlg : Real.log (1132287238815581 / 2500000000000000 : ℝ) ≤ (-(1980127598060602571469 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1132287238815581 / 2500000000000000 : ℝ) = - (1132287238815581 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1132287238815581 / 625000000000000 : ℚ)) - (U := (1485608303439397428531 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1132287238815581 / 625000000000000 : ℝ) ≤ - (1485608303439397428531 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (566041529583081 / 1250000000000000 : ℝ)) (q := - (1132287238815581 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1132287238815581 / 2500000000000000 : ℚ)) + (r' := (1132287238815581 / 625000000000000 : ℚ)) + (U := (-(1980127598060602571469 / 2500000000000000000000 : ℚ))) + (U' := (1485608303439397428531 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (566041529583081 / 1250000000000000 : ℚ)) + (q := (1132287238815581 / 2500000000000000 : ℚ)) + (U := (-(1980127598060602571469 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_4 : Uω (aρ 4) (bρ 4) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3656,25 +3243,21 @@ lemma U_445_4 : have hlg : Real.log (8898613921244529 / 20000000000000000 : ℝ) ≤ (-(202459186902655127247 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8898613921244529 / 20000000000000000 : ℝ) = - (8898613921244529 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8898613921244529 / 5000000000000000 : ℚ)) - (U := (144114403247344872753 / 250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8898613921244529 / 5000000000000000 : ℝ) ≤ - (144114403247344872753 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4446942428449529 / 10000000000000000 : ℝ)) (q := - (8898613921244529 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8898613921244529 / 20000000000000000 : ℚ)) + (r' := (8898613921244529 / 5000000000000000 : ℚ)) + (U := (-(202459186902655127247 / 250000000000000000000 : ℚ))) + (U' := (144114403247344872753 / 250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (4446942428449529 / 10000000000000000 : ℚ)) + (q := (8898613921244529 / 20000000000000000 : ℚ)) + (U := (-(202459186902655127247 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_5 : Uω (aρ 5) (bρ 5) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3682,25 +3265,21 @@ lemma U_445_5 : have hlg : Real.log (4327328021018731 / 10000000000000000 : ℝ) ≤ (-(1675269652300550677949 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4327328021018731 / 10000000000000000 : ℝ) = - (4327328021018731 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4327328021018731 / 2500000000000000 : ℚ)) - (U := (1097319068899449322051 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4327328021018731 / 2500000000000000 : ℝ) ≤ - (1097319068899449322051 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2160587234288731 / 5000000000000000 : ℝ)) (q := - (4327328021018731 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4327328021018731 / 10000000000000000 : ℚ)) + (r' := (4327328021018731 / 2500000000000000 : ℚ)) + (U := (-(1675269652300550677949 / 2000000000000000000000 : ℚ))) + (U' := (1097319068899449322051 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (2160587234288731 / 5000000000000000 : ℚ)) + (q := (4327328021018731 / 10000000000000000 : ℚ)) + (U := (-(1675269652300550677949 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_6 : Uω (aρ 6) (bρ 6) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3708,25 +3287,21 @@ lemma U_445_6 : have hlg : Real.log (1037865146618359 / 2500000000000000 : ℝ) ≤ (-(8791248716030945256763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1037865146618359 / 2500000000000000 : ℝ) = - (1037865146618359 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1037865146618359 / 625000000000000 : ℚ)) - (U := (5071694889969054743237 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1037865146618359 / 625000000000000 : ℝ) ≤ - (5071694889969054743237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (517084996828359 / 1250000000000000 : ℝ)) (q := - (1037865146618359 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1037865146618359 / 2500000000000000 : ℚ)) + (r' := (1037865146618359 / 625000000000000 : ℚ)) + (U := (-(8791248716030945256763 / 10000000000000000000000 : ℚ))) + (U' := (5071694889969054743237 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (517084996828359 / 1250000000000000 : ℚ)) + (q := (1037865146618359 / 2500000000000000 : ℚ)) + (U := (-(8791248716030945256763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_7 : Uω (aρ 7) (bρ 7) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3734,25 +3309,21 @@ lemma U_445_7 : have hlg : Real.log (1954704888585057 / 5000000000000000 : ℝ) ≤ (-(4695993410008529072567 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1954704888585057 / 5000000000000000 : ℝ) = - (1954704888585057 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1954704888585057 / 1250000000000000 : ℚ)) - (U := (2235478392991470927433 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1954704888585057 / 1250000000000000 : ℝ) ≤ - (2235478392991470927433 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (969059934195057 / 2500000000000000 : ℝ)) (q := - (1954704888585057 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1954704888585057 / 5000000000000000 : ℚ)) + (r' := (1954704888585057 / 1250000000000000 : ℚ)) + (U := (-(4695993410008529072567 / 5000000000000000000000 : ℚ))) + (U' := (2235478392991470927433 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (969059934195057 / 2500000000000000 : ℚ)) + (q := (1954704888585057 / 5000000000000000 : ℚ)) + (U := (-(4695993410008529072567 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_8 : Uω (aρ 8) (bρ 8) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3760,25 +3331,21 @@ lemma U_445_8 : have hlg : Real.log (7177504419484671 / 20000000000000000 : ℝ) ≤ (-(10247805242797003460311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7177504419484671 / 20000000000000000 : ℝ) = - (7177504419484671 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7177504419484671 / 5000000000000000 : ℚ)) - (U := (3615138363202996539689 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7177504419484671 / 5000000000000000 : ℝ) ≤ - (3615138363202996539689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3518466253264671 / 10000000000000000 : ℝ)) (q := - (7177504419484671 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7177504419484671 / 20000000000000000 : ℚ)) + (r' := (7177504419484671 / 5000000000000000 : ℚ)) + (U := (-(10247805242797003460311 / 10000000000000000000000 : ℚ))) + (U' := (3615138363202996539689 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (3518466253264671 / 10000000000000000 : ℚ)) + (q := (7177504419484671 / 20000000000000000 : ℚ)) + (U := (-(10247805242797003460311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_9 : Uω (aρ 9) (bρ 9) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3786,25 +3353,21 @@ lemma U_445_9 : have hlg : Real.log (6350917152066091 / 20000000000000000 : ℝ) ≤ (-(458853214865105613027 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6350917152066091 / 20000000000000000 : ℝ) = - (6350917152066091 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6350917152066091 / 5000000000000000 : ℚ)) - (U := (95664529374894386973 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6350917152066091 / 5000000000000000 : ℝ) ≤ - (95664529374894386973 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3032844614206091 / 10000000000000000 : ℝ)) (q := - (6350917152066091 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6350917152066091 / 20000000000000000 : ℚ)) + (r' := (6350917152066091 / 5000000000000000 : ℚ)) + (U := (-(458853214865105613027 / 400000000000000000000 : ℚ))) + (U' := (95664529374894386973 / 400000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (3032844614206091 / 10000000000000000 : ℚ)) + (q := (6350917152066091 / 20000000000000000 : ℚ)) + (U := (-(458853214865105613027 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_10 : Uω (aρ 10) (bρ 10) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3812,26 +3375,21 @@ lemma U_445_10 : have hlg : Real.log (2645072825576073 / 10000000000000000 : ℝ) ≤ (-(13298864942438442631833 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2645072825576073 / 10000000000000000 : ℝ) = - (2645072825576073 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2645072825576073 / 2500000000000000 : ℚ)) - (U := (564078663561557368167 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2645072825576073 / 2500000000000000 : ℝ) ≤ - (564078663561557368167 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1180316073393573 / 5000000000000000 : ℝ)) (q := - (2645072825576073 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2645072825576073 / 10000000000000000 : ℚ)) + (r' := (2645072825576073 / 2500000000000000 : ℚ)) + (U := (-(13298864942438442631833 / 10000000000000000000000 : ℚ))) + (U' := (564078663561557368167 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (1180316073393573 / 5000000000000000 : ℚ)) + (q := (2645072825576073 / 10000000000000000 : ℚ)) + (U := (-(13298864942438442631833 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_11 : Uω (aρ 11) (bρ 11) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3839,26 +3397,21 @@ lemma U_445_11 : have hlg : Real.log (1901244329463689 / 10000000000000000 : ℝ) ≤ (-(3320153020315792050137 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1901244329463689 / 10000000000000000 : ℝ) = - (1901244329463689 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1901244329463689 / 1250000000000000 : ℚ)) - (U := (838730061484207949863 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1901244329463689 / 1250000000000000 : ℝ) ≤ - (838730061484207949863 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (645725890383689 / 5000000000000000 : ℝ)) (q := - (1901244329463689 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1901244329463689 / 10000000000000000 : ℚ)) + (r' := (1901244329463689 / 1250000000000000 : ℚ)) + (U := (-(3320153020315792050137 / 2000000000000000000000 : ℚ))) + (U' := (838730061484207949863 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (933125602161 / 2000000000000 : ℚ)) + (s := (645725890383689 / 5000000000000000 : ℚ)) + (q := (1901244329463689 / 10000000000000000 : ℚ)) + (U := (-(3320153020315792050137 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_445_12 : Uω (aρ 12) (bρ 12) (933125602161 / 2000000000000 : ℝ) ≤ @@ -3974,25 +3527,21 @@ lemma U_446_1 : have hlg : Real.log (2307169377752123 / 5000000000000000 : ℝ) ≤ (-(966770645457505427377 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2307169377752123 / 5000000000000000 : ℝ) = - (2307169377752123 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2307169377752123 / 1250000000000000 : ℚ)) - (U := (766097305292494572623 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2307169377752123 / 1250000000000000 : ℝ) ≤ - (766097305292494572623 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1153575929880873 / 2500000000000000 : ℝ)) (q := - (2307169377752123 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2307169377752123 / 5000000000000000 : ℚ)) + (r' := (2307169377752123 / 1250000000000000 : ℚ)) + (U := (-(966770645457505427377 / 1250000000000000000000 : ℚ))) + (U' := (766097305292494572623 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (1153575929880873 / 2500000000000000 : ℚ)) + (q := (2307169377752123 / 5000000000000000 : ℚ)) + (U := (-(966770645457505427377 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_2 : Uω (aρ 2) (bρ 2) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4000,25 +3549,21 @@ lemma U_446_2 : have hlg : Real.log (1836149463606179 / 4000000000000000 : ℝ) ≤ (-(973279580652723789647 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1836149463606179 / 4000000000000000 : ℝ) = - (1836149463606179 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1836149463606179 / 1000000000000000 : ℚ)) - (U := (759588370097276210353 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1836149463606179 / 1000000000000000 : ℝ) ≤ - (759588370097276210353 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (918028507811179 / 2000000000000000 : ℝ)) (q := - (1836149463606179 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1836149463606179 / 4000000000000000 : ℚ)) + (r' := (1836149463606179 / 1000000000000000 : ℚ)) + (U := (-(973279580652723789647 / 1250000000000000000000 : ℚ))) + (U' := (759588370097276210353 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (918028507811179 / 2000000000000000 : ℚ)) + (q := (1836149463606179 / 4000000000000000 : ℚ)) + (U := (-(973279580652723789647 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_3 : Uω (aρ 3) (bρ 3) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4026,25 +3571,21 @@ lemma U_446_3 : have hlg : Real.log (9084788671070627 / 20000000000000000 : ℝ) ≤ (-(7891308327585915285363 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9084788671070627 / 20000000000000000 : ℝ) = - (9084788671070627 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9084788671070627 / 5000000000000000 : ℚ)) - (U := (5971635278414084714637 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9084788671070627 / 5000000000000000 : ℝ) ≤ - (5971635278414084714637 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4541579998445627 / 10000000000000000 : ℝ)) (q := - (9084788671070627 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9084788671070627 / 20000000000000000 : ℚ)) + (r' := (9084788671070627 / 5000000000000000 : ℚ)) + (U := (-(7891308327585915285363 / 10000000000000000000000 : ℚ))) + (U' := (5971635278414084714637 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (4541579998445627 / 10000000000000000 : ℚ)) + (q := (9084788671070627 / 20000000000000000 : ℚ)) + (U := (-(7891308327585915285363 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_4 : Uω (aρ 4) (bρ 4) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4052,25 +3593,21 @@ lemma U_446_4 : have hlg : Real.log (1785022792019079 / 4000000000000000 : ℝ) ≤ (-(4034315884058882351419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1785022792019079 / 4000000000000000 : ℝ) = - (1785022792019079 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1785022792019079 / 1000000000000000 : ℚ)) - (U := (2897155918941117648581 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1785022792019079 / 1000000000000000 : ℝ) ≤ - (2897155918941117648581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (892039893707079 / 2000000000000000 : ℝ)) (q := - (1785022792019079 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1785022792019079 / 4000000000000000 : ℚ)) + (r' := (1785022792019079 / 1000000000000000 : ℚ)) + (U := (-(4034315884058882351419 / 5000000000000000000000 : ℚ))) + (U' := (2897155918941117648581 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (892039893707079 / 2000000000000000 : ℚ)) + (q := (1785022792019079 / 4000000000000000 : ℚ)) + (U := (-(4034315884058882351419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_5 : Uω (aρ 5) (bρ 5) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4078,25 +3615,21 @@ lemma U_446_5 : have hlg : Real.log (4340589820726307 / 10000000000000000 : ℝ) ≤ (-(521609281376695497853 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4340589820726307 / 10000000000000000 : ℝ) = - (4340589820726307 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4340589820726307 / 2500000000000000 : ℚ)) - (U := (344824693998304502147 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4340589820726307 / 2500000000000000 : ℝ) ≤ - (344824693998304502147 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2167227534613807 / 5000000000000000 : ℝ)) (q := - (4340589820726307 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4340589820726307 / 10000000000000000 : ℚ)) + (r' := (4340589820726307 / 2500000000000000 : ℚ)) + (U := (-(521609281376695497853 / 625000000000000000000 : ℚ))) + (U' := (344824693998304502147 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (2167227534613807 / 5000000000000000 : ℚ)) + (q := (4340589820726307 / 10000000000000000 : ℚ)) + (U := (-(521609281376695497853 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_6 : Uω (aρ 6) (bρ 6) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4104,25 +3637,21 @@ lemma U_446_6 : have hlg : Real.log (416475075175237 / 1000000000000000 : ℝ) ≤ (-(4379643310814408410447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (416475075175237 / 1000000000000000 : ℝ) = - (416475075175237 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (416475075175237 / 250000000000000 : ℚ)) - (U := (2551828492185591589553 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (416475075175237 / 250000000000000 : ℝ) ≤ - (2551828492185591589553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207500865320987 / 500000000000000 : ℝ)) (q := - (416475075175237 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (416475075175237 / 1000000000000000 : ℚ)) + (r' := (416475075175237 / 250000000000000 : ℚ)) + (U := (-(4379643310814408410447 / 5000000000000000000000 : ℚ))) + (U' := (2551828492185591589553 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (207500865320987 / 500000000000000 : ℚ)) + (q := (416475075175237 / 1000000000000000 : ℚ)) + (U := (-(4379643310814408410447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_7 : Uω (aρ 7) (bρ 7) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4130,25 +3659,21 @@ lemma U_446_7 : have hlg : Real.log (313821256860759 / 800000000000000 : ℝ) ≤ (-(9357881489879827674907 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (313821256860759 / 800000000000000 : ℝ) = - (313821256860759 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (313821256860759 / 200000000000000 : ℚ)) - (U := (4505062116120172325093 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (313821256860759 / 200000000000000 : ℝ) ≤ - (4505062116120172325093 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (155588344207759 / 400000000000000 : ℝ)) (q := - (313821256860759 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (313821256860759 / 800000000000000 : ℚ)) + (r' := (313821256860759 / 200000000000000 : ℚ)) + (U := (-(9357881489879827674907 / 10000000000000000000000 : ℚ))) + (U' := (4505062116120172325093 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (155588344207759 / 400000000000000 : ℚ)) + (q := (313821256860759 / 800000000000000 : ℚ)) + (U := (-(9357881489879827674907 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_8 : Uω (aρ 8) (bρ 8) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4156,25 +3681,21 @@ lemma U_446_8 : have hlg : Real.log (7204517486101029 / 20000000000000000 : ℝ) ≤ (-(2042048030275987590759 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7204517486101029 / 20000000000000000 : ℝ) = - (7204517486101029 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7204517486101029 / 5000000000000000 : ℚ)) - (U := (730540690924012409241 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7204517486101029 / 5000000000000000 : ℝ) ≤ - (730540690924012409241 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3532236321116029 / 10000000000000000 : ℝ)) (q := - (7204517486101029 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7204517486101029 / 20000000000000000 : ℚ)) + (r' := (7204517486101029 / 5000000000000000 : ℚ)) + (U := (-(2042048030275987590759 / 2000000000000000000000 : ℚ))) + (U' := (730540690924012409241 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (3532236321116029 / 10000000000000000 : ℚ)) + (q := (7204517486101029 / 20000000000000000 : ℚ)) + (U := (-(2042048030275987590759 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_9 : Uω (aρ 9) (bρ 9) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4182,25 +3703,21 @@ lemma U_446_9 : have hlg : Real.log (6378642938132311 / 20000000000000000 : ℝ) ≤ (-(5713884519621729279943 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6378642938132311 / 20000000000000000 : ℝ) = - (6378642938132311 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6378642938132311 / 5000000000000000 : ℚ)) - (U := (1217587283378270720057 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6378642938132311 / 5000000000000000 : ℝ) ≤ - (1217587283378270720057 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3047327401507311 / 10000000000000000 : ℝ)) (q := - (6378642938132311 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6378642938132311 / 20000000000000000 : ℚ)) + (r' := (6378642938132311 / 5000000000000000 : ℚ)) + (U := (-(5713884519621729279943 / 5000000000000000000000 : ℚ))) + (U' := (1217587283378270720057 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (3047327401507311 / 10000000000000000 : ℚ)) + (q := (6378642938132311 / 20000000000000000 : ℚ)) + (U := (-(5713884519621729279943 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_10 : Uω (aρ 10) (bρ 10) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4208,26 +3725,21 @@ lemma U_446_10 : have hlg : Real.log (5319803115399497 / 20000000000000000 : ℝ) ≤ (-(13242959787489276770681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5319803115399497 / 20000000000000000 : ℝ) = - (5319803115399497 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5319803115399497 / 5000000000000000 : ℚ)) - (U := (619983818510723229319 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5319803115399497 / 5000000000000000 : ℝ) ≤ - (619983818510723229319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2377046612269497 / 10000000000000000 : ℝ)) (q := - (5319803115399497 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5319803115399497 / 20000000000000000 : ℚ)) + (r' := (5319803115399497 / 5000000000000000 : ℚ)) + (U := (-(13242959787489276770681 / 10000000000000000000000 : ℚ))) + (U' := (619983818510723229319 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (2377046612269497 / 10000000000000000 : ℚ)) + (q := (5319803115399497 / 20000000000000000 : ℚ)) + (U := (-(13242959787489276770681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_11 : Uω (aρ 11) (bρ 11) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4235,25 +3747,21 @@ lemma U_446_11 : have hlg : Real.log (768259118541357 / 4000000000000000 : ℝ) ≤ (-(16499225691449952125427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (768259118541357 / 4000000000000000 : ℝ) = - (768259118541357 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (768259118541357 / 500000000000000 : ℚ)) - (U := (4295189717550047874573 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (768259118541357 / 500000000000000 : ℝ) ≤ - (4295189717550047874573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263403143156357 / 2000000000000000 : ℝ)) (q := - (768259118541357 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (768259118541357 / 4000000000000000 : ℚ)) + (r' := (768259118541357 / 500000000000000 : ℚ)) + (U := (-(16499225691449952125427 / 10000000000000000000000 : ℚ))) + (U' := (4295189717550047874573 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (467887100957 / 1000000000000 : ℚ)) + (s := (263403143156357 / 2000000000000000 : ℚ)) + (q := (768259118541357 / 4000000000000000 : ℚ)) + (U := (-(16499225691449952125427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_446_12 : Uω (aρ 12) (bρ 12) (467887100957 / 1000000000000 : ℝ) ≤ @@ -4369,25 +3877,21 @@ lemma U_447_1 : have hlg : Real.log (1851032741813739 / 4000000000000000 : ℝ) ≤ (-(7705506384488545139841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1851032741813739 / 4000000000000000 : ℝ) = - (1851032741813739 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1851032741813739 / 1000000000000000 : ℚ)) - (U := (6157437221511454860159 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1851032741813739 / 1000000000000000 : ℝ) ≤ - (6157437221511454860159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (925509383763739 / 2000000000000000 : ℝ)) (q := - (1851032741813739 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1851032741813739 / 4000000000000000 : ℚ)) + (r' := (1851032741813739 / 1000000000000000 : ℚ)) + (U := (-(7705506384488545139841 / 10000000000000000000000 : ℚ))) + (U' := (6157437221511454860159 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (925509383763739 / 2000000000000000 : ℚ)) + (q := (1851032741813739 / 4000000000000000 : ℚ)) + (U := (-(7705506384488545139841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_2 : Uω (aρ 2) (bρ 2) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4395,25 +3899,21 @@ lemma U_447_2 : have hlg : Real.log (9207234645330419 / 20000000000000000 : ℝ) ≤ (-(969678404396364492027 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9207234645330419 / 20000000000000000 : ℝ) = - (9207234645330419 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9207234645330419 / 5000000000000000 : ℚ)) - (U := (763189546353635507973 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9207234645330419 / 5000000000000000 : ℝ) ≤ - (763189546353635507973 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4603386867590419 / 10000000000000000 : ℝ)) (q := - (9207234645330419 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9207234645330419 / 20000000000000000 : ℚ)) + (r' := (9207234645330419 / 5000000000000000 : ℚ)) + (U := (-(969678404396364492027 / 1250000000000000000000 : ℚ))) + (U' := (763189546353635507973 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (4603386867590419 / 10000000000000000 : ℚ)) + (q := (9207234645330419 / 20000000000000000 : ℚ)) + (U := (-(969678404396364492027 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_3 : Uω (aρ 3) (bρ 3) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4421,25 +3921,21 @@ lemma U_447_3 : have hlg : Real.log (2277819850978757 / 5000000000000000 : ℝ) ≤ (-(3931095660576254656589 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2277819850978757 / 5000000000000000 : ℝ) = - (2277819850978757 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2277819850978757 / 1250000000000000 : ℚ)) - (U := (3000376142423745343411 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2277819850978757 / 1250000000000000 : ℝ) ≤ - (3000376142423745343411 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1138706933131257 / 2500000000000000 : ℝ)) (q := - (2277819850978757 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2277819850978757 / 5000000000000000 : ℚ)) + (r' := (2277819850978757 / 1250000000000000 : ℚ)) + (U := (-(3931095660576254656589 / 5000000000000000000000 : ℚ))) + (U' := (3000376142423745343411 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (1138706933131257 / 2500000000000000 : ℚ)) + (q := (2277819850978757 / 5000000000000000 : ℚ)) + (U := (-(3931095660576254656589 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_4 : Uω (aρ 4) (bρ 4) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4447,25 +3943,21 @@ lemma U_447_4 : have hlg : Real.log (559475869735483 / 1250000000000000 : ℝ) ≤ (-(1004873039024965725031 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (559475869735483 / 1250000000000000 : ℝ) = - (559475869735483 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (559475869735483 / 312500000000000 : ℚ)) - (U := (727994911725034274969 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (559475869735483 / 312500000000000 : ℝ) ≤ - (727994911725034274969 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (559182053180341 / 1250000000000000 : ℝ)) (q := - (559475869735483 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (559475869735483 / 1250000000000000 : ℚ)) + (r' := (559475869735483 / 312500000000000 : ℚ)) + (U := (-(1004873039024965725031 / 1250000000000000000000 : ℚ))) + (U' := (727994911725034274969 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (559182053180341 / 1250000000000000 : ℚ)) + (q := (559475869735483 / 1250000000000000 : ℚ)) + (U := (-(1004873039024965725031 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_5 : Uω (aρ 5) (bρ 5) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4473,25 +3965,21 @@ lemma U_447_5 : have hlg : Real.log (4353851505737701 / 10000000000000000 : ℝ) ≤ (-(2078810588735672971517 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4353851505737701 / 10000000000000000 : ℝ) = - (4353851505737701 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4353851505737701 / 2500000000000000 : ℚ)) - (U := (1386925312764327028483 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4353851505737701 / 2500000000000000 : ℝ) ≤ - (1386925312764327028483 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2173867720242701 / 5000000000000000 : ℝ)) (q := - (4353851505737701 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4353851505737701 / 10000000000000000 : ℚ)) + (r' := (4353851505737701 / 2500000000000000 : ℚ)) + (U := (-(2078810588735672971517 / 2500000000000000000000 : ℚ))) + (U' := (1386925312764327028483 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (2173867720242701 / 5000000000000000 : ℚ)) + (q := (4353851505737701 / 10000000000000000 : ℚ)) + (U := (-(2078810588735672971517 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_6 : Uω (aρ 6) (bρ 6) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4499,24 +3987,21 @@ lemma U_447_6 : have hlg : Real.log (65281884623493 / 156250000000000 : ℝ) ≤ (-(8727427080123200181059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (65281884623493 / 156250000000000 : ℝ) = (65281884623493 / 39062500000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65281884623493 / 39062500000000 : ℚ)) - (U := (5135516525876799818941 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (65281884623493 / 39062500000000 : ℝ) ≤ - (5135516525876799818941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260209627247319 / 625000000000000 : ℝ)) (q := - (65281884623493 / 156250000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65281884623493 / 156250000000000 : ℚ)) + (r' := (65281884623493 / 39062500000000 : ℚ)) + (U := (-(8727427080123200181059 / 10000000000000000000000 : ℚ))) + (U' := (5135516525876799818941 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (260209627247319 / 625000000000000 : ℚ)) + (q := (65281884623493 / 156250000000000 : ℚ)) + (U := (-(8727427080123200181059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_7 : Uω (aρ 7) (bρ 7) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4524,25 +4009,21 @@ lemma U_447_7 : have hlg : Real.log (3936120871465577 / 10000000000000000 : ℝ) ≤ (-(4661947022709255165381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3936120871465577 / 10000000000000000 : ℝ) = - (3936120871465577 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3936120871465577 / 2500000000000000 : ℚ)) - (U := (2269524780290744834619 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3936120871465577 / 2500000000000000 : ℝ) ≤ - (2269524780290744834619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1951587963920577 / 5000000000000000 : ℝ)) (q := - (3936120871465577 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3936120871465577 / 10000000000000000 : ℚ)) + (r' := (3936120871465577 / 2500000000000000 : ℚ)) + (U := (-(4661947022709255165381 / 5000000000000000000000 : ℚ))) + (U' := (2269524780290744834619 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (1951587963920577 / 5000000000000000 : ℚ)) + (q := (3936120871465577 / 10000000000000000 : ℚ)) + (U := (-(4661947022709255165381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_8 : Uω (aρ 8) (bρ 8) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4550,25 +4031,21 @@ lemma U_447_8 : have hlg : Real.log (1807881634390941 / 5000000000000000 : ℝ) ≤ (-(2543205299478635574293 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1807881634390941 / 5000000000000000 : ℝ) = - (1807881634390941 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1807881634390941 / 1250000000000000 : ℚ)) - (U := (922530602021364425707 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1807881634390941 / 1250000000000000 : ℝ) ≤ - (922530602021364425707 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (886500593453441 / 2500000000000000 : ℝ)) (q := - (1807881634390941 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1807881634390941 / 5000000000000000 : ℚ)) + (r' := (1807881634390941 / 1250000000000000 : ℚ)) + (U := (-(2543205299478635574293 / 2500000000000000000000 : ℚ))) + (U' := (922530602021364425707 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (886500593453441 / 2500000000000000 : ℚ)) + (q := (1807881634390941 / 5000000000000000 : ℚ)) + (U := (-(2543205299478635574293 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_9 : Uω (aρ 9) (bρ 9) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4576,25 +4053,21 @@ lemma U_447_9 : have hlg : Real.log (1281271499489889 / 4000000000000000 : ℝ) ≤ (-(11384414167465334094829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1281271499489889 / 4000000000000000 : ℝ) = - (1281271499489889 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1281271499489889 / 1000000000000000 : ℚ)) - (U := (2478529438534665905171 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1281271499489889 / 1000000000000000 : ℝ) ≤ - (2478529438534665905171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (612359792411889 / 2000000000000000 : ℝ)) (q := - (1281271499489889 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1281271499489889 / 4000000000000000 : ℚ)) + (r' := (1281271499489889 / 1000000000000000 : ℚ)) + (U := (-(11384414167465334094829 / 10000000000000000000000 : ℚ))) + (U' := (2478529438534665905171 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (612359792411889 / 2000000000000000 : ℚ)) + (q := (1281271499489889 / 4000000000000000 : ℚ)) + (U := (-(11384414167465334094829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_10 : Uω (aρ 10) (bρ 10) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4602,26 +4075,21 @@ lemma U_447_10 : have hlg : Real.log (5349421281563489 / 20000000000000000 : ℝ) ≤ (-(2637487779295076324629 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5349421281563489 / 20000000000000000 : ℝ) = - (5349421281563489 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5349421281563489 / 5000000000000000 : ℚ)) - (U := (135100941904923675371 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5349421281563489 / 5000000000000000 : ℝ) ≤ - (135100941904923675371 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2393421779668489 / 10000000000000000 : ℝ)) (q := - (5349421281563489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5349421281563489 / 20000000000000000 : ℚ)) + (r' := (5349421281563489 / 5000000000000000 : ℚ)) + (U := (-(2637487779295076324629 / 2000000000000000000000 : ℚ))) + (U' := (135100941904923675371 / 2000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (2393421779668489 / 10000000000000000 : ℚ)) + (q := (5349421281563489 / 20000000000000000 : ℚ)) + (U := (-(2637487779295076324629 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_11 : Uω (aρ 11) (bρ 11) (938422801667 / 2000000000000 : ℝ) ≤ @@ -4629,26 +4097,21 @@ lemma U_447_11 : have hlg : Real.log (1939873172807547 / 10000000000000000 : ℝ) ≤ (-(16399624961174716983881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1939873172807547 / 10000000000000000 : ℝ) = - (1939873172807547 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1939873172807547 / 1250000000000000 : ℚ)) - (U := (4394790447825283016119 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1939873172807547 / 1250000000000000 : ℝ) ≤ - (4394790447825283016119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (671111734962547 / 5000000000000000 : ℝ)) (q := - (1939873172807547 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1939873172807547 / 10000000000000000 : ℚ)) + (r' := (1939873172807547 / 1250000000000000 : ℚ)) + (U := (-(16399624961174716983881 / 10000000000000000000000 : ℚ))) + (U' := (4394790447825283016119 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (938422801667 / 2000000000000 : ℚ)) + (s := (671111734962547 / 5000000000000000 : ℚ)) + (q := (1939873172807547 / 10000000000000000 : ℚ)) + (U := (-(16399624961174716983881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_447_12 : Uω (aρ 12) (bρ 12) (938422801667 / 2000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U37.lean b/LeanPool/Zeta5Irrational/Table/U37.lean index c835564868..341c292add 100644 --- a/LeanPool/Zeta5Irrational/Table/U37.lean +++ b/LeanPool/Zeta5Irrational/Table/U37.lean @@ -24,25 +24,21 @@ lemma U_448_1 : have hlg : Real.log (9281649905984419 / 20000000000000000 : ℝ) ≤ (-(1919232376114736975373 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9281649905984419 / 20000000000000000 : ℝ) = - (9281649905984419 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9281649905984419 / 5000000000000000 : ℚ)) - (U := (1546503525385263024627 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9281649905984419 / 5000000000000000 : ℝ) ≤ - (1546503525385263024627 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4640790116969419 / 10000000000000000 : ℝ)) (q := - (9281649905984419 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9281649905984419 / 20000000000000000 : ℚ)) + (r' := (9281649905984419 / 5000000000000000 : ℚ)) + (U := (-(1919232376114736975373 / 2500000000000000000000 : ℚ))) + (U' := (1546503525385263024627 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (47053570071 / 100000000000 : ℚ)) + (s := (4640790116969419 / 10000000000000000 : ℚ)) + (q := (9281649905984419 / 20000000000000000 : ℚ)) + (U := (-(1919232376114736975373 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_2 : Uω (aρ 2) (bρ 2) (47053570071 / 100000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_448_2 : have hlg : Real.log (9233721965000561 / 20000000000000000 : ℝ) ≤ (-(1545740118644833119621 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9233721965000561 / 20000000000000000 : ℝ) = - (9233721965000561 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9233721965000561 / 5000000000000000 : ℚ)) - (U := (1226848602555166880379 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9233721965000561 / 5000000000000000 : ℝ) ≤ - (1226848602555166880379 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4616631188495561 / 10000000000000000 : ℝ)) (q := - (9233721965000561 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9233721965000561 / 20000000000000000 : ℚ)) + (r' := (9233721965000561 / 5000000000000000 : ℚ)) + (U := (-(1545740118644833119621 / 2000000000000000000000 : ℚ))) + (U' := (1226848602555166880379 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (47053570071 / 100000000000 : ℚ)) + (s := (4616631188495561 / 10000000000000000 : ℚ)) + (q := (9233721965000561 / 20000000000000000 : ℚ)) + (U := (-(1545740118644833119621 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_3 : Uω (aρ 3) (bρ 3) (47053570071 / 100000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_448_3 : have hlg : Real.log (9137770109298861 / 20000000000000000 : ℝ) ≤ (-(391657943934962024627 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9137770109298861 / 20000000000000000 : ℝ) = - (9137770109298861 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9137770109298861 / 5000000000000000 : ℚ)) - (U := (301489236365037975373 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9137770109298861 / 5000000000000000 : ℝ) ≤ - (301489236365037975373 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4568075439143861 / 10000000000000000 : ℝ)) (q := - (9137770109298861 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9137770109298861 / 20000000000000000 : ℚ)) + (r' := (9137770109298861 / 5000000000000000 : ℚ)) + (U := (-(391657943934962024627 / 500000000000000000000 : ℚ))) + (U' := (301489236365037975373 / 500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (47053570071 / 100000000000 : ℚ)) + (s := (4568075439143861 / 10000000000000000 : ℚ)) + (q := (9137770109298861 / 20000000000000000 : ℚ)) + (U := (-(391657943934962024627 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_4 : Uω (aρ 4) (bρ 4) (47053570071 / 100000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_448_4 : have hlg : Real.log (4489056894499417 / 10000000000000000 : ℝ) ≤ (-(8009424585511980867437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4489056894499417 / 10000000000000000 : ℝ) = - (4489056894499417 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4489056894499417 / 2500000000000000 : ℚ)) - (U := (5853519020488019132563 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4489056894499417 / 2500000000000000 : ℝ) ≤ - (5853519020488019132563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2243356649954417 / 5000000000000000 : ℝ)) (q := - (4489056894499417 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4489056894499417 / 10000000000000000 : ℚ)) + (r' := (4489056894499417 / 2500000000000000 : ℚ)) + (U := (-(8009424585511980867437 / 10000000000000000000000 : ℚ))) + (U' := (5853519020488019132563 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (47053570071 / 100000000000 : ℚ)) + (s := (2243356649954417 / 5000000000000000 : ℚ)) + (q := (4489056894499417 / 10000000000000000 : ℚ)) + (U := (-(8009424585511980867437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_5 : Uω (aρ 5) (bρ 5) (47053570071 / 100000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_448_5 : have hlg : Real.log (1746845230840299 / 4000000000000000 : ℝ) ≤ (-(8284829247633143014031 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1746845230840299 / 4000000000000000 : ℝ) = - (1746845230840299 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1746845230840299 / 1000000000000000 : ℚ)) - (U := (5578114358366856985969 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1746845230840299 / 1000000000000000 : ℝ) ≤ - (5578114358366856985969 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (872203116889299 / 2000000000000000 : ℝ)) (q := - (1746845230840299 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1746845230840299 / 4000000000000000 : ℚ)) + (r' := (1746845230840299 / 1000000000000000 : ℚ)) + (U := (-(8284829247633143014031 / 10000000000000000000000 : ℚ))) + (U' := (5578114358366856985969 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (47053570071 / 100000000000 : ℚ)) + (s := (872203116889299 / 2000000000000000 : ℚ)) + (q := (1746845230840299 / 4000000000000000 : ℚ)) + (U := (-(8284829247633143014031 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_6 : Uω (aρ 6) (bρ 6) (47053570071 / 100000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_448_6 : have hlg : Real.log (2095665090905803 / 5000000000000000 : ℝ) ≤ (-(434783471547781231521 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2095665090905803 / 5000000000000000 : ℝ) = - (2095665090905803 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2095665090905803 / 1250000000000000 : ℚ)) - (U := (258363708752218768479 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2095665090905803 / 1250000000000000 : ℝ) ≤ - (258363708752218768479 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1044172542252053 / 2500000000000000 : ℝ)) (q := - (2095665090905803 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2095665090905803 / 5000000000000000 : ℚ)) + (r' := (2095665090905803 / 1250000000000000 : ℚ)) + (U := (-(434783471547781231521 / 500000000000000000000 : ℚ))) + (U' := (258363708752218768479 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (47053570071 / 100000000000 : ℚ)) + (s := (1044172542252053 / 2500000000000000 : ℚ)) + (q := (2095665090905803 / 5000000000000000 : ℚ)) + (U := (-(434783471547781231521 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_7 : Uω (aρ 7) (bρ 7) (47053570071 / 100000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_448_7 : have hlg : Real.log (7898950534522059 / 20000000000000000 : ℝ) ≤ (-(2322505915292548785069 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7898950534522059 / 20000000000000000 : ℝ) = - (7898950534522059 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7898950534522059 / 5000000000000000 : ℚ)) - (U := (1143229986207451214931 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7898950534522059 / 5000000000000000 : ℝ) ≤ - (1143229986207451214931 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3916641720667059 / 10000000000000000 : ℝ)) (q := - (7898950534522059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7898950534522059 / 20000000000000000 : ℚ)) + (r' := (7898950534522059 / 5000000000000000 : ℚ)) + (U := (-(2322505915292548785069 / 2500000000000000000000 : ℚ))) + (U' := (1143229986207451214931 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (47053570071 / 100000000000 : ℚ)) + (s := (3916641720667059 / 10000000000000000 : ℚ)) + (q := (7898950534522059 / 20000000000000000 : ℚ)) + (U := (-(2322505915292548785069 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_8 : Uω (aρ 8) (bρ 8) (47053570071 / 100000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_448_8 : have hlg : Real.log (7258531620454173 / 20000000000000000 : ℝ) ≤ (-(5067773603948575405307 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7258531620454173 / 20000000000000000 : ℝ) = - (7258531620454173 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7258531620454173 / 5000000000000000 : ℚ)) - (U := (1863698199051424594693 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7258531620454173 / 5000000000000000 : ℝ) ≤ - (1863698199051424594693 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3559764457939173 / 10000000000000000 : ℝ)) (q := - (7258531620454173 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7258531620454173 / 20000000000000000 : ℚ)) + (r' := (7258531620454173 / 5000000000000000 : ℚ)) + (U := (-(5067773603948575405307 / 5000000000000000000000 : ℚ))) + (U' := (1863698199051424594693 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (47053570071 / 100000000000 : ℚ)) + (s := (3559764457939173 / 10000000000000000 : ℚ)) + (q := (7258531620454173 / 20000000000000000 : ℚ)) + (U := (-(5067773603948575405307 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_9 : Uω (aρ 9) (bρ 9) (47053570071 / 100000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_448_9 : have hlg : Real.log (1608515247114633 / 5000000000000000 : ℝ) ≤ (-(7088289782332541623 / 6250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1608515247114633 / 5000000000000000 : ℝ) = - (1608515247114633 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1608515247114633 / 1250000000000000 : ℚ)) - (U := (1576049971417458377 / 6250000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1608515247114633 / 1250000000000000 : ℝ) ≤ - (1576049971417458377 / 6250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (769064863575883 / 2500000000000000 : ℝ)) (q := - (1608515247114633 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1608515247114633 / 5000000000000000 : ℚ)) + (r' := (1608515247114633 / 1250000000000000 : ℚ)) + (U := (-(7088289782332541623 / 6250000000000000000 : ℚ))) + (U' := (1576049971417458377 / 6250000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (47053570071 / 100000000000 : ℚ)) + (s := (769064863575883 / 2500000000000000 : ℚ)) + (q := (1608515247114633 / 5000000000000000 : ℚ)) + (U := (-(7088289782332541623 / 6250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_10 : Uω (aρ 10) (bρ 10) (47053570071 / 100000000000 : ℝ) ≤ @@ -258,25 +222,21 @@ lemma U_448_10 : have hlg : Real.log (168093779711803 / 625000000000000 : ℝ) ≤ (-(13132296129856771453691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (168093779711803 / 625000000000000 : ℝ) = - (168093779711803 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (168093779711803 / 156250000000000 : ℚ)) - (U := (730647476143228546309 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (168093779711803 / 156250000000000 : ℝ) ≤ - (730647476143228546309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (37652475783089 / 156250000000000 : ℝ)) (q := - (168093779711803 / 625000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (168093779711803 / 625000000000000 : ℚ)) + (r' := (168093779711803 / 156250000000000 : ℚ)) + (U := (-(13132296129856771453691 / 10000000000000000000000 : ℚ))) + (U' := (730647476143228546309 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (47053570071 / 100000000000 : ℚ)) + (s := (37652475783089 / 156250000000000 : ℚ)) + (q := (168093779711803 / 625000000000000 : ℚ)) + (U := (-(13132296129856771453691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_11 : Uω (aρ 11) (bρ 11) (47053570071 / 100000000000 : ℝ) ≤ @@ -284,26 +244,21 @@ lemma U_448_11 : have hlg : Real.log (1958930310284389 / 10000000000000000 : ℝ) ≤ (-(16301865280119978924169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1958930310284389 / 10000000000000000 : ℝ) = - (1958930310284389 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1958930310284389 / 1250000000000000 : ℚ)) - (U := (4492550128880021075831 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1958930310284389 / 1250000000000000 : ℝ) ≤ - (4492550128880021075831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (683547373056889 / 5000000000000000 : ℝ)) (q := - (1958930310284389 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1958930310284389 / 10000000000000000 : ℚ)) + (r' := (1958930310284389 / 1250000000000000 : ℚ)) + (U := (-(16301865280119978924169 / 10000000000000000000000 : ℚ))) + (U' := (4492550128880021075831 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (47053570071 / 100000000000 : ℚ)) + (s := (683547373056889 / 5000000000000000 : ℚ)) + (q := (1958930310284389 / 10000000000000000 : ℚ)) + (U := (-(16301865280119978924169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_448_12 : Uω (aρ 12) (bρ 12) (47053570071 / 100000000000 : ℝ) ≤ @@ -420,25 +375,21 @@ lemma U_449_1 : have hlg : Real.log (1861627220353087 / 4000000000000000 : ℝ) ≤ (-(7648434056806039205791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1861627220353087 / 4000000000000000 : ℝ) = - (1861627220353087 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1861627220353087 / 1000000000000000 : ℚ)) - (U := (6214509549193960794209 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1861627220353087 / 1000000000000000 : ℝ) ≤ - (6214509549193960794209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (930806662797087 / 2000000000000000 : ℝ)) (q := - (1861627220353087 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1861627220353087 / 4000000000000000 : ℚ)) + (r' := (1861627220353087 / 1000000000000000 : ℚ)) + (U := (-(7648434056806039205791 / 10000000000000000000000 : ℚ))) + (U' := (6214509549193960794209 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (930806662797087 / 2000000000000000 : ℚ)) + (q := (1861627220353087 / 4000000000000000 : ℚ)) + (U := (-(7648434056806039205791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_2 : Uω (aρ 2) (bρ 2) (943720001173 / 2000000000000 : ℝ) ≤ @@ -446,25 +397,21 @@ lemma U_449_2 : have hlg : Real.log (2315052319276699 / 5000000000000000 : ℝ) ≤ (-(7700056245118668029321 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2315052319276699 / 5000000000000000 : ℝ) = - (2315052319276699 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2315052319276699 / 1250000000000000 : ℚ)) - (U := (6162887360881331970679 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2315052319276699 / 1250000000000000 : ℝ) ≤ - (6162887360881331970679 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1157468875459199 / 2500000000000000 : ℝ)) (q := - (2315052319276699 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2315052319276699 / 5000000000000000 : ℚ)) + (r' := (2315052319276699 / 1250000000000000 : ℚ)) + (U := (-(7700056245118668029321 / 10000000000000000000000 : ℚ))) + (U' := (6162887360881331970679 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (1157468875459199 / 2500000000000000 : ℚ)) + (q := (2315052319276699 / 5000000000000000 : ℚ)) + (U := (-(7700056245118668029321 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_3 : Uω (aρ 3) (bρ 3) (943720001173 / 2000000000000 : ℝ) ≤ @@ -472,25 +419,21 @@ lemma U_449_3 : have hlg : Real.log (9164260787460347 / 20000000000000000 : ℝ) ≤ (-(3902105255140000568633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9164260787460347 / 20000000000000000 : ℝ) = - (9164260787460347 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9164260787460347 / 5000000000000000 : ℚ)) - (U := (3029366547859999431367 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9164260787460347 / 5000000000000000 : ℝ) ≤ - (3029366547859999431367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4581323118540347 / 10000000000000000 : ℝ)) (q := - (9164260787460347 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9164260787460347 / 20000000000000000 : ℚ)) + (r' := (9164260787460347 / 5000000000000000 : ℚ)) + (U := (-(3902105255140000568633 / 5000000000000000000000 : ℚ))) + (U' := (3029366547859999431367 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (4581323118540347 / 10000000000000000 : ℚ)) + (q := (9164260787460347 / 20000000000000000 : ℚ)) + (U := (-(3902105255140000568633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_4 : Uω (aρ 4) (bρ 4) (943720001173 / 2000000000000 : ℝ) ≤ @@ -498,25 +441,21 @@ lemma U_449_4 : have hlg : Real.log (4502306790258663 / 10000000000000000 : ℝ) ≤ (-(3989976034925886310423 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4502306790258663 / 10000000000000000 : ℝ) = - (4502306790258663 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4502306790258663 / 2500000000000000 : ℚ)) - (U := (2941495768074113689577 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4502306790258663 / 2500000000000000 : ℝ) ≤ - (2941495768074113689577 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2249985046331163 / 5000000000000000 : ℝ)) (q := - (4502306790258663 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4502306790258663 / 10000000000000000 : ℚ)) + (r' := (4502306790258663 / 2500000000000000 : ℚ)) + (U := (-(3989976034925886310423 / 5000000000000000000000 : ℚ))) + (U' := (2941495768074113689577 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (2249985046331163 / 5000000000000000 : ℚ)) + (q := (4502306790258663 / 10000000000000000 : ℚ)) + (U := (-(3989976034925886310423 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_5 : Uω (aρ 5) (bρ 5) (943720001173 / 2000000000000 : ℝ) ≤ @@ -524,25 +463,21 @@ lemma U_449_5 : have hlg : Real.log (8760749071701077 / 20000000000000000 : ℝ) ≤ (-(8254508612734525013499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8760749071701077 / 20000000000000000 : ℝ) = - (8760749071701077 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8760749071701077 / 5000000000000000 : ℚ)) - (U := (5608434993265474986501 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8760749071701077 / 5000000000000000 : ℝ) ≤ - (5608434993265474986501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4374295503181077 / 10000000000000000 : ℝ)) (q := - (8760749071701077 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8760749071701077 / 20000000000000000 : ℚ)) + (r' := (8760749071701077 / 5000000000000000 : ℚ)) + (U := (-(8254508612734525013499 / 10000000000000000000000 : ℚ))) + (U' := (5608434993265474986501 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (4374295503181077 / 10000000000000000 : ℚ)) + (q := (8760749071701077 / 20000000000000000 : ℚ)) + (U := (-(8254508612734525013499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_6 : Uω (aρ 6) (bρ 6) (943720001173 / 2000000000000 : ℝ) ≤ @@ -550,25 +485,21 @@ lemma U_449_6 : have hlg : Real.log (8409238904648603 / 20000000000000000 : ℝ) ≤ (-(8664013019972345318039 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8409238904648603 / 20000000000000000 : ℝ) = - (8409238904648603 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8409238904648603 / 5000000000000000 : ℚ)) - (U := (5198930586027654681961 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8409238904648603 / 5000000000000000 : ℝ) ≤ - (5198930586027654681961 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4190025711268603 / 10000000000000000 : ℝ)) (q := - (8409238904648603 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8409238904648603 / 20000000000000000 : ℚ)) + (r' := (8409238904648603 / 5000000000000000 : ℚ)) + (U := (-(8664013019972345318039 / 10000000000000000000000 : ℚ))) + (U' := (5198930586027654681961 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (4190025711268603 / 10000000000000000 : ℚ)) + (q := (8409238904648603 / 20000000000000000 : ℚ)) + (U := (-(8664013019972345318039 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_7 : Uω (aρ 7) (bρ 7) (943720001173 / 2000000000000 : ℝ) ≤ @@ -576,25 +507,21 @@ lemma U_449_7 : have hlg : Real.log (3962828906008327 / 10000000000000000 : ℝ) ≤ (-(9256269520445819727293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3962828906008327 / 10000000000000000 : ℝ) = - (3962828906008327 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3962828906008327 / 2500000000000000 : ℚ)) - (U := (4606674085554180272707 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3962828906008327 / 2500000000000000 : ℝ) ≤ - (4606674085554180272707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1965052999698327 / 5000000000000000 : ℝ)) (q := - (3962828906008327 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3962828906008327 / 10000000000000000 : ℚ)) + (r' := (3962828906008327 / 2500000000000000 : ℚ)) + (U := (-(9256269520445819727293 / 10000000000000000000000 : ℚ))) + (U' := (4606674085554180272707 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (1965052999698327 / 5000000000000000 : ℚ)) + (q := (3962828906008327 / 10000000000000000 : ℚ)) + (U := (-(9256269520445819727293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_8 : Uω (aρ 8) (bρ 8) (943720001173 / 2000000000000 : ℝ) ≤ @@ -602,25 +529,21 @@ lemma U_449_8 : have hlg : Real.log (1821383195155667 / 5000000000000000 : ℝ) ≤ (-(2524604255347409636449 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1821383195155667 / 5000000000000000 : ℝ) = - (1821383195155667 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1821383195155667 / 1250000000000000 : ℚ)) - (U := (941131646152590363551 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1821383195155667 / 1250000000000000 : ℝ) ≤ - (941131646152590363551 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (893380654835667 / 2500000000000000 : ℝ)) (q := - (1821383195155667 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1821383195155667 / 5000000000000000 : ℚ)) + (r' := (1821383195155667 / 1250000000000000 : ℚ)) + (U := (-(2524604255347409636449 / 2500000000000000000000 : ℚ))) + (U' := (941131646152590363551 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (893380654835667 / 2500000000000000 : ℚ)) + (q := (1821383195155667 / 5000000000000000 : ℚ)) + (U := (-(2524604255347409636449 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_9 : Uω (aρ 9) (bρ 9) (943720001173 / 2000000000000 : ℝ) ≤ @@ -628,25 +551,21 @@ lemma U_449_9 : have hlg : Real.log (807719195814421 / 2500000000000000 : ℝ) ≤ (-(11298315421504753008881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (807719195814421 / 2500000000000000 : ℝ) = - (807719195814421 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (807719195814421 / 625000000000000 : ℚ)) - (U := (2564628184495246991119 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (807719195814421 / 625000000000000 : ℝ) ≤ - (2564628184495246991119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (386338629199421 / 1250000000000000 : ℝ)) (q := - (807719195814421 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (807719195814421 / 2500000000000000 : ℚ)) + (r' := (807719195814421 / 625000000000000 : ℚ)) + (U := (-(11298315421504753008881 / 10000000000000000000000 : ℚ))) + (U' := (2564628184495246991119 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (386338629199421 / 1250000000000000 : ℚ)) + (q := (807719195814421 / 2500000000000000 : ℚ)) + (U := (-(11298315421504753008881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_10 : Uω (aρ 10) (bρ 10) (943720001173 / 2000000000000 : ℝ) ≤ @@ -654,25 +573,21 @@ lemma U_449_10 : have hlg : Real.log (338033931296161 / 1250000000000000 : ℝ) ≤ (-(6538762754409200956687 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (338033931296161 / 1250000000000000 : ℝ) = - (338033931296161 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (338033931296161 / 312500000000000 : ℚ)) - (U := (392709048590799043313 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (338033931296161 / 312500000000000 : ℝ) ≤ - (392709048590799043313 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (303257175164197 / 1250000000000000 : ℝ)) (q := - (338033931296161 / 1250000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (338033931296161 / 1250000000000000 : ℚ)) + (r' := (338033931296161 / 312500000000000 : ℚ)) + (U := (-(6538762754409200956687 / 5000000000000000000000 : ℚ))) + (U' := (392709048590799043313 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (303257175164197 / 1250000000000000 : ℚ)) + (q := (338033931296161 / 1250000000000000 : ℚ)) + (U := (-(6538762754409200956687 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_11 : Uω (aρ 11) (bρ 11) (943720001173 / 2000000000000 : ℝ) ≤ @@ -680,26 +595,21 @@ lemma U_449_11 : have hlg : Real.log (1977828229052923 / 10000000000000000 : ℝ) ≤ (-(8102928517530189352599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1977828229052923 / 10000000000000000 : ℝ) = - (1977828229052923 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1977828229052923 / 1250000000000000 : ℚ)) - (U := (2294279186969810647401 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1977828229052923 / 1250000000000000 : ℝ) ≤ - (2294279186969810647401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (695823792442923 / 5000000000000000 : ℝ)) (q := - (1977828229052923 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1977828229052923 / 10000000000000000 : ℚ)) + (r' := (1977828229052923 / 1250000000000000 : ℚ)) + (U := (-(8102928517530189352599 / 5000000000000000000000 : ℚ))) + (U' := (2294279186969810647401 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (943720001173 / 2000000000000 : ℚ)) + (s := (695823792442923 / 5000000000000000 : ℚ)) + (q := (1977828229052923 / 10000000000000000 : ℚ)) + (U := (-(8102928517530189352599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_449_12 : Uω (aρ 12) (bρ 12) (943720001173 / 2000000000000 : ℝ) ≤ @@ -816,25 +726,21 @@ lemma U_450_1 : have hlg : Real.log (4667311148210701 / 10000000000000000 : ℝ) ≤ (-(476251223671478843051 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4667311148210701 / 10000000000000000 : ℝ) = - (4667311148210701 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4667311148210701 / 2500000000000000 : ℚ)) - (U := (390182751703521156949 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4667311148210701 / 2500000000000000 : ℝ) ≤ - (390182751703521156949 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2333638254938201 / 5000000000000000 : ℝ)) (q := - (4667311148210701 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4667311148210701 / 10000000000000000 : ℚ)) + (r' := (4667311148210701 / 2500000000000000 : ℚ)) + (U := (-(476251223671478843051 / 625000000000000000000 : ℚ))) + (U' := (390182751703521156949 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (2333638254938201 / 5000000000000000 : ℚ)) + (q := (4667311148210701 / 10000000000000000 : ℚ)) + (U := (-(476251223671478843051 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_2 : Uω (aρ 2) (bρ 2) (473184300463 / 1000000000000 : ℝ) ≤ @@ -842,25 +748,21 @@ lemma U_450_2 : have hlg : Real.log (9286696581713851 / 20000000000000000 : ℝ) ≤ (-(3835746860328307421921 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9286696581713851 / 20000000000000000 : ℝ) = - (9286696581713851 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9286696581713851 / 5000000000000000 : ℚ)) - (U := (3095724942671692578079 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9286696581713851 / 5000000000000000 : ℝ) ≤ - (3095724942671692578079 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4643119807678851 / 10000000000000000 : ℝ)) (q := - (9286696581713851 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9286696581713851 / 20000000000000000 : ℚ)) + (r' := (9286696581713851 / 5000000000000000 : ℚ)) + (U := (-(3835746860328307421921 / 5000000000000000000000 : ℚ))) + (U' := (3095724942671692578079 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (4643119807678851 / 10000000000000000 : ℚ)) + (q := (9286696581713851 / 20000000000000000 : ℚ)) + (U := (-(3835746860328307421921 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_3 : Uω (aρ 3) (bρ 3) (473184300463 / 1000000000000 : ℝ) ≤ @@ -868,25 +770,21 @@ lemma U_450_3 : have hlg : Real.log (9190751438634959 / 20000000000000000 : ℝ) ≤ (-(971918216274480697521 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9190751438634959 / 20000000000000000 : ℝ) = - (9190751438634959 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9190751438634959 / 5000000000000000 : ℚ)) - (U := (760949734475519302479 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9190751438634959 / 5000000000000000 : ℝ) ≤ - (760949734475519302479 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4594570770949959 / 10000000000000000 : ℝ)) (q := - (9190751438634959 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9190751438634959 / 20000000000000000 : ℚ)) + (r' := (9190751438634959 / 5000000000000000 : ℚ)) + (U := (-(971918216274480697521 / 1250000000000000000000 : ℚ))) + (U' := (760949734475519302479 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (4594570770949959 / 10000000000000000 : ℚ)) + (q := (9190751438634959 / 20000000000000000 : ℚ)) + (U := (-(971918216274480697521 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_4 : Uω (aρ 4) (bρ 4) (473184300463 / 1000000000000 : ℝ) ≤ @@ -894,25 +792,21 @@ lemma U_450_4 : have hlg : Real.log (4515556645521627 / 10000000000000000 : ℝ) ≤ (-(1987641562899738892589 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4515556645521627 / 10000000000000000 : ℝ) = - (4515556645521627 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4515556645521627 / 2500000000000000 : ℚ)) - (U := (1478094338600261107411 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4515556645521627 / 2500000000000000 : ℝ) ≤ - (1478094338600261107411 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2256613402211627 / 5000000000000000 : ℝ)) (q := - (4515556645521627 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4515556645521627 / 10000000000000000 : ℚ)) + (r' := (4515556645521627 / 2500000000000000 : ℚ)) + (U := (-(1987641562899738892589 / 2500000000000000000000 : ℚ))) + (U' := (1478094338600261107411 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (2256613402211627 / 5000000000000000 : ℚ)) + (q := (4515556645521627 / 10000000000000000 : ℚ)) + (U := (-(1987641562899738892589 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_5 : Uω (aρ 5) (bρ 5) (473184300463 / 1000000000000 : ℝ) ≤ @@ -920,25 +814,21 @@ lemma U_450_5 : have hlg : Real.log (1757454353203847 / 4000000000000000 : ℝ) ≤ (-(8224279888071012172189 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1757454353203847 / 4000000000000000 : ℝ) = - (1757454353203847 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1757454353203847 / 1000000000000000 : ℚ)) - (U := (5638663717928987827811 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1757454353203847 / 1000000000000000 : ℝ) ≤ - (5638663717928987827811 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (877515039746847 / 2000000000000000 : ℝ)) (q := - (1757454353203847 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1757454353203847 / 4000000000000000 : ℚ)) + (r' := (1757454353203847 / 1000000000000000 : ℚ)) + (U := (-(8224279888071012172189 / 10000000000000000000000 : ℚ))) + (U' := (5638663717928987827811 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (877515039746847 / 2000000000000000 : ℚ)) + (q := (1757454353203847 / 4000000000000000 : ℚ)) + (U := (-(8224279888071012172189 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_6 : Uω (aρ 6) (bρ 6) (473184300463 / 1000000000000 : ℝ) ≤ @@ -946,25 +836,21 @@ lemma U_450_6 : have hlg : Real.log (8435816860506289 / 20000000000000000 : ℝ) ≤ (-(8632457199341266362179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8435816860506289 / 20000000000000000 : ℝ) = - (8435816860506289 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8435816860506289 / 5000000000000000 : ℚ)) - (U := (5230486406658733637821 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8435816860506289 / 5000000000000000 : ℝ) ≤ - (5230486406658733637821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4203360668361289 / 10000000000000000 : ℝ)) (q := - (8435816860506289 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8435816860506289 / 20000000000000000 : ℚ)) + (r' := (8435816860506289 / 5000000000000000 : ℚ)) + (U := (-(8632457199341266362179 / 10000000000000000000000 : ℚ))) + (U' := (5230486406658733637821 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (4203360668361289 / 10000000000000000 : ℚ)) + (q := (8435816860506289 / 20000000000000000 : ℚ)) + (U := (-(8632457199341266362179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_7 : Uω (aρ 7) (bρ 7) (473184300463 / 1000000000000 : ℝ) ≤ @@ -972,25 +858,21 @@ lemma U_450_7 : have hlg : Real.log (795236359092339 / 2000000000000000 : ℝ) ≤ (-(9222630815204496616637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (795236359092339 / 2000000000000000 : ℝ) = - (795236359092339 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (795236359092339 / 500000000000000 : ℚ)) - (U := (4640312790795503383363 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (795236359092339 / 500000000000000 : ℝ) ≤ - (4640312790795503383363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (394356877953839 / 1000000000000000 : ℝ)) (q := - (795236359092339 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (795236359092339 / 2000000000000000 : ℚ)) + (r' := (795236359092339 / 500000000000000 : ℚ)) + (U := (-(9222630815204496616637 / 10000000000000000000000 : ℚ))) + (U' := (4640312790795503383363 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (394356877953839 / 1000000000000000 : ℚ)) + (q := (795236359092339 / 2000000000000000 : ℚ)) + (U := (-(9222630815204496616637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_8 : Uω (aρ 8) (bρ 8) (473184300463 / 1000000000000 : ℝ) ≤ @@ -998,25 +880,21 @@ lemma U_450_8 : have hlg : Real.log (1462506012640659 / 4000000000000000 : ℝ) ≤ (-(10061429492772882776433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1462506012640659 / 4000000000000000 : ℝ) = - (1462506012640659 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1462506012640659 / 1000000000000000 : ℚ)) - (U := (3801514113227117223567 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1462506012640659 / 1000000000000000 : ℝ) ≤ - (3801514113227117223567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (717455380631659 / 2000000000000000 : ℝ)) (q := - (1462506012640659 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1462506012640659 / 4000000000000000 : ℚ)) + (r' := (1462506012640659 / 1000000000000000 : ℚ)) + (U := (-(10061429492772882776433 / 10000000000000000000000 : ℚ))) + (U' := (3801514113227117223567 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (717455380631659 / 2000000000000000 : ℚ)) + (q := (1462506012640659 / 4000000000000000 : ℚ)) + (U := (-(10061429492772882776433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_9 : Uω (aρ 9) (bρ 9) (473184300463 / 1000000000000 : ℝ) ≤ @@ -1024,25 +902,21 @@ lemma U_450_9 : have hlg : Real.log (6489435383967841 / 20000000000000000 : ℝ) ≤ (-(2813891859876060749109 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6489435383967841 / 20000000000000000 : ℝ) = - (6489435383967841 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6489435383967841 / 5000000000000000 : ℚ)) - (U := (651844041623939250891 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6489435383967841 / 5000000000000000 : ℝ) ≤ - (651844041623939250891 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3105147852282841 / 10000000000000000 : ℝ)) (q := - (6489435383967841 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6489435383967841 / 20000000000000000 : ℚ)) + (r' := (6489435383967841 / 5000000000000000 : ℚ)) + (U := (-(2813891859876060749109 / 2500000000000000000000 : ℚ))) + (U' := (651844041623939250891 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (3105147852282841 / 10000000000000000 : ℚ)) + (q := (6489435383967841 / 20000000000000000 : ℚ)) + (U := (-(2813891859876060749109 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_10 : Uω (aρ 10) (bρ 10) (473184300463 / 1000000000000 : ℝ) ≤ @@ -1050,26 +924,21 @@ lemma U_450_10 : have hlg : Real.log (1359511971652677 / 5000000000000000 : ℝ) ≤ (-(6511560604696648093569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1359511971652677 / 5000000000000000 : ℝ) = - (1359511971652677 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1359511971652677 / 1250000000000000 : ℚ)) - (U := (419911198303351906431 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1359511971652677 / 1250000000000000 : ℝ) ≤ - (419911198303351906431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (610579847105177 / 2500000000000000 : ℝ)) (q := - (1359511971652677 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1359511971652677 / 5000000000000000 : ℚ)) + (r' := (1359511971652677 / 1250000000000000 : ℚ)) + (U := (-(6511560604696648093569 / 5000000000000000000000 : ℚ))) + (U' := (419911198303351906431 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (610579847105177 / 2500000000000000 : ℚ)) + (q := (1359511971652677 / 5000000000000000 : ℚ)) + (U := (-(6511560604696648093569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_11 : Uω (aρ 11) (bρ 11) (473184300463 / 1000000000000 : ℝ) ≤ @@ -1077,26 +946,21 @@ lemma U_450_11 : have hlg : Real.log (1996575212109423 / 10000000000000000 : ℝ) ≤ (-(16111517734219643503701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1996575212109423 / 10000000000000000 : ℝ) = - (1996575212109423 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1996575212109423 / 1250000000000000 : ℚ)) - (U := (4682897674780356496299 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1996575212109423 / 1250000000000000 : ℝ) ≤ - (4682897674780356496299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (707949276116923 / 5000000000000000 : ℝ)) (q := - (1996575212109423 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1996575212109423 / 10000000000000000 : ℚ)) + (r' := (1996575212109423 / 1250000000000000 : ℚ)) + (U := (-(16111517734219643503701 / 10000000000000000000000 : ℚ))) + (U' := (4682897674780356496299 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (473184300463 / 1000000000000 : ℚ)) + (s := (707949276116923 / 5000000000000000 : ℚ)) + (q := (1996575212109423 / 10000000000000000 : ℚ)) + (U := (-(16111517734219643503701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_450_12 : Uω (aρ 12) (bρ 12) (473184300463 / 1000000000000 : ℝ) ≤ @@ -1213,25 +1077,21 @@ lemma U_451_1 : have hlg : Real.log (9361108489961869 / 20000000000000000 : ℝ) ≤ (-(948960701427451485171 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9361108489961869 / 20000000000000000 : ℝ) = - (9361108489961869 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9361108489961869 / 5000000000000000 : ℚ)) - (U := (783907249322548514829 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9361108489961869 / 5000000000000000 : ℝ) ≤ - (783907249322548514829 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4680519704651869 / 10000000000000000 : ℝ)) (q := - (9361108489961869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9361108489961869 / 20000000000000000 : ℚ)) + (r' := (9361108489961869 / 5000000000000000 : ℚ)) + (U := (-(948960701427451485171 / 1250000000000000000000 : ℚ))) + (U' := (783907249322548514829 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (4680519704651869 / 10000000000000000 : ℚ)) + (q := (9361108489961869 / 20000000000000000 : ℚ)) + (U := (-(948960701427451485171 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_2 : Uω (aρ 2) (bρ 2) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1239,25 +1099,21 @@ lemma U_451_2 : have hlg : Real.log (2328295969721429 / 5000000000000000 : ℝ) ≤ (-(3821506276829465306197 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2328295969721429 / 5000000000000000 : ℝ) = - (2328295969721429 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2328295969721429 / 1250000000000000 : ℚ)) - (U := (3109965526170534693803 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2328295969721429 / 1250000000000000 : ℝ) ≤ - (3109965526170534693803 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1164091026521429 / 2500000000000000 : ℝ)) (q := - (2328295969721429 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2328295969721429 / 5000000000000000 : ℚ)) + (r' := (2328295969721429 / 1250000000000000 : ℚ)) + (U := (-(3821506276829465306197 / 5000000000000000000000 : ℚ))) + (U' := (3109965526170534693803 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (1164091026521429 / 2500000000000000 : ℚ)) + (q := (2328295969721429 / 5000000000000000 : ℚ)) + (U := (-(3821506276829465306197 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_3 : Uω (aρ 3) (bρ 3) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1265,25 +1121,21 @@ lemma U_451_3 : have hlg : Real.log (4608621031527731 / 10000000000000000 : ℝ) ≤ (-(242080126779563267641 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4608621031527731 / 10000000000000000 : ℝ) = - (4608621031527731 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4608621031527731 / 2500000000000000 : ℚ)) - (U := (191136860907936732359 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4608621031527731 / 2500000000000000 : ℝ) ≤ - (191136860907936732359 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2303909198302731 / 5000000000000000 : ℝ)) (q := - (4608621031527731 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4608621031527731 / 10000000000000000 : ℚ)) + (r' := (4608621031527731 / 2500000000000000 : ℚ)) + (U := (-(242080126779563267641 / 312500000000000000000 : ℚ))) + (U' := (191136860907936732359 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (2303909198302731 / 5000000000000000 : ℚ)) + (q := (4608621031527731 / 10000000000000000 : ℚ)) + (U := (-(242080126779563267641 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_4 : Uω (aρ 4) (bρ 4) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1291,25 +1143,21 @@ lemma U_451_4 : have hlg : Real.log (362304516851529 / 800000000000000 : ℝ) ≤ (-(7921266621662072203433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (362304516851529 / 800000000000000 : ℝ) = - (362304516851529 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (362304516851529 / 200000000000000 : ℚ)) - (U := (5941676984337927796567 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (362304516851529 / 200000000000000 : ℝ) ≤ - (5941676984337927796567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (181059337436129 / 400000000000000 : ℝ)) (q := - (362304516851529 / 800000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (362304516851529 / 800000000000000 : ℚ)) + (r' := (362304516851529 / 200000000000000 : ℚ)) + (U := (-(7921266621662072203433 / 10000000000000000000000 : ℚ))) + (U' := (5941676984337927796567 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (181059337436129 / 400000000000000 : ℚ)) + (q := (362304516851529 / 800000000000000 : ℚ)) + (U := (-(7921266621662072203433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_5 : Uω (aρ 5) (bρ 5) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1317,25 +1165,21 @@ lemma U_451_5 : have hlg : Real.log (550862139948521 / 1250000000000000 : ℝ) ≤ (-(8194142516591679673101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (550862139948521 / 1250000000000000 : ℝ) = - (550862139948521 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (550862139948521 / 312500000000000 : ℚ)) - (U := (5668801089408320326899 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (550862139948521 / 312500000000000 : ℝ) ≤ - (5668801089408320326899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68763354267599 / 156250000000000 : ℝ)) (q := - (550862139948521 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (550862139948521 / 1250000000000000 : ℚ)) + (r' := (550862139948521 / 312500000000000 : ℚ)) + (U := (-(8194142516591679673101 / 10000000000000000000000 : ℚ))) + (U' := (5668801089408320326899 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (68763354267599 / 156250000000000 : ℚ)) + (q := (550862139948521 / 1250000000000000 : ℚ)) + (U := (-(8194142516591679673101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_6 : Uω (aρ 6) (bρ 6) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1343,25 +1187,21 @@ lemma U_451_6 : have hlg : Real.log (1692478847349581 / 4000000000000000 : ℝ) ≤ (-(8601001327470226045849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1692478847349581 / 4000000000000000 : ℝ) = - (1692478847349581 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1692478847349581 / 1000000000000000 : ℚ)) - (U := (5261942278529773954151 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1692478847349581 / 1000000000000000 : ℝ) ≤ - (5261942278529773954151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (843339009167581 / 2000000000000000 : ℝ)) (q := - (1692478847349581 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1692478847349581 / 4000000000000000 : ℚ)) + (r' := (1692478847349581 / 1000000000000000 : ℚ)) + (U := (-(8601001327470226045849 / 10000000000000000000000 : ℚ))) + (U' := (5261942278529773954151 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (843339009167581 / 2000000000000000 : ℚ)) + (q := (1692478847349581 / 4000000000000000 : ℚ)) + (U := (-(8601001327470226045849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_7 : Uω (aρ 7) (bρ 7) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1369,25 +1209,21 @@ lemma U_451_7 : have hlg : Real.log (7979067886537949 / 20000000000000000 : ℝ) ≤ (-(9189106745930102249407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7979067886537949 / 20000000000000000 : ℝ) = - (7979067886537949 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7979067886537949 / 5000000000000000 : ℚ)) - (U := (4673836860069897750593 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7979067886537949 / 5000000000000000 : ℝ) ≤ - (4673836860069897750593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3957030076387949 / 10000000000000000 : ℝ)) (q := - (7979067886537949 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7979067886537949 / 20000000000000000 : ℚ)) + (r' := (7979067886537949 / 5000000000000000 : ℚ)) + (U := (-(9189106745930102249407 / 10000000000000000000000 : ℚ))) + (U' := (4673836860069897750593 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (3957030076387949 / 10000000000000000 : ℚ)) + (q := (7979067886537949 / 20000000000000000 : ℚ)) + (U := (-(9189106745930102249407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_8 : Uω (aρ 8) (bρ 8) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1395,25 +1231,21 @@ lemma U_451_8 : have hlg : Real.log (917440439078489 / 2500000000000000 : ℝ) ≤ (-(2506145872626381178453 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (917440439078489 / 2500000000000000 : ℝ) = - (917440439078489 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (917440439078489 / 625000000000000 : ℚ)) - (U := (959590028873618821547 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (917440439078489 / 625000000000000 : ℝ) ≤ - (959590028873618821547 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (450128419227239 / 1250000000000000 : ℝ)) (q := - (917440439078489 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (917440439078489 / 2500000000000000 : ℚ)) + (r' := (917440439078489 / 625000000000000 : ℚ)) + (U := (-(2506145872626381178453 / 2500000000000000000000 : ℚ))) + (U' := (959590028873618821547 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (450128419227239 / 1250000000000000 : ℚ)) + (q := (917440439078489 / 2500000000000000 : ℚ)) + (U := (-(2506145872626381178453 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_9 : Uω (aρ 9) (bρ 9) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1421,25 +1253,21 @@ lemma U_451_9 : have hlg : Real.log (814638323778861 / 2500000000000000 : ℝ) ≤ (-(11213017700970506234207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (814638323778861 / 2500000000000000 : ℝ) = - (814638323778861 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (814638323778861 / 625000000000000 : ℚ)) - (U := (2649925905029493765793 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (814638323778861 / 625000000000000 : ℝ) ≤ - (2649925905029493765793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (389947007472611 / 1250000000000000 : ℝ)) (q := - (814638323778861 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (814638323778861 / 2500000000000000 : ℚ)) + (r' := (814638323778861 / 625000000000000 : ℚ)) + (U := (-(11213017700970506234207 / 10000000000000000000000 : ℚ))) + (U' := (2649925905029493765793 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (389947007472611 / 1250000000000000 : ℚ)) + (q := (814638323778861 / 2500000000000000 : ℚ)) + (U := (-(11213017700970506234207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_10 : Uω (aρ 10) (bρ 10) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1447,26 +1275,21 @@ lemma U_451_10 : have hlg : Real.log (2733758320944201 / 10000000000000000 : ℝ) ≤ (-(1296907755686059853951 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2733758320944201 / 10000000000000000 : ℝ) = - (2733758320944201 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2733758320944201 / 2500000000000000 : ℚ)) - (U := (89386604913940146049 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2733758320944201 / 2500000000000000 : ℝ) ≤ - (89386604913940146049 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1229272572466701 / 5000000000000000 : ℝ)) (q := - (2733758320944201 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2733758320944201 / 10000000000000000 : ℚ)) + (r' := (2733758320944201 / 2500000000000000 : ℚ)) + (U := (-(1296907755686059853951 / 1000000000000000000000 : ℚ))) + (U' := (89386604913940146049 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (1229272572466701 / 5000000000000000 : ℚ)) + (q := (2733758320944201 / 10000000000000000 : ℚ)) + (U := (-(1296907755686059853951 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_11 : Uω (aρ 11) (bρ 11) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1474,26 +1297,21 @@ lemma U_451_11 : have hlg : Real.log (2015178885922511 / 10000000000000000 : ℝ) ≤ (-(25630033977972161371 / 16000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2015178885922511 / 10000000000000000 : ℝ) = - (2015178885922511 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2015178885922511 / 1250000000000000 : ℚ)) - (U := (7641030676427838629 / 16000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2015178885922511 / 1250000000000000 : ℝ) ≤ - (7641030676427838629 / 16000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (719931450547511 / 5000000000000000 : ℝ)) (q := - (2015178885922511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2015178885922511 / 10000000000000000 : ℚ)) + (r' := (2015178885922511 / 1250000000000000 : ℚ)) + (U := (-(25630033977972161371 / 16000000000000000000 : ℚ))) + (U' := (7641030676427838629 / 16000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (949017200679 / 2000000000000 : ℚ)) + (s := (719931450547511 / 5000000000000000 : ℚ)) + (q := (2015178885922511 / 10000000000000000 : ℚ)) + (U := (-(25630033977972161371 / 16000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_451_12 : Uω (aρ 12) (bρ 12) (949017200679 / 2000000000000 : ℝ) ≤ @@ -1609,25 +1427,21 @@ lemma U_452_1 : have hlg : Real.log (234689867059907 / 500000000000000 : ℝ) ≤ (-(1890857924967793981321 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (234689867059907 / 500000000000000 : ℝ) = - (234689867059907 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (234689867059907 / 125000000000000 : ℚ)) - (U := (1574877976532206018679 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (234689867059907 / 125000000000000 : ℝ) ≤ - (1574877976532206018679 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7334004528627 / 15625000000000 : ℝ)) (q := - (234689867059907 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (234689867059907 / 500000000000000 : ℚ)) + (r' := (234689867059907 / 125000000000000 : ℚ)) + (U := (-(1890857924967793981321 / 2500000000000000000000 : ℚ))) + (U' := (1574877976532206018679 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (59479112527 / 125000000000 : ℚ)) + (s := (7334004528627 / 15625000000000 : ℚ)) + (q := (234689867059907 / 500000000000000 : ℚ)) + (U := (-(1890857924967793981321 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_2 : Uω (aρ 2) (bρ 2) (59479112527 / 125000000000 : ℝ) ≤ @@ -1635,25 +1449,21 @@ lemma U_452_2 : have hlg : Real.log (4669835584342829 / 10000000000000000 : ℝ) ≤ (-(1522922456383919548857 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4669835584342829 / 10000000000000000 : ℝ) = - (4669835584342829 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4669835584342829 / 2500000000000000 : ℚ)) - (U := (1249666264816080451143 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4669835584342829 / 2500000000000000 : ℝ) ≤ - (1249666264816080451143 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2334804198560329 / 5000000000000000 : ℝ)) (q := - (4669835584342829 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4669835584342829 / 10000000000000000 : ℚ)) + (r' := (4669835584342829 / 2500000000000000 : ℚ)) + (U := (-(1522922456383919548857 / 2000000000000000000000 : ℚ))) + (U' := (1249666264816080451143 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (59479112527 / 125000000000 : ℚ)) + (s := (2334804198560329 / 5000000000000000 : ℚ)) + (q := (4669835584342829 / 10000000000000000 : ℚ)) + (U := (-(1522922456383919548857 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_3 : Uω (aρ 3) (bρ 3) (59479112527 / 125000000000 : ℝ) ≤ @@ -1661,25 +1471,21 @@ lemma U_452_3 : have hlg : Real.log (9243732660951951 / 20000000000000000 : ℝ) ≤ (-(7717865013179724929687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9243732660951951 / 20000000000000000 : ℝ) = - (9243732660951951 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9243732660951951 / 5000000000000000 : ℚ)) - (U := (6145078592820275070313 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9243732660951951 / 5000000000000000 : ℝ) ≤ - (6145078592820275070313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4621065995736951 / 10000000000000000 : ℝ)) (q := - (9243732660951951 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9243732660951951 / 20000000000000000 : ℚ)) + (r' := (9243732660951951 / 5000000000000000 : ℚ)) + (U := (-(7717865013179724929687 / 10000000000000000000000 : ℚ))) + (U' := (6145078592820275070313 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (59479112527 / 125000000000 : ℚ)) + (s := (4621065995736951 / 10000000000000000 : ℚ)) + (q := (9243732660951951 / 20000000000000000 : ℚ)) + (U := (-(7717865013179724929687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_4 : Uω (aρ 4) (bρ 4) (59479112527 / 125000000000 : ℝ) ≤ @@ -1687,25 +1493,21 @@ lemma U_452_4 : have hlg : Real.log (2271028117988883 / 5000000000000000 : ℝ) ≤ (-(7892052675425208535167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2271028117988883 / 5000000000000000 : ℝ) = - (2271028117988883 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2271028117988883 / 1250000000000000 : ℚ)) - (U := (5970890930574791464833 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2271028117988883 / 1250000000000000 : ℝ) ≤ - (5970890930574791464833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1134934996951383 / 2500000000000000 : ℝ)) (q := - (2271028117988883 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2271028117988883 / 5000000000000000 : ℚ)) + (r' := (2271028117988883 / 1250000000000000 : ℚ)) + (U := (-(7892052675425208535167 / 10000000000000000000000 : ℚ))) + (U' := (5970890930574791464833 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (59479112527 / 125000000000 : ℚ)) + (s := (1134934996951383 / 2500000000000000 : ℚ)) + (q := (2271028117988883 / 5000000000000000 : ℚ)) + (U := (-(7892052675425208535167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_5 : Uω (aρ 5) (bρ 5) (59479112527 / 125000000000 : ℝ) ≤ @@ -1713,25 +1515,21 @@ lemma U_452_5 : have hlg : Real.log (8840316493168403 / 20000000000000000 : ℝ) ≤ (-(4082047973154115081541 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8840316493168403 / 20000000000000000 : ℝ) = - (8840316493168403 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8840316493168403 / 5000000000000000 : ℚ)) - (U := (2849423829845884918459 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8840316493168403 / 5000000000000000 : ℝ) ≤ - (2849423829845884918459 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4414133928353403 / 10000000000000000 : ℝ)) (q := - (8840316493168403 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8840316493168403 / 20000000000000000 : ℚ)) + (r' := (8840316493168403 / 5000000000000000 : ℚ)) + (U := (-(4082047973154115081541 / 5000000000000000000000 : ℚ))) + (U' := (2849423829845884918459 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (59479112527 / 125000000000 : ℚ)) + (s := (4414133928353403 / 10000000000000000 : ℚ)) + (q := (8840316493168403 / 20000000000000000 : ℚ)) + (U := (-(4082047973154115081541 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_6 : Uω (aρ 6) (bρ 6) (59479112527 / 125000000000 : ℝ) ≤ @@ -1739,24 +1537,21 @@ lemma U_452_6 : have hlg : Real.log (132640172482107 / 312500000000000 : ℝ) ≤ (-(8569644768926593276099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (132640172482107 / 312500000000000 : ℝ) = (132640172482107 / 78125000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (132640172482107 / 78125000000000 : ℚ)) - (U := (5293298837073406723901 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (132640172482107 / 78125000000000 : ℝ) ≤ - (5293298837073406723901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (528753606147481 / 1250000000000000 : ℝ)) (q := - (132640172482107 / 312500000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (132640172482107 / 312500000000000 : ℚ)) + (r' := (132640172482107 / 78125000000000 : ℚ)) + (U := (-(8569644768926593276099 / 10000000000000000000000 : ℚ))) + (U' := (5293298837073406723901 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (59479112527 / 125000000000 : ℚ)) + (s := (528753606147481 / 1250000000000000 : ℚ)) + (q := (132640172482107 / 312500000000000 : ℚ)) + (U := (-(8569644768926593276099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_7 : Uω (aρ 7) (bρ 7) (59479112527 / 125000000000 : ℝ) ≤ @@ -1764,25 +1559,21 @@ lemma U_452_7 : have hlg : Real.log (800577071394691 / 2000000000000000 : ℝ) ≤ (-(9155696521510087946207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (800577071394691 / 2000000000000000 : ℝ) = - (800577071394691 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (800577071394691 / 500000000000000 : ℚ)) - (U := (4707247084489912053793 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (800577071394691 / 500000000000000 : ℝ) ≤ - (4707247084489912053793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397048990503191 / 1000000000000000 : ℝ)) (q := - (800577071394691 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (800577071394691 / 2000000000000000 : ℚ)) + (r' := (800577071394691 / 500000000000000 : ℚ)) + (U := (-(9155696521510087946207 / 10000000000000000000000 : ℚ))) + (U' := (4707247084489912053793 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (59479112527 / 125000000000 : ℚ)) + (s := (397048990503191 / 1000000000000000 : ℚ)) + (q := (800577071394691 / 2000000000000000 : ℚ)) + (U := (-(9155696521510087946207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_8 : Uω (aρ 8) (bρ 8) (59479112527 / 125000000000 : ℝ) ≤ @@ -1790,25 +1581,21 @@ lemma U_452_8 : have hlg : Real.log (368325658632001 / 1000000000000000 : ℝ) ≤ (-(4993938948443957304859 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (368325658632001 / 1000000000000000 : ℝ) = - (368325658632001 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (368325658632001 / 250000000000000 : ℚ)) - (U := (1937532854556042695141 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (368325658632001 / 250000000000000 : ℝ) ≤ - (1937532854556042695141 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180738700753251 / 500000000000000 : ℝ)) (q := - (368325658632001 / 1000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (368325658632001 / 1000000000000000 : ℚ)) + (r' := (368325658632001 / 250000000000000 : ℚ)) + (U := (-(4993938948443957304859 / 5000000000000000000000 : ℚ))) + (U' := (1937532854556042695141 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (59479112527 / 125000000000 : ℚ)) + (s := (180738700753251 / 500000000000000 : ℚ)) + (q := (368325658632001 / 1000000000000000 : ℚ)) + (U := (-(4993938948443957304859 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_9 : Uω (aρ 9) (bρ 9) (59479112527 / 125000000000 : ℝ) ≤ @@ -1816,25 +1603,21 @@ lemma U_452_9 : have hlg : Real.log (130895346637183 / 400000000000000 : ℝ) ≤ (-(2792666058235790186179 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (130895346637183 / 400000000000000 : ℝ) = - (130895346637183 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (130895346637183 / 100000000000000 : ℚ)) - (U := (673069843264209813821 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (130895346637183 / 100000000000000 : ℝ) ≤ - (673069843264209813821 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62679876052883 / 200000000000000 : ℝ)) (q := - (130895346637183 / 400000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (130895346637183 / 400000000000000 : ℚ)) + (r' := (130895346637183 / 100000000000000 : ℚ)) + (U := (-(2792666058235790186179 / 2500000000000000000000 : ℚ))) + (U' := (673069843264209813821 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (59479112527 / 125000000000 : ℚ)) + (s := (62679876052883 / 200000000000000 : ℚ)) + (q := (130895346637183 / 400000000000000 : ℚ)) + (U := (-(2792666058235790186179 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_10 : Uω (aρ 10) (bρ 10) (59479112527 / 125000000000 : ℝ) ≤ @@ -1842,24 +1625,21 @@ lemma U_452_10 : have hlg : Real.log (27484749396081 / 100000000000000 : ℝ) ≤ (-(12915389020402956627827 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27484749396081 / 100000000000000 : ℝ) = (27484749396081 / 25000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27484749396081 / 25000000000000 : ℚ)) - (U := (947554585597043372173 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (27484749396081 / 25000000000000 : ℝ) ≤ - (947554585597043372173 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12373676917481 / 50000000000000 : ℝ)) (q := - (27484749396081 / 100000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27484749396081 / 100000000000000 : ℚ)) + (r' := (27484749396081 / 25000000000000 : ℚ)) + (U := (-(12915389020402956627827 / 10000000000000000000000 : ℚ))) + (U' := (947554585597043372173 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (59479112527 / 125000000000 : ℚ)) + (s := (12373676917481 / 50000000000000 : ℚ)) + (q := (27484749396081 / 100000000000000 : ℚ)) + (U := (-(12915389020402956627827 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_11 : Uω (aρ 11) (bρ 11) (59479112527 / 125000000000 : ℝ) ≤ @@ -1867,26 +1647,21 @@ lemma U_452_11 : have hlg : Real.log (2033646290193261 / 10000000000000000 : ℝ) ≤ (-(7963773541683381200579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2033646290193261 / 10000000000000000 : ℝ) = - (2033646290193261 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2033646290193261 / 1250000000000000 : ℚ)) - (U := (2433434162816618799421 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2033646290193261 / 1250000000000000 : ℝ) ≤ - (2433434162816618799421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (731777355435761 / 5000000000000000 : ℝ)) (q := - (2033646290193261 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2033646290193261 / 10000000000000000 : ℚ)) + (r' := (2033646290193261 / 1250000000000000 : ℚ)) + (U := (-(7963773541683381200579 / 5000000000000000000000 : ℚ))) + (U' := (2433434162816618799421 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (59479112527 / 125000000000 : ℚ)) + (s := (731777355435761 / 5000000000000000 : ℚ)) + (q := (2033646290193261 / 10000000000000000 : ℚ)) + (U := (-(7963773541683381200579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_452_12 : Uω (aρ 12) (bρ 12) (59479112527 / 125000000000 : ℝ) ≤ @@ -2003,25 +1778,21 @@ lemma U_453_1 : have hlg : Real.log (588380054608373 / 1250000000000000 : ℝ) ≤ (-(7535257392981299478961 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (588380054608373 / 1250000000000000 : ℝ) = - (588380054608373 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (588380054608373 / 312500000000000 : ℚ)) - (U := (6327686213018700521039 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (588380054608373 / 312500000000000 : ℝ) ≤ - (6327686213018700521039 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (294187880680873 / 625000000000000 : ℝ)) (q := - (588380054608373 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (588380054608373 / 1250000000000000 : ℚ)) + (r' := (588380054608373 / 312500000000000 : ℚ)) + (U := (-(7535257392981299478961 / 10000000000000000000000 : ℚ))) + (U' := (6327686213018700521039 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (190862880037 / 400000000000 : ℚ)) + (s := (294187880680873 / 625000000000000 : ℚ)) + (q := (588380054608373 / 1250000000000000 : ℚ)) + (U := (-(7535257392981299478961 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_2 : Uω (aρ 2) (bρ 2) (190862880037 / 400000000000 : ℝ) ≤ @@ -2029,25 +1800,21 @@ lemma U_453_2 : have hlg : Real.log (292692451599257 / 625000000000000 : ℝ) ≤ (-(7586292447160640009489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (292692451599257 / 625000000000000 : ℝ) = - (292692451599257 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (292692451599257 / 156250000000000 : ℚ)) - (U := (6276651158839359990511 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (292692451599257 / 156250000000000 : ℝ) ≤ - (6276651158839359990511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292678292552889 / 625000000000000 : ℝ)) (q := - (292692451599257 / 625000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (292692451599257 / 625000000000000 : ℚ)) + (r' := (292692451599257 / 156250000000000 : ℚ)) + (U := (-(7586292447160640009489 / 10000000000000000000000 : ℚ))) + (U' := (6276651158839359990511 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (190862880037 / 400000000000 : ℚ)) + (s := (292678292552889 / 625000000000000 : ℚ)) + (q := (292692451599257 / 625000000000000 : ℚ)) + (U := (-(7586292447160640009489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_3 : Uω (aρ 3) (bρ 3) (190862880037 / 400000000000 : ℝ) ≤ @@ -2055,25 +1822,21 @@ lemma U_453_3 : have hlg : Real.log (927022323255189 / 2000000000000000 : ℝ) ≤ (-(3844624062824249615123 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (927022323255189 / 2000000000000000 : ℝ) = - (927022323255189 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (927022323255189 / 500000000000000 : ℚ)) - (U := (3086847740175750384877 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (927022323255189 / 500000000000000 : ℝ) ≤ - (3086847740175750384877 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (463431356857189 / 1000000000000000 : ℝ)) (q := - (927022323255189 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (927022323255189 / 2000000000000000 : ℚ)) + (r' := (927022323255189 / 500000000000000 : ℚ)) + (U := (-(3844624062824249615123 / 5000000000000000000000 : ℚ))) + (U' := (3086847740175750384877 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (190862880037 / 400000000000 : ℚ)) + (s := (463431356857189 / 1000000000000000 : ℚ)) + (q := (927022323255189 / 2000000000000000 : ℚ)) + (U := (-(3844624062824249615123 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_4 : Uω (aρ 4) (bρ 4) (190862880037 / 400000000000 : ℝ) ≤ @@ -2081,25 +1844,21 @@ lemma U_453_4 : have hlg : Real.log (569413246483767 / 1250000000000000 : ℝ) ≤ (-(1572584782539127471169 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (569413246483767 / 1250000000000000 : ℝ) = - (569413246483767 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (569413246483767 / 312500000000000 : ℚ)) - (U := (1200003938660872528831 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (569413246483767 / 312500000000000 : ℝ) ≤ - (1200003938660872528831 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (569124557603159 / 1250000000000000 : ℝ)) (q := - (569413246483767 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (569413246483767 / 1250000000000000 : ℚ)) + (r' := (569413246483767 / 312500000000000 : ℚ)) + (U := (-(1572584782539127471169 / 2000000000000000000000 : ℚ))) + (U' := (1200003938660872528831 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (190862880037 / 400000000000 : ℚ)) + (s := (569124557603159 / 1250000000000000 : ℚ)) + (q := (569413246483767 / 1250000000000000 : ℚ)) + (U := (-(1572584782539127471169 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_5 : Uω (aρ 5) (bρ 5) (190862880037 / 400000000000 : ℝ) ≤ @@ -2107,25 +1866,21 @@ lemma U_453_5 : have hlg : Real.log (2216709632491869 / 5000000000000000 : ℝ) ≤ (-(1016767453779209346861 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2216709632491869 / 5000000000000000 : ℝ) = - (2216709632491869 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2216709632491869 / 1250000000000000 : ℚ)) - (U := (716100496970790653139 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2216709632491869 / 1250000000000000 : ℝ) ≤ - (716100496970790653139 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1106853241596869 / 2500000000000000 : ℝ)) (q := - (2216709632491869 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2216709632491869 / 5000000000000000 : ℚ)) + (r' := (2216709632491869 / 1250000000000000 : ℚ)) + (U := (-(1016767453779209346861 / 1250000000000000000000 : ℚ))) + (U' := (716100496970790653139 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (190862880037 / 400000000000 : ℚ)) + (s := (1106853241596869 / 2500000000000000 : ℚ)) + (q := (2216709632491869 / 5000000000000000 : ℚ)) + (U := (-(1016767453779209346861 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_6 : Uω (aρ 6) (bρ 6) (190862880037 / 400000000000 : ℝ) ≤ @@ -2133,25 +1888,21 @@ lemma U_453_6 : have hlg : Real.log (8515547272239381 / 20000000000000000 : ℝ) ≤ (-(8538386894358178531511 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8515547272239381 / 20000000000000000 : ℝ) = - (8515547272239381 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8515547272239381 / 5000000000000000 : ℚ)) - (U := (5324556711641821468489 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8515547272239381 / 5000000000000000 : ℝ) ≤ - (5324556711641821468489 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4243362083799381 / 10000000000000000 : ℝ)) (q := - (8515547272239381 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8515547272239381 / 20000000000000000 : ℚ)) + (r' := (8515547272239381 / 5000000000000000 : ℚ)) + (U := (-(8538386894358178531511 / 10000000000000000000000 : ℚ))) + (U' := (5324556711641821468489 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (190862880037 / 400000000000 : ℚ)) + (s := (4243362083799381 / 10000000000000000 : ℚ)) + (q := (8515547272239381 / 20000000000000000 : ℚ)) + (U := (-(8538386894358178531511 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_7 : Uω (aρ 7) (bρ 7) (190862880037 / 400000000000 : ℝ) ≤ @@ -2159,25 +1910,21 @@ lemma U_453_7 : have hlg : Real.log (8032472088031337 / 20000000000000000 : ℝ) ≤ (-(4561199679558233400381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8032472088031337 / 20000000000000000 : ℝ) = - (8032472088031337 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8032472088031337 / 5000000000000000 : ℚ)) - (U := (2370272123441766599619 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8032472088031337 / 5000000000000000 : ℝ) ≤ - (2370272123441766599619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3983948280351337 / 10000000000000000 : ℝ)) (q := - (8032472088031337 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8032472088031337 / 20000000000000000 : ℚ)) + (r' := (8032472088031337 / 5000000000000000 : ℚ)) + (U := (-(4561199679558233400381 / 5000000000000000000000 : ℚ))) + (U' := (2370272123441766599619 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (190862880037 / 400000000000 : ℚ)) + (s := (3983948280351337 / 10000000000000000 : ℚ)) + (q := (8032472088031337 / 20000000000000000 : ℚ)) + (U := (-(4561199679558233400381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_8 : Uω (aρ 8) (bρ 8) (190862880037 / 400000000000 : ℝ) ≤ @@ -2185,25 +1932,21 @@ lemma U_453_8 : have hlg : Real.log (7393499086308263 / 20000000000000000 : ℝ) ≤ (-(995131160783109617529 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7393499086308263 / 20000000000000000 : ℝ) = - (7393499086308263 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7393499086308263 / 5000000000000000 : ℚ)) - (U := (391163199816890382471 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7393499086308263 / 5000000000000000 : ℝ) ≤ - (391163199816890382471 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3628516929968263 / 10000000000000000 : ℝ)) (q := - (7393499086308263 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7393499086308263 / 20000000000000000 : ℚ)) + (r' := (7393499086308263 / 5000000000000000 : ℚ)) + (U := (-(995131160783109617529 / 1000000000000000000000 : ℚ))) + (U' := (391163199816890382471 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (190862880037 / 400000000000 : ℚ)) + (s := (3628516929968263 / 10000000000000000 : ℚ)) + (q := (7393499086308263 / 20000000000000000 : ℚ)) + (U := (-(995131160783109617529 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_9 : Uω (aρ 9) (bρ 9) (190862880037 / 400000000000 : ℝ) ≤ @@ -2211,25 +1954,21 @@ lemma U_453_9 : have hlg : Real.log (328620887630871 / 1000000000000000 : ℝ) ≤ (-(5564252546781204034449 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (328620887630871 / 1000000000000000 : ℝ) = - (328620887630871 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (328620887630871 / 250000000000000 : ℚ)) - (U := (1367219256218795965551 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (328620887630871 / 250000000000000 : ℝ) ≤ - (1367219256218795965551 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (157420061231871 / 500000000000000 : ℝ)) (q := - (328620887630871 / 1000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (328620887630871 / 1000000000000000 : ℚ)) + (r' := (328620887630871 / 250000000000000 : ℚ)) + (U := (-(5564252546781204034449 / 5000000000000000000000 : ℚ))) + (U' := (1367219256218795965551 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (190862880037 / 400000000000 : ℚ)) + (s := (157420061231871 / 500000000000000 : ℚ)) + (q := (328620887630871 / 1000000000000000 : ℚ)) + (U := (-(5564252546781204034449 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_10 : Uω (aρ 10) (bρ 10) (190862880037 / 400000000000 : ℝ) ≤ @@ -2237,24 +1976,21 @@ lemma U_453_10 : have hlg : Real.log (86349192049541 / 312500000000000 : ℝ) ≤ (-(12862050208008657540741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (86349192049541 / 312500000000000 : ℝ) = (86349192049541 / 78125000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86349192049541 / 78125000000000 : ℚ)) - (U := (1000893397991342459259 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (86349192049541 / 78125000000000 : ℝ) ≤ - (1000893397991342459259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (311361349585703 / 1250000000000000 : ℝ)) (q := - (86349192049541 / 312500000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86349192049541 / 312500000000000 : ℚ)) + (r' := (86349192049541 / 78125000000000 : ℚ)) + (U := (-(12862050208008657540741 / 10000000000000000000000 : ℚ))) + (U' := (1000893397991342459259 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (190862880037 / 400000000000 : ℚ)) + (s := (311361349585703 / 1250000000000000 : ℚ)) + (q := (86349192049541 / 312500000000000 : ℚ)) + (U := (-(12862050208008657540741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_11 : Uω (aρ 11) (bρ 11) (190862880037 / 400000000000 : ℝ) ≤ @@ -2262,24 +1998,21 @@ lemma U_453_11 : have hlg : Real.log (64124498075021 / 312500000000000 : ℝ) ≤ (-(3959444980566102260757 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (64124498075021 / 312500000000000 : ℝ) = (64124498075021 / 39062500000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64124498075021 / 39062500000000 : ℚ)) - (U := (1239158871683897739243 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64124498075021 / 39062500000000 : ℝ) ≤ - (1239158871683897739243 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (11617086004073 / 78125000000000 : ℝ)) (q := - (64124498075021 / 312500000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64124498075021 / 312500000000000 : ℚ)) + (r' := (64124498075021 / 39062500000000 : ℚ)) + (U := (-(3959444980566102260757 / 2500000000000000000000 : ℚ))) + (U' := (1239158871683897739243 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (190862880037 / 400000000000 : ℚ)) + (s := (11617086004073 / 78125000000000 : ℚ)) + (q := (64124498075021 / 312500000000000 : ℚ)) + (U := (-(3959444980566102260757 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_453_12 : Uω (aρ 12) (bρ 12) (190862880037 / 400000000000 : ℝ) ≤ @@ -2396,25 +2129,21 @@ lemma U_454_1 : have hlg : Real.log (4720283531992083 / 10000000000000000 : ℝ) ≤ (-(3753581121717678975279 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4720283531992083 / 10000000000000000 : ℝ) = - (4720283531992083 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4720283531992083 / 2500000000000000 : ℚ)) - (U := (3177890681282321024721 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4720283531992083 / 2500000000000000 : ℝ) ≤ - (3177890681282321024721 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2360124641189583 / 5000000000000000 : ℝ)) (q := - (4720283531992083 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4720283531992083 / 10000000000000000 : ℚ)) + (r' := (4720283531992083 / 2500000000000000 : ℚ)) + (U := (-(3753581121717678975279 / 5000000000000000000000 : ℚ))) + (U' := (3177890681282321024721 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (2360124641189583 / 5000000000000000 : ℚ)) + (q := (4720283531992083 / 10000000000000000 : ℚ)) + (U := (-(3753581121717678975279 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_2 : Uω (aρ 2) (bρ 2) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2422,25 +2151,21 @@ lemma U_454_2 : have hlg : Real.log (9392645726419257 / 20000000000000000 : ℝ) ≤ (-(184522768432317577 / 244140625000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9392645726419257 / 20000000000000000 : ℝ) = - (9392645726419257 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9392645726419257 / 5000000000000000 : ℚ)) - (U := (76964001599270899 / 122070312500000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9392645726419257 / 5000000000000000 : ℝ) ≤ - (76964001599270899 / 122070312500000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4696096957324257 / 10000000000000000 : ℝ)) (q := - (9392645726419257 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9392645726419257 / 20000000000000000 : ℚ)) + (r' := (9392645726419257 / 5000000000000000 : ℚ)) + (U := (-(184522768432317577 / 244140625000000000 : ℚ))) + (U' := (76964001599270899 / 122070312500000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (4696096957324257 / 10000000000000000 : ℚ)) + (q := (9392645726419257 / 20000000000000000 : ℚ)) + (U := (-(184522768432317577 / 244140625000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_3 : Uω (aρ 3) (bρ 3) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2448,25 +2173,21 @@ lemma U_454_3 : have hlg : Real.log (2324178444520037 / 5000000000000000 : ℝ) ≤ (-(7660712925159377773271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2324178444520037 / 5000000000000000 : ℝ) = - (2324178444520037 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2324178444520037 / 1250000000000000 : ℚ)) - (U := (6202230680840622226729 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2324178444520037 / 1250000000000000 : ℝ) ≤ - (6202230680840622226729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1161890278833787 / 2500000000000000 : ℝ)) (q := - (2324178444520037 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2324178444520037 / 5000000000000000 : ℚ)) + (r' := (2324178444520037 / 1250000000000000 : ℚ)) + (U := (-(7660712925159377773271 / 10000000000000000000000 : ℚ))) + (U' := (6202230680840622226729 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (1161890278833787 / 2500000000000000 : ℚ)) + (q := (2324178444520037 / 5000000000000000 : ℚ)) + (U := (-(7660712925159377773271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_4 : Uω (aρ 4) (bρ 4) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2474,25 +2195,21 @@ lemma U_454_4 : have hlg : Real.log (2284277834332367 / 5000000000000000 : ℝ) ≤ (-(156677596753044379399 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2284277834332367 / 5000000000000000 : ℝ) = - (2284277834332367 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2284277834332367 / 1250000000000000 : ℚ)) - (U := (120581275366955620601 / 200000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2284277834332367 / 1250000000000000 : ℝ) ≤ - (120581275366955620601 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1141563213912367 / 2500000000000000 : ℝ)) (q := - (2284277834332367 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2284277834332367 / 5000000000000000 : ℚ)) + (r' := (2284277834332367 / 1250000000000000 : ℚ)) + (U := (-(156677596753044379399 / 200000000000000000000 : ℚ))) + (U' := (120581275366955620601 / 200000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (1141563213912367 / 2500000000000000 : ℚ)) + (q := (2284277834332367 / 5000000000000000 : ℚ)) + (U := (-(156677596753044379399 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_5 : Uω (aρ 5) (bρ 5) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2500,25 +2217,21 @@ lemma U_454_5 : have hlg : Real.log (8893360351521979 / 20000000000000000 : ℝ) ≤ (-(810427302632192858973 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8893360351521979 / 20000000000000000 : ℝ) = - (8893360351521979 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8893360351521979 / 5000000000000000 : ℚ)) - (U := (575867057967807141027 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8893360351521979 / 5000000000000000 : ℝ) ≤ - (575867057967807141027 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4440691789176979 / 10000000000000000 : ℝ)) (q := - (8893360351521979 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8893360351521979 / 20000000000000000 : ℚ)) + (r' := (8893360351521979 / 5000000000000000 : ℚ)) + (U := (-(810427302632192858973 / 1000000000000000000000 : ℚ))) + (U' := (575867057967807141027 / 1000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (4440691789176979 / 10000000000000000 : ℚ)) + (q := (8893360351521979 / 20000000000000000 : ℚ)) + (U := (-(810427302632192858973 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_6 : Uω (aρ 6) (bρ 6) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2526,25 +2239,21 @@ lemma U_454_6 : have hlg : Real.log (8542122942245727 / 20000000000000000 : ℝ) ≤ (-(170144541608308100213 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8542122942245727 / 20000000000000000 : ℝ) = - (8542122942245727 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8542122942245727 / 5000000000000000 : ℚ)) - (U := (107114330511691899787 / 200000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8542122942245727 / 5000000000000000 : ℝ) ≤ - (107114330511691899787 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4256694755040727 / 10000000000000000 : ℝ)) (q := - (8542122942245727 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8542122942245727 / 20000000000000000 : ℚ)) + (r' := (8542122942245727 / 5000000000000000 : ℚ)) + (U := (-(170144541608308100213 / 200000000000000000000 : ℚ))) + (U' := (107114330511691899787 / 200000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (4256694755040727 / 10000000000000000 : ℚ)) + (q := (8542122942245727 / 20000000000000000 : ℚ)) + (U := (-(170144541608308100213 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_7 : Uω (aρ 7) (bρ 7) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2552,25 +2261,21 @@ lemma U_454_7 : have hlg : Real.log (2014793005867573 / 5000000000000000 : ℝ) ≤ (-(1817842896817785574473 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2014793005867573 / 5000000000000000 : ℝ) = - (2014793005867573 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2014793005867573 / 1250000000000000 : ℚ)) - (U := (954745824382214425527 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2014793005867573 / 1250000000000000 : ℝ) ≤ - (954745824382214425527 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (999351304256323 / 2500000000000000 : ℝ)) (q := - (2014793005867573 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2014793005867573 / 5000000000000000 : ℚ)) + (r' := (2014793005867573 / 1250000000000000 : ℚ)) + (U := (-(1817842896817785574473 / 2000000000000000000000 : ℚ))) + (U' := (954745824382214425527 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (999351304256323 / 2500000000000000 : ℚ)) + (q := (2014793005867573 / 5000000000000000 : ℚ)) + (U := (-(1817842896817785574473 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_8 : Uω (aρ 8) (bρ 8) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2578,25 +2283,21 @@ lemma U_454_8 : have hlg : Real.log (1484096259207923 / 4000000000000000 : ℝ) ≤ (-(9914883532630687762813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1484096259207923 / 4000000000000000 : ℝ) = - (1484096259207923 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1484096259207923 / 1000000000000000 : ℚ)) - (U := (3948060073369312237187 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1484096259207923 / 1000000000000000 : ℝ) ≤ - (3948060073369312237187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (728451228186923 / 2000000000000000 : ℝ)) (q := - (1484096259207923 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1484096259207923 / 4000000000000000 : ℚ)) + (r' := (1484096259207923 / 1000000000000000 : ℚ)) + (U := (-(9914883532630687762813 / 10000000000000000000000 : ℚ))) + (U' := (3948060073369312237187 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (728451228186923 / 2000000000000000 : ℚ)) + (q := (1484096259207923 / 4000000000000000 : ℚ)) + (U := (-(9914883532630687762813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_9 : Uω (aρ 9) (bρ 9) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2604,25 +2305,21 @@ lemma U_454_9 : have hlg : Real.log (1650014498387239 / 5000000000000000 : ℝ) ≤ (-(11086538371389681350551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1650014498387239 / 5000000000000000 : ℝ) = - (1650014498387239 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1650014498387239 / 1250000000000000 : ℚ)) - (U := (2776405234610318649449 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1650014498387239 / 1250000000000000 : ℝ) ≤ - (2776405234610318649449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (790699616700989 / 2500000000000000 : ℝ)) (q := - (1650014498387239 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1650014498387239 / 5000000000000000 : ℚ)) + (r' := (1650014498387239 / 1250000000000000 : ℚ)) + (U := (-(11086538371389681350551 / 10000000000000000000000 : ℚ))) + (U' := (2776405234610318649449 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (790699616700989 / 2500000000000000 : ℚ)) + (q := (1650014498387239 / 5000000000000000 : ℚ)) + (U := (-(11086538371389681350551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_10 : Uω (aρ 10) (bρ 10) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2630,26 +2327,21 @@ lemma U_454_10 : have hlg : Real.log (1388928137751341 / 5000000000000000 : ℝ) ≤ (-(1601131982700614138667 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1388928137751341 / 5000000000000000 : ℝ) = - (1388928137751341 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1388928137751341 / 1250000000000000 : ℚ)) - (U := (131735968049385861333 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1388928137751341 / 1250000000000000 : ℝ) ≤ - (131735968049385861333 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626753014438841 / 2500000000000000 : ℝ)) (q := - (1388928137751341 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1388928137751341 / 5000000000000000 : ℚ)) + (r' := (1388928137751341 / 1250000000000000 : ℚ)) + (U := (-(1601131982700614138667 / 1250000000000000000000 : ℚ))) + (U' := (131735968049385861333 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (626753014438841 / 2500000000000000 : ℚ)) + (q := (1388928137751341 / 5000000000000000 : ℚ)) + (U := (-(1601131982700614138667 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_11 : Uω (aρ 11) (bρ 11) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2657,26 +2349,21 @@ lemma U_454_11 : have hlg : Real.log (4140395741151013 / 20000000000000000 : ℝ) ≤ (-(15749408998553283782167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4140395741151013 / 20000000000000000 : ℝ) = - (4140395741151013 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4140395741151013 / 2500000000000000 : ℚ)) - (U := (5045006410446716217833 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4140395741151013 / 2500000000000000 : ℝ) ≤ - (5045006410446716217833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1510171874106013 / 10000000000000000 : ℝ)) (q := - (4140395741151013 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4140395741151013 / 20000000000000000 : ℚ)) + (r' := (4140395741151013 / 2500000000000000 : ℚ)) + (U := (-(15749408998553283782167 / 10000000000000000000000 : ℚ))) + (U' := (5045006410446716217833 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (478481499969 / 1000000000000 : ℚ)) + (s := (1510171874106013 / 10000000000000000 : ℚ)) + (q := (4140395741151013 / 20000000000000000 : ℚ)) + (U := (-(15749408998553283782167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_454_12 : Uω (aρ 12) (bρ 12) (478481499969 / 1000000000000 : ℝ) ≤ @@ -2790,23 +2477,21 @@ lemma U_455_1 : have hlg : Real.log (2366763313289 / 5000000000000 : ℝ) ≤ (-(1869786451919637710493 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (2366763313289 / 5000000000000 : ℝ) = (2366763313289 / 1250000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2366763313289 / 1250000000000 : ℚ)) - (U := (1595949449580362289507 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2366763313289 / 1250000000000 : ℝ) ≤ - (1595949449580362289507 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2366746236393 / 5000000000000 : ℝ)) (q := - (2366763313289 / 5000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2366763313289 / 5000000000000 : ℚ)) + (r' := (2366763313289 / 1250000000000 : ℚ)) + (U := (-(1869786451919637710493 / 2500000000000000000000 : ℚ))) + (U' := (1595949449580362289507 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (2366746236393 / 5000000000000 : ℚ)) + (q := (2366763313289 / 5000000000000 : ℚ)) + (U := (-(1869786451919637710493 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_2 : Uω (aρ 2) (bρ 2) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2814,25 +2499,21 @@ lemma U_455_2 : have hlg : Real.log (9419132994475907 / 20000000000000000 : ℝ) ≤ (-(3764946137423207459503 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9419132994475907 / 20000000000000000 : ℝ) = - (9419132994475907 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9419132994475907 / 5000000000000000 : ℚ)) - (U := (3166525665576792540497 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9419132994475907 / 5000000000000000 : ℝ) ≤ - (3166525665576792540497 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4709341226615907 / 10000000000000000 : ℝ)) (q := - (9419132994475907 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9419132994475907 / 20000000000000000 : ℚ)) + (r' := (9419132994475907 / 5000000000000000 : ℚ)) + (U := (-(3764946137423207459503 / 5000000000000000000000 : ℚ))) + (U' := (3166525665576792540497 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (4709341226615907 / 10000000000000000 : ℚ)) + (q := (9419132994475907 / 20000000000000000 : ℚ)) + (U := (-(3764946137423207459503 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_3 : Uω (aρ 3) (bρ 3) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2840,24 +2521,21 @@ lemma U_455_3 : have hlg : Real.log (29135013430497 / 62500000000000 : ℝ) ≤ (-(3816129473264321412793 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29135013430497 / 62500000000000 : ℝ) = (29135013430497 / 15625000000000 : ℝ) / 2 ^ 2 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29135013430497 / 15625000000000 : ℚ)) - (U := (3115342329735678587207 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (29135013430497 / 15625000000000 : ℝ) ≤ - (3115342329735678587207 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58260107953113 / 125000000000000 : ℝ)) (q := - (29135013430497 / 62500000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29135013430497 / 62500000000000 : ℚ)) + (r' := (29135013430497 / 15625000000000 : ℚ)) + (U := (-(3816129473264321412793 / 5000000000000000000000 : ℚ))) + (U' := (3115342329735678587207 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (58260107953113 / 125000000000000 : ℚ)) + (q := (29135013430497 / 62500000000000 : ℚ)) + (U := (-(3816129473264321412793 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_4 : Uω (aρ 4) (bρ 4) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2865,25 +2543,21 @@ lemma U_455_4 : have hlg : Real.log (9163610653402181 / 20000000000000000 : ℝ) ≤ (-(7804919958794561528009 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9163610653402181 / 20000000000000000 : ℝ) = - (9163610653402181 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9163610653402181 / 5000000000000000 : ℚ)) - (U := (6058023647205438471991 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9163610653402181 / 5000000000000000 : ℝ) ≤ - (6058023647205438471991 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4579509172957181 / 10000000000000000 : ℝ)) (q := - (9163610653402181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9163610653402181 / 20000000000000000 : ℚ)) + (r' := (9163610653402181 / 5000000000000000 : ℚ)) + (U := (-(7804919958794561528009 / 10000000000000000000000 : ℚ))) + (U' := (6058023647205438471991 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (4579509172957181 / 10000000000000000 : ℚ)) + (q := (9163610653402181 / 20000000000000000 : ℚ)) + (U := (-(7804919958794561528009 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_5 : Uω (aρ 5) (bρ 5) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2891,25 +2565,21 @@ lemma U_455_5 : have hlg : Real.log (8919881959757067 / 20000000000000000 : ℝ) ≤ (-(4037247798704166091837 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8919881959757067 / 20000000000000000 : ℝ) = - (8919881959757067 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8919881959757067 / 5000000000000000 : ℚ)) - (U := (2894224004295833908163 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8919881959757067 / 5000000000000000 : ℝ) ≤ - (2894224004295833908163 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4453970398647067 / 10000000000000000 : ℝ)) (q := - (8919881959757067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8919881959757067 / 20000000000000000 : ℚ)) + (r' := (8919881959757067 / 5000000000000000 : ℚ)) + (U := (-(4037247798704166091837 / 5000000000000000000000 : ℚ))) + (U' := (2894224004295833908163 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (4453970398647067 / 10000000000000000 : ℚ)) + (q := (8919881959757067 / 20000000000000000 : ℚ)) + (U := (-(4037247798704166091837 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_6 : Uω (aρ 6) (bρ 6) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2917,25 +2587,21 @@ lemma U_455_6 : have hlg : Real.log (428434902707557 / 1000000000000000 : ℝ) ≤ (-(4238082354837365660861 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (428434902707557 / 1000000000000000 : ℝ) = - (428434902707557 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (428434902707557 / 250000000000000 : ℚ)) - (U := (2693389448162634339139 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (428434902707557 / 250000000000000 : ℝ) ≤ - (2693389448162634339139 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (213501343409057 / 500000000000000 : ℝ)) (q := - (428434902707557 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (428434902707557 / 1000000000000000 : ℚ)) + (r' := (428434902707557 / 250000000000000 : ℚ)) + (U := (-(4238082354837365660861 / 5000000000000000000000 : ℚ))) + (U' := (2693389448162634339139 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (213501343409057 / 500000000000000 : ℚ)) + (q := (428434902707557 / 1000000000000000 : ℚ)) + (U := (-(4238082354837365660861 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_7 : Uω (aρ 7) (bρ 7) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2943,25 +2609,21 @@ lemma U_455_7 : have hlg : Real.log (8085870534744279 / 20000000000000000 : ℝ) ≤ (-(9056141129820026511853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8085870534744279 / 20000000000000000 : ℝ) = - (8085870534744279 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8085870534744279 / 5000000000000000 : ℚ)) - (U := (4806802476179973488147 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8085870534744279 / 5000000000000000 : ℝ) ≤ - (4806802476179973488147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4010860729534279 / 10000000000000000 : ℝ)) (q := - (8085870534744279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8085870534744279 / 20000000000000000 : ℚ)) + (r' := (8085870534744279 / 5000000000000000 : ℚ)) + (U := (-(9056141129820026511853 / 10000000000000000000000 : ℚ))) + (U' := (4806802476179973488147 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (4010860729534279 / 10000000000000000 : ℚ)) + (q := (8085870534744279 / 20000000000000000 : ℚ)) + (U := (-(9056141129820026511853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_8 : Uω (aρ 8) (bρ 8) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2969,25 +2631,21 @@ lemma U_455_8 : have hlg : Real.log (3723729921796121 / 10000000000000000 : ℝ) ≤ (-(617412037109097621673 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3723729921796121 / 10000000000000000 : ℝ) = - (3723729921796121 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3723729921796121 / 2500000000000000 : ℚ)) - (U := (249021938265902378327 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3723729921796121 / 2500000000000000 : ℝ) ≤ - (249021938265902378327 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1827995844861121 / 5000000000000000 : ℝ)) (q := - (3723729921796121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3723729921796121 / 10000000000000000 : ℚ)) + (r' := (3723729921796121 / 2500000000000000 : ℚ)) + (U := (-(617412037109097621673 / 625000000000000000000 : ℚ))) + (U' := (249021938265902378327 / 625000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (1827995844861121 / 5000000000000000 : ℚ)) + (q := (3723729921796121 / 10000000000000000 : ℚ)) + (U := (-(617412037109097621673 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_9 : Uω (aρ 9) (bρ 9) (959611599691 / 2000000000000 : ℝ) ≤ @@ -2995,25 +2653,21 @@ lemma U_455_9 : have hlg : Real.log (828461024130217 / 2500000000000000 : ℝ) ≤ (-(5522381092373664086313 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (828461024130217 / 2500000000000000 : ℝ) = - (828461024130217 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (828461024130217 / 625000000000000 : ℚ)) - (U := (1409090710626335913687 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (828461024130217 / 625000000000000 : ℝ) ≤ - (1409090710626335913687 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397148208441467 / 1250000000000000 : ℝ)) (q := - (828461024130217 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (828461024130217 / 2500000000000000 : ℚ)) + (r' := (828461024130217 / 625000000000000 : ℚ)) + (U := (-(5522381092373664086313 / 5000000000000000000000 : ℚ))) + (U' := (1409090710626335913687 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (397148208441467 / 1250000000000000 : ℚ)) + (q := (828461024130217 / 2500000000000000 : ℚ)) + (U := (-(5522381092373664086313 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_10 : Uω (aρ 10) (bρ 10) (959611599691 / 2000000000000 : ℝ) ≤ @@ -3021,26 +2675,21 @@ lemma U_455_10 : have hlg : Real.log (1396260828340487 / 5000000000000000 : ℝ) ≤ (-(3189100213102396916873 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1396260828340487 / 5000000000000000 : ℝ) = - (1396260828340487 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1396260828340487 / 1250000000000000 : ℚ)) - (U := (276635688397603083127 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1396260828340487 / 1250000000000000 : ℝ) ≤ - (276635688397603083127 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (630774955336737 / 2500000000000000 : ℝ)) (q := - (1396260828340487 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1396260828340487 / 5000000000000000 : ℚ)) + (r' := (1396260828340487 / 1250000000000000 : ℚ)) + (U := (-(3189100213102396916873 / 2500000000000000000000 : ℚ))) + (U' := (276635688397603083127 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (630774955336737 / 2500000000000000 : ℚ)) + (q := (1396260828340487 / 5000000000000000 : ℚ)) + (U := (-(3189100213102396916873 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_11 : Uω (aρ 11) (bρ 11) (959611599691 / 2000000000000 : ℝ) ≤ @@ -3048,24 +2697,21 @@ lemma U_455_11 : have hlg : Real.log (104414684974301 / 500000000000000 : ℝ) ≤ (-(978898607132638238711 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (104414684974301 / 500000000000000 : ℝ) = (104414684974301 / 62500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (104414684974301 / 62500000000000 : ℚ)) - (U := (320752355929861761289 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (104414684974301 / 62500000000000 : ℝ) ≤ - (320752355929861761289 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (38328013329051 / 250000000000000 : ℝ)) (q := - (104414684974301 / 500000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (104414684974301 / 500000000000000 : ℚ)) + (r' := (104414684974301 / 62500000000000 : ℚ)) + (U := (-(978898607132638238711 / 625000000000000000000 : ℚ))) + (U' := (320752355929861761289 / 625000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (959611599691 / 2000000000000 : ℚ)) + (s := (38328013329051 / 250000000000000 : ℚ)) + (q := (104414684974301 / 500000000000000 : ℚ)) + (U := (-(978898607132638238711 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_455_12 : Uω (aρ 12) (bρ 12) (959611599691 / 2000000000000 : ℝ) ≤ @@ -3181,25 +2827,21 @@ lemma U_456_1 : have hlg : Real.log (4746769720629249 / 10000000000000000 : ℝ) ≤ (-(7451207645873873946861 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4746769720629249 / 10000000000000000 : ℝ) = - (4746769720629249 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4746769720629249 / 2500000000000000 : ℚ)) - (U := (6411735960126126053139 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4746769720629249 / 2500000000000000 : ℝ) ≤ - (6411735960126126053139 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2373367831061749 / 5000000000000000 : ℝ)) (q := - (4746769720629249 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4746769720629249 / 10000000000000000 : ℚ)) + (r' := (4746769720629249 / 2500000000000000 : ℚ)) + (U := (-(7451207645873873946861 / 10000000000000000000000 : ℚ))) + (U' := (6411735960126126053139 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (240565049861 / 500000000000 : ℚ)) + (s := (2373367831061749 / 5000000000000000 : ℚ)) + (q := (4746769720629249 / 10000000000000000 : ℚ)) + (U := (-(7451207645873873946861 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_2 : Uω (aρ 2) (bρ 2) (240565049861 / 500000000000 : ℝ) ≤ @@ -3207,25 +2849,21 @@ lemma U_456_2 : have hlg : Real.log (9445620255406633 / 20000000000000000 : ℝ) ≤ (-(7501811039978996837427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9445620255406633 / 20000000000000000 : ℝ) = - (9445620255406633 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9445620255406633 / 5000000000000000 : ℚ)) - (U := (6361132566021003162573 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9445620255406633 / 5000000000000000 : ℝ) ≤ - (6361132566021003162573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4722585488781633 / 10000000000000000 : ℝ)) (q := - (9445620255406633 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9445620255406633 / 20000000000000000 : ℚ)) + (r' := (9445620255406633 / 5000000000000000 : ℚ)) + (U := (-(7501811039978996837427 / 10000000000000000000000 : ℚ))) + (U' := (6361132566021003162573 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (240565049861 / 500000000000 : ℚ)) + (s := (4722585488781633 / 10000000000000000 : ℚ)) + (q := (9445620255406633 / 20000000000000000 : ℚ)) + (U := (-(7501811039978996837427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_3 : Uω (aρ 3) (bρ 3) (240565049861 / 500000000000 : ℝ) ≤ @@ -3233,25 +2871,21 @@ lemma U_456_3 : have hlg : Real.log (2337423697952089 / 5000000000000000 : ℝ) ≤ (-(3801942864268135953877 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2337423697952089 / 5000000000000000 : ℝ) = - (2337423697952089 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2337423697952089 / 1250000000000000 : ℚ)) - (U := (3129528938731864046123 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2337423697952089 / 1250000000000000 : ℝ) ≤ - (3129528938731864046123 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1168514032883339 / 2500000000000000 : ℝ)) (q := - (2337423697952089 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2337423697952089 / 5000000000000000 : ℚ)) + (r' := (2337423697952089 / 1250000000000000 : ℚ)) + (U := (-(3801942864268135953877 / 5000000000000000000000 : ℚ))) + (U' := (3129528938731864046123 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (240565049861 / 500000000000 : ℚ)) + (s := (1168514032883339 / 2500000000000000 : ℚ)) + (q := (2337423697952089 / 5000000000000000 : ℚ)) + (U := (-(3801942864268135953877 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_4 : Uω (aρ 4) (bρ 4) (240565049861 / 500000000000 : ℝ) ≤ @@ -3259,25 +2893,21 @@ lemma U_456_4 : have hlg : Real.log (9190109892629631 / 20000000000000000 : ℝ) ≤ (-(3888021894446453529367 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9190109892629631 / 20000000000000000 : ℝ) = - (9190109892629631 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9190109892629631 / 5000000000000000 : ℚ)) - (U := (3043449908553546470633 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9190109892629631 / 5000000000000000 : ℝ) ≤ - (3043449908553546470633 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4592765413419631 / 10000000000000000 : ℝ)) (q := - (9190109892629631 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9190109892629631 / 20000000000000000 : ℚ)) + (r' := (9190109892629631 / 5000000000000000 : ℚ)) + (U := (-(3888021894446453529367 / 5000000000000000000000 : ℚ))) + (U' := (3043449908553546470633 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (240565049861 / 500000000000 : ℚ)) + (s := (4592765413419631 / 10000000000000000 : ℚ)) + (q := (9190109892629631 / 20000000000000000 : ℚ)) + (U := (-(3888021894446453529367 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_5 : Uω (aρ 5) (bρ 5) (240565049861 / 500000000000 : ℝ) ≤ @@ -3285,25 +2915,21 @@ lemma U_456_5 : have hlg : Real.log (8946403356574973 / 20000000000000000 : ℝ) ≤ (-(1608961362230212211269 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8946403356574973 / 20000000000000000 : ℝ) = - (8946403356574973 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8946403356574973 / 5000000000000000 : ℚ)) - (U := (1163627358969787788731 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8946403356574973 / 5000000000000000 : ℝ) ≤ - (1163627358969787788731 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4467248796699973 / 10000000000000000 : ℝ)) (q := - (8946403356574973 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8946403356574973 / 20000000000000000 : ℚ)) + (r' := (8946403356574973 / 5000000000000000 : ℚ)) + (U := (-(1608961362230212211269 / 2000000000000000000000 : ℚ))) + (U' := (1163627358969787788731 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (240565049861 / 500000000000 : ℚ)) + (s := (4467248796699973 / 10000000000000000 : ℚ)) + (q := (8946403356574973 / 20000000000000000 : ℚ)) + (U := (-(1608961362230212211269 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_6 : Uω (aρ 6) (bρ 6) (240565049861 / 500000000000 : ℝ) ≤ @@ -3311,25 +2937,21 @@ lemma U_456_6 : have hlg : Real.log (2148818153291737 / 5000000000000000 : ℝ) ≤ (-(8445199170563307895169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2148818153291737 / 5000000000000000 : ℝ) = - (2148818153291737 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2148818153291737 / 1250000000000000 : ℚ)) - (U := (5417744435436692104831 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2148818153291737 / 1250000000000000 : ℝ) ≤ - (5417744435436692104831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1070839607107987 / 2500000000000000 : ℝ)) (q := - (2148818153291737 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2148818153291737 / 5000000000000000 : ℚ)) + (r' := (2148818153291737 / 1250000000000000 : ℚ)) + (U := (-(8445199170563307895169 / 10000000000000000000000 : ℚ))) + (U' := (5417744435436692104831 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (240565049861 / 500000000000 : ℚ)) + (s := (1070839607107987 / 2500000000000000 : ℚ)) + (q := (2148818153291737 / 5000000000000000 : ℚ)) + (U := (-(8445199170563307895169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_7 : Uω (aρ 7) (bρ 7) (240565049861 / 500000000000 : ℝ) ≤ @@ -3337,25 +2959,21 @@ lemma U_456_7 : have hlg : Real.log (4056283818069307 / 10000000000000000 : ℝ) ≤ (-(9023178537642414456629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4056283818069307 / 10000000000000000 : ℝ) = - (4056283818069307 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4056283818069307 / 2500000000000000 : ℚ)) - (U := (4839765068357585543371 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4056283818069307 / 2500000000000000 : ℝ) ≤ - (4839765068357585543371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2012157416081807 / 5000000000000000 : ℝ)) (q := - (4056283818069307 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4056283818069307 / 10000000000000000 : ℚ)) + (r' := (4056283818069307 / 2500000000000000 : ℚ)) + (U := (-(9023178537642414456629 / 10000000000000000000000 : ℚ))) + (U' := (4839765068357585543371 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (240565049861 / 500000000000 : ℚ)) + (s := (2012157416081807 / 5000000000000000 : ℚ)) + (q := (4056283818069307 / 10000000000000000 : ℚ)) + (U := (-(9023178537642414456629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_8 : Uω (aρ 8) (bρ 8) (240565049861 / 500000000000 : ℝ) ≤ @@ -3363,25 +2981,21 @@ lemma U_456_8 : have hlg : Real.log (934304346261009 / 2500000000000000 : ℝ) ≤ (-(9842437726581167586699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (934304346261009 / 2500000000000000 : ℝ) = - (934304346261009 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (934304346261009 / 625000000000000 : ℚ)) - (U := (4020505879418832413301 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (934304346261009 / 625000000000000 : ℝ) ≤ - (4020505879418832413301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (229357726090817 / 625000000000000 : ℝ)) (q := - (934304346261009 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (934304346261009 / 2500000000000000 : ℚ)) + (r' := (934304346261009 / 625000000000000 : ℚ)) + (U := (-(9842437726581167586699 / 10000000000000000000000 : ℚ))) + (U' := (4020505879418832413301 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (240565049861 / 500000000000 : ℚ)) + (s := (229357726090817 / 625000000000000 : ℚ)) + (q := (934304346261009 / 2500000000000000 : ℚ)) + (U := (-(9842437726581167586699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_9 : Uω (aρ 9) (bρ 9) (240565049861 / 500000000000 : ℝ) ≤ @@ -3389,25 +3003,21 @@ lemma U_456_9 : have hlg : Real.log (3327654243446367 / 10000000000000000 : ℝ) ≤ (-(27507936702691674071 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3327654243446367 / 10000000000000000 : ℝ) = - (3327654243446367 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3327654243446367 / 2500000000000000 : ℚ)) - (U := (7149422312308325929 / 25000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3327654243446367 / 2500000000000000 : ℝ) ≤ - (7149422312308325929 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1595781481308867 / 5000000000000000 : ℝ)) (q := - (3327654243446367 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3327654243446367 / 10000000000000000 : ℚ)) + (r' := (3327654243446367 / 2500000000000000 : ℚ)) + (U := (-(27507936702691674071 / 25000000000000000000 : ℚ))) + (U' := (7149422312308325929 / 25000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (240565049861 / 500000000000 : ℚ)) + (s := (1595781481308867 / 5000000000000000 : ℚ)) + (q := (3327654243446367 / 10000000000000000 : ℚ)) + (U := (-(27507936702691674071 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_10 : Uω (aρ 10) (bρ 10) (240565049861 / 500000000000 : ℝ) ≤ @@ -3415,26 +3025,21 @@ lemma U_456_10 : have hlg : Real.log (1403585303736957 / 5000000000000000 : ℝ) ≤ (-(12704080176489435428207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1403585303736957 / 5000000000000000 : ℝ) = - (1403585303736957 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1403585303736957 / 1250000000000000 : ℚ)) - (U := (1158863429510564571793 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1403585303736957 / 1250000000000000 : ℝ) ≤ - (1158863429510564571793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (634788681041957 / 2500000000000000 : ℝ)) (q := - (1403585303736957 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1403585303736957 / 5000000000000000 : ℚ)) + (r' := (1403585303736957 / 1250000000000000 : ℚ)) + (U := (-(12704080176489435428207 / 10000000000000000000000 : ℚ))) + (U' := (1158863429510564571793 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (240565049861 / 500000000000 : ℚ)) + (s := (634788681041957 / 2500000000000000 : ℚ)) + (q := (1403585303736957 / 5000000000000000 : ℚ)) + (U := (-(12704080176489435428207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_11 : Uω (aρ 11) (bρ 11) (240565049861 / 500000000000 : ℝ) ≤ @@ -3442,26 +3047,21 @@ lemma U_456_11 : have hlg : Real.log (4212553302424011 / 20000000000000000 : ℝ) ≤ (-(15576633237813044959681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4212553302424011 / 20000000000000000 : ℝ) = - (4212553302424011 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4212553302424011 / 2500000000000000 : ℚ)) - (U := (5217782171186955040319 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4212553302424011 / 2500000000000000 : ℝ) ≤ - (5217782171186955040319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1555843437849011 / 10000000000000000 : ℝ)) (q := - (4212553302424011 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4212553302424011 / 20000000000000000 : ℚ)) + (r' := (4212553302424011 / 2500000000000000 : ℚ)) + (U := (-(15576633237813044959681 / 10000000000000000000000 : ℚ))) + (U' := (5217782171186955040319 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (240565049861 / 500000000000 : ℚ)) + (s := (1555843437849011 / 10000000000000000 : ℚ)) + (q := (4212553302424011 / 20000000000000000 : ℚ)) + (U := (-(15576633237813044959681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_456_12 : Uω (aρ 12) (bρ 12) (240565049861 / 500000000000 : ℝ) ≤ @@ -3578,25 +3178,21 @@ lemma U_457_1 : have hlg : Real.log (4773255907145541 / 10000000000000000 : ℝ) ≤ (-(7395564403113882945229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4773255907145541 / 10000000000000000 : ℝ) = - (4773255907145541 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4773255907145541 / 2500000000000000 : ℚ)) - (U := (6467379202886117054771 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4773255907145541 / 2500000000000000 : ℝ) ≤ - (6467379202886117054771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2386611018813041 / 5000000000000000 : ℝ)) (q := - (4773255907145541 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4773255907145541 / 10000000000000000 : ℚ)) + (r' := (4773255907145541 / 2500000000000000 : ℚ)) + (U := (-(7395564403113882945229 / 10000000000000000000000 : ℚ))) + (U' := (6467379202886117054771 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19351147979 / 40000000000 : ℚ)) + (s := (2386611018813041 / 5000000000000000 : ℚ)) + (q := (4773255907145541 / 10000000000000000 : ℚ)) + (U := (-(7395564403113882945229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_2 : Uω (aρ 2) (bρ 2) (19351147979 / 40000000000 : ℝ) ≤ @@ -3604,25 +3200,21 @@ lemma U_457_2 : have hlg : Real.log (1187324344516099 / 2500000000000000 : ℝ) ≤ (-(1489176811552806506841 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1187324344516099 / 2500000000000000 : ℝ) = - (1187324344516099 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1187324344516099 / 625000000000000 : ℚ)) - (U := (1283411909647193493159 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1187324344516099 / 625000000000000 : ℝ) ≤ - (1283411909647193493159 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (148408562249181 / 312500000000000 : ℝ)) (q := - (1187324344516099 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1187324344516099 / 2500000000000000 : ℚ)) + (r' := (1187324344516099 / 625000000000000 : ℚ)) + (U := (-(1489176811552806506841 / 2000000000000000000000 : ℚ))) + (U' := (1283411909647193493159 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19351147979 / 40000000000 : ℚ)) + (s := (148408562249181 / 312500000000000 : ℚ)) + (q := (1187324344516099 / 2500000000000000 : ℚ)) + (U := (-(1489176811552806506841 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_3 : Uω (aρ 3) (bρ 3) (19351147979 / 40000000000 : ℝ) ≤ @@ -3630,24 +3222,21 @@ lemma U_457_3 : have hlg : Real.log (117533446298563 / 250000000000000 : ℝ) ≤ (-(60379037993088768907 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (117533446298563 / 250000000000000 : ℝ) = (117533446298563 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (117533446298563 / 62500000000000 : ℚ)) - (U := (50524510854911231093 / 80000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (117533446298563 / 62500000000000 : ℝ) ≤ - (50524510854911231093 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117513776152001 / 250000000000000 : ℝ)) (q := - (117533446298563 / 250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (117533446298563 / 250000000000000 : ℚ)) + (r' := (117533446298563 / 62500000000000 : ℚ)) + (U := (-(60379037993088768907 / 80000000000000000000 : ℚ))) + (U' := (50524510854911231093 / 80000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19351147979 / 40000000000 : ℚ)) + (s := (117513776152001 / 250000000000000 : ℚ)) + (q := (117533446298563 / 250000000000000 : ℚ)) + (U := (-(60379037993088768907 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_4 : Uω (aρ 4) (bρ 4) (19351147979 / 40000000000 : ℝ) ≤ @@ -3655,25 +3244,21 @@ lemma U_457_4 : have hlg : Real.log (2310777035798767 / 5000000000000000 : ℝ) ≤ (-(482408790506011869709 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2310777035798767 / 5000000000000000 : ℝ) = - (2310777035798767 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2310777035798767 / 1250000000000000 : ℚ)) - (U := (384025184868988130291 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2310777035798767 / 1250000000000000 : ℝ) ≤ - (384025184868988130291 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1154819416613767 / 2500000000000000 : ℝ)) (q := - (2310777035798767 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2310777035798767 / 5000000000000000 : ℚ)) + (r' := (2310777035798767 / 1250000000000000 : ℚ)) + (U := (-(482408790506011869709 / 625000000000000000000 : ℚ))) + (U' := (384025184868988130291 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19351147979 / 40000000000 : ℚ)) + (s := (1154819416613767 / 2500000000000000 : ℚ)) + (q := (2310777035798767 / 5000000000000000 : ℚ)) + (U := (-(482408790506011869709 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_5 : Uω (aρ 5) (bρ 5) (19351147979 / 40000000000 : ℝ) ≤ @@ -3681,25 +3266,21 @@ lemma U_457_5 : have hlg : Real.log (8999445523455617 / 20000000000000000 : ℝ) ≤ (-(798569306100694326047 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8999445523455617 / 20000000000000000 : ℝ) = - (8999445523455617 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8999445523455617 / 5000000000000000 : ℚ)) - (U := (587725054499305673953 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8999445523455617 / 5000000000000000 : ℝ) ≤ - (587725054499305673953 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4493804966050617 / 10000000000000000 : ℝ)) (q := - (8999445523455617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8999445523455617 / 20000000000000000 : ℚ)) + (r' := (8999445523455617 / 5000000000000000 : ℚ)) + (U := (-(798569306100694326047 / 1000000000000000000000 : ℚ))) + (U' := (587725054499305673953 / 1000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19351147979 / 40000000000 : ℚ)) + (s := (4493804966050617 / 10000000000000000 : ℚ)) + (q := (8999445523455617 / 20000000000000000 : ℚ)) + (U := (-(798569306100694326047 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_6 : Uω (aρ 6) (bρ 6) (19351147979 / 40000000000 : ℝ) ≤ @@ -3707,25 +3288,21 @@ lemma U_457_6 : have hlg : Real.log (8648420093051619 / 20000000000000000 : ℝ) ≤ (-(2095889042436629020461 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8648420093051619 / 20000000000000000 : ℝ) = - (8648420093051619 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8648420093051619 / 5000000000000000 : ℚ)) - (U := (1369846859063370979539 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8648420093051619 / 5000000000000000 : ℝ) ≤ - (1369846859063370979539 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4310019910786619 / 10000000000000000 : ℝ)) (q := - (8648420093051619 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8648420093051619 / 20000000000000000 : ℚ)) + (r' := (8648420093051619 / 5000000000000000 : ℚ)) + (U := (-(2095889042436629020461 / 2500000000000000000000 : ℚ))) + (U' := (1369846859063370979539 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19351147979 / 40000000000 : ℚ)) + (s := (4310019910786619 / 10000000000000000 : ℚ)) + (q := (8648420093051619 / 20000000000000000 : ℚ)) + (U := (-(2095889042436629020461 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_7 : Uω (aρ 7) (bρ 7) (19351147979 / 40000000000 : ℝ) ≤ @@ -3733,24 +3310,21 @@ lemma U_457_7 : have hlg : Real.log (40829788327367 / 100000000000000 : ℝ) ≤ (-(4478791321964708754081 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (40829788327367 / 100000000000000 : ℝ) = (40829788327367 / 25000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40829788327367 / 25000000000000 : ℚ)) - (U := (2452680481035291245919 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (40829788327367 / 25000000000000 : ℝ) ≤ - (2452680481035291245919 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (10128047159921 / 25000000000000 : ℝ)) (q := - (40829788327367 / 100000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40829788327367 / 100000000000000 : ℚ)) + (r' := (40829788327367 / 25000000000000 : ℚ)) + (U := (-(4478791321964708754081 / 5000000000000000000000 : ℚ))) + (U' := (2452680481035291245919 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19351147979 / 40000000000 : ℚ)) + (s := (10128047159921 / 25000000000000 : ℚ)) + (q := (40829788327367 / 100000000000000 : ℚ)) + (U := (-(4478791321964708754081 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_8 : Uω (aρ 8) (bρ 8) (19351147979 / 40000000000 : ℝ) ≤ @@ -3758,25 +3332,21 @@ lemma U_457_8 : have hlg : Real.log (470523370080573 / 1250000000000000 : ℝ) ≤ (-(9770532012500916071231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (470523370080573 / 1250000000000000 : ℝ) = - (470523370080573 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (470523370080573 / 312500000000000 : ℚ)) - (U := (4092411593499083928769 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (470523370080573 / 312500000000000 : ℝ) ≤ - (4092411593499083928769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (462147096390521 / 1250000000000000 : ℝ)) (q := - (470523370080573 / 1250000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (470523370080573 / 1250000000000000 : ℚ)) + (r' := (470523370080573 / 312500000000000 : ℚ)) + (U := (-(9770532012500916071231 / 10000000000000000000000 : ℚ))) + (U' := (4092411593499083928769 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19351147979 / 40000000000 : ℚ)) + (s := (462147096390521 / 1250000000000000 : ℚ)) + (q := (470523370080573 / 1250000000000000 : ℚ)) + (U := (-(9770532012500916071231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_9 : Uω (aρ 9) (bρ 9) (19351147979 / 40000000000 : ℝ) ≤ @@ -3784,25 +3354,21 @@ lemma U_457_9 : have hlg : Real.log (6710519888274599 / 20000000000000000 : ℝ) ≤ (-(5460279227141323714019 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6710519888274599 / 20000000000000000 : ℝ) = - (6710519888274599 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6710519888274599 / 5000000000000000 : ℚ)) - (U := (1471192575858676285981 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6710519888274599 / 5000000000000000 : ℝ) ≤ - (1471192575858676285981 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3220288366469599 / 10000000000000000 : ℝ)) (q := - (6710519888274599 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6710519888274599 / 20000000000000000 : ℚ)) + (r' := (6710519888274599 / 5000000000000000 : ℚ)) + (U := (-(5460279227141323714019 / 5000000000000000000000 : ℚ))) + (U' := (1471192575858676285981 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19351147979 / 40000000000 : ℚ)) + (s := (3220288366469599 / 10000000000000000 : ℚ)) + (q := (6710519888274599 / 20000000000000000 : ℚ)) + (U := (-(5460279227141323714019 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_10 : Uω (aρ 10) (bρ 10) (19351147979 / 40000000000 : ℝ) ≤ @@ -3810,26 +3376,21 @@ lemma U_457_10 : have hlg : Real.log (2836420448410709 / 10000000000000000 : ℝ) ≤ (-(1260042240769293479831 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2836420448410709 / 10000000000000000 : ℝ) = - (2836420448410709 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2836420448410709 / 2500000000000000 : ℚ)) - (U := (126252119830706520169 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2836420448410709 / 2500000000000000 : ℝ) ≤ - (126252119830706520169 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1285584204255709 / 5000000000000000 : ℝ)) (q := - (2836420448410709 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2836420448410709 / 10000000000000000 : ℚ)) + (r' := (2836420448410709 / 2500000000000000 : ℚ)) + (U := (-(1260042240769293479831 / 1000000000000000000000 : ℚ))) + (U' := (126252119830706520169 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19351147979 / 40000000000 : ℚ)) + (s := (1285584204255709 / 5000000000000000 : ℚ)) + (q := (2836420448410709 / 10000000000000000 : ℚ)) + (U := (-(1260042240769293479831 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_11 : Uω (aρ 11) (bρ 11) (19351147979 / 40000000000 : ℝ) ≤ @@ -3837,26 +3398,21 @@ lemma U_457_11 : have hlg : Real.log (1070961552247659 / 5000000000000000 : ℝ) ≤ (-(15408810197614576507277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1070961552247659 / 5000000000000000 : ℝ) = - (1070961552247659 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1070961552247659 / 625000000000000 : ℚ)) - (U := (5385605211385423492723 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1070961552247659 / 625000000000000 : ℝ) ≤ - (5385605211385423492723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (400162586721409 / 2500000000000000 : ℝ)) (q := - (1070961552247659 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1070961552247659 / 5000000000000000 : ℚ)) + (r' := (1070961552247659 / 625000000000000 : ℚ)) + (U := (-(15408810197614576507277 / 10000000000000000000000 : ℚ))) + (U' := (5385605211385423492723 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19351147979 / 40000000000 : ℚ)) + (s := (400162586721409 / 2500000000000000 : ℚ)) + (q := (1070961552247659 / 5000000000000000 : ℚ)) + (U := (-(15408810197614576507277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_457_12 : Uω (aρ 12) (bρ 12) (19351147979 / 40000000000 : ℝ) ≤ @@ -3970,25 +3526,21 @@ lemma U_458_1 : have hlg : Real.log (9599484183152141 / 20000000000000000 : ℝ) ≤ (-(1468045813851038955841 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9599484183152141 / 20000000000000000 : ℝ) = - (9599484183152141 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9599484183152141 / 5000000000000000 : ℚ)) - (U := (1304542907348961044159 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9599484183152141 / 5000000000000000 : ℝ) ≤ - (1304542907348961044159 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4799708408957141 / 10000000000000000 : ℝ)) (q := - (9599484183152141 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9599484183152141 / 20000000000000000 : ℚ)) + (r' := (9599484183152141 / 5000000000000000 : ℚ)) + (U := (-(1468045813851038955841 / 2000000000000000000000 : ℚ))) + (U' := (1304542907348961044159 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (121606824807 / 250000000000 : ℚ)) + (s := (4799708408957141 / 10000000000000000 : ℚ)) + (q := (9599484183152141 / 20000000000000000 : ℚ)) + (U := (-(1468045813851038955841 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_2 : Uω (aρ 2) (bρ 2) (121606824807 / 250000000000 : ℝ) ≤ @@ -3996,25 +3548,21 @@ lemma U_458_2 : have hlg : Real.log (9551569229056067 / 20000000000000000 : ℝ) ≤ (-(7390268148614046540739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9551569229056067 / 20000000000000000 : ℝ) = - (9551569229056067 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9551569229056067 / 5000000000000000 : ℚ)) - (U := (6472675457385953459261 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9551569229056067 / 5000000000000000 : ℝ) ≤ - (6472675457385953459261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4775562467371067 / 10000000000000000 : ℝ)) (q := - (9551569229056067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9551569229056067 / 20000000000000000 : ℚ)) + (r' := (9551569229056067 / 5000000000000000 : ℚ)) + (U := (-(7390268148614046540739 / 10000000000000000000000 : ℚ))) + (U' := (6472675457385953459261 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (121606824807 / 250000000000 : ℚ)) + (s := (4775562467371067 / 10000000000000000 : ℚ)) + (q := (9551569229056067 / 20000000000000000 : ℚ)) + (U := (-(7390268148614046540739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_3 : Uω (aρ 3) (bρ 3) (121606824807 / 250000000000 : ℝ) ≤ @@ -4022,25 +3570,21 @@ lemma U_458_3 : have hlg : Real.log (4727828258009729 / 10000000000000000 : ℝ) ≤ (-(7491191374781335902451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4727828258009729 / 10000000000000000 : ℝ) = - (4727828258009729 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4727828258009729 / 2500000000000000 : ℚ)) - (U := (6371752231218664097549 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4727828258009729 / 2500000000000000 : ℝ) ≤ - (6371752231218664097549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2363522930342229 / 5000000000000000 : ℝ)) (q := - (4727828258009729 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4727828258009729 / 10000000000000000 : ℚ)) + (r' := (4727828258009729 / 2500000000000000 : ℚ)) + (U := (-(7491191374781335902451 / 10000000000000000000000 : ℚ))) + (U' := (6371752231218664097549 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (121606824807 / 250000000000 : ℚ)) + (s := (2363522930342229 / 5000000000000000 : ℚ)) + (q := (4727828258009729 / 10000000000000000 : ℚ)) + (U := (-(7491191374781335902451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_4 : Uω (aρ 4) (bρ 4) (121606824807 / 250000000000 : ℝ) ≤ @@ -4048,25 +3592,21 @@ lemma U_458_4 : have hlg : Real.log (4648053047121447 / 10000000000000000 : ℝ) ≤ (-(7661366600977939292389 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4648053047121447 / 10000000000000000 : ℝ) = - (4648053047121447 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4648053047121447 / 2500000000000000 : ℚ)) - (U := (6201577005022060707611 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4648053047121447 / 2500000000000000 : ℝ) ≤ - (6201577005022060707611 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2322894809986447 / 5000000000000000 : ℝ)) (q := - (4648053047121447 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4648053047121447 / 10000000000000000 : ℚ)) + (r' := (4648053047121447 / 2500000000000000 : ℚ)) + (U := (-(7661366600977939292389 / 10000000000000000000000 : ℚ))) + (U' := (6201577005022060707611 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (121606824807 / 250000000000 : ℚ)) + (s := (2322894809986447 / 5000000000000000 : ℚ)) + (q := (4648053047121447 / 10000000000000000 : ℚ)) + (U := (-(7661366600977939292389 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_5 : Uω (aρ 5) (bρ 5) (121606824807 / 250000000000 : ℝ) ≤ @@ -4074,25 +3614,21 @@ lemma U_458_5 : have hlg : Real.log (9052486866936173 / 20000000000000000 : ℝ) ≤ (-(7926927611440030024571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9052486866936173 / 20000000000000000 : ℝ) = - (9052486866936173 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9052486866936173 / 5000000000000000 : ℚ)) - (U := (5936015994559969975429 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9052486866936173 / 5000000000000000 : ℝ) ≤ - (5936015994559969975429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4520360312001173 / 10000000000000000 : ℝ)) (q := - (9052486866936173 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9052486866936173 / 20000000000000000 : ℚ)) + (r' := (9052486866936173 / 5000000000000000 : ℚ)) + (U := (-(7926927611440030024571 / 10000000000000000000000 : ℚ))) + (U' := (5936015994559969975429 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (121606824807 / 250000000000 : ℚ)) + (s := (4520360312001173 / 10000000000000000 : ℚ)) + (q := (9052486866936173 / 20000000000000000 : ℚ)) + (U := (-(7926927611440030024571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_6 : Uω (aρ 6) (bρ 6) (121606824807 / 250000000000 : ℝ) ≤ @@ -4100,25 +3636,21 @@ lemma U_458_6 : have hlg : Real.log (8701565422310579 / 20000000000000000 : ℝ) ≤ (-(8322293299607536327821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8701565422310579 / 20000000000000000 : ℝ) = - (8701565422310579 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8701565422310579 / 5000000000000000 : ℚ)) - (U := (5540650306392463672179 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8701565422310579 / 5000000000000000 : ℝ) ≤ - (5540650306392463672179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4336679242515579 / 10000000000000000 : ℝ)) (q := - (8701565422310579 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8701565422310579 / 20000000000000000 : ℚ)) + (r' := (8701565422310579 / 5000000000000000 : ℚ)) + (U := (-(8322293299607536327821 / 10000000000000000000000 : ℚ))) + (U' := (5540650306392463672179 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (121606824807 / 250000000000 : ℚ)) + (s := (4336679242515579 / 10000000000000000 : ℚ)) + (q := (8701565422310579 / 20000000000000000 : ℚ)) + (U := (-(8322293299607536327821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_7 : Uω (aρ 7) (bρ 7) (121606824807 / 250000000000 : ℝ) ≤ @@ -4126,25 +3658,21 @@ lemma U_458_7 : have hlg : Real.log (8219342221977243 / 20000000000000000 : ℝ) ≤ (-(4446210444125925813017 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8219342221977243 / 20000000000000000 : ℝ) = - (8219342221977243 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8219342221977243 / 5000000000000000 : ℚ)) - (U := (2485261358874074186983 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8219342221977243 / 5000000000000000 : ℝ) ≤ - (2485261358874074186983 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4078117422942243 / 10000000000000000 : ℝ)) (q := - (8219342221977243 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8219342221977243 / 20000000000000000 : ℚ)) + (r' := (8219342221977243 / 5000000000000000 : ℚ)) + (U := (-(4446210444125925813017 / 5000000000000000000000 : ℚ))) + (U' := (2485261358874074186983 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (121606824807 / 250000000000 : ℚ)) + (s := (4078117422942243 / 10000000000000000 : ℚ)) + (q := (8219342221977243 / 20000000000000000 : ℚ)) + (U := (-(4446210444125925813017 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_8 : Uω (aρ 8) (bρ 8) (121606824807 / 250000000000 : ℝ) ≤ @@ -4152,25 +3680,21 @@ lemma U_458_8 : have hlg : Real.log (947787383294077 / 2500000000000000 : ℝ) ≤ (-(4849579062306917657777 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (947787383294077 / 2500000000000000 : ℝ) = - (947787383294077 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (947787383294077 / 625000000000000 : ℚ)) - (U := (2081892740693082342223 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (947787383294077 / 625000000000000 : ℝ) ≤ - (2081892740693082342223 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (232788494916101 / 625000000000000 : ℝ)) (q := - (947787383294077 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (947787383294077 / 2500000000000000 : ℚ)) + (r' := (947787383294077 / 625000000000000 : ℚ)) + (U := (-(4849579062306917657777 / 5000000000000000000000 : ℚ))) + (U' := (2081892740693082342223 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (121606824807 / 250000000000 : ℚ)) + (s := (232788494916101 / 625000000000000 : ℚ)) + (q := (947787383294077 / 2500000000000000 : ℚ)) + (U := (-(4849579062306917657777 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_9 : Uω (aρ 9) (bρ 9) (121606824807 / 250000000000 : ℝ) ≤ @@ -4178,25 +3702,21 @@ lemma U_458_9 : have hlg : Real.log (6765693234574483 / 20000000000000000 : ℝ) ≤ (-(10838675429623092885493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6765693234574483 / 20000000000000000 : ℝ) = - (6765693234574483 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6765693234574483 / 5000000000000000 : ℚ)) - (U := (3024268176376907114507 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6765693234574483 / 5000000000000000 : ℝ) ≤ - (3024268176376907114507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3248975715239483 / 10000000000000000 : ℝ)) (q := - (6765693234574483 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6765693234574483 / 20000000000000000 : ℚ)) + (r' := (6765693234574483 / 5000000000000000 : ℚ)) + (U := (-(10838675429623092885493 / 10000000000000000000000 : ℚ))) + (U' := (3024268176376907114507 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (121606824807 / 250000000000 : ℚ)) + (s := (3248975715239483 / 10000000000000000 : ℚ)) + (q := (6765693234574483 / 20000000000000000 : ℚ)) + (U := (-(10838675429623092885493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_10 : Uω (aρ 10) (bρ 10) (121606824807 / 250000000000 : ℝ) ≤ @@ -4204,26 +3724,21 @@ lemma U_458_10 : have hlg : Real.log (1146243271097001 / 4000000000000000 : ℝ) ≤ (-(2499608972782357176879 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1146243271097001 / 4000000000000000 : ℝ) = - (1146243271097001 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1146243271097001 / 1000000000000000 : ℚ)) - (U := (272979748417642823121 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1146243271097001 / 1000000000000000 : ℝ) ≤ - (272979748417642823121 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (520611573929001 / 2000000000000000 : ℝ)) (q := - (1146243271097001 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1146243271097001 / 4000000000000000 : ℚ)) + (r' := (1146243271097001 / 1000000000000000 : ℚ)) + (U := (-(2499608972782357176879 / 2000000000000000000000 : ℚ))) + (U' := (272979748417642823121 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (121606824807 / 250000000000 : ℚ)) + (s := (520611573929001 / 2000000000000000 : ℚ)) + (q := (1146243271097001 / 4000000000000000 : ℚ)) + (U := (-(2499608972782357176879 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_11 : Uω (aρ 11) (bρ 11) (121606824807 / 250000000000 : ℝ) ≤ @@ -4231,26 +3746,21 @@ lemma U_458_11 : have hlg : Real.log (2177172565929523 / 10000000000000000 : ℝ) ≤ (-(1905697556669964850993 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2177172565929523 / 10000000000000000 : ℝ) = - (2177172565929523 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2177172565929523 / 1250000000000000 : ℚ)) - (U := (693604369455035149007 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2177172565929523 / 1250000000000000 : ℝ) ≤ - (693604369455035149007 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (822331636112023 / 5000000000000000 : ℝ)) (q := - (2177172565929523 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2177172565929523 / 10000000000000000 : ℚ)) + (r' := (2177172565929523 / 1250000000000000 : ℚ)) + (U := (-(1905697556669964850993 / 1250000000000000000000 : ℚ))) + (U' := (693604369455035149007 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (121606824807 / 250000000000 : ℚ)) + (s := (822331636112023 / 5000000000000000 : ℚ)) + (q := (2177172565929523 / 10000000000000000 : ℚ)) + (U := (-(1905697556669964850993 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_458_12 : Uω (aρ 12) (bρ 12) (121606824807 / 250000000000 : ℝ) ≤ @@ -4367,25 +3877,21 @@ lemma U_459_1 : have hlg : Real.log (2413114136977589 / 5000000000000000 : ℝ) ≤ (-(455324890955604488009 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2413114136977589 / 5000000000000000 : ℝ) = - (2413114136977589 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2413114136977589 / 1250000000000000 : ℚ)) - (U := (411109084419395511991 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2413114136977589 / 1250000000000000 : ℝ) ≤ - (411109084419395511991 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1206548694046339 / 2500000000000000 : ℝ)) (q := - (2413114136977589 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2413114136977589 / 5000000000000000 : ℚ)) + (r' := (2413114136977589 / 1250000000000000 : ℚ)) + (U := (-(455324890955604488009 / 625000000000000000000 : ℚ))) + (U' := (411109084419395511991 / 625000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (1206548694046339 / 2500000000000000 : ℚ)) + (q := (2413114136977589 / 5000000000000000 : ℚ)) + (U := (-(455324890955604488009 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_2 : Uω (aρ 2) (bρ 2) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4393,25 +3899,21 @@ lemma U_459_2 : have hlg : Real.log (4802271837324207 / 10000000000000000 : ℝ) ≤ (-(7334959870886187479617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4802271837324207 / 10000000000000000 : ℝ) = - (4802271837324207 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4802271837324207 / 2500000000000000 : ℚ)) - (U := (6527983735113812520383 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4802271837324207 / 2500000000000000 : ℝ) ≤ - (6527983735113812520383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2401025457716707 / 5000000000000000 : ℝ)) (q := - (4802271837324207 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4802271837324207 / 10000000000000000 : ℚ)) + (r' := (4802271837324207 / 2500000000000000 : ℚ)) + (U := (-(7334959870886187479617 / 10000000000000000000000 : ℚ))) + (U' := (6527983735113812520383 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (2401025457716707 / 5000000000000000 : ℚ)) + (q := (4802271837324207 / 10000000000000000 : ℚ)) + (U := (-(7334959870886187479617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_3 : Uω (aρ 3) (bρ 3) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4419,25 +3921,21 @@ lemma U_459_3 : have hlg : Real.log (1901727445976551 / 4000000000000000 : ℝ) ≤ (-(3717658526951898766839 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1901727445976551 / 4000000000000000 : ℝ) = - (1901727445976551 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1901727445976551 / 1000000000000000 : ℚ)) - (U := (3213813276048101233161 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1901727445976551 / 1000000000000000 : ℝ) ≤ - (3213813276048101233161 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (950708115403551 / 2000000000000000 : ℝ)) (q := - (1901727445976551 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1901727445976551 / 4000000000000000 : ℚ)) + (r' := (1901727445976551 / 1000000000000000 : ℚ)) + (U := (-(3717658526951898766839 / 5000000000000000000000 : ℚ))) + (U' := (3213813276048101233161 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (950708115403551 / 2000000000000000 : ℚ)) + (q := (1901727445976551 / 4000000000000000 : ℚ)) + (U := (-(3717658526951898766839 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_4 : Uω (aρ 4) (bρ 4) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4445,25 +3943,21 @@ lemma U_459_4 : have hlg : Real.log (9349103750871751 / 20000000000000000 : ℝ) ≤ (-(1520903579699353452909 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9349103750871751 / 20000000000000000 : ℝ) = - (9349103750871751 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9349103750871751 / 5000000000000000 : ℚ)) - (U := (1251685141500646547091 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9349103750871751 / 5000000000000000 : ℝ) ≤ - (1251685141500646547091 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4672301279071751 / 10000000000000000 : ℝ)) (q := - (9349103750871751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9349103750871751 / 20000000000000000 : ℚ)) + (r' := (9349103750871751 / 5000000000000000 : ℚ)) + (U := (-(1520903579699353452909 / 2000000000000000000000 : ℚ))) + (U' := (1251685141500646547091 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (4672301279071751 / 10000000000000000 : ℚ)) + (q := (9349103750871751 / 20000000000000000 : ℚ)) + (U := (-(1520903579699353452909 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_5 : Uω (aρ 5) (bρ 5) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4471,25 +3965,21 @@ lemma U_459_5 : have hlg : Real.log (182110548028867 / 400000000000000 : ℝ) ≤ (-(1573701274312190521749 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (182110548028867 / 400000000000000 : ℝ) = - (182110548028867 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (182110548028867 / 100000000000000 : ℚ)) - (U := (1198887446887809478251 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (182110548028867 / 100000000000000 : ℝ) ≤ - (1198887446887809478251 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90938296979567 / 200000000000000 : ℝ)) (q := - (182110548028867 / 400000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (182110548028867 / 400000000000000 : ℚ)) + (r' := (182110548028867 / 100000000000000 : ℚ)) + (U := (-(1573701274312190521749 / 2000000000000000000000 : ℚ))) + (U' := (1198887446887809478251 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (90938296979567 / 200000000000000 : ℚ)) + (q := (182110548028867 / 400000000000000 : ℚ)) + (U := (-(1573701274312190521749 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_6 : Uω (aρ 6) (bρ 6) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4497,25 +3987,21 @@ lemma U_459_6 : have hlg : Real.log (8754708640363831 / 20000000000000000 : ℝ) ≤ (-(4130702935387415911649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8754708640363831 / 20000000000000000 : ℝ) = - (8754708640363831 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8754708640363831 / 5000000000000000 : ℚ)) - (U := (2800768867612584088351 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8754708640363831 / 5000000000000000 : ℝ) ≤ - (2800768867612584088351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4363336463038831 / 10000000000000000 : ℝ)) (q := - (8754708640363831 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8754708640363831 / 20000000000000000 : ℚ)) + (r' := (8754708640363831 / 5000000000000000 : ℚ)) + (U := (-(4130702935387415911649 / 5000000000000000000000 : ℚ))) + (U' := (2800768867612584088351 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (4363336463038831 / 10000000000000000 : ℚ)) + (q := (8754708640363831 / 20000000000000000 : ℚ)) + (U := (-(4130702935387415911649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_7 : Uω (aρ 7) (bρ 7) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4523,25 +4009,21 @@ lemma U_459_7 : have hlg : Real.log (2068180353308557 / 5000000000000000 : ℝ) ≤ (-(4413843738031198771433 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2068180353308557 / 5000000000000000 : ℝ) = - (2068180353308557 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2068180353308557 / 1250000000000000 : ℚ)) - (U := (2517628064968801228567 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2068180353308557 / 1250000000000000 : ℝ) ≤ - (2517628064968801228567 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1026252654167307 / 2500000000000000 : ℝ)) (q := - (2068180353308557 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2068180353308557 / 5000000000000000 : ℚ)) + (r' := (2068180353308557 / 1250000000000000 : ℚ)) + (U := (-(4413843738031198771433 / 5000000000000000000000 : ℚ))) + (U' := (2517628064968801228567 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (1026252654167307 / 2500000000000000 : ℚ)) + (q := (2068180353308557 / 5000000000000000 : ℚ)) + (U := (-(4413843738031198771433 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_8 : Uω (aρ 8) (bρ 8) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4549,25 +4031,21 @@ lemma U_459_8 : have hlg : Real.log (3818105256282167 / 10000000000000000 : ℝ) ≤ (-(1203538498895373722573 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3818105256282167 / 10000000000000000 : ℝ) = - (3818105256282167 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3818105256282167 / 2500000000000000 : ℚ)) - (U := (529329451854626277427 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3818105256282167 / 2500000000000000 : ℝ) ≤ - (529329451854626277427 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1876020683669667 / 5000000000000000 : ℝ)) (q := - (3818105256282167 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3818105256282167 / 10000000000000000 : ℚ)) + (r' := (3818105256282167 / 2500000000000000 : ℚ)) + (U := (-(1203538498895373722573 / 1250000000000000000000 : ℚ))) + (U' := (529329451854626277427 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (1876020683669667 / 5000000000000000 : ℚ)) + (q := (3818105256282167 / 10000000000000000 : ℚ)) + (U := (-(1203538498895373722573 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_9 : Uω (aρ 9) (bρ 9) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4575,25 +4053,21 @@ lemma U_459_9 : have hlg : Real.log (3410414762510657 / 10000000000000000 : ℝ) ≤ (-(5378755886702058761049 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3410414762510657 / 10000000000000000 : ℝ) = - (3410414762510657 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3410414762510657 / 2500000000000000 : ℚ)) - (U := (1552715916297941238951 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3410414762510657 / 2500000000000000 : ℝ) ≤ - (1552715916297941238951 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1638813004078157 / 5000000000000000 : ℝ)) (q := - (3410414762510657 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3410414762510657 / 10000000000000000 : ℚ)) + (r' := (3410414762510657 / 2500000000000000 : ℚ)) + (U := (-(5378755886702058761049 / 5000000000000000000000 : ℚ))) + (U' := (1552715916297941238951 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (1638813004078157 / 5000000000000000 : ℚ)) + (q := (3410414762510657 / 10000000000000000 : ℚ)) + (U := (-(5378755886702058761049 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_10 : Uω (aρ 10) (bρ 10) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4601,26 +4075,21 @@ lemma U_459_10 : have hlg : Real.log (2894736050691567 / 10000000000000000 : ℝ) ≤ (-(619845579902810326079 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2894736050691567 / 10000000000000000 : ℝ) = - (2894736050691567 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2894736050691567 / 2500000000000000 : ℚ)) - (U := (73301600397189673921 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2894736050691567 / 2500000000000000 : ℝ) ≤ - (73301600397189673921 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1317413809006567 / 5000000000000000 : ℝ)) (q := - (2894736050691567 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2894736050691567 / 10000000000000000 : ℚ)) + (r' := (2894736050691567 / 2500000000000000 : ℚ)) + (U := (-(619845579902810326079 / 500000000000000000000 : ℚ))) + (U' := (73301600397189673921 / 500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (1317413809006567 / 5000000000000000 : ℚ)) + (q := (2894736050691567 / 10000000000000000 : ℚ)) + (U := (-(619845579902810326079 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_11 : Uω (aρ 11) (bρ 11) (489075898981 / 1000000000000 : ℝ) ≤ @@ -4628,25 +4097,21 @@ lemma U_459_11 : have hlg : Real.log (553014022654023 / 2500000000000000 : ℝ) ≤ (-(1885828314317794521397 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (553014022654023 / 2500000000000000 : ℝ) = - (553014022654023 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (553014022654023 / 312500000000000 : ℚ)) - (U := (713473611807205478603 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (553014022654023 / 312500000000000 : ℝ) ≤ - (713473611807205478603 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (105496520254199 / 625000000000000 : ℝ)) (q := - (553014022654023 / 2500000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (553014022654023 / 2500000000000000 : ℚ)) + (r' := (553014022654023 / 312500000000000 : ℚ)) + (U := (-(1885828314317794521397 / 1250000000000000000000 : ℚ))) + (U' := (713473611807205478603 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (489075898981 / 1000000000000 : ℚ)) + (s := (105496520254199 / 625000000000000 : ℚ)) + (q := (553014022654023 / 2500000000000000 : ℚ)) + (U := (-(1885828314317794521397 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_459_12 : Uω (aρ 12) (bρ 12) (489075898981 / 1000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U38.lean b/LeanPool/Zeta5Irrational/Table/U38.lean index 579e81df8c..2da0345ed0 100644 --- a/LeanPool/Zeta5Irrational/Table/U38.lean +++ b/LeanPool/Zeta5Irrational/Table/U38.lean @@ -24,25 +24,21 @@ lemma U_460_1 : have hlg : Real.log (9705428908632907 / 20000000000000000 : ℝ) ≤ (-(3615234313927837667861 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9705428908632907 / 20000000000000000 : ℝ) = - (9705428908632907 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9705428908632907 / 5000000000000000 : ℚ)) - (U := (3316237489072162332139 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9705428908632907 / 5000000000000000 : ℝ) ≤ - (3316237489072162332139 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4852681139377907 / 10000000000000000 : ℝ)) (q := - (9705428908632907 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9705428908632907 / 20000000000000000 : ℚ)) + (r' := (9705428908632907 / 5000000000000000 : ℚ)) + (U := (-(3615234313927837667861 / 5000000000000000000000 : ℚ))) + (U' := (3316237489072162332139 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (245862249367 / 500000000000 : ℚ)) + (s := (4852681139377907 / 10000000000000000 : ℚ)) + (q := (9705428908632907 / 20000000000000000 : ℚ)) + (U := (-(3615234313927837667861 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_2 : Uω (aρ 2) (bρ 2) (245862249367 / 500000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_460_2 : have hlg : Real.log (4828759046677849 / 10000000000000000 : ℝ) ≤ (-(7279955839745068222781 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4828759046677849 / 10000000000000000 : ℝ) = - (4828759046677849 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4828759046677849 / 2500000000000000 : ℚ)) - (U := (6582987766254931777219 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4828759046677849 / 2500000000000000 : ℝ) ≤ - (6582987766254931777219 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2414269668305349 / 5000000000000000 : ℝ)) (q := - (4828759046677849 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4828759046677849 / 10000000000000000 : ℚ)) + (r' := (4828759046677849 / 2500000000000000 : ℚ)) + (U := (-(7279955839745068222781 / 10000000000000000000000 : ℚ))) + (U' := (6582987766254931777219 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (245862249367 / 500000000000 : ℚ)) + (s := (2414269668305349 / 5000000000000000 : ℚ)) + (q := (4828759046677849 / 10000000000000000 : ℚ)) + (U := (-(7279955839745068222781 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_3 : Uω (aρ 3) (bρ 3) (245862249367 / 500000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_460_3 : have hlg : Real.log (478080892355451 / 1000000000000000 : ℝ) ≤ (-(1475950658839148611197 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (478080892355451 / 1000000000000000 : ℝ) = - (478080892355451 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (478080892355451 / 250000000000000 : ℚ)) - (U := (1296638062360851388803 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (478080892355451 / 250000000000000 : ℝ) ≤ - (1296638062360851388803 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239001759835701 / 500000000000000 : ℝ)) (q := - (478080892355451 / 1000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (478080892355451 / 1000000000000000 : ℚ)) + (r' := (478080892355451 / 250000000000000 : ℚ)) + (U := (-(1475950658839148611197 / 2000000000000000000000 : ℚ))) + (U' := (1296638062360851388803 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (245862249367 / 500000000000 : ℚ)) + (s := (239001759835701 / 500000000000000 : ℚ)) + (q := (478080892355451 / 1000000000000000 : ℚ)) + (U := (-(1475950658839148611197 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_4 : Uω (aρ 4) (bρ 4) (245862249367 / 500000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_460_4 : have hlg : Real.log (9402101118065153 / 20000000000000000 : ℝ) ≤ (-(3773995427686548841721 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9402101118065153 / 20000000000000000 : ℝ) = - (9402101118065153 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9402101118065153 / 5000000000000000 : ℚ)) - (U := (3157476375313451158279 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9402101118065153 / 5000000000000000 : ℝ) ≤ - (3157476375313451158279 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4698812648735153 / 10000000000000000 : ℝ)) (q := - (9402101118065153 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9402101118065153 / 20000000000000000 : ℚ)) + (r' := (9402101118065153 / 5000000000000000 : ℚ)) + (U := (-(3773995427686548841721 / 5000000000000000000000 : ℚ))) + (U' := (3157476375313451158279 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (245862249367 / 500000000000 : ℚ)) + (s := (4698812648735153 / 10000000000000000 : ℚ)) + (q := (9402101118065153 / 20000000000000000 : ℚ)) + (U := (-(3773995427686548841721 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_5 : Uω (aρ 5) (bρ 5) (245862249367 / 500000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_460_5 : have hlg : Real.log (4579283570534183 / 10000000000000000 : ℝ) ≤ (-(1249668051570219817 / 1600000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4579283570534183 / 10000000000000000 : ℝ) = - (4579283570534183 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4579283570534183 / 2500000000000000 : ℚ)) - (U := (968402925389780183 / 1600000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4579283570534183 / 2500000000000000 : ℝ) ≤ - (968402925389780183 / 1600000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2286734295536683 / 5000000000000000 : ℝ)) (q := - (4579283570534183 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4579283570534183 / 10000000000000000 : ℚ)) + (r' := (4579283570534183 / 2500000000000000 : ℚ)) + (U := (-(1249668051570219817 / 1600000000000000000 : ℚ))) + (U' := (968402925389780183 / 1600000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (245862249367 / 500000000000 : ℚ)) + (s := (2286734295536683 / 5000000000000000 : ℚ)) + (q := (4579283570534183 / 10000000000000000 : ℚ)) + (U := (-(1249668051570219817 / 1600000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_6 : Uω (aρ 6) (bρ 6) (245862249367 / 500000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_460_6 : have hlg : Real.log (4403924892835409 / 10000000000000000 : ℝ) ≤ (-(512555580040854648039 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4403924892835409 / 10000000000000000 : ℝ) = - (4403924892835409 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4403924892835409 / 2500000000000000 : ℚ)) - (U := (353878395334145351961 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4403924892835409 / 2500000000000000 : ℝ) ≤ - (353878395334145351961 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2194995805407909 / 5000000000000000 : ℝ)) (q := - (4403924892835409 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4403924892835409 / 10000000000000000 : ℚ)) + (r' := (4403924892835409 / 2500000000000000 : ℚ)) + (U := (-(512555580040854648039 / 625000000000000000000 : ℚ))) + (U' := (353878395334145351961 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (245862249367 / 500000000000 : ℚ)) + (s := (2194995805407909 / 5000000000000000 : ℚ)) + (q := (4403924892835409 / 10000000000000000 : ℚ)) + (U := (-(512555580040854648039 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_7 : Uω (aρ 7) (bρ 7) (245862249367 / 500000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_460_7 : have hlg : Real.log (4163047672003167 / 10000000000000000 : ℝ) ≤ (-(4381688364844639488627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4163047672003167 / 10000000000000000 : ℝ) = - (4163047672003167 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4163047672003167 / 2500000000000000 : ℚ)) - (U := (2549783438155360511373 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4163047672003167 / 2500000000000000 : ℝ) ≤ - (2549783438155360511373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2065949274955667 / 5000000000000000 : ℝ)) (q := - (4163047672003167 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4163047672003167 / 10000000000000000 : ℚ)) + (r' := (4163047672003167 / 2500000000000000 : ℚ)) + (U := (-(4381688364844639488627 / 5000000000000000000000 : ℚ))) + (U' := (2549783438155360511373 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (245862249367 / 500000000000 : ℚ)) + (s := (2065949274955667 / 5000000000000000 : ℚ)) + (q := (4163047672003167 / 10000000000000000 : ℚ)) + (U := (-(4381688364844639488627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_8 : Uω (aρ 8) (bρ 8) (245862249367 / 500000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_460_8 : have hlg : Real.log (3845054279069901 / 10000000000000000 : ℝ) ≤ (-(9557973728229765291131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3845054279069901 / 10000000000000000 : ℝ) = - (3845054279069901 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3845054279069901 / 2500000000000000 : ℚ)) - (U := (4304969877770234708869 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3845054279069901 / 2500000000000000 : ℝ) ≤ - (4304969877770234708869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1889726707692401 / 5000000000000000 : ℝ)) (q := - (3845054279069901 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3845054279069901 / 10000000000000000 : ℚ)) + (r' := (3845054279069901 / 2500000000000000 : ℚ)) + (U := (-(9557973728229765291131 / 10000000000000000000000 : ℚ))) + (U' := (4304969877770234708869 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (245862249367 / 500000000000 : ℚ)) + (s := (1889726707692401 / 5000000000000000 : ℚ)) + (q := (3845054279069901 / 10000000000000000 : ℚ)) + (U := (-(9557973728229765291131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_9 : Uω (aρ 9) (bρ 9) (245862249367 / 500000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_460_9 : have hlg : Real.log (3437964861470009 / 10000000000000000 : ℝ) ≤ (-(1334631757746133575117 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3437964861470009 / 10000000000000000 : ℝ) = - (3437964861470009 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3437964861470009 / 2500000000000000 : ℚ)) - (U := (398236193003866424883 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3437964861470009 / 2500000000000000 : ℝ) ≤ - (398236193003866424883 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1653120104272509 / 5000000000000000 : ℝ)) (q := - (3437964861470009 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3437964861470009 / 10000000000000000 : ℚ)) + (r' := (3437964861470009 / 2500000000000000 : ℚ)) + (U := (-(1334631757746133575117 / 1250000000000000000000 : ℚ))) + (U' := (398236193003866424883 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (245862249367 / 500000000000 : ℚ)) + (s := (1653120104272509 / 5000000000000000 : ℚ)) + (q := (3437964861470009 / 10000000000000000 : ℚ)) + (U := (-(1334631757746133575117 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_10 : Uω (aρ 10) (bρ 10) (245862249367 / 500000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_460_10 : have hlg : Real.log (1461903103366413 / 5000000000000000 : ℝ) ≤ (-(12296988295501843449263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1461903103366413 / 5000000000000000 : ℝ) = - (1461903103366413 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1461903103366413 / 1250000000000000 : ℚ)) - (U := (1565955310498156550737 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1461903103366413 / 1250000000000000 : ℝ) ≤ - (1565955310498156550737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (666620483141413 / 2500000000000000 : ℝ)) (q := - (1461903103366413 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1461903103366413 / 5000000000000000 : ℚ)) + (r' := (1461903103366413 / 1250000000000000 : ℚ)) + (U := (-(12296988295501843449263 / 10000000000000000000000 : ℚ))) + (U' := (1565955310498156550737 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (245862249367 / 500000000000 : ℚ)) + (s := (666620483141413 / 2500000000000000 : ℚ)) + (q := (1461903103366413 / 5000000000000000 : ℚ)) + (U := (-(12296988295501843449263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_11 : Uω (aρ 11) (bρ 11) (245862249367 / 500000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_460_11 : have hlg : Real.log (4493202270495279 / 20000000000000000 : ℝ) ≤ (-(14931666246709073635179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4493202270495279 / 20000000000000000 : ℝ) = - (4493202270495279 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4493202270495279 / 2500000000000000 : ℚ)) - (U := (5862749162290926364821 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4493202270495279 / 2500000000000000 : ℝ) ≤ - (5862749162290926364821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1730548415800279 / 10000000000000000 : ℝ)) (q := - (4493202270495279 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4493202270495279 / 20000000000000000 : ℚ)) + (r' := (4493202270495279 / 2500000000000000 : ℚ)) + (U := (-(14931666246709073635179 / 10000000000000000000000 : ℚ))) + (U' := (5862749162290926364821 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (245862249367 / 500000000000 : ℚ)) + (s := (1730548415800279 / 10000000000000000 : ℚ)) + (q := (4493202270495279 / 20000000000000000 : ℚ)) + (U := (-(14931666246709073635179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_460_12 : Uω (aρ 12) (bρ 12) (245862249367 / 500000000000 : ℝ) ≤ @@ -420,25 +374,21 @@ lemma U_461_1 : have hlg : Real.log (9758401265385517 / 20000000000000000 : ℝ) ≤ (-(1435207381605281826913 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9758401265385517 / 20000000000000000 : ℝ) = - (9758401265385517 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9758401265385517 / 5000000000000000 : ℚ)) - (U := (1337381339594718173087 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9758401265385517 / 5000000000000000 : ℝ) ≤ - (1337381339594718173087 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4879167498600517 / 10000000000000000 : ℝ)) (q := - (9758401265385517 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9758401265385517 / 20000000000000000 : ℚ)) + (r' := (9758401265385517 / 5000000000000000 : ℚ)) + (U := (-(1435207381605281826913 / 2000000000000000000000 : ℚ))) + (U' := (1337381339594718173087 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (4879167498600517 / 10000000000000000 : ℚ)) + (q := (9758401265385517 / 20000000000000000 : ℚ)) + (U := (-(1435207381605281826913 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_2 : Uω (aρ 2) (bρ 2) (494373098487 / 1000000000000 : ℝ) ≤ @@ -446,25 +396,21 @@ lemma U_461_2 : have hlg : Real.log (9710492485617961 / 20000000000000000 : ℝ) ≤ (-(3612626362959643324813 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9710492485617961 / 20000000000000000 : ℝ) = - (9710492485617961 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9710492485617961 / 5000000000000000 : ℚ)) - (U := (3318845440040356675187 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9710492485617961 / 5000000000000000 : ℝ) ≤ - (3318845440040356675187 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4855027731342961 / 10000000000000000 : ℝ)) (q := - (9710492485617961 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9710492485617961 / 20000000000000000 : ℚ)) + (r' := (9710492485617961 / 5000000000000000 : ℚ)) + (U := (-(3612626362959643324813 / 5000000000000000000000 : ℚ))) + (U' := (3318845440040356675187 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (4855027731342961 / 10000000000000000 : ℚ)) + (q := (9710492485617961 / 20000000000000000 : ℚ)) + (U := (-(3612626362959643324813 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_3 : Uω (aρ 3) (bρ 3) (494373098487 / 1000000000000 : ℝ) ≤ @@ -472,25 +418,21 @@ lemma U_461_3 : have hlg : Real.log (600912398081019 / 1250000000000000 : ℝ) ≤ (-(732449666129835809591 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (600912398081019 / 1250000000000000 : ℝ) = - (600912398081019 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (600912398081019 / 312500000000000 : ℚ)) - (U := (653844694470164190409 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (600912398081019 / 312500000000000 : ℝ) ≤ - (653844694470164190409 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (600816215171413 / 1250000000000000 : ℝ)) (q := - (600912398081019 / 1250000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (600912398081019 / 1250000000000000 : ℚ)) + (r' := (600912398081019 / 312500000000000 : ℚ)) + (U := (-(732449666129835809591 / 1000000000000000000000 : ℚ))) + (U' := (653844694470164190409 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (600816215171413 / 1250000000000000 : ℚ)) + (q := (600912398081019 / 1250000000000000 : ℚ)) + (U := (-(732449666129835809591 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_4 : Uω (aρ 4) (bρ 4) (494373098487 / 1000000000000 : ℝ) ≤ @@ -498,25 +440,21 @@ lemma U_461_4 : have hlg : Real.log (9455098200694723 / 20000000000000000 : ℝ) ≤ (-(7491781848650053319527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9455098200694723 / 20000000000000000 : ℝ) = - (9455098200694723 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9455098200694723 / 5000000000000000 : ℚ)) - (U := (6371161757349946680473 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9455098200694723 / 5000000000000000 : ℝ) ≤ - (6371161757349946680473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4725323733834723 / 10000000000000000 : ℝ)) (q := - (9455098200694723 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9455098200694723 / 20000000000000000 : ℚ)) + (r' := (9455098200694723 / 5000000000000000 : ℚ)) + (U := (-(7491781848650053319527 / 10000000000000000000000 : ℚ))) + (U' := (6371161757349946680473 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (4725323733834723 / 10000000000000000 : ℚ)) + (q := (9455098200694723 / 20000000000000000 : ℚ)) + (U := (-(7491781848650053319527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_5 : Uω (aρ 5) (bρ 5) (494373098487 / 1000000000000 : ℝ) ≤ @@ -524,25 +462,21 @@ lemma U_461_5 : have hlg : Real.log (4605803049788327 / 10000000000000000 : ℝ) ≤ (-(387634025740016904203 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4605803049788327 / 10000000000000000 : ℝ) = - (4605803049788327 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4605803049788327 / 2500000000000000 : ℚ)) - (U := (305513154559983095797 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4605803049788327 / 2500000000000000 : ℝ) ≤ - (305513154559983095797 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2300010776025827 / 5000000000000000 : ℝ)) (q := - (4605803049788327 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4605803049788327 / 10000000000000000 : ℚ)) + (r' := (4605803049788327 / 2500000000000000 : ℚ)) + (U := (-(387634025740016904203 / 500000000000000000000 : ℚ))) + (U' := (305513154559983095797 / 500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (2300010776025827 / 5000000000000000 : ℚ)) + (q := (4605803049788327 / 10000000000000000 : ℚ)) + (U := (-(387634025740016904203 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_6 : Uω (aρ 6) (bρ 6) (494373098487 / 1000000000000 : ℝ) ≤ @@ -550,25 +484,21 @@ lemma U_461_6 : have hlg : Real.log (8860988895759591 / 20000000000000000 : ℝ) ≤ (-(814073901128552071001 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8860988895759591 / 20000000000000000 : ℝ) = - (8860988895759591 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8860988895759591 / 5000000000000000 : ℚ)) - (U := (572220459471447928999 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8860988895759591 / 5000000000000000 : ℝ) ≤ - (572220459471447928999 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4416644723374591 / 10000000000000000 : ℝ)) (q := - (8860988895759591 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8860988895759591 / 20000000000000000 : ℚ)) + (r' := (8860988895759591 / 5000000000000000 : ℚ)) + (U := (-(814073901128552071001 / 1000000000000000000000 : ℚ))) + (U' := (572220459471447928999 / 1000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (4416644723374591 / 10000000000000000 : ℚ)) + (q := (8860988895759591 / 20000000000000000 : ℚ)) + (U := (-(814073901128552071001 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_7 : Uω (aρ 7) (bρ 7) (494373098487 / 1000000000000 : ℝ) ≤ @@ -576,25 +506,21 @@ lemma U_461_7 : have hlg : Real.log (335178564653041 / 800000000000000 : ℝ) ≤ (-(8699483085173201573619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (335178564653041 / 800000000000000 : ℝ) = - (335178564653041 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (335178564653041 / 200000000000000 : ℚ)) - (U := (5163460520826798426381 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (335178564653041 / 200000000000000 : ℝ) ≤ - (5163460520826798426381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (166351252988041 / 400000000000000 : ℝ)) (q := - (335178564653041 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (335178564653041 / 800000000000000 : ℚ)) + (r' := (335178564653041 / 200000000000000 : ℚ)) + (U := (-(8699483085173201573619 / 10000000000000000000000 : ℚ))) + (U' := (5163460520826798426381 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (166351252988041 / 400000000000000 : ℚ)) + (q := (335178564653041 / 800000000000000 : ℚ)) + (U := (-(8699483085173201573619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_8 : Uω (aρ 8) (bρ 8) (494373098487 / 1000000000000 : ℝ) ≤ @@ -602,25 +528,21 @@ lemma U_461_8 : have hlg : Real.log (7743993492561403 / 20000000000000000 : ℝ) ≤ (-(9488147633802443083583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7743993492561403 / 20000000000000000 : ℝ) = - (7743993492561403 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7743993492561403 / 5000000000000000 : ℚ)) - (U := (4374795972197556916417 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7743993492561403 / 5000000000000000 : ℝ) ≤ - (4374795972197556916417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3806852352276403 / 10000000000000000 : ℝ)) (q := - (7743993492561403 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7743993492561403 / 20000000000000000 : ℚ)) + (r' := (7743993492561403 / 5000000000000000 : ℚ)) + (U := (-(9488147633802443083583 / 10000000000000000000000 : ℚ))) + (U' := (4374795972197556916417 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (3806852352276403 / 10000000000000000 : ℚ)) + (q := (7743993492561403 / 20000000000000000 : ℚ)) + (U := (-(9488147633802443083583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_9 : Uω (aρ 9) (bρ 9) (494373098487 / 1000000000000 : ℝ) ≤ @@ -628,25 +550,21 @@ lemma U_461_9 : have hlg : Real.log (6930994757399517 / 20000000000000000 : ℝ) ≤ (-(10597289264973965425953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6930994757399517 / 20000000000000000 : ℝ) = - (6930994757399517 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6930994757399517 / 5000000000000000 : ℚ)) - (U := (3265654341026034574047 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6930994757399517 / 5000000000000000 : ℝ) ≤ - (3265654341026034574047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3334819245474517 / 10000000000000000 : ℝ)) (q := - (6930994757399517 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6930994757399517 / 20000000000000000 : ℚ)) + (r' := (6930994757399517 / 5000000000000000 : ℚ)) + (U := (-(10597289264973965425953 / 10000000000000000000000 : ℚ))) + (U' := (3265654341026034574047 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (3334819245474517 / 10000000000000000 : ℚ)) + (q := (6930994757399517 / 20000000000000000 : ℚ)) + (U := (-(10597289264973965425953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_10 : Uω (aρ 10) (bρ 10) (494373098487 / 1000000000000 : ℝ) ≤ @@ -654,26 +572,21 @@ lemma U_461_10 : have hlg : Real.log (1476410338670919 / 5000000000000000 : ℝ) ≤ (-(609912108571579113853 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1476410338670919 / 5000000000000000 : ℝ) = - (1476410338670919 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1476410338670919 / 1250000000000000 : ℚ)) - (U := (83235071728420886147 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1476410338670919 / 1250000000000000 : ℝ) ≤ - (83235071728420886147 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (674506219063419 / 2500000000000000 : ℝ)) (q := - (1476410338670919 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1476410338670919 / 5000000000000000 : ℚ)) + (r' := (1476410338670919 / 1250000000000000 : ℚ)) + (U := (-(609912108571579113853 / 500000000000000000000 : ℚ))) + (U' := (83235071728420886147 / 500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (674506219063419 / 2500000000000000 : ℚ)) + (q := (1476410338670919 / 5000000000000000 : ℚ)) + (U := (-(609912108571579113853 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_11 : Uω (aρ 11) (bρ 11) (494373098487 / 1000000000000 : ℝ) ≤ @@ -681,26 +594,21 @@ lemma U_461_11 : have hlg : Real.log (4561664214211997 / 20000000000000000 : ℝ) ≤ (-(1847555945715342408171 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4561664214211997 / 20000000000000000 : ℝ) = - (4561664214211997 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4561664214211997 / 2500000000000000 : ℚ)) - (U := (751745980409657591829 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4561664214211997 / 2500000000000000 : ℝ) ≤ - (751745980409657591829 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1772524361986997 / 10000000000000000 : ℝ)) (q := - (4561664214211997 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4561664214211997 / 20000000000000000 : ℚ)) + (r' := (4561664214211997 / 2500000000000000 : ℚ)) + (U := (-(1847555945715342408171 / 1250000000000000000000 : ℚ))) + (U' := (751745980409657591829 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (494373098487 / 1000000000000 : ℚ)) + (s := (1772524361986997 / 10000000000000000 : ℚ)) + (q := (4561664214211997 / 20000000000000000 : ℚ)) + (U := (-(1847555945715342408171 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_461_12 : Uω (aρ 12) (bρ 12) (494373098487 / 1000000000000 : ℝ) ≤ @@ -815,25 +723,21 @@ lemma U_462_1 : have hlg : Real.log (1226421702279061 / 2500000000000000 : ℝ) ≤ (-(3560949935065535102229 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1226421702279061 / 2500000000000000 : ℝ) = - (1226421702279061 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1226421702279061 / 625000000000000 : ℚ)) - (U := (3370521867934464897771 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1226421702279061 / 625000000000000 : ℝ) ≤ - (3370521867934464897771 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (306603365869843 / 625000000000000 : ℝ)) (q := - (1226421702279061 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1226421702279061 / 2500000000000000 : ℚ)) + (r' := (1226421702279061 / 625000000000000 : ℚ)) + (U := (-(3560949935065535102229 / 5000000000000000000000 : ℚ))) + (U' := (3370521867934464897771 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1553192807 / 3125000000 : ℚ)) + (s := (306603365869843 / 625000000000000 : ℚ)) + (q := (1226421702279061 / 2500000000000000 : ℚ)) + (U := (-(3560949935065535102229 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_2 : Uω (aρ 2) (bρ 2) (1553192807 / 3125000000 : ℝ) ≤ @@ -841,25 +745,21 @@ lemma U_462_2 : have hlg : Real.log (9763466851865697 / 20000000000000000 : ℝ) ≤ (-(3585423627245885930571 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9763466851865697 / 20000000000000000 : ℝ) = - (9763466851865697 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9763466851865697 / 5000000000000000 : ℚ)) - (U := (3346048175754114069429 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9763466851865697 / 5000000000000000 : ℝ) ≤ - (3346048175754114069429 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4881516100060697 / 10000000000000000 : ℝ)) (q := - (9763466851865697 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9763466851865697 / 20000000000000000 : ℚ)) + (r' := (9763466851865697 / 5000000000000000 : ℚ)) + (U := (-(3585423627245885930571 / 5000000000000000000000 : ℚ))) + (U' := (3346048175754114069429 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1553192807 / 3125000000 : ℚ)) + (s := (4881516100060697 / 10000000000000000 : ℚ)) + (q := (9763466851865697 / 20000000000000000 : ℚ)) + (U := (-(3585423627245885930571 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_3 : Uω (aρ 3) (bρ 3) (1553192807 / 3125000000 : ℝ) ≤ @@ -867,25 +767,21 @@ lemma U_462_3 : have hlg : Real.log (9667578798007611 / 20000000000000000 : ℝ) ≤ (-(1817385944381576922393 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9667578798007611 / 20000000000000000 : ℝ) = - (9667578798007611 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9667578798007611 / 5000000000000000 : ℚ)) - (U := (1648349957118423077607 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9667578798007611 / 5000000000000000 : ℝ) ≤ - (1648349957118423077607 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4833024152552611 / 10000000000000000 : ℝ)) (q := - (9667578798007611 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9667578798007611 / 20000000000000000 : ℚ)) + (r' := (9667578798007611 / 5000000000000000 : ℚ)) + (U := (-(1817385944381576922393 / 2500000000000000000000 : ℚ))) + (U' := (1648349957118423077607 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1553192807 / 3125000000 : ℚ)) + (s := (4833024152552611 / 10000000000000000 : ℚ)) + (q := (9667578798007611 / 20000000000000000 : ℚ)) + (U := (-(1817385944381576922393 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_4 : Uω (aρ 4) (bρ 4) (1553192807 / 3125000000 : ℝ) ≤ @@ -893,25 +789,21 @@ lemma U_462_4 : have hlg : Real.log (9508095003523313 / 20000000000000000 : ℝ) ≤ (-(1487177463258952670079 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9508095003523313 / 20000000000000000 : ℝ) = - (9508095003523313 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9508095003523313 / 5000000000000000 : ℚ)) - (U := (1285411257941047329921 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9508095003523313 / 5000000000000000 : ℝ) ≤ - (1285411257941047329921 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4751834539133313 / 10000000000000000 : ℝ)) (q := - (9508095003523313 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9508095003523313 / 20000000000000000 : ℚ)) + (r' := (9508095003523313 / 5000000000000000 : ℚ)) + (U := (-(1487177463258952670079 / 2000000000000000000000 : ℚ))) + (U' := (1285411257941047329921 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1553192807 / 3125000000 : ℚ)) + (s := (4751834539133313 / 10000000000000000 : ℚ)) + (q := (9508095003523313 / 20000000000000000 : ℚ)) + (U := (-(1487177463258952670079 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_5 : Uω (aρ 5) (bρ 5) (1553192807 / 3125000000 : ℝ) ≤ @@ -919,25 +811,21 @@ lemma U_462_5 : have hlg : Real.log (1852928858083447 / 4000000000000000 : ℝ) ≤ (-(7695268068651840452393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1852928858083447 / 4000000000000000 : ℝ) = - (1852928858083447 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1852928858083447 / 1000000000000000 : ℚ)) - (U := (6167675537348159547607 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1852928858083447 / 1000000000000000 : ℝ) ≤ - (6167675537348159547607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (925314749072447 / 2000000000000000 : ℝ)) (q := - (1852928858083447 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1852928858083447 / 4000000000000000 : ℚ)) + (r' := (1852928858083447 / 1000000000000000 : ℚ)) + (U := (-(7695268068651840452393 / 10000000000000000000000 : ℚ))) + (U' := (6167675537348159547607 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1553192807 / 3125000000 : ℚ)) + (s := (925314749072447 / 2000000000000000 : ℚ)) + (q := (1852928858083447 / 4000000000000000 : ℚ)) + (U := (-(7695268068651840452393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_6 : Uω (aρ 6) (bρ 6) (1553192807 / 3125000000 : ℝ) ≤ @@ -945,25 +833,21 @@ lemma U_462_6 : have hlg : Real.log (2228531501813731 / 5000000000000000 : ℝ) ≤ (-(8080950627273355186921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2228531501813731 / 5000000000000000 : ℝ) = - (2228531501813731 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2228531501813731 / 1250000000000000 : ℚ)) - (U := (5781992978726644813079 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2228531501813731 / 1250000000000000 : ℝ) ≤ - (5781992978726644813079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1110823959334981 / 2500000000000000 : ℝ)) (q := - (2228531501813731 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2228531501813731 / 5000000000000000 : ℚ)) + (r' := (2228531501813731 / 1250000000000000 : ℚ)) + (U := (-(8080950627273355186921 / 10000000000000000000000 : ℚ))) + (U' := (5781992978726644813079 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1553192807 / 3125000000 : ℚ)) + (s := (1110823959334981 / 2500000000000000 : ℚ)) + (q := (2228531501813731 / 5000000000000000 : ℚ)) + (U := (-(8080950627273355186921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_7 : Uω (aρ 7) (bρ 7) (1553192807 / 3125000000 : ℝ) ≤ @@ -971,25 +855,21 @@ lemma U_462_7 : have hlg : Real.log (8432827829585187 / 20000000000000000 : ℝ) ≤ (-(8636001089211850716229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8432827829585187 / 20000000000000000 : ℝ) = - (8432827829585187 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8432827829585187 / 5000000000000000 : ℚ)) - (U := (5226942516788149283771 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8432827829585187 / 5000000000000000 : ℝ) ≤ - (5226942516788149283771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4185659040430187 / 10000000000000000 : ℝ)) (q := - (8432827829585187 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8432827829585187 / 20000000000000000 : ℚ)) + (r' := (8432827829585187 / 5000000000000000 : ℚ)) + (U := (-(8636001089211850716229 / 10000000000000000000000 : ℚ))) + (U' := (5226942516788149283771 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1553192807 / 3125000000 : ℚ)) + (s := (4185659040430187 / 10000000000000000 : ℚ)) + (q := (8432827829585187 / 20000000000000000 : ℚ)) + (U := (-(8636001089211850716229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_8 : Uω (aρ 8) (bρ 8) (1553192807 / 3125000000 : ℝ) ≤ @@ -997,25 +877,21 @@ lemma U_462_8 : have hlg : Real.log (974733199612577 / 2500000000000000 : ℝ) ≤ (-(9418822182081979184731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (974733199612577 / 2500000000000000 : ℝ) = - (974733199612577 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (974733199612577 / 625000000000000 : ℚ)) - (U := (4444121423918020815269 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (974733199612577 / 625000000000000 : ℝ) ≤ - (4444121423918020815269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239639903692851 / 625000000000000 : ℝ)) (q := - (974733199612577 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (974733199612577 / 2500000000000000 : ℚ)) + (r' := (974733199612577 / 625000000000000 : ℚ)) + (U := (-(9418822182081979184731 / 10000000000000000000000 : ℚ))) + (U' := (4444121423918020815269 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1553192807 / 3125000000 : ℚ)) + (s := (239639903692851 / 625000000000000 : ℚ)) + (q := (974733199612577 / 2500000000000000 : ℚ)) + (U := (-(9418822182081979184731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_9 : Uω (aρ 9) (bρ 9) (1553192807 / 3125000000 : ℝ) ≤ @@ -1023,24 +899,21 @@ lemma U_462_9 : have hlg : Real.log (54578324412253 / 156250000000000 : ℝ) ≤ (-(10518204729532456955793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54578324412253 / 156250000000000 : ℝ) = (54578324412253 / 39062500000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54578324412253 / 39062500000000 : ℚ)) - (U := (3344738876467543044207 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54578324412253 / 39062500000000 : ℝ) ≤ - (3344738876467543044207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (420420501914173 / 1250000000000000 : ℝ)) (q := - (54578324412253 / 156250000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54578324412253 / 156250000000000 : ℚ)) + (r' := (54578324412253 / 39062500000000 : ℚ)) + (U := (-(10518204729532456955793 / 10000000000000000000000 : ℚ))) + (U' := (3344738876467543044207 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1553192807 / 3125000000 : ℚ)) + (s := (420420501914173 / 1250000000000000 : ℚ)) + (q := (54578324412253 / 156250000000000 : ℚ)) + (U := (-(10518204729532456955793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_10 : Uω (aρ 10) (bρ 10) (1553192807 / 3125000000 : ℝ) ≤ @@ -1048,26 +921,21 @@ lemma U_462_10 : have hlg : Real.log (2981781393102121 / 10000000000000000 : ℝ) ≤ (-(2420128375275408177111 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2981781393102121 / 10000000000000000 : ℝ) = - (2981781393102121 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2981781393102121 / 2500000000000000 : ℚ)) - (U := (352460345924591822889 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2981781393102121 / 2500000000000000 : ℝ) ≤ - (352460345924591822889 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1364730155122121 / 5000000000000000 : ℝ)) (q := - (2981781393102121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2981781393102121 / 10000000000000000 : ℚ)) + (r' := (2981781393102121 / 2500000000000000 : ℚ)) + (U := (-(2420128375275408177111 / 2000000000000000000000 : ℚ))) + (U' := (352460345924591822889 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1553192807 / 3125000000 : ℚ)) + (s := (1364730155122121 / 5000000000000000 : ℚ)) + (q := (2981781393102121 / 10000000000000000 : ℚ)) + (U := (-(2420128375275408177111 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_11 : Uω (aρ 11) (bρ 11) (1553192807 / 3125000000 : ℝ) ≤ @@ -1075,26 +943,21 @@ lemma U_462_11 : have hlg : Real.log (1157385405195211 / 5000000000000000 : ℝ) ≤ (-(1829093014460264202961 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1157385405195211 / 5000000000000000 : ℝ) = - (1157385405195211 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1157385405195211 / 625000000000000 : ℚ)) - (U := (770208911664735797039 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1157385405195211 / 625000000000000 : ℝ) ≤ - (770208911664735797039 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (453478942756461 / 2500000000000000 : ℝ)) (q := - (1157385405195211 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1157385405195211 / 5000000000000000 : ℚ)) + (r' := (1157385405195211 / 625000000000000 : ℚ)) + (U := (-(1829093014460264202961 / 1250000000000000000000 : ℚ))) + (U' := (770208911664735797039 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1553192807 / 3125000000 : ℚ)) + (s := (453478942756461 / 2500000000000000 : ℚ)) + (q := (1157385405195211 / 5000000000000000 : ℚ)) + (U := (-(1829093014460264202961 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_462_12 : Uω (aρ 12) (bρ 12) (1553192807 / 3125000000 : ℝ) ≤ @@ -1211,25 +1074,21 @@ lemma U_463_1 : have hlg : Real.log (4932172983618371 / 10000000000000000 : ℝ) ≤ (-(7068054340607733583047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4932172983618371 / 10000000000000000 : ℝ) = - (4932172983618371 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4932172983618371 / 2500000000000000 : ℚ)) - (U := (6794889265392266416953 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4932172983618371 / 2500000000000000 : ℝ) ≤ - (6794889265392266416953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2466070102695871 / 5000000000000000 : ℝ)) (q := - (4932172983618371 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4932172983618371 / 10000000000000000 : ℚ)) + (r' := (4932172983618371 / 2500000000000000 : ℚ)) + (U := (-(7068054340607733583047 / 10000000000000000000000 : ℚ))) + (U' := (6794889265392266416953 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (2466070102695871 / 5000000000000000 : ℚ)) + (q := (4932172983618371 / 10000000000000000 : ℚ)) + (U := (-(7068054340607733583047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_2 : Uω (aρ 2) (bρ 2) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1237,25 +1096,21 @@ lemma U_463_2 : have hlg : Real.log (1963288238504021 / 4000000000000000 : ℝ) ≤ (-(889592025465360876981 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1963288238504021 / 4000000000000000 : ℝ) = - (1963288238504021 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1963288238504021 / 1000000000000000 : ℚ)) - (U := (843275925284639123019 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1963288238504021 / 1000000000000000 : ℝ) ≤ - (843275925284639123019 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (981600888637021 / 2000000000000000 : ℝ)) (q := - (1963288238504021 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1963288238504021 / 4000000000000000 : ℚ)) + (r' := (1963288238504021 / 1000000000000000 : ℚ)) + (U := (-(889592025465360876981 / 1250000000000000000000 : ℚ))) + (U' := (843275925284639123019 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (981600888637021 / 2000000000000000 : ℚ)) + (q := (1963288238504021 / 4000000000000000 : ℚ)) + (U := (-(889592025465360876981 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_3 : Uω (aρ 3) (bρ 3) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1263,25 +1118,21 @@ lemma U_463_3 : have hlg : Real.log (1944111826954371 / 4000000000000000 : ℝ) ≤ (-(3607445660313601547497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1944111826954371 / 4000000000000000 : ℝ) = - (1944111826954371 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1944111826954371 / 1000000000000000 : ℚ)) - (U := (3324026142686398452503 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1944111826954371 / 1000000000000000 : ℝ) ≤ - (3324026142686398452503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (971903698357371 / 2000000000000000 : ℝ)) (q := - (1944111826954371 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1944111826954371 / 4000000000000000 : ℚ)) + (r' := (1944111826954371 / 1000000000000000 : ℚ)) + (U := (-(3607445660313601547497 / 5000000000000000000000 : ℚ))) + (U' := (3324026142686398452503 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (971903698357371 / 2000000000000000 : ℚ)) + (q := (1944111826954371 / 4000000000000000 : ℚ)) + (U := (-(3607445660313601547497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_4 : Uω (aρ 4) (bρ 4) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1289,25 +1140,21 @@ lemma U_463_4 : have hlg : Real.log (2390272882802007 / 5000000000000000 : ℝ) ≤ (-(59042430046709734459 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2390272882802007 / 5000000000000000 : ℝ) = - (2390272882802007 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2390272882802007 / 1250000000000000 : ℚ)) - (U := (51861118801290265541 / 80000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2390272882802007 / 1250000000000000 : ℝ) ≤ - (51861118801290265541 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1194586267322007 / 2500000000000000 : ℝ)) (q := - (2390272882802007 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2390272882802007 / 5000000000000000 : ℚ)) + (r' := (2390272882802007 / 1250000000000000 : ℚ)) + (U := (-(59042430046709734459 / 80000000000000000000 : ℚ))) + (U' := (51861118801290265541 / 80000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (1194586267322007 / 2500000000000000 : ℚ)) + (q := (2390272882802007 / 5000000000000000 : ℚ)) + (U := (-(59042430046709734459 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_5 : Uω (aρ 5) (bρ 5) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1315,25 +1162,21 @@ lemma U_463_5 : have hlg : Real.log (9317681726731767 / 20000000000000000 : ℝ) ≤ (-(7638184170449427090801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9317681726731767 / 20000000000000000 : ℝ) = - (9317681726731767 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9317681726731767 / 5000000000000000 : ℚ)) - (U := (6224759435550572909199 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9317681726731767 / 5000000000000000 : ℝ) ≤ - (6224759435550572909199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4653125184146767 / 10000000000000000 : ℝ)) (q := - (9317681726731767 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9317681726731767 / 20000000000000000 : ℚ)) + (r' := (9317681726731767 / 5000000000000000 : ℚ)) + (U := (-(7638184170449427090801 / 10000000000000000000000 : ℚ))) + (U' := (6224759435550572909199 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (4653125184146767 / 10000000000000000 : ℚ)) + (q := (9317681726731767 / 20000000000000000 : ℚ)) + (U := (-(7638184170449427090801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_6 : Uω (aρ 6) (bρ 6) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1341,25 +1184,21 @@ lemma U_463_6 : have hlg : Real.log (1793452231181081 / 4000000000000000 : ℝ) ≤ (-(125336246465165303943 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1793452231181081 / 4000000000000000 : ℝ) = - (1793452231181081 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1793452231181081 / 1000000000000000 : ℚ)) - (U := (91272247378584696057 / 156250000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1793452231181081 / 1000000000000000 : ℝ) ≤ - (91272247378584696057 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (893988997692081 / 2000000000000000 : ℝ)) (q := - (1793452231181081 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1793452231181081 / 4000000000000000 : ℚ)) + (r' := (1793452231181081 / 1000000000000000 : ℚ)) + (U := (-(125336246465165303943 / 156250000000000000000 : ℚ))) + (U' := (91272247378584696057 / 156250000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (893988997692081 / 2000000000000000 : ℚ)) + (q := (1793452231181081 / 4000000000000000 : ℚ)) + (U := (-(125336246465165303943 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_7 : Uω (aρ 7) (bρ 7) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1367,25 +1206,21 @@ lemma U_463_7 : have hlg : Real.log (530386661288787 / 1250000000000000 : ℝ) ≤ (-(2143231349051881482137 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (530386661288787 / 1250000000000000 : ℝ) = - (530386661288787 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (530386661288787 / 312500000000000 : ℚ)) - (U := (1322504552448118517863 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (530386661288787 / 312500000000000 : ℝ) ≤ - (1322504552448118517863 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (526566474241949 / 1250000000000000 : ℝ)) (q := - (530386661288787 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (530386661288787 / 1250000000000000 : ℚ)) + (r' := (530386661288787 / 312500000000000 : ℚ)) + (U := (-(2143231349051881482137 / 2500000000000000000000 : ℚ))) + (U' := (1322504552448118517863 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (526566474241949 / 1250000000000000 : ℚ)) + (q := (530386661288787 / 1250000000000000 : ℚ)) + (U := (-(2143231349051881482137 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_8 : Uω (aρ 8) (bρ 8) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1393,25 +1228,21 @@ lemma U_463_8 : have hlg : Real.log (7851725144125843 / 20000000000000000 : ℝ) ≤ (-(9349990018013522406539 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7851725144125843 / 20000000000000000 : ℝ) = - (7851725144125843 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7851725144125843 / 5000000000000000 : ℚ)) - (U := (4512953587986477593461 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7851725144125843 / 5000000000000000 : ℝ) ≤ - (4512953587986477593461 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3861612008780843 / 10000000000000000 : ℝ)) (q := - (7851725144125843 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7851725144125843 / 20000000000000000 : ℚ)) + (r' := (7851725144125843 / 5000000000000000 : ℚ)) + (U := (-(9349990018013522406539 / 10000000000000000000000 : ℚ))) + (U' := (4512953587986477593461 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (3861612008780843 / 10000000000000000 : ℚ)) + (q := (7851725144125843 / 20000000000000000 : ℚ)) + (U := (-(9349990018013522406539 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_9 : Uω (aρ 9) (bρ 9) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1419,25 +1250,21 @@ lemma U_463_9 : have hlg : Real.log (3520511445092123 / 10000000000000000 : ℝ) ≤ (-(10439788165175504274949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3520511445092123 / 10000000000000000 : ℝ) = - (3520511445092123 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3520511445092123 / 2500000000000000 : ℚ)) - (U := (3423155440824495725051 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3520511445092123 / 2500000000000000 : ℝ) ≤ - (3423155440824495725051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1695937691599623 / 5000000000000000 : ℝ)) (q := - (3520511445092123 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3520511445092123 / 10000000000000000 : ℚ)) + (r' := (3520511445092123 / 2500000000000000 : ℚ)) + (U := (-(10439788165175504274949 / 10000000000000000000000 : ℚ))) + (U' := (3423155440824495725051 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (1695937691599623 / 5000000000000000 : ℚ)) + (q := (3520511445092123 / 10000000000000000 : ℚ)) + (U := (-(10439788165175504274949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_10 : Uω (aρ 10) (bρ 10) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1445,25 +1272,21 @@ lemma U_463_10 : have hlg : Real.log (150534509511739 / 500000000000000 : ℝ) ≤ (-(12004157409170647831141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (150534509511739 / 500000000000000 : ℝ) = - (150534509511739 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (150534509511739 / 125000000000000 : ℚ)) - (U := (1858786196829352168859 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (150534509511739 / 125000000000000 : ℝ) ≤ - (1858786196829352168859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (69019797674489 / 250000000000000 : ℝ)) (q := - (150534509511739 / 500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (150534509511739 / 500000000000000 : ℚ)) + (r' := (150534509511739 / 125000000000000 : ℚ)) + (U := (-(12004157409170647831141 / 10000000000000000000000 : ℚ))) + (U' := (1858786196829352168859 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (69019797674489 / 250000000000000 : ℚ)) + (q := (150534509511739 / 500000000000000 : ℚ)) + (U := (-(12004157409170647831141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_11 : Uω (aρ 11) (bρ 11) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1471,25 +1294,21 @@ lemma U_463_11 : have hlg : Real.log (939374724944627 / 4000000000000000 : ℝ) ≤ (-(7244175858108899826303 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (939374724944627 / 4000000000000000 : ℝ) = - (939374724944627 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (939374724944627 / 500000000000000 : ℚ)) - (U := (3153031846391100173697 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (939374724944627 / 500000000000000 : ℝ) ≤ - (3153031846391100173697 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (370952355487627 / 2000000000000000 : ℝ)) (q := - (939374724944627 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (939374724944627 / 4000000000000000 : ℚ)) + (r' := (939374724944627 / 500000000000000 : ℚ)) + (U := (-(7244175858108899826303 / 5000000000000000000000 : ℚ))) + (U' := (3153031846391100173697 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (499670297993 / 1000000000000 : ℚ)) + (s := (370952355487627 / 2000000000000000 : ℚ)) + (q := (939374724944627 / 4000000000000000 : ℚ)) + (U := (-(7244175858108899826303 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_463_12 : Uω (aρ 12) (bρ 12) (499670297993 / 1000000000000 : ℝ) ≤ @@ -1605,25 +1424,21 @@ lemma U_464_1 : have hlg : Real.log (4985145326981051 / 10000000000000000 : ℝ) ≤ (-(3480612683152575500467 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4985145326981051 / 10000000000000000 : ℝ) = - (4985145326981051 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4985145326981051 / 2500000000000000 : ℚ)) - (U := (3450859119847424499533 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (4985145326981051 / 2500000000000000 : ℝ) ≤ - (3450859119847424499533 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2492556448528551 / 5000000000000000 : ℝ)) (q := - (4985145326981051 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4985145326981051 / 10000000000000000 : ℚ)) + (r' := (4985145326981051 / 2500000000000000 : ℚ)) + (U := (-(3480612683152575500467 / 5000000000000000000000 : ℚ))) + (U' := (3450859119847424499533 / 5000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2492556448528551 / 5000000000000000 : ℚ)) + (q := (4985145326981051 / 10000000000000000 : ℚ)) + (U := (-(3480612683152575500467 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_2 : Uω (aρ 2) (bρ 2) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1631,25 +1446,21 @@ lemma U_464_2 : have hlg : Real.log (9922389798688753 / 20000000000000000 : ℝ) ≤ (-(7009384736248986284349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9922389798688753 / 20000000000000000 : ℝ) = - (9922389798688753 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9922389798688753 / 5000000000000000 : ℚ)) - (U := (6853558869751013715651 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9922389798688753 / 5000000000000000 : ℝ) ≤ - (6853558869751013715651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4960981054293753 / 10000000000000000 : ℝ)) (q := - (9922389798688753 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9922389798688753 / 20000000000000000 : ℚ)) + (r' := (9922389798688753 / 5000000000000000 : ℚ)) + (U := (-(7009384736248986284349 / 10000000000000000000000 : ℚ))) + (U' := (6853558869751013715651 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (4960981054293753 / 10000000000000000 : ℚ)) + (q := (9922389798688753 / 20000000000000000 : ℚ)) + (U := (-(7009384736248986284349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_3 : Uω (aρ 3) (bρ 3) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1657,25 +1468,21 @@ lemma U_464_3 : have hlg : Real.log (4913259769204929 / 10000000000000000 : ℝ) ≤ (-(7106474668395118534257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4913259769204929 / 10000000000000000 : ℝ) = - (4913259769204929 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4913259769204929 / 2500000000000000 : ℚ)) - (U := (6756468937604881465743 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4913259769204929 / 2500000000000000 : ℝ) ≤ - (6756468937604881465743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2456253450182429 / 5000000000000000 : ℝ)) (q := - (4913259769204929 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4913259769204929 / 10000000000000000 : ℚ)) + (r' := (4913259769204929 / 2500000000000000 : ℚ)) + (U := (-(7106474668395118534257 / 10000000000000000000000 : ℚ))) + (U' := (6756468937604881465743 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2456253450182429 / 5000000000000000 : ℚ)) + (q := (4913259769204929 / 10000000000000000 : ℚ)) + (U := (-(7106474668395118534257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_4 : Uω (aρ 4) (bρ 4) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1683,25 +1490,21 @@ lemma U_464_4 : have hlg : Real.log (4833541889631461 / 10000000000000000 : ℝ) ≤ (-(3635027915338646864123 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4833541889631461 / 10000000000000000 : ℝ) = - (4833541889631461 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4833541889631461 / 2500000000000000 : ℚ)) - (U := (3296443887661353135877 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4833541889631461 / 2500000000000000 : ℝ) ≤ - (3296443887661353135877 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2415682661141461 / 5000000000000000 : ℝ)) (q := - (4833541889631461 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4833541889631461 / 10000000000000000 : ℚ)) + (r' := (4833541889631461 / 2500000000000000 : ℚ)) + (U := (-(3635027915338646864123 / 5000000000000000000000 : ℚ))) + (U' := (3296443887661353135877 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2415682661141461 / 5000000000000000 : ℚ)) + (q := (4833541889631461 / 10000000000000000 : ℚ)) + (U := (-(3635027915338646864123 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_5 : Uω (aρ 5) (bρ 5) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1709,25 +1512,21 @@ lemma U_464_5 : have hlg : Real.log (4711877193432331 / 10000000000000000 : ℝ) ≤ (-(300999483591545481661 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4711877193432331 / 10000000000000000 : ℝ) = - (4711877193432331 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4711877193432331 / 2500000000000000 : ℚ)) - (U := (253518260648454518339 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4711877193432331 / 2500000000000000 : ℝ) ≤ - (253518260648454518339 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2353112924609831 / 5000000000000000 : ℝ)) (q := - (4711877193432331 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4711877193432331 / 10000000000000000 : ℚ)) + (r' := (4711877193432331 / 2500000000000000 : ℚ)) + (U := (-(300999483591545481661 / 400000000000000000000 : ℚ))) + (U' := (253518260648454518339 / 400000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2353112924609831 / 5000000000000000 : ℚ)) + (q := (4711877193432331 / 10000000000000000 : ℚ)) + (U := (-(300999483591545481661 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_6 : Uω (aρ 6) (bρ 6) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1735,25 +1534,21 @@ lemma U_464_6 : have hlg : Real.log (9073525703441053 / 20000000000000000 : ℝ) ≤ (-(987964203752296207611 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9073525703441053 / 20000000000000000 : ℝ) = - (9073525703441053 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9073525703441053 / 5000000000000000 : ℚ)) - (U := (744903746997703792389 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9073525703441053 / 5000000000000000 : ℝ) ≤ - (744903746997703792389 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4523237540936053 / 10000000000000000 : ℝ)) (q := - (9073525703441053 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9073525703441053 / 20000000000000000 : ℚ)) + (r' := (9073525703441053 / 5000000000000000 : ℚ)) + (U := (-(987964203752296207611 / 1250000000000000000000 : ℚ))) + (U' := (744903746997703792389 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (4523237540936053 / 10000000000000000 : ℚ)) + (q := (9073525703441053 / 20000000000000000 : ℚ)) + (U := (-(987964203752296207611 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_7 : Uω (aρ 7) (bρ 7) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1761,25 +1556,21 @@ lemma U_464_7 : have hlg : Real.log (4296444785540659 / 10000000000000000 : ℝ) ≤ (-(168959441163534356641 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4296444785540659 / 10000000000000000 : ℝ) = - (4296444785540659 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4296444785540659 / 2500000000000000 : ℚ)) - (U := (108299430956465643359 / 200000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4296444785540659 / 2500000000000000 : ℝ) ≤ - (108299430956465643359 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2133131394668159 / 5000000000000000 : ℝ)) (q := - (4296444785540659 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4296444785540659 / 10000000000000000 : ℚ)) + (r' := (4296444785540659 / 2500000000000000 : ℚ)) + (U := (-(168959441163534356641 / 200000000000000000000 : ℚ))) + (U' := (108299430956465643359 / 200000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2133131394668159 / 5000000000000000 : ℚ)) + (q := (4296444785540659 / 10000000000000000 : ℚ)) + (U := (-(168959441163534356641 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_8 : Uω (aρ 8) (bρ 8) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1787,25 +1578,21 @@ lemma U_464_8 : have hlg : Real.log (3979703810172493 / 10000000000000000 : ℝ) ≤ (-(9213776955017311777019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3979703810172493 / 10000000000000000 : ℝ) = - (3979703810172493 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3979703810172493 / 2500000000000000 : ℚ)) - (U := (4649166650982688222981 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3979703810172493 / 2500000000000000 : ℝ) ≤ - (4649166650982688222981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1958161244969993 / 5000000000000000 : ℝ)) (q := - (3979703810172493 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3979703810172493 / 10000000000000000 : ℚ)) + (r' := (3979703810172493 / 2500000000000000 : ℚ)) + (U := (-(9213776955017311777019 / 10000000000000000000000 : ℚ))) + (U' := (4649166650982688222981 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (1958161244969993 / 5000000000000000 : ℚ)) + (q := (3979703810172493 / 10000000000000000 : ℚ)) + (U := (-(9213776955017311777019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_9 : Uω (aρ 9) (bρ 9) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1813,25 +1600,21 @@ lemma U_464_9 : have hlg : Real.log (3575460363905141 / 10000000000000000 : ℝ) ≤ (-(5142455757492057291689 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3575460363905141 / 10000000000000000 : ℝ) = - (3575460363905141 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3575460363905141 / 2500000000000000 : ℚ)) - (U := (1789016045507942708311 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3575460363905141 / 2500000000000000 : ℝ) ≤ - (1789016045507942708311 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1724400612882641 / 5000000000000000 : ℝ)) (q := - (3575460363905141 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3575460363905141 / 10000000000000000 : ℚ)) + (r' := (3575460363905141 / 2500000000000000 : ℚ)) + (U := (-(5142455757492057291689 / 5000000000000000000000 : ℚ))) + (U' := (1789016045507942708311 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (1724400612882641 / 5000000000000000 : ℚ)) + (q := (3575460363905141 / 10000000000000000 : ℚ)) + (U := (-(5142455757492057291689 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_10 : Uω (aρ 10) (bρ 10) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1839,26 +1622,21 @@ lemma U_464_10 : have hlg : Real.log (6136717874527443 / 20000000000000000 : ℝ) ≤ (-(11814422219193978853499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6136717874527443 / 20000000000000000 : ℝ) = - (6136717874527443 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6136717874527443 / 5000000000000000 : ℚ)) - (U := (2048521386806021146501 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6136717874527443 / 5000000000000000 : ℝ) ≤ - (2048521386806021146501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2823157405977443 / 10000000000000000 : ℝ)) (q := - (6136717874527443 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6136717874527443 / 20000000000000000 : ℚ)) + (r' := (6136717874527443 / 5000000000000000 : ℚ)) + (U := (-(11814422219193978853499 / 10000000000000000000000 : ℚ))) + (U' := (2048521386806021146501 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (2823157405977443 / 10000000000000000 : ℚ)) + (q := (6136717874527443 / 20000000000000000 : ℚ)) + (U := (-(11814422219193978853499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_11 : Uω (aρ 11) (bρ 11) (504967497499 / 1000000000000 : ℝ) ≤ @@ -1866,26 +1644,21 @@ lemma U_464_11 : have hlg : Real.log (1207509781695767 / 5000000000000000 : ℝ) ≤ (-(7104388521796205094697 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1207509781695767 / 5000000000000000 : ℝ) = - (1207509781695767 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1207509781695767 / 625000000000000 : ℚ)) - (U := (3292819182703794905303 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1207509781695767 / 625000000000000 : ℝ) ≤ - (3292819182703794905303 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (483738821109517 / 2500000000000000 : ℝ)) (q := - (1207509781695767 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1207509781695767 / 5000000000000000 : ℚ)) + (r' := (1207509781695767 / 625000000000000 : ℚ)) + (U := (-(7104388521796205094697 / 5000000000000000000000 : ℚ))) + (U' := (3292819182703794905303 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (504967497499 / 1000000000000 : ℚ)) + (s := (483738821109517 / 2500000000000000 : ℚ)) + (q := (1207509781695767 / 5000000000000000 : ℚ)) + (U := (-(7104388521796205094697 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_464_12 : Uω (aρ 12) (bρ 12) (504967497499 / 1000000000000 : ℝ) ≤ @@ -2001,25 +1774,21 @@ lemma U_465_1 : have hlg : Real.log (2015247065207743 / 4000000000000000 : ℝ) ≤ (-(685552559971335199247 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2015247065207743 / 4000000000000000 : ℝ) = - (2015247065207743 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2015247065207743 / 2000000000000000 : ℚ)) - (U := (7594620328664800753 / 1000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2015247065207743 / 2000000000000000 : ℝ) ≤ - (7594620328664800753 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1007617114814743 / 2000000000000000 : ℝ)) (q := - (2015247065207743 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2015247065207743 / 4000000000000000 : ℚ)) + (r' := (2015247065207743 / 2000000000000000 : ℚ)) + (U := (-(685552559971335199247 / 1000000000000000000000 : ℚ))) + (U' := (7594620328664800753 / 1000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (102052939401 / 200000000000 : ℚ)) + (s := (1007617114814743 / 2000000000000000 : ℚ)) + (q := (2015247065207743 / 4000000000000000 : ℚ)) + (U := (-(685552559971335199247 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_2 : Uω (aρ 2) (bρ 2) (102052939401 / 200000000000 : ℝ) ≤ @@ -2027,25 +1796,21 @@ lemma U_465_2 : have hlg : Real.log (1253542288414613 / 2500000000000000 : ℝ) ≤ (-(6903173572969198641041 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1253542288414613 / 2500000000000000 : ℝ) = - (1253542288414613 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1253542288414613 / 1250000000000000 : ℚ)) - (U := (28298230030801358959 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1253542288414613 / 1250000000000000 : ℝ) ≤ - (28298230030801358959 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (313372347991369 / 625000000000000 : ℝ)) (q := - (1253542288414613 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1253542288414613 / 2500000000000000 : ℚ)) + (r' := (1253542288414613 / 1250000000000000 : ℚ)) + (U := (-(6903173572969198641041 / 10000000000000000000000 : ℚ))) + (U' := (28298230030801358959 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (102052939401 / 200000000000 : ℚ)) + (s := (313372347991369 / 625000000000000 : ℚ)) + (q := (1253542288414613 / 2500000000000000 : ℚ)) + (U := (-(6903173572969198641041 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_3 : Uω (aρ 3) (bρ 3) (102052939401 / 200000000000 : ℝ) ≤ @@ -2053,25 +1818,21 @@ lemma U_465_3 : have hlg : Real.log (2483119897948543 / 5000000000000000 : ℝ) ≤ (-(3499610595096664125941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2483119897948543 / 5000000000000000 : ℝ) = - (2483119897948543 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2483119897948543 / 1250000000000000 : ℚ)) - (U := (3431861207903335874059 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2483119897948543 / 1250000000000000 : ℝ) ≤ - (3431861207903335874059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1241373739672293 / 2500000000000000 : ℝ)) (q := - (2483119897948543 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2483119897948543 / 5000000000000000 : ℚ)) + (r' := (2483119897948543 / 1250000000000000 : ℚ)) + (U := (-(3499610595096664125941 / 5000000000000000000000 : ℚ))) + (U' := (3431861207903335874059 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (102052939401 / 200000000000 : ℚ)) + (s := (1241373739672293 / 2500000000000000 : ℚ)) + (q := (2483119897948543 / 5000000000000000 : ℚ)) + (U := (-(3499610595096664125941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_4 : Uω (aρ 4) (bρ 4) (102052939401 / 200000000000 : ℝ) ≤ @@ -2079,25 +1840,21 @@ lemma U_465_4 : have hlg : Real.log (1954614996021967 / 4000000000000000 : ℝ) ≤ (-(7161011195376077060239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1954614996021967 / 4000000000000000 : ℝ) = - (1954614996021967 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1954614996021967 / 1000000000000000 : ℚ)) - (U := (6701932410623922939761 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1954614996021967 / 1000000000000000 : ℝ) ≤ - (6701932410623922939761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (976876905613967 / 2000000000000000 : ℝ)) (q := - (1954614996021967 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1954614996021967 / 4000000000000000 : ℚ)) + (r' := (1954614996021967 / 1000000000000000 : ℚ)) + (U := (-(7161011195376077060239 / 10000000000000000000000 : ℚ))) + (U' := (6701932410623922939761 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (102052939401 / 200000000000 : ℚ)) + (s := (976876905613967 / 2000000000000000 : ℚ)) + (q := (1954614996021967 / 4000000000000000 : ℚ)) + (U := (-(7161011195376077060239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_5 : Uω (aρ 5) (bρ 5) (102052939401 / 200000000000 : ℝ) ≤ @@ -2105,25 +1862,21 @@ lemma U_465_5 : have hlg : Real.log (9529824179286207 / 20000000000000000 : ℝ) ≤ (-(3706530023605786136097 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9529824179286207 / 20000000000000000 : ℝ) = - (9529824179286207 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9529824179286207 / 5000000000000000 : ℚ)) - (U := (3224941779394213863903 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9529824179286207 / 5000000000000000 : ℝ) ≤ - (3224941779394213863903 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4759323646581207 / 10000000000000000 : ℝ)) (q := - (9529824179286207 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9529824179286207 / 20000000000000000 : ℚ)) + (r' := (9529824179286207 / 5000000000000000 : ℚ)) + (U := (-(3706530023605786136097 / 5000000000000000000000 : ℚ))) + (U' := (3224941779394213863903 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (102052939401 / 200000000000 : ℚ)) + (s := (4759323646581207 / 10000000000000000 : ℚ)) + (q := (9529824179286207 / 20000000000000000 : ℚ)) + (U := (-(3706530023605786136097 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_6 : Uω (aρ 6) (bρ 6) (102052939401 / 200000000000 : ℝ) ≤ @@ -2131,25 +1884,21 @@ lemma U_465_6 : have hlg : Real.log (9179782807801253 / 20000000000000000 : ℝ) ≤ (-(311491491184998294687 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9179782807801253 / 20000000000000000 : ℝ) = - (9179782807801253 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9179782807801253 / 5000000000000000 : ℚ)) - (U := (243026253055001705313 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9179782807801253 / 5000000000000000 : ℝ) ≤ - (243026253055001705313 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4576522650236253 / 10000000000000000 : ℝ)) (q := - (9179782807801253 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9179782807801253 / 20000000000000000 : ℚ)) + (r' := (9179782807801253 / 5000000000000000 : ℚ)) + (U := (-(311491491184998294687 / 400000000000000000000 : ℚ))) + (U' := (243026253055001705313 / 400000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (102052939401 / 200000000000 : ℚ)) + (s := (4576522650236253 / 10000000000000000 : ℚ)) + (q := (9179782807801253 / 20000000000000000 : ℚ)) + (U := (-(311491491184998294687 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_7 : Uω (aρ 7) (bρ 7) (102052939401 / 200000000000 : ℝ) ≤ @@ -2157,25 +1906,21 @@ lemma U_465_7 : have hlg : Real.log (8699573814343349 / 20000000000000000 : ℝ) ≤ (-(66596658834443514293 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8699573814343349 / 20000000000000000 : ℝ) = - (8699573814343349 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8699573814343349 / 5000000000000000 : ℚ)) - (U := (44306890013556485707 / 80000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8699573814343349 / 5000000000000000 : ℝ) ≤ - (44306890013556485707 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4319975037538349 / 10000000000000000 : ℝ)) (q := - (8699573814343349 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8699573814343349 / 20000000000000000 : ℚ)) + (r' := (8699573814343349 / 5000000000000000 : ℚ)) + (U := (-(66596658834443514293 / 80000000000000000000 : ℚ))) + (U' := (44306890013556485707 / 80000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (102052939401 / 200000000000 : ℚ)) + (s := (4319975037538349 / 10000000000000000 : ℚ)) + (q := (8699573814343349 / 20000000000000000 : ℚ)) + (U := (-(66596658834443514293 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_8 : Uω (aρ 8) (bρ 8) (102052939401 / 200000000000 : ℝ) ≤ @@ -2183,25 +1928,21 @@ lemma U_465_8 : have hlg : Real.log (2016760738441907 / 5000000000000000 : ℝ) ≤ (-(4539726412331190736867 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2016760738441907 / 5000000000000000 : ℝ) = - (2016760738441907 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2016760738441907 / 1250000000000000 : ℚ)) - (U := (2391745390668809263133 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2016760738441907 / 1250000000000000 : ℝ) ≤ - (2391745390668809263133 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (992746457075657 / 2500000000000000 : ℝ)) (q := - (2016760738441907 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2016760738441907 / 5000000000000000 : ℚ)) + (r' := (2016760738441907 / 1250000000000000 : ℚ)) + (U := (-(4539726412331190736867 / 5000000000000000000000 : ℚ))) + (U' := (2391745390668809263133 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (102052939401 / 200000000000 : ℚ)) + (s := (992746457075657 / 2500000000000000 : ℚ)) + (q := (2016760738441907 / 5000000000000000 : ℚ)) + (U := (-(4539726412331190736867 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_9 : Uω (aρ 9) (bρ 9) (102052939401 / 200000000000 : ℝ) ≤ @@ -2209,25 +1950,21 @@ lemma U_465_9 : have hlg : Real.log (3630347308844513 / 10000000000000000 : ℝ) ≤ (-(5066283857032743146991 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3630347308844513 / 10000000000000000 : ℝ) = - (3630347308844513 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3630347308844513 / 2500000000000000 : ℚ)) - (U := (1865187945967256853009 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3630347308844513 / 2500000000000000 : ℝ) ≤ - (1865187945967256853009 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1752801560292013 / 5000000000000000 : ℝ)) (q := - (3630347308844513 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3630347308844513 / 10000000000000000 : ℚ)) + (r' := (3630347308844513 / 2500000000000000 : ℚ)) + (U := (-(5066283857032743146991 / 5000000000000000000000 : ℚ))) + (U' := (1865187945967256853009 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (102052939401 / 200000000000 : ℚ)) + (s := (1752801560292013 / 5000000000000000 : ℚ)) + (q := (3630347308844513 / 10000000000000000 : ℚ)) + (U := (-(5066283857032743146991 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_10 : Uω (aρ 10) (bρ 10) (102052939401 / 200000000000 : ℝ) ≤ @@ -2235,26 +1972,21 @@ lemma U_465_10 : have hlg : Real.log (6251679875568011 / 20000000000000000 : ℝ) ≤ (-(11628820653098059451003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6251679875568011 / 20000000000000000 : ℝ) = - (6251679875568011 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6251679875568011 / 5000000000000000 : ℚ)) - (U := (2234122952901940548997 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6251679875568011 / 5000000000000000 : ℝ) ≤ - (2234122952901940548997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2885147411958011 / 10000000000000000 : ℝ)) (q := - (6251679875568011 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6251679875568011 / 20000000000000000 : ℚ)) + (r' := (6251679875568011 / 5000000000000000 : ℚ)) + (U := (-(11628820653098059451003 / 10000000000000000000000 : ℚ))) + (U' := (2234122952901940548997 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (102052939401 / 200000000000 : ℚ)) + (s := (2885147411958011 / 10000000000000000 : ℚ)) + (q := (6251679875568011 / 20000000000000000 : ℚ)) + (U := (-(11628820653098059451003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_11 : Uω (aρ 11) (bρ 11) (102052939401 / 200000000000 : ℝ) ≤ @@ -2262,26 +1994,21 @@ lemma U_465_11 : have hlg : Real.log (2480702483671911 / 10000000000000000 : ℝ) ≤ (-(871277070376627645763 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2480702483671911 / 10000000000000000 : ℝ) = - (2480702483671911 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2480702483671911 / 1250000000000000 : ℚ)) - (U := (428373892685872354237 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2480702483671911 / 1250000000000000 : ℝ) ≤ - (428373892685872354237 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1006674564969411 / 5000000000000000 : ℝ)) (q := - (2480702483671911 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2480702483671911 / 10000000000000000 : ℚ)) + (r' := (2480702483671911 / 1250000000000000 : ℚ)) + (U := (-(871277070376627645763 / 625000000000000000000 : ℚ))) + (U' := (428373892685872354237 / 625000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (102052939401 / 200000000000 : ℚ)) + (s := (1006674564969411 / 5000000000000000 : ℚ)) + (q := (2480702483671911 / 10000000000000000 : ℚ)) + (U := (-(871277070376627645763 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_465_12 : Uω (aρ 12) (bρ 12) (102052939401 / 200000000000 : ℝ) ≤ @@ -2395,25 +2122,21 @@ lemma U_466_1 : have hlg : Real.log (2545544995980961 / 5000000000000000 : ℝ) ≤ (-(843866426616583228107 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2545544995980961 / 5000000000000000 : ℝ) = - (2545544995980961 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2545544995980961 / 2500000000000000 : ℚ)) - (U := (22567548758416771893 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2545544995980961 / 2500000000000000 : ℝ) ≤ - (22567548758416771893 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1272764559224711 / 2500000000000000 : ℝ)) (q := - (2545544995980961 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2545544995980961 / 5000000000000000 : ℚ)) + (r' := (2545544995980961 / 2500000000000000 : ℚ)) + (U := (-(843866426616583228107 / 1250000000000000000000 : ℚ))) + (U' := (22567548758416771893 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (1272764559224711 / 2500000000000000 : ℚ)) + (q := (2545544995980961 / 5000000000000000 : ℚ)) + (U := (-(843866426616583228107 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_2 : Uω (aρ 2) (bρ 2) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2421,25 +2144,21 @@ lemma U_466_2 : have hlg : Real.log (2026857344292803 / 4000000000000000 : ℝ) ≤ (-(6798078736206332217349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2026857344292803 / 4000000000000000 : ℝ) = - (2026857344292803 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2026857344292803 / 2000000000000000 : ℚ)) - (U := (133393066793667782651 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2026857344292803 / 2000000000000000 : ℝ) ≤ - (133393066793667782651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1013386797389803 / 2000000000000000 : ℝ)) (q := - (2026857344292803 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2026857344292803 / 4000000000000000 : ℚ)) + (r' := (2026857344292803 / 2000000000000000 : ℚ)) + (U := (-(6798078736206332217349 / 10000000000000000000000 : ℚ))) + (U' := (133393066793667782651 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (1013386797389803 / 2000000000000000 : ℚ)) + (q := (2026857344292803 / 4000000000000000 : ℚ)) + (U := (-(6798078736206332217349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_3 : Uω (aρ 3) (bρ 3) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2447,25 +2166,21 @@ lemma U_466_3 : have hlg : Real.log (5019219653009671 / 10000000000000000 : ℝ) ≤ (-(430819136700830867653 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5019219653009671 / 10000000000000000 : ℝ) = - (5019219653009671 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5019219653009671 / 5000000000000000 : ℚ)) - (U := (2397850986669132347 / 625000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5019219653009671 / 5000000000000000 : ℝ) ≤ - (2397850986669132347 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2509241338927171 / 5000000000000000 : ℝ)) (q := - (5019219653009671 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5019219653009671 / 10000000000000000 : ℚ)) + (r' := (5019219653009671 / 5000000000000000 : ℚ)) + (U := (-(430819136700830867653 / 625000000000000000000 : ℚ))) + (U' := (2397850986669132347 / 625000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (2509241338927171 / 5000000000000000 : ℚ)) + (q := (5019219653009671 / 10000000000000000 : ℚ)) + (U := (-(430819136700830867653 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_4 : Uω (aρ 4) (bρ 4) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2473,25 +2188,21 @@ lemma U_466_4 : have hlg : Real.log (9879065167484401 / 20000000000000000 : ℝ) ≤ (-(3526571922133105569901 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9879065167484401 / 20000000000000000 : ℝ) = - (9879065167484401 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9879065167484401 / 5000000000000000 : ℚ)) - (U := (3404899880866894430099 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9879065167484401 / 5000000000000000 : ℝ) ≤ - (3404899880866894430099 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4937402720384401 / 10000000000000000 : ℝ)) (q := - (9879065167484401 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9879065167484401 / 20000000000000000 : ℚ)) + (r' := (9879065167484401 / 5000000000000000 : ℚ)) + (U := (-(3526571922133105569901 / 5000000000000000000000 : ℚ))) + (U' := (3404899880866894430099 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (4937402720384401 / 10000000000000000 : ℚ)) + (q := (9879065167484401 / 20000000000000000 : ℚ)) + (U := (-(3526571922133105569901 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_5 : Uω (aρ 5) (bρ 5) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2499,25 +2210,21 @@ lemma U_466_5 : have hlg : Real.log (4817945599459521 / 10000000000000000 : ℝ) ≤ (-(3651187397247562346277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4817945599459521 / 10000000000000000 : ℝ) = - (4817945599459521 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4817945599459521 / 2500000000000000 : ℚ)) - (U := (3280284405752437653723 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4817945599459521 / 2500000000000000 : ℝ) ≤ - (3280284405752437653723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2406209335577021 / 5000000000000000 : ℝ)) (q := - (4817945599459521 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4817945599459521 / 10000000000000000 : ℚ)) + (r' := (4817945599459521 / 2500000000000000 : ℚ)) + (U := (-(3651187397247562346277 / 5000000000000000000000 : ℚ))) + (U' := (3280284405752437653723 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (2406209335577021 / 5000000000000000 : ℚ)) + (q := (4817945599459521 / 10000000000000000 : ℚ)) + (U := (-(3651187397247562346277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_6 : Uω (aρ 6) (bρ 6) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2525,25 +2232,21 @@ lemma U_466_6 : have hlg : Real.log (9286032725980071 / 20000000000000000 : ℝ) ≤ (-(7672208592147029240361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9286032725980071 / 20000000000000000 : ℝ) = - (9286032725980071 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9286032725980071 / 5000000000000000 : ℚ)) - (U := (6190735013852970759639 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9286032725980071 / 5000000000000000 : ℝ) ≤ - (6190735013852970759639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4629800573355071 / 10000000000000000 : ℝ)) (q := - (9286032725980071 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9286032725980071 / 20000000000000000 : ℚ)) + (r' := (9286032725980071 / 5000000000000000 : ℚ)) + (U := (-(7672208592147029240361 / 10000000000000000000000 : ℚ))) + (U' := (6190735013852970759639 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (4629800573355071 / 10000000000000000 : ℚ)) + (q := (9286032725980071 / 20000000000000000 : ℚ)) + (U := (-(7672208592147029240361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_7 : Uω (aρ 7) (bρ 7) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2551,25 +2254,21 @@ lemma U_466_7 : have hlg : Real.log (1100780000137463 / 2500000000000000 : ℝ) ≤ (-(4101358559010733619021 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1100780000137463 / 2500000000000000 : ℝ) = - (1100780000137463 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1100780000137463 / 625000000000000 : ℚ)) - (U := (2830113243989266380979 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1100780000137463 / 625000000000000 : ℝ) ≤ - (2830113243989266380979 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (273354326827169 / 625000000000000 : ℝ)) (q := - (1100780000137463 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1100780000137463 / 2500000000000000 : ℚ)) + (r' := (1100780000137463 / 625000000000000 : ℚ)) + (U := (-(4101358559010733619021 / 5000000000000000000000 : ℚ))) + (U' := (2830113243989266380979 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (273354326827169 / 625000000000000 : ℚ)) + (q := (1100780000137463 / 2500000000000000 : ℚ)) + (U := (-(4101358559010733619021 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_8 : Uω (aρ 8) (bρ 8) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2577,25 +2276,21 @@ lemma U_466_8 : have hlg : Real.log (817463306483847 / 2000000000000000 : ℝ) ≤ (-(1789392884586392307439 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (817463306483847 / 2000000000000000 : ℝ) = - (817463306483847 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (817463306483847 / 500000000000000 : ℚ)) - (U := (983195836613607692561 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (817463306483847 / 500000000000000 : ℝ) ≤ - (983195836613607692561 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (402560394431347 / 1000000000000000 : ℝ)) (q := - (817463306483847 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (817463306483847 / 2000000000000000 : ℚ)) + (r' := (817463306483847 / 500000000000000 : ℚ)) + (U := (-(1789392884586392307439 / 2000000000000000000000 : ℚ))) + (U' := (983195836613607692561 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (402560394431347 / 1000000000000000 : ℚ)) + (q := (817463306483847 / 2000000000000000 : ℚ)) + (U := (-(1789392884586392307439 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_9 : Uω (aρ 9) (bρ 9) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2603,25 +2298,21 @@ lemma U_466_9 : have hlg : Real.log (1842587622248539 / 5000000000000000 : ℝ) ≤ (-(9982670117907299539191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1842587622248539 / 5000000000000000 : ℝ) = - (1842587622248539 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1842587622248539 / 1250000000000000 : ℚ)) - (U := (3880273488092700460809 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1842587622248539 / 1250000000000000 : ℝ) ≤ - (3880273488092700460809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (890571749207289 / 2500000000000000 : ℝ)) (q := - (1842587622248539 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1842587622248539 / 5000000000000000 : ℚ)) + (r' := (1842587622248539 / 1250000000000000 : ℚ)) + (U := (-(9982670117907299539191 / 10000000000000000000000 : ℚ))) + (U' := (3880273488092700460809 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (890571749207289 / 2500000000000000 : ℚ)) + (q := (1842587622248539 / 5000000000000000 : ℚ)) + (U := (-(9982670117907299539191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_10 : Uω (aρ 10) (bρ 10) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2629,24 +2320,21 @@ lemma U_466_10 : have hlg : Real.log (63662900808441 / 200000000000000 : ℝ) ≤ (-(715447111252919705633 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63662900808441 / 200000000000000 : ℝ) = (63662900808441 / 50000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63662900808441 / 50000000000000 : ℚ)) - (U := (150986864122080294367 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (63662900808441 / 50000000000000 : ℝ) ≤ - (150986864122080294367 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29467856221741 / 100000000000000 : ℝ)) (q := - (63662900808441 / 200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63662900808441 / 200000000000000 : ℚ)) + (r' := (63662900808441 / 50000000000000 : ℚ)) + (U := (-(715447111252919705633 / 625000000000000000000 : ℚ))) + (U' := (150986864122080294367 / 625000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (29467856221741 / 100000000000000 : ℚ)) + (q := (63662900808441 / 200000000000000 : ℚ)) + (U := (-(715447111252919705633 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_11 : Uω (aρ 11) (bρ 11) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2654,26 +2342,21 @@ lemma U_466_11 : have hlg : Real.log (2545586826344193 / 10000000000000000 : ℝ) ≤ (-(13682238889552235011001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2545586826344193 / 10000000000000000 : ℝ) = - (2545586826344193 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2545586826344193 / 2500000000000000 : ℚ)) - (U := (180704716447764988999 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2545586826344193 / 2500000000000000 : ℝ) ≤ - (180704716447764988999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1045072910111693 / 5000000000000000 : ℝ)) (q := - (2545586826344193 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2545586826344193 / 10000000000000000 : ℚ)) + (r' := (2545586826344193 / 2500000000000000 : ℚ)) + (U := (-(13682238889552235011001 / 10000000000000000000000 : ℚ))) + (U' := (180704716447764988999 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (515561896511 / 1000000000000 : ℚ)) + (s := (1045072910111693 / 5000000000000000 : ℚ)) + (q := (2545586826344193 / 10000000000000000 : ℚ)) + (U := (-(13682238889552235011001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_466_12 : Uω (aρ 12) (bρ 12) (515561896511 / 1000000000000 : ℝ) ≤ @@ -2789,25 +2472,21 @@ lemma U_467_1 : have hlg : Real.log (20464219190211991 / 40000000000000000 : ℝ) ≤ (-(1340402996119632497453 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20464219190211991 / 40000000000000000 : ℝ) = - (20464219190211991 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20464219190211991 / 20000000000000000 : ℚ)) - (U := (45891364480367502547 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20464219190211991 / 20000000000000000 : ℝ) ≤ - (45891364480367502547 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2558011598722529 / 5000000000000000 : ℝ)) (q := - (20464219190211991 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20464219190211991 / 40000000000000000 : ℚ)) + (r' := (20464219190211991 / 20000000000000000 : ℚ)) + (U := (-(1340402996119632497453 / 2000000000000000000000 : ℚ))) + (U' := (45891364480367502547 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (2558011598722529 / 5000000000000000 : ℚ)) + (q := (20464219190211991 / 40000000000000000 : ℚ)) + (U := (-(1340402996119632497453 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_2 : Uω (aρ 2) (bρ 2) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2815,25 +2494,21 @@ lemma U_467_2 : have hlg : Real.log (20368436151556887 / 40000000000000000 : ℝ) ≤ (-(107982879792002849 / 160000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20368436151556887 / 40000000000000000 : ℝ) = - (20368436151556887 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20368436151556887 / 20000000000000000 : ℚ)) - (U := (2920669055997151 / 160000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20368436151556887 / 20000000000000000 : ℝ) ≤ - (2920669055997151 / 160000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2545950345313753 / 5000000000000000 : ℝ)) (q := - (20368436151556887 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20368436151556887 / 40000000000000000 : ℚ)) + (r' := (20368436151556887 / 20000000000000000 : ℚ)) + (U := (-(107982879792002849 / 160000000000000000 : ℚ))) + (U' := (2920669055997151 / 160000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (2545950345313753 / 5000000000000000 : ℚ)) + (q := (20368436151556887 / 40000000000000000 : ℚ)) + (U := (-(107982879792002849 / 160000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_3 : Uω (aρ 3) (bρ 3) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2841,25 +2516,21 @@ lemma U_467_3 : have hlg : Real.log (20176751806438181 / 40000000000000000 : ℝ) ≤ (-(1710871032282440537927 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20176751806438181 / 40000000000000000 : ℝ) = - (20176751806438181 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20176751806438181 / 20000000000000000 : ℚ)) - (U := (21996918467559462073 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20176751806438181 / 20000000000000000 : ℝ) ≤ - (21996918467559462073 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5043454624418153 / 10000000000000000 : ℝ)) (q := - (20176751806438181 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20176751806438181 / 40000000000000000 : ℚ)) + (r' := (20176751806438181 / 20000000000000000 : ℚ)) + (U := (-(1710871032282440537927 / 2500000000000000000000 : ℚ))) + (U' := (21996918467559462073 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (5043454624418153 / 10000000000000000 : ℚ)) + (q := (20176751806438181 / 40000000000000000 : ℚ)) + (U := (-(1710871032282440537927 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_4 : Uω (aρ 4) (bρ 4) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2867,25 +2538,21 @@ lemma U_467_4 : have hlg : Real.log (19858031797039747 / 40000000000000000 : ℝ) ≤ (-(3501354518816356370809 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19858031797039747 / 40000000000000000 : ℝ) = - (19858031797039747 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19858031797039747 / 10000000000000000 : ℚ)) - (U := (3430117284183643629191 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19858031797039747 / 10000000000000000 : ℝ) ≤ - (3430117284183643629191 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (77537325012249 / 156250000000000 : ℝ)) (q := - (19858031797039747 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19858031797039747 / 40000000000000000 : ℚ)) + (r' := (19858031797039747 / 10000000000000000 : ℚ)) + (U := (-(3501354518816356370809 / 5000000000000000000000 : ℚ))) + (U' := (3430117284183643629191 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (77537325012249 / 156250000000000 : ℚ)) + (q := (19858031797039747 / 40000000000000000 : ℚ)) + (U := (-(3501354518816356370809 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_5 : Uω (aρ 5) (bρ 5) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2893,25 +2560,21 @@ lemma U_467_5 : have hlg : Real.log (19371755092659821 / 40000000000000000 : ℝ) ≤ (-(7250633714693489879047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19371755092659821 / 40000000000000000 : ℝ) = - (19371755092659821 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19371755092659821 / 10000000000000000 : ℚ)) - (U := (6612309891306510120953 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19371755092659821 / 10000000000000000 : ℝ) ≤ - (6612309891306510120953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4837440367928973 / 10000000000000000 : ℝ)) (q := - (19371755092659821 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19371755092659821 / 40000000000000000 : ℚ)) + (r' := (19371755092659821 / 10000000000000000 : ℚ)) + (U := (-(7250633714693489879047 / 10000000000000000000000 : ℚ))) + (U' := (6612309891306510120953 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (4837440367928973 / 10000000000000000 : ℚ)) + (q := (19371755092659821 / 40000000000000000 : ℚ)) + (U := (-(7250633714693489879047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_6 : Uω (aρ 6) (bρ 6) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2919,25 +2582,21 @@ lemma U_467_6 : have hlg : Real.log (18672207568306617 / 40000000000000000 : ℝ) ≤ (-(380921630778540381131 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18672207568306617 / 40000000000000000 : ℝ) = - (18672207568306617 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18672207568306617 / 10000000000000000 : ℚ)) - (U := (312225549521459618869 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18672207568306617 / 10000000000000000 : ℝ) ≤ - (312225549521459618869 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4654906980892371 / 10000000000000000 : ℝ)) (q := - (18672207568306617 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18672207568306617 / 40000000000000000 : ℚ)) + (r' := (18672207568306617 / 10000000000000000 : ℚ)) + (U := (-(380921630778540381131 / 500000000000000000000 : ℚ))) + (U' := (312225549521459618869 / 500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (4654906980892371 / 10000000000000000 : ℚ)) + (q := (18672207568306617 / 40000000000000000 : ℚ)) + (U := (-(380921630778540381131 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_7 : Uω (aρ 7) (bρ 7) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2945,25 +2604,21 @@ lemma U_467_7 : have hlg : Real.log (17713007176213467 / 40000000000000000 : ℝ) ≤ (-(1629160430370876043877 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17713007176213467 / 40000000000000000 : ℝ) = - (17713007176213467 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17713007176213467 / 10000000000000000 : ℚ)) - (U := (1143428290829123956123 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17713007176213467 / 10000000000000000 : ℝ) ≤ - (1143428290829123956123 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1099742041401449 / 2500000000000000 : ℝ)) (q := - (17713007176213467 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17713007176213467 / 40000000000000000 : ℚ)) + (r' := (17713007176213467 / 10000000000000000 : ℚ)) + (U := (-(1629160430370876043877 / 2000000000000000000000 : ℚ))) + (U' := (1143428290829123956123 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (1099742041401449 / 2500000000000000 : ℚ)) + (q := (17713007176213467 / 40000000000000000 : ℚ)) + (U := (-(1629160430370876043877 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_8 : Uω (aρ 8) (bρ 8) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2971,25 +2626,21 @@ lemma U_467_8 : have hlg : Real.log (3290129197766279 / 8000000000000000 : ℝ) ≤ (-(4442573536579649517609 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3290129197766279 / 8000000000000000 : ℝ) = - (3290129197766279 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3290129197766279 / 2000000000000000 : ℚ)) - (U := (2488898266420350482391 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3290129197766279 / 2000000000000000 : ℝ) ≤ - (2488898266420350482391 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101283230581369 / 250000000000000 : ℝ)) (q := - (3290129197766279 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3290129197766279 / 8000000000000000 : ℚ)) + (r' := (3290129197766279 / 2000000000000000 : ℚ)) + (U := (-(4442573536579649517609 / 5000000000000000000000 : ℚ))) + (U' := (2488898266420350482391 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (101283230581369 / 250000000000000 : ℚ)) + (q := (3290129197766279 / 8000000000000000 : ℚ)) + (U := (-(4442573536579649517609 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_9 : Uω (aρ 9) (bρ 9) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -2997,25 +2648,21 @@ lemma U_467_9 : have hlg : Real.log (14843979615067633 / 40000000000000000 : ℝ) ≤ (-(4956425418371077082301 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14843979615067633 / 40000000000000000 : ℝ) = - (14843979615067633 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14843979615067633 / 10000000000000000 : ℚ)) - (U := (1975046384628922917699 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14843979615067633 / 10000000000000000 : ℝ) ≤ - (1975046384628922917699 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3588961664732879 / 10000000000000000 : ℝ)) (q := - (14843979615067633 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14843979615067633 / 40000000000000000 : ℚ)) + (r' := (14843979615067633 / 10000000000000000 : ℚ)) + (U := (-(4956425418371077082301 / 5000000000000000000000 : ℚ))) + (U' := (1975046384628922917699 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (3588961664732879 / 10000000000000000 : ℚ)) + (q := (14843979615067633 / 40000000000000000 : ℚ)) + (U := (-(4956425418371077082301 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_10 : Uω (aρ 10) (bρ 10) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -3023,26 +2670,21 @@ lemma U_467_10 : have hlg : Real.log (12840375760971143 / 40000000000000000 : ℝ) ≤ (-(5681424454436483179861 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12840375760971143 / 40000000000000000 : ℝ) = - (12840375760971143 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12840375760971143 / 10000000000000000 : ℚ)) - (U := (1250047348563516820139 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12840375760971143 / 10000000000000000 : ℝ) ≤ - (1250047348563516820139 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1487859385589817 / 5000000000000000 : ℝ)) (q := - (12840375760971143 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12840375760971143 / 40000000000000000 : ℚ)) + (r' := (12840375760971143 / 10000000000000000 : ℚ)) + (U := (-(5681424454436483179861 / 5000000000000000000000 : ℚ))) + (U' := (1250047348563516820139 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (1487859385589817 / 5000000000000000 : ℚ)) + (q := (12840375760971143 / 40000000000000000 : ℚ)) + (U := (-(5681424454436483179861 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_11 : Uω (aρ 11) (bρ 11) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -3050,26 +2692,21 @@ lemma U_467_11 : have hlg : Real.log (10303653818006349 / 40000000000000000 : ℝ) ≤ (-(13563808816514087504783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10303653818006349 / 40000000000000000 : ℝ) = - (10303653818006349 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10303653818006349 / 10000000000000000 : ℚ)) - (U := (299134789485912495217 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10303653818006349 / 10000000000000000 : ℝ) ≤ - (299134789485912495217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2125834425902237 / 10000000000000000 : ℝ)) (q := - (10303653818006349 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10303653818006349 / 40000000000000000 : ℚ)) + (r' := (10303653818006349 / 10000000000000000 : ℚ)) + (U := (-(13563808816514087504783 / 10000000000000000000000 : ℚ))) + (U' := (299134789485912495217 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (2125834425902237 / 10000000000000000 : ℚ)) + (q := (10303653818006349 / 40000000000000000 : ℚ)) + (U := (-(13563808816514087504783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_12 : Uω (aρ 12) (bρ 12) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -3077,26 +2714,21 @@ lemma U_467_12 : have hlg : Real.log (5923771554627799 / 40000000000000000 : ℝ) ≤ (-(2387382650451925792207 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5923771554627799 / 40000000000000000 : ℝ) = - (5923771554627799 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5923771554627799 / 5000000000000000 : ℚ)) - (U := (211919275673074207793 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5923771554627799 / 5000000000000000 : ℝ) ≤ - (211919275673074207793 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (179796695448981 / 5000000000000000 : ℝ)) (q := - (5923771554627799 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5923771554627799 / 40000000000000000 : ℚ)) + (r' := (5923771554627799 / 5000000000000000 : ℚ)) + (U := (-(2387382650451925792207 / 1250000000000000000000 : ℚ))) + (U' := (211919275673074207793 / 1250000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (16577867570387 / 32000000000000 : ℚ)) + (s := (179796695448981 / 5000000000000000 : ℚ)) + (q := (5923771554627799 / 40000000000000000 : ℚ)) + (U := (-(2387382650451925792207 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_467_13 : Uω (aρ 13) (bρ 13) (16577867570387 / 32000000000000 : ℝ) ≤ @@ -3208,25 +2840,21 @@ lemma U_468_1 : have hlg : Real.log (10282039203278277 / 20000000000000000 : ℝ) ≤ (-(3326668334306610783819 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10282039203278277 / 20000000000000000 : ℝ) = - (10282039203278277 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10282039203278277 / 10000000000000000 : ℚ)) - (U := (139067567193389216181 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10282039203278277 / 10000000000000000 : ℝ) ≤ - (139067567193389216181 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2570494077490701 / 5000000000000000 : ℝ)) (q := - (10282039203278277 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10282039203278277 / 20000000000000000 : ℚ)) + (r' := (10282039203278277 / 10000000000000000 : ℚ)) + (U := (-(3326668334306610783819 / 5000000000000000000000 : ℚ))) + (U' := (139067567193389216181 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (2570494077490701 / 5000000000000000 : ℚ)) + (q := (10282039203278277 / 20000000000000000 : ℚ)) + (U := (-(3326668334306610783819 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_2 : Uω (aρ 2) (bρ 2) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3234,25 +2862,21 @@ lemma U_468_2 : have hlg : Real.log (10234149410058897 / 20000000000000000 : ℝ) ≤ (-(6700021636373269278519 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10234149410058897 / 20000000000000000 : ℝ) = - (10234149410058897 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10234149410058897 / 10000000000000000 : ℚ)) - (U := (231450166626730721481 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10234149410058897 / 10000000000000000 : ℝ) ≤ - (231450166626730721481 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2558433687136011 / 5000000000000000 : ℝ)) (q := - (10234149410058897 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10234149410058897 / 20000000000000000 : ℚ)) + (r' := (10234149410058897 / 10000000000000000 : ℚ)) + (U := (-(6700021636373269278519 / 10000000000000000000000 : ℚ))) + (U' := (231450166626730721481 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (2558433687136011 / 5000000000000000 : ℚ)) + (q := (10234149410058897 / 20000000000000000 : ℚ)) + (U := (-(6700021636373269278519 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_3 : Uω (aρ 3) (bρ 3) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3260,25 +2884,21 @@ lemma U_468_3 : have hlg : Real.log (10138312428535819 / 20000000000000000 : ℝ) ≤ (-(6794107161476389452203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10138312428535819 / 20000000000000000 : ℝ) = - (10138312428535819 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10138312428535819 / 10000000000000000 : ℚ)) - (U := (137364641523610547797 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10138312428535819 / 10000000000000000 : ℝ) ≤ - (137364641523610547797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79194164048421 / 156250000000000 : ℝ)) (q := - (10138312428535819 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10138312428535819 / 20000000000000000 : ℚ)) + (r' := (10138312428535819 / 10000000000000000 : ℚ)) + (U := (-(6794107161476389452203 / 10000000000000000000000 : ℚ))) + (U' := (137364641523610547797 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (79194164048421 / 156250000000000 : ℚ)) + (q := (10138312428535819 / 20000000000000000 : ℚ)) + (U := (-(6794107161476389452203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_4 : Uω (aρ 4) (bρ 4) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3286,25 +2906,21 @@ lemma U_468_4 : have hlg : Real.log (9978966414926927 / 20000000000000000 : ℝ) ≤ (-(695252753712603288749 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9978966414926927 / 20000000000000000 : ℝ) = - (9978966414926927 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9978966414926927 / 5000000000000000 : ℚ)) - (U := (691041606887396711251 / 1000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9978966414926927 / 5000000000000000 : ℝ) ≤ - (691041606887396711251 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1246843666638763 / 2500000000000000 : ℝ)) (q := - (9978966414926927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9978966414926927 / 20000000000000000 : ℚ)) + (r' := (9978966414926927 / 5000000000000000 : ℚ)) + (U := (-(695252753712603288749 / 1000000000000000000000 : ℚ))) + (U' := (691041606887396711251 / 1000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (1246843666638763 / 2500000000000000 : ℚ)) + (q := (9978966414926927 / 20000000000000000 : ℚ)) + (U := (-(695252753712603288749 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_5 : Uω (aρ 5) (bρ 5) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3312,25 +2928,21 @@ lemma U_468_5 : have hlg : Real.log (194717266146073 / 400000000000000 : ℝ) ≤ (-(1439831914742107004137 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (194717266146073 / 400000000000000 : ℝ) = - (194717266146073 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194717266146073 / 100000000000000 : ℚ)) - (U := (1332756806457892995863 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (194717266146073 / 100000000000000 : ℝ) ≤ - (1332756806457892995863 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (194498459130671 / 400000000000000 : ℝ)) (q := - (194717266146073 / 400000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194717266146073 / 400000000000000 : ℚ)) + (r' := (194717266146073 / 100000000000000 : ℚ)) + (U := (-(1439831914742107004137 / 2000000000000000000000 : ℚ))) + (U' := (1332756806457892995863 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (194498459130671 / 400000000000000 : ℚ)) + (q := (194717266146073 / 400000000000000 : ℚ)) + (U := (-(1439831914742107004137 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_6 : Uω (aρ 6) (bρ 6) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3338,25 +2950,21 @@ lemma U_468_6 : have hlg : Real.log (9386173325681481 / 20000000000000000 : ℝ) ≤ (-(1512989178853868331933 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9386173325681481 / 20000000000000000 : ℝ) = - (9386173325681481 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9386173325681481 / 5000000000000000 : ℚ)) - (U := (1259599542346131668067 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9386173325681481 / 5000000000000000 : ℝ) ≤ - (1259599542346131668067 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2340005935892303 / 5000000000000000 : ℝ)) (q := - (9386173325681481 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9386173325681481 / 20000000000000000 : ℚ)) + (r' := (9386173325681481 / 5000000000000000 : ℚ)) + (U := (-(1512989178853868331933 / 2000000000000000000000 : ℚ))) + (U' := (1259599542346131668067 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (2340005935892303 / 5000000000000000 : ℚ)) + (q := (9386173325681481 / 20000000000000000 : ℚ)) + (U := (-(1512989178853868331933 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_7 : Uω (aρ 7) (bρ 7) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3364,25 +2972,21 @@ lemma U_468_7 : have hlg : Real.log (4453381688665273 / 10000000000000000 : ℝ) ≤ (-(8089213548594952910653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4453381688665273 / 10000000000000000 : ℝ) = - (4453381688665273 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4453381688665273 / 2500000000000000 : ℚ)) - (U := (5773730057405047089347 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4453381688665273 / 2500000000000000 : ℝ) ≤ - (5773730057405047089347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4424263304193671 / 10000000000000000 : ℝ)) (q := - (4453381688665273 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4453381688665273 / 10000000000000000 : ℚ)) + (r' := (4453381688665273 / 2500000000000000 : ℚ)) + (U := (-(8089213548594952910653 / 10000000000000000000000 : ℚ))) + (U' := (5773730057405047089347 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (4424263304193671 / 10000000000000000 : ℚ)) + (q := (4453381688665273 / 10000000000000000 : ℚ)) + (U := (-(8089213548594952910653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_8 : Uω (aρ 8) (bρ 8) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3390,25 +2994,21 @@ lemma U_468_8 : have hlg : Real.log (165520069342137 / 400000000000000 : ℝ) ≤ (-(8823720942157960686819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (165520069342137 / 400000000000000 : ℝ) = - (165520069342137 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (165520069342137 / 100000000000000 : ℚ)) - (U := (5039222663842039313181 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (165520069342137 / 100000000000000 : ℝ) ≤ - (5039222663842039313181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (163081801812399 / 400000000000000 : ℝ)) (q := - (165520069342137 / 400000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (165520069342137 / 400000000000000 : ℚ)) + (r' := (165520069342137 / 100000000000000 : ℚ)) + (U := (-(8823720942157960686819 / 10000000000000000000000 : ℚ))) + (U' := (5039222663842039313181 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (163081801812399 / 400000000000000 : ℚ)) + (q := (165520069342137 / 400000000000000 : ℚ)) + (U := (-(8823720942157960686819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_9 : Uω (aρ 9) (bρ 9) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3416,25 +3016,21 @@ lemma U_468_9 : have hlg : Real.log (1494720940629161 / 4000000000000000 : ℝ) ≤ (-(9843548329673441358901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1494720940629161 / 4000000000000000 : ℝ) = - (1494720940629161 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1494720940629161 / 1000000000000000 : ℚ)) - (U := (4019395276326558641099 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1494720940629161 / 1000000000000000 : ℝ) ≤ - (4019395276326558641099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (361561190970893 / 1000000000000000 : ℝ)) (q := - (1494720940629161 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1494720940629161 / 4000000000000000 : ℚ)) + (r' := (1494720940629161 / 1000000000000000 : ℚ)) + (U := (-(9843548329673441358901 / 10000000000000000000000 : ℚ))) + (U' := (4019395276326558641099 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (361561190970893 / 1000000000000000 : ℚ)) + (q := (1494720940629161 / 4000000000000000 : ℚ)) + (U := (-(9843548329673441358901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_10 : Uω (aρ 10) (bρ 10) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3442,25 +3038,21 @@ lemma U_468_10 : have hlg : Real.log (258960579675723 / 800000000000000 : ℝ) ≤ (-(1409919848820797437973 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (258960579675723 / 800000000000000 : ℝ) = - (258960579675723 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (258960579675723 / 200000000000000 : ℚ)) - (U := (322948101929202562027 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (258960579675723 / 200000000000000 : ℝ) ≤ - (322948101929202562027 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3755725914939 / 12500000000000 : ℝ)) (q := - (258960579675723 / 800000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (258960579675723 / 800000000000000 : ℚ)) + (r' := (258960579675723 / 200000000000000 : ℚ)) + (U := (-(1409919848820797437973 / 1250000000000000000000 : ℚ))) + (U' := (322948101929202562027 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (3755725914939 / 12500000000000 : ℚ)) + (q := (258960579675723 / 800000000000000 : ℚ)) + (U := (-(1409919848820797437973 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_11 : Uω (aρ 11) (bρ 11) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3468,26 +3060,21 @@ lemma U_468_11 : have hlg : Real.log (2606089612812773 / 10000000000000000 : ℝ) ≤ (-(13447342272511465768649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2606089612812773 / 10000000000000000 : ℝ) = - (2606089612812773 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2606089612812773 / 2500000000000000 : ℚ)) - (U := (415601333488534231351 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2606089612812773 / 2500000000000000 : ℝ) ≤ - (415601333488534231351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2161222091888671 / 10000000000000000 : ℝ)) (q := - (2606089612812773 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2606089612812773 / 10000000000000000 : ℚ)) + (r' := (2606089612812773 / 2500000000000000 : ℚ)) + (U := (-(13447342272511465768649 / 10000000000000000000000 : ℚ))) + (U' := (415601333488534231351 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (2161222091888671 / 10000000000000000 : ℚ)) + (q := (2606089612812773 / 10000000000000000 : ℚ)) + (U := (-(13447342272511465768649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_12 : Uω (aρ 12) (bρ 12) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3495,25 +3082,21 @@ lemma U_468_12 : have hlg : Real.log (784255736301877 / 5000000000000000 : ℝ) ≤ (-(18524580292131774241723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (784255736301877 / 5000000000000000 : ℝ) = - (784255736301877 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (784255736301877 / 625000000000000 : ℚ)) - (U := (2269835116868225758277 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (784255736301877 / 625000000000000 : ℝ) ≤ - (2269835116868225758277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (509765908155633 / 10000000000000000 : ℝ)) (q := - (784255736301877 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (784255736301877 / 5000000000000000 : ℚ)) + (r' := (784255736301877 / 625000000000000 : ℚ)) + (U := (-(18524580292131774241723 / 10000000000000000000000 : ℚ))) + (U' := (2269835116868225758277 / 10000000000000000000000 : ℚ)) + 3 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8328877226211 / 16000000000000 : ℚ)) + (s := (509765908155633 / 10000000000000000 : ℚ)) + (q := (784255736301877 / 5000000000000000 : ℚ)) + (U := (-(18524580292131774241723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_468_13 : Uω (aρ 13) (bρ 13) (8328877226211 / 16000000000000 : ℝ) ≤ @@ -3626,25 +3209,21 @@ lemma U_469_1 : have hlg : Real.log (20663937616968653 / 40000000000000000 : ℝ) ≤ (-(1651223542470804826287 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20663937616968653 / 40000000000000000 : ℝ) = - (20663937616968653 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20663937616968653 / 20000000000000000 : ℚ)) - (U := (81644408279195173713 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20663937616968653 / 20000000000000000 : ℝ) ≤ - (81644408279195173713 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2582976554775757 / 5000000000000000 : ℝ)) (q := - (20663937616968653 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20663937616968653 / 40000000000000000 : ℚ)) + (r' := (20663937616968653 / 20000000000000000 : ℚ)) + (U := (-(1651223542470804826287 / 2500000000000000000000 : ℚ))) + (U' := (81644408279195173713 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (2582976554775757 / 5000000000000000 : ℚ)) + (q := (20663937616968653 / 40000000000000000 : ℚ)) + (U := (-(1651223542470804826287 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_2 : Uω (aρ 2) (bρ 2) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3652,25 +3231,21 @@ lemma U_469_2 : have hlg : Real.log (20568161449194411 / 40000000000000000 : ℝ) ≤ (-(1330270268776452498909 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20568161449194411 / 40000000000000000 : ℝ) = - (20568161449194411 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20568161449194411 / 20000000000000000 : ℚ)) - (U := (56024091823547501091 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20568161449194411 / 20000000000000000 : ℝ) ≤ - (56024091823547501091 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5141834038174393 / 10000000000000000 : ℝ)) (q := - (20568161449194411 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20568161449194411 / 40000000000000000 : ℚ)) + (r' := (20568161449194411 / 20000000000000000 : ℚ)) + (U := (-(1330270268776452498909 / 2000000000000000000000 : ℚ))) + (U' := (56024091823547501091 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (5141834038174393 / 10000000000000000 : ℚ)) + (q := (20568161449194411 / 40000000000000000 : ℚ)) + (U := (-(1330270268776452498909 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_3 : Uω (aρ 3) (bρ 3) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3678,25 +3253,21 @@ lemma U_469_3 : have hlg : Real.log (4075299553210723 / 8000000000000000 : ℝ) ≤ (-(337248643719215027449 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4075299553210723 / 8000000000000000 : ℝ) = - (4075299553210723 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4075299553210723 / 4000000000000000 : ℚ)) - (U := (9324946430784972551 / 500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4075299553210723 / 4000000000000000 : ℝ) ≤ - (9324946430784972551 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1018679660590799 / 2000000000000000 : ℝ)) (q := - (4075299553210723 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4075299553210723 / 8000000000000000 : ℚ)) + (r' := (4075299553210723 / 4000000000000000 : ℚ)) + (U := (-(337248643719215027449 / 500000000000000000000 : ℚ))) + (U' := (9324946430784972551 / 500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (1018679660590799 / 2000000000000000 : ℚ)) + (q := (4075299553210723 / 8000000000000000 : ℚ)) + (U := (-(337248643719215027449 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_4 : Uω (aρ 4) (bρ 4) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3704,25 +3275,21 @@ lemma U_469_4 : have hlg : Real.log (20057833439830469 / 40000000000000000 : ℝ) ≤ (-(3451298405747701115753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20057833439830469 / 40000000000000000 : ℝ) = - (20057833439830469 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20057833439830469 / 20000000000000000 : ℚ)) - (U := (14437495752298884247 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20057833439830469 / 20000000000000000 : ℝ) ≤ - (14437495752298884247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2506180160453711 / 5000000000000000 : ℝ)) (q := - (20057833439830469 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20057833439830469 / 40000000000000000 : ℚ)) + (r' := (20057833439830469 / 20000000000000000 : ℚ)) + (U := (-(3451298405747701115753 / 5000000000000000000000 : ℚ))) + (U' := (14437495752298884247 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (2506180160453711 / 5000000000000000 : ℚ)) + (q := (20057833439830469 / 40000000000000000 : ℚ)) + (U := (-(3451298405747701115753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_5 : Uω (aρ 5) (bρ 5) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3730,25 +3297,21 @@ lemma U_469_5 : have hlg : Real.log (3914339396338771 / 8000000000000000 : ℝ) ≤ (-(7147949625221588208791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3914339396338771 / 8000000000000000 : ℝ) = - (3914339396338771 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3914339396338771 / 2000000000000000 : ℚ)) - (U := (6714993980778411791209 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3914339396338771 / 2000000000000000 : ℝ) ≤ - (6714993980778411791209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (977496402234823 / 2000000000000000 : ℝ)) (q := - (3914339396338771 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3914339396338771 / 8000000000000000 : ℚ)) + (r' := (3914339396338771 / 2000000000000000 : ℚ)) + (U := (-(7147949625221588208791 / 10000000000000000000000 : ℚ))) + (U' := (6714993980778411791209 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (977496402234823 / 2000000000000000 : ℚ)) + (q := (3914339396338771 / 8000000000000000 : ℚ)) + (U := (-(7147949625221588208791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_6 : Uω (aρ 6) (bρ 6) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3756,25 +3319,21 @@ lemma U_469_6 : have hlg : Real.log (18872482749682987 / 40000000000000000 : ℝ) ≤ (-(3755872658039831526277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18872482749682987 / 40000000000000000 : ℝ) = - (18872482749682987 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18872482749682987 / 10000000000000000 : ℚ)) - (U := (3175599144960168473723 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18872482749682987 / 10000000000000000 : ℝ) ≤ - (3175599144960168473723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4705115270308681 / 10000000000000000 : ℝ)) (q := - (18872482749682987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18872482749682987 / 40000000000000000 : ℚ)) + (r' := (18872482749682987 / 10000000000000000 : ℚ)) + (U := (-(3755872658039831526277 / 5000000000000000000000 : ℚ))) + (U' := (3175599144960168473723 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (4705115270308681 / 10000000000000000 : ℚ)) + (q := (18872482749682987 / 40000000000000000 : ℚ)) + (U := (-(3755872658039831526277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_7 : Uω (aρ 7) (bρ 7) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3782,25 +3341,21 @@ lemma U_469_7 : have hlg : Real.log (17914038867081701 / 40000000000000000 : ℝ) ≤ (-(8032947538949810997407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17914038867081701 / 40000000000000000 : ℝ) = - (17914038867081701 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17914038867081701 / 10000000000000000 : ℚ)) - (U := (5829996067050189002593 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17914038867081701 / 10000000000000000 : ℝ) ≤ - (5829996067050189002593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2224777354884019 / 5000000000000000 : ℝ)) (q := - (17914038867081701 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17914038867081701 / 40000000000000000 : ℚ)) + (r' := (17914038867081701 / 10000000000000000 : ℚ)) + (U := (-(8032947538949810997407 / 10000000000000000000000 : ℚ))) + (U' := (5829996067050189002593 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (2224777354884019 / 5000000000000000 : ℚ)) + (q := (17914038867081701 / 40000000000000000 : ℚ)) + (U := (-(8032947538949810997407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_8 : Uω (aρ 8) (bρ 8) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3808,25 +3363,21 @@ lemma U_469_8 : have hlg : Real.log (16653349321475323 / 40000000000000000 : ℝ) ≤ (-(8762680969486746709881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16653349321475323 / 40000000000000000 : ℝ) = - (16653349321475323 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16653349321475323 / 10000000000000000 : ℚ)) - (U := (5100262636513253290119 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16653349321475323 / 10000000000000000 : ℝ) ≤ - (5100262636513253290119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4102751588304849 / 10000000000000000 : ℝ)) (q := - (16653349321475323 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16653349321475323 / 40000000000000000 : ℚ)) + (r' := (16653349321475323 / 10000000000000000 : ℚ)) + (U := (-(8762680969486746709881 / 10000000000000000000000 : ℚ))) + (U' := (5100262636513253290119 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (4102751588304849 / 10000000000000000 : ℚ)) + (q := (16653349321475323 / 40000000000000000 : ℚ)) + (U := (-(8762680969486746709881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_9 : Uω (aρ 9) (bρ 9) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3834,25 +3385,21 @@ lemma U_469_9 : have hlg : Real.log (15050391423875193 / 40000000000000000 : ℝ) ≤ (-(9774754545064592874979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15050391423875193 / 40000000000000000 : ℝ) = - (15050391423875193 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15050391423875193 / 10000000000000000 : ℚ)) - (U := (4088189060935407125021 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15050391423875193 / 10000000000000000 : ℝ) ≤ - (4088189060935407125021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (227639891741549 / 625000000000000 : ℝ)) (q := - (15050391423875193 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15050391423875193 / 40000000000000000 : ℚ)) + (r' := (15050391423875193 / 10000000000000000 : ℚ)) + (U := (-(9774754545064592874979 / 10000000000000000000000 : ℚ))) + (U' := (4088189060935407125021 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (227639891741549 / 625000000000000 : ℚ)) + (q := (15050391423875193 / 40000000000000000 : ℚ)) + (U := (-(9774754545064592874979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_10 : Uω (aρ 10) (bρ 10) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3860,26 +3407,21 @@ lemma U_469_10 : have hlg : Real.log (13055543894188003 / 40000000000000000 : ℝ) ≤ (-(2799166476393955032353 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13055543894188003 / 40000000000000000 : ℝ) = - (13055543894188003 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13055543894188003 / 10000000000000000 : ℚ)) - (U := (666569425106044967647 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13055543894188003 / 10000000000000000 : ℝ) ≤ - (666569425106044967647 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3033373536516189 / 10000000000000000 : ℝ)) (q := - (13055543894188003 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13055543894188003 / 40000000000000000 : ℚ)) + (r' := (13055543894188003 / 10000000000000000 : ℚ)) + (U := (-(2799166476393955032353 / 2500000000000000000000 : ℚ))) + (U' := (666569425106044967647 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (3033373536516189 / 10000000000000000 : ℚ)) + (q := (13055543894188003 / 40000000000000000 : ℚ)) + (U := (-(2799166476393955032353 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_11 : Uω (aρ 11) (bρ 11) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3887,26 +3429,21 @@ lemma U_469_11 : have hlg : Real.log (2108898059612717 / 8000000000000000 : ℝ) ≤ (-(3333189941798207716189 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2108898059612717 / 8000000000000000 : ℝ) = - (2108898059612717 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2108898059612717 / 2000000000000000 : ℚ)) - (U := (132545959701792283811 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2108898059612717 / 2000000000000000 : ℝ) ≤ - (132545959701792283811 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109816168232949 / 500000000000000 : ℝ)) (q := - (2108898059612717 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2108898059612717 / 8000000000000000 : ℚ)) + (r' := (2108898059612717 / 2000000000000000 : ℚ)) + (U := (-(3333189941798207716189 / 2500000000000000000000 : ℚ))) + (U' := (132545959701792283811 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (109816168232949 / 500000000000000 : ℚ)) + (q := (2108898059612717 / 8000000000000000 : ℚ)) + (U := (-(3333189941798207716189 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_12 : Uω (aρ 12) (bρ 12) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -3914,26 +3451,21 @@ lemma U_469_12 : have hlg : Real.log (6556100873289057 / 40000000000000000 : ℝ) ≤ (-(18084834061631598644507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6556100873289057 / 40000000000000000 : ℝ) = - (6556100873289057 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6556100873289057 / 5000000000000000 : ℚ)) - (U := (2709581347368401355493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6556100873289057 / 5000000000000000 : ℝ) ≤ - (2709581347368401355493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156457187239179 / 2500000000000000 : ℝ)) (q := - (6556100873289057 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6556100873289057 / 40000000000000000 : ℚ)) + (r' := (6556100873289057 / 5000000000000000 : ℚ)) + (U := (-(18084834061631598644507 / 10000000000000000000000 : ℚ))) + (U' := (2709581347368401355493 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (16737641334457 / 32000000000000 : ℚ)) + (s := (156457187239179 / 2500000000000000 : ℚ)) + (q := (6556100873289057 / 40000000000000000 : ℚ)) + (U := (-(18084834061631598644507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_469_13 : Uω (aρ 13) (bρ 13) (16737641334457 / 32000000000000 : ℝ) ≤ @@ -4046,25 +3578,21 @@ lemma U_470_1 : have hlg : Real.log (41427734439953681 / 80000000000000000 : ℝ) ≤ (-(1316152127732697187741 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41427734439953681 / 80000000000000000 : ℝ) = - (41427734439953681 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41427734439953681 / 40000000000000000 : ℚ)) - (U := (70142232867302812259 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41427734439953681 / 40000000000000000 : ℝ) ≤ - (70142232867302812259 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5178435585737639 / 10000000000000000 : ℝ)) (q := - (41427734439953681 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41427734439953681 / 80000000000000000 : ℚ)) + (r' := (41427734439953681 / 40000000000000000 : ℚ)) + (U := (-(1316152127732697187741 / 2000000000000000000000 : ℚ))) + (U' := (70142232867302812259 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (5178435585737639 / 10000000000000000 : ℚ)) + (q := (41427734439953681 / 80000000000000000 : ℚ)) + (U := (-(1316152127732697187741 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_2 : Uω (aρ 2) (bρ 2) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4072,25 +3600,21 @@ lemma U_470_2 : have hlg : Real.log (1649447419928433 / 3200000000000000 : ℝ) ≤ (-(1656776186842113214311 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1649447419928433 / 3200000000000000 : ℝ) = - (1649447419928433 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1649447419928433 / 1600000000000000 : ℚ)) - (U := (76091763907886785689 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1649447419928433 / 1600000000000000 : ℝ) ≤ - (76091763907886785689 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (206172694512477 / 400000000000000 : ℝ)) (q := - (1649447419928433 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1649447419928433 / 3200000000000000 : ℚ)) + (r' := (1649447419928433 / 1600000000000000 : ℚ)) + (U := (-(1656776186842113214311 / 2500000000000000000000 : ℚ))) + (U' := (76091763907886785689 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (206172694512477 / 400000000000000 : ℚ)) + (q := (1649447419928433 / 3200000000000000 : ℚ)) + (U := (-(1656776186842113214311 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_3 : Uω (aρ 3) (bρ 3) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4098,25 +3622,21 @@ lemma U_470_3 : have hlg : Real.log (40852868336149581 / 80000000000000000 : ℝ) ≤ (-(6720495992657626363703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40852868336149581 / 80000000000000000 : ℝ) = - (40852868336149581 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40852868336149581 / 40000000000000000 : ℚ)) - (U := (210975810342373636297 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40852868336149581 / 40000000000000000 : ℝ) ≤ - (210975810342373636297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2552942089323307 / 5000000000000000 : ℝ)) (q := - (40852868336149581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40852868336149581 / 80000000000000000 : ℚ)) + (r' := (40852868336149581 / 40000000000000000 : ℚ)) + (U := (-(6720495992657626363703 / 10000000000000000000000 : ℚ))) + (U' := (210975810342373636297 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (2552942089323307 / 5000000000000000 : ℚ)) + (q := (40852868336149581 / 80000000000000000 : ℚ)) + (U := (-(6720495992657626363703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_4 : Uω (aρ 4) (bρ 4) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4124,25 +3644,21 @@ lemma U_470_4 : have hlg : Real.log (40215567176451669 / 80000000000000000 : ℝ) ≤ (-(1719431176382352272803 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40215567176451669 / 80000000000000000 : ℝ) = - (40215567176451669 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40215567176451669 / 40000000000000000 : ℚ)) - (U := (13436774367647727197 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40215567176451669 / 40000000000000000 : ℝ) ≤ - (13436774367647727197 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1226770768991 / 2441406250000 : ℝ)) (q := - (40215567176451669 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40215567176451669 / 80000000000000000 : ℚ)) + (r' := (40215567176451669 / 40000000000000000 : ℚ)) + (U := (-(1719431176382352272803 / 2500000000000000000000 : ℚ))) + (U' := (13436774367647727197 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (1226770768991 / 2441406250000 : ℚ)) + (q := (40215567176451669 / 80000000000000000 : ℚ)) + (U := (-(1719431176382352272803 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_5 : Uω (aρ 5) (bρ 5) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4150,25 +3666,21 @@ lemma U_470_5 : have hlg : Real.log (39243363475385473 / 80000000000000000 : ℝ) ≤ (-(3561221438257288238383 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39243363475385473 / 80000000000000000 : ℝ) = - (39243363475385473 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39243363475385473 / 20000000000000000 : ℚ)) - (U := (3370250364742711761617 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39243363475385473 / 20000000000000000 : ℝ) ≤ - (3370250364742711761617 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4899992063855587 / 10000000000000000 : ℝ)) (q := - (39243363475385473 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39243363475385473 / 80000000000000000 : ℚ)) + (r' := (39243363475385473 / 20000000000000000 : ℚ)) + (U := (-(3561221438257288238383 / 5000000000000000000000 : ℚ))) + (U' := (3370250364742711761617 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (4899992063855587 / 10000000000000000 : ℚ)) + (q := (39243363475385473 / 80000000000000000 : ℚ)) + (U := (-(3561221438257288238383 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_6 : Uω (aρ 6) (bρ 6) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4176,25 +3688,21 @@ lemma U_470_6 : have hlg : Real.log (7569019877782629 / 16000000000000000 : ℝ) ≤ (-(7485251371864224695571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7569019877782629 / 16000000000000000 : ℝ) = - (7569019877782629 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7569019877782629 / 4000000000000000 : ℚ)) - (U := (6377692234135775304429 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7569019877782629 / 4000000000000000 : ℝ) ≤ - (6377692234135775304429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (943533283475501 / 2000000000000000 : ℝ)) (q := - (7569019877782629 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7569019877782629 / 16000000000000000 : ℚ)) + (r' := (7569019877782629 / 4000000000000000 : ℚ)) + (U := (-(7485251371864224695571 / 10000000000000000000000 : ℚ))) + (U' := (6377692234135775304429 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (943533283475501 / 2000000000000000 : ℚ)) + (q := (7569019877782629 / 16000000000000000 : ℚ)) + (U := (-(7485251371864224695571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_7 : Uω (aρ 7) (bρ 7) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4202,25 +3710,21 @@ lemma U_470_7 : have hlg : Real.log (35928584326409349 / 80000000000000000 : ℝ) ≤ (-(8004934346840263548131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35928584326409349 / 80000000000000000 : ℝ) = - (35928584326409349 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35928584326409349 / 20000000000000000 : ℚ)) - (U := (5858009259159736451869 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35928584326409349 / 20000000000000000 : ℝ) ≤ - (5858009259159736451869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1115549758127889 / 2500000000000000 : ℝ)) (q := - (35928584326409349 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35928584326409349 / 80000000000000000 : ℚ)) + (r' := (35928584326409349 / 20000000000000000 : ℚ)) + (U := (-(8004934346840263548131 / 10000000000000000000000 : ℚ))) + (U' := (5858009259159736451869 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (1115549758127889 / 2500000000000000 : ℚ)) + (q := (35928584326409349 / 80000000000000000 : ℚ)) + (U := (-(8004934346840263548131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_8 : Uω (aρ 8) (bρ 8) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4228,25 +3732,21 @@ lemma U_470_8 : have hlg : Real.log (33408027328974557 / 80000000000000000 : ℝ) ≤ (-(2183076059643294649347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33408027328974557 / 80000000000000000 : ℝ) = - (33408027328974557 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33408027328974557 / 20000000000000000 : ℚ)) - (U := (1282659841856705350653 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33408027328974557 / 20000000000000000 : ℝ) ≤ - (1282659841856705350653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2057800717246429 / 5000000000000000 : ℝ)) (q := - (33408027328974557 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33408027328974557 / 80000000000000000 : ℚ)) + (r' := (33408027328974557 / 20000000000000000 : ℚ)) + (U := (-(2183076059643294649347 / 2500000000000000000000 : ℚ))) + (U' := (1282659841856705350653 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (2057800717246429 / 5000000000000000 : ℚ)) + (q := (33408027328974557 / 80000000000000000 : ℚ)) + (U := (-(2183076059643294649347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_9 : Uω (aρ 9) (bρ 9) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4254,25 +3754,21 @@ lemma U_470_9 : have hlg : Real.log (30203929687630289 / 80000000000000000 : ℝ) ≤ (-(9740545961313508592881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30203929687630289 / 80000000000000000 : ℝ) = - (30203929687630289 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30203929687630289 / 20000000000000000 : ℚ)) - (U := (4122397644686491407119 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30203929687630289 / 20000000000000000 : ℝ) ≤ - (4122397644686491407119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3655542652516791 / 10000000000000000 : ℝ)) (q := - (30203929687630289 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30203929687630289 / 80000000000000000 : ℚ)) + (r' := (30203929687630289 / 20000000000000000 : ℚ)) + (U := (-(9740545961313508592881 / 10000000000000000000000 : ℚ))) + (U' := (4122397644686491407119 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (3655542652516791 / 10000000000000000 : ℚ)) + (q := (30203929687630289 / 80000000000000000 : ℚ)) + (U := (-(9740545961313508592881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_10 : Uω (aρ 10) (bρ 10) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4280,26 +3776,21 @@ lemma U_470_10 : have hlg : Real.log (5243700283042729 / 16000000000000000 : ℝ) ≤ (-(139445163964400578137 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5243700283042729 / 16000000000000000 : ℝ) = - (5243700283042729 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5243700283042729 / 4000000000000000 : ℚ)) - (U := (33841631110599421863 / 125000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5243700283042729 / 4000000000000000 : ℝ) ≤ - (33841631110599421863 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (304774461790763 / 1000000000000000 : ℝ)) (q := - (5243700283042729 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5243700283042729 / 16000000000000000 : ℚ)) + (r' := (5243700283042729 / 4000000000000000 : ℚ)) + (U := (-(139445163964400578137 / 125000000000000000000 : ℚ))) + (U' := (33841631110599421863 / 125000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (304774461790763 / 1000000000000000 : ℚ)) + (q := (5243700283042729 / 16000000000000000 : ℚ)) + (U := (-(139445163964400578137 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_11 : Uω (aρ 11) (bρ 11) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4307,26 +3798,21 @@ lemma U_470_11 : have hlg : Real.log (4241739979860997 / 16000000000000000 : ℝ) ≤ (-(13276151640471082417553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4241739979860997 / 16000000000000000 : ℝ) = - (4241739979860997 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4241739979860997 / 4000000000000000 : ℚ)) - (U := (586791965528917582447 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4241739979860997 / 4000000000000000 : ℝ) ≤ - (586791965528917582447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (442754173027093 / 2000000000000000 : ℝ)) (q := - (4241739979860997 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4241739979860997 / 16000000000000000 : ℚ)) + (r' := (4241739979860997 / 4000000000000000 : ℚ)) + (U := (-(13276151640471082417553 / 10000000000000000000000 : ℚ))) + (U' := (586791965528917582447 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (442754173027093 / 2000000000000000 : ℚ)) + (q := (4241739979860997 / 16000000000000000 : ℚ)) + (U := (-(13276151640471082417553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_12 : Uω (aρ 12) (bρ 12) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4334,26 +3820,21 @@ lemma U_470_12 : have hlg : Real.log (13365930292119409 / 80000000000000000 : ℝ) ≤ (-(17893176801322932681187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13365930292119409 / 80000000000000000 : ℝ) = - (13365930292119409 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13365930292119409 / 10000000000000000 : ℚ)) - (U := (2901238607677067318813 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13365930292119409 / 10000000000000000 : ℝ) ≤ - (2901238607677067318813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (676778560024071 / 10000000000000000 : ℝ)) (q := - (13365930292119409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13365930292119409 / 80000000000000000 : ℚ)) + (r' := (13365930292119409 / 10000000000000000 : ℚ)) + (U := (-(17893176801322932681187 / 10000000000000000000000 : ℚ))) + (U' := (2901238607677067318813 / 10000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (33555169550949 / 64000000000000 : ℚ)) + (s := (676778560024071 / 10000000000000000 : ℚ)) + (q := (13365930292119409 / 80000000000000000 : ℚ)) + (U := (-(17893176801322932681187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_470_13 : Uω (aρ 13) (bρ 13) (33555169550949 / 64000000000000 : ℝ) ≤ @@ -4465,25 +3946,21 @@ lemma U_471_1 : have hlg : Real.log (10381898410766941 / 20000000000000000 : ℝ) ≤ (-(6556685210681737118977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10381898410766941 / 20000000000000000 : ℝ) = - (10381898410766941 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10381898410766941 / 10000000000000000 : ℚ)) - (U := (374786592318262881023 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10381898410766941 / 10000000000000000 : ℝ) ≤ - (374786592318262881023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5190918061198191 / 10000000000000000 : ℝ)) (q := - (10381898410766941 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10381898410766941 / 20000000000000000 : ℚ)) + (r' := (10381898410766941 / 10000000000000000 : ℚ)) + (U := (-(6556685210681737118977 / 10000000000000000000000 : ℚ))) + (U' := (374786592318262881023 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (5190918061198191 / 10000000000000000 : ℚ)) + (q := (10381898410766941 / 20000000000000000 : ℚ)) + (U := (-(6556685210681737118977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_2 : Uω (aρ 2) (bρ 2) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4491,25 +3968,21 @@ lemma U_471_2 : have hlg : Real.log (258350300491989 / 500000000000000 : ℝ) ≤ (-(6602916803099730944047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (258350300491989 / 500000000000000 : ℝ) = - (258350300491989 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (258350300491989 / 250000000000000 : ℚ)) - (U := (328554999900269055953 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (258350300491989 / 250000000000000 : ℝ) ≤ - (328554999900269055953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (516680068262081 / 1000000000000000 : ℝ)) (q := - (258350300491989 / 500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (258350300491989 / 500000000000000 : ℚ)) + (r' := (258350300491989 / 250000000000000 : ℚ)) + (U := (-(6602916803099730944047 / 10000000000000000000000 : ℚ))) + (U' := (328554999900269055953 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (516680068262081 / 1000000000000000 : ℚ)) + (q := (258350300491989 / 500000000000000 : ℚ)) + (U := (-(6602916803099730944047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_3 : Uω (aρ 3) (bρ 3) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4517,25 +3990,21 @@ lemma U_471_3 : have hlg : Real.log (2047637053545741 / 4000000000000000 : ℝ) ≤ (-(1339215778672726434163 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2047637053545741 / 4000000000000000 : ℝ) = - (2047637053545741 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2047637053545741 / 2000000000000000 : ℚ)) - (U := (47078581927273565837 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2047637053545741 / 2000000000000000 : ℝ) ≤ - (47078581927273565837 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1023674007403991 / 2000000000000000 : ℝ)) (q := - (2047637053545741 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2047637053545741 / 4000000000000000 : ℚ)) + (r' := (2047637053545741 / 2000000000000000 : ℚ)) + (U := (-(1339215778672726434163 / 2000000000000000000000 : ℚ))) + (U' := (47078581927273565837 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (1023674007403991 / 2000000000000000 : ℚ)) + (q := (2047637053545741 / 4000000000000000 : ℚ)) + (U := (-(1339215778672726434163 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_4 : Uω (aρ 4) (bρ 4) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4543,25 +4012,21 @@ lemma U_471_4 : have hlg : Real.log (251971670415769 / 500000000000000 : ℝ) ≤ (-(6852914359553545011063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (251971670415769 / 500000000000000 : ℝ) = - (251971670415769 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (251971670415769 / 250000000000000 : ℚ)) - (U := (78557443446454988937 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (251971670415769 / 250000000000000 : ℝ) ≤ - (78557443446454988937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (503734576698701 / 1000000000000000 : ℝ)) (q := - (251971670415769 / 500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (251971670415769 / 500000000000000 : ℚ)) + (r' := (251971670415769 / 250000000000000 : ℚ)) + (U := (-(6852914359553545011063 / 10000000000000000000000 : ℚ))) + (U' := (78557443446454988937 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (503734576698701 / 1000000000000000 : ℚ)) + (q := (251971670415769 / 500000000000000 : ℚ)) + (U := (-(6852914359553545011063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_5 : Uω (aρ 5) (bρ 5) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4569,25 +4034,21 @@ lemma U_471_5 : have hlg : Real.log (9835833105782713 / 20000000000000000 : ℝ) ≤ (-(7097001165159826073773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9835833105782713 / 20000000000000000 : ℝ) = - (9835833105782713 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9835833105782713 / 5000000000000000 : ℚ)) - (U := (6765942440840173926227 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9835833105782713 / 5000000000000000 : ℝ) ≤ - (6765942440840173926227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4912501975473963 / 10000000000000000 : ℝ)) (q := - (9835833105782713 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9835833105782713 / 20000000000000000 : ℚ)) + (r' := (9835833105782713 / 5000000000000000 : ℚ)) + (U := (-(7097001165159826073773 / 10000000000000000000000 : ℚ))) + (U' := (6765942440840173926227 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (4912501975473963 / 10000000000000000 : ℚ)) + (q := (9835833105782713 / 20000000000000000 : ℚ)) + (U := (-(7097001165159826073773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_6 : Uω (aρ 6) (bρ 6) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4595,25 +4056,21 @@ lemma U_471_6 : have hlg : Real.log (9486307955393467 / 20000000000000000 : ℝ) ≤ (-(3729413909532381592127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9486307955393467 / 20000000000000000 : ℝ) = - (9486307955393467 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9486307955393467 / 5000000000000000 : ℚ)) - (U := (3202057893467618407873 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9486307955393467 / 5000000000000000 : ℝ) ≤ - (3202057893467618407873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4730217200224717 / 10000000000000000 : ℝ)) (q := - (9486307955393467 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9486307955393467 / 20000000000000000 : ℚ)) + (r' := (9486307955393467 / 5000000000000000 : ℚ)) + (U := (-(3729413909532381592127 / 5000000000000000000000 : ℚ))) + (U' := (3202057893467618407873 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (4730217200224717 / 10000000000000000 : ℚ)) + (q := (9486307955393467 / 20000000000000000 : ℚ)) + (U := (-(3729413909532381592127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_7 : Uω (aρ 7) (bρ 7) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4621,25 +4078,21 @@ lemma U_471_7 : have hlg : Real.log (9007271820033613 / 20000000000000000 : ℝ) ≤ (-(15580078944028729029 / 19531250000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9007271820033613 / 20000000000000000 : ℝ) = - (9007271820033613 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9007271820033613 / 5000000000000000 : ℚ)) - (U := (11495982786440020971 / 19531250000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9007271820033613 / 5000000000000000 : ℝ) ≤ - (11495982786440020971 / 19531250000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4474842445624863 / 10000000000000000 : ℝ)) (q := - (9007271820033613 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9007271820033613 / 20000000000000000 : ℚ)) + (r' := (9007271820033613 / 5000000000000000 : ℚ)) + (U := (-(15580078944028729029 / 19531250000000000000 : ℚ))) + (U' := (11495982786440020971 / 19531250000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (4474842445624863 / 10000000000000000 : ℚ)) + (q := (9007271820033613 / 20000000000000000 : ℚ)) + (U := (-(15580078944028729029 / 19531250000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_8 : Uω (aρ 8) (bρ 8) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4647,25 +4100,21 @@ lemma U_471_8 : have hlg : Real.log (2094334187160359 / 5000000000000000 : ℝ) ≤ (-(8702022194771938875817 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2094334187160359 / 5000000000000000 : ℝ) = - (2094334187160359 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2094334187160359 / 1250000000000000 : ℚ)) - (U := (5160921411228061124183 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2094334187160359 / 1250000000000000 : ℝ) ≤ - (5160921411228061124183 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2064224512786343 / 5000000000000000 : ℝ)) (q := - (2094334187160359 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2094334187160359 / 5000000000000000 : ℚ)) + (r' := (2094334187160359 / 1250000000000000 : ℚ)) + (U := (-(8702022194771938875817 / 10000000000000000000000 : ℚ))) + (U' := (5160921411228061124183 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (2064224512786343 / 5000000000000000 : ℚ)) + (q := (2094334187160359 / 5000000000000000 : ℚ)) + (U := (-(8702022194771938875817 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_9 : Uω (aρ 9) (bρ 9) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4673,25 +4122,21 @@ lemma U_471_9 : have hlg : Real.log (1515352670795999 / 4000000000000000 : ℝ) ≤ (-(9706461627251655129437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1515352670795999 / 4000000000000000 : ℝ) = - (1515352670795999 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1515352670795999 / 1000000000000000 : ℚ)) - (U := (4156481978748344870563 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1515352670795999 / 1000000000000000 : ℝ) ≤ - (4156481978748344870563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (733768251854249 / 2000000000000000 : ℝ)) (q := - (1515352670795999 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1515352670795999 / 4000000000000000 : ℚ)) + (r' := (1515352670795999 / 1000000000000000 : ℚ)) + (U := (-(9706461627251655129437 / 10000000000000000000000 : ℚ))) + (U' := (4156481978748344870563 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (733768251854249 / 2000000000000000 : ℚ)) + (q := (1515352670795999 / 4000000000000000 : ℚ)) + (U := (-(9706461627251655129437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_10 : Uω (aρ 10) (bρ 10) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4699,26 +4144,21 @@ lemma U_471_10 : have hlg : Real.log (1645365549227177 / 5000000000000000 : ℝ) ≤ (-(2778688335021342273317 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1645365549227177 / 5000000000000000 : ℝ) = - (1645365549227177 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1645365549227177 / 1250000000000000 : ℚ)) - (U := (687047566478657726683 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1645365549227177 / 1250000000000000 : ℝ) ≤ - (687047566478657726683 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1531049567847479 / 5000000000000000 : ℝ)) (q := - (1645365549227177 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1645365549227177 / 5000000000000000 : ℚ)) + (r' := (1645365549227177 / 1250000000000000 : ℚ)) + (U := (-(2778688335021342273317 / 2500000000000000000000 : ℚ))) + (U' := (687047566478657726683 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (1531049567847479 / 5000000000000000 : ℚ)) + (q := (1645365549227177 / 5000000000000000 : ℚ)) + (U := (-(2778688335021342273317 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_11 : Uω (aρ 11) (bρ 11) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4726,26 +4166,21 @@ lemma U_471_11 : have hlg : Real.log (5332038196182559 / 20000000000000000 : ℝ) ≤ (-(6609993535840864133789 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5332038196182559 / 20000000000000000 : ℝ) = - (5332038196182559 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5332038196182559 / 5000000000000000 : ℚ)) - (U := (321478267159135866211 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5332038196182559 / 5000000000000000 : ℝ) ≤ - (321478267159135866211 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2231151761173809 / 10000000000000000 : ℝ)) (q := - (5332038196182559 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5332038196182559 / 20000000000000000 : ℚ)) + (r' := (5332038196182559 / 5000000000000000 : ℚ)) + (U := (-(6609993535840864133789 / 5000000000000000000000 : ℚ))) + (U' := (321478267159135866211 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (2231151761173809 / 10000000000000000 : ℚ)) + (q := (5332038196182559 / 20000000000000000 : ℚ)) + (U := (-(6609993535840864133789 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_12 : Uω (aρ 12) (bρ 12) (4204382054123 / 8000000000000 : ℝ) ≤ @@ -4753,25 +4188,21 @@ lemma U_471_12 : have hlg : Real.log (340155394699111 / 2000000000000000 : ℝ) ≤ (-(3542999804663610854087 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (340155394699111 / 2000000000000000 : ℝ) = - (340155394699111 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (340155394699111 / 250000000000000 : ℚ)) - (U := (615883277136389145913 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (340155394699111 / 250000000000000 : ℝ) ≤ - (615883277136389145913 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4527297554171 / 62500000000000 : ℝ)) (q := - (340155394699111 / 2000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (340155394699111 / 2000000000000000 : ℚ)) + (r' := (340155394699111 / 250000000000000 : ℚ)) + (U := (-(3542999804663610854087 / 2000000000000000000000 : ℚ))) + (U' := (615883277136389145913 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4204382054123 / 8000000000000 : ℚ)) + (s := (4527297554171 / 62500000000000 : ℚ)) + (q := (340155394699111 / 2000000000000000 : ℚ)) + (U := (-(3542999804663610854087 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_471_13 : Uω (aρ 13) (bρ 13) (4204382054123 / 8000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U39.lean b/LeanPool/Zeta5Irrational/Table/U39.lean index caf636a1b2..bc23161093 100644 --- a/LeanPool/Zeta5Irrational/Table/U39.lean +++ b/LeanPool/Zeta5Irrational/Table/U39.lean @@ -24,25 +24,21 @@ lemma U_472_1 : have hlg : Real.log (8325490568660087 / 16000000000000000 : ℝ) ≤ (-(3266333803415444261449 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8325490568660087 / 16000000000000000 : ℝ) = - (8325490568660087 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8325490568660087 / 8000000000000000 : ℚ)) - (U := (199402098084555738551 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8325490568660087 / 8000000000000000 : ℝ) ≤ - (199402098084555738551 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (520340053593839 / 1000000000000000 : ℝ)) (q := - (8325490568660087 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8325490568660087 / 16000000000000000 : ℚ)) + (r' := (8325490568660087 / 8000000000000000 : ℚ)) + (U := (-(3266333803415444261449 / 5000000000000000000000 : ℚ))) + (U' := (199402098084555738551 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (520340053593839 / 1000000000000000 : ℚ)) + (q := (8325490568660087 / 16000000000000000 : ℚ)) + (U := (-(3266333803415444261449 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_2 : Uω (aρ 2) (bρ 2) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_472_2 : have hlg : Real.log (41435910640050719 / 80000000000000000 : ℝ) ≤ (-(3289393613990012216949 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41435910640050719 / 80000000000000000 : ℝ) = - (41435910640050719 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41435910640050719 / 40000000000000000 : ℚ)) - (U := (176342287509987783051 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41435910640050719 / 40000000000000000 : ℝ) ≤ - (176342287509987783051 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5179283997635961 / 10000000000000000 : ℝ)) (q := - (41435910640050719 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41435910640050719 / 80000000000000000 : ℚ)) + (r' := (41435910640050719 / 40000000000000000 : ℚ)) + (U := (-(3289393613990012216949 / 5000000000000000000000 : ℚ))) + (U' := (176342287509987783051 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (5179283997635961 / 10000000000000000 : ℚ)) + (q := (41435910640050719 / 80000000000000000 : ℚ)) + (U := (-(3289393613990012216949 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_3 : Uω (aρ 3) (bρ 3) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_472_3 : have hlg : Real.log (41052613736908707 / 80000000000000000 : ℝ) ≤ (-(3335860642552980259753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41052613736908707 / 80000000000000000 : ℝ) = - (41052613736908707 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41052613736908707 / 40000000000000000 : ℚ)) - (U := (129875258947019740247 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41052613736908707 / 40000000000000000 : ℝ) ≤ - (129875258947019740247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2565427939100229 / 5000000000000000 : ℝ)) (q := - (41052613736908707 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41052613736908707 / 80000000000000000 : ℚ)) + (r' := (41052613736908707 / 40000000000000000 : ℚ)) + (U := (-(3335860642552980259753 / 5000000000000000000000 : ℚ))) + (U' := (129875258947019740247 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (2565427939100229 / 5000000000000000 : ℚ)) + (q := (41052613736908707 / 80000000000000000 : ℚ)) + (U := (-(3335860642552980259753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_4 : Uω (aρ 4) (bρ 4) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_472_4 : have hlg : Real.log (40415367151409243 / 80000000000000000 : ℝ) ≤ (-(853520683420242002753 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40415367151409243 / 80000000000000000 : ℝ) = - (40415367151409243 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40415367151409243 / 40000000000000000 : ℚ)) - (U := (12913291954757997247 / 1250000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40415367151409243 / 40000000000000000 : ℝ) ≤ - (12913291954757997247 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (157807450402831 / 312500000000000 : ℝ)) (q := - (40415367151409243 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40415367151409243 / 80000000000000000 : ℚ)) + (r' := (40415367151409243 / 40000000000000000 : ℚ)) + (U := (-(853520683420242002753 / 1250000000000000000000 : ℚ))) + (U' := (12913291954757997247 / 1250000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (157807450402831 / 312500000000000 : ℚ)) + (q := (40415367151409243 / 80000000000000000 : ℚ)) + (U := (-(853520683420242002753 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_5 : Uω (aρ 5) (bρ 5) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_472_5 : have hlg : Real.log (39443300810923579 / 80000000000000000 : ℝ) ≤ (-(3535812079804980335119 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39443300810923579 / 80000000000000000 : ℝ) = - (39443300810923579 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39443300810923579 / 20000000000000000 : ℚ)) - (U := (3395659723195019664881 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39443300810923579 / 20000000000000000 : ℝ) ≤ - (3395659723195019664881 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (307813234194011 / 625000000000000 : ℝ)) (q := - (39443300810923579 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39443300810923579 / 80000000000000000 : ℚ)) + (r' := (39443300810923579 / 20000000000000000 : ℚ)) + (U := (-(3535812079804980335119 / 5000000000000000000000 : ℚ))) + (U' := (3395659723195019664881 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (307813234194011 / 625000000000000 : ℚ)) + (q := (39443300810923579 / 80000000000000000 : ℚ)) + (U := (-(3535812079804980335119 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_6 : Uω (aρ 6) (bρ 6) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_472_6 : have hlg : Real.log (7609072561782843 / 16000000000000000 : ℝ) ≤ (-(743247428260968271397 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7609072561782843 / 16000000000000000 : ℝ) = - (7609072561782843 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7609072561782843 / 4000000000000000 : ℚ)) - (U := (643046932339031728603 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7609072561782843 / 4000000000000000 : ℝ) ≤ - (643046932339031728603 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (948553524348367 / 2000000000000000 : ℝ)) (q := - (7609072561782843 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7609072561782843 / 16000000000000000 : ℚ)) + (r' := (7609072561782843 / 4000000000000000 : ℚ)) + (U := (-(743247428260968271397 / 1000000000000000000000 : ℚ))) + (U' := (643046932339031728603 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (948553524348367 / 2000000000000000 : ℚ)) + (q := (7609072561782843 / 16000000000000000 : ℚ)) + (U := (-(743247428260968271397 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_7 : Uω (aρ 7) (bρ 7) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_472_7 : have hlg : Real.log (7225917325218623 / 16000000000000000 : ℝ) ≤ (-(397457265176319725381 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7225917325218623 / 16000000000000000 : ℝ) = - (7225917325218623 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7225917325218623 / 4000000000000000 : ℚ)) - (U := (295689915123680274619 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7225917325218623 / 4000000000000000 : ℝ) ≤ - (295689915123680274619 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56093561959957 / 125000000000000 : ℝ)) (q := - (7225917325218623 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7225917325218623 / 16000000000000000 : ℚ)) + (r' := (7225917325218623 / 4000000000000000 : ℚ)) + (U := (-(397457265176319725381 / 500000000000000000000 : ℚ))) + (U' := (295689915123680274619 / 500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (56093561959957 / 125000000000000 : ℚ)) + (q := (7225917325218623 / 16000000000000000 : ℚ)) + (U := (-(397457265176319725381 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_8 : Uω (aρ 8) (bρ 8) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_472_8 : have hlg : Real.log (33610657723676827 / 80000000000000000 : ℝ) ≤ (-(8671834233232153227217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33610657723676827 / 80000000000000000 : ℝ) = - (33610657723676827 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33610657723676827 / 20000000000000000 : ℚ)) - (U := (5191109372767846772783 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33610657723676827 / 20000000000000000 : ℝ) ≤ - (5191109372767846772783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (517661797816561 / 1250000000000000 : ℝ)) (q := - (33610657723676827 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33610657723676827 / 80000000000000000 : ℚ)) + (r' := (33610657723676827 / 20000000000000000 : ℚ)) + (U := (-(8671834233232153227217 / 10000000000000000000000 : ℚ))) + (U' := (5191109372767846772783 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (517661797816561 / 1250000000000000 : ℚ)) + (q := (33610657723676827 / 80000000000000000 : ℚ)) + (U := (-(8671834233232153227217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_9 : Uω (aρ 9) (bρ 9) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_472_9 : have hlg : Real.log (30410154283032899 / 80000000000000000 : ℝ) ≤ (-(1209062573808391051687 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30410154283032899 / 80000000000000000 : ℝ) = - (30410154283032899 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30410154283032899 / 20000000000000000 : ℚ)) - (U := (523805376941608948313 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30410154283032899 / 20000000000000000 : ℝ) ≤ - (523805376941608948313 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1841067075365753 / 5000000000000000 : ℝ)) (q := - (30410154283032899 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30410154283032899 / 80000000000000000 : ℚ)) + (r' := (30410154283032899 / 20000000000000000 : ℚ)) + (U := (-(1209062573808391051687 / 1250000000000000000000 : ℚ))) + (U' := (523805376941608948313 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (1841067075365753 / 5000000000000000 : ℚ)) + (q := (30410154283032899 / 80000000000000000 : ℚ)) + (U := (-(1209062573808391051687 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_10 : Uω (aρ 10) (bρ 10) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_472_10 : have hlg : Real.log (5286626166611991 / 16000000000000000 : ℝ) ≤ (-(11074084550028256930173 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5286626166611991 / 16000000000000000 : ℝ) = - (5286626166611991 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5286626166611991 / 4000000000000000 : ℚ)) - (U := (2788859055971743069827 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5286626166611991 / 4000000000000000 : ℝ) ≤ - (2788859055971743069827 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (307643732173327 / 1000000000000000 : ℝ)) (q := - (5286626166611991 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5286626166611991 / 16000000000000000 : ℚ)) + (r' := (5286626166611991 / 4000000000000000 : ℚ)) + (U := (-(11074084550028256930173 / 10000000000000000000000 : ℚ))) + (U' := (2788859055971743069827 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (307643732173327 / 1000000000000000 : ℚ)) + (q := (5286626166611991 / 16000000000000000 : ℚ)) + (U := (-(11074084550028256930173 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_11 : Uω (aρ 11) (bρ 11) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_472_11 : have hlg : Real.log (21447345430718583 / 80000000000000000 : ℝ) ≤ (-(263285150516408844729 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21447345430718583 / 80000000000000000 : ℝ) = - (21447345430718583 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21447345430718583 / 20000000000000000 : ℚ)) - (U := (13973721603591155271 / 200000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21447345430718583 / 20000000000000000 : ℝ) ≤ - (13973721603591155271 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2248467597352927 / 10000000000000000 : ℝ)) (q := - (21447345430718583 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21447345430718583 / 80000000000000000 : ℚ)) + (r' := (21447345430718583 / 20000000000000000 : ℚ)) + (U := (-(263285150516408844729 / 200000000000000000000 : ℚ))) + (U' := (13973721603591155271 / 200000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (2248467597352927 / 10000000000000000 : ℚ)) + (q := (21447345430718583 / 80000000000000000 : ℚ)) + (U := (-(263285150516408844729 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_12 : Uω (aρ 12) (bρ 12) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_472_12 : have hlg : Real.log (13835554275365503 / 80000000000000000 : ℝ) ≤ (-(3509569916371714106323 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (13835554275365503 / 80000000000000000 : ℝ) = - (13835554275365503 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13835554275365503 / 10000000000000000 : ℚ)) - (U := (649313165428285893677 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13835554275365503 / 10000000000000000 : ℝ) ≤ - (649313165428285893677 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (769219905199657 / 10000000000000000 : ℝ)) (q := - (13835554275365503 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13835554275365503 / 80000000000000000 : ℚ)) + (r' := (13835554275365503 / 10000000000000000 : ℚ)) + (U := (-(3509569916371714106323 / 2000000000000000000000 : ℚ))) + (U' := (649313165428285893677 / 2000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (33714943315019 / 64000000000000 : ℚ)) + (s := (769219905199657 / 10000000000000000 : ℚ)) + (q := (13835554275365503 / 80000000000000000 : ℚ)) + (U := (-(3509569916371714106323 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_472_13 : Uω (aρ 13) (bρ 13) (33714943315019 / 64000000000000 : ℝ) ≤ @@ -443,25 +392,21 @@ lemma U_473_1 : have hlg : Real.log (4172731204067239 / 8000000000000000 : ℝ) ≤ (-(6508707550010153423257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4172731204067239 / 8000000000000000 : ℝ) = - (4172731204067239 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4172731204067239 / 4000000000000000 : ℚ)) - (U := (422764252989846576743 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4172731204067239 / 4000000000000000 : ℝ) ≤ - (422764252989846576743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (521588300996341 / 1000000000000000 : ℝ)) (q := - (4172731204067239 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4172731204067239 / 8000000000000000 : ℚ)) + (r' := (4172731204067239 / 4000000000000000 : ℚ)) + (U := (-(6508707550010153423257 / 10000000000000000000000 : ℚ))) + (U' := (422764252989846576743 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (521588300996341 / 1000000000000000 : ℚ)) + (q := (4172731204067239 / 8000000000000000 : ℚ)) + (U := (-(6508707550010153423257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_2 : Uω (aρ 2) (bρ 2) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -469,25 +414,21 @@ lemma U_473_2 : have hlg : Real.log (20767886591173289 / 40000000000000000 : ℝ) ≤ (-(3277357870479055754481 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20767886591173289 / 40000000000000000 : ℝ) = - (20767886591173289 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20767886591173289 / 20000000000000000 : ℚ)) - (U := (188378031020944245519 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20767886591173289 / 20000000000000000 : ℝ) ≤ - (188378031020944245519 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5191767307891957 / 10000000000000000 : ℝ)) (q := - (20767886591173289 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20767886591173289 / 40000000000000000 : ℚ)) + (r' := (20767886591173289 / 20000000000000000 : ℚ)) + (U := (-(3277357870479055754481 / 5000000000000000000000 : ℚ))) + (U' := (188378031020944245519 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (5191767307891957 / 10000000000000000 : ℚ)) + (q := (20767886591173289 / 40000000000000000 : ℚ)) + (U := (-(3277357870479055754481 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_3 : Uω (aρ 3) (bρ 3) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -495,25 +436,21 @@ lemma U_473_3 : have hlg : Real.log (20576243167316043 / 40000000000000000 : ℝ) ≤ (-(830927859826774090171 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20576243167316043 / 40000000000000000 : ℝ) = - (20576243167316043 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20576243167316043 / 20000000000000000 : ℚ)) - (U := (35506115548225909829 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20576243167316043 / 20000000000000000 : ℝ) ≤ - (35506115548225909829 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2571670851156667 / 5000000000000000 : ℝ)) (q := - (20576243167316043 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20576243167316043 / 40000000000000000 : ℚ)) + (r' := (20576243167316043 / 20000000000000000 : ℚ)) + (U := (-(830927859826774090171 / 1250000000000000000000 : ℚ))) + (U' := (35506115548225909829 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (2571670851156667 / 5000000000000000 : ℚ)) + (q := (20576243167316043 / 40000000000000000 : ℚ)) + (U := (-(830927859826774090171 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_4 : Uω (aρ 4) (bρ 4) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -521,25 +458,21 @@ lemma U_473_4 : have hlg : Real.log (20257633416314663 / 40000000000000000 : ℝ) ≤ (-(6803477725022190286487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20257633416314663 / 40000000000000000 : ℝ) = - (20257633416314663 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20257633416314663 / 20000000000000000 : ℚ)) - (U := (127994077977809713513 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20257633416314663 / 20000000000000000 : ℝ) ≤ - (127994077977809713513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1265582751969411 / 2500000000000000 : ℝ)) (q := - (20257633416314663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20257633416314663 / 40000000000000000 : ℚ)) + (r' := (20257633416314663 / 20000000000000000 : ℚ)) + (U := (-(6803477725022190286487 / 10000000000000000000000 : ℚ))) + (U' := (127994077977809713513 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (1265582751969411 / 2500000000000000 : ℚ)) + (q := (20257633416314663 / 40000000000000000 : ℚ)) + (U := (-(6803477725022190286487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_5 : Uω (aρ 5) (bρ 5) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -547,25 +480,21 @@ lemma U_473_5 : have hlg : Real.log (19771634321509881 / 40000000000000000 : ℝ) ≤ (-(704631153085188042397 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19771634321509881 / 40000000000000000 : ℝ) = - (19771634321509881 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19771634321509881 / 10000000000000000 : ℚ)) - (U := (681663207514811957603 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19771634321509881 / 10000000000000000 : ℝ) ≤ - (681663207514811957603 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4937521379810253 / 10000000000000000 : ℝ)) (q := - (19771634321509881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19771634321509881 / 40000000000000000 : ℚ)) + (r' := (19771634321509881 / 10000000000000000 : ℚ)) + (U := (-(704631153085188042397 / 1000000000000000000000 : ℚ))) + (U' := (681663207514811957603 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (4937521379810253 / 10000000000000000 : ℚ)) + (q := (19771634321509881 / 40000000000000000 : ℚ)) + (U := (-(704631153085188042397 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_6 : Uω (aρ 6) (bρ 6) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -573,25 +502,21 @@ lemma U_473_6 : have hlg : Real.log (19072746181188913 / 40000000000000000 : ℝ) ≤ (-(7406190390433035913379 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19072746181188913 / 40000000000000000 : ℝ) = - (19072746181188913 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19072746181188913 / 10000000000000000 : ℚ)) - (U := (6456753215566964086621 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19072746181188913 / 10000000000000000 : ℝ) ≤ - (6456753215566964086621 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4755317684789769 / 10000000000000000 : ℝ)) (q := - (19072746181188913 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19072746181188913 / 40000000000000000 : ℚ)) + (r' := (19072746181188913 / 10000000000000000 : ℚ)) + (U := (-(7406190390433035913379 / 10000000000000000000000 : ℚ))) + (U' := (6456753215566964086621 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (4755317684789769 / 10000000000000000 : ℚ)) + (q := (19072746181188913 / 40000000000000000 : ℚ)) + (U := (-(7406190390433035913379 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_7 : Uω (aρ 7) (bρ 7) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -599,25 +524,21 @@ lemma U_473_7 : have hlg : Real.log (3623008239469197 / 8000000000000000 : ℝ) ≤ (-(7921368550378337604691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3623008239469197 / 8000000000000000 : ℝ) = - (3623008239469197 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3623008239469197 / 2000000000000000 : ℚ)) - (U := (5941575055621662395309 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3623008239469197 / 2000000000000000 : ℝ) ≤ - (5941575055621662395309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (900025314725661 / 2000000000000000 : ℝ)) (q := - (3623008239469197 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3623008239469197 / 8000000000000000 : ℚ)) + (r' := (3623008239469197 / 2000000000000000 : ℚ)) + (U := (-(7921368550378337604691 / 10000000000000000000000 : ℚ))) + (U' := (5941575055621662395309 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (900025314725661 / 2000000000000000 : ℚ)) + (q := (3623008239469197 / 8000000000000000 : ℚ)) + (U := (-(7921368550378337604691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_8 : Uω (aρ 8) (bρ 8) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -625,25 +546,21 @@ lemma U_473_8 : have hlg : Real.log (16855979799603761 / 40000000000000000 : ℝ) ≤ (-(4320869877513572204633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16855979799603761 / 40000000000000000 : ℝ) = - (16855979799603761 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16855979799603761 / 10000000000000000 : ℚ)) - (U := (2610601925486427795367 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16855979799603761 / 10000000000000000 : ℝ) ≤ - (2610601925486427795367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4154137526097193 / 10000000000000000 : ℝ)) (q := - (16855979799603761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16855979799603761 / 40000000000000000 : ℚ)) + (r' := (16855979799603761 / 10000000000000000 : ℚ)) + (U := (-(4320869877513572204633 / 5000000000000000000000 : ℚ))) + (U' := (2610601925486427795367 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (4154137526097193 / 10000000000000000 : ℚ)) + (q := (16855979799603761 / 40000000000000000 : ℚ)) + (U := (-(4320869877513572204633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_9 : Uω (aρ 9) (bρ 9) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -651,25 +568,21 @@ lemma U_473_9 : have hlg : Real.log (610264650713451 / 1600000000000000 : ℝ) ≤ (-(1927732381998579928349 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (610264650713451 / 1600000000000000 : ℝ) = - (610264650713451 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (610264650713451 / 400000000000000 : ℚ)) - (U := (844856339201420071651 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (610264650713451 / 400000000000000 : ℝ) ≤ - (844856339201420071651 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (73908427771469 / 200000000000000 : ℝ)) (q := - (610264650713451 / 1600000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (610264650713451 / 1600000000000000 : ℚ)) + (r' := (610264650713451 / 400000000000000 : ℚ)) + (U := (-(1927732381998579928349 / 2000000000000000000000 : ℚ))) + (U' := (844856339201420071651 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (73908427771469 / 200000000000000 : ℚ)) + (q := (610264650713451 / 1600000000000000 : ℚ)) + (U := (-(1927732381998579928349 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_10 : Uω (aρ 10) (bρ 10) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -677,26 +590,21 @@ lemma U_473_10 : have hlg : Real.log (13270174230327283 / 40000000000000000 : ℝ) ≤ (-(11033604756957846854013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13270174230327283 / 40000000000000000 : ℝ) = - (13270174230327283 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13270174230327283 / 10000000000000000 : ℚ)) - (U := (2829338849042153145987 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13270174230327283 / 10000000000000000 : ℝ) ≤ - (2829338849042153145987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1545379701656977 / 5000000000000000 : ℝ)) (q := - (13270174230327283 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13270174230327283 / 40000000000000000 : ℚ)) + (r' := (13270174230327283 / 10000000000000000 : ℚ)) + (U := (-(11033604756957846854013 / 10000000000000000000000 : ℚ))) + (U' := (2829338849042153145987 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (1545379701656977 / 5000000000000000 : ℚ)) + (q := (13270174230327283 / 40000000000000000 : ℚ)) + (U := (-(11033604756957846854013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_11 : Uω (aρ 11) (bρ 11) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -704,26 +612,21 @@ lemma U_473_11 : have hlg : Real.log (10783141901968263 / 40000000000000000 : ℝ) ≤ (-(262179094799017356733 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10783141901968263 / 40000000000000000 : ℝ) = - (10783141901968263 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10783141901968263 / 10000000000000000 : ℚ)) - (U := (15079777320982643267 / 200000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10783141901968263 / 10000000000000000 : ℝ) ≤ - (15079777320982643267 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (566429966334861 / 2500000000000000 : ℝ)) (q := - (10783141901968263 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10783141901968263 / 40000000000000000 : ℚ)) + (r' := (10783141901968263 / 10000000000000000 : ℚ)) + (U := (-(262179094799017356733 / 200000000000000000000 : ℚ))) + (U' := (15079777320982643267 / 200000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (566429966334861 / 2500000000000000 : ℚ)) + (q := (10783141901968263 / 40000000000000000 : ℚ)) + (U := (-(262179094799017356733 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_12 : Uω (aρ 12) (bρ 12) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -731,26 +634,21 @@ lemma U_473_12 : have hlg : Real.log (7027880383189607 / 40000000000000000 : ℝ) ≤ (-(17389943031897199826591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7027880383189607 / 40000000000000000 : ℝ) = - (7027880383189607 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7027880383189607 / 5000000000000000 : ℚ)) - (U := (3404472377102800173409 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7027880383189607 / 5000000000000000 : ℝ) ≤ - (3404472377102800173409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (202947300658779 / 2500000000000000 : ℝ)) (q := - (7027880383189607 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7027880383189607 / 40000000000000000 : ℚ)) + (r' := (7027880383189607 / 5000000000000000 : ℚ)) + (U := (-(17389943031897199826591 / 10000000000000000000000 : ℚ))) + (U' := (3404472377102800173409 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (16897415098527 / 32000000000000 : ℚ)) + (s := (202947300658779 / 2500000000000000 : ℚ)) + (q := (7027880383189607 / 40000000000000000 : ℚ)) + (U := (-(17389943031897199826591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_473_13 : Uω (aρ 13) (bρ 13) (16897415098527 / 32000000000000 : ℝ) ≤ @@ -861,25 +759,21 @@ lemma U_474_1 : have hlg : Real.log (41827171235204113 / 80000000000000000 : ℝ) ≤ (-(25939219060423466283 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41827171235204113 / 80000000000000000 : ℝ) = - (41827171235204113 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41827171235204113 / 40000000000000000 : ℚ)) - (U := (1786668151576533717 / 40000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41827171235204113 / 40000000000000000 : ℝ) ≤ - (1786668151576533717 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1307091370819593 / 2500000000000000 : ℝ)) (q := - (41827171235204113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41827171235204113 / 80000000000000000 : ℚ)) + (r' := (41827171235204113 / 40000000000000000 : ℚ)) + (U := (-(25939219060423466283 / 40000000000000000000 : ℚ))) + (U' := (1786668151576533717 / 40000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (1307091370819593 / 2500000000000000 : ℚ)) + (q := (41827171235204113 / 80000000000000000 : ℚ)) + (U := (-(25939219060423466283 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_2 : Uω (aρ 2) (bρ 2) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -887,25 +781,21 @@ lemma U_474_2 : have hlg : Real.log (8327127141148561 / 16000000000000000 : ℝ) ≤ (-(1306140412601594962099 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8327127141148561 / 16000000000000000 : ℝ) = - (8327127141148561 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8327127141148561 / 8000000000000000 : ℚ)) - (U := (80153947998405037901 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8327127141148561 / 8000000000000000 : ℝ) ≤ - (80153947998405037901 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1040850122684609 / 2000000000000000 : ℝ)) (q := - (8327127141148561 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8327127141148561 / 16000000000000000 : ℚ)) + (r' := (8327127141148561 / 8000000000000000 : ℚ)) + (U := (-(1306140412601594962099 / 2000000000000000000000 : ℚ))) + (U' := (80153947998405037901 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (1040850122684609 / 2000000000000000 : ℚ)) + (q := (8327127141148561 / 16000000000000000 : ℚ)) + (U := (-(1306140412601594962099 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_3 : Uω (aρ 3) (bρ 3) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -913,25 +803,21 @@ lemma U_474_3 : have hlg : Real.log (41252358864580941 / 80000000000000000 : ℝ) ≤ (-(3311591693361606929099 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41252358864580941 / 80000000000000000 : ℝ) = - (41252358864580941 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41252358864580941 / 40000000000000000 : ℚ)) - (U := (154144208138393070901 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41252358864580941 / 40000000000000000 : ℝ) ≤ - (154144208138393070901 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5155827509482579 / 10000000000000000 : ℝ)) (q := - (41252358864580941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41252358864580941 / 80000000000000000 : ℚ)) + (r' := (41252358864580941 / 40000000000000000 : ℚ)) + (U := (-(3311591693361606929099 / 5000000000000000000000 : ℚ))) + (U' := (154144208138393070901 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (5155827509482579 / 10000000000000000 : ℚ)) + (q := (41252358864580941 / 80000000000000000 : ℚ)) + (U := (-(3311591693361606929099 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_4 : Uω (aρ 4) (bρ 4) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -939,25 +825,21 @@ lemma U_474_4 : have hlg : Real.log (40615166311687373 / 80000000000000000 : ℝ) ≤ (-(677885083085293050957 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40615166311687373 / 80000000000000000 : ℝ) = - (40615166311687373 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40615166311687373 / 40000000000000000 : ℚ)) - (U := (15262097214706949043 / 1000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40615166311687373 / 40000000000000000 : ℝ) ≤ - (15262097214706949043 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5074823552324187 / 10000000000000000 : ℝ)) (q := - (40615166311687373 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40615166311687373 / 80000000000000000 : ℚ)) + (r' := (40615166311687373 / 40000000000000000 : ℚ)) + (U := (-(677885083085293050957 / 1000000000000000000000 : ℚ))) + (U' := (15262097214706949043 / 1000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (5074823552324187 / 10000000000000000 : ℚ)) + (q := (40615166311687373 / 80000000000000000 : ℚ)) + (U := (-(677885083085293050957 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_5 : Uω (aρ 5) (bρ 5) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -965,25 +847,21 @@ lemma U_474_5 : have hlg : Real.log (39643235923632449 / 80000000000000000 : ℝ) ≤ (-(28084251809523764379 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39643235923632449 / 80000000000000000 : ℝ) = - (39643235923632449 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39643235923632449 / 20000000000000000 : ℚ)) - (U := (27367522614476235621 / 40000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39643235923632449 / 20000000000000000 : ℝ) ≤ - (27367522614476235621 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (309376929665341 / 625000000000000 : ℝ)) (q := - (39643235923632449 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39643235923632449 / 80000000000000000 : ℚ)) + (r' := (39643235923632449 / 20000000000000000 : ℚ)) + (U := (-(28084251809523764379 / 40000000000000000000 : ℚ))) + (U' := (27367522614476235621 / 40000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (309376929665341 / 625000000000000 : ℚ)) + (q := (39643235923632449 / 80000000000000000 : ℚ)) + (U := (-(28084251809523764379 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_6 : Uω (aρ 6) (bρ 6) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -991,25 +869,21 @@ lemma U_474_6 : have hlg : Real.log (38245620493287529 / 80000000000000000 : ℝ) ≤ (-(1475995154688466043879 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38245620493287529 / 80000000000000000 : ℝ) = - (38245620493287529 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38245620493287529 / 20000000000000000 : ℚ)) - (U := (1296593566511533956121 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38245620493287529 / 20000000000000000 : ℝ) ≤ - (1296593566511533956121 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2383933696099613 / 5000000000000000 : ℝ)) (q := - (38245620493287529 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38245620493287529 / 80000000000000000 : ℚ)) + (r' := (38245620493287529 / 20000000000000000 : ℚ)) + (U := (-(1475995154688466043879 / 2000000000000000000000 : ℚ))) + (U' := (1296593566511533956121 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (2383933696099613 / 5000000000000000 : ℚ)) + (q := (38245620493287529 / 80000000000000000 : ℚ)) + (U := (-(1475995154688466043879 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_7 : Uω (aρ 7) (bρ 7) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1017,25 +891,21 @@ lemma U_474_7 : have hlg : Real.log (36330574615994797 / 80000000000000000 : ℝ) ≤ (-(7893669714757767057957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36330574615994797 / 80000000000000000 : ℝ) = - (36330574615994797 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36330574615994797 / 20000000000000000 : ℚ)) - (U := (5969273891242232942043 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36330574615994797 / 20000000000000000 : ℝ) ≤ - (5969273891242232942043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4512767303636043 / 10000000000000000 : ℝ)) (q := - (36330574615994797 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36330574615994797 / 80000000000000000 : ℚ)) + (r' := (36330574615994797 / 20000000000000000 : ℚ)) + (U := (-(7893669714757767057957 / 10000000000000000000000 : ℚ))) + (U' := (5969273891242232942043 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (4512767303636043 / 10000000000000000 : ℚ)) + (q := (36330574615994797 / 80000000000000000 : ℚ)) + (U := (-(7893669714757767057957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_8 : Uω (aρ 8) (bρ 8) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1043,25 +913,21 @@ lemma U_474_8 : have hlg : Real.log (33813252703021321 / 80000000000000000 : ℝ) ≤ (-(8611738167075583192321 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33813252703021321 / 80000000000000000 : ℝ) = - (33813252703021321 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33813252703021321 / 20000000000000000 : ℚ)) - (U := (5251205438924416807679 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33813252703021321 / 20000000000000000 : ℝ) ≤ - (5251205438924416807679 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2083489238366337 / 5000000000000000 : ℝ)) (q := - (33813252703021321 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33813252703021321 / 80000000000000000 : ℚ)) + (r' := (33813252703021321 / 20000000000000000 : ℚ)) + (U := (-(8611738167075583192321 / 10000000000000000000000 : ℚ))) + (U' := (5251205438924416807679 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (2083489238366337 / 5000000000000000 : ℚ)) + (q := (33813252703021321 / 80000000000000000 : ℚ)) + (U := (-(8611738167075583192321 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_9 : Uω (aρ 9) (bρ 9) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1069,25 +935,21 @@ lemma U_474_9 : have hlg : Real.log (30616288416902789 / 80000000000000000 : ℝ) ≤ (-(9604944656117145227967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30616288416902789 / 80000000000000000 : ℝ) = - (30616288416902789 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30616288416902789 / 20000000000000000 : ℚ)) - (U := (4257998949882854772033 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30616288416902789 / 20000000000000000 : ℝ) ≤ - (4257998949882854772033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3708703033563041 / 10000000000000000 : ℝ)) (q := - (30616288416902789 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30616288416902789 / 80000000000000000 : ℚ)) + (r' := (30616288416902789 / 20000000000000000 : ℚ)) + (U := (-(9604944656117145227967 / 10000000000000000000000 : ℚ))) + (U' := (4257998949882854772033 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (3708703033563041 / 10000000000000000 : ℚ)) + (q := (30616288416902789 / 80000000000000000 : ℚ)) + (U := (-(9604944656117145227967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_10 : Uω (aρ 10) (bρ 10) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1095,26 +957,21 @@ lemma U_474_10 : have hlg : Real.log (5329500512359669 / 16000000000000000 : ℝ) ≤ (-(5496656002181523759141 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5329500512359669 / 16000000000000000 : ℝ) = - (5329500512359669 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5329500512359669 / 4000000000000000 : ℚ)) - (U := (1434815800818476240859 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5329500512359669 / 4000000000000000 : ℝ) ≤ - (1434815800818476240859 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (310506560328193 / 1000000000000000 : ℝ)) (q := - (5329500512359669 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5329500512359669 / 16000000000000000 : ℚ)) + (r' := (5329500512359669 / 4000000000000000 : ℚ)) + (U := (-(5496656002181523759141 / 5000000000000000000000 : ℚ))) + (U' := (1434815800818476240859 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (310506560328193 / 1000000000000000 : ℚ)) + (q := (5329500512359669 / 16000000000000000 : ℚ)) + (U := (-(5496656002181523759141 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_11 : Uω (aρ 11) (bρ 11) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1122,26 +979,21 @@ lemma U_474_11 : have hlg : Real.log (4336994733821961 / 16000000000000000 : ℝ) ≤ (-(13054070711118162002301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4336994733821961 / 16000000000000000 : ℝ) = - (4336994733821961 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4336994733821961 / 4000000000000000 : ℚ)) - (U := (808872894881837997699 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4336994733821961 / 4000000000000000 : ℝ) ≤ - (808872894881837997699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (456582001262959 / 2000000000000000 : ℝ)) (q := - (4336994733821961 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4336994733821961 / 16000000000000000 : ℚ)) + (r' := (4336994733821961 / 4000000000000000 : ℚ)) + (U := (-(13054070711118162002301 / 10000000000000000000000 : ℚ))) + (U' := (808872894881837997699 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (456582001262959 / 2000000000000000 : ℚ)) + (q := (4336994733821961 / 16000000000000000 : ℚ)) + (U := (-(13054070711118162002301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_12 : Uω (aρ 12) (bρ 12) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1149,26 +1001,21 @@ lemma U_474_12 : have hlg : Real.log (14268203677230981 / 80000000000000000 : ℝ) ≤ (-(17239930913919872437509 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14268203677230981 / 80000000000000000 : ℝ) = - (14268203677230981 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14268203677230981 / 10000000000000000 : ℚ)) - (U := (3554484495080127562491 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14268203677230981 / 10000000000000000 : ℝ) ≤ - (3554484495080127562491 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (852417605030089 / 10000000000000000 : ℝ)) (q := - (14268203677230981 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14268203677230981 / 80000000000000000 : ℚ)) + (r' := (14268203677230981 / 10000000000000000 : ℚ)) + (U := (-(17239930913919872437509 / 10000000000000000000000 : ℚ))) + (U' := (3554484495080127562491 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (33874717079089 / 64000000000000 : ℚ)) + (s := (852417605030089 / 10000000000000000 : ℚ)) + (q := (14268203677230981 / 80000000000000000 : ℚ)) + (U := (-(17239930913919872437509 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_474_13 : Uω (aρ 13) (bρ 13) (33874717079089 / 64000000000000 : ℝ) ≤ @@ -1280,25 +1127,21 @@ lemma U_475_1 : have hlg : Real.log (5240878803364487 / 10000000000000000 : ℝ) ≤ (-(6460958978972525251067 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5240878803364487 / 10000000000000000 : ℝ) = - (5240878803364487 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5240878803364487 / 5000000000000000 : ℚ)) - (U := (470512824027474748933 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5240878803364487 / 5000000000000000 : ℝ) ≤ - (470512824027474748933 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5240847955888349 / 10000000000000000 : ℝ)) (q := - (5240878803364487 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5240878803364487 / 10000000000000000 : ℚ)) + (r' := (5240878803364487 / 5000000000000000 : ℚ)) + (U := (-(6460958978972525251067 / 10000000000000000000000 : ℚ))) + (U' := (470512824027474748933 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (5240847955888349 / 10000000000000000 : ℚ)) + (q := (5240878803364487 / 10000000000000000 : ℚ)) + (U := (-(6460958978972525251067 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_2 : Uω (aρ 2) (bρ 2) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1306,25 +1149,21 @@ lemma U_475_2 : have hlg : Real.log (1043387455259377 / 2000000000000000 : ℝ) ≤ (-(3253372958554693937133 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1043387455259377 / 2000000000000000 : ℝ) = - (1043387455259377 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1043387455259377 / 1000000000000000 : ℚ)) - (U := (212362942945306062867 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1043387455259377 / 1000000000000000 : ℝ) ≤ - (212362942945306062867 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1043346782852629 / 2000000000000000 : ℝ)) (q := - (1043387455259377 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1043387455259377 / 2000000000000000 : ℚ)) + (r' := (1043387455259377 / 1000000000000000 : ℚ)) + (U := (-(3253372958554693937133 / 5000000000000000000000 : ℚ))) + (U' := (212362942945306062867 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (1043346782852629 / 2000000000000000 : ℚ)) + (q := (1043387455259377 / 2000000000000000 : ℚ)) + (U := (-(3253372958554693937133 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_3 : Uω (aρ 3) (bρ 3) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1332,25 +1171,21 @@ lemma U_475_3 : have hlg : Real.log (10338057831811619 / 20000000000000000 : ℝ) ≤ (-(1649750631088205402597 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10338057831811619 / 20000000000000000 : ℝ) = - (10338057831811619 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10338057831811619 / 10000000000000000 : ℚ)) - (U := (83117319661794597403 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10338057831811619 / 10000000000000000 : ℝ) ≤ - (83117319661794597403 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2584156649915497 / 5000000000000000 : ℝ)) (q := - (10338057831811619 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10338057831811619 / 20000000000000000 : ℚ)) + (r' := (10338057831811619 / 10000000000000000 : ℚ)) + (U := (-(1649750631088205402597 / 2500000000000000000000 : ℚ))) + (U' := (83117319661794597403 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (2584156649915497 / 5000000000000000 : ℚ)) + (q := (10338057831811619 / 20000000000000000 : ℚ)) + (U := (-(1649750631088205402597 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_4 : Uω (aρ 4) (bρ 4) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1358,25 +1193,21 @@ lemma U_475_4 : have hlg : Real.log (2544691599379543 / 5000000000000000 : ℝ) ≤ (-(3377142242700800895389 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2544691599379543 / 5000000000000000 : ℝ) = - (2544691599379543 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2544691599379543 / 2500000000000000 : ℚ)) - (U := (88593658799199104611 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2544691599379543 / 2500000000000000 : ℝ) ≤ - (88593658799199104611 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5087316046602547 / 10000000000000000 : ℝ)) (q := - (2544691599379543 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2544691599379543 / 5000000000000000 : ℚ)) + (r' := (2544691599379543 / 2500000000000000 : ℚ)) + (U := (-(3377142242700800895389 / 5000000000000000000000 : ℚ))) + (U' := (88593658799199104611 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (5087316046602547 / 10000000000000000 : ℚ)) + (q := (2544691599379543 / 5000000000000000 : ℚ)) + (U := (-(3377142242700800895389 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_5 : Uω (aρ 5) (bρ 5) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1384,25 +1215,21 @@ lemma U_475_5 : have hlg : Real.log (9935800664233037 / 20000000000000000 : ℝ) ≤ (-(1748969525043867698289 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9935800664233037 / 20000000000000000 : ℝ) = - (9935800664233037 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9935800664233037 / 5000000000000000 : ℚ)) - (U := (1716766376456132301711 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9935800664233037 / 5000000000000000 : ℝ) ≤ - (1716766376456132301711 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1240635058163103 / 2500000000000000 : ℝ)) (q := - (9935800664233037 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9935800664233037 / 20000000000000000 : ℚ)) + (r' := (9935800664233037 / 5000000000000000 : ℚ)) + (U := (-(1748969525043867698289 / 2500000000000000000000 : ℚ))) + (U' := (1716766376456132301711 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (1240635058163103 / 2500000000000000 : ℚ)) + (q := (9935800664233037 / 20000000000000000 : ℚ)) + (U := (-(1748969525043867698289 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_6 : Uω (aρ 6) (bρ 6) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1410,25 +1237,21 @@ lemma U_475_6 : have hlg : Real.log (2396609200802933 / 5000000000000000 : ℝ) ≤ (-(3676915032743383951457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2396609200802933 / 5000000000000000 : ℝ) = - (2396609200802933 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2396609200802933 / 1250000000000000 : ℚ)) - (U := (3254556770256616048543 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2396609200802933 / 1250000000000000 : ℝ) ≤ - (3254556770256616048543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4780416746771107 / 10000000000000000 : ℝ)) (q := - (2396609200802933 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2396609200802933 / 5000000000000000 : ℚ)) + (r' := (2396609200802933 / 1250000000000000 : ℚ)) + (U := (-(3676915032743383951457 / 5000000000000000000000 : ℚ))) + (U' := (3254556770256616048543 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (4780416746771107 / 10000000000000000 : ℚ)) + (q := (2396609200802933 / 5000000000000000 : ℚ)) + (U := (-(3676915032743383951457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_7 : Uω (aρ 7) (bρ 7) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1436,25 +1259,21 @@ lemma U_475_7 : have hlg : Real.log (4553882914965921 / 10000000000000000 : ℝ) ≤ (-(7866048355351224914357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4553882914965921 / 10000000000000000 : ℝ) = - (4553882914965921 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4553882914965921 / 2500000000000000 : ℚ)) - (U := (5996895250648775085643 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4553882914965921 / 2500000000000000 : ℝ) ≤ - (5996895250648775085643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4525407154251217 / 10000000000000000 : ℝ)) (q := - (4553882914965921 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4553882914965921 / 10000000000000000 : ℚ)) + (r' := (4553882914965921 / 2500000000000000 : ℚ)) + (U := (-(7866048355351224914357 / 10000000000000000000000 : ℚ))) + (U' := (5996895250648775085643 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (4525407154251217 / 10000000000000000 : ℚ)) + (q := (4553882914965921 / 10000000000000000 : ℚ)) + (U := (-(7866048355351224914357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_8 : Uω (aρ 8) (bρ 8) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1462,25 +1281,21 @@ lemma U_475_8 : have hlg : Real.log (4239317139495231 / 10000000000000000 : ℝ) ≤ (-(858182888206397318407 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4239317139495231 / 10000000000000000 : ℝ) = - (4239317139495231 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4239317139495231 / 2500000000000000 : ℚ)) - (U := (528111472393602681593 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4239317139495231 / 2500000000000000 : ℝ) ≤ - (528111472393602681593 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4179817254649837 / 10000000000000000 : ℝ)) (q := - (4239317139495231 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4239317139495231 / 10000000000000000 : ℚ)) + (r' := (4239317139495231 / 2500000000000000 : ℚ)) + (U := (-(858182888206397318407 / 1000000000000000000000 : ℚ))) + (U' := (528111472393602681593 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (4179817254649837 / 10000000000000000 : ℚ)) + (q := (4239317139495231 / 10000000000000000 : ℚ)) + (U := (-(858182888206397318407 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_9 : Uω (aρ 9) (bρ 9) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1488,25 +1303,21 @@ lemma U_475_9 : have hlg : Real.log (1919957635388529 / 5000000000000000 : ℝ) ≤ (-(2392836977549402281269 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1919957635388529 / 5000000000000000 : ℝ) = - (1919957635388529 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1919957635388529 / 1250000000000000 : ℚ)) - (U := (1072898923950597718731 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1919957635388529 / 1250000000000000 : ℝ) ≤ - (1072898923950597718731 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3721979145573491 / 10000000000000000 : ℝ)) (q := - (1919957635388529 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1919957635388529 / 5000000000000000 : ℚ)) + (r' := (1919957635388529 / 1250000000000000 : ℚ)) + (U := (-(2392836977549402281269 / 2500000000000000000000 : ℚ))) + (U' := (1072898923950597718731 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (3721979145573491 / 10000000000000000 : ℚ)) + (q := (1919957635388529 / 5000000000000000 : ℚ)) + (U := (-(2392836977549402281269 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_10 : Uω (aρ 10) (bρ 10) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1514,25 +1325,21 @@ lemma U_475_10 : have hlg : Real.log (267545940105391 / 800000000000000 : ℝ) ≤ (-(10953204368456377232327 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (267545940105391 / 800000000000000 : ℝ) = - (267545940105391 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (267545940105391 / 200000000000000 : ℚ)) - (U := (2909739237543622767673 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (267545940105391 / 200000000000000 : ℝ) ≤ - (2909739237543622767673 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62387122802983 / 200000000000000 : ℝ)) (q := - (267545940105391 / 800000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (267545940105391 / 800000000000000 : ℚ)) + (r' := (267545940105391 / 200000000000000 : ℚ)) + (U := (-(10953204368456377232327 / 10000000000000000000000 : ℚ))) + (U' := (2909739237543622767673 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (62387122802983 / 200000000000000 : ℚ)) + (q := (267545940105391 / 800000000000000 : ℚ)) + (U := (-(10953204368456377232327 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_11 : Uω (aρ 11) (bρ 11) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1540,26 +1347,21 @@ lemma U_475_11 : have hlg : Real.log (2725427574771609 / 10000000000000000 : ℝ) ≤ (-(3249899421236699954177 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2725427574771609 / 10000000000000000 : ℝ) = - (2725427574771609 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2725427574771609 / 2500000000000000 : ℚ)) - (U := (215836480263300045823 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2725427574771609 / 2500000000000000 : ℝ) ≤ - (215836480263300045823 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2300039413262593 / 10000000000000000 : ℝ)) (q := - (2725427574771609 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2725427574771609 / 10000000000000000 : ℚ)) + (r' := (2725427574771609 / 2500000000000000 : ℚ)) + (U := (-(3249899421236699954177 / 2500000000000000000000 : ℚ))) + (U' := (215836480263300045823 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (2300039413262593 / 10000000000000000 : ℚ)) + (q := (2725427574771609 / 10000000000000000 : ℚ)) + (U := (-(3249899421236699954177 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_12 : Uω (aρ 12) (bρ 12) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1567,26 +1369,21 @@ lemma U_475_12 : have hlg : Real.log (1809243093871961 / 10000000000000000 : ℝ) ≤ (-(854838257289714201947 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1809243093871961 / 10000000000000000 : ℝ) = - (1809243093871961 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1809243093871961 / 1250000000000000 : ℚ)) - (U := (184882513160285798053 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1809243093871961 / 1250000000000000 : ℝ) ≤ - (184882513160285798053 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (891370548148297 / 10000000000000000 : ℝ)) (q := - (1809243093871961 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1809243093871961 / 10000000000000000 : ℚ)) + (r' := (1809243093871961 / 1250000000000000 : ℚ)) + (U := (-(854838257289714201947 / 500000000000000000000 : ℚ))) + (U' := (184882513160285798053 / 500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8488650990281 / 16000000000000 : ℚ)) + (s := (891370548148297 / 10000000000000000 : ℚ)) + (q := (1809243093871961 / 10000000000000000 : ℚ)) + (U := (-(854838257289714201947 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_475_13 : Uω (aρ 13) (bρ 13) (8488650990281 / 16000000000000 : ℝ) ≤ @@ -1698,25 +1495,21 @@ lemma U_476_1 : have hlg : Real.log (42026889615827843 / 80000000000000000 : ℝ) ≤ (-(6437169920414059672691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42026889615827843 / 80000000000000000 : ℝ) = - (42026889615827843 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42026889615827843 / 40000000000000000 : ℚ)) - (U := (494301882585940327309 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42026889615827843 / 40000000000000000 : ℝ) ≤ - (494301882585940327309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5253330427798367 / 10000000000000000 : ℝ)) (q := - (42026889615827843 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42026889615827843 / 80000000000000000 : ℚ)) + (r' := (42026889615827843 / 40000000000000000 : ℚ)) + (U := (-(6437169920414059672691 / 10000000000000000000000 : ℚ))) + (U' := (494301882585940327309 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (5253330427798367 / 10000000000000000 : ℚ)) + (q := (42026889615827843 / 80000000000000000 : ℚ)) + (U := (-(6437169920414059672691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_2 : Uω (aρ 2) (bρ 2) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1724,25 +1517,21 @@ lemma U_476_2 : have hlg : Real.log (41835360696377779 / 80000000000000000 : ℝ) ≤ (-(6482847028228737411169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41835360696377779 / 80000000000000000 : ℝ) = - (41835360696377779 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41835360696377779 / 40000000000000000 : ℚ)) - (U := (448624774771262588831 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41835360696377779 / 40000000000000000 : ℝ) ≤ - (448624774771262588831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5229217210445851 / 10000000000000000 : ℝ)) (q := - (41835360696377779 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41835360696377779 / 80000000000000000 : ℚ)) + (r' := (41835360696377779 / 40000000000000000 : ℚ)) + (U := (-(6482847028228737411169 / 10000000000000000000000 : ℚ))) + (U' := (448624774771262588831 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (5229217210445851 / 10000000000000000 : ℚ)) + (q := (41835360696377779 / 80000000000000000 : ℚ)) + (U := (-(6482847028228737411169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_3 : Uω (aρ 3) (bρ 3) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1750,25 +1539,21 @@ lemma U_476_3 : have hlg : Real.log (41452103723115147 / 80000000000000000 : ℝ) ≤ (-(6574880008487592758289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41452103723115147 / 80000000000000000 : ℝ) = - (41452103723115147 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41452103723115147 / 40000000000000000 : ℚ)) - (U := (356591794512407241711 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41452103723115147 / 40000000000000000 : ℝ) ≤ - (356591794512407241711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5180799073480193 / 10000000000000000 : ℝ)) (q := - (41452103723115147 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41452103723115147 / 80000000000000000 : ℚ)) + (r' := (41452103723115147 / 40000000000000000 : ℚ)) + (U := (-(6574880008487592758289 / 10000000000000000000000 : ℚ))) + (U' := (356591794512407241711 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (5180799073480193 / 10000000000000000 : ℚ)) + (q := (41452103723115147 / 80000000000000000 : ℚ)) + (U := (-(6574880008487592758289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_4 : Uω (aρ 4) (bρ 4) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1776,25 +1561,21 @@ lemma U_476_4 : have hlg : Real.log (1632598586770399 / 3200000000000000 : ℝ) ≤ (-(105152787365977387829 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1632598586770399 / 3200000000000000 : ℝ) = - (1632598586770399 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1632598586770399 / 1600000000000000 : ℚ)) - (U := (3151459555897612171 / 156250000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1632598586770399 / 1600000000000000 : ℝ) ≤ - (3151459555897612171 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25499042455407 / 50000000000000 : ℝ)) (q := - (1632598586770399 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1632598586770399 / 3200000000000000 : ℚ)) + (r' := (1632598586770399 / 1600000000000000 : ℚ)) + (U := (-(105152787365977387829 / 156250000000000000000 : ℚ))) + (U' := (3151459555897612171 / 156250000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (25499042455407 / 50000000000000 : ℚ)) + (q := (1632598586770399 / 3200000000000000 : ℚ)) + (U := (-(105152787365977387829 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_5 : Uω (aρ 5) (bρ 5) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1802,25 +1583,21 @@ lemma U_476_5 : have hlg : Real.log (39843168847047383 / 80000000000000000 : ℝ) ≤ (-(1742689163167899786689 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39843168847047383 / 80000000000000000 : ℝ) = - (39843168847047383 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39843168847047383 / 20000000000000000 : ℚ)) - (U := (1723046738332100213311 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39843168847047383 / 20000000000000000 : ℝ) ≤ - (1723046738332100213311 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1243762363715813 / 2500000000000000 : ℝ)) (q := - (39843168847047383 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39843168847047383 / 80000000000000000 : ℚ)) + (r' := (39843168847047383 / 20000000000000000 : ℚ)) + (U := (-(1742689163167899786689 / 2500000000000000000000 : ℚ))) + (U' := (1723046738332100213311 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (1243762363715813 / 2500000000000000 : ℚ)) + (q := (39843168847047383 / 80000000000000000 : ℚ)) + (U := (-(1742689163167899786689 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_6 : Uω (aρ 6) (bρ 6) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1828,25 +1605,21 @@ lemma U_476_6 : have hlg : Real.log (38445872532141979 / 80000000000000000 : ℝ) ≤ (-(7327752903325907666223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38445872532141979 / 80000000000000000 : ℝ) = - (38445872532141979 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38445872532141979 / 20000000000000000 : ℚ)) - (U := (6535190702674092333777 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38445872532141979 / 20000000000000000 : ℝ) ≤ - (6535190702674092333777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4792965751276901 / 10000000000000000 : ℝ)) (q := - (38445872532141979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38445872532141979 / 80000000000000000 : ℚ)) + (r' := (38445872532141979 / 20000000000000000 : ℚ)) + (U := (-(7327752903325907666223 / 10000000000000000000000 : ℚ))) + (U' := (6535190702674092333777 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (4792965751276901 / 10000000000000000 : ℚ)) + (q := (38445872532141979 / 80000000000000000 : ℚ)) + (U := (-(7327752903325907666223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_7 : Uω (aρ 7) (bρ 7) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1854,25 +1627,21 @@ lemma U_476_7 : have hlg : Real.log (36531548535282223 / 80000000000000000 : ℝ) ≤ (-(244953251082135055187 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36531548535282223 / 80000000000000000 : ℝ) = - (36531548535282223 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36531548535282223 / 20000000000000000 : ℚ)) - (U := (188263736605364944813 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36531548535282223 / 20000000000000000 : ℝ) ≤ - (188263736605364944813 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2269023066410981 / 5000000000000000 : ℝ)) (q := - (36531548535282223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36531548535282223 / 80000000000000000 : ℚ)) + (r' := (36531548535282223 / 20000000000000000 : ℚ)) + (U := (-(244953251082135055187 / 312500000000000000000 : ℚ))) + (U' := (188263736605364944813 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (2269023066410981 / 5000000000000000 : ℚ)) + (q := (36531548535282223 / 80000000000000000 : ℚ)) + (U := (-(244953251082135055187 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_8 : Uω (aρ 8) (bρ 8) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1880,25 +1649,21 @@ lemma U_476_8 : have hlg : Real.log (34015812917868879 / 80000000000000000 : ℝ) ≤ (-(855201131837044779203 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34015812917868879 / 80000000000000000 : ℝ) = - (34015812917868879 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34015812917868879 / 20000000000000000 : ℚ)) - (U := (531093228762955220797 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34015812917868879 / 20000000000000000 : ℝ) ≤ - (531093228762955220797 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2096326939904313 / 5000000000000000 : ℝ)) (q := - (34015812917868879 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34015812917868879 / 80000000000000000 : ℚ)) + (r' := (34015812917868879 / 20000000000000000 : ℚ)) + (U := (-(855201131837044779203 / 1000000000000000000000 : ℚ))) + (U' := (531093228762955220797 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (2096326939904313 / 5000000000000000 : ℚ)) + (q := (34015812917868879 / 80000000000000000 : ℚ)) + (U := (-(855201131837044779203 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_9 : Uω (aρ 9) (bρ 9) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1906,25 +1671,21 @@ lemma U_476_9 : have hlg : Real.log (30822334019602451 / 80000000000000000 : ℝ) ≤ (-(190757415289597866371 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30822334019602451 / 80000000000000000 : ℝ) = - (30822334019602451 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30822334019602451 / 20000000000000000 : ℚ)) - (U := (86501456830402133629 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30822334019602451 / 20000000000000000 : ℝ) ≤ - (86501456830402133629 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3735249783602019 / 10000000000000000 : ℝ)) (q := - (30822334019602451 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30822334019602451 / 80000000000000000 : ℚ)) + (r' := (30822334019602451 / 20000000000000000 : ℚ)) + (U := (-(190757415289597866371 / 200000000000000000000 : ℚ))) + (U' := (86501456830402133629 / 200000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (3735249783602019 / 10000000000000000 : ℚ)) + (q := (30822334019602451 / 80000000000000000 : ℚ)) + (U := (-(190757415289597866371 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_10 : Uω (aρ 10) (bρ 10) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1932,26 +1693,21 @@ lemma U_476_10 : have hlg : Real.log (26861623664032427 / 80000000000000000 : ℝ) ≤ (-(10913279957409600345849 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26861623664032427 / 80000000000000000 : ℝ) = - (26861623664032427 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26861623664032427 / 20000000000000000 : ℚ)) - (U := (2949663648590399654151 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26861623664032427 / 20000000000000000 : ℝ) ≤ - (2949663648590399654151 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3133631228204513 / 10000000000000000 : ℝ)) (q := - (26861623664032427 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26861623664032427 / 80000000000000000 : ℚ)) + (r' := (26861623664032427 / 20000000000000000 : ℚ)) + (U := (-(10913279957409600345849 / 10000000000000000000000 : ℚ))) + (U' := (2949663648590399654151 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (3133631228204513 / 10000000000000000 : ℚ)) + (q := (26861623664032427 / 80000000000000000 : ℚ)) + (U := (-(10913279957409600345849 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_11 : Uω (aρ 11) (bρ 11) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1959,26 +1715,21 @@ lemma U_476_11 : have hlg : Real.log (21921629978898067 / 80000000000000000 : ℝ) ≤ (-(6472764072437904424893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (21921629978898067 / 80000000000000000 : ℝ) = - (21921629978898067 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21921629978898067 / 20000000000000000 : ℚ)) - (U := (458707730562095575107 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21921629978898067 / 20000000000000000 : ℝ) ≤ - (458707730562095575107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2317109433125923 / 10000000000000000 : ℝ)) (q := - (21921629978898067 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21921629978898067 / 80000000000000000 : ℚ)) + (r' := (21921629978898067 / 20000000000000000 : ℚ)) + (U := (-(6472764072437904424893 / 5000000000000000000000 : ℚ))) + (U' := (458707730562095575107 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (2317109433125923 / 10000000000000000 : ℚ)) + (q := (21921629978898067 / 80000000000000000 : ℚ)) + (U := (-(6472764072437904424893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_12 : Uω (aρ 12) (bρ 12) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -1986,26 +1737,21 @@ lemma U_476_12 : have hlg : Real.log (14673827234924079 / 80000000000000000 : ℝ) ≤ (-(16959611872217714546673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14673827234924079 / 80000000000000000 : ℝ) = - (14673827234924079 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14673827234924079 / 10000000000000000 : ℚ)) - (U := (3834803536782285453327 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14673827234924079 / 10000000000000000 : ℝ) ≤ - (3834803536782285453327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (464429421908713 / 5000000000000000 : ℝ)) (q := - (14673827234924079 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14673827234924079 / 80000000000000000 : ℚ)) + (r' := (14673827234924079 / 10000000000000000 : ℚ)) + (U := (-(16959611872217714546673 / 10000000000000000000000 : ℚ))) + (U' := (3834803536782285453327 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34034490843159 / 64000000000000 : ℚ)) + (s := (464429421908713 / 5000000000000000 : ℚ)) + (q := (14673827234924079 / 80000000000000000 : ℚ)) + (U := (-(16959611872217714546673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_476_13 : Uω (aρ 13) (bρ 13) (34034490843159 / 64000000000000 : ℝ) ≤ @@ -2117,25 +1863,21 @@ lemma U_477_1 : have hlg : Real.log (4212674880195987 / 8000000000000000 : ℝ) ≤ (-(1603359330041331640883 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4212674880195987 / 8000000000000000 : ℝ) = - (4212674880195987 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4212674880195987 / 4000000000000000 : ℚ)) - (U := (129508620708668359117 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4212674880195987 / 4000000000000000 : ℝ) ≤ - (129508620708668359117 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1053162579802681 / 2000000000000000 : ℝ)) (q := - (4212674880195987 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4212674880195987 / 8000000000000000 : ℚ)) + (r' := (4212674880195987 / 4000000000000000 : ℚ)) + (U := (-(1603359330041331640883 / 2500000000000000000000 : ℚ))) + (U' := (129508620708668359117 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (1053162579802681 / 2000000000000000 : ℚ)) + (q := (4212674880195987 / 8000000000000000 : ℚ)) + (U := (-(1603359330041331640883 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_2 : Uω (aρ 2) (bρ 2) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2143,25 +1885,21 @@ lemma U_477_2 : have hlg : Real.log (4193522316388401 / 8000000000000000 : ℝ) ≤ (-(6459005123300066603403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4193522316388401 / 8000000000000000 : ℝ) = - (4193522316388401 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4193522316388401 / 4000000000000000 : ℚ)) - (U := (472466679699933396597 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4193522316388401 / 4000000000000000 : ℝ) ≤ - (472466679699933396597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (131042512550111 / 250000000000000 : ℝ)) (q := - (4193522316388401 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4193522316388401 / 8000000000000000 : ℚ)) + (r' := (4193522316388401 / 4000000000000000 : ℚ)) + (U := (-(6459005123300066603403 / 10000000000000000000000 : ℚ))) + (U' := (472466679699933396597 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (131042512550111 / 250000000000000 : ℚ)) + (q := (4193522316388401 / 8000000000000000 : ℚ)) + (U := (-(6459005123300066603403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_3 : Uω (aρ 3) (bρ 3) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2169,25 +1907,21 @@ lemma U_477_3 : have hlg : Real.log (20775988026334369 / 40000000000000000 : ℝ) ≤ (-(1310163111631396293071 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20775988026334369 / 40000000000000000 : ℝ) = - (20775988026334369 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20775988026334369 / 20000000000000000 : ℚ)) - (U := (76131248968603706929 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20775988026334369 / 20000000000000000 : ℝ) ≤ - (76131248968603706929 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2596642415275311 / 5000000000000000 : ℝ)) (q := - (20775988026334369 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20775988026334369 / 40000000000000000 : ℚ)) + (r' := (20775988026334369 / 20000000000000000 : ℚ)) + (U := (-(1310163111631396293071 / 2000000000000000000000 : ℚ))) + (U' := (76131248968603706929 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (2596642415275311 / 5000000000000000 : ℚ)) + (q := (20775988026334369 / 40000000000000000 : ℚ)) + (U := (-(1310163111631396293071 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_4 : Uω (aρ 4) (bρ 4) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2195,25 +1929,21 @@ lemma U_477_4 : have hlg : Real.log (20457431775354757 / 40000000000000000 : ℝ) ≤ (-(6705332253855386408567 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20457431775354757 / 40000000000000000 : ℝ) = - (20457431775354757 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20457431775354757 / 20000000000000000 : ℚ)) - (U := (226139549144613591433 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20457431775354757 / 20000000000000000 : ℝ) ≤ - (226139549144613591433 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (639037610765727 / 1250000000000000 : ℝ)) (q := - (20457431775354757 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20457431775354757 / 40000000000000000 : ℚ)) + (r' := (20457431775354757 / 20000000000000000 : ℚ)) + (U := (-(6705332253855386408567 / 10000000000000000000000 : ℚ))) + (U' := (226139549144613591433 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (639037610765727 / 1250000000000000 : ℚ)) + (q := (20457431775354757 / 40000000000000000 : ℚ)) + (U := (-(6705332253855386408567 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_5 : Uω (aρ 5) (bρ 5) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2221,25 +1951,21 @@ lemma U_477_5 : have hlg : Real.log (19971567249032607 / 40000000000000000 : ℝ) ≤ (-(3472849145369206145161 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19971567249032607 / 40000000000000000 : ℝ) = - (19971567249032607 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19971567249032607 / 10000000000000000 : ℚ)) - (U := (3458622657630793854839 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (19971567249032607 / 10000000000000000 : ℝ) ≤ - (3458622657630793854839 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4987558542299741 / 10000000000000000 : ℝ)) (q := - (19971567249032607 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19971567249032607 / 40000000000000000 : ℚ)) + (r' := (19971567249032607 / 10000000000000000 : ℚ)) + (U := (-(3472849145369206145161 / 5000000000000000000000 : ℚ))) + (U' := (3458622657630793854839 / 5000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (4987558542299741 / 10000000000000000 : ℚ)) + (q := (19971567249032607 / 40000000000000000 : ℚ)) + (U := (-(3472849145369206145161 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_6 : Uω (aρ 6) (bρ 6) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2247,25 +1973,21 @@ lemma U_477_6 : have hlg : Real.log (3854599646214253 / 8000000000000000 : ℝ) ≤ (-(7301743926598747382951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3854599646214253 / 8000000000000000 : ℝ) = - (3854599646214253 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3854599646214253 / 2000000000000000 : ℚ)) - (U := (6561199679401252617049 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3854599646214253 / 2000000000000000 : ℝ) ≤ - (6561199679401252617049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (480551440845907 / 1000000000000000 : ℝ)) (q := - (3854599646214253 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3854599646214253 / 8000000000000000 : ℚ)) + (r' := (3854599646214253 / 2000000000000000 : ℚ)) + (U := (-(7301743926598747382951 / 10000000000000000000000 : ℚ))) + (U' := (6561199679401252617049 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (480551440845907 / 1000000000000000 : ℚ)) + (q := (3854599646214253 / 8000000000000000 : ℚ)) + (U := (-(7301743926598747382951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_7 : Uω (aρ 7) (bρ 7) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2273,25 +1995,21 @@ lemma U_477_7 : have hlg : Real.log (18316015145861673 / 40000000000000000 : ℝ) ≤ (-(1562207263759628217761 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18316015145861673 / 40000000000000000 : ℝ) = - (18316015145861673 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18316015145861673 / 10000000000000000 : ℚ)) - (U := (1210381457440371782239 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18316015145861673 / 10000000000000000 : ℝ) ≤ - (1210381457440371782239 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2275342123307137 / 5000000000000000 : ℝ)) (q := - (18316015145861673 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18316015145861673 / 40000000000000000 : ℚ)) + (r' := (18316015145861673 / 10000000000000000 : ℚ)) + (U := (-(1562207263759628217761 / 2000000000000000000000 : ℚ))) + (U' := (1210381457440371782239 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (2275342123307137 / 5000000000000000 : ℚ)) + (q := (18316015145861673 / 40000000000000000 : ℚ)) + (U := (-(1562207263759628217761 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_8 : Uω (aρ 8) (bρ 8) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2299,25 +2017,21 @@ lemma U_477_8 : have hlg : Real.log (17058540093797051 / 40000000000000000 : ℝ) ≤ (-(8522284899989832254591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17058540093797051 / 40000000000000000 : ℝ) = - (17058540093797051 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17058540093797051 / 10000000000000000 : ℚ)) - (U := (5340658706010167745409 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17058540093797051 / 10000000000000000 : ℝ) ≤ - (5340658706010167745409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4205488371921963 / 10000000000000000 : ℝ)) (q := - (17058540093797051 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17058540093797051 / 40000000000000000 : ℚ)) + (r' := (17058540093797051 / 10000000000000000 : ℚ)) + (U := (-(8522284899989832254591 / 10000000000000000000000 : ℚ))) + (U' := (5340658706010167745409 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (4205488371921963 / 10000000000000000 : ℚ)) + (q := (17058540093797051 / 40000000000000000 : ℚ)) + (U := (-(8522284899989832254591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_9 : Uω (aρ 9) (bρ 9) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2325,25 +2039,21 @@ lemma U_477_9 : have hlg : Real.log (3092532420961119 / 8000000000000000 : ℝ) ≤ (-(950451232191955561317 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3092532420961119 / 8000000000000000 : ℝ) = - (3092532420961119 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3092532420961119 / 2000000000000000 : ℚ)) - (U := (435843128408044438683 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3092532420961119 / 2000000000000000 : ℝ) ≤ - (435843128408044438683 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (749703001157247 / 2000000000000000 : ℝ)) (q := - (3092532420961119 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3092532420961119 / 8000000000000000 : ℚ)) + (r' := (3092532420961119 / 2000000000000000 : ℚ)) + (U := (-(950451232191955561317 / 1000000000000000000000 : ℚ))) + (U' := (435843128408044438683 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (749703001157247 / 2000000000000000 : ℚ)) + (q := (3092532420961119 / 8000000000000000 : ℚ)) + (U := (-(950451232191955561317 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_10 : Uω (aρ 10) (bρ 10) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2351,26 +2061,21 @@ lemma U_477_10 : have hlg : Real.log (2696859236296747 / 8000000000000000 : ℝ) ≤ (-(10873536910612324331361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2696859236296747 / 8000000000000000 : ℝ) = - (2696859236296747 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2696859236296747 / 2000000000000000 : ℚ)) - (U := (2989406695387675668639 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2696859236296747 / 2000000000000000 : ℝ) ≤ - (2989406695387675668639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (629578215524061 / 2000000000000000 : ℝ)) (q := - (2696859236296747 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2696859236296747 / 8000000000000000 : ℚ)) + (r' := (2696859236296747 / 2000000000000000 : ℚ)) + (U := (-(10873536910612324331361 / 10000000000000000000000 : ℚ))) + (U' := (2989406695387675668639 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (629578215524061 / 2000000000000000 : ℚ)) + (q := (2696859236296747 / 8000000000000000 : ℚ)) + (U := (-(10873536910612324331361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_11 : Uω (aρ 11) (bρ 11) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2378,26 +2083,21 @@ lemma U_477_11 : have hlg : Real.log (11019803511520029 / 40000000000000000 : ℝ) ≤ (-(12891854801988329159687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11019803511520029 / 40000000000000000 : ℝ) = - (11019803511520029 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11019803511520029 / 10000000000000000 : ℚ)) - (U := (971088804011670840313 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11019803511520029 / 10000000000000000 : ℝ) ≤ - (971088804011670840313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (583530342210863 / 2500000000000000 : ℝ)) (q := - (11019803511520029 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11019803511520029 / 40000000000000000 : ℚ)) + (r' := (11019803511520029 / 10000000000000000 : ℚ)) + (U := (-(12891854801988329159687 / 10000000000000000000000 : ℚ))) + (U' := (971088804011670840313 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (583530342210863 / 2500000000000000 : ℚ)) + (q := (11019803511520029 / 40000000000000000 : ℚ)) + (U := (-(12891854801988329159687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_12 : Uω (aρ 12) (bρ 12) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2405,26 +2105,21 @@ lemma U_477_12 : have hlg : Real.log (7434266967437877 / 40000000000000000 : ℝ) ≤ (-(2103474338028338746597 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7434266967437877 / 40000000000000000 : ℝ) = - (7434266967437877 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7434266967437877 / 5000000000000000 : ℚ)) - (U := (495827588096661253403 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7434266967437877 / 5000000000000000 : ℝ) ≤ - (495827588096661253403 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (60315824592961 / 625000000000000 : ℝ)) (q := - (7434266967437877 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7434266967437877 / 40000000000000000 : ℚ)) + (r' := (7434266967437877 / 5000000000000000 : ℚ)) + (U := (-(2103474338028338746597 / 1250000000000000000000 : ℚ))) + (U' := (495827588096661253403 / 1250000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17057188862597 / 32000000000000 : ℚ)) + (s := (60315824592961 / 625000000000000 : ℚ)) + (q := (7434266967437877 / 40000000000000000 : ℚ)) + (U := (-(2103474338028338746597 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_477_13 : Uω (aρ 13) (bρ 13) (17057188862597 / 32000000000000 : ℝ) ≤ @@ -2537,25 +2232,21 @@ lemma U_478_1 : have hlg : Real.log (42226607985331693 / 80000000000000000 : ℝ) ≤ (-(6389760910873824690131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42226607985331693 / 80000000000000000 : ℝ) = - (42226607985331693 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42226607985331693 / 40000000000000000 : ℚ)) - (U := (541710892126175309869 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42226607985331693 / 40000000000000000 : ℝ) ≤ - (541710892126175309869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (659786921192299 / 1250000000000000 : ℝ)) (q := - (42226607985331693 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42226607985331693 / 80000000000000000 : ℚ)) + (r' := (42226607985331693 / 40000000000000000 : ℚ)) + (U := (-(6389760910873824690131 / 10000000000000000000000 : ℚ))) + (U' := (541710892126175309869 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (659786921192299 / 1250000000000000 : ℚ)) + (q := (42226607985331693 / 80000000000000000 : ℚ)) + (U := (-(6389760910873824690131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_2 : Uω (aρ 2) (bρ 2) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2563,25 +2254,21 @@ lemma U_478_2 : have hlg : Real.log (8407017122605121 / 16000000000000000 : ℝ) ≤ (-(6435219931206354359771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8407017122605121 / 16000000000000000 : ℝ) = - (8407017122605121 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8407017122605121 / 8000000000000000 : ℚ)) - (U := (496251871793645640229 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8407017122605121 / 8000000000000000 : ℝ) ≤ - (496251871793645640229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (525418378897187 / 1000000000000000 : ℝ)) (q := - (8407017122605121 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8407017122605121 / 16000000000000000 : ℚ)) + (r' := (8407017122605121 / 8000000000000000 : ℚ)) + (U := (-(6435219931206354359771 / 10000000000000000000000 : ℚ))) + (U' := (496251871793645640229 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (525418378897187 / 1000000000000000 : ℚ)) + (q := (8407017122605121 / 16000000000000000 : ℚ)) + (U := (-(6435219931206354359771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_3 : Uω (aρ 3) (bρ 3) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2589,25 +2276,21 @@ lemma U_478_3 : have hlg : Real.log (41651848316384409 / 80000000000000000 : ℝ) ≤ (-(6526808894415663314091 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41651848316384409 / 80000000000000000 : ℝ) = - (41651848316384409 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41651848316384409 / 40000000000000000 : ℚ)) - (U := (404662908584336685909 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41651848316384409 / 40000000000000000 : ℝ) ≤ - (404662908584336685909 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5205770571161571 / 10000000000000000 : ℝ)) (q := - (41651848316384409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41651848316384409 / 80000000000000000 : ℚ)) + (r' := (41651848316384409 / 40000000000000000 : ℚ)) + (U := (-(6526808894415663314091 / 10000000000000000000000 : ℚ))) + (U' := (404662908584336685909 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (5205770571161571 / 10000000000000000 : ℚ)) + (q := (41651848316384409 / 80000000000000000 : ℚ)) + (U := (-(6526808894415663314091 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_4 : Uω (aρ 4) (bρ 4) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2615,25 +2298,21 @@ lemma U_478_4 : have hlg : Real.log (41014762235867349 / 80000000000000000 : ℝ) ≤ (-(1670236444950892870231 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41014762235867349 / 80000000000000000 : ℝ) = - (41014762235867349 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41014762235867349 / 40000000000000000 : ℚ)) - (U := (62631505799107129769 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41014762235867349 / 40000000000000000 : ℝ) ≤ - (62631505799107129769 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2562396616048653 / 5000000000000000 : ℝ)) (q := - (41014762235867349 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41014762235867349 / 80000000000000000 : ℚ)) + (r' := (41014762235867349 / 40000000000000000 : ℚ)) + (U := (-(1670236444950892870231 / 2500000000000000000000 : ℚ))) + (U' := (62631505799107129769 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (2562396616048653 / 5000000000000000 : ℚ)) + (q := (41014762235867349 / 80000000000000000 : ℚ)) + (U := (-(1670236444950892870231 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_5 : Uω (aρ 5) (bρ 5) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2641,25 +2320,21 @@ lemma U_478_5 : have hlg : Real.log (40043099614031753 / 80000000000000000 : ℝ) ≤ (-(3460351350126436706987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40043099614031753 / 80000000000000000 : ℝ) = - (40043099614031753 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40043099614031753 / 40000000000000000 : ℚ)) - (U := (5384551373563293013 / 5000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (40043099614031753 / 40000000000000000 : ℝ) ≤ - (5384551373563293013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5000067495973407 / 10000000000000000 : ℝ)) (q := - (40043099614031753 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40043099614031753 / 80000000000000000 : ℚ)) + (r' := (40043099614031753 / 40000000000000000 : ℚ)) + (U := (-(3460351350126436706987 / 5000000000000000000000 : ℚ))) + (U' := (5384551373563293013 / 5000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (5000067495973407 / 10000000000000000 : ℚ)) + (q := (40043099614031753 / 80000000000000000 : ℚ)) + (U := (-(3460351350126436706987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_6 : Uω (aρ 6) (bρ 6) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2667,25 +2342,21 @@ lemma U_478_6 : have hlg : Real.log (38646119013703849 / 80000000000000000 : ℝ) ≤ (-(7275802777793215124253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38646119013703849 / 80000000000000000 : ℝ) = - (38646119013703849 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38646119013703849 / 20000000000000000 : ℚ)) - (U := (6587140828206784875747 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38646119013703849 / 20000000000000000 : ℝ) ≤ - (6587140828206784875747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4818062721031431 / 10000000000000000 : ℝ)) (q := - (38646119013703849 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38646119013703849 / 80000000000000000 : ℚ)) + (r' := (38646119013703849 / 20000000000000000 : ℚ)) + (U := (-(7275802777793215124253 / 10000000000000000000000 : ℚ))) + (U' := (6587140828206784875747 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (4818062721031431 / 10000000000000000 : ℚ)) + (q := (38646119013703849 / 80000000000000000 : ℚ)) + (U := (-(7275802777793215124253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_7 : Uω (aρ 7) (bρ 7) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2693,25 +2364,21 @@ lemma U_478_7 : have hlg : Real.log (36732508617790769 / 80000000000000000 : ℝ) ≤ (-(194591119444156857651 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36732508617790769 / 80000000000000000 : ℝ) = - (36732508617790769 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36732508617790769 / 20000000000000000 : ℚ)) - (U := (151982470705843142349 / 250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36732508617790769 / 20000000000000000 : ℝ) ≤ - (151982470705843142349 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4563321502813161 / 10000000000000000 : ℝ)) (q := - (36732508617790769 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36732508617790769 / 80000000000000000 : ℚ)) + (r' := (36732508617790769 / 20000000000000000 : ℚ)) + (U := (-(194591119444156857651 / 250000000000000000000 : ℚ))) + (U' := (151982470705843142349 / 250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (4563321502813161 / 10000000000000000 : ℚ)) + (q := (36732508617790769 / 80000000000000000 : ℚ)) + (U := (-(194591119444156857651 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_8 : Uω (aρ 8) (bρ 8) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2719,25 +2386,21 @@ lemma U_478_8 : have hlg : Real.log (1368733560120661 / 3200000000000000 : ℝ) ≤ (-(8492649056459973840639 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1368733560120661 / 3200000000000000 : ℝ) = - (1368733560120661 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1368733560120661 / 800000000000000 : ℚ)) - (U := (5370294549540026159361 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1368733560120661 / 800000000000000 : ℝ) ≤ - (5370294549540026159361 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (10545801876149 / 25000000000000 : ℝ)) (q := - (1368733560120661 / 3200000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1368733560120661 / 3200000000000000 : ℚ)) + (r' := (1368733560120661 / 800000000000000 : ℚ)) + (U := (-(8492649056459973840639 / 10000000000000000000000 : ℚ))) + (U' := (5370294549540026159361 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (10545801876149 / 25000000000000 : ℚ)) + (q := (1368733560120661 / 3200000000000000 : ℚ)) + (U := (-(8492649056459973840639 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_9 : Uω (aρ 9) (bρ 9) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2745,25 +2408,21 @@ lemma U_478_9 : have hlg : Real.log (6205658593083737 / 16000000000000000 : ℝ) ≤ (-(9471271696007942156663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6205658593083737 / 16000000000000000 : ℝ) = - (6205658593083737 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6205658593083737 / 4000000000000000 : ℚ)) - (U := (4391671909992057843337 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6205658593083737 / 4000000000000000 : ℝ) ≤ - (4391671909992057843337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188088743471007 / 500000000000000 : ℝ)) (q := - (6205658593083737 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6205658593083737 / 16000000000000000 : ℚ)) + (r' := (6205658593083737 / 4000000000000000 : ℚ)) + (U := (-(9471271696007942156663 / 10000000000000000000000 : ℚ))) + (U' := (4391671909992057843337 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (188088743471007 / 500000000000000 : ℚ)) + (q := (6205658593083737 / 16000000000000000 : ℚ)) + (U := (-(9471271696007942156663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_10 : Uω (aρ 10) (bρ 10) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2771,26 +2430,21 @@ lemma U_478_10 : have hlg : Real.log (27075500931979433 / 80000000000000000 : ℝ) ≤ (-(5416986698976334785817 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27075500931979433 / 80000000000000000 : ℝ) = - (27075500931979433 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27075500931979433 / 20000000000000000 : ℚ)) - (U := (1514485104023665214183 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27075500931979433 / 20000000000000000 : ℝ) ≤ - (1514485104023665214183 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3162135894555327 / 10000000000000000 : ℝ)) (q := - (27075500931979433 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27075500931979433 / 80000000000000000 : ℚ)) + (r' := (27075500931979433 / 20000000000000000 : ℚ)) + (U := (-(5416986698976334785817 / 5000000000000000000000 : ℚ))) + (U' := (1514485104023665214183 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (3162135894555327 / 10000000000000000 : ℚ)) + (q := (27075500931979433 / 80000000000000000 : ℚ)) + (U := (-(5416986698976334785817 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_11 : Uω (aρ 11) (bρ 11) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2798,26 +2452,21 @@ lemma U_478_11 : have hlg : Real.log (22157356774028233 / 80000000000000000 : ℝ) ≤ (-(12838570585395820165127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22157356774028233 / 80000000000000000 : ℝ) = - (22157356774028233 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22157356774028233 / 20000000000000000 : ℚ)) - (U := (1024373020604179834873 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22157356774028233 / 20000000000000000 : ℝ) ≤ - (1024373020604179834873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2351076481272527 / 10000000000000000 : ℝ)) (q := - (22157356774028233 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22157356774028233 / 80000000000000000 : ℚ)) + (r' := (22157356774028233 / 20000000000000000 : ℚ)) + (U := (-(12838570585395820165127 / 10000000000000000000000 : ℚ))) + (U' := (1024373020604179834873 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (2351076481272527 / 10000000000000000 : ℚ)) + (q := (22157356774028233 / 80000000000000000 : ℚ)) + (U := (-(12838570585395820165127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_12 : Uω (aρ 12) (bρ 12) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2825,26 +2474,21 @@ lemma U_478_12 : have hlg : Real.log (15058626839837021 / 80000000000000000 : ℝ) ≤ (-(4175188987432682907409 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15058626839837021 / 80000000000000000 : ℝ) = - (15058626839837021 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15058626839837021 / 10000000000000000 : ℚ)) - (U := (1023414864817317092591 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15058626839837021 / 10000000000000000 : ℝ) ≤ - (1023414864817317092591 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (250023523602431 / 2500000000000000 : ℝ)) (q := - (15058626839837021 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15058626839837021 / 80000000000000000 : ℚ)) + (r' := (15058626839837021 / 10000000000000000 : ℚ)) + (U := (-(4175188987432682907409 / 2500000000000000000000 : ℚ))) + (U' := (1023414864817317092591 / 2500000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34194264607229 / 64000000000000 : ℚ)) + (s := (250023523602431 / 2500000000000000 : ℚ)) + (q := (15058626839837021 / 80000000000000000 : ℚ)) + (U := (-(4175188987432682907409 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_478_13 : Uω (aρ 13) (bρ 13) (34194264607229 / 64000000000000 : ℝ) ≤ @@ -2957,25 +2601,21 @@ lemma U_479_1 : have hlg : Real.log (84553075151977277 / 160000000000000000 : ℝ) ≤ (-(637794369480791432831 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84553075151977277 / 160000000000000000 : ℝ) = - (84553075151977277 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84553075151977277 / 80000000000000000 : ℚ)) - (U := (55352810819208567169 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84553075151977277 / 80000000000000000 : ℝ) ≤ - (55352810819208567169 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1321134151135911 / 2500000000000000 : ℝ)) (q := - (84553075151977277 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84553075151977277 / 160000000000000000 : ℚ)) + (r' := (84553075151977277 / 80000000000000000 : ℚ)) + (U := (-(637794369480791432831 / 1000000000000000000000 : ℚ))) + (U' := (55352810819208567169 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (1321134151135911 / 2500000000000000 : ℚ)) + (q := (84553075151977277 / 160000000000000000 : ℚ)) + (U := (-(637794369480791432831 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_2 : Uω (aρ 2) (bρ 2) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -2983,25 +2623,21 @@ lemma U_479_2 : have hlg : Real.log (84170033661501037 / 160000000000000000 : ℝ) ≤ (-(321167425913844597629 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84170033661501037 / 160000000000000000 : ℝ) = - (84170033661501037 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84170033661501037 / 80000000000000000 : ℚ)) - (U := (25406164236155402371 / 500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (84170033661501037 / 80000000000000000 : ℝ) ≤ - (25406164236155402371 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2630212715372057 / 5000000000000000 : ℝ)) (q := - (84170033661501037 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84170033661501037 / 160000000000000000 : ℚ)) + (r' := (84170033661501037 / 80000000000000000 : ℚ)) + (U := (-(321167425913844597629 / 500000000000000000000 : ℚ))) + (U' := (25406164236155402371 / 500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (2630212715372057 / 5000000000000000 : ℚ)) + (q := (84170033661501037 / 160000000000000000 : ℚ)) + (U := (-(321167425913844597629 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_3 : Uω (aρ 3) (bρ 3) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3009,25 +2645,21 @@ lemma U_479_3 : have hlg : Real.log (16680713769480353 / 32000000000000000 : ℝ) ≤ (-(1302965429178912640407 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16680713769480353 / 32000000000000000 : ℝ) = - (16680713769480353 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16680713769480353 / 16000000000000000 : ℚ)) - (U := (83328931421087359593 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (16680713769480353 / 16000000000000000 : ℝ) ≤ - (83328931421087359593 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1042402687066341 / 2000000000000000 : ℝ)) (q := - (16680713769480353 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16680713769480353 / 32000000000000000 : ℚ)) + (r' := (16680713769480353 / 16000000000000000 : ℚ)) + (U := (-(1302965429178912640407 / 2000000000000000000000 : ℚ))) + (U' := (83328931421087359593 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (1042402687066341 / 2000000000000000 : ℚ)) + (q := (16680713769480353 / 32000000000000000 : ℚ)) + (U := (-(1302965429178912640407 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_4 : Uω (aρ 4) (bρ 4) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3035,25 +2667,21 @@ lemma U_479_4 : have hlg : Real.log (82129423010569821 / 160000000000000000 : ℝ) ≤ (-(3334387412826117338583 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (82129423010569821 / 160000000000000000 : ℝ) = - (82129423010569821 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82129423010569821 / 80000000000000000 : ℚ)) - (U := (131348488673882661417 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (82129423010569821 / 80000000000000000 : ℝ) ≤ - (131348488673882661417 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (641379923349089 / 1250000000000000 : ℝ)) (q := - (82129423010569821 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82129423010569821 / 160000000000000000 : ℚ)) + (r' := (82129423010569821 / 80000000000000000 : ℚ)) + (U := (-(3334387412826117338583 / 5000000000000000000000 : ℚ))) + (U' := (131348488673882661417 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (641379923349089 / 1250000000000000 : ℚ)) + (q := (82129423010569821 / 160000000000000000 : ℚ)) + (U := (-(3334387412826117338583 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_5 : Uω (aρ 5) (bρ 5) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3061,25 +2689,21 @@ lemma U_479_5 : have hlg : Real.log (80186163945248261 / 160000000000000000 : ℝ) ≤ (-(276329133748210301077 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80186163945248261 / 160000000000000000 : ℝ) = - (80186163945248261 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80186163945248261 / 80000000000000000 : ℚ)) - (U := (929738371789698923 / 400000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (80186163945248261 / 80000000000000000 : ℝ) ≤ - (929738371789698923 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5006321922962517 / 10000000000000000 : ℝ)) (q := - (80186163945248261 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80186163945248261 / 160000000000000000 : ℚ)) + (r' := (80186163945248261 / 80000000000000000 : ℚ)) + (U := (-(276329133748210301077 / 400000000000000000000 : ℚ))) + (U' := (929738371789698923 / 400000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (5006321922962517 / 10000000000000000 : ℚ)) + (q := (80186163945248261 / 160000000000000000 : ℚ)) + (U := (-(276329133748210301077 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_6 : Uω (aρ 6) (bρ 6) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3087,25 +2711,21 @@ lemma U_479_6 : have hlg : Real.log (77392359551862197 / 160000000000000000 : ℝ) ≤ (-(7262857527910127196811 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (77392359551862197 / 160000000000000000 : ℝ) = - (77392359551862197 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77392359551862197 / 40000000000000000 : ℚ)) - (U := (6600086078089872803189 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (77392359551862197 / 40000000000000000 : ℝ) ≤ - (6600086078089872803189 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4824336748929259 / 10000000000000000 : ℝ)) (q := - (77392359551862197 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77392359551862197 / 160000000000000000 : ℚ)) + (r' := (77392359551862197 / 40000000000000000 : ℚ)) + (U := (-(7262857527910127196811 / 10000000000000000000000 : ℚ))) + (U' := (6600086078089872803189 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (4824336748929259 / 10000000000000000 : ℚ)) + (q := (77392359551862197 / 160000000000000000 : ℚ)) + (U := (-(7262857527910127196811 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_7 : Uω (aρ 7) (bρ 7) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3113,25 +2733,21 @@ lemma U_479_7 : have hlg : Real.log (73565493006656277 / 160000000000000000 : ℝ) ≤ (-(7769977439395536664309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (73565493006656277 / 160000000000000000 : ℝ) = - (73565493006656277 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (73565493006656277 / 40000000000000000 : ℚ)) - (U := (6092966166604463335691 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (73565493006656277 / 40000000000000000 : ℝ) ≤ - (6092966166604463335691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4569639811538519 / 10000000000000000 : ℝ)) (q := - (73565493006656277 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (73565493006656277 / 160000000000000000 : ℚ)) + (r' := (73565493006656277 / 40000000000000000 : ℚ)) + (U := (-(7769977439395536664309 / 10000000000000000000000 : ℚ))) + (U' := (6092966166604463335691 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (4569639811538519 / 10000000000000000 : ℚ)) + (q := (73565493006656277 / 160000000000000000 : ℚ)) + (U := (-(7769977439395536664309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_8 : Uω (aρ 8) (bρ 8) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3139,25 +2755,21 @@ lemma U_479_8 : have hlg : Real.log (68537930528878301 / 160000000000000000 : ℝ) ≤ (-(8477864923492468921267 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (68537930528878301 / 160000000000000000 : ℝ) = - (68537930528878301 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (68537930528878301 / 40000000000000000 : ℚ)) - (U := (5385078682507531078733 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (68537930528878301 / 40000000000000000 : ℝ) ≤ - (5385078682507531078733 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (264046009572267 / 625000000000000 : ℝ)) (q := - (68537930528878301 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (68537930528878301 / 160000000000000000 : ℚ)) + (r' := (68537930528878301 / 40000000000000000 : ℚ)) + (U := (-(8477864923492468921267 / 10000000000000000000000 : ℚ))) + (U' := (5385078682507531078733 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (264046009572267 / 625000000000000 : ℚ)) + (q := (68537930528878301 / 160000000000000000 : ℚ)) + (U := (-(8477864923492468921267 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_9 : Uω (aρ 9) (bρ 9) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3165,25 +2777,21 @@ lemma U_479_9 : have hlg : Real.log (62159538752414389 / 160000000000000000 : ℝ) ≤ (-(9454695290100289161531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (62159538752414389 / 160000000000000000 : ℝ) = - (62159538752414389 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62159538752414389 / 40000000000000000 : ℚ)) - (U := (4408248315899710838469 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62159538752414389 / 40000000000000000 : ℝ) ≤ - (4408248315899710838469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3768402809458283 / 10000000000000000 : ℝ)) (q := - (62159538752414389 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62159538752414389 / 160000000000000000 : ℚ)) + (r' := (62159538752414389 / 40000000000000000 : ℚ)) + (U := (-(9454695290100289161531 / 10000000000000000000000 : ℚ))) + (U' := (4408248315899710838469 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (3768402809458283 / 10000000000000000 : ℚ)) + (q := (62159538752414389 / 160000000000000000 : ℚ)) + (U := (-(9454695290100289161531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_10 : Uω (aρ 10) (bρ 10) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3191,26 +2799,21 @@ lemma U_479_10 : have hlg : Real.log (54257865842343221 / 160000000000000000 : ℝ) ≤ (-(10814258403181725422127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54257865842343221 / 160000000000000000 : ℝ) = - (54257865842343221 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54257865842343221 / 40000000000000000 : ℚ)) - (U := (3048685202818274577873 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54257865842343221 / 40000000000000000 : ℝ) ≤ - (3048685202818274577873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3169252729194387 / 10000000000000000 : ℝ)) (q := - (54257865842343221 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54257865842343221 / 160000000000000000 : ℚ)) + (r' := (54257865842343221 / 40000000000000000 : ℚ)) + (U := (-(10814258403181725422127 / 10000000000000000000000 : ℚ))) + (U' := (3048685202818274577873 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (3169252729194387 / 10000000000000000 : ℚ)) + (q := (54257865842343221 / 160000000000000000 : ℚ)) + (U := (-(10814258403181725422127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_11 : Uω (aρ 11) (bρ 11) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3218,26 +2821,21 @@ lemma U_479_11 : have hlg : Real.log (44432295892864621 / 160000000000000000 : ℝ) ≤ (-(12812072247175655142927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44432295892864621 / 160000000000000000 : ℝ) = - (44432295892864621 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44432295892864621 / 40000000000000000 : ℚ)) - (U := (1050871358824344857073 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44432295892864621 / 40000000000000000 : ℝ) ≤ - (1050871358824344857073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1179766555857281 / 5000000000000000 : ℝ)) (q := - (44432295892864621 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44432295892864621 / 160000000000000000 : ℚ)) + (r' := (44432295892864621 / 40000000000000000 : ℚ)) + (U := (-(12812072247175655142927 / 10000000000000000000000 : ℚ))) + (U' := (1050871358824344857073 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (1179766555857281 / 5000000000000000 : ℚ)) + (q := (44432295892864621 / 160000000000000000 : ℚ)) + (U := (-(12812072247175655142927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_12 : Uω (aρ 12) (bρ 12) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3245,26 +2843,21 @@ lemma U_479_12 : have hlg : Real.log (30304185472766581 / 160000000000000000 : ℝ) ≤ (-(16638879770636086593247 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (30304185472766581 / 160000000000000000 : ℝ) = - (30304185472766581 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30304185472766581 / 20000000000000000 : ℚ)) - (U := (4155535638363913406753 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30304185472766581 / 20000000000000000 : ℝ) ≤ - (4155535638363913406753 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1017219405887307 / 10000000000000000 : ℝ)) (q := - (30304185472766581 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30304185472766581 / 160000000000000000 : ℚ)) + (r' := (30304185472766581 / 20000000000000000 : ℚ)) + (U := (-(16638879770636086593247 / 10000000000000000000000 : ℚ))) + (U' := (4155535638363913406753 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (68468416096493 / 128000000000000 : ℚ)) + (s := (1017219405887307 / 10000000000000000 : ℚ)) + (q := (30304185472766581 / 160000000000000000 : ℚ)) + (U := (-(16638879770636086593247 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_479_13 : Uω (aρ 13) (bρ 13) (68468416096493 / 128000000000000 : ℝ) ≤ @@ -3377,25 +2970,21 @@ lemma U_480_1 : have hlg : Real.log (1322702098936339 / 2500000000000000 : ℝ) ≤ (-(10185824683330590031 / 16000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1322702098936339 / 2500000000000000 : ℝ) = - (1322702098936339 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1322702098936339 / 1250000000000000 : ℚ)) - (U := (904530201469409969 / 16000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1322702098936339 / 1250000000000000 : ℝ) ≤ - (904530201469409969 / 16000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1322694459844553 / 2500000000000000 : ℝ)) (q := - (1322702098936339 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1322702098936339 / 2500000000000000 : ℚ)) + (r' := (1322702098936339 / 1250000000000000 : ℚ)) + (U := (-(10185824683330590031 / 16000000000000000000 : ℚ))) + (U' := (904530201469409969 / 16000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (1322694459844553 / 2500000000000000 : ℚ)) + (q := (1322702098936339 / 2500000000000000 : ℚ)) + (U := (-(10185824683330590031 / 16000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_2 : Uω (aρ 2) (bρ 2) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3403,25 +2992,21 @@ lemma U_480_2 : have hlg : Real.log (10533737010983287 / 20000000000000000 : ℝ) ≤ (-(1602872795690252040067 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10533737010983287 / 20000000000000000 : ℝ) = - (10533737010983287 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10533737010983287 / 10000000000000000 : ℚ)) - (U := (129995155059747959933 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10533737010983287 / 10000000000000000 : ℝ) ≤ - (129995155059747959933 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5266667071380787 / 10000000000000000 : ℝ)) (q := - (10533737010983287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10533737010983287 / 20000000000000000 : ℚ)) + (r' := (10533737010983287 / 10000000000000000 : ℚ)) + (U := (-(1602872795690252040067 / 2500000000000000000000 : ℚ))) + (U' := (129995155059747959933 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (5266667071380787 / 10000000000000000 : ℚ)) + (q := (10533737010983287 / 20000000000000000 : ℚ)) + (U := (-(1602872795690252040067 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_3 : Uω (aρ 3) (bρ 3) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3429,25 +3014,21 @@ lemma U_480_3 : have hlg : Real.log (10437930128683687 / 20000000000000000 : ℝ) ≤ (-(6502859740324113881097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10437930128683687 / 20000000000000000 : ℝ) = - (10437930128683687 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10437930128683687 / 10000000000000000 : ℚ)) - (U := (428612062675886118903 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10437930128683687 / 10000000000000000 : ℝ) ≤ - (428612062675886118903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5218256295431187 / 10000000000000000 : ℝ)) (q := - (10437930128683687 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10437930128683687 / 20000000000000000 : ℚ)) + (r' := (10437930128683687 / 10000000000000000 : ℚ)) + (U := (-(6502859740324113881097 / 10000000000000000000000 : ℚ))) + (U' := (428612062675886118903 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (5218256295431187 / 10000000000000000 : ℚ)) + (q := (10437930128683687 / 20000000000000000 : ℚ)) + (U := (-(6502859740324113881097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_4 : Uω (aρ 4) (bρ 4) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3455,25 +3036,21 @@ lemma U_480_4 : have hlg : Real.log (5139332590770681 / 10000000000000000 : ℝ) ≤ (-(6656618678513322478103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5139332590770681 / 10000000000000000 : ℝ) = - (5139332590770681 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5139332590770681 / 5000000000000000 : ℚ)) - (U := (274853124486677521897 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5139332590770681 / 5000000000000000 : ℝ) ≤ - (274853124486677521897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2568642764676931 / 5000000000000000 : ℝ)) (q := - (5139332590770681 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5139332590770681 / 10000000000000000 : ℚ)) + (r' := (5139332590770681 / 5000000000000000 : ℚ)) + (U := (-(6656618678513322478103 / 10000000000000000000000 : ℚ))) + (U' := (274853124486677521897 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (2568642764676931 / 5000000000000000 : ℚ)) + (q := (5139332590770681 / 10000000000000000 : ℚ)) + (U := (-(6656618678513322478103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_5 : Uω (aρ 5) (bρ 5) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3481,25 +3058,21 @@ lemma U_480_5 : have hlg : Real.log (2508941512434543 / 5000000000000000 : ℝ) ≤ (-(21549279880243073947 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2508941512434543 / 5000000000000000 : ℝ) = - (2508941512434543 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2508941512434543 / 2500000000000000 : ℚ)) - (U := (111569504131926053 / 31250000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2508941512434543 / 2500000000000000 : ℝ) ≤ - (111569504131926053 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626572039610709 / 1250000000000000 : ℝ)) (q := - (2508941512434543 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2508941512434543 / 5000000000000000 : ℚ)) + (r' := (2508941512434543 / 2500000000000000 : ℚ)) + (U := (-(21549279880243073947 / 31250000000000000000 : ℚ))) + (U' := (111569504131926053 / 31250000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (626572039610709 / 1250000000000000 : ℚ)) + (q := (2508941512434543 / 5000000000000000 : ℚ)) + (U := (-(21549279880243073947 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_6 : Uω (aρ 6) (bρ 6) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3507,25 +3080,21 @@ lemma U_480_6 : have hlg : Real.log (4843280024696013 / 10000000000000000 : ℝ) ≤ (-(7249929102216071350707 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4843280024696013 / 10000000000000000 : ℝ) = - (4843280024696013 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4843280024696013 / 2500000000000000 : ℚ)) - (U := (6613014503783928649293 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4843280024696013 / 2500000000000000 : ℝ) ≤ - (6613014503783928649293 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2415305345839763 / 5000000000000000 : ℝ)) (q := - (4843280024696013 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4843280024696013 / 10000000000000000 : ℚ)) + (r' := (4843280024696013 / 2500000000000000 : ℚ)) + (U := (-(7249929102216071350707 / 10000000000000000000000 : ℚ))) + (U' := (6613014503783928649293 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (2415305345839763 / 5000000000000000 : ℚ)) + (q := (4843280024696013 / 10000000000000000 : ℚ)) + (U := (-(7249929102216071350707 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_7 : Uω (aρ 7) (bρ 7) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3533,25 +3102,21 @@ lemma U_480_7 : have hlg : Real.log (2302061471369069 / 5000000000000000 : ℝ) ≤ (-(7756328985092475948893 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2302061471369069 / 5000000000000000 : ℝ) = - (2302061471369069 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2302061471369069 / 1250000000000000 : ℚ)) - (U := (6106614620907524051107 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2302061471369069 / 1250000000000000 : ℝ) ≤ - (6106614620907524051107 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17874835580171 / 39062500000000 : ℝ)) (q := - (2302061471369069 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2302061471369069 / 5000000000000000 : ℚ)) + (r' := (2302061471369069 / 1250000000000000 : ℚ)) + (U := (-(7756328985092475948893 / 10000000000000000000000 : ℚ))) + (U' := (6106614620907524051107 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (17874835580171 / 39062500000000 : ℚ)) + (q := (2302061471369069 / 5000000000000000 : ℚ)) + (U := (-(7756328985092475948893 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_8 : Uω (aρ 8) (bρ 8) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3559,25 +3124,21 @@ lemma U_480_8 : have hlg : Real.log (8579897360264411 / 20000000000000000 : ℝ) ≤ (-(8463103222789283762703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8579897360264411 / 20000000000000000 : ℝ) = - (8579897360264411 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8579897360264411 / 5000000000000000 : ℚ)) - (U := (5399840383210716237297 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8579897360264411 / 5000000000000000 : ℝ) ≤ - (5399840383210716237297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4231151034651911 / 10000000000000000 : ℝ)) (q := - (8579897360264411 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8579897360264411 / 20000000000000000 : ℚ)) + (r' := (8579897360264411 / 5000000000000000 : ℚ)) + (U := (-(8463103222789283762703 / 10000000000000000000000 : ℚ))) + (U' := (5399840383210716237297 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (4231151034651911 / 10000000000000000 : ℚ)) + (q := (8579897360264411 / 20000000000000000 : ℚ)) + (U := (-(8463103222789283762703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_9 : Uω (aρ 9) (bρ 9) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3585,25 +3146,21 @@ lemma U_480_9 : have hlg : Real.log (1945702532055567 / 5000000000000000 : ℝ) ≤ (-(4719074005300819373633 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1945702532055567 / 5000000000000000 : ℝ) = - (1945702532055567 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1945702532055567 / 1250000000000000 : ℚ)) - (U := (2212397797699180626367 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1945702532055567 / 1250000000000000 : ℝ) ≤ - (2212397797699180626367 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (471878678871221 / 1250000000000000 : ℝ)) (q := - (1945702532055567 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1945702532055567 / 5000000000000000 : ℚ)) + (r' := (1945702532055567 / 1250000000000000 : ℚ)) + (U := (-(4719074005300819373633 / 5000000000000000000000 : ℚ))) + (U' := (2212397797699180626367 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (471878678871221 / 1250000000000000 : ℚ)) + (q := (1945702532055567 / 5000000000000000 : ℚ)) + (U := (-(4719074005300819373633 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_10 : Uω (aρ 10) (bρ 10) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3611,26 +3168,21 @@ lemma U_480_10 : have hlg : Real.log (3397793772506151 / 10000000000000000 : ℝ) ≤ (-(10794587619119258863077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3397793772506151 / 10000000000000000 : ℝ) = - (3397793772506151 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3397793772506151 / 2500000000000000 : ℚ)) - (U := (3068355986880741136923 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3397793772506151 / 2500000000000000 : ℝ) ≤ - (3068355986880741136923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1588182940627401 / 5000000000000000 : ℝ)) (q := - (3397793772506151 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3397793772506151 / 10000000000000000 : ℚ)) + (r' := (3397793772506151 / 2500000000000000 : ℚ)) + (U := (-(10794587619119258863077 / 10000000000000000000000 : ℚ))) + (U' := (3068355986880741136923 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (1588182940627401 / 5000000000000000 : ℚ)) + (q := (3397793772506151 / 10000000000000000 : ℚ)) + (U := (-(10794587619119258863077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_11 : Uω (aρ 11) (bρ 11) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3638,26 +3190,21 @@ lemma U_480_11 : have hlg : Real.log (5568721028559307 / 20000000000000000 : ℝ) ≤ (-(12785668633140302686513 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5568721028559307 / 20000000000000000 : ℝ) = - (5568721028559307 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5568721028559307 / 5000000000000000 : ℚ)) - (U := (1077274972859697313487 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5568721028559307 / 5000000000000000 : ℝ) ≤ - (1077274972859697313487 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2367975991006807 / 10000000000000000 : ℝ)) (q := - (5568721028559307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5568721028559307 / 20000000000000000 : ℚ)) + (r' := (5568721028559307 / 5000000000000000 : ℚ)) + (U := (-(12785668633140302686513 / 10000000000000000000000 : ℚ))) + (U' := (1077274972859697313487 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (2367975991006807 / 10000000000000000 : ℚ)) + (q := (5568721028559307 / 20000000000000000 : ℚ)) + (U := (-(12785668633140302686513 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_12 : Uω (aρ 12) (bρ 12) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3665,25 +3212,21 @@ lemma U_480_12 : have hlg : Real.log (476392968685189 / 2500000000000000 : ℝ) ≤ (-(8289014659856279049473 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (476392968685189 / 2500000000000000 : ℝ) = - (476392968685189 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (476392968685189 / 312500000000000 : ℚ)) - (U := (2108193044643720950527 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (476392968685189 / 312500000000000 : ℝ) ≤ - (2108193044643720950527 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (258524702153503 / 2500000000000000 : ℝ)) (q := - (476392968685189 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (476392968685189 / 2500000000000000 : ℚ)) + (r' := (476392968685189 / 312500000000000 : ℚ)) + (U := (-(8289014659856279049473 / 5000000000000000000000 : ℚ))) + (U' := (2108193044643720950527 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2142134468079 / 4000000000000 : ℚ)) + (s := (258524702153503 / 2500000000000000 : ℚ)) + (q := (476392968685189 / 2500000000000000 : ℚ)) + (U := (-(8289014659856279049473 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_480_13 : Uω (aρ 13) (bρ 13) (2142134468079 / 4000000000000 : ℝ) ≤ @@ -3795,25 +3338,21 @@ lemma U_481_1 : have hlg : Real.log (84752793510513459 / 160000000000000000 : ℝ) ≤ (-(635435107480579353849 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84752793510513459 / 160000000000000000 : ℝ) = - (84752793510513459 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84752793510513459 / 80000000000000000 : ℚ)) - (U := (57712072819420646151 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84752793510513459 / 80000000000000000 : ℝ) ≤ - (57712072819420646151 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2648509537021349 / 5000000000000000 : ℝ)) (q := - (84752793510513459 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84752793510513459 / 160000000000000000 : ℚ)) + (r' := (84752793510513459 / 80000000000000000 : ℚ)) + (U := (-(635435107480579353849 / 1000000000000000000000 : ℚ))) + (U' := (57712072819420646151 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (2648509537021349 / 5000000000000000 : ℚ)) + (q := (84752793510513459 / 160000000000000000 : ℚ)) + (U := (-(635435107480579353849 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_2 : Uω (aρ 2) (bρ 2) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3821,25 +3360,21 @@ lemma U_481_2 : have hlg : Real.log (84369758505179243 / 160000000000000000 : ℝ) ≤ (-(799955986413626136757 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84369758505179243 / 160000000000000000 : ℝ) = - (84369758505179243 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84369758505179243 / 80000000000000000 : ℚ)) - (U := (66477988961373863243 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84369758505179243 / 80000000000000000 : ℝ) ≤ - (66477988961373863243 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5272908710885921 / 10000000000000000 : ℝ)) (q := - (84369758505179243 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84369758505179243 / 160000000000000000 : ℚ)) + (r' := (84369758505179243 / 80000000000000000 : ℚ)) + (U := (-(799955986413626136757 / 1250000000000000000000 : ℚ))) + (U' := (66477988961373863243 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (5272908710885921 / 10000000000000000 : ℚ)) + (q := (84369758505179243 / 160000000000000000 : ℚ)) + (U := (-(799955986413626136757 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_3 : Uω (aρ 3) (bρ 3) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3847,25 +3382,21 @@ lemma U_481_3 : have hlg : Real.log (83603313179088739 / 160000000000000000 : ℝ) ≤ (-(6490906643397133693603 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83603313179088739 / 160000000000000000 : ℝ) = - (83603313179088739 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83603313179088739 / 80000000000000000 : ℚ)) - (U := (440565159602866306397 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83603313179088739 / 80000000000000000 : ℝ) ≤ - (440565159602866306397 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (326531196967163 / 625000000000000 : ℝ)) (q := - (83603313179088739 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83603313179088739 / 160000000000000000 : ℚ)) + (r' := (83603313179088739 / 80000000000000000 : ℚ)) + (U := (-(6490906643397133693603 / 10000000000000000000000 : ℚ))) + (U' := (440565159602866306397 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (326531196967163 / 625000000000000 : ℚ)) + (q := (83603313179088739 / 160000000000000000 : ℚ)) + (U := (-(6490906643397133693603 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_4 : Uω (aρ 4) (bρ 4) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3873,25 +3404,21 @@ lemma U_481_4 : have hlg : Real.log (16465843959474311 / 32000000000000000 : ℝ) ≤ (-(6644477302373994372467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16465843959474311 / 32000000000000000 : ℝ) = - (16465843959474311 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16465843959474311 / 16000000000000000 : ℚ)) - (U := (286994500626005627533 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (16465843959474311 / 16000000000000000 : ℝ) ≤ - (286994500626005627533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16073536436953 / 31250000000000 : ℝ)) (q := - (16465843959474311 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16465843959474311 / 32000000000000000 : ℚ)) + (r' := (16465843959474311 / 16000000000000000 : ℚ)) + (U := (-(6644477302373994372467 / 10000000000000000000000 : ℚ))) + (U' := (286994500626005627533 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (16073536436953 / 31250000000000 : ℚ)) + (q := (16465843959474311 / 32000000000000000 : ℚ)) + (U := (-(6644477302373994372467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_5 : Uω (aρ 5) (bρ 5) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3899,25 +3426,21 @@ lemma U_481_5 : have hlg : Real.log (80386092587023787 / 160000000000000000 : ℝ) ≤ (-(6883326315246774074947 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80386092587023787 / 160000000000000000 : ℝ) = - (80386092587023787 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80386092587023787 / 80000000000000000 : ℚ)) - (U := (48145487753225925053 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (80386092587023787 / 80000000000000000 : ℝ) ≤ - (48145487753225925053 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5018830677866489 / 10000000000000000 : ℝ)) (q := - (80386092587023787 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80386092587023787 / 160000000000000000 : ℚ)) + (r' := (80386092587023787 / 80000000000000000 : ℚ)) + (U := (-(6883326315246774074947 / 10000000000000000000000 : ℚ))) + (U' := (48145487753225925053 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (5018830677866489 / 10000000000000000 : ℚ)) + (q := (80386092587023787 / 160000000000000000 : ℚ)) + (U := (-(6883326315246774074947 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_6 : Uω (aρ 6) (bρ 6) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3925,25 +3448,21 @@ lemma U_481_6 : have hlg : Real.log (77592600559880403 / 160000000000000000 : ℝ) ≤ (-(7237017456809963206417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (77592600559880403 / 160000000000000000 : ℝ) = - (77592600559880403 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77592600559880403 / 40000000000000000 : ℚ)) - (U := (6625926149190036793583 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (77592600559880403 / 40000000000000000 : ℝ) ≤ - (6625926149190036793583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2418442274806783 / 5000000000000000 : ℝ)) (q := - (77592600559880403 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77592600559880403 / 160000000000000000 : ℚ)) + (r' := (77592600559880403 / 40000000000000000 : ℚ)) + (U := (-(7237017456809963206417 / 10000000000000000000000 : ℚ))) + (U' := (6625926149190036793583 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (2418442274806783 / 5000000000000000 : ℚ)) + (q := (77592600559880403 / 160000000000000000 : ℚ)) + (U := (-(7237017456809963206417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_7 : Uω (aρ 7) (bρ 7) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3951,25 +3470,21 @@ lemma U_481_7 : have hlg : Real.log (73766439474050131 / 160000000000000000 : ℝ) ≤ (-(7742699362116177004641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (73766439474050131 / 160000000000000000 : ℝ) = - (73766439474050131 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (73766439474050131 / 40000000000000000 : ℚ)) - (U := (6120244243883822995359 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (73766439474050131 / 40000000000000000 : ℝ) ≤ - (6120244243883822995359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2291137897322391 / 5000000000000000 : ℝ)) (q := - (73766439474050131 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (73766439474050131 / 160000000000000000 : ℚ)) + (r' := (73766439474050131 / 40000000000000000 : ℚ)) + (U := (-(7742699362116177004641 / 10000000000000000000000 : ℚ))) + (U' := (6120244243883822995359 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (2291137897322391 / 5000000000000000 : ℚ)) + (q := (73766439474050131 / 160000000000000000 : ℚ)) + (U := (-(7742699362116177004641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_8 : Uω (aρ 8) (bρ 8) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -3977,25 +3492,21 @@ lemma U_481_8 : have hlg : Real.log (68740423084680027 / 160000000000000000 : ℝ) ≤ (-(33793455538278231109 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (68740423084680027 / 160000000000000000 : ℝ) = - (68740423084680027 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (68740423084680027 / 40000000000000000 : ℚ)) - (U := (21658318885721768891 / 40000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (68740423084680027 / 40000000000000000 : ℝ) ≤ - (21658318885721768891 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4237565397313519 / 10000000000000000 : ℝ)) (q := - (68740423084680027 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (68740423084680027 / 160000000000000000 : ℚ)) + (r' := (68740423084680027 / 40000000000000000 : ℚ)) + (U := (-(33793455538278231109 / 40000000000000000000 : ℚ))) + (U' := (21658318885721768891 / 40000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (4237565397313519 / 10000000000000000 : ℚ)) + (q := (68740423084680027 / 160000000000000000 : ℚ)) + (U := (-(33793455538278231109 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_9 : Uω (aρ 9) (bρ 9) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -4003,25 +3514,21 @@ lemma U_481_9 : have hlg : Real.log (12473082561275951 / 32000000000000000 : ℝ) ≤ (-(9421629749586235676443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12473082561275951 / 32000000000000000 : ℝ) = - (12473082561275951 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12473082561275951 / 8000000000000000 : ℚ)) - (U := (4441313856413764323557 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12473082561275951 / 8000000000000000 : ℝ) ≤ - (4441313856413764323557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (756330948177197 / 2000000000000000 : ℝ)) (q := - (12473082561275951 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12473082561275951 / 32000000000000000 : ℚ)) + (r' := (12473082561275951 / 8000000000000000 : ℚ)) + (U := (-(9421629749586235676443 / 10000000000000000000000 : ℚ))) + (U' := (4441313856413764323557 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (756330948177197 / 2000000000000000 : ℚ)) + (q := (12473082561275951 / 32000000000000000 : ℚ)) + (U := (-(9421629749586235676443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_10 : Uω (aρ 10) (bρ 10) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -4029,26 +3536,21 @@ lemma U_481_10 : have hlg : Real.log (10894301122940959 / 32000000000000000 : ℝ) ≤ (-(10774960825271525424907 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10894301122940959 / 32000000000000000 : ℝ) = - (10894301122940959 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10894301122940959 / 8000000000000000 : ℚ)) - (U := (3087982780728474575093 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (10894301122940959 / 8000000000000000 : ℝ) ≤ - (3087982780728474575093 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (636695075084323 / 2000000000000000 : ℝ)) (q := - (10894301122940959 / 32000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10894301122940959 / 32000000000000000 : ℚ)) + (r' := (10894301122940959 / 8000000000000000 : ℚ)) + (U := (-(10774960825271525424907 / 10000000000000000000000 : ℚ))) + (U' := (3087982780728474575093 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (636695075084323 / 2000000000000000 : ℚ)) + (q := (10894301122940959 / 32000000000000000 : ℚ)) + (U := (-(10774960825271525424907 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_11 : Uω (aρ 11) (bρ 11) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -4056,26 +3558,21 @@ lemma U_481_11 : have hlg : Real.log (44667131727406203 / 160000000000000000 : ℝ) ≤ (-(6379679458388677789959 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44667131727406203 / 160000000000000000 : ℝ) = - (44667131727406203 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44667131727406203 / 40000000000000000 : ℚ)) - (U := (551792344611322210041 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44667131727406203 / 40000000000000000 : ℝ) ≤ - (551792344611322210041 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2376405265714291 / 10000000000000000 : ℝ)) (q := - (44667131727406203 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44667131727406203 / 160000000000000000 : ℚ)) + (r' := (44667131727406203 / 40000000000000000 : ℚ)) + (U := (-(6379679458388677789959 / 5000000000000000000000 : ℚ))) + (U' := (551792344611322210041 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (2376405265714291 / 10000000000000000 : ℚ)) + (q := (44667131727406203 / 160000000000000000 : ℚ)) + (U := (-(6379679458388677789959 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_12 : Uω (aρ 12) (bρ 12) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -4083,26 +3580,21 @@ lemma U_481_12 : have hlg : Real.log (30672242057537979 / 160000000000000000 : ℝ) ≤ (-(3303631472747489113263 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (30672242057537979 / 160000000000000000 : ℝ) = - (30672242057537979 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30672242057537979 / 20000000000000000 : ℚ)) - (U := (855251609052510886737 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30672242057537979 / 20000000000000000 : ℝ) ≤ - (855251609052510886737 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1050744153665763 / 10000000000000000 : ℝ)) (q := - (30672242057537979 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30672242057537979 / 160000000000000000 : ℚ)) + (r' := (30672242057537979 / 20000000000000000 : ℚ)) + (U := (-(3303631472747489113263 / 2000000000000000000000 : ℚ))) + (U' := (855251609052510886737 / 2000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (68628189860563 / 128000000000000 : ℚ)) + (s := (1050744153665763 / 10000000000000000 : ℚ)) + (q := (30672242057537979 / 160000000000000000 : ℚ)) + (U := (-(3303631472747489113263 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_481_13 : Uω (aρ 13) (bρ 13) (68628189860563 / 128000000000000 : ℝ) ≤ @@ -4215,25 +3707,21 @@ lemma U_482_1 : have hlg : Real.log (42426326343872691 / 80000000000000000 : ℝ) ≤ (-(3171287802603740539783 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42426326343872691 / 80000000000000000 : ℝ) = - (42426326343872691 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42426326343872691 / 40000000000000000 : ℚ)) - (U := (294448098896259460217 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42426326343872691 / 40000000000000000 : ℝ) ≤ - (294448098896259460217 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (662907538567213 / 1250000000000000 : ℝ)) (q := - (42426326343872691 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42426326343872691 / 80000000000000000 : ℚ)) + (r' := (42426326343872691 / 40000000000000000 : ℚ)) + (U := (-(3171287802603740539783 / 5000000000000000000000 : ℚ))) + (U' := (294448098896259460217 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (662907538567213 / 1250000000000000 : ℚ)) + (q := (42426326343872691 / 80000000000000000 : ℚ)) + (U := (-(3171287802603740539783 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_2 : Uω (aρ 2) (bρ 2) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4241,25 +3729,21 @@ lemma U_482_2 : have hlg : Real.log (42234810456735991 / 80000000000000000 : ℝ) ≤ (-(159695465267239470827 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42234810456735991 / 80000000000000000 : ℝ) = - (42234810456735991 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42234810456735991 / 40000000000000000 : ℚ)) - (U := (13591329807760529173 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42234810456735991 / 40000000000000000 : ℝ) ≤ - (13591329807760529173 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5279150349263529 / 10000000000000000 : ℝ)) (q := - (42234810456735991 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42234810456735991 / 80000000000000000 : ℚ)) + (r' := (42234810456735991 / 40000000000000000 : ℚ)) + (U := (-(159695465267239470827 / 250000000000000000000 : ℚ))) + (U' := (13591329807760529173 / 250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (5279150349263529 / 10000000000000000 : ℚ)) + (q := (42234810456735991 / 80000000000000000 : ℚ)) + (U := (-(159695465267239470827 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_3 : Uω (aρ 3) (bρ 3) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4267,25 +3751,21 @@ lemma U_482_3 : have hlg : Real.log (41851592648187839 / 80000000000000000 : ℝ) ≤ (-(1619741955232353905561 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41851592648187839 / 80000000000000000 : ℝ) = - (41851592648187839 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41851592648187839 / 40000000000000000 : ℚ)) - (U := (113125995517646094439 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41851592648187839 / 40000000000000000 : ℝ) ≤ - (113125995517646094439 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5230742003476491 / 10000000000000000 : ℝ)) (q := - (41851592648187839 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41851592648187839 / 80000000000000000 : ℚ)) + (r' := (41851592648187839 / 40000000000000000 : ℚ)) + (U := (-(1619741955232353905561 / 2500000000000000000000 : ℚ))) + (U' := (113125995517646094439 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (5230742003476491 / 10000000000000000 : ℚ)) + (q := (41851592648187839 / 80000000000000000 : ℚ)) + (U := (-(1619741955232353905561 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_4 : Uω (aρ 4) (bρ 4) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4293,24 +3773,21 @@ lemma U_482_4 : have hlg : Real.log (13188658887367 / 25600000000000 : ℝ) ≤ (-(6632350661352732514341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13188658887367 / 25600000000000 : ℝ) = (13188658887367 / 12800000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13188658887367 / 12800000000000 : ℚ)) - (U := (299121141647267485659 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (13188658887367 / 12800000000000 : ℝ) ≤ - (299121141647267485659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (20599111113 / 40000000000 : ℝ)) (q := - (13188658887367 / 25600000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13188658887367 / 25600000000000 : ℚ)) + (r' := (13188658887367 / 12800000000000 : ℚ)) + (U := (-(6632350661352732514341 / 10000000000000000000000 : ℚ))) + (U' := (299121141647267485659 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (20599111113 / 40000000000 : ℚ)) + (q := (13188658887367 / 25600000000000 : ℚ)) + (U := (-(6632350661352732514341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_5 : Uω (aρ 5) (bρ 5) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4318,25 +3795,21 @@ lemma U_482_5 : have hlg : Real.log (40243028256793767 / 80000000000000000 : ℝ) ≤ (-(3435449282817292923889 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40243028256793767 / 80000000000000000 : ℝ) = - (40243028256793767 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40243028256793767 / 40000000000000000 : ℚ)) - (U := (30286618682707076111 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40243028256793767 / 40000000000000000 : ℝ) ≤ - (30286618682707076111 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5025085006027973 / 10000000000000000 : ℝ)) (q := - (40243028256793767 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40243028256793767 / 80000000000000000 : ℚ)) + (r' := (40243028256793767 / 40000000000000000 : ℚ)) + (U := (-(3435449282817292923889 / 5000000000000000000000 : ℚ))) + (U' := (30286618682707076111 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (5025085006027973 / 10000000000000000 : ℚ)) + (q := (40243028256793767 / 80000000000000000 : ℚ)) + (U := (-(3435449282817292923889 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_6 : Uω (aρ 6) (bρ 6) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4344,25 +3817,21 @@ lemma U_482_6 : have hlg : Real.log (7769272004873171 / 16000000000000000 : ℝ) ≤ (-(3612061273981600181139 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7769272004873171 / 16000000000000000 : ℝ) = - (7769272004873171 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7769272004873171 / 4000000000000000 : ℚ)) - (U := (3319410529018399818861 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7769272004873171 / 4000000000000000 : ℝ) ≤ - (3319410529018399818861 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (968631664612199 / 2000000000000000 : ℝ)) (q := - (7769272004873171 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7769272004873171 / 16000000000000000 : ℚ)) + (r' := (7769272004873171 / 4000000000000000 : ℚ)) + (U := (-(3612061273981600181139 / 5000000000000000000000 : ℚ))) + (U' := (3319410529018399818861 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (968631664612199 / 2000000000000000 : ℚ)) + (q := (7769272004873171 / 16000000000000000 : ℚ)) + (U := (-(3612061273981600181139 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_7 : Uω (aρ 7) (bρ 7) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4370,25 +3839,21 @@ lemma U_482_7 : have hlg : Real.log (36933455092172003 / 80000000000000000 : ℝ) ≤ (-(7729088517948928495677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36933455092172003 / 80000000000000000 : ℝ) = - (36933455092172003 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36933455092172003 / 20000000000000000 : ℚ)) - (U := (6133855088051071504323 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36933455092172003 / 20000000000000000 : ℝ) ≤ - (6133855088051071504323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1147148367693133 / 2500000000000000 : ℝ)) (q := - (36933455092172003 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36933455092172003 / 80000000000000000 : ℚ)) + (r' := (36933455092172003 / 20000000000000000 : ℚ)) + (U := (-(7729088517948928495677 / 10000000000000000000000 : ℚ))) + (U' := (6133855088051071504323 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (1147148367693133 / 2500000000000000 : ℚ)) + (q := (36933455092172003 / 80000000000000000 : ℚ)) + (U := (-(7729088517948928495677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_8 : Uω (aρ 8) (bρ 8) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4396,25 +3861,21 @@ lemma U_482_8 : have hlg : Real.log (1376833263107851 / 3200000000000000 : ℝ) ≤ (-(4216823419692748033009 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1376833263107851 / 3200000000000000 : ℝ) = - (1376833263107851 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1376833263107851 / 800000000000000 : ℚ)) - (U := (2714648383307251966991 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1376833263107851 / 800000000000000 : ℝ) ≤ - (2714648383307251966991 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5304974054367 / 12500000000000 : ℝ)) (q := - (1376833263107851 / 3200000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1376833263107851 / 3200000000000000 : ℚ)) + (r' := (1376833263107851 / 800000000000000 : ℚ)) + (U := (-(4216823419692748033009 / 5000000000000000000000 : ℚ))) + (U' := (2714648383307251966991 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (5304974054367 / 12500000000000 : ℚ)) + (q := (1376833263107851 / 3200000000000000 : ℚ)) + (U := (-(4216823419692748033009 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_9 : Uω (aρ 9) (bρ 9) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4422,25 +3883,21 @@ lemma U_482_9 : have hlg : Real.log (31234167074635759 / 80000000000000000 : ℝ) ≤ (-(2351285099938865213181 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31234167074635759 / 80000000000000000 : ℝ) = - (31234167074635759 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31234167074635759 / 20000000000000000 : ℚ)) - (U := (1114450801561134786819 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31234167074635759 / 20000000000000000 : ℝ) ≤ - (1114450801561134786819 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3788278746088471 / 10000000000000000 : ℝ)) (q := - (31234167074635759 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31234167074635759 / 80000000000000000 : ℚ)) + (r' := (31234167074635759 / 20000000000000000 : ℚ)) + (U := (-(2351285099938865213181 / 2500000000000000000000 : ℚ))) + (U' := (1114450801561134786819 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (3788278746088471 / 10000000000000000 : ℚ)) + (q := (31234167074635759 / 80000000000000000 : ℚ)) + (U := (-(2351285099938865213181 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_10 : Uω (aρ 10) (bρ 10) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4448,26 +3905,21 @@ lemma U_482_10 : have hlg : Real.log (27289140900890719 / 80000000000000000 : ℝ) ≤ (-(84026389085341504191 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27289140900890719 / 80000000000000000 : ℝ) = - (27289140900890719 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27289140900890719 / 20000000000000000 : ℚ)) - (U := (24277857836533495809 / 78125000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27289140900890719 / 20000000000000000 : ℝ) ≤ - (24277857836533495809 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3190581236147211 / 10000000000000000 : ℝ)) (q := - (27289140900890719 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27289140900890719 / 80000000000000000 : ℚ)) + (r' := (27289140900890719 / 20000000000000000 : ℚ)) + (U := (-(84026389085341504191 / 78125000000000000000 : ℚ))) + (U' := (24277857836533495809 / 78125000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (3190581236147211 / 10000000000000000 : ℚ)) + (q := (27289140900890719 / 80000000000000000 : ℚ)) + (U := (-(84026389085341504191 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_11 : Uω (aρ 11) (bρ 11) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4475,26 +3927,21 @@ lemma U_482_11 : have hlg : Real.log (4478438754372667 / 16000000000000000 : ℝ) ≤ (-(2546628456716178291753 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4478438754372667 / 16000000000000000 : ℝ) = - (4478438754372667 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4478438754372667 / 4000000000000000 : ℚ)) - (U := (225960264483821708247 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4478438754372667 / 4000000000000000 : ℝ) ≤ - (225960264483821708247 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (476964216019073 / 2000000000000000 : ℝ)) (q := - (4478438754372667 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4478438754372667 / 16000000000000000 : ℚ)) + (r' := (4478438754372667 / 4000000000000000 : ℚ)) + (U := (-(2546628456716178291753 / 2000000000000000000000 : ℚ))) + (U' := (225960264483821708247 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (476964216019073 / 2000000000000000 : ℚ)) + (q := (4478438754372667 / 16000000000000000 : ℚ)) + (U := (-(2546628456716178291753 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_12 : Uω (aρ 12) (bρ 12) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4502,26 +3949,21 @@ lemma U_482_12 : have hlg : Real.log (15426774638283691 / 80000000000000000 : ℝ) ≤ (-(16459220212367328245369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15426774638283691 / 80000000000000000 : ℝ) = - (15426774638283691 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15426774638283691 / 10000000000000000 : ℚ)) - (U := (4335195196632671754631 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15426774638283691 / 10000000000000000 : ℝ) ≤ - (4335195196632671754631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (533583196692727 / 5000000000000000 : ℝ)) (q := - (15426774638283691 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15426774638283691 / 80000000000000000 : ℚ)) + (r' := (15426774638283691 / 10000000000000000 : ℚ)) + (U := (-(16459220212367328245369 / 10000000000000000000000 : ℚ))) + (U' := (4335195196632671754631 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34354038371299 / 64000000000000 : ℚ)) + (s := (533583196692727 / 5000000000000000 : ℚ)) + (q := (15426774638283691 / 80000000000000000 : ℚ)) + (U := (-(16459220212367328245369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_482_13 : Uω (aρ 13) (bρ 13) (34354038371299 / 64000000000000 : ℝ) ≤ @@ -4633,25 +4075,21 @@ lemma U_483_1 : have hlg : Real.log (84952511863626233 / 160000000000000000 : ℝ) ≤ (-(6330813985629369780369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84952511863626233 / 160000000000000000 : ℝ) = - (84952511863626233 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84952511863626233 / 80000000000000000 : ℚ)) - (U := (600657817370630219631 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84952511863626233 / 80000000000000000 : ℝ) ≤ - (600657817370630219631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2654750771431913 / 5000000000000000 : ℝ)) (q := - (84952511863626233 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84952511863626233 / 160000000000000000 : ℚ)) + (r' := (84952511863626233 / 80000000000000000 : ℚ)) + (U := (-(6330813985629369780369 / 10000000000000000000000 : ℚ))) + (U' := (600657817370630219631 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (2654750771431913 / 5000000000000000 : ℚ)) + (q := (84952511863626233 / 160000000000000000 : ℚ)) + (U := (-(6330813985629369780369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_2 : Uω (aρ 2) (bρ 2) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4659,25 +4097,21 @@ lemma U_483_2 : have hlg : Real.log (84569483312776481 / 160000000000000000 : ℝ) ≤ (-(3188001653894608997351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84569483312776481 / 160000000000000000 : ℝ) = - (84569483312776481 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84569483312776481 / 80000000000000000 : ℚ)) - (U := (277734247605391002649 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84569483312776481 / 80000000000000000 : ℝ) ≤ - (277734247605391002649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5285391986517607 / 10000000000000000 : ℝ)) (q := - (84569483312776481 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84569483312776481 / 160000000000000000 : ℚ)) + (r' := (84569483312776481 / 80000000000000000 : ℚ)) + (U := (-(3188001653894608997351 / 5000000000000000000000 : ℚ))) + (U' := (277734247605391002649 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (5285391986517607 / 10000000000000000 : ℚ)) + (q := (84569483312776481 / 160000000000000000 : ℚ)) + (U := (-(3188001653894608997351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_3 : Uω (aρ 3) (bρ 3) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4685,25 +4119,21 @@ lemma U_483_3 : have hlg : Real.log (83803057381445937 / 160000000000000000 : ℝ) ≤ (-(3233521619429571196959 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83803057381445937 / 160000000000000000 : ℝ) = - (83803057381445937 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83803057381445937 / 80000000000000000 : ℚ)) - (U := (232214282070428803041 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83803057381445937 / 80000000000000000 : ℝ) ≤ - (232214282070428803041 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5236984851451289 / 10000000000000000 : ℝ)) (q := - (83803057381445937 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83803057381445937 / 160000000000000000 : ℚ)) + (r' := (83803057381445937 / 80000000000000000 : ℚ)) + (U := (-(3233521619429571196959 / 5000000000000000000000 : ℚ))) + (U' := (232214282070428803041 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (5236984851451289 / 10000000000000000 : ℚ)) + (q := (83803057381445937 / 160000000000000000 : ℚ)) + (U := (-(3233521619429571196959 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_4 : Uω (aρ 4) (bρ 4) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4711,25 +4141,21 @@ lemma U_483_4 : have hlg : Real.log (16505803239739541 / 32000000000000000 : ℝ) ≤ (-(6620238719698710557651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16505803239739541 / 32000000000000000 : ℝ) = - (16505803239739541 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16505803239739541 / 16000000000000000 : ℚ)) - (U := (311233083301289442349 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (16505803239739541 / 16000000000000000 : ℝ) ≤ - (311233083301289442349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128900597116819 / 250000000000000 : ℝ)) (q := - (16505803239739541 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16505803239739541 / 32000000000000000 : ℚ)) + (r' := (16505803239739541 / 16000000000000000 : ℚ)) + (U := (-(6620238719698710557651 / 10000000000000000000000 : ℚ))) + (U' := (311233083301289442349 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (128900597116819 / 250000000000000 : ℚ)) + (q := (16505803239739541 / 32000000000000000 : ℚ)) + (U := (-(6620238719698710557651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_5 : Uω (aρ 5) (bρ 5) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4737,25 +4163,21 @@ lemma U_483_5 : have hlg : Real.log (80586020178575737 / 160000000000000000 : ℝ) ≤ (-(3429243137104443273827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80586020178575737 / 160000000000000000 : ℝ) = - (80586020178575737 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80586020178575737 / 80000000000000000 : ℚ)) - (U := (36492764395556726173 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (80586020178575737 / 80000000000000000 : ℝ) ≤ - (36492764395556726173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2515669650746257 / 5000000000000000 : ℝ)) (q := - (80586020178575737 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80586020178575737 / 160000000000000000 : ℚ)) + (r' := (80586020178575737 / 80000000000000000 : ℚ)) + (U := (-(3429243137104443273827 / 5000000000000000000000 : ℚ))) + (U' := (36492764395556726173 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (2515669650746257 / 5000000000000000 : ℚ)) + (q := (80586020178575737 / 160000000000000000 : ℚ)) + (U := (-(3429243137104443273827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_6 : Uω (aρ 6) (bρ 6) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4763,25 +4185,21 @@ lemma U_483_6 : have hlg : Real.log (77792838864313353 / 160000000000000000 : ℝ) ≤ (-(7211244332118761894243 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (77792838864313353 / 160000000000000000 : ℝ) = - (77792838864313353 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77792838864313353 / 40000000000000000 : ℚ)) - (U := (6651699273881238105757 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (77792838864313353 / 40000000000000000 : ℝ) ≤ - (6651699273881238105757 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1212358003087429 / 2500000000000000 : ℝ)) (q := - (77792838864313353 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77792838864313353 / 160000000000000000 : ℚ)) + (r' := (77792838864313353 / 40000000000000000 : ℚ)) + (U := (-(7211244332118761894243 / 10000000000000000000000 : ℚ))) + (U' := (6651699273881238105757 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (1212358003087429 / 2500000000000000 : ℚ)) + (q := (77792838864313353 / 160000000000000000 : ℚ)) + (U := (-(7211244332118761894243 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_7 : Uω (aρ 7) (bρ 7) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4789,25 +4207,21 @@ lemma U_483_7 : have hlg : Real.log (73967379221621257 / 160000000000000000 : ℝ) ≤ (-(3857748200147473405413 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (73967379221621257 / 160000000000000000 : ℝ) = - (73967379221621257 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (73967379221621257 / 40000000000000000 : ℚ)) - (U := (3073723602852526594587 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (73967379221621257 / 40000000000000000 : ℝ) ≤ - (3073723602852526594587 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1148727734443301 / 2500000000000000 : ℝ)) (q := - (73967379221621257 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (73967379221621257 / 160000000000000000 : ℚ)) + (r' := (73967379221621257 / 40000000000000000 : ℚ)) + (U := (-(3857748200147473405413 / 5000000000000000000000 : ℚ))) + (U' := (3073723602852526594587 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (1148727734443301 / 2500000000000000 : ℚ)) + (q := (73967379221621257 / 160000000000000000 : ℚ)) + (U := (-(3857748200147473405413 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_8 : Uω (aρ 8) (bρ 8) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4815,25 +4229,21 @@ lemma U_483_8 : have hlg : Real.log (68942899112957753 / 160000000000000000 : ℝ) ≤ (-(210473800453005356507 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (68942899112957753 / 160000000000000000 : ℝ) = - (68942899112957753 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (68942899112957753 / 40000000000000000 : ℚ)) - (U := (136099789696994643493 / 250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (68942899112957753 / 40000000000000000 : ℝ) ≤ - (136099789696994643493 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2125196287765133 / 5000000000000000 : ℝ)) (q := - (68942899112957753 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (68942899112957753 / 160000000000000000 : ℚ)) + (r' := (68942899112957753 / 40000000000000000 : ℚ)) + (U := (-(210473800453005356507 / 250000000000000000000 : ℚ))) + (U' := (136099789696994643493 / 250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (2125196287765133 / 5000000000000000 : ℚ)) + (q := (68942899112957753 / 160000000000000000 : ℚ)) + (U := (-(210473800453005356507 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_9 : Uω (aρ 9) (bρ 9) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4841,25 +4251,21 @@ lemma U_483_9 : have hlg : Real.log (62571245109110529 / 160000000000000000 : ℝ) ≤ (-(2347169963608201734619 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (62571245109110529 / 160000000000000000 : ℝ) = - (62571245109110529 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62571245109110529 / 40000000000000000 : ℚ)) - (U := (1118565937891798265381 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62571245109110529 / 40000000000000000 : ℝ) ≤ - (1118565937891798265381 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3794901453409363 / 10000000000000000 : ℝ)) (q := - (62571245109110529 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62571245109110529 / 160000000000000000 : ℚ)) + (r' := (62571245109110529 / 40000000000000000 : ℚ)) + (U := (-(2347169963608201734619 / 2500000000000000000000 : ℚ))) + (U' := (1118565937891798265381 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (3794901453409363 / 10000000000000000 : ℚ)) + (q := (62571245109110529 / 160000000000000000 : ℚ)) + (U := (-(2347169963608201734619 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_10 : Uω (aρ 10) (bρ 10) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4867,26 +4273,21 @@ lemma U_483_10 : have hlg : Real.log (54685029115109073 / 160000000000000000 : ℝ) ≤ (-(10735838335119840614069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54685029115109073 / 160000000000000000 : ℝ) = - (54685029115109073 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54685029115109073 / 40000000000000000 : ℚ)) - (U := (3127105270880159385931 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54685029115109073 / 40000000000000000 : ℝ) ≤ - (3127105270880159385931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3197683487654181 / 10000000000000000 : ℝ)) (q := - (54685029115109073 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54685029115109073 / 160000000000000000 : ℚ)) + (r' := (54685029115109073 / 40000000000000000 : ℚ)) + (U := (-(10735838335119840614069 / 10000000000000000000000 : ℚ))) + (U' := (3127105270880159385931 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (3197683487654181 / 10000000000000000 : ℚ)) + (q := (54685029115109073 / 160000000000000000 : ℚ)) + (U := (-(10735838335119840614069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_11 : Uω (aρ 11) (bρ 11) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4894,26 +4295,21 @@ lemma U_483_11 : have hlg : Real.log (44901536813439489 / 160000000000000000 : ℝ) ≤ (-(12707017930806615344121 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44901536813439489 / 160000000000000000 : ℝ) = - (44901536813439489 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44901536813439489 / 40000000000000000 : ℚ)) - (U := (1155925675193384655879 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44901536813439489 / 40000000000000000 : ℝ) ≤ - (1155925675193384655879 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2393223576150483 / 10000000000000000 : ℝ)) (q := - (44901536813439489 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44901536813439489 / 160000000000000000 : ℚ)) + (r' := (44901536813439489 / 40000000000000000 : ℚ)) + (U := (-(12707017930806615344121 / 10000000000000000000000 : ℚ))) + (U' := (1155925675193384655879 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (2393223576150483 / 10000000000000000 : ℚ)) + (q := (44901536813439489 / 160000000000000000 : ℚ)) + (U := (-(12707017930806615344121 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_12 : Uω (aρ 12) (bρ 12) (68787963624633 / 128000000000000 : ℝ) ≤ @@ -4921,26 +4317,21 @@ lemma U_483_12 : have hlg : Real.log (6206630563877357 / 32000000000000000 : ℝ) ≤ (-(3280235471263865683437 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6206630563877357 / 32000000000000000 : ℝ) = - (6206630563877357 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6206630563877357 / 4000000000000000 : ℚ)) - (U := (878647610536134316563 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6206630563877357 / 4000000000000000 : ℝ) ≤ - (878647610536134316563 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (216675134715779 / 2000000000000000 : ℝ)) (q := - (6206630563877357 / 32000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6206630563877357 / 32000000000000000 : ℚ)) + (r' := (6206630563877357 / 4000000000000000 : ℚ)) + (U := (-(3280235471263865683437 / 2000000000000000000000 : ℚ))) + (U' := (878647610536134316563 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (68787963624633 / 128000000000000 : ℚ)) + (s := (216675134715779 / 2000000000000000 : ℚ)) + (q := (6206630563877357 / 32000000000000000 : ℚ)) + (U := (-(3280235471263865683437 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_483_13 : Uω (aρ 13) (bρ 13) (68787963624633 / 128000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U40.lean b/LeanPool/Zeta5Irrational/Table/U40.lean index 4e3d545438..83163f9bc9 100644 --- a/LeanPool/Zeta5Irrational/Table/U40.lean +++ b/LeanPool/Zeta5Irrational/Table/U40.lean @@ -24,25 +24,21 @@ lemma U_484_1 : have hlg : Real.log (4252618551908039 / 8000000000000000 : ℝ) ≤ (-(49367704558822225637 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4252618551908039 / 8000000000000000 : ℝ) = - (4252618551908039 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4252618551908039 / 4000000000000000 : ℚ)) - (U := (4784418902115274363 / 78125000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4252618551908039 / 4000000000000000 : ℝ) ≤ - (4784418902115274363 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (265787138851083 / 500000000000000 : ℝ)) (q := - (4252618551908039 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4252618551908039 / 8000000000000000 : ℚ)) + (r' := (4252618551908039 / 4000000000000000 : ℚ)) + (U := (-(49367704558822225637 / 78125000000000000000 : ℚ))) + (U' := (4784418902115274363 / 78125000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (265787138851083 / 500000000000000 : ℚ)) + (q := (4252618551908039 / 8000000000000000 : ℚ)) + (U := (-(49367704558822225637 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_2 : Uω (aρ 2) (bρ 2) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_484_2 : have hlg : Real.log (21167336425781133 / 40000000000000000 : ℝ) ≤ (-(3182100974805846120097 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21167336425781133 / 40000000000000000 : ℝ) = - (21167336425781133 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21167336425781133 / 20000000000000000 : ℚ)) - (U := (283634926694153879903 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21167336425781133 / 20000000000000000 : ℝ) ≤ - (283634926694153879903 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5291633622652129 / 10000000000000000 : ℝ)) (q := - (21167336425781133 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21167336425781133 / 40000000000000000 : ℚ)) + (r' := (21167336425781133 / 20000000000000000 : ℚ)) + (U := (-(3182100974805846120097 / 5000000000000000000000 : ℚ))) + (U' := (283634926694153879903 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (5291633622652129 / 10000000000000000 : ℚ)) + (q := (21167336425781133 / 40000000000000000 : ℚ)) + (U := (-(3182100974805846120097 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_3 : Uω (aρ 3) (bρ 3) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_484_3 : have hlg : Real.log (20975732358603649 / 40000000000000000 : ℝ) ≤ (-(129102657264926025039 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20975732358603649 / 40000000000000000 : ℝ) = - (20975732358603649 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20975732358603649 / 20000000000000000 : ℚ)) - (U := (9526778795073974961 / 200000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20975732358603649 / 20000000000000000 : ℝ) ≤ - (9526778795073974961 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5243227695413387 / 10000000000000000 : ℝ)) (q := - (20975732358603649 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20975732358603649 / 40000000000000000 : ℚ)) + (r' := (20975732358603649 / 20000000000000000 : ℚ)) + (U := (-(129102657264926025039 / 200000000000000000000 : ℚ))) + (U' := (9526778795073974961 / 200000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (5243227695413387 / 10000000000000000 : ℚ)) + (q := (20975732358603649 / 40000000000000000 : ℚ)) + (U := (-(129102657264926025039 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_4 : Uω (aρ 4) (bρ 4) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_484_4 : have hlg : Real.log (20657228563920487 / 40000000000000000 : ℝ) ≤ (-(1652035360447789156013 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20657228563920487 / 40000000000000000 : ℝ) = - (20657228563920487 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20657228563920487 / 20000000000000000 : ℚ)) - (U := (80832590302210843987 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20657228563920487 / 20000000000000000 : ℝ) ≤ - (80832590302210843987 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2581134989568403 / 5000000000000000 : ℝ)) (q := - (20657228563920487 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20657228563920487 / 40000000000000000 : ℚ)) + (r' := (20657228563920487 / 20000000000000000 : ℚ)) + (U := (-(1652035360447789156013 / 2500000000000000000000 : ℚ))) + (U' := (80832590302210843987 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (2581134989568403 / 5000000000000000 : ℚ)) + (q := (20657228563920487 / 40000000000000000 : ℚ)) + (U := (-(1652035360447789156013 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_5 : Uω (aρ 5) (bρ 5) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_484_5 : have hlg : Real.log (20171495895740663 / 40000000000000000 : ℝ) ≤ (-(1369217880496384891111 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20171495895740663 / 40000000000000000 : ℝ) = - (20171495895740663 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20171495895740663 / 20000000000000000 : ℚ)) - (U := (17076480103615108889 / 2000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20171495895740663 / 20000000000000000 : ℝ) ≤ - (17076480103615108889 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2518796782190947 / 5000000000000000 : ℝ)) (q := - (20171495895740663 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20171495895740663 / 40000000000000000 : ℚ)) + (r' := (20171495895740663 / 20000000000000000 : ℚ)) + (U := (-(1369217880496384891111 / 2000000000000000000000 : ℚ))) + (U' := (17076480103615108889 / 2000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (2518796782190947 / 5000000000000000 : ℚ)) + (q := (20171495895740663 / 40000000000000000 : ℚ)) + (U := (-(1369217880496384891111 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_6 : Uω (aρ 6) (bρ 6) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_484_6 : have hlg : Real.log (3894647850461749 / 8000000000000000 : ℝ) ≤ (-(3599191382945151200059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3894647850461749 / 8000000000000000 : ℝ) = - (3894647850461749 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3894647850461749 / 2000000000000000 : ℚ)) - (U := (3332280420054848799941 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3894647850461749 / 2000000000000000 : ℝ) ≤ - (3332280420054848799941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (971141123561187 / 2000000000000000 : ℝ)) (q := - (3894647850461749 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3894647850461749 / 8000000000000000 : ℚ)) + (r' := (3894647850461749 / 2000000000000000 : ℚ)) + (U := (-(3599191382945151200059 / 5000000000000000000000 : ℚ))) + (U' := (3332280420054848799941 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (971141123561187 / 2000000000000000 : ℚ)) + (q := (3894647850461749 / 8000000000000000 : ℚ)) + (U := (-(3599191382945151200059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_7 : Uω (aρ 7) (bρ 7) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_484_7 : have hlg : Real.log (3703392329638651 / 8000000000000000 : ℝ) ≤ (-(3850961478539558197473 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3703392329638651 / 8000000000000000 : ℝ) = - (3703392329638651 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3703392329638651 / 2000000000000000 : ℚ)) - (U := (3080510324460441802527 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3703392329638651 / 2000000000000000 : ℝ) ≤ - (3080510324460441802527 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (460122819650819 / 1000000000000000 : ℝ)) (q := - (3703392329638651 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3703392329638651 / 8000000000000000 : ℚ)) + (r' := (3703392329638651 / 2000000000000000 : ℚ)) + (U := (-(3850961478539558197473 / 5000000000000000000000 : ℚ))) + (U' := (3080510324460441802527 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (460122819650819 / 1000000000000000 : ℚ)) + (q := (3703392329638651 / 8000000000000000 : ℚ)) + (U := (-(3850961478539558197473 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_8 : Uω (aρ 8) (bρ 8) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_484_8 : have hlg : Real.log (17261032743991579 / 40000000000000000 : ℝ) ≤ (-(8404279351985589500927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17261032743991579 / 40000000000000000 : ℝ) = - (17261032743991579 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17261032743991579 / 10000000000000000 : ℚ)) - (U := (5458664254014410499073 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17261032743991579 / 10000000000000000 : ℝ) ≤ - (5458664254014410499073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (532100674468419 / 1250000000000000 : ℝ)) (q := - (17261032743991579 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17261032743991579 / 40000000000000000 : ℚ)) + (r' := (17261032743991579 / 10000000000000000 : ℚ)) + (U := (-(8404279351985589500927 / 10000000000000000000000 : ℚ))) + (U' := (5458664254014410499073 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (532100674468419 / 1250000000000000 : ℚ)) + (q := (17261032743991579 / 40000000000000000 : ℚ)) + (U := (-(8404279351985589500927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_9 : Uω (aρ 9) (bρ 9) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_484_9 : have hlg : Real.log (15668536435040589 / 40000000000000000 : ℝ) ≤ (-(4686124003779445722807 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15668536435040589 / 40000000000000000 : ℝ) = - (15668536435040589 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15668536435040589 / 10000000000000000 : ℚ)) - (U := (2245347799220554277193 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15668536435040589 / 10000000000000000 : ℝ) ≤ - (2245347799220554277193 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3801522869631857 / 10000000000000000 : ℝ)) (q := - (15668536435040589 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15668536435040589 / 40000000000000000 : ℚ)) + (r' := (15668536435040589 / 10000000000000000 : ℚ)) + (U := (-(4686124003779445722807 / 5000000000000000000000 : ℚ))) + (U' := (2245347799220554277193 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (3801522869631857 / 10000000000000000 : ℚ)) + (q := (15668536435040589 / 40000000000000000 : ℚ)) + (U := (-(4686124003779445722807 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_10 : Uω (aρ 10) (bρ 10) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_484_10 : have hlg : Real.log (2739587387332633 / 8000000000000000 : ℝ) ≤ (-(10716342206642952717589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2739587387332633 / 8000000000000000 : ℝ) = - (2739587387332633 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2739587387332633 / 2000000000000000 : ℚ)) - (U := (3146601399357047282411 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2739587387332633 / 2000000000000000 : ℝ) ≤ - (3146601399357047282411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (640956430787629 / 2000000000000000 : ℝ)) (q := - (2739587387332633 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2739587387332633 / 8000000000000000 : ℚ)) + (r' := (2739587387332633 / 2000000000000000 : ℚ)) + (U := (-(10716342206642952717589 / 10000000000000000000000 : ℚ))) + (U' := (3146601399357047282411 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (640956430787629 / 2000000000000000 : ℚ)) + (q := (2739587387332633 / 8000000000000000 : ℚ)) + (U := (-(10716342206642952717589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_11 : Uω (aρ 11) (bρ 11) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_484_11 : have hlg : Real.log (11254645163716239 / 40000000000000000 : ℝ) ≤ (-(6340492533616705606711 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11254645163716239 / 40000000000000000 : ℝ) = - (11254645163716239 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11254645163716239 / 10000000000000000 : ℚ)) - (U := (590979269383294393289 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11254645163716239 / 10000000000000000 : ℝ) ≤ - (590979269383294393289 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1200806446834841 / 5000000000000000 : ℝ)) (q := - (11254645163716239 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11254645163716239 / 40000000000000000 : ℚ)) + (r' := (11254645163716239 / 10000000000000000 : ℚ)) + (U := (-(6340492533616705606711 / 5000000000000000000000 : ℚ))) + (U' := (590979269383294393289 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (1200806446834841 / 5000000000000000 : ℚ)) + (q := (11254645163716239 / 40000000000000000 : ℚ)) + (U := (-(6340492533616705606711 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_12 : Uω (aρ 12) (bρ 12) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_484_12 : have hlg : Real.log (1560556402166403 / 8000000000000000 : ℝ) ≤ (-(8171995575870492649569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1560556402166403 / 8000000000000000 : ℝ) = - (1560556402166403 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1560556402166403 / 1000000000000000 : ℚ)) - (U := (2225212128629507350431 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1560556402166403 / 1000000000000000 : ℝ) ≤ - (2225212128629507350431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (109938141391257 / 1000000000000000 : ℝ)) (q := - (1560556402166403 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1560556402166403 / 8000000000000000 : ℚ)) + (r' := (1560556402166403 / 1000000000000000 : ℚ)) + (U := (-(8171995575870492649569 / 5000000000000000000000 : ℚ))) + (U' := (2225212128629507350431 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17216962626667 / 32000000000000 : ℚ)) + (s := (109938141391257 / 1000000000000000 : ℚ)) + (q := (1560556402166403 / 8000000000000000 : ℚ)) + (U := (-(8171995575870492649569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_484_13 : Uω (aρ 13) (bρ 13) (17216962626667 / 32000000000000 : ℝ) ≤ @@ -444,25 +393,21 @@ lemma U_485_1 : have hlg : Real.log (85152230211353759 / 160000000000000000 : ℝ) ≤ (-(6307332166479452008709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85152230211353759 / 160000000000000000 : ℝ) = - (85152230211353759 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85152230211353759 / 80000000000000000 : ℚ)) - (U := (624139636520547991291 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85152230211353759 / 80000000000000000 : ℝ) ≤ - (624139636520547991291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2660992005505899 / 5000000000000000 : ℝ)) (q := - (85152230211353759 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85152230211353759 / 160000000000000000 : ℚ)) + (r' := (85152230211353759 / 80000000000000000 : ℚ)) + (U := (-(6307332166479452008709 / 10000000000000000000000 : ℚ))) + (U' := (624139636520547991291 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (2660992005505899 / 5000000000000000 : ℚ)) + (q := (85152230211353759 / 160000000000000000 : ℚ)) + (U := (-(6307332166479452008709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_2 : Uω (aρ 2) (bρ 2) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -470,25 +415,21 @@ lemma U_485_2 : have hlg : Real.log (84769208084547807 / 160000000000000000 : ℝ) ≤ (-(6352414503277472699569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84769208084547807 / 160000000000000000 : ℝ) = - (84769208084547807 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84769208084547807 / 80000000000000000 : ℚ)) - (U := (579057299722527300431 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84769208084547807 / 80000000000000000 : ℝ) ≤ - (579057299722527300431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2648937628835527 / 5000000000000000 : ℝ)) (q := - (84769208084547807 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84769208084547807 / 160000000000000000 : ℚ)) + (r' := (84769208084547807 / 80000000000000000 : ℚ)) + (U := (-(6352414503277472699569 / 10000000000000000000000 : ℚ))) + (U' := (579057299722527300431 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (2648937628835527 / 5000000000000000 : ℚ)) + (q := (84769208084547807 / 160000000000000000 : ℚ)) + (U := (-(6352414503277472699569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_3 : Uω (aρ 3) (bρ 3) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -496,25 +437,21 @@ lemma U_485_3 : have hlg : Real.log (84002801455396183 / 160000000000000000 : ℝ) ≤ (-(644323666027210507003 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84002801455396183 / 160000000000000000 : ℝ) = - (84002801455396183 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84002801455396183 / 80000000000000000 : ℚ)) - (U := (48823514272789492997 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (84002801455396183 / 80000000000000000 : ℝ) ≤ - (48823514272789492997 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5249470535377101 / 10000000000000000 : ℝ)) (q := - (84002801455396183 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84002801455396183 / 160000000000000000 : ℚ)) + (r' := (84002801455396183 / 80000000000000000 : ℚ)) + (U := (-(644323666027210507003 / 1000000000000000000000 : ℚ))) + (U' := (48823514272789492997 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (5249470535377101 / 10000000000000000 : ℚ)) + (q := (84002801455396183 / 160000000000000000 : ℚ)) + (U := (-(644323666027210507003 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_4 : Uω (aρ 4) (bρ 4) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -522,25 +459,21 @@ lemma U_485_4 : have hlg : Real.log (82728812217343327 / 160000000000000000 : ℝ) ≤ (-(1319211758427744412517 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (82728812217343327 / 160000000000000000 : ℝ) = - (82728812217343327 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82728812217343327 / 80000000000000000 : ℚ)) - (U := (67082602172255587483 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (82728812217343327 / 80000000000000000 : ℝ) ≤ - (67082602172255587483 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2584258030842747 / 5000000000000000 : ℝ)) (q := - (82728812217343327 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82728812217343327 / 160000000000000000 : ℚ)) + (r' := (82728812217343327 / 80000000000000000 : ℚ)) + (U := (-(1319211758427744412517 / 2000000000000000000000 : ℚ))) + (U' := (67082602172255587483 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (2584258030842747 / 5000000000000000 : ℚ)) + (q := (82728812217343327 / 160000000000000000 : ℚ)) + (U := (-(1319211758427744412517 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_5 : Uω (aρ 5) (bρ 5) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -548,25 +481,21 @@ lemma U_485_5 : have hlg : Real.log (80785946727717703 / 160000000000000000 : ℝ) ≤ (-(3416853956054903156221 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80785946727717703 / 160000000000000000 : ℝ) = - (80785946727717703 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80785946727717703 / 80000000000000000 : ℚ)) - (U := (48881945445096843779 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (80785946727717703 / 80000000000000000 : ℝ) ≤ - (48881945445096843779 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5043847794817291 / 10000000000000000 : ℝ)) (q := - (80785946727717703 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80785946727717703 / 160000000000000000 : ℚ)) + (r' := (80785946727717703 / 80000000000000000 : ℚ)) + (U := (-(3416853956054903156221 / 5000000000000000000000 : ℚ))) + (U' := (48881945445096843779 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (5043847794817291 / 10000000000000000 : ℚ)) + (q := (80785946727717703 / 160000000000000000 : ℚ)) + (U := (-(3416853956054903156221 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_6 : Uω (aρ 6) (bρ 6) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -574,25 +503,21 @@ lemma U_485_6 : have hlg : Real.log (77993074486092727 / 160000000000000000 : ℝ) ≤ (-(1437107561212252026653 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (77993074486092727 / 160000000000000000 : ℝ) = - (77993074486092727 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (77993074486092727 / 40000000000000000 : ℚ)) - (U := (1335481159987747973347 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (77993074486092727 / 40000000000000000 : ℝ) ≤ - (1335481159987747973347 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4861979139754169 / 10000000000000000 : ℝ)) (q := - (77993074486092727 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (77993074486092727 / 160000000000000000 : ℚ)) + (r' := (77993074486092727 / 40000000000000000 : ℚ)) + (U := (-(1437107561212252026653 / 2000000000000000000000 : ℚ))) + (U' := (1335481159987747973347 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (4861979139754169 / 10000000000000000 : ℚ)) + (q := (77993074486092727 / 160000000000000000 : ℚ)) + (U := (-(1437107561212252026653 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_7 : Uω (aρ 7) (bρ 7) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -600,25 +525,21 @@ lemma U_485_7 : have hlg : Real.log (14833662460930483 / 32000000000000000 : ℝ) ≤ (-(7688368136445735574367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14833662460930483 / 32000000000000000 : ℝ) = - (14833662460930483 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14833662460930483 / 8000000000000000 : ℚ)) - (U := (6174575469554264425633 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (14833662460930483 / 8000000000000000 : ℝ) ≤ - (6174575469554264425633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (460754524783413 / 1000000000000000 : ℝ)) (q := - (14833662460930483 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14833662460930483 / 32000000000000000 : ℚ)) + (r' := (14833662460930483 / 8000000000000000 : ℚ)) + (U := (-(7688368136445735574367 / 10000000000000000000000 : ℚ))) + (U' := (6174575469554264425633 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (460754524783413 / 1000000000000000 : ℚ)) + (q := (14833662460930483 / 32000000000000000 : ℚ)) + (U := (-(7688368136445735574367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_8 : Uω (aρ 8) (bρ 8) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -626,25 +547,21 @@ lemma U_485_8 : have hlg : Real.log (69145358762895607 / 160000000000000000 : ℝ) ≤ (-(4194814386260065118497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (69145358762895607 / 160000000000000000 : ℝ) = - (69145358762895607 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69145358762895607 / 40000000000000000 : ℚ)) - (U := (2736657416739934881503 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69145358762895607 / 40000000000000000 : ℝ) ≤ - (2736657416739934881503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4263217706454529 / 10000000000000000 : ℝ)) (q := - (69145358762895607 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69145358762895607 / 160000000000000000 : ℚ)) + (r' := (69145358762895607 / 40000000000000000 : ℚ)) + (U := (-(4194814386260065118497 / 5000000000000000000000 : ℚ))) + (U' := (2736657416739934881503 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (4263217706454529 / 10000000000000000 : ℚ)) + (q := (69145358762895607 / 160000000000000000 : ℚ)) + (U := (-(4194814386260065118497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_9 : Uω (aρ 9) (bρ 9) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -652,25 +569,21 @@ lemma U_485_9 : have hlg : Real.log (62777036096304591 / 160000000000000000 : ℝ) ≤ (-(9355844753686533661381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (62777036096304591 / 160000000000000000 : ℝ) = - (62777036096304591 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62777036096304591 / 40000000000000000 : ℚ)) - (U := (4507098852313466338619 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62777036096304591 / 40000000000000000 : ℝ) ≤ - (4507098852313466338619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (952035750372663 / 2500000000000000 : ℝ)) (q := - (62777036096304591 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62777036096304591 / 160000000000000000 : ℚ)) + (r' := (62777036096304591 / 40000000000000000 : ℚ)) + (U := (-(9355844753686533661381 / 10000000000000000000000 : ℚ))) + (U' := (4507098852313466338619 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (952035750372663 / 2500000000000000 : ℚ)) + (q := (62777036096304591 / 160000000000000000 : ℚ)) + (U := (-(9355844753686533661381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_10 : Uω (aρ 10) (bρ 10) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -678,26 +591,21 @@ lemma U_485_10 : have hlg : Real.log (54898437886583623 / 160000000000000000 : ℝ) ≤ (-(1337111150499449144981 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54898437886583623 / 160000000000000000 : ℝ) = - (54898437886583623 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54898437886583623 / 40000000000000000 : ℚ)) - (U := (395756800250550855019 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54898437886583623 / 40000000000000000 : ℝ) ≤ - (395756800250550855019 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3211877258770531 / 10000000000000000 : ℝ)) (q := - (54898437886583623 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54898437886583623 / 160000000000000000 : ℚ)) + (r' := (54898437886583623 / 40000000000000000 : ℚ)) + (U := (-(1337111150499449144981 / 1250000000000000000000 : ℚ))) + (U' := (395756800250550855019 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (3211877258770531 / 10000000000000000 : ℚ)) + (q := (54898437886583623 / 160000000000000000 : ℚ)) + (U := (-(1337111150499449144981 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_11 : Uω (aρ 11) (bρ 11) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -705,26 +613,21 @@ lemma U_485_11 : have hlg : Real.log (45135520169009759 / 160000000000000000 : ℝ) ≤ (-(6327521456465553556581 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45135520169009759 / 160000000000000000 : ℝ) = - (45135520169009759 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45135520169009759 / 40000000000000000 : ℚ)) - (U := (603950346534446443419 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45135520169009759 / 40000000000000000 : ℝ) ≤ - (603950346534446443419 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1204994585139399 / 5000000000000000 : ℝ)) (q := - (45135520169009759 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45135520169009759 / 160000000000000000 : ℚ)) + (r' := (45135520169009759 / 40000000000000000 : ℚ)) + (U := (-(6327521456465553556581 / 5000000000000000000000 : ℚ))) + (U' := (603950346534446443419 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (1204994585139399 / 5000000000000000 : ℚ)) + (q := (45135520169009759 / 160000000000000000 : ℚ)) + (U := (-(6327521456465553556581 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_12 : Uω (aρ 12) (bρ 12) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -732,26 +635,21 @@ lemma U_485_12 : have hlg : Real.log (6277509011950307 / 32000000000000000 : ℝ) ≤ (-(407190663593972207153 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6277509011950307 / 32000000000000000 : ℝ) = - (6277509011950307 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6277509011950307 / 4000000000000000 : ℚ)) - (U := (112669721631027792847 / 250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6277509011950307 / 4000000000000000 : ℝ) ≤ - (112669721631027792847 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (27879809457663 / 250000000000000 : ℝ)) (q := - (6277509011950307 / 32000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6277509011950307 / 32000000000000000 : ℚ)) + (r' := (6277509011950307 / 4000000000000000 : ℚ)) + (U := (-(407190663593972207153 / 250000000000000000000 : ℚ))) + (U' := (112669721631027792847 / 250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (68947737388703 / 128000000000000 : ℚ)) + (s := (27879809457663 / 250000000000000 : ℚ)) + (q := (6277509011950307 / 32000000000000000 : ℚ)) + (U := (-(407190663593972207153 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_485_13 : Uω (aρ 13) (bρ 13) (68947737388703 / 128000000000000 : ℝ) ≤ @@ -864,25 +762,21 @@ lemma U_486_1 : have hlg : Real.log (42626044691604937 / 80000000000000000 : ℝ) ≤ (-(786951487770795011317 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42626044691604937 / 80000000000000000 : ℝ) = - (42626044691604937 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42626044691604937 / 40000000000000000 : ℚ)) - (U := (79482487604204988683 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42626044691604937 / 40000000000000000 : ℝ) ≤ - (79482487604204988683 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1332056311208707 / 2500000000000000 : ℝ)) (q := - (42626044691604937 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42626044691604937 / 80000000000000000 : ℚ)) + (r' := (42626044691604937 / 40000000000000000 : ℚ)) + (U := (-(786951487770795011317 / 1250000000000000000000 : ℚ))) + (U' := (79482487604204988683 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (1332056311208707 / 2500000000000000 : ℚ)) + (q := (42626044691604937 / 80000000000000000 : ℚ)) + (U := (-(786951487770795011317 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_2 : Uω (aρ 2) (bρ 2) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -890,25 +784,21 @@ lemma U_486_2 : have hlg : Real.log (42434535228538897 / 80000000000000000 : ℝ) ≤ (-(792580117002899229761 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42434535228538897 / 80000000000000000 : ℝ) = - (42434535228538897 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42434535228538897 / 40000000000000000 : ℚ)) - (U := (73853858372100770239 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42434535228538897 / 40000000000000000 : ℝ) ≤ - (73853858372100770239 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2652058445789159 / 5000000000000000 : ℝ)) (q := - (42434535228538897 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42434535228538897 / 80000000000000000 : ℚ)) + (r' := (42434535228538897 / 40000000000000000 : ℚ)) + (U := (-(792580117002899229761 / 1250000000000000000000 : ℚ))) + (U' := (73853858372100770239 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (2652058445789159 / 5000000000000000 : ℚ)) + (q := (42434535228538897 / 80000000000000000 : ℚ)) + (U := (-(792580117002899229761 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_3 : Uω (aρ 3) (bρ 3) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -916,25 +806,21 @@ lemma U_486_3 : have hlg : Real.log (42051336722252341 / 80000000000000000 : ℝ) ≤ (-(6431354596238415003153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42051336722252341 / 80000000000000000 : ℝ) = - (42051336722252341 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42051336722252341 / 40000000000000000 : ℚ)) - (U := (500117206761584996847 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42051336722252341 / 40000000000000000 : ℝ) ≤ - (500117206761584996847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5255713371356679 / 10000000000000000 : ℝ)) (q := - (42051336722252341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42051336722252341 / 80000000000000000 : ℚ)) + (r' := (42051336722252341 / 40000000000000000 : ℚ)) + (U := (-(6431354596238415003153 / 10000000000000000000000 : ℚ))) + (U' := (500117206761584996847 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (5255713371356679 / 10000000000000000 : ℚ)) + (q := (42051336722252341 / 80000000000000000 : ℚ)) + (U := (-(6431354596238415003153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_4 : Uω (aρ 4) (bρ 4) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -942,25 +828,21 @@ lemma U_486_4 : have hlg : Real.log (41414355042013509 / 80000000000000000 : ℝ) ≤ (-(3291995367689427495473 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41414355042013509 / 80000000000000000 : ℝ) = - (41414355042013509 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41414355042013509 / 40000000000000000 : ℚ)) - (U := (173740533810572504527 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41414355042013509 / 40000000000000000 : ℝ) ≤ - (173740533810572504527 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5174762132361971 / 10000000000000000 : ℝ)) (q := - (41414355042013509 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41414355042013509 / 80000000000000000 : ℚ)) + (r' := (41414355042013509 / 40000000000000000 : ℚ)) + (U := (-(3291995367689427495473 / 5000000000000000000000 : ℚ))) + (U' := (173740533810572504527 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (5174762132361971 / 10000000000000000 : ℚ)) + (q := (41414355042013509 / 80000000000000000 : ℚ)) + (U := (-(3291995367689427495473 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_5 : Uω (aρ 5) (bρ 5) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -968,25 +850,21 @@ lemma U_486_5 : have hlg : Real.log (40442954806902749 / 80000000000000000 : ℝ) ≤ (-(1705335441222945381761 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40442954806902749 / 80000000000000000 : ℝ) = - (40442954806902749 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40442954806902749 / 40000000000000000 : ℚ)) - (U := (27532509527054618239 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40442954806902749 / 40000000000000000 : ℝ) ≤ - (27532509527054618239 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5050101992919281 / 10000000000000000 : ℝ)) (q := - (40442954806902749 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40442954806902749 / 80000000000000000 : ℚ)) + (r' := (40442954806902749 / 40000000000000000 : ℚ)) + (U := (-(1705335441222945381761 / 2500000000000000000000 : ℚ))) + (U' := (27532509527054618239 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (5050101992919281 / 10000000000000000 : ℚ)) + (q := (40442954806902749 / 80000000000000000 : ℚ)) + (U := (-(1705335441222945381761 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_6 : Uω (aρ 6) (bρ 6) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -994,25 +872,21 @@ lemma U_486_6 : have hlg : Real.log (39046595648734657 / 80000000000000000 : ℝ) ≤ (-(1793177352395991703339 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39046595648734657 / 80000000000000000 : ℝ) = - (39046595648734657 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39046595648734657 / 20000000000000000 : ℚ)) - (U := (1672558549104008296661 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39046595648734657 / 20000000000000000 : ℝ) ≤ - (1672558549104008296661 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2434126289258629 / 5000000000000000 : ℝ)) (q := - (39046595648734657 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39046595648734657 / 80000000000000000 : ℚ)) + (r' := (39046595648734657 / 20000000000000000 : ℚ)) + (U := (-(1793177352395991703339 / 2500000000000000000000 : ℚ))) + (U' := (1672558549104008296661 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (2434126289258629 / 5000000000000000 : ℚ)) + (q := (39046595648734657 / 80000000000000000 : ℚ)) + (U := (-(1793177352395991703339 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_7 : Uω (aρ 7) (bρ 7) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1020,25 +894,21 @@ lemma U_486_7 : have hlg : Real.log (37134388182037397 / 80000000000000000 : ℝ) ≤ (-(7674831886757274297583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37134388182037397 / 80000000000000000 : ℝ) = - (37134388182037397 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37134388182037397 / 20000000000000000 : ℚ)) - (U := (6188111719242725702417 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37134388182037397 / 20000000000000000 : ℝ) ≤ - (6188111719242725702417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4613862092602943 / 10000000000000000 : ℝ)) (q := - (37134388182037397 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37134388182037397 / 80000000000000000 : ℚ)) + (r' := (37134388182037397 / 20000000000000000 : ℚ)) + (U := (-(7674831886757274297583 / 10000000000000000000000 : ℚ))) + (U' := (6188111719242725702417 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (4613862092602943 / 10000000000000000 : ℚ)) + (q := (37134388182037397 / 80000000000000000 : ℚ)) + (U := (-(7674831886757274297583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_8 : Uω (aρ 8) (bρ 8) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1046,25 +916,21 @@ lemma U_486_8 : have hlg : Real.log (34623291246055249 / 80000000000000000 : ℝ) ≤ (-(837500021158687506521 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34623291246055249 / 80000000000000000 : ℝ) = - (34623291246055249 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34623291246055249 / 20000000000000000 : ℚ)) - (U := (548794339441312493479 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34623291246055249 / 20000000000000000 : ℝ) ≤ - (548794339441312493479 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2134814754973703 / 5000000000000000 : ℝ)) (q := - (34623291246055249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34623291246055249 / 80000000000000000 : ℚ)) + (r' := (34623291246055249 / 20000000000000000 : ℚ)) + (U := (-(837500021158687506521 / 1000000000000000000000 : ℚ))) + (U' := (548794339441312493479 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (2134814754973703 / 5000000000000000 : ℚ)) + (q := (34623291246055249 / 80000000000000000 : ℚ)) + (U := (-(837500021158687506521 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_9 : Uω (aρ 9) (bρ 9) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1072,25 +938,21 @@ lemma U_486_9 : have hlg : Real.log (31439958115515213 / 80000000000000000 : ℝ) ≤ (-(29185843712424599397 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31439958115515213 / 80000000000000000 : ℝ) = - (31439958115515213 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31439958115515213 / 20000000000000000 : ℚ)) - (U := (14135855056325400603 / 31250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31439958115515213 / 20000000000000000 : ℝ) ≤ - (14135855056325400603 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3814761855672397 / 10000000000000000 : ℝ)) (q := - (31439958115515213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31439958115515213 / 80000000000000000 : ℚ)) + (r' := (31439958115515213 / 20000000000000000 : ℚ)) + (U := (-(29185843712424599397 / 31250000000000000000 : ℚ))) + (U' := (14135855056325400603 / 31250000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (3814761855672397 / 10000000000000000 : ℚ)) + (q := (31439958115515213 / 80000000000000000 : ℚ)) + (U := (-(29185843712424599397 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_10 : Uω (aρ 10) (bρ 10) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1098,26 +960,21 @@ lemma U_486_10 : have hlg : Real.log (27502549861650857 / 80000000000000000 : ℝ) ≤ (-(10677479115380574000047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27502549861650857 / 80000000000000000 : ℝ) = - (27502549861650857 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27502549861650857 / 20000000000000000 : ℚ)) - (U := (3185464490619425999953 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27502549861650857 / 20000000000000000 : ℝ) ≤ - (3185464490619425999953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (804742206425327 / 2500000000000000 : ℝ)) (q := - (27502549861650857 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27502549861650857 / 80000000000000000 : ℚ)) + (r' := (27502549861650857 / 20000000000000000 : ℚ)) + (U := (-(10677479115380574000047 / 10000000000000000000000 : ℚ))) + (U' := (3185464490619425999953 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (804742206425327 / 2500000000000000 : ℚ)) + (q := (27502549861650857 / 80000000000000000 : ℚ)) + (U := (-(10677479115380574000047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_11 : Uω (aρ 11) (bρ 11) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1125,26 +982,21 @@ lemma U_486_11 : have hlg : Real.log (22626178219963501 / 80000000000000000 : ℝ) ≤ (-(2525838139806847648551 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22626178219963501 / 80000000000000000 : ℝ) = - (22626178219963501 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22626178219963501 / 20000000000000000 : ℚ)) - (U := (246750581393152351449 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22626178219963501 / 20000000000000000 : ℝ) ≤ - (246750581393152351449 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2418352541484469 / 10000000000000000 : ℝ)) (q := - (22626178219963501 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22626178219963501 / 80000000000000000 : ℚ)) + (r' := (22626178219963501 / 20000000000000000 : ℚ)) + (U := (-(2525838139806847648551 / 2000000000000000000000 : ℚ))) + (U' := (246750581393152351449 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (2418352541484469 / 10000000000000000 : ℚ)) + (q := (22626178219963501 / 80000000000000000 : ℚ)) + (U := (-(2525838139806847648551 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_12 : Uω (aρ 12) (bρ 12) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1152,26 +1004,21 @@ lemma U_486_12 : have hlg : Real.log (15781234614494777 / 80000000000000000 : ℝ) ≤ (-(16232050823419908826121 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15781234614494777 / 80000000000000000 : ℝ) = - (15781234614494777 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15781234614494777 / 10000000000000000 : ℚ)) - (U := (4562364585580091173879 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15781234614494777 / 10000000000000000 : ℝ) ≤ - (4562364585580091173879 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (70676046050143 / 625000000000000 : ℝ)) (q := - (15781234614494777 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15781234614494777 / 80000000000000000 : ℚ)) + (r' := (15781234614494777 / 10000000000000000 : ℚ)) + (U := (-(16232050823419908826121 / 10000000000000000000000 : ℚ))) + (U' := (4562364585580091173879 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34513812135369 / 64000000000000 : ℚ)) + (s := (70676046050143 / 625000000000000 : ℚ)) + (q := (15781234614494777 / 80000000000000000 : ℚ)) + (U := (-(16232050823419908826121 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_486_13 : Uω (aρ 13) (bρ 13) (34513812135369 / 64000000000000 : ℝ) ≤ @@ -1284,25 +1131,21 @@ lemma U_487_1 : have hlg : Real.log (85351948553733837 / 160000000000000000 : ℝ) ≤ (-(6283905358389822733931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85351948553733837 / 160000000000000000 : ℝ) = - (85351948553733837 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85351948553733837 / 80000000000000000 : ℚ)) - (U := (647566444610177266069 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85351948553733837 / 80000000000000000 : ℝ) ≤ - (647566444610177266069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5334466478491339 / 10000000000000000 : ℝ)) (q := - (85351948553733837 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85351948553733837 / 160000000000000000 : ℚ)) + (r' := (85351948553733837 / 80000000000000000 : ℚ)) + (U := (-(6283905358389822733931 / 10000000000000000000000 : ℚ))) + (U' := (647566444610177266069 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (5334466478491339 / 10000000000000000 : ℚ)) + (q := (85351948553733837 / 160000000000000000 : ℚ)) + (U := (-(6283905358389822733931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_2 : Uω (aρ 2) (bρ 2) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1310,25 +1153,21 @@ lemma U_487_2 : have hlg : Real.log (84968932820745869 / 160000000000000000 : ℝ) ≤ (-(6328881215201098496097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84968932820745869 / 160000000000000000 : ℝ) = - (84968932820745869 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84968932820745869 / 80000000000000000 : ℚ)) - (U := (602590587798901503903 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84968932820745869 / 80000000000000000 : ℝ) ≤ - (602590587798901503903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5310358524377843 / 10000000000000000 : ℝ)) (q := - (84968932820745869 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84968932820745869 / 160000000000000000 : ℚ)) + (r' := (84968932820745869 / 80000000000000000 : ℚ)) + (U := (-(6328881215201098496097 / 10000000000000000000000 : ℚ))) + (U' := (602590587798901503903 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (5310358524377843 / 10000000000000000 : ℚ)) + (q := (84968932820745869 / 160000000000000000 : ℚ)) + (U := (-(6328881215201098496097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_3 : Uω (aρ 3) (bρ 3) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1336,25 +1175,21 @@ lemma U_487_3 : have hlg : Real.log (84202545401853533 / 160000000000000000 : ℝ) ≤ (-(1604871659391791879599 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84202545401853533 / 160000000000000000 : ℝ) = - (84202545401853533 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84202545401853533 / 80000000000000000 : ℚ)) - (U := (127996291358208120401 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84202545401853533 / 80000000000000000 : ℝ) ≤ - (127996291358208120401 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5261956203366301 / 10000000000000000 : ℝ)) (q := - (84202545401853533 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84202545401853533 / 160000000000000000 : ℚ)) + (r' := (84202545401853533 / 80000000000000000 : ℚ)) + (U := (-(1604871659391791879599 / 2500000000000000000000 : ℚ))) + (U' := (127996291358208120401 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (5261956203366301 / 10000000000000000 : ℚ)) + (q := (84202545401853533 / 160000000000000000 : ℚ)) + (U := (-(1604871659391791879599 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_4 : Uω (aρ 4) (bρ 4) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1362,25 +1197,21 @@ lemma U_487_4 : have hlg : Real.log (3317144314243061 / 6400000000000000 : ℝ) ≤ (-(3285968618138589291277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3317144314243061 / 6400000000000000 : ℝ) = - (3317144314243061 / 3200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3317144314243061 / 3200000000000000 : ℚ)) - (U := (179767283361410708723 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (3317144314243061 / 3200000000000000 : ℝ) ≤ - (179767283361410708723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (207240327648367 / 400000000000000 : ℝ)) (q := - (3317144314243061 / 6400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3317144314243061 / 6400000000000000 : ℚ)) + (r' := (3317144314243061 / 3200000000000000 : ℚ)) + (U := (-(3285968618138589291277 / 5000000000000000000000 : ℚ))) + (U' := (179767283361410708723 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (207240327648367 / 400000000000000 : ℚ)) + (q := (3317144314243061 / 6400000000000000 : ℚ)) + (U := (-(3285968618138589291277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_5 : Uω (aρ 5) (bρ 5) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1388,25 +1219,21 @@ lemma U_487_5 : have hlg : Real.log (80985872242185869 / 160000000000000000 : ℝ) ≤ (-(6808990922769527856703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80985872242185869 / 160000000000000000 : ℝ) = - (80985872242185869 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80985872242185869 / 80000000000000000 : ℚ)) - (U := (122480880230472143297 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (80985872242185869 / 80000000000000000 : ℝ) ≤ - (122480880230472143297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5056356158807843 / 10000000000000000 : ℝ)) (q := - (80985872242185869 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80985872242185869 / 160000000000000000 : ℚ)) + (r' := (80985872242185869 / 80000000000000000 : ℚ)) + (U := (-(6808990922769527856703 / 10000000000000000000000 : ℚ))) + (U' := (122480880230472143297 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (5056356158807843 / 10000000000000000 : ℚ)) + (q := (80985872242185869 / 160000000000000000 : ℚ)) + (U := (-(6808990922769527856703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_6 : Uω (aρ 6) (bρ 6) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1414,25 +1241,21 @@ lemma U_487_6 : have hlg : Real.log (78193307445934141 / 160000000000000000 : ℝ) ≤ (-(7159897533578763198489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (78193307445934141 / 160000000000000000 : ℝ) = - (78193307445934141 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78193307445934141 / 40000000000000000 : ℚ)) - (U := (6703046072421236801511 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (78193307445934141 / 40000000000000000 : ℝ) ≤ - (6703046072421236801511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4874525934416377 / 10000000000000000 : ℝ)) (q := - (78193307445934141 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78193307445934141 / 160000000000000000 : ℚ)) + (r' := (78193307445934141 / 40000000000000000 : ℚ)) + (U := (-(7159897533578763198489 / 10000000000000000000000 : ℚ))) + (U' := (6703046072421236801511 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (4874525934416377 / 10000000000000000 : ℚ)) + (q := (78193307445934141 / 160000000000000000 : ℚ)) + (U := (-(7159897533578763198489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_7 : Uω (aρ 7) (bρ 7) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1440,25 +1263,21 @@ lemma U_487_7 : have hlg : Real.log (74369238777818021 / 160000000000000000 : ℝ) ≤ (-(7661314156593136158591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (74369238777818021 / 160000000000000000 : ℝ) = - (74369238777818021 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (74369238777818021 / 40000000000000000 : ℚ)) - (U := (6201629449406863841409 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (74369238777818021 / 40000000000000000 : ℝ) ≤ - (6201629449406863841409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2310089365830931 / 5000000000000000 : ℝ)) (q := - (74369238777818021 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (74369238777818021 / 160000000000000000 : ℚ)) + (r' := (74369238777818021 / 40000000000000000 : ℚ)) + (U := (-(7661314156593136158591 / 10000000000000000000000 : ℚ))) + (U' := (6201629449406863841409 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (2310089365830931 / 5000000000000000 : ℚ)) + (q := (74369238777818021 / 160000000000000000 : ℚ)) + (U := (-(7661314156593136158591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_8 : Uω (aρ 8) (bρ 8) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1466,25 +1285,21 @@ lemma U_487_8 : have hlg : Real.log (69347802181864277 / 160000000000000000 : ℝ) ≤ (-(8360393601371293797627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (69347802181864277 / 160000000000000000 : ℝ) = - (69347802181864277 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69347802181864277 / 40000000000000000 : ℚ)) - (U := (5502550004628706202373 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69347802181864277 / 40000000000000000 : ℝ) ≤ - (5502550004628706202373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1069010202126911 / 2500000000000000 : ℝ)) (q := - (69347802181864277 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69347802181864277 / 160000000000000000 : ℚ)) + (r' := (69347802181864277 / 40000000000000000 : ℚ)) + (U := (-(8360393601371293797627 / 10000000000000000000000 : ℚ))) + (U' := (5502550004628706202373 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (1069010202126911 / 2500000000000000 : ℚ)) + (q := (69347802181864277 / 160000000000000000 : ℚ)) + (U := (-(8360393601371293797627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_9 : Uω (aρ 9) (bρ 9) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1492,25 +1307,21 @@ lemma U_487_9 : have hlg : Real.log (62982786197452141 / 160000000000000000 : ℝ) ≤ (-(932312360618953778177 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (62982786197452141 / 160000000000000000 : ℝ) = - (62982786197452141 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62982786197452141 / 40000000000000000 : ℚ)) - (U := (453981999981046221823 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62982786197452141 / 40000000000000000 : ℝ) ≤ - (453981999981046221823 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3821379438816127 / 10000000000000000 : ℝ)) (q := - (62982786197452141 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62982786197452141 / 160000000000000000 : ℚ)) + (r' := (62982786197452141 / 40000000000000000 : ℚ)) + (U := (-(932312360618953778177 / 1000000000000000000000 : ℚ))) + (U' := (453981999981046221823 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (3821379438816127 / 10000000000000000 : ℚ)) + (q := (62982786197452141 / 160000000000000000 : ℚ)) + (U := (-(932312360618953778177 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_10 : Uω (aρ 10) (bρ 10) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1518,26 +1329,21 @@ lemma U_487_10 : have hlg : Real.log (55111733443456581 / 160000000000000000 : ℝ) ≤ (-(10658111730682012403533 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55111733443456581 / 160000000000000000 : ℝ) = - (55111733443456581 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55111733443456581 / 40000000000000000 : ℚ)) - (U := (3204831875317987596467 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55111733443456581 / 40000000000000000 : ℝ) ≤ - (3204831875317987596467 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1613028439030841 / 5000000000000000 : ℝ)) (q := - (55111733443456581 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55111733443456581 / 160000000000000000 : ℚ)) + (r' := (55111733443456581 / 40000000000000000 : ℚ)) + (U := (-(10658111730682012403533 / 10000000000000000000000 : ℚ))) + (U' := (3204831875317987596467 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (1613028439030841 / 5000000000000000 : ℚ)) + (q := (55111733443456581 / 160000000000000000 : ℚ)) + (U := (-(10658111730682012403533 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_11 : Uω (aρ 11) (bρ 11) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1545,26 +1351,21 @@ lemma U_487_11 : have hlg : Real.log (1814763621402669 / 6400000000000000 : ℝ) ≤ (-(6301713833760821665297 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1814763621402669 / 6400000000000000 : ℝ) = - (1814763621402669 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1814763621402669 / 1600000000000000 : ℚ)) - (U := (629757969239178334703 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1814763621402669 / 1600000000000000 : ℝ) ≤ - (629757969239178334703 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48534062814359 / 200000000000000 : ℝ)) (q := - (1814763621402669 / 6400000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1814763621402669 / 6400000000000000 : ℚ)) + (r' := (1814763621402669 / 1600000000000000 : ℚ)) + (U := (-(6301713833760821665297 / 5000000000000000000000 : ℚ))) + (U' := (629757969239178334703 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (48534062814359 / 200000000000000 : ℚ)) + (q := (1814763621402669 / 6400000000000000 : ℚ)) + (U := (-(6301713833760821665297 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_12 : Uω (aρ 12) (bρ 12) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1572,26 +1373,21 @@ lemma U_487_12 : have hlg : Real.log (6347192319383009 / 32000000000000000 : ℝ) ≤ (-(3235446682644510697477 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6347192319383009 / 32000000000000000 : ℝ) = - (6347192319383009 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6347192319383009 / 4000000000000000 : ℚ)) - (U := (923436399155489302523 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6347192319383009 / 4000000000000000 : ℝ) ≤ - (923436399155489302523 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114626212013399 / 1000000000000000 : ℝ)) (q := - (6347192319383009 / 32000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6347192319383009 / 32000000000000000 : ℚ)) + (r' := (6347192319383009 / 4000000000000000 : ℚ)) + (U := (-(3235446682644510697477 / 2000000000000000000000 : ℚ))) + (U' := (923436399155489302523 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69107511152773 / 128000000000000 : ℚ)) + (s := (114626212013399 / 1000000000000000 : ℚ)) + (q := (6347192319383009 / 32000000000000000 : ℚ)) + (U := (-(3235446682644510697477 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_487_13 : Uω (aρ 13) (bρ 13) (69107511152773 / 128000000000000 : ℝ) ≤ @@ -1705,25 +1501,21 @@ lemma U_488_1 : have hlg : Real.log (10681475965366287 / 20000000000000000 : ℝ) ≤ (-(62722125030626558607 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10681475965366287 / 20000000000000000 : ℝ) = - (10681475965366287 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10681475965366287 / 10000000000000000 : ℚ)) - (U := (6592592999373441393 / 100000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10681475965366287 / 10000000000000000 : ℝ) ≤ - (6592592999373441393 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (667588463997739 / 1250000000000000 : ℝ)) (q := - (10681475965366287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10681475965366287 / 20000000000000000 : ℚ)) + (r' := (10681475965366287 / 10000000000000000 : ℚ)) + (U := (-(62722125030626558607 / 100000000000000000000 : ℚ))) + (U' := (6592592999373441393 / 100000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (667588463997739 / 1250000000000000 : ℚ)) + (q := (10681475965366287 / 20000000000000000 : ℚ)) + (U := (-(62722125030626558607 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_2 : Uω (aρ 2) (bρ 2) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1731,25 +1523,21 @@ lemma U_488_2 : have hlg : Real.log (166149990577311 / 312500000000000 : ℝ) ≤ (-(1263427061655700437097 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (166149990577311 / 312500000000000 : ℝ) = - (166149990577311 / 156250000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (166149990577311 / 156250000000000 : ℚ)) - (U := (122867298944299562903 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (166149990577311 / 156250000000000 : ℝ) ≤ - (122867298944299562903 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5316600156073529 / 10000000000000000 : ℝ)) (q := - (166149990577311 / 312500000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (166149990577311 / 312500000000000 : ℚ)) + (r' := (166149990577311 / 156250000000000 : ℚ)) + (U := (-(1263427061655700437097 / 2000000000000000000000 : ℚ))) + (U' := (122867298944299562903 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (5316600156073529 / 10000000000000000 : ℚ)) + (q := (166149990577311 / 312500000000000 : ℚ)) + (U := (-(1263427061655700437097 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_3 : Uω (aρ 3) (bρ 3) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1757,25 +1545,21 @@ lemma U_488_3 : have hlg : Real.log (10537802165944457 / 20000000000000000 : ℝ) ≤ (-(6407632750799801970241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10537802165944457 / 20000000000000000 : ℝ) = - (10537802165944457 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10537802165944457 / 10000000000000000 : ℚ)) - (U := (523839052200198029759 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10537802165944457 / 10000000000000000 : ℝ) ≤ - (523839052200198029759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2634099515710041 / 5000000000000000 : ℝ)) (q := - (10537802165944457 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10537802165944457 / 20000000000000000 : ℚ)) + (r' := (10537802165944457 / 10000000000000000 : ℚ)) + (U := (-(6407632750799801970241 / 10000000000000000000000 : ℚ))) + (U' := (523839052200198029759 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (2634099515710041 / 5000000000000000 : ℚ)) + (q := (10537802165944457 / 20000000000000000 : ℚ)) + (U := (-(6407632750799801970241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_4 : Uω (aρ 4) (bρ 4) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1783,25 +1567,21 @@ lemma U_488_4 : have hlg : Real.log (10378563191729213 / 20000000000000000 : ℝ) ≤ (-(3279949129863435104927 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10378563191729213 / 20000000000000000 : ℝ) = - (10378563191729213 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10378563191729213 / 10000000000000000 : ℚ)) - (U := (185786771636564895073 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10378563191729213 / 10000000000000000 : ℝ) ≤ - (185786771636564895073 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2593627119134919 / 5000000000000000 : ℝ)) (q := - (10378563191729213 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10378563191729213 / 20000000000000000 : ℚ)) + (r' := (10378563191729213 / 10000000000000000 : ℚ)) + (U := (-(3279949129863435104927 / 5000000000000000000000 : ℚ))) + (U' := (185786771636564895073 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (2593627119134919 / 5000000000000000 : ℚ)) + (q := (10378563191729213 / 20000000000000000 : ℚ)) + (U := (-(3279949129863435104927 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_5 : Uω (aρ 5) (bρ 5) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1809,25 +1589,21 @@ lemma U_488_5 : have hlg : Real.log (5067864663363369 / 10000000000000000 : ℝ) ≤ (-(6796655347826442500329 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5067864663363369 / 10000000000000000 : ℝ) = - (5067864663363369 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5067864663363369 / 5000000000000000 : ℚ)) - (U := (134816455173557499671 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5067864663363369 / 5000000000000000 : ℝ) ≤ - (134816455173557499671 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5062610292602363 / 10000000000000000 : ℝ)) (q := - (5067864663363369 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5067864663363369 / 10000000000000000 : ℚ)) + (r' := (5067864663363369 / 5000000000000000 : ℚ)) + (U := (-(6796655347826442500329 / 10000000000000000000000 : ℚ))) + (U' := (134816455173557499671 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (5062610292602363 / 10000000000000000 : ℚ)) + (q := (5067864663363369 / 10000000000000000 : ℚ)) + (U := (-(6796655347826442500329 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_6 : Uω (aρ 6) (bρ 6) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1835,25 +1611,21 @@ lemma U_488_6 : have hlg : Real.log (4893338933377709 / 10000000000000000 : ℝ) ≤ (-(3573551067666562741491 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4893338933377709 / 10000000000000000 : ℝ) = - (4893338933377709 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4893338933377709 / 2500000000000000 : ℚ)) - (U := (3357920735333437258509 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4893338933377709 / 2500000000000000 : ℝ) ≤ - (3357920735333437258509 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4880799207771043 / 10000000000000000 : ℝ)) (q := - (4893338933377709 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4893338933377709 / 10000000000000000 : ℚ)) + (r' := (4893338933377709 / 2500000000000000 : ℚ)) + (U := (-(3573551067666562741491 / 5000000000000000000000 : ℚ))) + (U' := (3357920735333437258509 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (4880799207771043 / 10000000000000000 : ℚ)) + (q := (4893338933377709 / 10000000000000000 : ℚ)) + (U := (-(3573551067666562741491 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_7 : Uω (aρ 7) (bρ 7) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1861,24 +1633,21 @@ lemma U_488_7 : have hlg : Real.log (116358905550973 / 250000000000000 : ℝ) ≤ (-(305912595789937330659 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (116358905550973 / 250000000000000 : ℝ) = (116358905550973 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (116358905550973 / 62500000000000 : ℚ)) - (U := (248605148450062669341 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (116358905550973 / 62500000000000 : ℝ) ≤ - (248605148450062669341 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (925299033170693 / 2000000000000000 : ℝ)) (q := - (116358905550973 / 250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (116358905550973 / 250000000000000 : ℚ)) + (r' := (116358905550973 / 62500000000000 : ℚ)) + (U := (-(305912595789937330659 / 400000000000000000000 : ℚ))) + (U' := (248605148450062669341 / 400000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (925299033170693 / 2000000000000000 : ℚ)) + (q := (116358905550973 / 250000000000000 : ℚ)) + (U := (-(305912595789937330659 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_8 : Uω (aρ 8) (bρ 8) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1886,25 +1655,21 @@ lemma U_488_8 : have hlg : Real.log (8681127231287437 / 20000000000000000 : ℝ) ≤ (-(8345808874379213789631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8681127231287437 / 20000000000000000 : ℝ) = - (8681127231287437 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8681127231287437 / 5000000000000000 : ℚ)) - (U := (5517134731620786210369 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8681127231287437 / 5000000000000000 : ℝ) ≤ - (5517134731620786210369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2141225802201531 / 5000000000000000 : ℝ)) (q := - (8681127231287437 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8681127231287437 / 20000000000000000 : ℚ)) + (r' := (8681127231287437 / 5000000000000000 : ℚ)) + (U := (-(8345808874379213789631 / 10000000000000000000000 : ℚ))) + (U' := (5517134731620786210369 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (2141225802201531 / 5000000000000000 : ℚ)) + (q := (8681127231287437 / 20000000000000000 : ℚ)) + (U := (-(8345808874379213789631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_9 : Uω (aρ 9) (bρ 9) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1912,25 +1677,21 @@ lemma U_488_9 : have hlg : Real.log (3942852878019037 / 10000000000000000 : ℝ) ≤ (-(9306805504687874914537 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3942852878019037 / 10000000000000000 : ℝ) = - (3942852878019037 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3942852878019037 / 2500000000000000 : ℚ)) - (U := (4556138101312125085463 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3942852878019037 / 2500000000000000 : ℝ) ≤ - (4556138101312125085463 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3827995757513699 / 10000000000000000 : ℝ)) (q := - (3942852878019037 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3942852878019037 / 10000000000000000 : ℚ)) + (r' := (3942852878019037 / 2500000000000000 : ℚ)) + (U := (-(9306805504687874914537 / 10000000000000000000000 : ℚ))) + (U' := (4556138101312125085463 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (3827995757513699 / 10000000000000000 : ℚ)) + (q := (3942852878019037 / 10000000000000000 : ℚ)) + (U := (-(9306805504687874914537 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_10 : Uω (aρ 10) (bρ 10) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1938,24 +1699,21 @@ lemma U_488_10 : have hlg : Real.log (55218339231969 / 160000000000000 : ℝ) ≤ (-(531939342072332120009 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55218339231969 / 160000000000000 : ℝ) = (55218339231969 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55218339231969 / 40000000000000 : ℚ)) - (U := (161207838227667879991 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55218339231969 / 40000000000000 : ℝ) ≤ - (161207838227667879991 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (12932565755867 / 40000000000000 : ℝ)) (q := - (55218339231969 / 160000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55218339231969 / 160000000000000 : ℚ)) + (r' := (55218339231969 / 40000000000000 : ℚ)) + (U := (-(531939342072332120009 / 500000000000000000000 : ℚ))) + (U' := (161207838227667879991 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (12932565755867 / 40000000000000 : ℚ)) + (q := (55218339231969 / 160000000000000 : ℚ)) + (U := (-(531939342072332120009 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_11 : Uω (aρ 11) (bρ 11) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1963,26 +1721,21 @@ lemma U_488_11 : have hlg : Real.log (5685715438202167 / 20000000000000000 : ℝ) ≤ (-(1572219133875210761649 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5685715438202167 / 20000000000000000 : ℝ) = - (5685715438202167 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5685715438202167 / 5000000000000000 : ℚ)) - (U := (160648816874789238351 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5685715438202167 / 5000000000000000 : ℝ) ≤ - (160648816874789238351 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19023758588889 / 78125000000000 : ℝ)) (q := - (5685715438202167 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5685715438202167 / 20000000000000000 : ℚ)) + (r' := (5685715438202167 / 5000000000000000 : ℚ)) + (U := (-(1572219133875210761649 / 1250000000000000000000 : ℚ))) + (U' := (160648816874789238351 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (19023758588889 / 78125000000000 : ℚ)) + (q := (5685715438202167 / 20000000000000000 : ℚ)) + (U := (-(1572219133875210761649 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_12 : Uω (aρ 12) (bρ 12) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -1990,26 +1743,21 @@ lemma U_488_12 : have hlg : Real.log (3988509910166249 / 20000000000000000 : ℝ) ≤ (-(16123145677231630302739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3988509910166249 / 20000000000000000 : ℝ) = - (3988509910166249 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3988509910166249 / 2500000000000000 : ℚ)) - (U := (4671269731768369697261 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3988509910166249 / 2500000000000000 : ℝ) ≤ - (4671269731768369697261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (580767834013437 / 5000000000000000 : ℝ)) (q := - (3988509910166249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3988509910166249 / 20000000000000000 : ℚ)) + (r' := (3988509910166249 / 2500000000000000 : ℚ)) + (U := (-(16123145677231630302739 / 10000000000000000000000 : ℚ))) + (U' := (4671269731768369697261 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8648424754351 / 16000000000000 : ℚ)) + (s := (580767834013437 / 5000000000000000 : ℚ)) + (q := (3988509910166249 / 20000000000000000 : ℚ)) + (U := (-(16123145677231630302739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_488_13 : Uω (aρ 13) (bρ 13) (8648424754351 / 16000000000000 : ℝ) ≤ @@ -2121,25 +1869,21 @@ lemma U_489_1 : have hlg : Real.log (17110333378160783 / 32000000000000000 : ℝ) ≤ (-(1252106660842020123547 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17110333378160783 / 32000000000000000 : ℝ) = - (17110333378160783 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17110333378160783 / 16000000000000000 : ℚ)) - (U := (134187699757979876453 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (17110333378160783 / 16000000000000000 : ℝ) ≤ - (134187699757979876453 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (534694894530713 / 1000000000000000 : ℝ)) (q := - (17110333378160783 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17110333378160783 / 32000000000000000 : ℚ)) + (r' := (17110333378160783 / 16000000000000000 : ℚ)) + (U := (-(1252106660842020123547 / 2000000000000000000000 : ℚ))) + (U' := (134187699757979876453 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (534694894530713 / 1000000000000000 : ℚ)) + (q := (17110333378160783 / 32000000000000000 : ℚ)) + (U := (-(1252106660842020123547 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_2 : Uω (aρ 2) (bρ 2) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2147,25 +1891,21 @@ lemma U_489_2 : have hlg : Real.log (85168657521620947 / 160000000000000000 : ℝ) ≤ (-(6305403182837248309091 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85168657521620947 / 160000000000000000 : ℝ) = - (85168657521620947 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85168657521620947 / 80000000000000000 : ℚ)) - (U := (626068620162751690909 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85168657521620947 / 80000000000000000 : ℝ) ≤ - (626068620162751690909 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5322841786669259 / 10000000000000000 : ℝ)) (q := - (85168657521620947 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85168657521620947 / 160000000000000000 : ℚ)) + (r' := (85168657521620947 / 80000000000000000 : ℚ)) + (U := (-(6305403182837248309091 / 10000000000000000000000 : ℚ))) + (U' := (626068620162751690909 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (5322841786669259 / 10000000000000000 : ℚ)) + (q := (85168657521620947 / 160000000000000000 : ℚ)) + (U := (-(6305403182837248309091 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_3 : Uω (aρ 3) (bρ 3) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2173,25 +1913,21 @@ lemma U_489_3 : have hlg : Real.log (84402289221723403 / 160000000000000000 : ℝ) ≤ (-(3197896451298350055509 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84402289221723403 / 160000000000000000 : ℝ) = - (84402289221723403 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84402289221723403 / 80000000000000000 : ℚ)) - (U := (267839450201649944491 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84402289221723403 / 80000000000000000 : ℝ) ≤ - (267839450201649944491 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2637220927766033 / 5000000000000000 : ℝ)) (q := - (84402289221723403 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84402289221723403 / 160000000000000000 : ℚ)) + (r' := (84402289221723403 / 80000000000000000 : ℚ)) + (U := (-(3197896451298350055509 / 5000000000000000000000 : ℚ))) + (U' := (267839450201649944491 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (2637220927766033 / 5000000000000000 : ℚ)) + (q := (84402289221723403 / 160000000000000000 : ℚ)) + (U := (-(3197896451298350055509 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_4 : Uω (aρ 4) (bρ 4) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2199,25 +1935,21 @@ lemma U_489_4 : have hlg : Real.log (16625680623527751 / 32000000000000000 : ℝ) ≤ (-(1636968442687012044419 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16625680623527751 / 32000000000000000 : ℝ) = - (16625680623527751 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16625680623527751 / 16000000000000000 : ℚ)) - (U := (95899508062987955581 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (16625680623527751 / 16000000000000000 : ℝ) ≤ - (95899508062987955581 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1038700054717297 / 2000000000000000 : ℝ)) (q := - (16625680623527751 / 32000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16625680623527751 / 32000000000000000 : ℚ)) + (r' := (16625680623527751 / 16000000000000000 : ℚ)) + (U := (-(1636968442687012044419 / 2500000000000000000000 : ℚ))) + (U' := (95899508062987955581 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (1038700054717297 / 2000000000000000 : ℚ)) + (q := (16625680623527751 / 32000000000000000 : ℚ)) + (U := (-(1636968442687012044419 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_5 : Uω (aρ 5) (bρ 5) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2225,25 +1957,21 @@ lemma U_489_5 : have hlg : Real.log (81185796729639979 / 160000000000000000 : ℝ) ≤ (-(1696083750571734394177 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (81185796729639979 / 160000000000000000 : ℝ) = - (81185796729639979 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (81185796729639979 / 80000000000000000 : ℚ)) - (U := (36784200178265605823 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (81185796729639979 / 80000000000000000 : ℝ) ≤ - (36784200178265605823 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2534432197210819 / 5000000000000000 : ℝ)) (q := - (81185796729639979 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (81185796729639979 / 160000000000000000 : ℚ)) + (r' := (81185796729639979 / 80000000000000000 : ℚ)) + (U := (-(1696083750571734394177 / 2500000000000000000000 : ℚ))) + (U' := (36784200178265605823 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (2534432197210819 / 5000000000000000 : ℚ)) + (q := (81185796729639979 / 160000000000000000 : ℚ)) + (U := (-(1696083750571734394177 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_6 : Uω (aρ 6) (bρ 6) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2251,25 +1979,21 @@ lemma U_489_6 : have hlg : Real.log (15678707552867983 / 32000000000000000 : ℝ) ≤ (-(22294759913439966139 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15678707552867983 / 32000000000000000 : ℝ) = - (15678707552867983 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15678707552867983 / 8000000000000000 : ℚ)) - (U := (21026938855310033861 / 31250000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (15678707552867983 / 8000000000000000 : ℝ) ≤ - (21026938855310033861 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (488707239889913 / 1000000000000000 : ℝ)) (q := - (15678707552867983 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15678707552867983 / 32000000000000000 : ℚ)) + (r' := (15678707552867983 / 8000000000000000 : ℚ)) + (U := (-(22294759913439966139 / 31250000000000000000 : ℚ))) + (U' := (21026938855310033861 / 31250000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (488707239889913 / 1000000000000000 : ℚ)) + (q := (15678707552867983 / 32000000000000000 : ℚ)) + (U := (-(22294759913439966139 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_7 : Uω (aρ 7) (bρ 7) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2277,25 +2001,21 @@ lemma U_489_7 : have hlg : Real.log (14914031739038511 / 32000000000000000 : ℝ) ≤ (-(7634334050232765267451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14914031739038511 / 32000000000000000 : ℝ) = - (14914031739038511 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14914031739038511 / 8000000000000000 : ℚ)) - (U := (6228609555767234732549 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (14914031739038511 / 8000000000000000 : ℝ) ≤ - (6228609555767234732549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (463281139601571 / 1000000000000000 : ℝ)) (q := - (14914031739038511 / 32000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14914031739038511 / 32000000000000000 : ℚ)) + (r' := (14914031739038511 / 8000000000000000 : ℚ)) + (U := (-(7634334050232765267451 / 10000000000000000000000 : ℚ))) + (U' := (6228609555767234732549 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (463281139601571 / 1000000000000000 : ℚ)) + (q := (14914031739038511 / 32000000000000000 : ℚ)) + (U := (-(7634334050232765267451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_8 : Uω (aρ 8) (bρ 8) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2303,25 +2023,21 @@ lemma U_489_8 : have hlg : Real.log (69550229515448811 / 160000000000000000 : ℝ) ≤ (-(4165622981717381617827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (69550229515448811 / 160000000000000000 : ℝ) = - (69550229515448811 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69550229515448811 / 40000000000000000 : ℚ)) - (U := (2765848821282618382173 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69550229515448811 / 40000000000000000 : ℝ) ≤ - (2765848821282618382173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2144430949943871 / 5000000000000000 : ℝ)) (q := - (69550229515448811 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69550229515448811 / 160000000000000000 : ℚ)) + (r' := (69550229515448811 / 40000000000000000 : ℚ)) + (U := (-(4165622981717381617827 / 5000000000000000000000 : ℚ))) + (U' := (2765848821282618382173 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (2144430949943871 / 5000000000000000 : ℚ)) + (q := (69550229515448811 / 160000000000000000 : ℚ)) + (U := (-(4165622981717381617827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_9 : Uω (aρ 9) (bρ 9) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2329,25 +2045,21 @@ lemma U_489_9 : have hlg : Real.log (63188495835948627 / 160000000000000000 : ℝ) ≤ (-(9290515580424209657449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63188495835948627 / 160000000000000000 : ℝ) = - (63188495835948627 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63188495835948627 / 40000000000000000 : ℚ)) - (U := (4572428025575790342551 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63188495835948627 / 40000000000000000 : ℝ) ≤ - (4572428025575790342551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3834610818310219 / 10000000000000000 : ℝ)) (q := - (63188495835948627 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63188495835948627 / 160000000000000000 : ℚ)) + (r' := (63188495835948627 / 40000000000000000 : ℚ)) + (U := (-(9290515580424209657449 / 10000000000000000000000 : ℚ))) + (U' := (4572428025575790342551 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (3834610818310219 / 10000000000000000 : ℚ)) + (q := (63188495835948627 / 160000000000000000 : ℚ)) + (U := (-(9290515580424209657449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_10 : Uω (aρ 10) (bρ 10) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2355,26 +2067,21 @@ lemma U_489_10 : have hlg : Real.log (55324917272051771 / 160000000000000000 : ℝ) ≤ (-(10619504240865397292307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55324917272051771 / 160000000000000000 : ℝ) = - (55324917272051771 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55324917272051771 / 40000000000000000 : ℚ)) - (U := (3243439365134602707693 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55324917272051771 / 40000000000000000 : ℝ) ≤ - (3243439365134602707693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101256954103691 / 312500000000000 : ℝ)) (q := - (55324917272051771 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55324917272051771 / 160000000000000000 : ℚ)) + (r' := (55324917272051771 / 40000000000000000 : ℚ)) + (U := (-(10619504240865397292307 / 10000000000000000000000 : ℚ))) + (U' := (3243439365134602707693 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (101256954103691 / 312500000000000 : ℚ)) + (q := (55324917272051771 / 160000000000000000 : ℚ)) + (U := (-(10619504240865397292307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_11 : Uω (aρ 11) (bρ 11) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2382,26 +2089,21 @@ lemma U_489_11 : have hlg : Real.log (9120451277367631 / 32000000000000000 : ℝ) ≤ (-(12552166172502945745251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9120451277367631 / 32000000000000000 : ℝ) = - (9120451277367631 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9120451277367631 / 8000000000000000 : ℚ)) - (U := (1310777433497054254749 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9120451277367631 / 8000000000000000 : ℝ) ≤ - (1310777433497054254749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (244336654687141 / 1000000000000000 : ℝ)) (q := - (9120451277367631 / 32000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9120451277367631 / 32000000000000000 : ℚ)) + (r' := (9120451277367631 / 8000000000000000 : ℚ)) + (U := (-(12552166172502945745251 / 10000000000000000000000 : ℚ))) + (U' := (1310777433497054254749 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (244336654687141 / 1000000000000000 : ℚ)) + (q := (9120451277367631 / 32000000000000000 : ℚ)) + (U := (-(12552166172502945745251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_12 : Uω (aρ 12) (bρ 12) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2409,26 +2111,21 @@ lemma U_489_12 : have hlg : Real.log (32078875815043427 / 160000000000000000 : ℝ) ≤ (-(16069760752416665406813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (32078875815043427 / 160000000000000000 : ℝ) = - (32078875815043427 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32078875815043427 / 20000000000000000 : ℚ)) - (U := (4724654656583334593187 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32078875815043427 / 20000000000000000 : ℝ) ≤ - (4724654656583334593187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1176644072082069 / 10000000000000000 : ℝ)) (q := - (32078875815043427 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32078875815043427 / 160000000000000000 : ℚ)) + (r' := (32078875815043427 / 20000000000000000 : ℚ)) + (U := (-(16069760752416665406813 / 10000000000000000000000 : ℚ))) + (U' := (4724654656583334593187 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69267284916843 / 128000000000000 : ℚ)) + (s := (1176644072082069 / 10000000000000000 : ℚ)) + (q := (32078875815043427 / 160000000000000000 : ℚ)) + (U := (-(16069760752416665406813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_489_13 : Uω (aρ 13) (bρ 13) (69267284916843 / 128000000000000 : ℝ) ≤ @@ -2541,25 +2238,21 @@ lemma U_490_1 : have hlg : Real.log (42825763028679659 / 80000000000000000 : ℝ) ≤ (-(3124433864984652654599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42825763028679659 / 80000000000000000 : ℝ) = - (42825763028679659 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42825763028679659 / 40000000000000000 : ℚ)) - (U := (341302036515347345401 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42825763028679659 / 40000000000000000 : ℝ) ≤ - (341302036515347345401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5353190178467571 / 10000000000000000 : ℝ)) (q := - (42825763028679659 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42825763028679659 / 80000000000000000 : ℚ)) + (r' := (42825763028679659 / 40000000000000000 : ℚ)) + (U := (-(3124433864984652654599 / 5000000000000000000000 : ℚ))) + (U' := (341302036515347345401 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (5353190178467571 / 10000000000000000 : ℚ)) + (q := (42825763028679659 / 80000000000000000 : ℚ)) + (U := (-(3124433864984652654599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_2 : Uω (aρ 2) (bρ 2) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2567,25 +2260,21 @@ lemma U_490_2 : have hlg : Real.log (1705370397177799 / 3200000000000000 : ℝ) ≤ (-(15734212016432925827 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1705370397177799 / 3200000000000000 : ℝ) = - (1705370397177799 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1705370397177799 / 1600000000000000 : ℚ)) - (U := (1594467491067074173 / 25000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1705370397177799 / 1600000000000000 : ℝ) ≤ - (1594467491067074173 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53290834161689 / 100000000000000 : ℝ)) (q := - (1705370397177799 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1705370397177799 / 3200000000000000 : ℚ)) + (r' := (1705370397177799 / 1600000000000000 : ℚ)) + (U := (-(15734212016432925827 / 25000000000000000000 : ℚ))) + (U' := (1594467491067074173 / 25000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (53290834161689 / 100000000000000 : ℚ)) + (q := (1705370397177799 / 3200000000000000 : ℚ)) + (U := (-(15734212016432925827 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_3 : Uω (aρ 3) (bρ 3) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2593,25 +2282,21 @@ lemma U_490_3 : have hlg : Real.log (42251080542234311 / 80000000000000000 : ℝ) ≤ (-(797995882467076955683 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42251080542234311 / 80000000000000000 : ℝ) = - (42251080542234311 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42251080542234311 / 40000000000000000 : ℚ)) - (U := (68438092907923044317 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42251080542234311 / 40000000000000000 : ℝ) ≤ - (68438092907923044317 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2640342337858117 / 5000000000000000 : ℝ)) (q := - (42251080542234311 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42251080542234311 / 80000000000000000 : ℚ)) + (r' := (42251080542234311 / 40000000000000000 : ℚ)) + (U := (-(797995882467076955683 / 1250000000000000000000 : ℚ))) + (U' := (68438092907923044317 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (2640342337858117 / 5000000000000000 : ℚ)) + (q := (42251080542234311 / 80000000000000000 : ℚ)) + (U := (-(797995882467076955683 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_4 : Uω (aρ 4) (bρ 4) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2619,25 +2304,21 @@ lemma U_490_4 : have hlg : Real.log (41614150303915131 / 80000000000000000 : ℝ) ≤ (-(6535863734487156375171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41614150303915131 / 80000000000000000 : ℝ) = - (41614150303915131 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41614150303915131 / 40000000000000000 : ℚ)) - (U := (395608068512843624829 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41614150303915131 / 40000000000000000 : ℝ) ≤ - (395608068512843624829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5199746297201439 / 10000000000000000 : ℝ)) (q := - (41614150303915131 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41614150303915131 / 80000000000000000 : ℚ)) + (r' := (41614150303915131 / 40000000000000000 : ℚ)) + (U := (-(6535863734487156375171 / 10000000000000000000000 : ℚ))) + (U' := (395608068512843624829 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (5199746297201439 / 10000000000000000 : ℚ)) + (q := (41614150303915131 / 80000000000000000 : ℚ)) + (U := (-(6535863734487156375171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_5 : Uω (aρ 5) (bρ 5) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2645,25 +2326,21 @@ lemma U_490_5 : have hlg : Real.log (40642879295304887 / 80000000000000000 : ℝ) ≤ (-(3386014924257870962009 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40642879295304887 / 80000000000000000 : ℝ) = - (40642879295304887 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40642879295304887 / 40000000000000000 : ℚ)) - (U := (79720977242129037991 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40642879295304887 / 40000000000000000 : ℝ) ≤ - (79720977242129037991 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2537559232191939 / 5000000000000000 : ℝ)) (q := - (40642879295304887 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40642879295304887 / 80000000000000000 : ℚ)) + (r' := (40642879295304887 / 40000000000000000 : ℚ)) + (U := (-(3386014924257870962009 / 5000000000000000000000 : ℚ))) + (U' := (79720977242129037991 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (2537559232191939 / 5000000000000000 : ℚ)) + (q := (40642879295304887 / 80000000000000000 : ℚ)) + (U := (-(3386014924257870962009 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_6 : Uω (aρ 6) (bρ 6) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2671,25 +2348,21 @@ lemma U_490_6 : have hlg : Real.log (39246825969676887 / 80000000000000000 : ℝ) ≤ (-(7121560602100884678399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39246825969676887 / 80000000000000000 : ℝ) = - (39246825969676887 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39246825969676887 / 20000000000000000 : ℚ)) - (U := (6741383003899115321601 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39246825969676887 / 20000000000000000 : ℝ) ≤ - (6741383003899115321601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2446672754058439 / 5000000000000000 : ℝ)) (q := - (39246825969676887 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39246825969676887 / 80000000000000000 : ℚ)) + (r' := (39246825969676887 / 20000000000000000 : ℚ)) + (U := (-(7121560602100884678399 / 10000000000000000000000 : ℚ))) + (U' := (6741383003899115321601 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (2446672754058439 / 5000000000000000 : ℚ)) + (q := (39246825969676887 / 80000000000000000 : ℚ)) + (U := (-(7121560602100884678399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_7 : Uω (aρ 7) (bρ 7) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2697,25 +2370,21 @@ lemma U_490_7 : have hlg : Real.log (37335308106097219 / 80000000000000000 : ℝ) ≤ (-(7620871572269016417851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37335308106097219 / 80000000000000000 : ℝ) = - (37335308106097219 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37335308106097219 / 20000000000000000 : ℚ)) - (U := (6242072033730983582149 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37335308106097219 / 20000000000000000 : ℝ) ≤ - (6242072033730983582149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4639127422981961 / 10000000000000000 : ℝ)) (q := - (37335308106097219 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37335308106097219 / 80000000000000000 : ℚ)) + (r' := (37335308106097219 / 20000000000000000 : ℚ)) + (U := (-(7620871572269016417851 / 10000000000000000000000 : ℚ))) + (U' := (6242072033730983582149 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (4639127422981961 / 10000000000000000 : ℚ)) + (q := (37335308106097219 / 80000000000000000 : ℚ)) + (U := (-(7620871572269016417851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_8 : Uω (aρ 8) (bρ 8) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2723,25 +2392,21 @@ lemma U_490_8 : have hlg : Real.log (34825718597617907 / 80000000000000000 : ℝ) ≤ (-(2079176200419582819051 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34825718597617907 / 80000000000000000 : ℝ) = - (34825718597617907 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34825718597617907 / 20000000000000000 : ℚ)) - (U := (1386559701080417180949 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34825718597617907 / 20000000000000000 : ℝ) ≤ - (1386559701080417180949 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4295271697202133 / 10000000000000000 : ℝ)) (q := - (34825718597617907 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34825718597617907 / 80000000000000000 : ℚ)) + (r' := (34825718597617907 / 20000000000000000 : ℚ)) + (U := (-(2079176200419582819051 / 2500000000000000000000 : ℚ))) + (U' := (1386559701080417180949 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (4295271697202133 / 10000000000000000 : ℚ)) + (q := (34825718597617907 / 80000000000000000 : ℚ)) + (U := (-(2079176200419582819051 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_9 : Uω (aρ 9) (bρ 9) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2749,25 +2414,21 @@ lemma U_490_9 : have hlg : Real.log (31645667806187247 / 80000000000000000 : ℝ) ≤ (-(4637126865470083261903 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31645667806187247 / 80000000000000000 : ℝ) = - (31645667806187247 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31645667806187247 / 20000000000000000 : ℚ)) - (U := (2294344937529916738097 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31645667806187247 / 20000000000000000 : ℝ) ≤ - (2294344937529916738097 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (960306156926117 / 2500000000000000 : ℝ)) (q := - (31645667806187247 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31645667806187247 / 80000000000000000 : ℚ)) + (r' := (31645667806187247 / 20000000000000000 : ℚ)) + (U := (-(4637126865470083261903 / 5000000000000000000000 : ℚ))) + (U' := (2294344937529916738097 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (960306156926117 / 2500000000000000 : ℚ)) + (q := (31645667806187247 / 80000000000000000 : ℚ)) + (U := (-(4637126865470083261903 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_10 : Uω (aρ 10) (bρ 10) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2775,26 +2436,21 @@ lemma U_490_10 : have hlg : Real.log (1108629354904607 / 3200000000000000 : ℝ) ≤ (-(5300131861877623017487 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1108629354904607 / 3200000000000000 : ℝ) = - (1108629354904607 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1108629354904607 / 800000000000000 : ℚ)) - (U := (1631339941122376982513 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1108629354904607 / 800000000000000 : ℝ) ≤ - (1631339941122376982513 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (64946003556129 / 200000000000000 : ℝ)) (q := - (1108629354904607 / 3200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1108629354904607 / 3200000000000000 : ℚ)) + (r' := (1108629354904607 / 800000000000000 : ℚ)) + (U := (-(5300131861877623017487 / 5000000000000000000000 : ℚ))) + (U' := (1631339941122376982513 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (64946003556129 / 200000000000000 : ℚ)) + (q := (1108629354904607 / 3200000000000000 : ℚ)) + (U := (-(5300131861877623017487 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_11 : Uω (aρ 11) (bρ 11) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2802,26 +2458,21 @@ lemma U_490_11 : have hlg : Real.log (22859345099191703 / 80000000000000000 : ℝ) ≤ (-(12526666245270194488077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22859345099191703 / 80000000000000000 : ℝ) = - (22859345099191703 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22859345099191703 / 20000000000000000 : ℚ)) - (U := (1336277360729805511923 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22859345099191703 / 20000000000000000 : ℝ) ≤ - (1336277360729805511923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1225839805327791 / 5000000000000000 : ℝ)) (q := - (22859345099191703 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22859345099191703 / 80000000000000000 : ℚ)) + (r' := (22859345099191703 / 20000000000000000 : ℚ)) + (U := (-(12526666245270194488077 / 10000000000000000000000 : ℚ))) + (U' := (1336277360729805511923 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (1225839805327791 / 5000000000000000 : ℚ)) + (q := (22859345099191703 / 80000000000000000 : ℚ)) + (U := (-(12526666245270194488077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_12 : Uω (aρ 12) (bρ 12) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2829,26 +2480,21 @@ lemma U_490_12 : have hlg : Real.log (16124200725712223 / 80000000000000000 : ℝ) ≤ (-(16017053398384051458857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16124200725712223 / 80000000000000000 : ℝ) = - (16124200725712223 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16124200725712223 / 10000000000000000 : ℚ)) - (U := (4777362010615948541143 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16124200725712223 / 10000000000000000 : ℝ) ≤ - (4777362010615948541143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (148949201746339 / 1250000000000000 : ℝ)) (q := - (16124200725712223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16124200725712223 / 80000000000000000 : ℚ)) + (r' := (16124200725712223 / 10000000000000000 : ℚ)) + (U := (-(16017053398384051458857 / 10000000000000000000000 : ℚ))) + (U' := (4777362010615948541143 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34673585899439 / 64000000000000 : ℚ)) + (s := (148949201746339 / 1250000000000000 : ℚ)) + (q := (16124200725712223 / 80000000000000000 : ℚ)) + (U := (-(16017053398384051458857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_490_13 : Uω (aρ 13) (bρ 13) (34673585899439 / 64000000000000 : ℝ) ≤ @@ -2960,25 +2606,21 @@ lemma U_491_1 : have hlg : Real.log (17150277044520221 / 32000000000000000 : ℝ) ≤ (-(249488629943552077721 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17150277044520221 / 32000000000000000 : ℝ) = - (17150277044520221 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17150277044520221 / 16000000000000000 : ℚ)) - (U := (27770242176447922279 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (17150277044520221 / 16000000000000000 : ℝ) ≤ - (27770242176447922279 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (535943141146381 / 1000000000000000 : ℝ)) (q := - (17150277044520221 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17150277044520221 / 32000000000000000 : ℚ)) + (r' := (17150277044520221 / 16000000000000000 : ℚ)) + (U := (-(249488629943552077721 / 400000000000000000000 : ℚ))) + (U' := (27770242176447922279 / 400000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (535943141146381 / 1000000000000000 : ℚ)) + (q := (17150277044520221 / 32000000000000000 : ℚ)) + (U := (-(249488629943552077721 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_2 : Uω (aρ 2) (bρ 2) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -2986,25 +2628,21 @@ lemma U_491_2 : have hlg : Real.log (85368382187420993 / 160000000000000000 : ℝ) ≤ (-(6281980147295564591557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85368382187420993 / 160000000000000000 : ℝ) = - (85368382187420993 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85368382187420993 / 80000000000000000 : ℚ)) - (U := (649491655704435408443 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85368382187420993 / 80000000000000000 : ℝ) ≤ - (649491655704435408443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (666915630572037 / 1250000000000000 : ℝ)) (q := - (85368382187420993 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85368382187420993 / 160000000000000000 : ℚ)) + (r' := (85368382187420993 / 80000000000000000 : ℚ)) + (U := (-(6281980147295564591557 / 10000000000000000000000 : ℚ))) + (U' := (649491655704435408443 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (666915630572037 / 1250000000000000 : ℚ)) + (q := (85368382187420993 / 160000000000000000 : ℚ)) + (U := (-(6281980147295564591557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_3 : Uω (aρ 3) (bρ 3) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3012,25 +2650,21 @@ lemma U_491_3 : have hlg : Real.log (84602032915902633 / 160000000000000000 : ℝ) ≤ (-(6372155189116117571223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84602032915902633 / 160000000000000000 : ℝ) = - (84602032915902633 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84602032915902633 / 80000000000000000 : ℚ)) - (U := (559316613883882428777 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84602032915902633 / 80000000000000000 : ℝ) ≤ - (559316613883882428777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5286927491986501 / 10000000000000000 : ℝ)) (q := - (84602032915902633 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84602032915902633 / 160000000000000000 : ℚ)) + (r' := (84602032915902633 / 80000000000000000 : ℚ)) + (U := (-(6372155189116117571223 / 10000000000000000000000 : ℚ))) + (U' := (559316613883882428777 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (5286927491986501 / 10000000000000000 : ℚ)) + (q := (84602032915902633 / 160000000000000000 : ℚ)) + (U := (-(6372155189116117571223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_4 : Uω (aρ 4) (bρ 4) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3038,25 +2672,21 @@ lemma U_491_4 : have hlg : Real.log (83328198004745153 / 160000000000000000 : ℝ) ≤ (-(3261934058108181114563 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83328198004745153 / 160000000000000000 : ℝ) = - (83328198004745153 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83328198004745153 / 80000000000000000 : ℚ)) - (U := (203801843391818885437 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83328198004745153 / 80000000000000000 : ℝ) ≤ - (203801843391818885437 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325374519322301 / 625000000000000 : ℝ)) (q := - (83328198004745153 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83328198004745153 / 160000000000000000 : ℚ)) + (r' := (83328198004745153 / 80000000000000000 : ℚ)) + (U := (-(3261934058108181114563 / 5000000000000000000000 : ℚ))) + (U' := (203801843391818885437 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (325374519322301 / 625000000000000 : ℚ)) + (q := (83328198004745153 / 160000000000000000 : ℚ)) + (U := (-(3261934058108181114563 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_5 : Uω (aρ 5) (bρ 5) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3064,25 +2694,21 @@ lemma U_491_5 : have hlg : Real.log (81385720197664297 / 160000000000000000 : ℝ) ≤ (-(1689934962254301555617 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (81385720197664297 / 160000000000000000 : ℝ) = - (81385720197664297 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (81385720197664297 / 80000000000000000 : ℚ)) - (U := (42932988495698444383 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (81385720197664297 / 80000000000000000 : ℝ) ≤ - (42932988495698444383 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5081372502606709 / 10000000000000000 : ℝ)) (q := - (81385720197664297 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (81385720197664297 / 160000000000000000 : ℚ)) + (r' := (81385720197664297 / 80000000000000000 : ℚ)) + (U := (-(1689934962254301555617 / 2500000000000000000000 : ℚ))) + (U' := (42932988495698444383 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (5081372502606709 / 10000000000000000 : ℚ)) + (q := (81385720197664297 / 160000000000000000 : ℚ)) + (U := (-(1689934962254301555617 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_6 : Uω (aρ 6) (bρ 6) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3090,25 +2716,21 @@ lemma U_491_6 : have hlg : Real.log (78593765461601849 / 160000000000000000 : ℝ) ≤ (-(3554407191258538788113 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (78593765461601849 / 160000000000000000 : ℝ) = - (78593765461601849 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78593765461601849 / 40000000000000000 : ℚ)) - (U := (3377064611741461211887 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (78593765461601849 / 40000000000000000 : ℝ) ≤ - (3377064611741461211887 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4899618535738903 / 10000000000000000 : ℝ)) (q := - (78593765461601849 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78593765461601849 / 160000000000000000 : ℚ)) + (r' := (78593765461601849 / 40000000000000000 : ℚ)) + (U := (-(3554407191258538788113 / 5000000000000000000000 : ℚ))) + (U' := (3377064611741461211887 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (4899618535738903 / 10000000000000000 : ℚ)) + (q := (78593765461601849 / 160000000000000000 : ℚ)) + (U := (-(3554407191258538788113 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_7 : Uω (aρ 7) (bρ 7) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3116,25 +2738,21 @@ lemma U_491_7 : have hlg : Real.log (2990842884410353 / 6400000000000000 : ℝ) ≤ (-(7607427410292149149329 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2990842884410353 / 6400000000000000 : ℝ) = - (2990842884410353 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2990842884410353 / 1600000000000000 : ℚ)) - (U := (6255516195707850850671 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2990842884410353 / 1600000000000000 : ℝ) ≤ - (6255516195707850850671 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (185817729903241 / 400000000000000 : ℝ)) (q := - (2990842884410353 / 6400000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2990842884410353 / 6400000000000000 : ℚ)) + (r' := (2990842884410353 / 1600000000000000 : ℚ)) + (U := (-(7607427410292149149329 / 10000000000000000000000 : ℚ))) + (U' := (6255516195707850850671 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (185817729903241 / 400000000000000 : ℚ)) + (q := (2990842884410353 / 6400000000000000 : ℚ)) + (U := (-(7607427410292149149329 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_8 : Uω (aρ 8) (bρ 8) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3142,25 +2760,21 @@ lemma U_491_8 : have hlg : Real.log (69752640907475889 / 160000000000000000 : ℝ) ≤ (-(4151092661282270086939 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (69752640907475889 / 160000000000000000 : ℝ) = - (69752640907475889 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69752640907475889 / 40000000000000000 : ℚ)) - (U := (2780379141717729913061 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69752640907475889 / 40000000000000000 : ℝ) ≤ - (2780379141717729913061 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2150840499286579 / 5000000000000000 : ℝ)) (q := - (69752640907475889 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69752640907475889 / 160000000000000000 : ℚ)) + (r' := (69752640907475889 / 40000000000000000 : ℚ)) + (U := (-(4151092661282270086939 / 5000000000000000000000 : ℚ))) + (U' := (2780379141717729913061 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (2150840499286579 / 5000000000000000 : ℚ)) + (q := (69752640907475889 / 160000000000000000 : ℚ)) + (U := (-(4151092661282270086939 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_9 : Uω (aρ 9) (bρ 9) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3168,25 +2782,21 @@ lemma U_491_9 : have hlg : Real.log (63394165429205193 / 160000000000000000 : ℝ) ≤ (-(1157252481795129172497 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63394165429205193 / 160000000000000000 : ℝ) = - (63394165429205193 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63394165429205193 / 40000000000000000 : ℚ)) - (U := (575615468954870827503 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63394165429205193 / 40000000000000000 : ℝ) ≤ - (575615468954870827503 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3847837192149321 / 10000000000000000 : ℝ)) (q := - (63394165429205193 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63394165429205193 / 160000000000000000 : ℚ)) + (r' := (63394165429205193 / 40000000000000000 : ℚ)) + (U := (-(1157252481795129172497 / 1250000000000000000000 : ℚ))) + (U' := (575615468954870827503 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (3847837192149321 / 10000000000000000 : ℚ)) + (q := (63394165429205193 / 160000000000000000 : ℚ)) + (U := (-(1157252481795129172497 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_10 : Uω (aρ 10) (bρ 10) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3194,26 +2804,21 @@ lemma U_491_10 : have hlg : Real.log (11107598166272613 / 32000000000000000 : ℝ) ≤ (-(165329141977207929739 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11107598166272613 / 32000000000000000 : ℝ) = - (11107598166272613 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11107598166272613 / 8000000000000000 : ℚ)) - (U := (51279351866542070261 / 156250000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (11107598166272613 / 8000000000000000 : ℝ) ≤ - (51279351866542070261 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (650874880182811 / 2000000000000000 : ℝ)) (q := - (11107598166272613 / 32000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11107598166272613 / 32000000000000000 : ℚ)) + (r' := (11107598166272613 / 8000000000000000 : ℚ)) + (U := (-(165329141977207929739 / 156250000000000000000 : ℚ))) + (U' := (51279351866542070261 / 156250000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (650874880182811 / 2000000000000000 : ℚ)) + (q := (11107598166272613 / 32000000000000000 : ℚ)) + (U := (-(165329141977207929739 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_11 : Uω (aρ 11) (bρ 11) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3221,26 +2826,21 @@ lemma U_491_11 : have hlg : Real.log (45835025944617849 / 160000000000000000 : ℝ) ≤ (-(6250626286282757761457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45835025944617849 / 160000000000000000 : ℝ) = - (45835025944617849 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45835025944617849 / 40000000000000000 : ℚ)) - (U := (680845516717242238543 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45835025944617849 / 40000000000000000 : ℝ) ≤ - (680845516717242238543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2459980416275903 / 10000000000000000 : ℝ)) (q := - (45835025944617849 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45835025944617849 / 160000000000000000 : ℚ)) + (r' := (45835025944617849 / 40000000000000000 : ℚ)) + (U := (-(6250626286282757761457 / 5000000000000000000000 : ℚ))) + (U' := (680845516717242238543 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (2459980416275903 / 10000000000000000 : ℚ)) + (q := (45835025944617849 / 160000000000000000 : ℚ)) + (U := (-(6250626286282757761457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_12 : Uω (aρ 12) (bρ 12) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3248,26 +2848,21 @@ lemma U_491_12 : have hlg : Real.log (32416703437324241 / 160000000000000000 : ℝ) ≤ (-(1995624982888555183189 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (32416703437324241 / 160000000000000000 : ℝ) = - (32416703437324241 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32416703437324241 / 20000000000000000 : ℚ)) - (U := (603676943236444816811 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32416703437324241 / 20000000000000000 : ℝ) ≤ - (603676943236444816811 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (603195099774601 / 5000000000000000 : ℝ)) (q := - (32416703437324241 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32416703437324241 / 160000000000000000 : ℚ)) + (r' := (32416703437324241 / 20000000000000000 : ℚ)) + (U := (-(1995624982888555183189 / 1250000000000000000000 : ℚ))) + (U' := (603676943236444816811 / 1250000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69427058680913 / 128000000000000 : ℚ)) + (s := (603195099774601 / 5000000000000000 : ℚ)) + (q := (32416703437324241 / 160000000000000000 : ℚ)) + (U := (-(1995624982888555183189 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_491_13 : Uω (aρ 13) (bρ 13) (69427058680913 / 128000000000000 : ℝ) ≤ @@ -3380,25 +2975,21 @@ lemma U_492_1 : have hlg : Real.log (4292562219326693 / 8000000000000000 : ℝ) ≤ (-(6225577328427986757589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4292562219326693 / 8000000000000000 : ℝ) = - (4292562219326693 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4292562219326693 / 4000000000000000 : ℚ)) - (U := (705894474572013242411 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4292562219326693 / 4000000000000000 : ℝ) ≤ - (705894474572013242411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268283632214821 / 500000000000000 : ℝ)) (q := - (4292562219326693 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4292562219326693 / 8000000000000000 : ℚ)) + (r' := (4292562219326693 / 4000000000000000 : ℚ)) + (U := (-(6225577328427986757589 / 10000000000000000000000 : ℚ))) + (U' := (705894474572013242411 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (268283632214821 / 500000000000000 : ℚ)) + (q := (4292562219326693 / 8000000000000000 : ℚ)) + (U := (-(6225577328427986757589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_2 : Uω (aρ 2) (bρ 2) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3406,25 +2997,21 @@ lemma U_492_2 : have hlg : Real.log (21367061126811181 / 40000000000000000 : ℝ) ≤ (-(3135144586463325143691 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21367061126811181 / 40000000000000000 : ℝ) = - (21367061126811181 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21367061126811181 / 20000000000000000 : ℚ)) - (U := (330591315036674856309 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21367061126811181 / 20000000000000000 : ℝ) ≤ - (330591315036674856309 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2670783335947639 / 5000000000000000 : ℝ)) (q := - (21367061126811181 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21367061126811181 / 40000000000000000 : ℚ)) + (r' := (21367061126811181 / 20000000000000000 : ℚ)) + (U := (-(3135144586463325143691 / 5000000000000000000000 : ℚ))) + (U' := (330591315036674856309 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (2670783335947639 / 5000000000000000 : ℚ)) + (q := (21367061126811181 / 40000000000000000 : ℚ)) + (U := (-(3135144586463325143691 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_3 : Uω (aρ 3) (bρ 3) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3432,25 +3019,21 @@ lemma U_492_3 : have hlg : Real.log (21175476179034053 / 40000000000000000 : ℝ) ≤ (-(6360357257749035855581 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21175476179034053 / 40000000000000000 : ℝ) = - (21175476179034053 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21175476179034053 / 20000000000000000 : ℚ)) - (U := (571114545250964144419 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21175476179034053 / 20000000000000000 : ℝ) ≤ - (571114545250964144419 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2646585152178357 / 5000000000000000 : ℝ)) (q := - (21175476179034053 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21175476179034053 / 40000000000000000 : ℚ)) + (r' := (21175476179034053 / 20000000000000000 : ℚ)) + (U := (-(6360357257749035855581 / 10000000000000000000000 : ℚ))) + (U' := (571114545250964144419 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (2646585152178357 / 5000000000000000 : ℚ)) + (q := (21175476179034053 / 40000000000000000 : ℚ)) + (U := (-(6360357257749035855581 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_4 : Uω (aρ 4) (bρ 4) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3458,25 +3041,21 @@ lemma U_492_4 : have hlg : Real.log (20857023827179691 / 40000000000000000 : ℝ) ≤ (-(3255943440666472898293 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20857023827179691 / 40000000000000000 : ℝ) = - (20857023827179691 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20857023827179691 / 20000000000000000 : ℚ)) - (U := (209792460833527101707 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20857023827179691 / 20000000000000000 : ℝ) ≤ - (209792460833527101707 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5212238309494533 / 10000000000000000 : ℝ)) (q := - (20857023827179691 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20857023827179691 / 40000000000000000 : ℚ)) + (r' := (20857023827179691 / 20000000000000000 : ℚ)) + (U := (-(3255943440666472898293 / 5000000000000000000000 : ℚ))) + (U' := (209792460833527101707 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (5212238309494533 / 10000000000000000 : ℚ)) + (q := (20857023827179691 / 40000000000000000 : ℚ)) + (U := (-(3255943440666472898293 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_5 : Uω (aρ 5) (bρ 5) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3484,25 +3063,21 @@ lemma U_492_5 : have hlg : Real.log (4074284077586997 / 8000000000000000 : ℝ) ≤ (-(6747464966434608471673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4074284077586997 / 8000000000000000 : ℝ) = - (4074284077586997 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4074284077586997 / 4000000000000000 : ℚ)) - (U := (184006836565391528327 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4074284077586997 / 4000000000000000 : ℝ) ≤ - (184006836565391528327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (254381325460359 / 500000000000000 : ℝ)) (q := - (4074284077586997 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4074284077586997 / 8000000000000000 : ℚ)) + (r' := (4074284077586997 / 4000000000000000 : ℚ)) + (U := (-(6747464966434608471673 / 10000000000000000000000 : ℚ))) + (U' := (184006836565391528327 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (254381325460359 / 500000000000000 : ℚ)) + (q := (4074284077586997 / 8000000000000000 : ℚ)) + (U := (-(6747464966434608471673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_6 : Uω (aρ 6) (bρ 6) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3510,25 +3085,21 @@ lemma U_492_6 : have hlg : Real.log (19673469583397039 / 40000000000000000 : ℝ) ≤ (-(1419216894299342846093 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19673469583397039 / 40000000000000000 : ℝ) = - (19673469583397039 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19673469583397039 / 10000000000000000 : ℚ)) - (U := (1353371826900657153907 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19673469583397039 / 10000000000000000 : ℝ) ≤ - (1353371826900657153907 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4905891482078207 / 10000000000000000 : ℝ)) (q := - (19673469583397039 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19673469583397039 / 40000000000000000 : ℚ)) + (r' := (19673469583397039 / 10000000000000000 : ℚ)) + (U := (-(1419216894299342846093 / 2000000000000000000000 : ℚ))) + (U' := (1353371826900657153907 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (4905891482078207 / 10000000000000000 : ℚ)) + (q := (19673469583397039 / 40000000000000000 : ℚ)) + (U := (-(1419216894299342846093 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_7 : Uω (aρ 7) (bρ 7) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3536,25 +3107,21 @@ lemma U_492_7 : have hlg : Real.log (18717881598994987 / 40000000000000000 : ℝ) ≤ (-(7594001513948014470251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18717881598994987 / 40000000000000000 : ℝ) = - (18717881598994987 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18717881598994987 / 10000000000000000 : ℚ)) - (U := (6268942092051985529749 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18717881598994987 / 10000000000000000 : ℝ) ≤ - (6268942092051985529749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4651758870637181 / 10000000000000000 : ℝ)) (q := - (18717881598994987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18717881598994987 / 40000000000000000 : ℚ)) + (r' := (18717881598994987 / 10000000000000000 : ℚ)) + (U := (-(7594001513948014470251 / 10000000000000000000000 : ℚ))) + (U' := (6268942092051985529749 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (4651758870637181 / 10000000000000000 : ℚ)) + (q := (18717881598994987 / 40000000000000000 : ℚ)) + (U := (-(7594001513948014470251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_8 : Uω (aρ 8) (bρ 8) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3562,25 +3129,21 @@ lemma U_492_8 : have hlg : Real.log (17463460167469257 / 40000000000000000 : ℝ) ≤ (-(2071921864965059653457 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17463460167469257 / 40000000000000000 : ℝ) = - (17463460167469257 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17463460167469257 / 10000000000000000 : ℚ)) - (U := (1393814036534940346543 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17463460167469257 / 10000000000000000 : ℝ) ≤ - (1393814036534940346543 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1077022451553579 / 2500000000000000 : ℝ)) (q := - (17463460167469257 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17463460167469257 / 40000000000000000 : ℚ)) + (r' := (17463460167469257 / 10000000000000000 : ℚ)) + (U := (-(2071921864965059653457 / 2500000000000000000000 : ℚ))) + (U' := (1393814036534940346543 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (1077022451553579 / 2500000000000000 : ℚ)) + (q := (17463460167469257 / 40000000000000000 : ℚ)) + (U := (-(2071921864965059653457 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_9 : Uω (aρ 9) (bρ 9) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3588,25 +3151,21 @@ lemma U_492_9 : have hlg : Real.log (15874246334424941 / 40000000000000000 : ℝ) ≤ (-(9241813849391177808397 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15874246334424941 / 40000000000000000 : ℝ) = - (15874246334424941 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15874246334424941 / 10000000000000000 : ℚ)) - (U := (4621129756608822191603 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15874246334424941 / 10000000000000000 : ℝ) ≤ - (4621129756608822191603 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1927224259026079 / 5000000000000000 : ℝ)) (q := - (15874246334424941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15874246334424941 / 40000000000000000 : ℚ)) + (r' := (15874246334424941 / 10000000000000000 : ℚ)) + (U := (-(9241813849391177808397 / 10000000000000000000000 : ℚ))) + (U' := (4621129756608822191603 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (1927224259026079 / 5000000000000000 : ℚ)) + (q := (15874246334424941 / 40000000000000000 : ℚ)) + (U := (-(9241813849391177808397 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_10 : Uω (aρ 10) (bρ 10) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3614,26 +3173,21 @@ lemma U_492_10 : have hlg : Real.log (2782224335433059 / 8000000000000000 : ℝ) ≤ (-(2640477031809797859469 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2782224335433059 / 8000000000000000 : ℝ) = - (2782224335433059 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2782224335433059 / 2000000000000000 : ℚ)) - (U := (825258869690202140531 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2782224335433059 / 2000000000000000 : ℝ) ≤ - (825258869690202140531 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (652289044583467 / 2000000000000000 : ℝ)) (q := - (2782224335433059 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2782224335433059 / 8000000000000000 : ℚ)) + (r' := (2782224335433059 / 2000000000000000 : ℚ)) + (U := (-(2640477031809797859469 / 2500000000000000000000 : ℚ))) + (U' := (825258869690202140531 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (652289044583467 / 2000000000000000 : ℚ)) + (q := (2782224335433059 / 8000000000000000 : ℚ)) + (U := (-(2640477031809797859469 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_11 : Uω (aρ 11) (bρ 11) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3641,26 +3195,21 @@ lemma U_492_11 : have hlg : Real.log (2297563230746221 / 8000000000000000 : ℝ) ≤ (-(2495184889494876055977 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2297563230746221 / 8000000000000000 : ℝ) = - (2297563230746221 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2297563230746221 / 2000000000000000 : ℚ)) - (U := (277403831705123944023 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2297563230746221 / 2000000000000000 : ℝ) ≤ - (277403831705123944023 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61706727185131 / 250000000000000 : ℝ)) (q := - (2297563230746221 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2297563230746221 / 8000000000000000 : ℚ)) + (r' := (2297563230746221 / 2000000000000000 : ℚ)) + (U := (-(2495184889494876055977 / 2000000000000000000000 : ℚ))) + (U' := (277403831705123944023 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (61706727185131 / 250000000000000 : ℚ)) + (q := (2297563230746221 / 8000000000000000 : ℚ)) + (U := (-(2495184889494876055977 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_12 : Uω (aρ 12) (bρ 12) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3668,26 +3217,21 @@ lemma U_492_12 : have hlg : Real.log (8145956564381167 / 40000000000000000 : ℝ) ≤ (-(1591357776262880250737 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8145956564381167 / 40000000000000000 : ℝ) = - (8145956564381167 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8145956564381167 / 5000000000000000 : ℚ)) - (U := (488083764637119749263 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8145956564381167 / 5000000000000000 : ℝ) ≤ - (488083764637119749263 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1221039389415271 / 10000000000000000 : ℝ)) (q := - (8145956564381167 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8145956564381167 / 40000000000000000 : ℚ)) + (r' := (8145956564381167 / 5000000000000000 : ℚ)) + (U := (-(1591357776262880250737 / 1000000000000000000000 : ℚ))) + (U' := (488083764637119749263 / 1000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17376736390737 / 32000000000000 : ℚ)) + (s := (1221039389415271 / 10000000000000000 : ℚ)) + (q := (8145956564381167 / 40000000000000000 : ℚ)) + (U := (-(1591357776262880250737 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_492_13 : Uω (aρ 13) (bρ 13) (17376736390737 / 32000000000000 : ℝ) ≤ @@ -3800,25 +3344,21 @@ lemma U_493_1 : have hlg : Real.log (85951103549162159 / 160000000000000000 : ℝ) ≤ (-(1553488109489150942229 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85951103549162159 / 160000000000000000 : ℝ) = - (85951103549162159 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85951103549162159 / 80000000000000000 : ℚ)) - (U := (179379841260849057771 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85951103549162159 / 80000000000000000 : ℝ) ≤ - (179379841260849057771 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5371913876965973 / 10000000000000000 : ℝ)) (q := - (85951103549162159 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85951103549162159 / 160000000000000000 : ℚ)) + (r' := (85951103549162159 / 80000000000000000 : ℚ)) + (U := (-(1553488109489150942229 / 2500000000000000000000 : ℚ))) + (U' := (179379841260849057771 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (5371913876965973 / 10000000000000000 : ℚ)) + (q := (85951103549162159 / 160000000000000000 : ℚ)) + (U := (-(1553488109489150942229 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_2 : Uω (aρ 2) (bρ 2) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3826,25 +3366,21 @@ lemma U_493_2 : have hlg : Real.log (85568106818391623 / 160000000000000000 : ℝ) ≤ (-(6258611851501049440367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85568106818391623 / 160000000000000000 : ℝ) = - (85568106818391623 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85568106818391623 / 80000000000000000 : ℚ)) - (U := (672859951498950559633 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85568106818391623 / 80000000000000000 : ℝ) ≤ - (672859951498950559633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (668476037266207 / 1250000000000000 : ℝ)) (q := - (85568106818391623 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85568106818391623 / 160000000000000000 : ℚ)) + (r' := (85568106818391623 / 80000000000000000 : ℚ)) + (U := (-(6258611851501049440367 / 10000000000000000000000 : ℚ))) + (U' := (672859951498950559633 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (668476037266207 / 1250000000000000 : ℚ)) + (q := (85568106818391623 / 160000000000000000 : ℚ)) + (U := (-(6258611851501049440367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_3 : Uω (aρ 3) (bρ 3) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3852,25 +3388,21 @@ lemma U_493_3 : have hlg : Real.log (84801776485279623 / 160000000000000000 : ℝ) ≤ (-(1587143308191476179277 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84801776485279623 / 160000000000000000 : ℝ) = - (84801776485279623 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84801776485279623 / 80000000000000000 : ℚ)) - (U := (145724642558523820723 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (84801776485279623 / 80000000000000000 : ℝ) ≤ - (145724642558523820723 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (331213319552541 / 625000000000000 : ℝ)) (q := - (84801776485279623 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84801776485279623 / 160000000000000000 : ℚ)) + (r' := (84801776485279623 / 80000000000000000 : ℚ)) + (U := (-(1587143308191476179277 / 2500000000000000000000 : ℚ))) + (U' := (145724642558523820723 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (331213319552541 / 625000000000000 : ℚ)) + (q := (84801776485279623 / 160000000000000000 : ℚ)) + (U := (-(1587143308191476179277 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_4 : Uω (aρ 4) (bρ 4) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3878,25 +3410,21 @@ lemma U_493_4 : have hlg : Real.log (83527992520084831 / 160000000000000000 : ℝ) ≤ (-(6499919995358701146053 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83527992520084831 / 160000000000000000 : ℝ) = - (83527992520084831 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83527992520084831 / 80000000000000000 : ℚ)) - (U := (431551807641298853947 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83527992520084831 / 80000000000000000 : ℝ) ≤ - (431551807641298853947 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5218484298256307 / 10000000000000000 : ℝ)) (q := - (83527992520084831 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83527992520084831 / 160000000000000000 : ℚ)) + (r' := (83527992520084831 / 80000000000000000 : ℚ)) + (U := (-(6499919995358701146053 / 10000000000000000000000 : ℚ))) + (U' := (431551807641298853947 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (5218484298256307 / 10000000000000000 : ℚ)) + (q := (83527992520084831 / 160000000000000000 : ℚ)) + (U := (-(6499919995358701146053 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_5 : Uω (aρ 5) (bρ 5) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3904,25 +3432,21 @@ lemma U_493_5 : have hlg : Real.log (16317128530753699 / 32000000000000000 : ℝ) ≤ (-(1683801290887367162087 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16317128530753699 / 32000000000000000 : ℝ) = - (16317128530753699 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16317128530753699 / 16000000000000000 : ℚ)) - (U := (49066659862632837913 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (16317128530753699 / 16000000000000000 : ℝ) ≤ - (49066659862632837913 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1018776096860353 / 2000000000000000 : ℝ)) (q := - (16317128530753699 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16317128530753699 / 32000000000000000 : ℚ)) + (r' := (16317128530753699 / 16000000000000000 : ℚ)) + (U := (-(1683801290887367162087 / 2500000000000000000000 : ℚ))) + (U' := (49066659862632837913 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (1018776096860353 / 2000000000000000 : ℚ)) + (q := (16317128530753699 / 32000000000000000 : ℚ)) + (U := (-(1683801290887367162087 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_6 : Uω (aρ 6) (bρ 6) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3930,25 +3454,21 @@ lemma U_493_6 : have hlg : Real.log (15758798111560779 / 32000000000000000 : ℝ) ≤ (-(7083370827149970993019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15758798111560779 / 32000000000000000 : ℝ) = - (15758798111560779 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15758798111560779 / 8000000000000000 : ℚ)) - (U := (6779572778850029006981 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (15758798111560779 / 8000000000000000 : ℝ) ≤ - (6779572778850029006981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (491216434744619 / 1000000000000000 : ℝ)) (q := - (15758798111560779 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15758798111560779 / 32000000000000000 : ℚ)) + (r' := (15758798111560779 / 8000000000000000 : ℚ)) + (U := (-(7083370827149970993019 / 10000000000000000000000 : ℚ))) + (U' := (6779572778850029006981 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (491216434744619 / 1000000000000000 : ℚ)) + (q := (15758798111560779 / 32000000000000000 : ℚ)) + (U := (-(7083370827149970993019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_7 : Uω (aρ 7) (bρ 7) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3956,25 +3476,21 @@ lemma U_493_7 : have hlg : Real.log (74971979075916063 / 160000000000000000 : ℝ) ≤ (-(3790296916546084192099 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (74971979075916063 / 160000000000000000 : ℝ) = - (74971979075916063 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (74971979075916063 / 40000000000000000 : ℚ)) - (U := (3141174886453915807901 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (74971979075916063 / 40000000000000000 : ℝ) ≤ - (3141174886453915807901 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4658074292970211 / 10000000000000000 : ℝ)) (q := - (74971979075916063 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (74971979075916063 / 160000000000000000 : ℚ)) + (r' := (74971979075916063 / 40000000000000000 : ℚ)) + (U := (-(3790296916546084192099 / 5000000000000000000000 : ℚ))) + (U' := (3141174886453915807901 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (4658074292970211 / 10000000000000000 : ℚ)) + (q := (74971979075916063 / 160000000000000000 : ℚ)) + (U := (-(3790296916546084192099 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_8 : Uω (aρ 8) (bρ 8) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -3982,25 +3498,21 @@ lemma U_493_8 : have hlg : Real.log (69955036500040647 / 160000000000000000 : ℝ) ≤ (-(8273211147642510212537 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (69955036500040647 / 160000000000000000 : ℝ) = - (69955036500040647 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69955036500040647 / 40000000000000000 : ℚ)) - (U := (5589732458357489787463 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69955036500040647 / 40000000000000000 : ℝ) ≤ - (5589732458357489787463 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (539312265290723 / 1250000000000000 : ℝ)) (q := - (69955036500040647 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69955036500040647 / 160000000000000000 : ℚ)) + (r' := (69955036500040647 / 40000000000000000 : ℚ)) + (U := (-(8273211147642510212537 / 10000000000000000000000 : ℚ))) + (U' := (5589732458357489787463 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (539312265290723 / 1250000000000000 : ℚ)) + (q := (69955036500040647 / 160000000000000000 : ℚ)) + (U := (-(8273211147642510212537 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_9 : Uω (aρ 9) (bρ 9) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -4008,25 +3520,21 @@ lemma U_493_9 : have hlg : Real.log (12719959077751323 / 32000000000000000 : ℝ) ≤ (-(115320445191368720493 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12719959077751323 / 32000000000000000 : ℝ) = - (12719959077751323 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12719959077751323 / 8000000000000000 : ℚ)) - (U := (57966349883631279507 / 125000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12719959077751323 / 8000000000000000 : ℝ) ≤ - (57966349883631279507 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48263232647191 / 125000000000000 : ℝ)) (q := - (12719959077751323 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12719959077751323 / 32000000000000000 : ℚ)) + (r' := (12719959077751323 / 8000000000000000 : ℚ)) + (U := (-(115320445191368720493 / 125000000000000000000 : ℚ))) + (U' := (57966349883631279507 / 125000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (48263232647191 / 125000000000000 : ℚ)) + (q := (12719959077751323 / 32000000000000000 : ℚ)) + (U := (-(115320445191368720493 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_10 : Uω (aρ 10) (bρ 10) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -4034,26 +3542,21 @@ lemma U_493_10 : have hlg : Real.log (55750955553708511 / 160000000000000000 : ℝ) ≤ (-(10542792645437616091663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55750955553708511 / 160000000000000000 : ℝ) = - (55750955553708511 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55750955553708511 / 40000000000000000 : ℚ)) - (U := (3320150960562383908337 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55750955553708511 / 40000000000000000 : ℝ) ≤ - (3320150960562383908337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3268512665889267 / 10000000000000000 : ℝ)) (q := - (55750955553708511 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55750955553708511 / 160000000000000000 : ℚ)) + (r' := (55750955553708511 / 40000000000000000 : ℚ)) + (U := (-(10542792645437616091663 / 10000000000000000000000 : ℚ))) + (U' := (3320150960562383908337 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (3268512665889267 / 10000000000000000 : ℚ)) + (q := (55750955553708511 / 160000000000000000 : ℚ)) + (U := (-(10542792645437616091663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_11 : Uω (aρ 11) (bρ 11) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -4061,26 +3564,21 @@ lemma U_493_11 : have hlg : Real.log (9213481436800803 / 32000000000000000 : ℝ) ≤ (-(778167573294784877017 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9213481436800803 / 32000000000000000 : ℝ) = - (9213481436800803 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9213481436800803 / 8000000000000000 : ℚ)) - (U := (88266402080215122983 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9213481436800803 / 8000000000000000 : ℝ) ≤ - (88266402080215122983 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (495309149176241 / 2000000000000000 : ℝ)) (q := - (9213481436800803 / 32000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9213481436800803 / 32000000000000000 : ℚ)) + (r' := (9213481436800803 / 8000000000000000 : ℚ)) + (U := (-(778167573294784877017 / 625000000000000000000 : ℚ))) + (U' := (88266402080215122983 / 625000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (495309149176241 / 2000000000000000 : ℚ)) + (q := (9213481436800803 / 32000000000000000 : ℚ)) + (U := (-(778167573294784877017 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_12 : Uω (aρ 12) (bρ 12) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -4088,26 +3586,21 @@ lemma U_493_12 : have hlg : Real.log (32749811854259119 / 160000000000000000 : ℝ) ≤ (-(15862765972973506168137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (32749811854259119 / 160000000000000000 : ℝ) = - (32749811854259119 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32749811854259119 / 20000000000000000 : ℚ)) - (U := (4931649436026493831863 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32749811854259119 / 20000000000000000 : ℝ) ≤ - (4931649436026493831863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1235546426348093 / 10000000000000000 : ℝ)) (q := - (32749811854259119 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32749811854259119 / 160000000000000000 : ℚ)) + (r' := (32749811854259119 / 20000000000000000 : ℚ)) + (U := (-(15862765972973506168137 / 10000000000000000000000 : ℚ))) + (U' := (4931649436026493831863 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69586832444983 / 128000000000000 : ℚ)) + (s := (1235546426348093 / 10000000000000000 : ℚ)) + (q := (32749811854259119 / 160000000000000000 : ℚ)) + (U := (-(15862765972973506168137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_493_13 : Uω (aρ 13) (bρ 13) (69586832444983 / 128000000000000 : ℝ) ≤ @@ -4220,25 +3713,21 @@ lemma U_494_1 : have hlg : Real.log (43025481355245261 / 80000000000000000 : ℝ) ≤ (-(1240468209150847565031 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43025481355245261 / 80000000000000000 : ℝ) = - (43025481355245261 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43025481355245261 / 40000000000000000 : ℚ)) - (U := (145826151449152434969 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43025481355245261 / 40000000000000000 : ℝ) ≤ - (145826151449152434969 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2689077554736517 / 5000000000000000 : ℝ)) (q := - (43025481355245261 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43025481355245261 / 80000000000000000 : ℚ)) + (r' := (43025481355245261 / 40000000000000000 : ℚ)) + (U := (-(1240468209150847565031 / 2000000000000000000000 : ℚ))) + (U' := (145826151449152434969 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (2689077554736517 / 5000000000000000 : ℚ)) + (q := (43025481355245261 / 80000000000000000 : ℚ)) + (U := (-(1240468209150847565031 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_2 : Uω (aρ 2) (bρ 2) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4246,25 +3735,21 @@ lemma U_494_2 : have hlg : Real.log (42833984560446017 / 80000000000000000 : ℝ) ≤ (-(1561737037791314671991 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42833984560446017 / 80000000000000000 : ℝ) = - (42833984560446017 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42833984560446017 / 40000000000000000 : ℚ)) - (U := (171130912958685328009 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42833984560446017 / 40000000000000000 : ℝ) ≤ - (171130912958685328009 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5354049923283223 / 10000000000000000 : ℝ)) (q := - (42833984560446017 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42833984560446017 / 80000000000000000 : ℚ)) + (r' := (42833984560446017 / 40000000000000000 : ℚ)) + (U := (-(1561737037791314671991 / 2500000000000000000000 : ℚ))) + (U' := (171130912958685328009 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (5354049923283223 / 10000000000000000 : ℚ)) + (q := (42833984560446017 / 80000000000000000 : ℚ)) + (U := (-(1561737037791314671991 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_3 : Uω (aρ 3) (bρ 3) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4272,25 +3757,21 @@ lemma U_494_3 : have hlg : Real.log (8490164822344261 / 16000000000000000 : ℝ) ≤ (-(792100385176676737587 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8490164822344261 / 16000000000000000 : ℝ) = - (8490164822344261 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8490164822344261 / 8000000000000000 : ℚ)) - (U := (74333590198323262413 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8490164822344261 / 8000000000000000 : ℝ) ≤ - (74333590198323262413 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1061131183490409 / 2000000000000000 : ℝ)) (q := - (8490164822344261 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8490164822344261 / 16000000000000000 : ℚ)) + (r' := (8490164822344261 / 8000000000000000 : ℚ)) + (U := (-(792100385176676737587 / 1250000000000000000000 : ℚ))) + (U' := (74333590198323262413 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (1061131183490409 / 2000000000000000 : ℚ)) + (q := (8490164822344261 / 16000000000000000 : ℚ)) + (U := (-(792100385176676737587 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_4 : Uω (aρ 4) (bρ 4) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4298,25 +3779,21 @@ lemma U_494_4 : have hlg : Real.log (41813944819587733 / 80000000000000000 : ℝ) ≤ (-(3243983711969671616221 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41813944819587733 / 80000000000000000 : ℝ) = - (41813944819587733 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41813944819587733 / 40000000000000000 : ℚ)) - (U := (221752189530328383779 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41813944819587733 / 40000000000000000 : ℝ) ≤ - (221752189530328383779 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1306182568870913 / 2500000000000000 : ℝ)) (q := - (41813944819587733 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41813944819587733 / 80000000000000000 : ℚ)) + (r' := (41813944819587733 / 40000000000000000 : ℚ)) + (U := (-(3243983711969671616221 / 5000000000000000000000 : ℚ))) + (U' := (221752189530328383779 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (1306182568870913 / 2500000000000000 : ℚ)) + (q := (41813944819587733 / 80000000000000000 : ℚ)) + (U := (-(3243983711969671616221 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_5 : Uω (aρ 5) (bρ 5) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4324,25 +3801,21 @@ lemma U_494_5 : have hlg : Real.log (40842801752338581 / 80000000000000000 : ℝ) ≤ (-(1344592080656173711347 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40842801752338581 / 80000000000000000 : ℝ) = - (40842801752338581 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40842801752338581 / 40000000000000000 : ℚ)) - (U := (41702279943826288653 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40842801752338581 / 40000000000000000 : ℝ) ≤ - (41702279943826288653 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1275033607001591 / 2500000000000000 : ℝ)) (q := - (40842801752338581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40842801752338581 / 80000000000000000 : ℚ)) + (r' := (40842801752338581 / 40000000000000000 : ℚ)) + (U := (-(1344592080656173711347 / 2000000000000000000000 : ℚ))) + (U' := (41702279943826288653 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (1275033607001591 / 2500000000000000 : ℚ)) + (q := (40842801752338581 / 80000000000000000 : ℚ)) + (U := (-(1344592080656173711347 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_6 : Uω (aρ 6) (bρ 6) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4350,25 +3823,21 @@ lemma U_494_6 : have hlg : Real.log (39447051068363761 / 80000000000000000 : ℝ) ≤ (-(1767668351937252963239 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39447051068363761 / 80000000000000000 : ℝ) = - (39447051068363761 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39447051068363761 / 20000000000000000 : ℚ)) - (U := (1698067549562747036761 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39447051068363761 / 20000000000000000 : ℝ) ≤ - (1698067549562747036761 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4918437132152659 / 10000000000000000 : ℝ)) (q := - (39447051068363761 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39447051068363761 / 80000000000000000 : ℚ)) + (r' := (39447051068363761 / 20000000000000000 : ℚ)) + (U := (-(1767668351937252963239 / 2500000000000000000000 : ℚ))) + (U' := (1698067549562747036761 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (4918437132152659 / 10000000000000000 : ℚ)) + (q := (39447051068363761 / 80000000000000000 : ℚ)) + (U := (-(1767668351937252963239 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_7 : Uω (aρ 7) (bρ 7) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4376,25 +3845,21 @@ lemma U_494_7 : have hlg : Real.log (37536215078294857 / 80000000000000000 : ℝ) ≤ (-(3783602158894347139321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37536215078294857 / 80000000000000000 : ℝ) = - (37536215078294857 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37536215078294857 / 20000000000000000 : ℚ)) - (U := (3147869644105652860679 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37536215078294857 / 20000000000000000 : ℝ) ≤ - (3147869644105652860679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4664389515395433 / 10000000000000000 : ℝ)) (q := - (37536215078294857 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37536215078294857 / 80000000000000000 : ℚ)) + (r' := (37536215078294857 / 20000000000000000 : ℚ)) + (U := (-(3783602158894347139321 / 5000000000000000000000 : ℚ))) + (U' := (3147869644105652860679 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (4664389515395433 / 10000000000000000 : ℚ)) + (q := (37536215078294857 / 80000000000000000 : ℚ)) + (U := (-(3783602158894347139321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_8 : Uω (aρ 8) (bρ 8) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4402,25 +3867,21 @@ lemma U_494_8 : have hlg : Real.log (35028114207731197 / 80000000000000000 : ℝ) ≤ (-(412937816014834911931 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35028114207731197 / 80000000000000000 : ℝ) = - (35028114207731197 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35028114207731197 / 20000000000000000 : ℚ)) - (U := (280209364285165088069 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35028114207731197 / 20000000000000000 : ℝ) ≤ - (280209364285165088069 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2160452974547259 / 5000000000000000 : ℝ)) (q := - (35028114207731197 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35028114207731197 / 80000000000000000 : ℚ)) + (r' := (35028114207731197 / 20000000000000000 : ℚ)) + (U := (-(412937816014834911931 / 500000000000000000000 : ℚ))) + (U' := (280209364285165088069 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (2160452974547259 / 5000000000000000 : ℚ)) + (q := (35028114207731197 / 80000000000000000 : ℚ)) + (U := (-(412937816014834911931 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_9 : Uω (aρ 9) (bρ 9) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4428,25 +3889,21 @@ lemma U_494_9 : have hlg : Real.log (31851297816458373 / 80000000000000000 : ℝ) ≤ (-(920948505196492789883 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31851297816458373 / 80000000000000000 : ℝ) = - (31851297816458373 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31851297816458373 / 20000000000000000 : ℚ)) - (U := (465345855403507210117 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31851297816458373 / 20000000000000000 : ℝ) ≤ - (465345855403507210117 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (483458434954539 / 1250000000000000 : ℝ)) (q := - (31851297816458373 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31851297816458373 / 80000000000000000 : ℚ)) + (r' := (31851297816458373 / 20000000000000000 : ℚ)) + (U := (-(920948505196492789883 / 1000000000000000000000 : ℚ))) + (U' := (465345855403507210117 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (483458434954539 / 1250000000000000 : ℚ)) + (q := (31851297816458373 / 80000000000000000 : ℚ)) + (U := (-(920948505196492789883 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_10 : Uω (aρ 10) (bρ 10) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4454,26 +3911,21 @@ lemma U_494_10 : have hlg : Real.log (27928698770740433 / 80000000000000000 : ℝ) ≤ (-(10523718442281250153947 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27928698770740433 / 80000000000000000 : ℝ) = - (27928698770740433 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27928698770740433 / 20000000000000000 : ℚ)) - (U := (3339225163718749846053 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27928698770740433 / 20000000000000000 : ℝ) ≤ - (3339225163718749846053 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3275576751701827 / 10000000000000000 : ℝ)) (q := - (27928698770740433 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27928698770740433 / 80000000000000000 : ℚ)) + (r' := (27928698770740433 / 20000000000000000 : ℚ)) + (U := (-(10523718442281250153947 / 10000000000000000000000 : ℚ))) + (U' := (3339225163718749846053 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (3275576751701827 / 10000000000000000 : ℚ)) + (q := (27928698770740433 / 80000000000000000 : ℚ)) + (U := (-(10523718442281250153947 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_11 : Uω (aρ 11) (bρ 11) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4481,26 +3933,21 @@ lemma U_494_11 : have hlg : Real.log (4618345461216777 / 16000000000000000 : ℝ) ≤ (-(12425522060461687284879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4618345461216777 / 16000000000000000 : ℝ) = - (4618345461216777 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4618345461216777 / 4000000000000000 : ℚ)) - (U := (1437421545538312715121 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4618345461216777 / 4000000000000000 : ℝ) ≤ - (1437421545538312715121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (248481051174269 / 1000000000000000 : ℝ)) (q := - (4618345461216777 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4618345461216777 / 16000000000000000 : ℚ)) + (r' := (4618345461216777 / 4000000000000000 : ℚ)) + (U := (-(12425522060461687284879 / 10000000000000000000000 : ℚ))) + (U' := (1437421545538312715121 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (248481051174269 / 1000000000000000 : ℚ)) + (q := (4618345461216777 / 16000000000000000 : ℚ)) + (U := (-(12425522060461687284879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_12 : Uω (aρ 12) (bρ 12) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4508,26 +3955,21 @@ lemma U_494_12 : have hlg : Real.log (16457349912420733 / 80000000000000000 : ℝ) ≤ (-(7906272266414078093663 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16457349912420733 / 80000000000000000 : ℝ) = - (16457349912420733 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16457349912420733 / 10000000000000000 : ℚ)) - (U := (2490935438085921906337 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16457349912420733 / 10000000000000000 : ℝ) ≤ - (2490935438085921906337 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (624958130005951 / 5000000000000000 : ℝ)) (q := - (16457349912420733 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16457349912420733 / 80000000000000000 : ℚ)) + (r' := (16457349912420733 / 10000000000000000 : ℚ)) + (U := (-(7906272266414078093663 / 5000000000000000000000 : ℚ))) + (U' := (2490935438085921906337 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34833359663509 / 64000000000000 : ℚ)) + (s := (624958130005951 / 5000000000000000 : ℚ)) + (q := (16457349912420733 / 80000000000000000 : ℚ)) + (U := (-(7906272266414078093663 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_494_13 : Uω (aρ 13) (bρ 13) (34833359663509 / 64000000000000 : ℝ) ≤ @@ -4640,25 +4082,21 @@ lemma U_495_1 : have hlg : Real.log (17230164374104697 / 32000000000000000 : ℝ) ≤ (-(123814862410195933307 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17230164374104697 / 32000000000000000 : ℝ) = - (17230164374104697 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17230164374104697 / 16000000000000000 : ℚ)) - (U := (14814573649804066693 / 200000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (17230164374104697 / 16000000000000000 : ℝ) ≤ - (14814573649804066693 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (538439634181817 / 1000000000000000 : ℝ)) (q := - (17230164374104697 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17230164374104697 / 32000000000000000 : ℚ)) + (r' := (17230164374104697 / 16000000000000000 : ℚ)) + (U := (-(123814862410195933307 / 200000000000000000000 : ℚ))) + (U' := (14814573649804066693 / 200000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (538439634181817 / 1000000000000000 : ℚ)) + (q := (17230164374104697 / 32000000000000000 : ℚ)) + (U := (-(123814862410195933307 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_2 : Uω (aρ 2) (bρ 2) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4666,25 +4104,21 @@ lemma U_495_2 : have hlg : Real.log (17153566282955233 / 32000000000000000 : ℝ) ≤ (-(3117649020088563942417 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17153566282955233 / 32000000000000000 : ℝ) = - (17153566282955233 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17153566282955233 / 16000000000000000 : ℚ)) - (U := (348086881411436057583 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (17153566282955233 / 16000000000000000 : ℝ) ≤ - (348086881411436057583 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1072058309471951 / 2000000000000000 : ℝ)) (q := - (17153566282955233 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17153566282955233 / 32000000000000000 : ℚ)) + (r' := (17153566282955233 / 16000000000000000 : ℚ)) + (U := (-(3117649020088563942417 / 5000000000000000000000 : ℚ))) + (U' := (348086881411436057583 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (1072058309471951 / 2000000000000000 : ℚ)) + (q := (17153566282955233 / 32000000000000000 : ℚ)) + (U := (-(3117649020088563942417 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_3 : Uω (aρ 3) (bρ 3) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4692,25 +4126,21 @@ lemma U_495_3 : have hlg : Real.log (85001519930734413 / 160000000000000000 : ℝ) ≤ (-(6325046771053860354781 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85001519930734413 / 160000000000000000 : ℝ) = - (85001519930734413 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85001519930734413 / 80000000000000000 : ℚ)) - (U := (606425031946139645219 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85001519930734413 / 80000000000000000 : ℝ) ≤ - (606425031946139645219 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (663987339775567 / 1250000000000000 : ℝ)) (q := - (85001519930734413 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85001519930734413 / 160000000000000000 : ℚ)) + (r' := (85001519930734413 / 80000000000000000 : ℚ)) + (U := (-(6325046771053860354781 / 10000000000000000000000 : ℚ))) + (U' := (606425031946139645219 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (663987339775567 / 1250000000000000 : ℚ)) + (q := (85001519930734413 / 160000000000000000 : ℚ)) + (U := (-(6325046771053860354781 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_4 : Uω (aρ 4) (bρ 4) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4718,25 +4148,21 @@ lemma U_495_4 : have hlg : Real.log (83727786666321213 / 160000000000000000 : ℝ) ≤ (-(1619007283210977189607 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83727786666321213 / 160000000000000000 : ℝ) = - (83727786666321213 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83727786666321213 / 80000000000000000 : ℚ)) - (U := (113860667539022810393 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83727786666321213 / 80000000000000000 : ℝ) ≤ - (113860667539022810393 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2615488120608943 / 5000000000000000 : ℝ)) (q := - (83727786666321213 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83727786666321213 / 160000000000000000 : ℚ)) + (r' := (83727786666321213 / 80000000000000000 : ℚ)) + (U := (-(1619007283210977189607 / 2500000000000000000000 : ℚ))) + (U' := (113860667539022810393 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (2615488120608943 / 5000000000000000 : ℚ)) + (q := (83727786666321213 / 160000000000000000 : ℚ)) + (U := (-(1619007283210977189607 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_5 : Uω (aρ 5) (bρ 5) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4744,25 +4170,21 @@ lemma U_495_5 : have hlg : Real.log (81785564105388597 / 160000000000000000 : ℝ) ≤ (-(6710730648684770959207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (81785564105388597 / 160000000000000000 : ℝ) = - (81785564105388597 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (81785564105388597 / 80000000000000000 : ℚ)) - (U := (220741154315229040793 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (81785564105388597 / 80000000000000000 : ℝ) ≤ - (220741154315229040793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5106388340436309 / 10000000000000000 : ℝ)) (q := - (81785564105388597 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (81785564105388597 / 160000000000000000 : ℚ)) + (r' := (81785564105388597 / 80000000000000000 : ℚ)) + (U := (-(6710730648684770959207 / 10000000000000000000000 : ℚ))) + (U' := (220741154315229040793 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (5106388340436309 / 10000000000000000 : ℚ)) + (q := (81785564105388597 / 160000000000000000 : ℚ)) + (U := (-(6710730648684770959207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_6 : Uω (aρ 6) (bρ 6) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4770,25 +4192,21 @@ lemma U_495_6 : have hlg : Real.log (78994213072824829 / 160000000000000000 : ℝ) ≤ (-(1764498042931787618447 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (78994213072824829 / 160000000000000000 : ℝ) = - (78994213072824829 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78994213072824829 / 40000000000000000 : ℚ)) - (U := (1701237858568212381553 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (78994213072824829 / 40000000000000000 : ℝ) ≤ - (1701237858568212381553 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2462354918252919 / 5000000000000000 : ℝ)) (q := - (78994213072824829 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78994213072824829 / 160000000000000000 : ℚ)) + (r' := (78994213072824829 / 40000000000000000 : ℚ)) + (U := (-(1764498042931787618447 / 2500000000000000000000 : ℚ))) + (U' := (1701237858568212381553 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (2462354918252919 / 5000000000000000 : ℚ)) + (q := (78994213072824829 / 160000000000000000 : ℚ)) + (U := (-(1764498042931787618447 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_7 : Uω (aρ 7) (bρ 7) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4796,25 +4214,21 @@ lemma U_495_7 : have hlg : Real.log (75172879644487933 / 160000000000000000 : ℝ) ≤ (-(1888458229577260486051 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (75172879644487933 / 160000000000000000 : ℝ) = - (75172879644487933 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (75172879644487933 / 40000000000000000 : ℚ)) - (U := (1577277671922739513949 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (75172879644487933 / 40000000000000000 : ℝ) ≤ - (1577277671922739513949 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2335352269361863 / 5000000000000000 : ℝ)) (q := - (75172879644487933 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (75172879644487933 / 160000000000000000 : ℚ)) + (r' := (75172879644487933 / 40000000000000000 : ℚ)) + (U := (-(1888458229577260486051 / 2500000000000000000000 : ℚ))) + (U' := (1577277671922739513949 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (2335352269361863 / 5000000000000000 : ℚ)) + (q := (75172879644487933 / 160000000000000000 : ℚ)) + (U := (-(1888458229577260486051 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_8 : Uω (aρ 8) (bρ 8) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4822,25 +4236,21 @@ lemma U_495_8 : have hlg : Real.log (70157416433532973 / 160000000000000000 : ℝ) ≤ (-(4122161456257221488253 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70157416433532973 / 160000000000000000 : ℝ) = - (70157416433532973 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70157416433532973 / 40000000000000000 : ℚ)) - (U := (2809310346742778511747 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70157416433532973 / 40000000000000000 : ℝ) ≤ - (2809310346742778511747 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1081828322173589 / 2500000000000000 : ℝ)) (q := - (70157416433532973 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70157416433532973 / 160000000000000000 : ℚ)) + (r' := (70157416433532973 / 40000000000000000 : ℚ)) + (U := (-(4122161456257221488253 / 5000000000000000000000 : ℚ))) + (U' := (2809310346742778511747 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (1081828322173589 / 2500000000000000 : ℚ)) + (q := (70157416433532973 / 160000000000000000 : ℚ)) + (U := (-(4122161456257221488253 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_9 : Uω (aρ 9) (bρ 9) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4848,25 +4258,21 @@ lemma U_495_9 : have hlg : Real.log (63805386120366957 / 160000000000000000 : ℝ) ≤ (-(9193362059771989769797 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63805386120366957 / 160000000000000000 : ℝ) = - (63805386120366957 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63805386120366957 / 40000000000000000 : ℚ)) - (U := (4669581546228010230203 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63805386120366957 / 40000000000000000 : ℝ) ≤ - (4669581546228010230203 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (968568781977151 / 2500000000000000 : ℝ)) (q := - (63805386120366957 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63805386120366957 / 160000000000000000 : ℚ)) + (r' := (63805386120366957 / 40000000000000000 : ℚ)) + (U := (-(9193362059771989769797 / 10000000000000000000000 : ℚ))) + (U' := (4669581546228010230203 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (968568781977151 / 2500000000000000 : ℚ)) + (q := (63805386120366957 / 160000000000000000 : ℚ)) + (U := (-(9193362059771989769797 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_10 : Uω (aρ 10) (bρ 10) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4874,26 +4280,21 @@ lemma U_495_10 : have hlg : Real.log (55963812845365133 / 160000000000000000 : ℝ) ≤ (-(5252342660226903689753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55963812845365133 / 160000000000000000 : ℝ) = - (55963812845365133 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55963812845365133 / 40000000000000000 : ℚ)) - (U := (1679129142773096310247 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55963812845365133 / 40000000000000000 : ℝ) ≤ - (1679129142773096310247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410329687753547 / 1250000000000000 : ℝ)) (q := - (55963812845365133 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55963812845365133 / 160000000000000000 : ℚ)) + (r' := (55963812845365133 / 40000000000000000 : ℚ)) + (U := (-(5252342660226903689753 / 5000000000000000000000 : ℚ))) + (U' := (1679129142773096310247 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (410329687753547 / 1250000000000000 : ℚ)) + (q := (55963812845365133 / 160000000000000000 : ℚ)) + (U := (-(5252342660226903689753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_11 : Uω (aρ 11) (bρ 11) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4901,26 +4302,21 @@ lemma U_495_11 : have hlg : Real.log (46299407845621909 / 160000000000000000 : ℝ) ≤ (-(2480089286429880528157 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46299407845621909 / 160000000000000000 : ℝ) = - (46299407845621909 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46299407845621909 / 40000000000000000 : ℚ)) - (U := (292499434770119471843 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46299407845621909 / 40000000000000000 : ℝ) ≤ - (292499434770119471843 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2493063503265473 / 10000000000000000 : ℝ)) (q := - (46299407845621909 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46299407845621909 / 160000000000000000 : ℚ)) + (r' := (46299407845621909 / 40000000000000000 : ℚ)) + (U := (-(2480089286429880528157 / 2000000000000000000000 : ℚ))) + (U' := (292499434770119471843 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (2493063503265473 / 10000000000000000 : ℚ)) + (q := (46299407845621909 / 160000000000000000 : ℚ)) + (U := (-(2480089286429880528157 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_12 : Uω (aρ 12) (bρ 12) (69746606209053 / 128000000000000 : ℝ) ≤ @@ -4928,26 +4324,21 @@ lemma U_495_12 : have hlg : Real.log (33078527600011461 / 160000000000000000 : ℝ) ≤ (-(3152578911133758865109 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33078527600011461 / 160000000000000000 : ℝ) = - (33078527600011461 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33078527600011461 / 20000000000000000 : ℚ)) - (U := (1006304170666241134891 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (33078527600011461 / 20000000000000000 : ℝ) ≤ - (1006304170666241134891 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1264153569249167 / 10000000000000000 : ℝ)) (q := - (33078527600011461 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33078527600011461 / 160000000000000000 : ℚ)) + (r' := (33078527600011461 / 20000000000000000 : ℚ)) + (U := (-(3152578911133758865109 / 2000000000000000000000 : ℚ))) + (U' := (1006304170666241134891 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69746606209053 / 128000000000000 : ℚ)) + (s := (1264153569249167 / 10000000000000000 : ℚ)) + (q := (33078527600011461 / 160000000000000000 : ℚ)) + (U := (-(3152578911133758865109 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_495_13 : Uω (aρ 13) (bρ 13) (69746606209053 / 128000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U41.lean b/LeanPool/Zeta5Irrational/Table/U41.lean index b9038d79e2..af2023f004 100644 --- a/LeanPool/Zeta5Irrational/Table/U41.lean +++ b/LeanPool/Zeta5Irrational/Table/U41.lean @@ -24,25 +24,21 @@ lemma U_496_1 : have hlg : Real.log (10781335128658193 / 20000000000000000 : ℝ) ≤ (-(6179158631021010828439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10781335128658193 / 20000000000000000 : ℝ) = - (10781335128658193 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10781335128658193 / 10000000000000000 : ℚ)) - (U := (752313171978989171561 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10781335128658193 / 10000000000000000 : ℝ) ≤ - (752313171978989171561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5390637574001943 / 10000000000000000 : ℝ)) (q := - (10781335128658193 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10781335128658193 / 20000000000000000 : ℚ)) + (r' := (10781335128658193 / 10000000000000000 : ℚ)) + (U := (-(6179158631021010828439 / 10000000000000000000000 : ℚ))) + (U' := (752313171978989171561 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (5390637574001943 / 10000000000000000 : ℚ)) + (q := (10781335128658193 / 20000000000000000 : ℚ)) + (U := (-(6179158631021010828439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_2 : Uω (aρ 2) (bρ 2) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_496_2 : have hlg : Real.log (536673085625463 / 1000000000000000 : ℝ) ≤ (-(6223661486905342670339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (536673085625463 / 1000000000000000 : ℝ) = - (536673085625463 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (536673085625463 / 500000000000000 : ℚ)) - (U := (707810316094657329661 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (536673085625463 / 500000000000000 : ℝ) ≤ - (707810316094657329661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (536653317036301 / 1000000000000000 : ℝ)) (q := - (536673085625463 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (536673085625463 / 1000000000000000 : ℚ)) + (r' := (536673085625463 / 500000000000000 : ℚ)) + (U := (-(6223661486905342670339 / 10000000000000000000000 : ℚ))) + (U' := (707810316094657329661 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (536653317036301 / 1000000000000000 : ℚ)) + (q := (536673085625463 / 1000000000000000 : ℚ)) + (U := (-(6223661486905342670339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_3 : Uω (aρ 3) (bρ 3) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_496_3 : have hlg : Real.log (10637673950907967 / 20000000000000000 : ℝ) ≤ (-(1578326067291152192927 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10637673950907967 / 20000000000000000 : ℝ) = - (10637673950907967 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10637673950907967 / 10000000000000000 : ℚ)) - (U := (154541883458847807073 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10637673950907967 / 10000000000000000 : ℝ) ≤ - (154541883458847807073 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5318141515111717 / 10000000000000000 : ℝ)) (q := - (10637673950907967 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10637673950907967 / 20000000000000000 : ℚ)) + (r' := (10637673950907967 / 10000000000000000 : ℚ)) + (U := (-(1578326067291152192927 / 2500000000000000000000 : ℚ))) + (U' := (154541883458847807073 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (5318141515111717 / 10000000000000000 : ℚ)) + (q := (10637673950907967 / 20000000000000000 : ℚ)) + (U := (-(1578326067291152192927 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_4 : Uω (aρ 4) (bρ 4) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_496_4 : have hlg : Real.log (10478460450231381 / 20000000000000000 : ℝ) ≤ (-(6464105087964167300301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10478460450231381 / 20000000000000000 : ℝ) = - (10478460450231381 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10478460450231381 / 10000000000000000 : ℚ)) - (U := (467366715035832699699 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10478460450231381 / 10000000000000000 : ℝ) ≤ - (467366715035832699699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5237222195500131 / 10000000000000000 : ℝ)) (q := - (10478460450231381 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10478460450231381 / 20000000000000000 : ℚ)) + (r' := (10478460450231381 / 10000000000000000 : ℚ)) + (U := (-(6464105087964167300301 / 10000000000000000000000 : ℚ))) + (U' := (467366715035832699699 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (5237222195500131 / 10000000000000000 : ℚ)) + (q := (10478460450231381 / 20000000000000000 : ℚ)) + (U := (-(6464105087964167300301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_5 : Uω (aρ 5) (bρ 5) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_496_5 : have hlg : Real.log (10235690557102619 / 20000000000000000 : ℝ) ≤ (-(6698515862953343862829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10235690557102619 / 20000000000000000 : ℝ) = - (10235690557102619 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10235690557102619 / 10000000000000000 : ℚ)) - (U := (232955940046656137171 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10235690557102619 / 10000000000000000 : ℝ) ≤ - (232955940046656137171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5112642221706369 / 10000000000000000 : ℝ)) (q := - (10235690557102619 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10235690557102619 / 20000000000000000 : ℚ)) + (r' := (10235690557102619 / 10000000000000000 : ℚ)) + (U := (-(6698515862953343862829 / 10000000000000000000000 : ℚ))) + (U' := (232955940046656137171 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (5112642221706369 / 10000000000000000 : ℚ)) + (q := (10235690557102619 / 20000000000000000 : ℚ)) + (U := (-(6698515862953343862829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_6 : Uω (aρ 6) (bρ 6) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_496_6 : have hlg : Real.log (9886790421068631 / 20000000000000000 : ℝ) ≤ (-(7045327077678014554961 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9886790421068631 / 20000000000000000 : ℝ) = - (9886790421068631 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9886790421068631 / 5000000000000000 : ℚ)) - (U := (6817616528321985445039 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9886790421068631 / 5000000000000000 : ℝ) ≤ - (6817616528321985445039 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4930982460812381 / 10000000000000000 : ℝ)) (q := - (9886790421068631 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9886790421068631 / 20000000000000000 : ℚ)) + (r' := (9886790421068631 / 5000000000000000 : ℚ)) + (U := (-(7045327077678014554961 / 10000000000000000000000 : ℚ))) + (U' := (6817616528321985445039 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (4930982460812381 / 10000000000000000 : ℚ)) + (q := (9886790421068631 / 20000000000000000 : ℚ)) + (U := (-(7045327077678014554961 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_7 : Uω (aρ 7) (bρ 7) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_496_7 : have hlg : Real.log (9409165943257819 / 20000000000000000 : ℝ) ≤ (-(1508095917026171862497 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9409165943257819 / 20000000000000000 : ℝ) = - (9409165943257819 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9409165943257819 / 5000000000000000 : ℚ)) - (U := (1264492804173828137503 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9409165943257819 / 5000000000000000 : ℝ) ≤ - (1264492804173828137503 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4677019363761569 / 10000000000000000 : ℝ)) (q := - (9409165943257819 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9409165943257819 / 20000000000000000 : ℚ)) + (r' := (9409165943257819 / 5000000000000000 : ℚ)) + (U := (-(1508095917026171862497 / 2000000000000000000000 : ℚ))) + (U' := (1264492804173828137503 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (4677019363761569 / 10000000000000000 : ℚ)) + (q := (9409165943257819 / 20000000000000000 : ℚ)) + (U := (-(1508095917026171862497 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_8 : Uω (aρ 8) (bρ 8) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_496_8 : have hlg : Real.log (8782325071442361 / 20000000000000000 : ℝ) ≤ (-(514369428705734080287 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8782325071442361 / 20000000000000000 : ℝ) = - (8782325071442361 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8782325071442361 / 5000000000000000 : ℚ)) - (U := (352064546669265919713 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8782325071442361 / 5000000000000000 : ℝ) ≤ - (352064546669265919713 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4333720143286111 / 10000000000000000 : ℝ)) (q := - (8782325071442361 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8782325071442361 / 20000000000000000 : ℚ)) + (r' := (8782325071442361 / 5000000000000000 : ℚ)) + (U := (-(514369428705734080287 / 625000000000000000000 : ℚ))) + (U' := (352064546669265919713 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (4333720143286111 / 10000000000000000 : ℚ)) + (q := (8782325071442361 / 20000000000000000 : ℚ)) + (U := (-(514369428705734080287 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_9 : Uω (aρ 9) (bρ 9) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -232,24 +200,21 @@ lemma U_496_9 : have hlg : Real.log (63908166900943 / 160000000000000 : ℝ) ≤ (-(9177266539706387383039 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63908166900943 / 160000000000000 : ℝ) = (63908166900943 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63908166900943 / 40000000000000 : ℚ)) - (U := (4685677066293612616961 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63908166900943 / 40000000000000 : ℝ) ≤ - (4685677066293612616961 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (31047052502573 / 80000000000000 : ℝ)) (q := - (63908166900943 / 160000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63908166900943 / 160000000000000 : ℚ)) + (r' := (63908166900943 / 40000000000000 : ℚ)) + (U := (-(9177266539706387383039 / 10000000000000000000000 : ℚ))) + (U' := (4685677066293612616961 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (31047052502573 / 80000000000000 : ℚ)) + (q := (63908166900943 / 160000000000000 : ℚ)) + (U := (-(9177266539706387383039 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_10 : Uω (aρ 10) (bρ 10) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -257,26 +222,21 @@ lemma U_496_10 : have hlg : Real.log (7008775204647261 / 20000000000000000 : ℝ) ≤ (-(10485693084161377691493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7008775204647261 / 20000000000000000 : ℝ) = - (7008775204647261 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7008775204647261 / 5000000000000000 : ℚ)) - (U := (3377250521838622308507 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7008775204647261 / 5000000000000000 : ℝ) ≤ - (3377250521838622308507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3289694938346011 / 10000000000000000 : ℝ)) (q := - (7008775204647261 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7008775204647261 / 20000000000000000 : ℚ)) + (r' := (7008775204647261 / 5000000000000000 : ℚ)) + (U := (-(10485693084161377691493 / 10000000000000000000000 : ℚ))) + (U' := (3377250521838622308507 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (3289694938346011 / 10000000000000000 : ℚ)) + (q := (7008775204647261 / 20000000000000000 : ℚ)) + (U := (-(10485693084161377691493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_11 : Uω (aρ 11) (bρ 11) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -284,26 +244,21 @@ lemma U_496_11 : have hlg : Real.log (5801908477093199 / 20000000000000000 : ℝ) ≤ (-(193366462786153684599 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5801908477093199 / 20000000000000000 : ℝ) = - (5801908477093199 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5801908477093199 / 5000000000000000 : ℚ)) - (U := (23242031057596315401 / 156250000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5801908477093199 / 5000000000000000 : ℝ) ≤ - (23242031057596315401 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2501304836996949 / 10000000000000000 : ℝ)) (q := - (5801908477093199 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5801908477093199 / 20000000000000000 : ℚ)) + (r' := (5801908477093199 / 5000000000000000 : ℚ)) + (U := (-(193366462786153684599 / 156250000000000000000 : ℚ))) + (U' := (23242031057596315401 / 156250000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (2501304836996949 / 10000000000000000 : ℚ)) + (q := (5801908477093199 / 20000000000000000 : ℚ)) + (U := (-(193366462786153684599 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_12 : Uω (aρ 12) (bρ 12) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -311,25 +266,21 @@ lemma U_496_12 : have hlg : Real.log (415516632565571 / 2000000000000000 : ℝ) ≤ (-(1964224768782355217967 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (415516632565571 / 2000000000000000 : ℝ) = - (415516632565571 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (415516632565571 / 250000000000000 : ℚ)) - (U := (635077157342644782033 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (415516632565571 / 250000000000000 : ℝ) ≤ - (635077157342644782033 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63913139112223 / 500000000000000 : ℝ)) (q := - (415516632565571 / 2000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (415516632565571 / 2000000000000000 : ℚ)) + (r' := (415516632565571 / 250000000000000 : ℚ)) + (U := (-(1964224768782355217967 / 1250000000000000000000 : ℚ))) + (U' := (635077157342644782033 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4364155818193 / 8000000000000 : ℚ)) + (s := (63913139112223 / 500000000000000 : ℚ)) + (q := (415516632565571 / 2000000000000000 : ℚ)) + (U := (-(1964224768782355217967 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_496_13 : Uω (aρ 13) (bρ 13) (4364155818193 / 8000000000000 : ℝ) ≤ @@ -441,25 +392,21 @@ lemma U_497_1 : have hlg : Real.log (86350540186721179 / 160000000000000000 : ℝ) ≤ (-(6167587546193927183517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (86350540186721179 / 160000000000000000 : ℝ) = - (86350540186721179 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86350540186721179 / 80000000000000000 : ℚ)) - (U := (763884256806072816483 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (86350540186721179 / 80000000000000000 : ℝ) ≤ - (763884256806072816483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5396878806024913 / 10000000000000000 : ℝ)) (q := - (86350540186721179 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86350540186721179 / 160000000000000000 : ℚ)) + (r' := (86350540186721179 / 80000000000000000 : ℚ)) + (U := (-(6167587546193927183517 / 10000000000000000000000 : ℚ))) + (U' := (763884256806072816483 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (5396878806024913 / 10000000000000000 : ℚ)) + (q := (86350540186721179 / 160000000000000000 : ℚ)) + (U := (-(6167587546193927183517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_2 : Uω (aρ 2) (bρ 2) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -467,25 +414,21 @@ lemma U_497_2 : have hlg : Real.log (85967555976815707 / 160000000000000000 : ℝ) ≤ (-(6212038459828908181177 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85967555976815707 / 160000000000000000 : ℝ) = - (85967555976815707 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85967555976815707 / 80000000000000000 : ℚ)) - (U := (719433343171091818823 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85967555976815707 / 80000000000000000 : ℝ) ≤ - (719433343171091818823 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5372774792296729 / 10000000000000000 : ℝ)) (q := - (85967555976815707 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85967555976815707 / 160000000000000000 : ℚ)) + (r' := (85967555976815707 / 80000000000000000 : ℚ)) + (U := (-(6212038459828908181177 / 10000000000000000000000 : ℚ))) + (U' := (719433343171091818823 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (5372774792296729 / 10000000000000000 : ℚ)) + (q := (85967555976815707 / 160000000000000000 : ℚ)) + (U := (-(6212038459828908181177 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_3 : Uω (aρ 3) (bρ 3) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -493,25 +436,21 @@ lemma U_497_3 : have hlg : Real.log (17040252650627759 / 32000000000000000 : ℝ) ≤ (-(6153882366540572167 / 9765625000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17040252650627759 / 32000000000000000 : ℝ) = - (17040252650627759 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17040252650627759 / 16000000000000000 : ℚ)) - (U := (615133066076615333 / 9765625000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (17040252650627759 / 16000000000000000 : ℝ) ≤ - (615133066076615333 / 9765625000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1064876861637423 / 2000000000000000 : ℝ)) (q := - (17040252650627759 / 32000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17040252650627759 / 32000000000000000 : ℚ)) + (r' := (17040252650627759 / 16000000000000000 : ℚ)) + (U := (-(6153882366540572167 / 9765625000000000000 : ℚ))) + (U' := (615133066076615333 / 9765625000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (1064876861637423 / 2000000000000000 : ℚ)) + (q := (17040252650627759 / 32000000000000000 : ℚ)) + (U := (-(6153882366540572167 / 9765625000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_4 : Uω (aρ 4) (bρ 4) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -519,25 +458,21 @@ lemma U_497_4 : have hlg : Real.log (83927580446092347 / 160000000000000000 : ℝ) ≤ (-(6452195255314039757353 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83927580446092347 / 160000000000000000 : ℝ) = - (83927580446092347 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83927580446092347 / 80000000000000000 : ℚ)) - (U := (479276547685960242647 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (83927580446092347 / 80000000000000000 : ℝ) ≤ - (479276547685960242647 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5243468138371309 / 10000000000000000 : ℝ)) (q := - (83927580446092347 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83927580446092347 / 160000000000000000 : ℚ)) + (r' := (83927580446092347 / 80000000000000000 : ℚ)) + (U := (-(6452195255314039757353 / 10000000000000000000000 : ℚ))) + (U' := (479276547685960242647 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (5243468138371309 / 10000000000000000 : ℚ)) + (q := (83927580446092347 / 160000000000000000 : ℚ)) + (U := (-(6452195255314039757353 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_5 : Uω (aρ 5) (bρ 5) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -545,25 +480,21 @@ lemma U_497_5 : have hlg : Real.log (81985484559887883 / 160000000000000000 : ℝ) ≤ (-(668631600941429284913 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (81985484559887883 / 160000000000000000 : ℝ) = - (81985484559887883 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (81985484559887883 / 80000000000000000 : ℚ)) - (U := (24515579358570715087 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (81985484559887883 / 80000000000000000 : ℝ) ≤ - (24515579358570715087 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5118896071930751 / 10000000000000000 : ℝ)) (q := - (81985484559887883 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (81985484559887883 / 160000000000000000 : ℚ)) + (r' := (81985484559887883 / 80000000000000000 : ℚ)) + (U := (-(668631600941429284913 / 1000000000000000000000 : ℚ))) + (U' := (24515579358570715087 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (5118896071930751 / 10000000000000000 : ℚ)) + (q := (81985484559887883 / 160000000000000000 : ℚ)) + (U := (-(668631600941429284913 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_6 : Uω (aρ 6) (bρ 6) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -571,25 +502,21 @@ lemma U_497_6 : have hlg : Real.log (79194433026340883 / 160000000000000000 : ℝ) ≤ (-(6867849691752660767 / 9765625000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (79194433026340883 / 160000000000000000 : ℝ) = - (79194433026340883 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (79194433026340883 / 40000000000000000 : ℚ)) - (U := (6670181173481714233 / 9765625000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (79194433026340883 / 40000000000000000 : ℝ) ≤ - (6670181173481714233 / 9765625000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154289218918043 / 312500000000000 : ℝ)) (q := - (79194433026340883 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (79194433026340883 / 160000000000000000 : ℚ)) + (r' := (79194433026340883 / 40000000000000000 : ℚ)) + (U := (-(6867849691752660767 / 9765625000000000000 : ℚ))) + (U' := (6670181173481714233 / 9765625000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (154289218918043 / 312500000000000 : ℚ)) + (q := (79194433026340883 / 160000000000000000 : ℚ)) + (U := (-(6867849691752660767 / 9765625000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_7 : Uω (aρ 7) (bρ 7) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -597,25 +524,21 @@ lemma U_497_7 : have hlg : Real.log (75373773867730363 / 160000000000000000 : ℝ) ≤ (-(7527144268936852965187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (75373773867730363 / 160000000000000000 : ℝ) = - (75373773867730363 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (75373773867730363 / 40000000000000000 : ℚ)) - (U := (6335799337063147034813 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (75373773867730363 / 40000000000000000 : ℝ) ≤ - (6335799337063147034813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4683333991311061 / 10000000000000000 : ℝ)) (q := - (75373773867730363 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (75373773867730363 / 160000000000000000 : ℚ)) + (r' := (75373773867730363 / 40000000000000000 : ℚ)) + (U := (-(7527144268936852965187 / 10000000000000000000000 : ℚ))) + (U' := (6335799337063147034813 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (4683333991311061 / 10000000000000000 : ℚ)) + (q := (75373773867730363 / 160000000000000000 : ℚ)) + (U := (-(7527144268936852965187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_8 : Uω (aρ 8) (bρ 8) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -623,25 +546,21 @@ lemma U_497_8 : have hlg : Real.log (70359780846663291 / 160000000000000000 : ℝ) ≤ (-(513470005995439371749 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70359780846663291 / 160000000000000000 : ℝ) = - (70359780846663291 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70359780846663291 / 40000000000000000 : ℚ)) - (U := (352963969379560628251 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70359780846663291 / 40000000000000000 : ℝ) ≤ - (352963969379560628251 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4340126515017677 / 10000000000000000 : ℝ)) (q := - (70359780846663291 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70359780846663291 / 160000000000000000 : ℚ)) + (r' := (70359780846663291 / 40000000000000000 : ℚ)) + (U := (-(513470005995439371749 / 625000000000000000000 : ℚ))) + (U' := (352963969379560628251 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (4340126515017677 / 10000000000000000 : ℚ)) + (q := (70359780846663291 / 160000000000000000 : ℚ)) + (U := (-(513470005995439371749 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_9 : Uω (aρ 9) (bρ 9) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -649,25 +568,21 @@ lemma U_497_9 : have hlg : Real.log (64010938024132779 / 160000000000000000 : ℝ) ≤ (-(366447935732025427061 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (64010938024132779 / 160000000000000000 : ℝ) = - (64010938024132779 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64010938024132779 / 40000000000000000 : ℚ)) - (U := (188069808507974572939 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64010938024132779 / 40000000000000000 : ℝ) ≤ - (188069808507974572939 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3887486790561363 / 10000000000000000 : ℝ)) (q := - (64010938024132779 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64010938024132779 / 160000000000000000 : ℚ)) + (r' := (64010938024132779 / 40000000000000000 : ℚ)) + (U := (-(366447935732025427061 / 400000000000000000000 : ℚ))) + (U' := (188069808507974572939 / 400000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (3887486790561363 / 10000000000000000 : ℚ)) + (q := (64010938024132779 / 160000000000000000 : ℚ)) + (U := (-(366447935732025427061 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_10 : Uω (aρ 10) (bρ 10) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -675,26 +590,21 @@ lemma U_497_10 : have hlg : Real.log (56176564087184987 / 160000000000000000 : ℝ) ≤ (-(1308342692389497524921 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56176564087184987 / 160000000000000000 : ℝ) = - (56176564087184987 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56176564087184987 / 40000000000000000 : ℚ)) - (U := (424525258360502475079 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56176564087184987 / 40000000000000000 : ℝ) ≤ - (424525258360502475079 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3296749081937889 / 10000000000000000 : ℝ)) (q := - (56176564087184987 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56176564087184987 / 160000000000000000 : ℚ)) + (r' := (56176564087184987 / 40000000000000000 : ℚ)) + (U := (-(1308342692389497524921 / 1250000000000000000000 : ℚ))) + (U' := (424525258360502475079 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (3296749081937889 / 10000000000000000 : ℚ)) + (q := (56176564087184987 / 160000000000000000 : ℚ)) + (U := (-(1308342692389497524921 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_11 : Uω (aρ 11) (bρ 11) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -702,26 +612,21 @@ lemma U_497_11 : have hlg : Real.log (46531035444361763 / 160000000000000000 : ℝ) ≤ (-(3087635739603101573631 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46531035444361763 / 160000000000000000 : ℝ) = - (46531035444361763 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46531035444361763 / 40000000000000000 : ℚ)) - (U := (378100161896898426369 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46531035444361763 / 40000000000000000 : ℝ) ≤ - (378100161896898426369 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1254767313894993 / 5000000000000000 : ℝ)) (q := - (46531035444361763 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46531035444361763 / 160000000000000000 : ℚ)) + (r' := (46531035444361763 / 40000000000000000 : ℚ)) + (U := (-(3087635739603101573631 / 2500000000000000000000 : ℚ))) + (U' := (378100161896898426369 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (1254767313894993 / 5000000000000000 : ℚ)) + (q := (46531035444361763 / 160000000000000000 : ℚ)) + (U := (-(3087635739603101573631 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_12 : Uω (aρ 12) (bρ 12) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -729,26 +634,21 @@ lemma U_497_12 : have hlg : Real.log (33403142406979611 / 160000000000000000 : ℝ) ≤ (-(3133047669711312742019 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (33403142406979611 / 160000000000000000 : ℝ) = - (33403142406979611 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33403142406979611 / 20000000000000000 : ℚ)) - (U := (1025835412088687257981 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33403142406979611 / 20000000000000000 : ℝ) ≤ - (1025835412088687257981 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1292248094802217 / 10000000000000000 : ℝ)) (q := - (33403142406979611 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33403142406979611 / 160000000000000000 : ℚ)) + (r' := (33403142406979611 / 20000000000000000 : ℚ)) + (U := (-(3133047669711312742019 / 2000000000000000000000 : ℚ))) + (U' := (1025835412088687257981 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (69906379973123 / 128000000000000 : ℚ)) + (s := (1292248094802217 / 10000000000000000 : ℚ)) + (q := (33403142406979611 / 160000000000000000 : ℚ)) + (U := (-(3133047669711312742019 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_497_13 : Uω (aρ 13) (bρ 13) (69906379973123 / 128000000000000 : ℝ) ≤ @@ -859,25 +759,21 @@ lemma U_498_1 : have hlg : Real.log (43225199671447423 / 80000000000000000 : ℝ) ≤ (-(6156029835042409091741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43225199671447423 / 80000000000000000 : ℝ) = - (43225199671447423 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43225199671447423 / 40000000000000000 : ℚ)) - (U := (775441967957590908259 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43225199671447423 / 40000000000000000 : ℝ) ≤ - (775441967957590908259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5403120037887637 / 10000000000000000 : ℝ)) (q := - (43225199671447423 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43225199671447423 / 80000000000000000 : ℚ)) + (r' := (43225199671447423 / 40000000000000000 : ℚ)) + (U := (-(6156029835042409091741 / 10000000000000000000000 : ℚ))) + (U' := (775441967957590908259 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (5403120037887637 / 10000000000000000 : ℚ)) + (q := (43225199671447423 / 80000000000000000 : ℚ)) + (U := (-(6156029835042409091741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_2 : Uω (aρ 2) (bρ 2) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -885,25 +781,21 @@ lemma U_498_2 : have hlg : Real.log (8606741824503083 / 16000000000000000 : ℝ) ≤ (-(1550107231884159405343 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8606741824503083 / 16000000000000000 : ℝ) = - (8606741824503083 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8606741824503083 / 8000000000000000 : ℚ)) - (U := (182760718865840594657 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8606741824503083 / 8000000000000000 : ℝ) ≤ - (182760718865840594657 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1075803282632927 / 2000000000000000 : ℝ)) (q := - (8606741824503083 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8606741824503083 / 16000000000000000 : ℚ)) + (r' := (8606741824503083 / 8000000000000000 : ℚ)) + (U := (-(1550107231884159405343 / 2500000000000000000000 : ℚ))) + (U' := (182760718865840594657 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (1075803282632927 / 2000000000000000 : ℚ)) + (q := (8606741824503083 / 16000000000000000 : ℚ)) + (U := (-(1550107231884159405343 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_3 : Uω (aρ 3) (bρ 3) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -911,25 +803,21 @@ lemma U_498_3 : have hlg : Real.log (42650567434233643 / 80000000000000000 : ℝ) ≤ (-(1257972112255709486683 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42650567434233643 / 80000000000000000 : ℝ) = - (42650567434233643 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42650567434233643 / 40000000000000000 : ℚ)) - (U := (128322248344290513317 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42650567434233643 / 40000000000000000 : ℝ) ≤ - (128322248344290513317 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (166582096795131 / 312500000000000 : ℝ)) (q := - (42650567434233643 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42650567434233643 / 80000000000000000 : ℚ)) + (r' := (42650567434233643 / 40000000000000000 : ℚ)) + (U := (-(1257972112255709486683 / 2000000000000000000000 : ℚ))) + (U' := (128322248344290513317 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (166582096795131 / 312500000000000 : ℚ)) + (q := (42650567434233643 / 80000000000000000 : ℚ)) + (U := (-(1257972112255709486683 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_4 : Uω (aρ 4) (bρ 4) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -937,25 +825,21 @@ lemma U_498_4 : have hlg : Real.log (42013738599685479 / 80000000000000000 : ℝ) ≤ (-(6440299601029007882821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42013738599685479 / 80000000000000000 : ℝ) = - (42013738599685479 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42013738599685479 / 40000000000000000 : ℚ)) - (U := (491172201970992117179 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42013738599685479 / 40000000000000000 : ℝ) ≤ - (491172201970992117179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5249714069872151 / 10000000000000000 : ℝ)) (q := - (42013738599685479 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42013738599685479 / 80000000000000000 : ℚ)) + (r' := (42013738599685479 / 40000000000000000 : ℚ)) + (U := (-(6440299601029007882821 / 10000000000000000000000 : ℚ))) + (U' := (491172201970992117179 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (5249714069872151 / 10000000000000000 : ℚ)) + (q := (42013738599685479 / 80000000000000000 : ℚ)) + (U := (-(6440299601029007882821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_5 : Uω (aρ 5) (bρ 5) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -963,25 +847,21 @@ lemma U_498_5 : have hlg : Real.log (41042722207749283 / 80000000000000000 : ℝ) ≤ (-(6674131051530196510577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41042722207749283 / 80000000000000000 : ℝ) = - (41042722207749283 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41042722207749283 / 40000000000000000 : ℚ)) - (U := (257340751469803489423 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41042722207749283 / 40000000000000000 : ℝ) ≤ - (257340751469803489423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2562574945611551 / 5000000000000000 : ℝ)) (q := - (41042722207749283 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41042722207749283 / 80000000000000000 : ℚ)) + (r' := (41042722207749283 / 40000000000000000 : ℚ)) + (U := (-(6674131051530196510577 / 10000000000000000000000 : ℚ))) + (U' := (257340751469803489423 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (2562574945611551 / 5000000000000000 : ℚ)) + (q := (41042722207749283 / 80000000000000000 : ℚ)) + (U := (-(6674131051530196510577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_6 : Uω (aρ 6) (bρ 6) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -989,25 +869,21 @@ lemma U_498_6 : have hlg : Real.log (39647271024314323 / 80000000000000000 : ℝ) ≤ (-(438752821916816559511 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39647271024314323 / 80000000000000000 : ℝ) = - (39647271024314323 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39647271024314323 / 20000000000000000 : ℚ)) - (U := (427681153458183440489 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39647271024314323 / 20000000000000000 : ℝ) ≤ - (427681153458183440489 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2471763735252181 / 5000000000000000 : ℝ)) (q := - (39647271024314323 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39647271024314323 / 80000000000000000 : ℚ)) + (r' := (39647271024314323 / 20000000000000000 : ℚ)) + (U := (-(438752821916816559511 / 625000000000000000000 : ℚ))) + (U' := (427681153458183440489 / 625000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (2471763735252181 / 5000000000000000 : ℚ)) + (q := (39647271024314323 / 80000000000000000 : ℚ)) + (U := (-(438752821916816559511 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_7 : Uω (aρ 7) (bρ 7) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1015,25 +891,21 @@ lemma U_498_7 : have hlg : Real.log (37737109307936711 / 80000000000000000 : ℝ) ≤ (-(7513826920613636684123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37737109307936711 / 80000000000000000 : ℝ) = - (37737109307936711 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37737109307936711 / 20000000000000000 : ℚ)) - (U := (6349116685386363315877 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37737109307936711 / 20000000000000000 : ℝ) ≤ - (6349116685386363315877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4689648422169959 / 10000000000000000 : ℝ)) (q := - (37737109307936711 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37737109307936711 / 80000000000000000 : ℚ)) + (r' := (37737109307936711 / 20000000000000000 : ℚ)) + (U := (-(7513826920613636684123 / 10000000000000000000000 : ℚ))) + (U' := (6349116685386363315877 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (4689648422169959 / 10000000000000000 : ℚ)) + (q := (37737109307936711 / 80000000000000000 : ℚ)) + (U := (-(7513826920613636684123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_8 : Uω (aρ 8) (bρ 8) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1041,25 +913,21 @@ lemma U_498_8 : have hlg : Real.log (35230478637993371 / 80000000000000000 : ℝ) ≤ (-(2050287639504809022989 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35230478637993371 / 80000000000000000 : ℝ) = - (35230478637993371 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35230478637993371 / 20000000000000000 : ℚ)) - (U := (1415448261995190977011 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35230478637993371 / 20000000000000000 : ℝ) ≤ - (1415448261995190977011 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1086633101506031 / 2500000000000000 : ℝ)) (q := - (35230478637993371 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35230478637993371 / 80000000000000000 : ℚ)) + (r' := (35230478637993371 / 20000000000000000 : ℚ)) + (U := (-(2050287639504809022989 / 2500000000000000000000 : ℚ))) + (U' := (1415448261995190977011 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (1086633101506031 / 2500000000000000 : ℚ)) + (q := (35230478637993371 / 80000000000000000 : ℚ)) + (U := (-(2050287639504809022989 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_9 : Uω (aρ 9) (bρ 9) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1067,25 +935,21 @@ lemma U_498_9 : have hlg : Real.log (6411369953907939 / 16000000000000000 : ℝ) ≤ (-(9145157522639751445491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6411369953907939 / 16000000000000000 : ℝ) = - (6411369953907939 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6411369953907939 / 4000000000000000 : ℚ)) - (U := (4717786083360248554509 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6411369953907939 / 4000000000000000 : ℝ) ≤ - (4717786083360248554509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (778818163454141 / 2000000000000000 : ℝ)) (q := - (6411369953907939 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6411369953907939 / 16000000000000000 : ℚ)) + (r' := (6411369953907939 / 4000000000000000 : ℚ)) + (U := (-(9145157522639751445491 / 10000000000000000000000 : ℚ))) + (U' := (4717786083360248554509 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (778818163454141 / 2000000000000000 : ℚ)) + (q := (6411369953907939 / 16000000000000000 : ℚ)) + (U := (-(9145157522639751445491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_10 : Uω (aρ 10) (bρ 10) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1093,26 +957,21 @@ lemma U_498_10 : have hlg : Real.log (28141450182058891 / 80000000000000000 : ℝ) ≤ (-(10447830492519363594599 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28141450182058891 / 80000000000000000 : ℝ) = - (28141450182058891 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28141450182058891 / 20000000000000000 : ℚ)) - (U := (3415113113480636405401 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28141450182058891 / 20000000000000000 : ℝ) ≤ - (3415113113480636405401 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (206487497118469 / 625000000000000 : ℝ)) (q := - (28141450182058891 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28141450182058891 / 80000000000000000 : ℚ)) + (r' := (28141450182058891 / 20000000000000000 : ℚ)) + (U := (-(10447830492519363594599 / 10000000000000000000000 : ℚ))) + (U' := (3415113113480636405401 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (206487497118469 / 625000000000000 : ℚ)) + (q := (28141450182058891 / 80000000000000000 : ℚ)) + (U := (-(10447830492519363594599 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_11 : Uω (aρ 11) (bρ 11) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1120,26 +979,21 @@ lemma U_498_11 : have hlg : Real.log (4664671163400139 / 16000000000000000 : ℝ) ≤ (-(12325713800658735169931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4664671163400139 / 16000000000000000 : ℝ) = - (4664671163400139 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4664671163400139 / 4000000000000000 : ℚ)) - (U := (1537229805341264830069 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4664671163400139 / 4000000000000000 : ℝ) ≤ - (1537229805341264830069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (503550597767191 / 2000000000000000 : ℝ)) (q := - (4664671163400139 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4664671163400139 / 16000000000000000 : ℚ)) + (r' := (4664671163400139 / 4000000000000000 : ℚ)) + (U := (-(12325713800658735169931 / 10000000000000000000000 : ℚ))) + (U' := (1537229805341264830069 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (503550597767191 / 2000000000000000 : ℚ)) + (q := (4664671163400139 / 16000000000000000 : ℚ)) + (U := (-(12325713800658735169931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_12 : Uω (aρ 12) (bρ 12) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1147,26 +1001,21 @@ lemma U_498_12 : have hlg : Real.log (16781997422714663 / 80000000000000000 : ℝ) ≤ (-(7808599520102826369753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16781997422714663 / 80000000000000000 : ℝ) = - (16781997422714663 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16781997422714663 / 10000000000000000 : ℚ)) - (U := (2588608184397173630247 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16781997422714663 / 10000000000000000 : ℝ) ≤ - (2588608184397173630247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1306113486949447 / 10000000000000000 : ℝ)) (q := - (16781997422714663 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16781997422714663 / 80000000000000000 : ℚ)) + (r' := (16781997422714663 / 10000000000000000 : ℚ)) + (U := (-(7808599520102826369753 / 5000000000000000000000 : ℚ))) + (U' := (2588608184397173630247 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (34993133427579 / 64000000000000 : ℚ)) + (s := (1306113486949447 / 10000000000000000 : ℚ)) + (q := (16781997422714663 / 80000000000000000 : ℚ)) + (U := (-(7808599520102826369753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_498_13 : Uω (aρ 13) (bρ 13) (34993133427579 / 64000000000000 : ℝ) ≤ @@ -1279,25 +1128,21 @@ lemma U_499_1 : have hlg : Real.log (86550258497790977 / 160000000000000000 : ℝ) ≤ (-(3072242733343819264019 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (86550258497790977 / 160000000000000000 : ℝ) = - (86550258497790977 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86550258497790977 / 80000000000000000 : ℚ)) - (U := (393493168156180735981 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (86550258497790977 / 80000000000000000 : ℝ) ≤ - (393493168156180735981 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5409361269590669 / 10000000000000000 : ℝ)) (q := - (86550258497790977 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86550258497790977 / 160000000000000000 : ℚ)) + (r' := (86550258497790977 / 80000000000000000 : ℚ)) + (U := (-(3072242733343819264019 / 5000000000000000000000 : ℚ))) + (U' := (393493168156180735981 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (5409361269590669 / 10000000000000000 : ℚ)) + (q := (86550258497790977 / 160000000000000000 : ℚ)) + (U := (-(3072242733343819264019 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_2 : Uω (aρ 2) (bρ 2) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1305,25 +1150,21 @@ lemma U_499_2 : have hlg : Real.log (86167280504749081 / 160000000000000000 : ℝ) ≤ (-(6188832858726643796807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (86167280504749081 / 160000000000000000 : ℝ) = - (86167280504749081 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86167280504749081 / 80000000000000000 : ℚ)) - (U := (742638944273356203193 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (86167280504749081 / 80000000000000000 : ℝ) ≤ - (742638944273356203193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84144656765163 / 156250000000000 : ℝ)) (q := - (86167280504749081 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86167280504749081 / 160000000000000000 : ℚ)) + (r' := (86167280504749081 / 80000000000000000 : ℚ)) + (U := (-(6188832858726643796807 / 10000000000000000000000 : ℚ))) + (U' := (742638944273356203193 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (84144656765163 / 156250000000000 : ℚ)) + (q := (86167280504749081 / 160000000000000000 : ℚ)) + (U := (-(6188832858726643796807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_3 : Uω (aρ 3) (bρ 3) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1331,25 +1172,21 @@ lemma U_499_3 : have hlg : Real.log (85401006453356393 / 160000000000000000 : ℝ) ≤ (-(6278159290806943346951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (85401006453356393 / 160000000000000000 : ℝ) = - (85401006453356393 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85401006453356393 / 80000000000000000 : ℚ)) - (U := (653312512193056653049 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85401006453356393 / 80000000000000000 : ℝ) ≤ - (653312512193056653049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2668434941448173 / 5000000000000000 : ℝ)) (q := - (85401006453356393 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85401006453356393 / 160000000000000000 : ℚ)) + (r' := (85401006453356393 / 80000000000000000 : ℚ)) + (U := (-(6278159290806943346951 / 10000000000000000000000 : ℚ))) + (U' := (653312512193056653049 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (2668434941448173 / 5000000000000000 : ℚ)) + (q := (85401006453356393 / 160000000000000000 : ℚ)) + (U := (-(6278159290806943346951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_4 : Uω (aρ 4) (bρ 4) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1357,25 +1194,21 @@ lemma U_499_4 : have hlg : Real.log (84127373862011169 / 160000000000000000 : ℝ) ≤ (-(6428418091365539699 / 10000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84127373862011169 / 160000000000000000 : ℝ) = - (84127373862011169 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84127373862011169 / 80000000000000000 : ℚ)) - (U := (503053711634460301 / 10000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (84127373862011169 / 80000000000000000 : ℝ) ≤ - (503053711634460301 / 10000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5255959990043193 / 10000000000000000 : ℝ)) (q := - (84127373862011169 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84127373862011169 / 160000000000000000 : ℚ)) + (r' := (84127373862011169 / 80000000000000000 : ℚ)) + (U := (-(6428418091365539699 / 10000000000000000000 : ℚ))) + (U' := (503053711634460301 / 10000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (5255959990043193 / 10000000000000000 : ℚ)) + (q := (84127373862011169 / 160000000000000000 : ℚ)) + (U := (-(6428418091365539699 / 10000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_5 : Uω (aρ 5) (bρ 5) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1383,25 +1216,21 @@ lemma U_499_5 : have hlg : Real.log (82185404024557753 / 160000000000000000 : ℝ) ≤ (-(832745119112230134817 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (82185404024557753 / 160000000000000000 : ℝ) = - (82185404024557753 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82185404024557753 / 80000000000000000 : ℚ)) - (U := (33688856262769865183 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (82185404024557753 / 80000000000000000 : ℝ) ≤ - (33688856262769865183 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1282850919924129 / 2500000000000000 : ℝ)) (q := - (82185404024557753 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82185404024557753 / 160000000000000000 : ℚ)) + (r' := (82185404024557753 / 80000000000000000 : ℚ)) + (U := (-(832745119112230134817 / 1250000000000000000000 : ℚ))) + (U' := (33688856262769865183 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (1282850919924129 / 2500000000000000 : ℚ)) + (q := (82185404024557753 / 160000000000000000 : ℚ)) + (U := (-(832745119112230134817 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_6 : Uω (aρ 6) (bρ 6) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1409,25 +1238,21 @@ lemma U_499_6 : have hlg : Real.log (15878930087565661 / 32000000000000000 : ℝ) ≤ (-(3503714117845335411479 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15878930087565661 / 32000000000000000 : ℝ) = - (15878930087565661 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15878930087565661 / 8000000000000000 : ℚ)) - (U := (3427757685154664588521 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (15878930087565661 / 8000000000000000 : ℝ) ≤ - (3427757685154664588521 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (989959971299067 / 2000000000000000 : ℝ)) (q := - (15878930087565661 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15878930087565661 / 32000000000000000 : ℚ)) + (r' := (15878930087565661 / 8000000000000000 : ℚ)) + (U := (-(3503714117845335411479 / 5000000000000000000000 : ℚ))) + (U' := (3427757685154664588521 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (989959971299067 / 2000000000000000 : ℚ)) + (q := (15878930087565661 / 32000000000000000 : ℚ)) + (U := (-(3503714117845335411479 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_7 : Uω (aρ 7) (bρ 7) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1435,25 +1260,21 @@ lemma U_499_7 : have hlg : Real.log (75574661796839249 / 160000000000000000 : ℝ) ≤ (-(937565936406325238339 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (75574661796839249 / 160000000000000000 : ℝ) = - (75574661796839249 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (75574661796839249 / 40000000000000000 : ℚ)) - (U := (795302014343674761661 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (75574661796839249 / 40000000000000000 : ℝ) ≤ - (795302014343674761661 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4695962657131703 / 10000000000000000 : ℝ)) (q := - (75574661796839249 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (75574661796839249 / 160000000000000000 : ℚ)) + (r' := (75574661796839249 / 40000000000000000 : ℚ)) + (U := (-(937565936406325238339 / 1250000000000000000000 : ℚ))) + (U' := (795302014343674761661 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (4695962657131703 / 10000000000000000 : ℚ)) + (q := (75574661796839249 / 160000000000000000 : ℚ)) + (U := (-(937565936406325238339 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_8 : Uω (aρ 8) (bρ 8) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1461,25 +1282,21 @@ lemma U_499_8 : have hlg : Real.log (70562129876487961 / 160000000000000000 : ℝ) ≤ (-(1637360436293184612359 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70562129876487961 / 160000000000000000 : ℝ) = - (70562129876487961 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70562129876487961 / 40000000000000000 : ℚ)) - (U := (1135228284906815387641 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70562129876487961 / 40000000000000000 : ℝ) ≤ - (1135228284906815387641 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (272058613651737 / 625000000000000 : ℝ)) (q := - (70562129876487961 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70562129876487961 / 160000000000000000 : ℚ)) + (r' := (70562129876487961 / 40000000000000000 : ℚ)) + (U := (-(1637360436293184612359 / 2000000000000000000000 : ℚ))) + (U' := (1135228284906815387641 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (272058613651737 / 625000000000000 : ℚ)) + (q := (70562129876487961 / 160000000000000000 : ℚ)) + (U := (-(1637360436293184612359 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_9 : Uω (aρ 9) (bρ 9) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1487,25 +1304,21 @@ lemma U_499_9 : have hlg : Real.log (64216451494584217 / 160000000000000000 : ℝ) ≤ (-(4564571915178486632409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (64216451494584217 / 160000000000000000 : ℝ) = - (64216451494584217 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64216451494584217 / 40000000000000000 : ℚ)) - (U := (2366899887821513367591 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64216451494584217 / 40000000000000000 : ℝ) ≤ - (2366899887821513367591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (121896676532807 / 312500000000000 : ℝ)) (q := - (64216451494584217 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64216451494584217 / 160000000000000000 : ℚ)) + (r' := (64216451494584217 / 40000000000000000 : ℚ)) + (U := (-(4564571915178486632409 / 5000000000000000000000 : ℚ))) + (U' := (2366899887821513367591 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (121896676532807 / 312500000000000 : ℚ)) + (q := (64216451494584217 / 160000000000000000 : ℚ)) + (U := (-(4564571915178486632409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_10 : Uω (aρ 10) (bρ 10) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1513,26 +1326,21 @@ lemma U_499_10 : have hlg : Real.log (56389210635193161 / 160000000000000000 : ℝ) ≤ (-(2607239938261753790789 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (56389210635193161 / 160000000000000000 : ℝ) = - (56389210635193161 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56389210635193161 / 40000000000000000 : ℚ)) - (U := (858495963238246209211 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56389210635193161 / 40000000000000000 : ℝ) ≤ - (858495963238246209211 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1655423787560471 / 5000000000000000 : ℝ)) (q := - (56389210635193161 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56389210635193161 / 160000000000000000 : ℚ)) + (r' := (56389210635193161 / 40000000000000000 : ℚ)) + (U := (-(2607239938261753790789 / 2500000000000000000000 : ℚ))) + (U' := (858495963238246209211 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (1655423787560471 / 5000000000000000 : ℚ)) + (q := (56389210635193161 / 160000000000000000 : ℚ)) + (U := (-(2607239938261753790789 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_11 : Uω (aρ 11) (bρ 11) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1540,26 +1348,21 @@ lemma U_499_11 : have hlg : Real.log (46762297278161161 / 160000000000000000 : ℝ) ≤ (-(6150482750929794706883 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (46762297278161161 / 160000000000000000 : ℝ) = - (46762297278161161 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46762297278161161 / 40000000000000000 : ℚ)) - (U := (780989052070205293117 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46762297278161161 / 40000000000000000 : ℝ) ≤ - (780989052070205293117 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1262980015848471 / 5000000000000000 : ℝ)) (q := - (46762297278161161 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46762297278161161 / 160000000000000000 : ℚ)) + (r' := (46762297278161161 / 40000000000000000 : ℚ)) + (U := (-(6150482750929794706883 / 5000000000000000000000 : ℚ))) + (U' := (780989052070205293117 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (1262980015848471 / 5000000000000000 : ℚ)) + (q := (46762297278161161 / 160000000000000000 : ℚ)) + (U := (-(6150482750929794706883 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_12 : Uω (aρ 12) (bρ 12) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1567,26 +1370,21 @@ lemma U_499_12 : have hlg : Real.log (6744783631096493 / 32000000000000000 : ℝ) ≤ (-(15569664912888544190381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6744783631096493 / 32000000000000000 : ℝ) = - (6744783631096493 / 4000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6744783631096493 / 4000000000000000 : ℚ)) - (U := (5224750496111455809619 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6744783631096493 / 4000000000000000 : ℝ) ≤ - (5224750496111455809619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263972547609421 / 2000000000000000 : ℝ)) (q := - (6744783631096493 / 32000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6744783631096493 / 32000000000000000 : ℚ)) + (r' := (6744783631096493 / 4000000000000000 : ℚ)) + (U := (-(15569664912888544190381 / 10000000000000000000000 : ℚ))) + (U' := (5224750496111455809619 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (70066153737193 / 128000000000000 : ℚ)) + (s := (263972547609421 / 2000000000000000 : ℚ)) + (q := (6744783631096493 / 32000000000000000 : ℚ)) + (U := (-(15569664912888544190381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_499_13 : Uω (aρ 13) (bρ 13) (70066153737193 / 128000000000000 : ℝ) ≤ @@ -1698,25 +1496,21 @@ lemma U_500_1 : have hlg : Real.log (21662529412853499 / 40000000000000000 : ℝ) ≤ (-(6132954410357619226903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21662529412853499 / 40000000000000000 : ℝ) = - (21662529412853499 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21662529412853499 / 20000000000000000 : ℚ)) - (U := (798517392642380773097 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21662529412853499 / 20000000000000000 : ℝ) ≤ - (798517392642380773097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2707801250567281 / 5000000000000000 : ℝ)) (q := - (21662529412853499 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21662529412853499 / 40000000000000000 : ℚ)) + (r' := (21662529412853499 / 20000000000000000 : ℚ)) + (U := (-(6132954410357619226903 / 10000000000000000000000 : ℚ))) + (U' := (798517392642380773097 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (2707801250567281 / 5000000000000000 : ℚ)) + (q := (21662529412853499 / 40000000000000000 : ℚ)) + (U := (-(6132954410357619226903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_2 : Uω (aρ 2) (bρ 2) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1724,25 +1518,21 @@ lemma U_500_2 : have hlg : Real.log (21566785688999999 / 40000000000000000 : ℝ) ≤ (-(6177250222205826174879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21566785688999999 / 40000000000000000 : ℝ) = - (21566785688999999 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21566785688999999 / 20000000000000000 : ℚ)) - (U := (754221580794173825121 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21566785688999999 / 20000000000000000 : ℝ) ≤ - (754221580794173825121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1347874912929453 / 2500000000000000 : ℝ)) (q := - (21566785688999999 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21566785688999999 / 40000000000000000 : ℚ)) + (r' := (21566785688999999 / 20000000000000000 : ℚ)) + (U := (-(6177250222205826174879 / 10000000000000000000000 : ℚ))) + (U' := (754221580794173825121 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (1347874912929453 / 2500000000000000 : ℚ)) + (q := (21566785688999999 / 40000000000000000 : ℚ)) + (U := (-(6177250222205826174879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_3 : Uω (aρ 3) (bρ 3) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1750,25 +1540,21 @@ lemma U_500_3 : have hlg : Real.log (21375219501978207 / 40000000000000000 : ℝ) ≤ (-(195827240620468206163 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21375219501978207 / 40000000000000000 : ℝ) = - (21375219501978207 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21375219501978207 / 20000000000000000 : ℚ)) - (U := (20781253223281793837 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21375219501978207 / 20000000000000000 : ℝ) ≤ - (20781253223281793837 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1335778166139229 / 2500000000000000 : ℝ)) (q := - (21375219501978207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21375219501978207 / 40000000000000000 : ℚ)) + (r' := (21375219501978207 / 20000000000000000 : ℚ)) + (U := (-(195827240620468206163 / 312500000000000000000 : ℚ))) + (U' := (20781253223281793837 / 312500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (1335778166139229 / 2500000000000000 : ℚ)) + (q := (21375219501978207 / 40000000000000000 : ℚ)) + (U := (-(195827240620468206163 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_4 : Uω (aρ 4) (bρ 4) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1776,25 +1562,21 @@ lemma U_500_4 : have hlg : Real.log (21056817608583931 / 40000000000000000 : ℝ) ≤ (-(3208275346350256311827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21056817608583931 / 40000000000000000 : ℝ) = - (21056817608583931 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21056817608583931 / 20000000000000000 : ℚ)) - (U := (257460555149743688173 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21056817608583931 / 20000000000000000 : ℝ) ≤ - (257460555149743688173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2631102949462389 / 5000000000000000 : ℝ)) (q := - (21056817608583931 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21056817608583931 / 40000000000000000 : ℚ)) + (r' := (21056817608583931 / 20000000000000000 : ℚ)) + (U := (-(3208275346350256311827 / 5000000000000000000000 : ℚ))) + (U' := (257460555149743688173 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (2631102949462389 / 5000000000000000 : ℚ)) + (q := (21056817608583931 / 40000000000000000 : ℚ)) + (U := (-(3208275346350256311827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_5 : Uω (aρ 5) (bρ 5) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1802,25 +1584,21 @@ lemma U_500_5 : have hlg : Real.log (20571340846991449 / 40000000000000000 : ℝ) ≤ (-(831225709655945375553 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20571340846991449 / 40000000000000000 : ℝ) = - (20571340846991449 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20571340846991449 / 20000000000000000 : ℚ)) - (U := (35208265719054624447 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20571340846991449 / 20000000000000000 : ℝ) ≤ - (35208265719054624447 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5137657437463537 / 10000000000000000 : ℝ)) (q := - (20571340846991449 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20571340846991449 / 40000000000000000 : ℚ)) + (r' := (20571340846991449 / 20000000000000000 : ℚ)) + (U := (-(831225709655945375553 / 1250000000000000000000 : ℚ))) + (U' := (35208265719054624447 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (5137657437463537 / 10000000000000000 : ℚ)) + (q := (20571340846991449 / 40000000000000000 : ℚ)) + (U := (-(831225709655945375553 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_6 : Uω (aρ 6) (bρ 6) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1828,25 +1606,21 @@ lemma U_500_6 : have hlg : Real.log (19873689549085887 / 40000000000000000 : ℝ) ≤ (-(6994827298646218981741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19873689549085887 / 40000000000000000 : ℝ) = - (19873689549085887 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19873689549085887 / 10000000000000000 : ℚ)) - (U := (6868116307353781018259 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19873689549085887 / 10000000000000000 : ℝ) ≤ - (6868116307353781018259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1239018040912689 / 2500000000000000 : ℝ)) (q := - (19873689549085887 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19873689549085887 / 40000000000000000 : ℚ)) + (r' := (19873689549085887 / 10000000000000000 : ℚ)) + (U := (-(6994827298646218981741 / 10000000000000000000000 : ℚ))) + (U' := (6868116307353781018259 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (1239018040912689 / 2500000000000000 : ℚ)) + (q := (19873689549085887 / 40000000000000000 : ℚ)) + (U := (-(6994827298646218981741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_7 : Uω (aρ 7) (bρ 7) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1854,25 +1628,21 @@ lemma U_500_7 : have hlg : Real.log (18918775854235273 / 40000000000000000 : ℝ) ≤ (-(7487245932138787324571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18918775854235273 / 40000000000000000 : ℝ) = - (18918775854235273 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18918775854235273 / 10000000000000000 : ℚ)) - (U := (6375697673861212675429 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18918775854235273 / 10000000000000000 : ℝ) ≤ - (6375697673861212675429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4702276696985449 / 10000000000000000 : ℝ)) (q := - (18918775854235273 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18918775854235273 / 40000000000000000 : ℚ)) + (r' := (18918775854235273 / 10000000000000000 : ℚ)) + (U := (-(7487245932138787324571 / 10000000000000000000000 : ℚ))) + (U' := (6375697673861212675429 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (4702276696985449 / 10000000000000000 : ℚ)) + (q := (18918775854235273 / 40000000000000000 : ℚ)) + (U := (-(7487245932138787324571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_8 : Uω (aρ 8) (bρ 8) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1880,25 +1650,21 @@ lemma U_500_8 : have hlg : Real.log (3533164933252231 / 8000000000000000 : ℝ) ≤ (-(4086237451230692446593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3533164933252231 / 8000000000000000 : ℝ) = - (3533164933252231 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3533164933252231 / 2000000000000000 : ℚ)) - (U := (2845234351769307553407 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3533164933252231 / 2000000000000000 : ℝ) ≤ - (2845234351769307553407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (435934275433839 / 1000000000000000 : ℝ)) (q := - (3533164933252231 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3533164933252231 / 8000000000000000 : ℚ)) + (r' := (3533164933252231 / 2000000000000000 : ℚ)) + (U := (-(4086237451230692446593 / 5000000000000000000000 : ℚ))) + (U' := (2845234351769307553407 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (435934275433839 / 1000000000000000 : ℚ)) + (q := (3533164933252231 / 8000000000000000 : ℚ)) + (U := (-(4086237451230692446593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_9 : Uω (aρ 9) (bρ 9) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1906,25 +1672,21 @@ lemma U_500_9 : have hlg : Real.log (16079798484777499 / 40000000000000000 : ℝ) ≤ (-(2278289304907380917197 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16079798484777499 / 40000000000000000 : ℝ) = - (16079798484777499 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16079798484777499 / 10000000000000000 : ℚ)) - (U := (1187446596592619082803 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16079798484777499 / 10000000000000000 : ℝ) ≤ - (1187446596592619082803 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1953647645978281 / 5000000000000000 : ℝ)) (q := - (16079798484777499 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16079798484777499 / 40000000000000000 : ℚ)) + (r' := (16079798484777499 / 10000000000000000 : ℚ)) + (U := (-(2278289304907380917197 / 2500000000000000000000 : ℚ))) + (U' := (1187446596592619082803 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (1953647645978281 / 5000000000000000 : ℚ)) + (q := (16079798484777499 / 40000000000000000 : ℚ)) + (U := (-(2278289304907380917197 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_10 : Uω (aρ 10) (bρ 10) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1932,25 +1694,21 @@ lemma U_500_10 : have hlg : Real.log (564954950661303 / 1600000000000000 : ℝ) ≤ (-(10410129130832395465343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (564954950661303 / 1600000000000000 : ℝ) = - (564954950661303 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (564954950661303 / 400000000000000 : ℚ)) - (U := (3452814475167604534657 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (564954950661303 / 400000000000000 : ℝ) ≤ - (3452814475167604534657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33178919663291 / 100000000000000 : ℝ)) (q := - (564954950661303 / 1600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (564954950661303 / 1600000000000000 : ℚ)) + (r' := (564954950661303 / 400000000000000 : ℚ)) + (U := (-(10410129130832395465343 / 10000000000000000000000 : ℚ))) + (U' := (3452814475167604534657 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (33178919663291 / 100000000000000 : ℚ)) + (q := (564954950661303 / 1600000000000000 : ℚ)) + (U := (-(10410129130832395465343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_11 : Uω (aρ 11) (bρ 11) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1958,25 +1716,21 @@ lemma U_500_11 : have hlg : Real.log (468777932565549 / 1600000000000000 : ℝ) ≤ (-(12276297427255723426533 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (468777932565549 / 1600000000000000 : ℝ) = - (468777932565549 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (468777932565549 / 400000000000000 : ℚ)) - (U := (1586646178744276573467 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (468777932565549 / 400000000000000 : ℝ) ≤ - (1586646178744276573467 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101366234653487 / 400000000000000 : ℝ)) (q := - (468777932565549 / 1600000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (468777932565549 / 1600000000000000 : ℚ)) + (r' := (468777932565549 / 400000000000000 : ℚ)) + (U := (-(12276297427255723426533 / 10000000000000000000000 : ℚ))) + (U' := (1586646178744276573467 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (101366234653487 / 400000000000000 : ℚ)) + (q := (468777932565549 / 1600000000000000 : ℚ)) + (U := (-(12276297427255723426533 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_12 : Uω (aρ 12) (bρ 12) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -1984,26 +1738,21 @@ lemma U_500_12 : have hlg : Real.log (8470735269235369 / 40000000000000000 : ℝ) ≤ (-(3880655349478368086291 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8470735269235369 / 40000000000000000 : ℝ) = - (8470735269235369 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8470735269235369 / 5000000000000000 : ℚ)) - (U := (1317948502771631913709 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8470735269235369 / 5000000000000000 : ℝ) ≤ - (1317948502771631913709 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1333499440570497 / 10000000000000000 : ℝ)) (q := - (8470735269235369 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8470735269235369 / 40000000000000000 : ℚ)) + (r' := (8470735269235369 / 5000000000000000 : ℚ)) + (U := (-(3880655349478368086291 / 2500000000000000000000 : ℚ))) + (U' := (1317948502771631913709 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17536510154807 / 32000000000000 : ℚ)) + (s := (1333499440570497 / 10000000000000000 : ℚ)) + (q := (8470735269235369 / 40000000000000000 : ℚ)) + (U := (-(3880655349478368086291 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_500_13 : Uω (aρ 13) (bρ 13) (17536510154807 / 32000000000000 : ℝ) ≤ @@ -2115,25 +1864,21 @@ lemma U_501_1 : have hlg : Real.log (43424917977429129 / 80000000000000000 : ℝ) ≤ (-(1527483027803754788683 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43424917977429129 / 80000000000000000 : ℝ) = - (43424917977429129 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43424917977429129 / 40000000000000000 : ℚ)) - (U := (205384922946245211317 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43424917977429129 / 40000000000000000 : ℝ) ≤ - (205384922946245211317 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2714042481873563 / 5000000000000000 : ℝ)) (q := - (43424917977429129 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43424917977429129 / 80000000000000000 : ℚ)) + (r' := (43424917977429129 / 40000000000000000 : ℚ)) + (U := (-(1527483027803754788683 / 2500000000000000000000 : ℚ))) + (U' := (205384922946245211317 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (2714042481873563 / 5000000000000000 : ℚ)) + (q := (43424917977429129 / 80000000000000000 : ℚ)) + (U := (-(1527483027803754788683 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_2 : Uω (aρ 2) (bρ 2) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2141,25 +1886,21 @@ lemma U_501_2 : have hlg : Real.log (43233433616608557 / 80000000000000000 : ℝ) ≤ (-(3077062560900137648367 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43233433616608557 / 80000000000000000 : ℝ) = - (43233433616608557 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43233433616608557 / 40000000000000000 : ℚ)) - (U := (388673340599862351633 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43233433616608557 / 40000000000000000 : ℝ) ≤ - (388673340599862351633 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5403982886051983 / 10000000000000000 : ℝ)) (q := - (43233433616608557 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43233433616608557 / 80000000000000000 : ℚ)) + (r' := (43233433616608557 / 40000000000000000 : ℚ)) + (U := (-(3077062560900137648367 / 5000000000000000000000 : ℚ))) + (U' := (388673340599862351633 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (5403982886051983 / 10000000000000000 : ℚ)) + (q := (43233433616608557 / 80000000000000000 : ℚ)) + (U := (-(3077062560900137648367 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_3 : Uω (aρ 3) (bρ 3) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2167,25 +1908,21 @@ lemma U_501_3 : have hlg : Real.log (42850310513225973 / 80000000000000000 : ℝ) ≤ (-(6243137428800446165823 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42850310513225973 / 80000000000000000 : ℝ) = - (42850310513225973 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42850310513225973 / 40000000000000000 : ℚ)) - (U := (688334374199553834177 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42850310513225973 / 40000000000000000 : ℝ) ≤ - (688334374199553834177 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5355598216556337 / 10000000000000000 : ℝ)) (q := - (42850310513225973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42850310513225973 / 80000000000000000 : ℚ)) + (r' := (42850310513225973 / 40000000000000000 : ℚ)) + (U := (-(6243137428800446165823 / 10000000000000000000000 : ℚ))) + (U' := (688334374199553834177 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (5355598216556337 / 10000000000000000 : ℚ)) + (q := (42850310513225973 / 80000000000000000 : ℚ)) + (U := (-(6243137428800446165823 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_4 : Uω (aρ 4) (bρ 4) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2193,25 +1930,21 @@ lemma U_501_4 : have hlg : Real.log (8442706330932121 / 16000000000000000 : ℝ) ≤ (-(3196429047235951039163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8442706330932121 / 16000000000000000 : ℝ) = - (8442706330932121 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8442706330932121 / 8000000000000000 : ℚ)) - (U := (269306854264048960837 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8442706330932121 / 8000000000000000 : ℝ) ≤ - (269306854264048960837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1054939536595999 / 2000000000000000 : ℝ)) (q := - (8442706330932121 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8442706330932121 / 16000000000000000 : ℚ)) + (r' := (8442706330932121 / 8000000000000000 : ℚ)) + (U := (-(3196429047235951039163 / 5000000000000000000000 : ℚ))) + (U' := (269306854264048960837 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (1054939536595999 / 2000000000000000 : ℚ)) + (q := (8442706330932121 / 16000000000000000 : ℚ)) + (U := (-(3196429047235951039163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_5 : Uω (aρ 5) (bρ 5) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2219,25 +1952,21 @@ lemma U_501_5 : have hlg : Real.log (41242640690703941 / 80000000000000000 : ℝ) ≤ (-(3312769725239216942567 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41242640690703941 / 80000000000000000 : ℝ) = - (41242640690703941 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41242640690703941 / 40000000000000000 : ℚ)) - (U := (152966176260783057433 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41242640690703941 / 40000000000000000 : ℝ) ≤ - (152966176260783057433 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5150164861325829 / 10000000000000000 : ℝ)) (q := - (41242640690703941 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41242640690703941 / 80000000000000000 : ℚ)) + (r' := (41242640690703941 / 40000000000000000 : ℚ)) + (U := (-(3312769725239216942567 / 5000000000000000000000 : ℚ))) + (U' := (152966176260783057433 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (5150164861325829 / 10000000000000000 : ℚ)) + (q := (41242640690703941 / 80000000000000000 : ℚ)) + (U := (-(3312769725239216942567 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_6 : Uω (aρ 6) (bρ 6) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2245,25 +1974,21 @@ lemma U_501_6 : have hlg : Real.log (39847485915437389 / 80000000000000000 : ℝ) ≤ (-(6969673196046202864671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39847485915437389 / 80000000000000000 : ℝ) = - (39847485915437389 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39847485915437389 / 20000000000000000 : ℚ)) - (U := (6893270409953797135329 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39847485915437389 / 20000000000000000 : ℝ) ≤ - (6893270409953797135329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4968616542649191 / 10000000000000000 : ℝ)) (q := - (39847485915437389 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39847485915437389 / 80000000000000000 : ℚ)) + (r' := (39847485915437389 / 20000000000000000 : ℚ)) + (U := (-(6969673196046202864671 / 10000000000000000000000 : ℚ))) + (U' := (6893270409953797135329 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (4968616542649191 / 10000000000000000 : ℚ)) + (q := (39847485915437389 / 80000000000000000 : ℚ)) + (U := (-(6969673196046202864671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_7 : Uω (aρ 7) (bρ 7) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2271,25 +1996,21 @@ lemma U_501_7 : have hlg : Real.log (37937990999817837 / 80000000000000000 : ℝ) ≤ (-(746073623083452947819 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37937990999817837 / 80000000000000000 : ℝ) = - (37937990999817837 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37937990999817837 / 20000000000000000 : ℚ)) - (U := (640220737516547052181 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37937990999817837 / 20000000000000000 : ℝ) ≤ - (640220737516547052181 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4714904194504303 / 10000000000000000 : ℝ)) (q := - (37937990999817837 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37937990999817837 / 80000000000000000 : ℚ)) + (r' := (37937990999817837 / 20000000000000000 : ℚ)) + (U := (-(746073623083452947819 / 1000000000000000000000 : ℚ))) + (U' := (640220737516547052181 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (4714904194504303 / 10000000000000000 : ℚ)) + (q := (37937990999817837 / 80000000000000000 : ℚ)) + (U := (-(746073623083452947819 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_8 : Uω (aρ 8) (bρ 8) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2297,25 +2018,21 @@ lemma U_501_8 : have hlg : Real.log (35432812436667113 / 80000000000000000 : ℝ) ≤ (-(4071941691674149917709 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35432812436667113 / 80000000000000000 : ℝ) = - (35432812436667113 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35432812436667113 / 20000000000000000 : ℚ)) - (U := (2859530111325850082291 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35432812436667113 / 20000000000000000 : ℝ) ≤ - (2859530111325850082291 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2186075602528311 / 5000000000000000 : ℝ)) (q := - (35432812436667113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35432812436667113 / 80000000000000000 : ℚ)) + (r' := (35432812436667113 / 20000000000000000 : ℚ)) + (U := (-(4071941691674149917709 / 5000000000000000000000 : ℚ))) + (U' := (2859530111325850082291 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (2186075602528311 / 5000000000000000 : ℚ)) + (q := (35432812436667113 / 80000000000000000 : ℚ)) + (U := (-(4071941691674149917709 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_9 : Uω (aρ 9) (bρ 9) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2323,25 +2040,21 @@ lemma U_501_9 : have hlg : Real.log (6452465048739989 / 16000000000000000 : ℝ) ≤ (-(4540632429122172497341 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6452465048739989 / 16000000000000000 : ℝ) = - (6452465048739989 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6452465048739989 / 4000000000000000 : ℚ)) - (U := (2390839373877827502659 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6452465048739989 / 4000000000000000 : ℝ) ≤ - (2390839373877827502659 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (392049503517483 / 1000000000000000 : ℝ)) (q := - (6452465048739989 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6452465048739989 / 16000000000000000 : ℚ)) + (r' := (6452465048739989 / 4000000000000000 : ℚ)) + (U := (-(4540632429122172497341 / 5000000000000000000000 : ℚ))) + (U' := (2390839373877827502659 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (392049503517483 / 1000000000000000 : ℚ)) + (q := (6452465048739989 / 16000000000000000 : ℚ)) + (U := (-(4540632429122172497341 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_10 : Uω (aρ 10) (bρ 10) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2349,26 +2062,21 @@ lemma U_501_10 : have hlg : Real.log (28353993531541789 / 80000000000000000 : ℝ) ≤ (-(2074517497181400129451 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28353993531541789 / 80000000000000000 : ℝ) = - (28353993531541789 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28353993531541789 / 20000000000000000 : ℚ)) - (U := (698071224018599870549 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28353993531541789 / 20000000000000000 : ℝ) ≤ - (698071224018599870549 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3331971140630291 / 10000000000000000 : ℝ)) (q := - (28353993531541789 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28353993531541789 / 80000000000000000 : ℚ)) + (r' := (28353993531541789 / 20000000000000000 : ℚ)) + (U := (-(2074517497181400129451 / 2000000000000000000000 : ℚ))) + (U' := (698071224018599870549 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (3331971140630291 / 10000000000000000 : ℚ)) + (q := (28353993531541789 / 80000000000000000 : ℚ)) + (U := (-(2074517497181400129451 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_11 : Uω (aρ 11) (bρ 11) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2376,26 +2084,21 @@ lemma U_501_11 : have hlg : Real.log (23554259836225581 / 80000000000000000 : ℝ) ≤ (-(1222719945283823425943 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23554259836225581 / 80000000000000000 : ℝ) = - (23554259836225581 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23554259836225581 / 20000000000000000 : ℚ)) - (U := (163574415316176574057 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23554259836225581 / 20000000000000000 : ℝ) ≤ - (163574415316176574057 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2550514343006239 / 10000000000000000 : ℝ)) (q := - (23554259836225581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23554259836225581 / 80000000000000000 : ℚ)) + (r' := (23554259836225581 / 20000000000000000 : ℚ)) + (U := (-(1222719945283823425943 / 1000000000000000000000 : ℚ))) + (U' := (163574415316176574057 / 1000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (2550514343006239 / 10000000000000000 : ℚ)) + (q := (23554259836225581 / 80000000000000000 : ℚ)) + (U := (-(1222719945283823425943 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_12 : Uω (aρ 12) (bρ 12) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2403,26 +2106,21 @@ lemma U_501_12 : have hlg : Real.log (17099196916817357 / 80000000000000000 : ℝ) ≤ (-(15429951354170808899491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17099196916817357 / 80000000000000000 : ℝ) = - (17099196916817357 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17099196916817357 / 10000000000000000 : ℚ)) - (U := (5364464054829191100509 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17099196916817357 / 10000000000000000 : ℝ) ≤ - (5364464054829191100509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1360448709839183 / 10000000000000000 : ℝ)) (q := - (17099196916817357 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17099196916817357 / 80000000000000000 : ℚ)) + (r' := (17099196916817357 / 10000000000000000 : ℚ)) + (U := (-(15429951354170808899491 / 10000000000000000000000 : ℚ))) + (U' := (5364464054829191100509 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35152907191649 / 64000000000000 : ℚ)) + (s := (1360448709839183 / 10000000000000000 : ℚ)) + (q := (17099196916817357 / 80000000000000000 : ℚ)) + (U := (-(15429951354170808899491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_501_13 : Uω (aρ 13) (bρ 13) (35152907191649 / 64000000000000 : ℝ) ≤ @@ -2535,25 +2233,21 @@ lemma U_502_1 : have hlg : Real.log (544059714082891 / 1000000000000000 : ℝ) ≤ (-(304348134677823892373 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (544059714082891 / 1000000000000000 : ℝ) = - (544059714082891 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (544059714082891 / 500000000000000 : ℚ)) - (U := (42225455472176107627 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (544059714082891 / 500000000000000 : ℝ) ≤ - (42225455472176107627 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1088113485145939 / 2000000000000000 : ℝ)) (q := - (544059714082891 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (544059714082891 / 1000000000000000 : ℚ)) + (r' := (544059714082891 / 500000000000000 : ℚ)) + (U := (-(304348134677823892373 / 500000000000000000000 : ℚ))) + (U' := (42225455472176107627 / 500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (1088113485145939 / 2000000000000000 : ℚ)) + (q := (544059714082891 / 1000000000000000 : ℚ)) + (U := (-(304348134677823892373 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_2 : Uω (aρ 2) (bρ 2) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2561,25 +2255,21 @@ lemma U_502_2 : have hlg : Real.log (2166664791922889 / 4000000000000000 : ℝ) ≤ (-(3065526689465984201931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2166664791922889 / 4000000000000000 : ℝ) = - (2166664791922889 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2166664791922889 / 2000000000000000 : ℚ)) - (U := (400209212034015798069 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2166664791922889 / 2000000000000000 : ℝ) ≤ - (400209212034015798069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33852913226227 / 62500000000000 : ℝ)) (q := - (2166664791922889 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2166664791922889 / 4000000000000000 : ℚ)) + (r' := (2166664791922889 / 2000000000000000 : ℚ)) + (U := (-(3065526689465984201931 / 5000000000000000000000 : ℚ))) + (U' := (400209212034015798069 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (33852913226227 / 62500000000000 : ℚ)) + (q := (2166664791922889 / 4000000000000000 : ℚ)) + (U := (-(3065526689465984201931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_3 : Uω (aρ 3) (bρ 3) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2587,25 +2277,21 @@ lemma U_502_3 : have hlg : Real.log (2147509098123207 / 4000000000000000 : ℝ) ≤ (-(3109928746905706661603 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2147509098123207 / 4000000000000000 : ℝ) = - (2147509098123207 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2147509098123207 / 2000000000000000 : ℚ)) - (U := (355807154594293338397 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2147509098123207 / 2000000000000000 : ℝ) ≤ - (355807154594293338397 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (536808375354791 / 1000000000000000 : ℝ)) (q := - (2147509098123207 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2147509098123207 / 4000000000000000 : ℚ)) + (r' := (2147509098123207 / 2000000000000000 : ℚ)) + (U := (-(3109928746905706661603 / 5000000000000000000000 : ℚ))) + (U' := (355807154594293338397 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (536808375354791 / 1000000000000000 : ℚ)) + (q := (2147509098123207 / 4000000000000000 : ℚ)) + (U := (-(3109928746905706661603 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_4 : Uω (aρ 4) (bρ 4) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2613,25 +2299,21 @@ lemma U_502_4 : have hlg : Real.log (5289178489179933 / 10000000000000000 : ℝ) ≤ (-(1592305384936174259601 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5289178489179933 / 10000000000000000 : ℝ) = - (5289178489179933 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5289178489179933 / 5000000000000000 : ℚ)) - (U := (140562565813825740399 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5289178489179933 / 5000000000000000 : ℝ) ≤ - (140562565813825740399 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5287189422356741 / 10000000000000000 : ℝ)) (q := - (5289178489179933 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5289178489179933 / 10000000000000000 : ℚ)) + (r' := (5289178489179933 / 5000000000000000 : ℚ)) + (U := (-(1592305384936174259601 / 2500000000000000000000 : ℚ))) + (U' := (140562565813825740399 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (5287189422356741 / 10000000000000000 : ℚ)) + (q := (5289178489179933 / 10000000000000000 : ℚ)) + (U := (-(1592305384936174259601 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_5 : Uω (aρ 5) (bρ 5) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2639,25 +2321,21 @@ lemma U_502_5 : have hlg : Real.log (10335649800367549 / 20000000000000000 : ℝ) ≤ (-(6601332083711793922337 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10335649800367549 / 20000000000000000 : ℝ) = - (10335649800367549 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10335649800367549 / 10000000000000000 : ℚ)) - (U := (330139719288206077663 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10335649800367549 / 10000000000000000 : ℝ) ≤ - (330139719288206077663 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (161333505115607 / 312500000000000 : ℝ)) (q := - (10335649800367549 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10335649800367549 / 20000000000000000 : ℚ)) + (r' := (10335649800367549 / 10000000000000000 : ℚ)) + (U := (-(6601332083711793922337 / 10000000000000000000000 : ℚ))) + (U' := (330139719288206077663 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (161333505115607 / 312500000000000 : ℚ)) + (q := (10335649800367549 / 20000000000000000 : ℚ)) + (U := (-(6601332083711793922337 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_6 : Uω (aρ 6) (bρ 6) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2665,25 +2343,21 @@ lemma U_502_6 : have hlg : Real.log (998689787140121 / 2000000000000000 : ℝ) ≤ (-(6944582519792693022809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (998689787140121 / 2000000000000000 : ℝ) = - (998689787140121 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (998689787140121 / 500000000000000 : ℚ)) - (U := (6918361086207306977191 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (998689787140121 / 500000000000000 : ℝ) ≤ - (6918361086207306977191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (996232121974617 / 2000000000000000 : ℝ)) (q := - (998689787140121 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (998689787140121 / 2000000000000000 : ℚ)) + (r' := (998689787140121 / 500000000000000 : ℚ)) + (U := (-(6944582519792693022809 / 10000000000000000000000 : ℚ))) + (U' := (6918361086207306977191 / 10000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (996232121974617 / 2000000000000000 : ℚ)) + (q := (998689787140121 / 2000000000000000 : ℚ)) + (U := (-(6944582519792693022809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_7 : Uω (aρ 7) (bρ 7) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2691,25 +2365,21 @@ lemma U_502_7 : have hlg : Real.log (4754803400861627 / 10000000000000000 : ℝ) ≤ (-(7434297431019868095343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4754803400861627 / 10000000000000000 : ℝ) = - (4754803400861627 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4754803400861627 / 2500000000000000 : ℚ)) - (U := (6428646174980131904657 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4754803400861627 / 2500000000000000 : ℝ) ≤ - (6428646174980131904657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4727530920955129 / 10000000000000000 : ℝ)) (q := - (4754803400861627 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4754803400861627 / 10000000000000000 : ℚ)) + (r' := (4754803400861627 / 2500000000000000 : ℚ)) + (U := (-(7434297431019868095343 / 10000000000000000000000 : ℚ))) + (U' := (6428646174980131904657 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (4727530920955129 / 10000000000000000 : ℚ)) + (q := (4754803400861627 / 10000000000000000 : ℚ)) + (U := (-(7434297431019868095343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_8 : Uω (aρ 8) (bρ 8) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2717,25 +2387,21 @@ lemma U_502_8 : have hlg : Real.log (2220873001058891 / 5000000000000000 : ℝ) ≤ (-(1014421937012309681831 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2220873001058891 / 5000000000000000 : ℝ) = - (2220873001058891 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2220873001058891 / 1250000000000000 : ℚ)) - (U := (718446013737690318169 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2220873001058891 / 1250000000000000 : ℝ) ≤ - (718446013737690318169 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4384957774807439 / 10000000000000000 : ℝ)) (q := - (2220873001058891 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2220873001058891 / 5000000000000000 : ℚ)) + (r' := (2220873001058891 / 1250000000000000 : ℚ)) + (U := (-(1014421937012309681831 / 1250000000000000000000 : ℚ))) + (U' := (718446013737690318169 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (4384957774807439 / 10000000000000000 : ℚ)) + (q := (2220873001058891 / 5000000000000000 : ℚ)) + (U := (-(1014421937012309681831 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_9 : Uω (aρ 9) (bρ 9) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2743,25 +2409,21 @@ lemma U_502_9 : have hlg : Real.log (8091258695623841 / 20000000000000000 : ℝ) ≤ (-(4524739837311758777763 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8091258695623841 / 20000000000000000 : ℝ) = - (8091258695623841 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8091258695623841 / 5000000000000000 : ℚ)) - (U := (2406731965688241222237 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8091258695623841 / 5000000000000000 : ℝ) ≤ - (2406731965688241222237 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (983422523638929 / 2500000000000000 : ℝ)) (q := - (8091258695623841 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8091258695623841 / 20000000000000000 : ℚ)) + (r' := (8091258695623841 / 5000000000000000 : ℚ)) + (U := (-(4524739837311758777763 / 5000000000000000000000 : ℚ))) + (U' := (2406731965688241222237 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (983422523638929 / 2500000000000000 : ℚ)) + (q := (8091258695623841 / 20000000000000000 : ℚ)) + (U := (-(4524739837311758777763 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_10 : Uω (aρ 10) (bρ 10) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2769,26 +2431,21 @@ lemma U_502_10 : have hlg : Real.log (7115047206429829 / 20000000000000000 : ℝ) ≤ (-(5167602033692465113331 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7115047206429829 / 20000000000000000 : ℝ) = - (7115047206429829 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7115047206429829 / 5000000000000000 : ℚ)) - (U := (1763869769307534886669 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7115047206429829 / 5000000000000000 : ℝ) ≤ - (1763869769307534886669 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102112965053 / 305175781250 : ℝ)) (q := - (7115047206429829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7115047206429829 / 20000000000000000 : ℚ)) + (r' := (7115047206429829 / 5000000000000000 : ℚ)) + (U := (-(5167602033692465113331 / 5000000000000000000000 : ℚ))) + (U' := (1763869769307534886669 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (102112965053 / 305175781250 : ℚ)) + (q := (7115047206429829 / 20000000000000000 : ℚ)) + (U := (-(5167602033692465113331 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_11 : Uω (aρ 11) (bρ 11) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2796,26 +2453,21 @@ lemma U_502_11 : have hlg : Real.log (2958681104557373 / 10000000000000000 : ℝ) ≤ (-(1522301870274884627343 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2958681104557373 / 10000000000000000 : ℝ) = - (2958681104557373 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2958681104557373 / 2500000000000000 : ℚ)) - (U := (210566080475115372657 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2958681104557373 / 2500000000000000 : ℝ) ≤ - (210566080475115372657 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2566829267746621 / 10000000000000000 : ℝ)) (q := - (2958681104557373 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2958681104557373 / 10000000000000000 : ℚ)) + (r' := (2958681104557373 / 2500000000000000 : ℚ)) + (U := (-(1522301870274884627343 / 1250000000000000000000 : ℚ))) + (U' := (210566080475115372657 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (2566829267746621 / 10000000000000000 : ℚ)) + (q := (2958681104557373 / 10000000000000000 : ℚ)) + (U := (-(1522301870274884627343 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_12 : Uω (aρ 12) (bρ 12) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2823,26 +2475,21 @@ lemma U_502_12 : have hlg : Real.log (2156909797056681 / 10000000000000000 : ℝ) ≤ (-(1917385680481320352707 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2156909797056681 / 10000000000000000 : ℝ) = - (2156909797056681 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2156909797056681 / 1250000000000000 : ℚ)) - (U := (681916245643679647293 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2156909797056681 / 1250000000000000 : ℝ) ≤ - (681916245643679647293 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1386986749430237 / 10000000000000000 : ℝ)) (q := - (2156909797056681 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2156909797056681 / 10000000000000000 : ℚ)) + (r' := (2156909797056681 / 1250000000000000 : ℚ)) + (U := (-(1917385680481320352707 / 1250000000000000000000 : ℚ))) + (U' := (681916245643679647293 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8808198518421 / 16000000000000 : ℚ)) + (s := (1386986749430237 / 10000000000000000 : ℚ)) + (q := (2156909797056681 / 10000000000000000 : ℚ)) + (U := (-(1917385680481320352707 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_502_13 : Uω (aρ 13) (bρ 13) (8808198518421 / 16000000000000 : ℝ) ≤ @@ -2955,25 +2602,21 @@ lemma U_503_1 : have hlg : Real.log (8724927254666151 / 16000000000000000 : ℝ) ≤ (-(6064045915001829464321 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8724927254666151 / 16000000000000000 : ℝ) = - (8724927254666151 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8724927254666151 / 8000000000000000 : ℚ)) - (U := (867425887998170535679 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8724927254666151 / 8000000000000000 : ℝ) ≤ - (867425887998170535679 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1090609977417319 / 2000000000000000 : ℝ)) (q := - (8724927254666151 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8724927254666151 / 16000000000000000 : ℚ)) + (r' := (8724927254666151 / 8000000000000000 : ℚ)) + (U := (-(6064045915001829464321 / 10000000000000000000000 : ℚ))) + (U' := (867425887998170535679 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (1090609977417319 / 2000000000000000 : ℚ)) + (q := (8724927254666151 / 16000000000000000 : ℚ)) + (U := (-(6064045915001829464321 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_2 : Uω (aρ 2) (bρ 2) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -2981,25 +2624,21 @@ lemma U_503_2 : have hlg : Real.log (1737326321746531 / 3200000000000000 : ℝ) ≤ (-(1221606949584324856063 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1737326321746531 / 3200000000000000 : ℝ) = - (1737326321746531 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1737326321746531 / 1600000000000000 : ℚ)) - (U := (164687411015675143937 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1737326321746531 / 1600000000000000 : ℝ) ≤ - (164687411015675143937 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (217157973687189 / 400000000000000 : ℝ)) (q := - (1737326321746531 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1737326321746531 / 3200000000000000 : ℚ)) + (r' := (1737326321746531 / 1600000000000000 : ℚ)) + (U := (-(1221606949584324856063 / 2000000000000000000000 : ℚ))) + (U' := (164687411015675143937 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (217157973687189 / 400000000000000 : ℚ)) + (q := (1737326321746531 / 3200000000000000 : ℚ)) + (U := (-(1221606949584324856063 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_3 : Uω (aρ 3) (bρ 3) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3007,25 +2646,21 @@ lemma U_503_3 : have hlg : Real.log (8610010670417763 / 16000000000000000 : ℝ) ≤ (-(3098315821178827396319 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8610010670417763 / 16000000000000000 : ℝ) = - (8610010670417763 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8610010670417763 / 8000000000000000 : ℚ)) - (U := (367420080321172603681 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8610010670417763 / 8000000000000000 : ℝ) ≤ - (367420080321172603681 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (538056927563611 / 1000000000000000 : ℝ)) (q := - (8610010670417763 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8610010670417763 / 16000000000000000 : ℚ)) + (r' := (8610010670417763 / 8000000000000000 : ℚ)) + (U := (-(3098315821178827396319 / 5000000000000000000000 : ℚ))) + (U' := (367420080321172603681 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (538056927563611 / 1000000000000000 : ℚ)) + (q := (8610010670417763 / 16000000000000000 : ℚ)) + (U := (-(3098315821178827396319 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_4 : Uω (aρ 4) (bρ 4) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3033,25 +2668,21 @@ lemma U_503_4 : have hlg : Real.log (42413323994768167 / 80000000000000000 : ℝ) ≤ (-(634564076381066350629 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42413323994768167 / 80000000000000000 : ℝ) = - (42413323994768167 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42413323994768167 / 40000000000000000 : ℚ)) - (U := (58583103918933649371 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42413323994768167 / 40000000000000000 : ℝ) ≤ - (58583103918933649371 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1324920279342737 / 2500000000000000 : ℝ)) (q := - (42413323994768167 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42413323994768167 / 80000000000000000 : ℚ)) + (r' := (42413323994768167 / 40000000000000000 : ℚ)) + (U := (-(634564076381066350629 / 1000000000000000000000 : ℚ))) + (U' := (58583103918933649371 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (1324920279342737 / 2500000000000000 : ℚ)) + (q := (42413323994768167 / 80000000000000000 : ℚ)) + (U := (-(634564076381066350629 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_5 : Uω (aρ 5) (bρ 5) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3059,25 +2690,21 @@ lemma U_503_5 : have hlg : Real.log (41442557229805003 / 80000000000000000 : ℝ) ≤ (-(3288591645766013384659 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41442557229805003 / 80000000000000000 : ℝ) = - (41442557229805003 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41442557229805003 / 40000000000000000 : ℚ)) - (U := (177144255733986615341 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41442557229805003 / 40000000000000000 : ℝ) ≤ - (177144255733986615341 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5175179345465157 / 10000000000000000 : ℝ)) (q := - (41442557229805003 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41442557229805003 / 80000000000000000 : ℚ)) + (r' := (41442557229805003 / 40000000000000000 : ℚ)) + (U := (-(3288591645766013384659 / 5000000000000000000000 : ℚ))) + (U' := (177144255733986615341 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (5175179345465157 / 10000000000000000 : ℚ)) + (q := (41442557229805003 / 80000000000000000 : ℚ)) + (U := (-(3288591645766013384659 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_6 : Uω (aρ 6) (bρ 6) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3085,25 +2712,21 @@ lemma U_503_6 : have hlg : Real.log (40047695818072167 / 80000000000000000 : ℝ) ≤ (-(6919554951870387697571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40047695818072167 / 80000000000000000 : ℝ) = - (40047695818072167 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40047695818072167 / 40000000000000000 : ℚ)) - (U := (11916851129612302429 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (40047695818072167 / 40000000000000000 : ℝ) ≤ - (11916851129612302429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1248426091917987 / 2500000000000000 : ℝ)) (q := - (40047695818072167 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40047695818072167 / 80000000000000000 : ℚ)) + (r' := (40047695818072167 / 40000000000000000 : ℚ)) + (U := (-(6919554951870387697571 / 10000000000000000000000 : ℚ))) + (U' := (11916851129612302429 / 10000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (1248426091917987 / 2500000000000000 : ℚ)) + (q := (40047695818072167 / 80000000000000000 : ℚ)) + (U := (-(6919554951870387697571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_7 : Uω (aρ 7) (bρ 7) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3111,25 +2734,21 @@ lemma U_503_7 : have hlg : Real.log (38138860354343527 / 80000000000000000 : ℝ) ≤ (-(7407929150169422584079 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38138860354343527 / 80000000000000000 : ℝ) = - (38138860354343527 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38138860354343527 / 20000000000000000 : ℚ)) - (U := (6455014455830577415921 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38138860354343527 / 20000000000000000 : ℝ) ≤ - (6455014455830577415921 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1185039220624947 / 2500000000000000 : ℝ)) (q := - (38138860354343527 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38138860354343527 / 80000000000000000 : ℚ)) + (r' := (38138860354343527 / 20000000000000000 : ℚ)) + (U := (-(7407929150169422584079 / 10000000000000000000000 : ℚ))) + (U' := (6455014455830577415921 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (1185039220624947 / 2500000000000000 : ℚ)) + (q := (38138860354343527 / 80000000000000000 : ℚ)) + (U := (-(7407929150169422584079 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_8 : Uω (aρ 8) (bρ 8) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3137,25 +2756,21 @@ lemma U_503_8 : have hlg : Real.log (35635116139077731 / 80000000000000000 : ℝ) ≤ (-(8086950740760240682239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35635116139077731 / 80000000000000000 : ℝ) = - (35635116139077731 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35635116139077731 / 20000000000000000 : ℚ)) - (U := (5775992865239759317761 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35635116139077731 / 20000000000000000 : ℝ) ≤ - (5775992865239759317761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4397762480023339 / 10000000000000000 : ℝ)) (q := - (35635116139077731 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35635116139077731 / 80000000000000000 : ℚ)) + (r' := (35635116139077731 / 20000000000000000 : ℚ)) + (U := (-(8086950740760240682239 / 10000000000000000000000 : ℚ))) + (U' := (5775992865239759317761 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (4397762480023339 / 10000000000000000 : ℚ)) + (q := (35635116139077731 / 80000000000000000 : ℚ)) + (U := (-(8086950740760240682239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_9 : Uω (aρ 9) (bρ 9) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3163,25 +2778,21 @@ lemma U_503_9 : have hlg : Real.log (32467725773847159 / 80000000000000000 : ℝ) ≤ (-(4508900456673071142313 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (32467725773847159 / 80000000000000000 : ℝ) = - (32467725773847159 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32467725773847159 / 20000000000000000 : ℚ)) - (U := (2422571346326928857687 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32467725773847159 / 20000000000000000 : ℝ) ≤ - (2422571346326928857687 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (246680032317231 / 625000000000000 : ℝ)) (q := - (32467725773847159 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32467725773847159 / 80000000000000000 : ℚ)) + (r' := (32467725773847159 / 20000000000000000 : ℚ)) + (U := (-(4508900456673071142313 / 5000000000000000000000 : ℚ))) + (U' := (2422571346326928857687 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (246680032317231 / 625000000000000 : ℚ)) + (q := (32467725773847159 / 80000000000000000 : ℚ)) + (U := (-(4508900456673071142313 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_10 : Uω (aρ 10) (bρ 10) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3189,26 +2800,21 @@ lemma U_503_10 : have hlg : Real.log (28566334052394611 / 80000000000000000 : ℝ) ≤ (-(5148988703631236251007 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28566334052394611 / 80000000000000000 : ℝ) = - (28566334052394611 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28566334052394611 / 20000000000000000 : ℚ)) - (U := (1782483099368763748993 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28566334052394611 / 20000000000000000 : ℝ) ≤ - (1782483099368763748993 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3360091620207559 / 10000000000000000 : ℝ)) (q := - (28566334052394611 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28566334052394611 / 80000000000000000 : ℚ)) + (r' := (28566334052394611 / 20000000000000000 : ℚ)) + (U := (-(5148988703631236251007 / 5000000000000000000000 : ℚ))) + (U' := (1782483099368763748993 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (3360091620207559 / 10000000000000000 : ℚ)) + (q := (28566334052394611 / 80000000000000000 : ℚ)) + (U := (-(5148988703631236251007 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_11 : Uω (aρ 11) (bρ 11) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3216,26 +2822,21 @@ lemma U_503_11 : have hlg : Real.log (23784466929877283 / 80000000000000000 : ℝ) ≤ (-(2425987833100888042973 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23784466929877283 / 80000000000000000 : ℝ) = - (23784466929877283 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23784466929877283 / 20000000000000000 : ℚ)) - (U := (346600888099111957027 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23784466929877283 / 20000000000000000 : ℝ) ≤ - (346600888099111957027 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2583101465783227 / 10000000000000000 : ℝ)) (q := - (23784466929877283 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23784466929877283 / 80000000000000000 : ℚ)) + (r' := (23784466929877283 / 20000000000000000 : ℚ)) + (U := (-(2425987833100888042973 / 2000000000000000000000 : ℚ))) + (U' := (346600888099111957027 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (2583101465783227 / 10000000000000000 : ℚ)) + (q := (23784466929877283 / 80000000000000000 : ℚ)) + (U := (-(2425987833100888042973 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_12 : Uω (aρ 12) (bρ 12) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3243,26 +2844,21 @@ lemma U_503_12 : have hlg : Real.log (3481961518105123 / 16000000000000000 : ℝ) ≤ (-(15249929318392561796379 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3481961518105123 / 16000000000000000 : ℝ) = - (3481961518105123 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3481961518105123 / 2000000000000000 : ℚ)) - (U := (5544486090607438203621 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3481961518105123 / 2000000000000000 : ℝ) ≤ - (5544486090607438203621 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (141313672763031 / 1000000000000000 : ℝ)) (q := - (3481961518105123 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3481961518105123 / 16000000000000000 : ℚ)) + (r' := (3481961518105123 / 2000000000000000 : ℚ)) + (U := (-(15249929318392561796379 / 10000000000000000000000 : ℚ))) + (U' := (5544486090607438203621 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35312680955719 / 64000000000000 : ℚ)) + (s := (141313672763031 / 1000000000000000 : ℚ)) + (q := (3481961518105123 / 16000000000000000 : ℚ)) + (U := (-(15249929318392561796379 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_503_13 : Uω (aρ 13) (bρ 13) (35312680955719 / 64000000000000 : ℝ) ≤ @@ -3375,25 +2971,21 @@ lemma U_504_1 : have hlg : Real.log (21862247708772351 / 40000000000000000 : ℝ) ≤ (-(60411815348335259041 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21862247708772351 / 40000000000000000 : ℝ) = - (21862247708772351 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21862247708772351 / 20000000000000000 : ℚ)) - (U := (8902902681664740959 / 100000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21862247708772351 / 20000000000000000 : ℝ) ≤ - (8902902681664740959 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5465532347822113 / 10000000000000000 : ℝ)) (q := - (21862247708772351 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21862247708772351 / 40000000000000000 : ℚ)) + (r' := (21862247708772351 / 20000000000000000 : ℚ)) + (U := (-(60411815348335259041 / 100000000000000000000 : ℚ))) + (U' := (8902902681664740959 / 100000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (5465532347822113 / 10000000000000000 : ℚ)) + (q := (21862247708772351 / 40000000000000000 : ℚ)) + (U := (-(60411815348335259041 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_2 : Uω (aρ 2) (bρ 2) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3401,25 +2993,21 @@ lemma U_504_2 : have hlg : Real.log (21766510116169791 / 40000000000000000 : ℝ) ≤ (-(3042534492391497808847 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21766510116169791 / 40000000000000000 : ℝ) = - (21766510116169791 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21766510116169791 / 20000000000000000 : ℚ)) - (U := (423201409108502191153 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21766510116169791 / 20000000000000000 : ℝ) ≤ - (423201409108502191153 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5441432564030833 / 10000000000000000 : ℝ)) (q := - (21766510116169791 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21766510116169791 / 40000000000000000 : ℚ)) + (r' := (21766510116169791 / 20000000000000000 : ℚ)) + (U := (-(3042534492391497808847 / 5000000000000000000000 : ℚ))) + (U' := (423201409108502191153 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (5441432564030833 / 10000000000000000 : ℚ)) + (q := (21766510116169791 / 40000000000000000 : ℚ)) + (U := (-(3042534492391497808847 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_3 : Uω (aρ 3) (bρ 3) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3427,25 +3015,21 @@ lemma U_504_3 : have hlg : Real.log (21574962341257021 / 40000000000000000 : ℝ) ≤ (-(6173459623665779297577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21574962341257021 / 40000000000000000 : ℝ) = - (21574962341257021 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21574962341257021 / 20000000000000000 : ℚ)) - (U := (758012179334220702423 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21574962341257021 / 20000000000000000 : ℝ) ≤ - (758012179334220702423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (168532961966389 / 312500000000000 : ℝ)) (q := - (21574962341257021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21574962341257021 / 40000000000000000 : ℚ)) + (r' := (21574962341257021 / 20000000000000000 : ℚ)) + (U := (-(6173459623665779297577 / 10000000000000000000000 : ℚ))) + (U' := (758012179334220702423 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (168532961966389 / 312500000000000 : ℚ)) + (q := (21574962341257021 / 40000000000000000 : ℚ)) + (U := (-(6173459623665779297577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_4 : Uω (aρ 4) (bρ 4) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3453,25 +3037,21 @@ lemma U_504_4 : have hlg : Real.log (21256609949949273 / 40000000000000000 : ℝ) ≤ (-(1580528875958493533667 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21256609949949273 / 40000000000000000 : ℝ) = - (21256609949949273 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21256609949949273 / 20000000000000000 : ℚ)) - (U := (152339074791506466333 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21256609949949273 / 20000000000000000 : ℝ) ≤ - (152339074791506466333 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2656086384167787 / 5000000000000000 : ℝ)) (q := - (21256609949949273 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21256609949949273 / 40000000000000000 : ℚ)) + (r' := (21256609949949273 / 20000000000000000 : ℚ)) + (U := (-(1580528875958493533667 / 2500000000000000000000 : ℚ))) + (U' := (152339074791506466333 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (2656086384167787 / 5000000000000000 : ℚ)) + (q := (21256609949949273 / 40000000000000000 : ℚ)) + (U := (-(1580528875958493533667 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_5 : Uω (aρ 5) (bρ 5) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3479,25 +3059,21 @@ lemma U_504_5 : have hlg : Real.log (20771257389598851 / 40000000000000000 : ℝ) ≤ (-(6553092790598556143351 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20771257389598851 / 40000000000000000 : ℝ) = - (20771257389598851 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20771257389598851 / 20000000000000000 : ℚ)) - (U := (378379012401443856649 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20771257389598851 / 20000000000000000 : ℝ) ≤ - (378379012401443856649 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5187686407495363 / 10000000000000000 : ℝ)) (q := - (20771257389598851 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20771257389598851 / 40000000000000000 : ℚ)) + (r' := (20771257389598851 / 20000000000000000 : ℚ)) + (U := (-(6553092790598556143351 / 10000000000000000000000 : ℚ))) + (U' := (378379012401443856649 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (5187686407495363 / 10000000000000000 : ℚ)) + (q := (20771257389598851 / 40000000000000000 : ℚ)) + (U := (-(6553092790598556143351 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_6 : Uω (aρ 6) (bρ 6) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3505,25 +3081,21 @@ lemma U_504_6 : have hlg : Real.log (20073899461071497 / 40000000000000000 : ℝ) ≤ (-(3447295084451065829983 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20073899461071497 / 40000000000000000 : ℝ) = - (20073899461071497 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20073899461071497 / 20000000000000000 : ℚ)) - (U := (18440817048934170017 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20073899461071497 / 20000000000000000 : ℝ) ≤ - (18440817048934170017 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2503123909185843 / 5000000000000000 : ℝ)) (q := - (20073899461071497 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20073899461071497 / 40000000000000000 : ℚ)) + (r' := (20073899461071497 / 20000000000000000 : ℚ)) + (U := (-(3447295084451065829983 / 5000000000000000000000 : ℚ))) + (U' := (18440817048934170017 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (2503123909185843 / 5000000000000000 : ℚ)) + (q := (20073899461071497 / 40000000000000000 : ℚ)) + (U := (-(3447295084451065829983 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_7 : Uω (aρ 7) (bρ 7) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3531,25 +3103,21 @@ lemma U_504_7 : have hlg : Real.log (19119645233276717 / 40000000000000000 : ℝ) ≤ (-(3690815504439367221797 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19119645233276717 / 40000000000000000 : ℝ) = - (19119645233276717 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19119645233276717 / 10000000000000000 : ℚ)) - (U := (3240656298560632778203 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19119645233276717 / 10000000000000000 : ℝ) ≤ - (3240656298560632778203 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (594097760654287 / 1250000000000000 : ℝ)) (q := - (19119645233276717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19119645233276717 / 40000000000000000 : ℚ)) + (r' := (19119645233276717 / 10000000000000000 : ℚ)) + (U := (-(3690815504439367221797 / 5000000000000000000000 : ℚ))) + (U' := (3240656298560632778203 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (594097760654287 / 1250000000000000 : ℚ)) + (q := (19119645233276717 / 40000000000000000 : ℚ)) + (U := (-(3690815504439367221797 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_8 : Uω (aρ 8) (bρ 8) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3557,25 +3125,21 @@ lemma U_504_8 : have hlg : Real.log (3573625686803071 / 8000000000000000 : ℝ) ≤ (-(1007326077744263590559 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3573625686803071 / 8000000000000000 : ℝ) = - (3573625686803071 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3573625686803071 / 2000000000000000 : ℚ)) - (U := (725541873005736409441 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3573625686803071 / 2000000000000000 : ℝ) ≤ - (725541873005736409441 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (882113067388723 / 2000000000000000 : ℝ)) (q := - (3573625686803071 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3573625686803071 / 8000000000000000 : ℚ)) + (r' := (3573625686803071 / 2000000000000000 : ℚ)) + (U := (-(1007326077744263590559 / 1250000000000000000000 : ℚ))) + (U' := (725541873005736409441 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (882113067388723 / 2000000000000000 : ℚ)) + (q := (3573625686803071 / 8000000000000000 : ℚ)) + (U := (-(1007326077744263590559 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_9 : Uω (aρ 9) (bρ 9) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3583,25 +3147,21 @@ lemma U_504_9 : have hlg : Real.log (16285199201546043 / 40000000000000000 : ℝ) ≤ (-(1123278478412851818853 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16285199201546043 / 40000000000000000 : ℝ) = - (16285199201546043 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16285199201546043 / 10000000000000000 : ℚ)) - (U := (609589472337148181147 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16285199201546043 / 10000000000000000 : ℝ) ≤ - (609589472337148181147 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3960066349068959 / 10000000000000000 : ℝ)) (q := - (16285199201546043 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16285199201546043 / 40000000000000000 : ℚ)) + (r' := (16285199201546043 / 10000000000000000 : ℚ)) + (U := (-(1123278478412851818853 / 1250000000000000000000 : ℚ))) + (U' := (609589472337148181147 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (3960066349068959 / 10000000000000000 : ℚ)) + (q := (16285199201546043 / 40000000000000000 : ℚ)) + (U := (-(1123278478412851818853 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_10 : Uω (aρ 10) (bρ 10) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3609,26 +3169,21 @@ lemma U_504_10 : have hlg : Real.log (14336214918596509 / 40000000000000000 : ℝ) ≤ (-(10260906059422783887687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14336214918596509 / 40000000000000000 : ℝ) = - (14336214918596509 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14336214918596509 / 10000000000000000 : ℚ)) - (U := (3602037546577216112313 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14336214918596509 / 10000000000000000 : ℝ) ≤ - (3602037546577216112313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421766655136149 / 1250000000000000 : ℝ)) (q := - (14336214918596509 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14336214918596509 / 40000000000000000 : ℚ)) + (r' := (14336214918596509 / 10000000000000000 : ℚ)) + (U := (-(10260906059422783887687 / 10000000000000000000000 : ℚ))) + (U' := (3602037546577216112313 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (421766655136149 / 1250000000000000 : ℚ)) + (q := (14336214918596509 / 40000000000000000 : ℚ)) + (U := (-(10260906059422783887687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_11 : Uω (aρ 11) (bρ 11) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3636,26 +3191,21 @@ lemma U_504_11 : have hlg : Real.log (11949658663093087 / 40000000000000000 : ℝ) ≤ (-(755110462113986613171 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11949658663093087 / 40000000000000000 : ℝ) = - (11949658663093087 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11949658663093087 / 10000000000000000 : ℚ)) - (U := (111323513261013386829 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11949658663093087 / 10000000000000000 : ℝ) ≤ - (111323513261013386829 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2599331739542481 / 10000000000000000 : ℝ)) (q := - (11949658663093087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11949658663093087 / 40000000000000000 : ℚ)) + (r' := (11949658663093087 / 10000000000000000 : ℚ)) + (U := (-(755110462113986613171 / 625000000000000000000 : ℚ))) + (U' := (111323513261013386829 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (2599331739542481 / 10000000000000000 : ℚ)) + (q := (11949658663093087 / 40000000000000000 : ℚ)) + (U := (-(755110462113986613171 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_12 : Uω (aρ 12) (bρ 12) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3663,26 +3213,21 @@ lemma U_504_12 : have hlg : Real.log (8781434594056657 / 40000000000000000 : ℝ) ≤ (-(1516239665633792455279 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8781434594056657 / 40000000000000000 : ℝ) = - (8781434594056657 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8781434594056657 / 5000000000000000 : ℚ)) - (U := (563201875266207544721 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8781434594056657 / 5000000000000000 : ℝ) ≤ - (563201875266207544721 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (719459900854633 / 5000000000000000 : ℝ)) (q := - (8781434594056657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8781434594056657 / 40000000000000000 : ℚ)) + (r' := (8781434594056657 / 5000000000000000 : ℚ)) + (U := (-(1516239665633792455279 / 1000000000000000000000 : ℚ))) + (U' := (563201875266207544721 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17696283918877 / 32000000000000 : ℚ)) + (s := (719459900854633 / 5000000000000000 : ℚ)) + (q := (8781434594056657 / 40000000000000000 : ℚ)) + (U := (-(1516239665633792455279 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_504_13 : Uω (aρ 13) (bρ 13) (17696283918877 / 32000000000000 : ℝ) ≤ @@ -3794,25 +3339,21 @@ lemma U_505_1 : have hlg : Real.log (43824354559290113 / 80000000000000000 : ℝ) ≤ (-(6018369313981465330427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43824354559290113 / 80000000000000000 : ℝ) = - (43824354559290113 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43824354559290113 / 40000000000000000 : ℚ)) - (U := (913102489018534669573 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43824354559290113 / 40000000000000000 : ℝ) ≤ - (913102489018534669573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5478014807940497 / 10000000000000000 : ℝ)) (q := - (43824354559290113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43824354559290113 / 80000000000000000 : ℚ)) + (r' := (43824354559290113 / 40000000000000000 : ℚ)) + (U := (-(6018369313981465330427 / 10000000000000000000000 : ℚ))) + (U' := (913102489018534669573 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (5478014807940497 / 10000000000000000 : ℚ)) + (q := (43824354559290113 / 80000000000000000 : ℚ)) + (U := (-(6018369313981465330427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_2 : Uω (aρ 2) (bρ 2) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3820,25 +3361,21 @@ lemma U_505_2 : have hlg : Real.log (43632882404600209 / 80000000000000000 : ℝ) ≤ (-(6062155847207341966241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43632882404600209 / 80000000000000000 : ℝ) = - (43632882404600209 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43632882404600209 / 40000000000000000 : ℚ)) - (U := (869315955792658033759 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43632882404600209 / 40000000000000000 : ℝ) ≤ - (869315955792658033759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5453915781778021 / 10000000000000000 : ℝ)) (q := - (43632882404600209 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43632882404600209 / 80000000000000000 : ℚ)) + (r' := (43632882404600209 / 40000000000000000 : ℚ)) + (U := (-(6062155847207341966241 / 10000000000000000000000 : ℚ))) + (U' := (869315955792658033759 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (5453915781778021 / 10000000000000000 : ℚ)) + (q := (43632882404600209 / 80000000000000000 : ℚ)) + (U := (-(6062155847207341966241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_3 : Uω (aρ 3) (bρ 3) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3846,25 +3383,21 @@ lemma U_505_3 : have hlg : Real.log (43249795954150029 / 80000000000000000 : ℝ) ≤ (-(384396324293936033753 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43249795954150029 / 80000000000000000 : ℝ) = - (43249795954150029 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43249795954150029 / 40000000000000000 : ℚ)) - (U := (48820663393563966247 / 625000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43249795954150029 / 40000000000000000 : ℝ) ≤ - (48820663393563966247 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1351385068878869 / 2500000000000000 : ℝ)) (q := - (43249795954150029 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43249795954150029 / 80000000000000000 : ℚ)) + (r' := (43249795954150029 / 40000000000000000 : ℚ)) + (U := (-(384396324293936033753 / 625000000000000000000 : ℚ))) + (U' := (48820663393563966247 / 625000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (1351385068878869 / 2500000000000000 : ℚ)) + (q := (43249795954150029 / 80000000000000000 : ℚ)) + (U := (-(384396324293936033753 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_4 : Uω (aρ 4) (bρ 4) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3872,25 +3405,21 @@ lemma U_505_4 : have hlg : Real.log (8522623126014137 / 16000000000000000 : ℝ) ≤ (-(6298645498833575554591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8522623126014137 / 16000000000000000 : ℝ) = - (8522623126014137 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8522623126014137 / 8000000000000000 : ℚ)) - (U := (632826304166424445409 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8522623126014137 / 8000000000000000 : ℝ) ≤ - (632826304166424445409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (16639576173627 / 31250000000000 : ℝ)) (q := - (8522623126014137 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8522623126014137 / 16000000000000000 : ℚ)) + (r' := (8522623126014137 / 8000000000000000 : ℚ)) + (U := (-(6298645498833575554591 / 10000000000000000000000 : ℚ))) + (U' := (632826304166424445409 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (16639576173627 / 31250000000000 : ℚ)) + (q := (8522623126014137 / 16000000000000000 : ℚ)) + (U := (-(6298645498833575554591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_5 : Uω (aρ 5) (bρ 5) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3898,25 +3427,21 @@ lemma U_505_5 : have hlg : Real.log (41642471853104017 / 80000000000000000 : ℝ) ≤ (-(6529060299625747032463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41642471853104017 / 80000000000000000 : ℝ) = - (41642471853104017 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41642471853104017 / 40000000000000000 : ℚ)) - (U := (402411503374252967537 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41642471853104017 / 40000000000000000 : ℝ) ≤ - (402411503374252967537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5200193350653973 / 10000000000000000 : ℝ)) (q := - (41642471853104017 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41642471853104017 / 80000000000000000 : ℚ)) + (r' := (41642471853104017 / 40000000000000000 : ℚ)) + (U := (-(6529060299625747032463 / 10000000000000000000000 : ℚ))) + (U' := (402411503374252967537 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (5200193350653973 / 10000000000000000 : ℚ)) + (q := (41642471853104017 / 80000000000000000 : ℚ)) + (U := (-(6529060299625747032463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_6 : Uω (aρ 6) (bρ 6) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3924,25 +3449,21 @@ lemma U_505_6 : have hlg : Real.log (40247900807027701 / 80000000000000000 : ℝ) ≤ (-(858710982215112154227 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40247900807027701 / 80000000000000000 : ℝ) = - (40247900807027701 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40247900807027701 / 40000000000000000 : ℚ)) - (U := (7722993159887845773 / 1250000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40247900807027701 / 40000000000000000 : ℝ) ≤ - (7722993159887845773 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2509395482137447 / 5000000000000000 : ℝ)) (q := - (40247900807027701 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40247900807027701 / 80000000000000000 : ℚ)) + (r' := (40247900807027701 / 40000000000000000 : ℚ)) + (U := (-(858710982215112154227 / 1250000000000000000000 : ℚ))) + (U' := (7722993159887845773 / 1250000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (2509395482137447 / 5000000000000000 : ℚ)) + (q := (40247900807027701 / 80000000000000000 : ℚ)) + (U := (-(858710982215112154227 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_7 : Uω (aρ 7) (bρ 7) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3950,25 +3471,21 @@ lemma U_505_7 : have hlg : Real.log (1533588702705877 / 3200000000000000 : ℝ) ≤ (-(58843221046640534947 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1533588702705877 / 3200000000000000 : ℝ) = - (1533588702705877 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1533588702705877 / 800000000000000 : ℚ)) - (U := (52060327801359465053 / 80000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1533588702705877 / 800000000000000 : ℝ) ≤ - (52060327801359465053 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (47654065351897 / 100000000000000 : ℝ)) (q := - (1533588702705877 / 3200000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1533588702705877 / 3200000000000000 : ℚ)) + (r' := (1533588702705877 / 800000000000000 : ℚ)) + (U := (-(58843221046640534947 / 80000000000000000000 : ℚ))) + (U' := (52060327801359465053 / 80000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (47654065351897 / 100000000000000 : ℚ)) + (q := (1533588702705877 / 3200000000000000 : ℚ)) + (U := (-(58843221046640534947 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_8 : Uω (aρ 8) (bρ 8) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -3976,25 +3493,21 @@ lemma U_505_8 : have hlg : Real.log (35837390267996993 / 80000000000000000 : ℝ) ≤ (-(2007587162204019625203 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35837390267996993 / 80000000000000000 : ℝ) = - (35837390267996993 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35837390267996993 / 20000000000000000 : ℚ)) - (U := (1458148739295980374797 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35837390267996993 / 20000000000000000 : ℝ) ≤ - (1458148739295980374797 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4423366361617217 / 10000000000000000 : ℝ)) (q := - (35837390267996993 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35837390267996993 / 80000000000000000 : ℚ)) + (r' := (35837390267996993 / 20000000000000000 : ℚ)) + (U := (-(2007587162204019625203 / 2500000000000000000000 : ℚ))) + (U' := (1458148739295980374797 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (4423366361617217 / 10000000000000000 : ℚ)) + (q := (35837390267996993 / 80000000000000000 : ℚ)) + (U := (-(2007587162204019625203 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_9 : Uω (aρ 9) (bρ 9) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -4002,25 +3515,21 @@ lemma U_505_9 : have hlg : Real.log (32673052853042553 / 80000000000000000 : ℝ) ≤ (-(8954759677569814852371 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (32673052853042553 / 80000000000000000 : ℝ) = - (32673052853042553 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32673052853042553 / 20000000000000000 : ℚ)) - (U := (4908183928430185147629 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32673052853042553 / 20000000000000000 : ℝ) ≤ - (4908183928430185147629 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3973247636238607 / 10000000000000000 : ℝ)) (q := - (32673052853042553 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32673052853042553 / 80000000000000000 : ℚ)) + (r' := (32673052853042553 / 20000000000000000 : ℚ)) + (U := (-(8954759677569814852371 / 10000000000000000000000 : ℚ))) + (U' := (4908183928430185147629 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (3973247636238607 / 10000000000000000 : ℚ)) + (q := (32673052853042553 / 80000000000000000 : ℚ)) + (U := (-(8954759677569814852371 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_10 : Uω (aρ 10) (bρ 10) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -4028,26 +3537,21 @@ lemma U_505_10 : have hlg : Real.log (1151139071792921 / 3200000000000000 : ℝ) ≤ (-(255599714979519626207 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1151139071792921 / 3200000000000000 : ℝ) = - (1151139071792921 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1151139071792921 / 800000000000000 : ℚ)) - (U := (90973875170480373793 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1151139071792921 / 800000000000000 : ℝ) ≤ - (90973875170480373793 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (135526506207149 / 400000000000000 : ℝ)) (q := - (1151139071792921 / 3200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1151139071792921 / 3200000000000000 : ℚ)) + (r' := (1151139071792921 / 800000000000000 : ℚ)) + (U := (-(255599714979519626207 / 250000000000000000000 : ℚ))) + (U' := (90973875170480373793 / 250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (135526506207149 / 400000000000000 : ℚ)) + (q := (1151139071792921 / 3200000000000000 : ℚ)) + (U := (-(255599714979519626207 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_11 : Uω (aρ 11) (bρ 11) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -4055,26 +3559,21 @@ lemma U_505_11 : have hlg : Real.log (24014003147253777 / 80000000000000000 : ℝ) ≤ (-(6016947547431752205949 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24014003147253777 / 80000000000000000 : ℝ) = - (24014003147253777 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24014003147253777 / 20000000000000000 : ℚ)) - (U := (914524255568247794051 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24014003147253777 / 20000000000000000 : ℝ) ≤ - (914524255568247794051 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2615520869491413 / 10000000000000000 : ℝ)) (q := - (24014003147253777 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24014003147253777 / 80000000000000000 : ℚ)) + (r' := (24014003147253777 / 20000000000000000 : ℚ)) + (U := (-(6016947547431752205949 / 5000000000000000000000 : ℚ))) + (U' := (914524255568247794051 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (2615520869491413 / 10000000000000000 : ℚ)) + (q := (24014003147253777 / 80000000000000000 : ℚ)) + (U := (-(6016947547431752205949 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_12 : Uω (aρ 12) (bρ 12) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -4082,26 +3581,21 @@ lemma U_505_12 : have hlg : Real.log (17714540691209181 / 80000000000000000 : ℝ) ≤ (-(1884551029486662392393 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17714540691209181 / 80000000000000000 : ℝ) = - (17714540691209181 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17714540691209181 / 10000000000000000 : ℚ)) - (U := (714750896638337607607 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17714540691209181 / 10000000000000000 : ℝ) ≤ - (714750896638337607607 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (91522209510329 / 625000000000000 : ℝ)) (q := - (17714540691209181 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17714540691209181 / 80000000000000000 : ℚ)) + (r' := (17714540691209181 / 10000000000000000 : ℚ)) + (U := (-(1884551029486662392393 / 1250000000000000000000 : ℚ))) + (U' := (714750896638337607607 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35472454719789 / 64000000000000 : ℚ)) + (s := (91522209510329 / 625000000000000 : ℚ)) + (q := (17714540691209181 / 80000000000000000 : ℚ)) + (U := (-(1884551029486662392393 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_505_13 : Uω (aρ 13) (bρ 13) (35472454719789 / 64000000000000 : ℝ) ≤ @@ -4212,25 +3706,21 @@ lemma U_506_1 : have hlg : Real.log (2745263356161489 / 5000000000000000 : ℝ) ≤ (-(59956090150079933539 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2745263356161489 / 5000000000000000 : ℝ) = - (2745263356161489 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2745263356161489 / 2500000000000000 : ℚ)) - (U := (9358627879920066461 / 100000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2745263356161489 / 2500000000000000 : ℝ) ≤ - (9358627879920066461 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1372624316861489 / 2500000000000000 : ℝ)) (q := - (2745263356161489 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2745263356161489 / 5000000000000000 : ℚ)) + (r' := (2745263356161489 / 2500000000000000 : ℚ)) + (U := (-(59956090150079933539 / 100000000000000000000 : ℚ))) + (U' := (9358627879920066461 / 100000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (1372624316861489 / 2500000000000000 : ℚ)) + (q := (2745263356161489 / 5000000000000000 : ℚ)) + (U := (-(59956090150079933539 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_2 : Uω (aρ 2) (bρ 2) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4238,25 +3728,21 @@ lemma U_506_2 : have hlg : Real.log (5466593070069701 / 10000000000000000 : ℝ) ≤ (-(6039295094548093923991 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5466593070069701 / 10000000000000000 : ℝ) = - (5466593070069701 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5466593070069701 / 5000000000000000 : ℚ)) - (U := (892176708451906076009 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5466593070069701 / 5000000000000000 : ℝ) ≤ - (892176708451906076009 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2733199497724701 / 5000000000000000 : ℝ)) (q := - (5466593070069701 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5466593070069701 / 10000000000000000 : ℚ)) + (r' := (5466593070069701 / 5000000000000000 : ℚ)) + (U := (-(6039295094548093923991 / 10000000000000000000000 : ℚ))) + (U' := (892176708451906076009 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (2733199497724701 / 5000000000000000 : ℚ)) + (q := (5466593070069701 / 10000000000000000 : ℚ)) + (U := (-(6039295094548093923991 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_3 : Uω (aρ 3) (bρ 3) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4264,24 +3750,21 @@ lemma U_506_3 : have hlg : Real.log (27093541979627 / 50000000000000 : ℝ) ≤ (-(6127276090160940364943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27093541979627 / 50000000000000 : ℝ) = (27093541979627 / 25000000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27093541979627 / 25000000000000 : ℚ)) - (U := (804195712839059635057 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (27093541979627 / 25000000000000 : ℝ) ≤ - (804195712839059635057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13545064383777 / 25000000000000 : ℝ)) (q := - (27093541979627 / 50000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27093541979627 / 50000000000000 : ℚ)) + (r' := (27093541979627 / 25000000000000 : ℚ)) + (U := (-(6127276090160940364943 / 10000000000000000000000 : ℚ))) + (U' := (804195712839059635057 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (13545064383777 / 25000000000000 : ℚ)) + (q := (27093541979627 / 50000000000000 : ℚ)) + (U := (-(6127276090160940364943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_4 : Uω (aρ 4) (bρ 4) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4289,25 +3772,21 @@ lemma U_506_4 : have hlg : Real.log (10678252796628263 / 20000000000000000 : ℝ) ≤ (-(3137615244832883098359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10678252796628263 / 20000000000000000 : ℝ) = - (10678252796628263 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10678252796628263 / 10000000000000000 : ℚ)) - (U := (328120656667116901641 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10678252796628263 / 10000000000000000 : ℝ) ≤ - (328120656667116901641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5337155939353263 / 10000000000000000 : ℝ)) (q := - (10678252796628263 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10678252796628263 / 20000000000000000 : ℚ)) + (r' := (10678252796628263 / 10000000000000000 : ℚ)) + (U := (-(3137615244832883098359 / 5000000000000000000000 : ℚ))) + (U' := (328120656667116901641 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (5337155939353263 / 10000000000000000 : ℚ)) + (q := (10678252796628263 / 20000000000000000 : ℚ)) + (U := (-(3137615244832883098359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_5 : Uω (aρ 5) (bρ 5) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4315,25 +3794,21 @@ lemma U_506_5 : have hlg : Real.log (10435607113736623 / 20000000000000000 : ℝ) ≤ (-(6505085539363036308551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10435607113736623 / 20000000000000000 : ℝ) = - (10435607113736623 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10435607113736623 / 10000000000000000 : ℚ)) - (U := (426386263636963691449 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10435607113736623 / 10000000000000000 : ℝ) ≤ - (426386263636963691449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5212700175796623 / 10000000000000000 : ℝ)) (q := - (10435607113736623 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10435607113736623 / 20000000000000000 : ℚ)) + (r' := (10435607113736623 / 10000000000000000 : ℚ)) + (U := (-(6505085539363036308551 / 10000000000000000000000 : ℚ))) + (U' := (426386263636963691449 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (5212700175796623 / 10000000000000000 : ℚ)) + (q := (10435607113736623 / 20000000000000000 : ℚ)) + (U := (-(6505085539363036308551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_6 : Uω (aρ 6) (bρ 6) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4341,25 +3816,21 @@ lemma U_506_6 : have hlg : Real.log (10087000370461153 / 20000000000000000 : ℝ) ≤ (-(6844847704947540843917 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10087000370461153 / 20000000000000000 : ℝ) = - (10087000370461153 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10087000370461153 / 10000000000000000 : ℚ)) - (U := (86624098052459156083 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10087000370461153 / 10000000000000000 : ℝ) ≤ - (86624098052459156083 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5031333807661153 / 10000000000000000 : ℝ)) (q := - (10087000370461153 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10087000370461153 / 20000000000000000 : ℚ)) + (r' := (10087000370461153 / 10000000000000000 : ℚ)) + (U := (-(6844847704947540843917 / 10000000000000000000000 : ℚ))) + (U' := (86624098052459156083 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (5031333807661153 / 10000000000000000 : ℚ)) + (q := (10087000370461153 / 20000000000000000 : ℚ)) + (U := (-(6844847704947540843917 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_7 : Uω (aρ 7) (bρ 7) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4367,25 +3838,21 @@ lemma U_506_7 : have hlg : Real.log (192200708407459 / 400000000000000 : ℝ) ≤ (-(3664621821379332739513 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (192200708407459 / 400000000000000 : ℝ) = - (192200708407459 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192200708407459 / 100000000000000 : ℚ)) - (U := (3266849981620667260487 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (192200708407459 / 100000000000000 : ℝ) ≤ - (3266849981620667260487 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95560604766659 / 200000000000000 : ℝ)) (q := - (192200708407459 / 400000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192200708407459 / 400000000000000 : ℚ)) + (r' := (192200708407459 / 100000000000000 : ℚ)) + (U := (-(3664621821379332739513 / 5000000000000000000000 : ℚ))) + (U' := (3266849981620667260487 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (95560604766659 / 200000000000000 : ℚ)) + (q := (192200708407459 / 400000000000000 : ℚ)) + (U := (-(3664621821379332739513 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_8 : Uω (aρ 8) (bρ 8) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4393,25 +3860,21 @@ lemma U_506_8 : have hlg : Real.log (2246157275151393 / 5000000000000000 : ℝ) ≤ (-(4001085167470894044969 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2246157275151393 / 5000000000000000 : ℝ) = - (2246157275151393 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2246157275151393 / 1250000000000000 : ℚ)) - (U := (2930386635529105955031 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2246157275151393 / 1250000000000000 : ℝ) ≤ - (2930386635529105955031 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1109041392476393 / 2500000000000000 : ℝ)) (q := - (2246157275151393 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2246157275151393 / 5000000000000000 : ℚ)) + (r' := (2246157275151393 / 1250000000000000 : ℚ)) + (U := (-(4001085167470894044969 / 5000000000000000000000 : ℚ))) + (U' := (2930386635529105955031 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (1109041392476393 / 2500000000000000 : ℚ)) + (q := (2246157275151393 / 5000000000000000 : ℚ)) + (U := (-(4001085167470894044969 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_9 : Uω (aρ 9) (bρ 9) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4419,25 +3882,21 @@ lemma U_506_9 : have hlg : Real.log (8193922326007617 / 20000000000000000 : ℝ) ≤ (-(35693582933142942329 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8193922326007617 / 20000000000000000 : ℝ) = - (8193922326007617 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8193922326007617 / 5000000000000000 : ℚ)) - (U := (19758191490857057671 / 40000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8193922326007617 / 5000000000000000 : ℝ) ≤ - (19758191490857057671 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3986424423667617 / 10000000000000000 : ℝ)) (q := - (8193922326007617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8193922326007617 / 20000000000000000 : ℚ)) + (r' := (8193922326007617 / 5000000000000000 : ℚ)) + (U := (-(35693582933142942329 / 40000000000000000000 : ℚ))) + (U' := (19758191490857057671 / 40000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (3986424423667617 / 10000000000000000 : ℚ)) + (q := (8193922326007617 / 20000000000000000 : ℚ)) + (U := (-(35693582933142942329 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_10 : Uω (aρ 10) (bρ 10) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4445,25 +3904,21 @@ lemma U_506_10 : have hlg : Real.log (722111888233093 / 2000000000000000 : ℝ) ≤ (-(10187223622840232274999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (722111888233093 / 2000000000000000 : ℝ) = - (722111888233093 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (722111888233093 / 500000000000000 : ℚ)) - (U := (3675719983159767725001 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (722111888233093 / 500000000000000 : ℝ) ≤ - (3675719983159767725001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (340218001348593 / 1000000000000000 : ℝ)) (q := - (722111888233093 / 2000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (722111888233093 / 2000000000000000 : ℚ)) + (r' := (722111888233093 / 500000000000000 : ℚ)) + (U := (-(10187223622840232274999 / 10000000000000000000000 : ℚ))) + (U' := (3675719983159767725001 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (340218001348593 / 1000000000000000 : ℚ)) + (q := (722111888233093 / 2000000000000000 : ℚ)) + (U := (-(10187223622840232274999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_11 : Uω (aρ 11) (bρ 11) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4471,25 +3926,21 @@ lemma U_506_11 : have hlg : Real.log (603213185757801 / 2000000000000000 : ℝ) ≤ (-(5993158914446563252359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (603213185757801 / 2000000000000000 : ℝ) = - (603213185757801 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (603213185757801 / 500000000000000 : ℚ)) - (U := (938312888553436747641 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (603213185757801 / 500000000000000 : ℝ) ≤ - (938312888553436747641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (263166961493801 / 1000000000000000 : ℝ)) (q := - (603213185757801 / 2000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (603213185757801 / 2000000000000000 : ℚ)) + (r' := (603213185757801 / 500000000000000 : ℚ)) + (U := (-(5993158914446563252359 / 5000000000000000000000 : ℚ))) + (U' := (938312888553436747641 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (263166961493801 / 1000000000000000 : ℚ)) + (q := (603213185757801 / 2000000000000000 : ℚ)) + (U := (-(5993158914446563252359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_12 : Uω (aρ 12) (bρ 12) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4497,26 +3948,21 @@ lemma U_506_12 : have hlg : Real.log (2233111664528861 / 10000000000000000 : ℝ) ≤ (-(14991891141000413337327 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2233111664528861 / 10000000000000000 : ℝ) = - (2233111664528861 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2233111664528861 / 1250000000000000 : ℚ)) - (U := (5802524267999586662673 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2233111664528861 / 1250000000000000 : ℝ) ≤ - (5802524267999586662673 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (744730591551361 / 5000000000000000 : ℝ)) (q := - (2233111664528861 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2233111664528861 / 10000000000000000 : ℚ)) + (r' := (2233111664528861 / 1250000000000000 : ℚ)) + (U := (-(14991891141000413337327 / 10000000000000000000000 : ℚ))) + (U' := (5802524267999586662673 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (1111010675057 / 2000000000000 : ℚ)) + (s := (744730591551361 / 5000000000000000 : ℚ)) + (q := (2233111664528861 / 10000000000000000 : ℚ)) + (U := (-(14991891141000413337327 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_506_13 : Uω (aρ 13) (bρ 13) (1111010675057 / 2000000000000 : ℝ) ≤ @@ -4629,25 +4075,21 @@ lemma U_507_1 : have hlg : Real.log (44024072835442519 / 80000000000000000 : ℝ) ≤ (-(373306275130817100621 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44024072835442519 / 80000000000000000 : ℝ) = - (44024072835442519 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44024072835442519 / 40000000000000000 : ℚ)) - (U := (59910712556682899379 / 625000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44024072835442519 / 40000000000000000 : ℝ) ≤ - (59910712556682899379 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5502979726342661 / 10000000000000000 : ℝ)) (q := - (44024072835442519 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44024072835442519 / 80000000000000000 : ℚ)) + (r' := (44024072835442519 / 40000000000000000 : ℚ)) + (U := (-(373306275130817100621 / 625000000000000000000 : ℚ))) + (U' := (59910712556682899379 / 625000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (5502979726342661 / 10000000000000000 : ℚ)) + (q := (44024072835442519 / 80000000000000000 : ℚ)) + (U := (-(373306275130817100621 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_2 : Uω (aρ 2) (bρ 2) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4655,25 +4097,21 @@ lemma U_507_2 : have hlg : Real.log (43832606700323227 / 80000000000000000 : ℝ) ≤ (-(3008243243902837444081 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43832606700323227 / 80000000000000000 : ℝ) = - (43832606700323227 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43832606700323227 / 40000000000000000 : ℚ)) - (U := (457492657597162555919 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43832606700323227 / 40000000000000000 : ℝ) ≤ - (457492657597162555919 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2739441102536419 / 5000000000000000 : ℝ)) (q := - (43832606700323227 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43832606700323227 / 80000000000000000 : ℚ)) + (r' := (43832606700323227 / 40000000000000000 : ℚ)) + (U := (-(3008243243902837444081 / 5000000000000000000000 : ℚ))) + (U' := (457492657597162555919 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (2739441102536419 / 5000000000000000 : ℚ)) + (q := (43832606700323227 / 80000000000000000 : ℚ)) + (U := (-(3008243243902837444081 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_3 : Uω (aρ 3) (bρ 3) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4681,25 +4119,21 @@ lemma U_507_3 : have hlg : Real.log (43449538322676247 / 80000000000000000 : ℝ) ≤ (-(6104264082439977002931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43449538322676247 / 80000000000000000 : ℝ) = - (43449538322676247 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43449538322676247 / 40000000000000000 : ℚ)) - (U := (827207720560022997069 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43449538322676247 / 40000000000000000 : ℝ) ≤ - (827207720560022997069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5430511217011093 / 10000000000000000 : ℝ)) (q := - (43449538322676247 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43449538322676247 / 80000000000000000 : ℚ)) + (r' := (43449538322676247 / 40000000000000000 : ℚ)) + (U := (-(6104264082439977002931 / 10000000000000000000000 : ℚ))) + (U' := (827207720560022997069 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (5430511217011093 / 10000000000000000 : ℚ)) + (q := (43449538322676247 / 80000000000000000 : ℚ)) + (U := (-(6104264082439977002931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_4 : Uω (aρ 4) (bρ 4) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4707,25 +4141,21 @@ lemma U_507_4 : have hlg : Real.log (42812906570442639 / 80000000000000000 : ℝ) ≤ (-(6251870219006976036533 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42812906570442639 / 80000000000000000 : ℝ) = - (42812906570442639 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42812906570442639 / 40000000000000000 : ℚ)) - (U := (679601583993023963467 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42812906570442639 / 40000000000000000 : ℝ) ≤ - (679601583993023963467 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5349647460017691 / 10000000000000000 : ℝ)) (q := - (42812906570442639 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42812906570442639 / 80000000000000000 : ℚ)) + (r' := (42812906570442639 / 40000000000000000 : ℚ)) + (U := (-(6251870219006976036533 / 10000000000000000000000 : ℚ))) + (U' := (679601583993023963467 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (5349647460017691 / 10000000000000000 : ℚ)) + (q := (42812906570442639 / 80000000000000000 : ℚ)) + (U := (-(6251870219006976036533 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_5 : Uω (aρ 5) (bρ 5) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4733,25 +4163,21 @@ lemma U_507_5 : have hlg : Real.log (41842384588114851 / 80000000000000000 : ℝ) ≤ (-(6481168232575320061883 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41842384588114851 / 80000000000000000 : ℝ) = - (41842384588114851 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41842384588114851 / 40000000000000000 : ℚ)) - (U := (450303570424679938117 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41842384588114851 / 40000000000000000 : ℝ) ≤ - (450303570424679938117 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (653150860471343 / 1250000000000000 : ℝ)) (q := - (41842384588114851 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41842384588114851 / 80000000000000000 : ℚ)) + (r' := (41842384588114851 / 40000000000000000 : ℚ)) + (U := (-(6481168232575320061883 / 10000000000000000000000 : ℚ))) + (U' := (450303570424679938117 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (653150860471343 / 1250000000000000 : ℚ)) + (q := (41842384588114851 / 80000000000000000 : ℚ)) + (U := (-(6481168232575320061883 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_6 : Uω (aρ 6) (bρ 6) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4759,25 +4185,21 @@ lemma U_507_6 : have hlg : Real.log (8089620191124223 / 16000000000000000 : ℝ) ≤ (-(3410034699783073694907 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8089620191124223 / 16000000000000000 : ℝ) = - (8089620191124223 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8089620191124223 / 8000000000000000 : ℚ)) - (U := (55701201716926305093 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (8089620191124223 / 8000000000000000 : ℝ) ≤ - (55701201716926305093 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (504387635078731 / 1000000000000000 : ℝ)) (q := - (8089620191124223 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8089620191124223 / 16000000000000000 : ℚ)) + (r' := (8089620191124223 / 8000000000000000 : ℚ)) + (U := (-(3410034699783073694907 / 5000000000000000000000 : ℚ))) + (U' := (55701201716926305093 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (504387635078731 / 1000000000000000 : ℚ)) + (q := (8089620191124223 / 16000000000000000 : ℚ)) + (U := (-(3410034699783073694907 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_7 : Uω (aρ 7) (bρ 7) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4785,25 +4207,21 @@ lemma U_507_7 : have hlg : Real.log (38540562831702879 / 80000000000000000 : ℝ) ≤ (-(1460630734883897880289 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38540562831702879 / 80000000000000000 : ℝ) = - (38540562831702879 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38540562831702879 / 20000000000000000 : ℚ)) - (U := (1311957986316102119711 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38540562831702879 / 20000000000000000 : ℝ) ≤ - (1311957986316102119711 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4790653200567751 / 10000000000000000 : ℝ)) (q := - (38540562831702879 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38540562831702879 / 80000000000000000 : ℚ)) + (r' := (38540562831702879 / 20000000000000000 : ℚ)) + (U := (-(1460630734883897880289 / 2000000000000000000000 : ℚ))) + (U' := (1311957986316102119711 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (4790653200567751 / 10000000000000000 : ℚ)) + (q := (38540562831702879 / 80000000000000000 : ℚ)) + (U := (-(1460630734883897880289 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_8 : Uω (aρ 8) (bρ 8) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4811,25 +4229,21 @@ lemma U_507_8 : have hlg : Real.log (36039635334013223 / 80000000000000000 : ℝ) ≤ (-(3987036599165787142513 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36039635334013223 / 80000000000000000 : ℝ) = - (36039635334013223 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36039635334013223 / 20000000000000000 : ℚ)) - (U := (2944435203834212857487 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36039635334013223 / 20000000000000000 : ℝ) ≤ - (2944435203834212857487 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4448962977485337 / 10000000000000000 : ℝ)) (q := - (36039635334013223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36039635334013223 / 80000000000000000 : ℚ)) + (r' := (36039635334013223 / 20000000000000000 : ℚ)) + (U := (-(3987036599165787142513 / 5000000000000000000000 : ℚ))) + (U' := (2944435203834212857487 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (4448962977485337 / 10000000000000000 : ℚ)) + (q := (36039635334013223 / 80000000000000000 : ℚ)) + (U := (-(3987036599165787142513 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_9 : Uω (aρ 9) (bρ 9) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4837,25 +4251,21 @@ lemma U_507_9 : have hlg : Real.log (32878307933950143 / 80000000000000000 : ℝ) ≤ (-(8892135271530491175893 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (32878307933950143 / 80000000000000000 : ℝ) = - (32878307933950143 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32878307933950143 / 20000000000000000 : ℚ)) - (U := (4970808334469508824107 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32878307933950143 / 20000000000000000 : ℝ) ≤ - (4970808334469508824107 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3999596755829567 / 10000000000000000 : ℝ)) (q := - (32878307933950143 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32878307933950143 / 80000000000000000 : ℚ)) + (r' := (32878307933950143 / 20000000000000000 : ℚ)) + (U := (-(8892135271530491175893 / 10000000000000000000000 : ℚ))) + (U' := (4970808334469508824107 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (3999596755829567 / 10000000000000000 : ℚ)) + (q := (32878307933950143 / 80000000000000000 : ℚ)) + (U := (-(8892135271530491175893 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_10 : Uω (aρ 10) (bρ 10) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4863,26 +4273,21 @@ lemma U_507_10 : have hlg : Real.log (28990426634305347 / 80000000000000000 : ℝ) ≤ (-(5075304873631269541131 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28990426634305347 / 80000000000000000 : ℝ) = - (28990426634305347 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28990426634305347 / 20000000000000000 : ℚ)) - (U := (1856166929368730458869 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28990426634305347 / 20000000000000000 : ℝ) ≤ - (1856166929368730458869 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (427023183051671 / 1250000000000000 : ℝ)) (q := - (28990426634305347 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28990426634305347 / 80000000000000000 : ℚ)) + (r' := (28990426634305347 / 20000000000000000 : ℚ)) + (U := (-(5075304873631269541131 / 5000000000000000000000 : ℚ))) + (U' := (1856166929368730458869 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (427023183051671 / 1250000000000000 : ℚ)) + (q := (28990426634305347 / 80000000000000000 : ℚ)) + (U := (-(5075304873631269541131 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_11 : Uω (aρ 11) (bρ 11) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4890,26 +4295,21 @@ lemma U_507_11 : have hlg : Real.log (24242893131011923 / 80000000000000000 : ℝ) ≤ (-(11939031264853494913149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24242893131011923 / 80000000000000000 : ℝ) = - (24242893131011923 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24242893131011923 / 20000000000000000 : ℚ)) - (U := (1923912341146505086851 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24242893131011923 / 20000000000000000 : ℝ) ≤ - (1923912341146505086851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (661944678698753 / 2500000000000000 : ℝ)) (q := - (24242893131011923 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24242893131011923 / 80000000000000000 : ℚ)) + (r' := (24242893131011923 / 20000000000000000 : ℚ)) + (U := (-(11939031264853494913149 / 10000000000000000000000 : ℚ))) + (U' := (1923912341146505086851 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (661944678698753 / 2500000000000000 : ℚ)) + (q := (24242893131011923 / 80000000000000000 : ℚ)) + (U := (-(11939031264853494913149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_12 : Uω (aρ 12) (bρ 12) (35632228483859 / 64000000000000 : ℝ) ≤ @@ -4917,26 +4317,21 @@ lemma U_507_12 : have hlg : Real.log (3602798532646971 / 16000000000000000 : ℝ) ≤ (-(2981755615627733624033 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3602798532646971 / 16000000000000000 : ℝ) = - (3602798532646971 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3602798532646971 / 2000000000000000 : ℚ)) - (U := (1177127466172266375967 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3602798532646971 / 2000000000000000 : ℝ) ≤ - (1177127466172266375967 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (302850738907149 / 2000000000000000 : ℝ)) (q := - (3602798532646971 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3602798532646971 / 16000000000000000 : ℚ)) + (r' := (3602798532646971 / 2000000000000000 : ℚ)) + (U := (-(2981755615627733624033 / 2000000000000000000000 : ℚ))) + (U' := (1177127466172266375967 / 2000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35632228483859 / 64000000000000 : ℚ)) + (s := (302850738907149 / 2000000000000000 : ℚ)) + (q := (3602798532646971 / 16000000000000000 : ℚ)) + (U := (-(2981755615627733624033 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_507_13 : Uω (aρ 13) (bρ 13) (35632228483859 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U42.lean b/LeanPool/Zeta5Irrational/Table/U42.lean index 1327a14988..ef35a60916 100644 --- a/LeanPool/Zeta5Irrational/Table/U42.lean +++ b/LeanPool/Zeta5Irrational/Table/U42.lean @@ -24,25 +24,21 @@ lemma U_508_1 : have hlg : Real.log (4412393196988273 / 8000000000000000 : ℝ) ≤ (-(5950243241019627244583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4412393196988273 / 8000000000000000 : ℝ) = - (4412393196988273 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4412393196988273 / 4000000000000000 : ℚ)) - (U := (981228561980372755417 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4412393196988273 / 4000000000000000 : ℝ) ≤ - (981228561980372755417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1103092436926949 / 2000000000000000 : ℝ)) (q := - (4412393196988273 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4412393196988273 / 8000000000000000 : ℚ)) + (r' := (4412393196988273 / 4000000000000000 : ℚ)) + (U := (-(5950243241019627244583 / 10000000000000000000000 : ℚ))) + (U' := (981228561980372755417 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (1103092436926949 / 2000000000000000 : ℚ)) + (q := (4412393196988273 / 8000000000000000 : ℚ)) + (U := (-(5950243241019627244583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_2 : Uω (aρ 2) (bρ 2) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_508_2 : have hlg : Real.log (21966234412003739 / 40000000000000000 : ℝ) ≤ (-(1498432447403128669001 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21966234412003739 / 40000000000000000 : ℝ) = - (21966234412003739 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21966234412003739 / 20000000000000000 : ℚ)) - (U := (234435503346871330999 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21966234412003739 / 20000000000000000 : ℝ) ≤ - (234435503346871330999 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1372841352668983 / 2500000000000000 : ℝ)) (q := - (21966234412003739 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21966234412003739 / 40000000000000000 : ℚ)) + (r' := (21966234412003739 / 20000000000000000 : ℚ)) + (U := (-(1498432447403128669001 / 2500000000000000000000 : ℚ))) + (U' := (234435503346871330999 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (1372841352668983 / 2500000000000000 : ℚ)) + (q := (21966234412003739 / 40000000000000000 : ℚ)) + (U := (-(1498432447403128669001 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_3 : Uω (aρ 3) (bρ 3) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_508_3 : have hlg : Real.log (21774704710184083 / 40000000000000000 : ℝ) ≤ (-(3040652460816649757537 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21774704710184083 / 40000000000000000 : ℝ) = - (21774704710184083 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21774704710184083 / 20000000000000000 : ℚ)) - (U := (425083440683350242463 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21774704710184083 / 20000000000000000 : ℝ) ≤ - (425083440683350242463 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (680374583264513 / 1250000000000000 : ℝ)) (q := - (21774704710184083 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21774704710184083 / 40000000000000000 : ℚ)) + (r' := (21774704710184083 / 20000000000000000 : ℚ)) + (U := (-(3040652460816649757537 / 5000000000000000000000 : ℚ))) + (U' := (425083440683350242463 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (680374583264513 / 1250000000000000 : ℚ)) + (q := (21774704710184083 / 40000000000000000 : ℚ)) + (U := (-(3040652460816649757537 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_4 : Uω (aρ 4) (bρ 4) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_508_4 : have hlg : Real.log (21456400891532543 / 40000000000000000 : ℝ) ≤ (-(3114282215668375516407 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21456400891532543 / 40000000000000000 : ℝ) = - (21456400891532543 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21456400891532543 / 20000000000000000 : ℚ)) - (U := (351453685831624483593 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21456400891532543 / 20000000000000000 : ℝ) ≤ - (351453685831624483593 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2681069468927667 / 5000000000000000 : ℝ)) (q := - (21456400891532543 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21456400891532543 / 40000000000000000 : ℚ)) + (r' := (21456400891532543 / 20000000000000000 : ℚ)) + (U := (-(3114282215668375516407 / 5000000000000000000000 : ℚ))) + (U' := (351453685831624483593 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (2681069468927667 / 5000000000000000 : ℚ)) + (q := (21456400891532543 / 40000000000000000 : ℚ)) + (U := (-(3114282215668375516407 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_5 : Uω (aρ 5) (bρ 5) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_508_5 : have hlg : Real.log (20971170127983213 / 40000000000000000 : ℝ) ≤ (-(645730810402355959231 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20971170127983213 / 40000000000000000 : ℝ) = - (20971170127983213 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20971170127983213 / 20000000000000000 : ℚ)) - (U := (47416369897644040769 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20971170127983213 / 20000000000000000 : ℝ) ≤ - (47416369897644040769 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5237713475415669 / 10000000000000000 : ℝ)) (q := - (20971170127983213 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20971170127983213 / 40000000000000000 : ℚ)) + (r' := (20971170127983213 / 20000000000000000 : ℚ)) + (U := (-(645730810402355959231 / 1000000000000000000000 : ℚ))) + (U' := (47416369897644040769 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (5237713475415669 / 10000000000000000 : ℚ)) + (q := (20971170127983213 / 40000000000000000 : ℚ)) + (U := (-(645730810402355959231 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_6 : Uω (aρ 6) (bρ 6) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_508_6 : have hlg : Real.log (20274099618647413 / 40000000000000000 : ℝ) ≤ (-(271814105316008456471 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20274099618647413 / 40000000000000000 : ℝ) = - (20274099618647413 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20274099618647413 / 20000000000000000 : ℚ)) - (U := (5444766803991543529 / 400000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20274099618647413 / 20000000000000000 : ℝ) ≤ - (5444766803991543529 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5056418595887769 / 10000000000000000 : ℝ)) (q := - (20274099618647413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20274099618647413 / 40000000000000000 : ℚ)) + (r' := (20274099618647413 / 20000000000000000 : ℚ)) + (U := (-(271814105316008456471 / 400000000000000000000 : ℚ))) + (U' := (5444766803991543529 / 400000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (5056418595887769 / 10000000000000000 : ℚ)) + (q := (20274099618647413 / 40000000000000000 : ℚ)) + (U := (-(271814105316008456471 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_7 : Uω (aρ 7) (bρ 7) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_508_7 : have hlg : Real.log (3864098104164537 / 8000000000000000 : ℝ) ≤ (-(7277132358554394793971 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3864098104164537 / 8000000000000000 : ℝ) = - (3864098104164537 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3864098104164537 / 2000000000000000 : ℚ)) - (U := (6585811247445605206029 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3864098104164537 / 2000000000000000 : ℝ) ≤ - (6585811247445605206029 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (960655085547081 / 2000000000000000 : ℝ)) (q := - (3864098104164537 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3864098104164537 / 8000000000000000 : ℚ)) + (r' := (3864098104164537 / 2000000000000000 : ℚ)) + (U := (-(7277132358554394793971 / 10000000000000000000000 : ℚ))) + (U' := (6585811247445605206029 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (960655085547081 / 2000000000000000 : ℚ)) + (q := (3864098104164537 / 8000000000000000 : ℚ)) + (U := (-(7277132358554394793971 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_8 : Uω (aρ 8) (bρ 8) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_508_8 : have hlg : Real.log (18070373562374121 / 40000000000000000 : ℝ) ≤ (-(7946056761336366334497 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18070373562374121 / 40000000000000000 : ℝ) = - (18070373562374121 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18070373562374121 / 10000000000000000 : ℚ)) - (U := (5916886844663633665503 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18070373562374121 / 10000000000000000 : ℝ) ≤ - (5916886844663633665503 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4461758599851123 / 10000000000000000 : ℝ)) (q := - (18070373562374121 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18070373562374121 / 40000000000000000 : ℚ)) + (r' := (18070373562374121 / 10000000000000000 : ℚ)) + (U := (-(7946056761336366334497 / 10000000000000000000000 : ℚ))) + (U' := (5916886844663633665503 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (4461758599851123 / 10000000000000000 : ℚ)) + (q := (18070373562374121 / 40000000000000000 : ℚ)) + (U := (-(7946056761336366334497 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_9 : Uω (aρ 9) (bρ 9) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_508_9 : have hlg : Real.log (16490454459150151 / 40000000000000000 : ℝ) ≤ (-(1772195515441329619083 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16490454459150151 / 40000000000000000 : ℝ) = - (16490454459150151 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16490454459150151 / 10000000000000000 : ℚ)) - (U := (1000393205758670380917 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16490454459150151 / 10000000000000000 : ℝ) ≤ - (1000393205758670380917 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2006382338299569 / 5000000000000000 : ℝ)) (q := - (16490454459150151 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16490454459150151 / 40000000000000000 : ℚ)) + (r' := (16490454459150151 / 10000000000000000 : ℚ)) + (U := (-(1772195515441329619083 / 2000000000000000000000 : ℚ))) + (U' := (1000393205758670380917 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (2006382338299569 / 5000000000000000 : ℚ)) + (q := (16490454459150151 / 40000000000000000 : ℚ)) + (U := (-(1772195515441329619083 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_10 : Uω (aρ 10) (bρ 10) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_508_10 : have hlg : Real.log (14548165346591567 / 40000000000000000 : ℝ) ≤ (-(10114145609446987792001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14548165346591567 / 40000000000000000 : ℝ) = - (14548165346591567 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14548165346591567 / 10000000000000000 : ℚ)) - (U := (3748797996553012207999 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14548165346591567 / 10000000000000000 : ℝ) ≤ - (3748797996553012207999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1715089576907423 / 5000000000000000 : ℝ)) (q := - (14548165346591567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14548165346591567 / 40000000000000000 : ℚ)) + (r' := (14548165346591567 / 10000000000000000 : ℚ)) + (U := (-(10114145609446987792001 / 10000000000000000000000 : ℚ))) + (U' := (3748797996553012207999 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (1715089576907423 / 5000000000000000 : ℚ)) + (q := (14548165346591567 / 40000000000000000 : ℚ)) + (U := (-(10114145609446987792001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_11 : Uω (aρ 11) (bρ 11) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_508_11 : have hlg : Real.log (12178551563170123 / 40000000000000000 : ℝ) ≤ (-(1189203117663709979711 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12178551563170123 / 40000000000000000 : ℝ) = - (12178551563170123 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12178551563170123 / 10000000000000000 : ℚ)) - (U := (197091242936290020289 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12178551563170123 / 10000000000000000 : ℝ) ≤ - (197091242936290020289 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (665962222077281 / 2500000000000000 : ℝ)) (q := - (12178551563170123 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12178551563170123 / 40000000000000000 : ℚ)) + (r' := (12178551563170123 / 10000000000000000 : ℚ)) + (U := (-(1189203117663709979711 / 1000000000000000000000 : ℚ))) + (U' := (197091242936290020289 / 1000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (665962222077281 / 2500000000000000 : ℚ)) + (q := (12178551563170123 / 40000000000000000 : ℚ)) + (U := (-(1189203117663709979711 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_12 : Uω (aρ 12) (bρ 12) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_508_12 : have hlg : Real.log (9080949655730931 / 40000000000000000 : ℝ) ≤ (-(2965401357108477598221 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9080949655730931 / 40000000000000000 : ℝ) = - (9080949655730931 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9080949655730931 / 5000000000000000 : ℚ)) - (U := (1193481724691522401779 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9080949655730931 / 5000000000000000 : ℝ) ≤ - (1193481724691522401779 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48085875977329 / 312500000000000 : ℝ)) (q := - (9080949655730931 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9080949655730931 / 40000000000000000 : ℚ)) + (r' := (9080949655730931 / 5000000000000000 : ℚ)) + (U := (-(2965401357108477598221 / 2000000000000000000000 : ℚ))) + (U' := (1193481724691522401779 / 2000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (17856057682947 / 32000000000000 : ℚ)) + (s := (48085875977329 / 312500000000000 : ℚ)) + (q := (9080949655730931 / 40000000000000000 : ℚ)) + (U := (-(2965401357108477598221 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_508_13 : Uω (aρ 13) (bρ 13) (17856057682947 / 32000000000000 : ℝ) ≤ @@ -443,25 +392,21 @@ lemma U_509_1 : have hlg : Real.log (44223791101920841 / 80000000000000000 : ℝ) ≤ (-(5927637299159037206243 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44223791101920841 / 80000000000000000 : ℝ) = - (44223791101920841 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44223791101920841 / 40000000000000000 : ℚ)) - (U := (1003834503840962793757 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44223791101920841 / 40000000000000000 : ℝ) ≤ - (1003834503840962793757 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (172748270072697 / 312500000000000 : ℝ)) (q := - (44223791101920841 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44223791101920841 / 80000000000000000 : ℚ)) + (r' := (44223791101920841 / 40000000000000000 : ℚ)) + (U := (-(5927637299159037206243 / 10000000000000000000000 : ℚ))) + (U' := (1003834503840962793757 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (172748270072697 / 312500000000000 : ℚ)) + (q := (44223791101920841 / 80000000000000000 : ℚ)) + (U := (-(5927637299159037206243 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_2 : Uω (aρ 2) (bρ 2) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -469,25 +414,21 @@ lemma U_509_2 : have hlg : Real.log (44032330931719793 / 80000000000000000 : ℝ) ≤ (-(5971024764218213295379 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44032330931719793 / 80000000000000000 : ℝ) = - (44032330931719793 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44032330931719793 / 40000000000000000 : ℚ)) - (U := (960447038781786704621 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44032330931719793 / 40000000000000000 : ℝ) ≤ - (960447038781786704621 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2751924306143021 / 5000000000000000 : ℝ)) (q := - (44032330931719793 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44032330931719793 / 80000000000000000 : ℚ)) + (r' := (44032330931719793 / 40000000000000000 : ℚ)) + (U := (-(5971024764218213295379 / 10000000000000000000000 : ℚ))) + (U' := (960447038781786704621 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (2751924306143021 / 5000000000000000 : ℚ)) + (q := (44032330931719793 / 80000000000000000 : ℚ)) + (U := (-(5971024764218213295379 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_3 : Uω (aρ 3) (bρ 3) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -495,25 +436,21 @@ lemma U_509_3 : have hlg : Real.log (43649280460874297 / 80000000000000000 : ℝ) ≤ (-(6058398365511501288333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43649280460874297 / 80000000000000000 : ℝ) = - (43649280460874297 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43649280460874297 / 40000000000000000 : ℚ)) - (U := (873073437488498711667 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43649280460874297 / 40000000000000000 : ℝ) ≤ - (873073437488498711667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1363870525231167 / 2500000000000000 : ℝ)) (q := - (43649280460874297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43649280460874297 / 80000000000000000 : ℚ)) + (r' := (43649280460874297 / 40000000000000000 : ℚ)) + (U := (-(6058398365511501288333 / 10000000000000000000000 : ℚ))) + (U' := (873073437488498711667 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (1363870525231167 / 2500000000000000 : ℚ)) + (q := (43649280460874297 / 80000000000000000 : ℚ)) + (U := (-(6058398365511501288333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_4 : Uω (aρ 4) (bρ 4) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -521,25 +458,21 @@ lemma U_509_4 : have hlg : Real.log (43012696825574837 / 80000000000000000 : ℝ) ≤ (-(620531287292092823143 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43012696825574837 / 80000000000000000 : ℝ) = - (43012696825574837 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43012696825574837 / 40000000000000000 : ℚ)) - (U := (72615893007907176857 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43012696825574837 / 40000000000000000 : ℝ) ≤ - (72615893007907176857 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5374630373164803 / 10000000000000000 : ℝ)) (q := - (43012696825574837 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43012696825574837 / 80000000000000000 : ℚ)) + (r' := (43012696825574837 / 40000000000000000 : ℚ)) + (U := (-(620531287292092823143 / 1000000000000000000000 : ℚ))) + (U' := (72615893007907176857 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (5374630373164803 / 10000000000000000 : ℚ)) + (q := (43012696825574837 / 80000000000000000 : ℚ)) + (U := (-(620531287292092823143 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_5 : Uω (aρ 5) (bρ 5) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -547,25 +480,21 @@ lemma U_509_5 : have hlg : Real.log (42042295461826521 / 80000000000000000 : ℝ) ≤ (-(201047027513926073651 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42042295461826521 / 80000000000000000 : ℝ) = - (42042295461826521 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42042295461826521 / 40000000000000000 : ℚ)) - (U := (15561466329823926349 / 312500000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42042295461826521 / 40000000000000000 : ℝ) ≤ - (15561466329823926349 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1312554987890681 / 2500000000000000 : ℝ)) (q := - (42042295461826521 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42042295461826521 / 80000000000000000 : ℚ)) + (r' := (42042295461826521 / 40000000000000000 : ℚ)) + (U := (-(201047027513926073651 / 312500000000000000000 : ℚ))) + (U' := (15561466329823926349 / 312500000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (1312554987890681 / 2500000000000000 : ℚ)) + (q := (42042295461826521 / 80000000000000000 : ℚ)) + (U := (-(201047027513926073651 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_6 : Uω (aρ 6) (bρ 6) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -573,25 +502,21 @@ lemma U_509_6 : have hlg : Real.log (8129659267142937 / 16000000000000000 : ℝ) ≤ (-(1692674274647282850247 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8129659267142937 / 16000000000000000 : ℝ) = - (8129659267142937 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8129659267142937 / 8000000000000000 : ℚ)) - (U := (40193676102717149753 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (8129659267142937 / 8000000000000000 : ℝ) ≤ - (40193676102717149753 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1013792109034953 / 2000000000000000 : ℝ)) (q := - (8129659267142937 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8129659267142937 / 16000000000000000 : ℚ)) + (r' := (8129659267142937 / 8000000000000000 : ℚ)) + (U := (-(1692674274647282850247 / 2500000000000000000000 : ℚ))) + (U' := (40193676102717149753 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (1013792109034953 / 2000000000000000 : ℚ)) + (q := (8129659267142937 / 16000000000000000 : ℚ)) + (U := (-(1692674274647282850247 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_7 : Uω (aρ 7) (bρ 7) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -599,25 +524,21 @@ lemma U_509_7 : have hlg : Real.log (7748279266887633 / 16000000000000000 : ℝ) ≤ (-(3625589665429885931267 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7748279266887633 / 16000000000000000 : ℝ) = - (7748279266887633 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7748279266887633 / 4000000000000000 : ℚ)) - (U := (3305882137570114068733 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7748279266887633 / 4000000000000000 : ℝ) ≤ - (3305882137570114068733 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (963179385123127 / 2000000000000000 : ℝ)) (q := - (7748279266887633 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7748279266887633 / 16000000000000000 : ℚ)) + (r' := (7748279266887633 / 4000000000000000 : ℚ)) + (U := (-(3625589665429885931267 / 5000000000000000000000 : ℚ))) + (U' := (3305882137570114068733 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (963179385123127 / 2000000000000000 : ℚ)) + (q := (7748279266887633 / 16000000000000000 : ℚ)) + (U := (-(3625589665429885931267 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_8 : Uω (aρ 8) (bρ 8) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -625,25 +546,21 @@ lemma U_509_8 : have hlg : Real.log (36241851835888241 / 80000000000000000 : ℝ) ≤ (-(7918120550604440884439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36241851835888241 / 80000000000000000 : ℝ) = - (36241851835888241 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36241851835888241 / 20000000000000000 : ℚ)) - (U := (5944823055395559115561 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36241851835888241 / 20000000000000000 : ℝ) ≤ - (5944823055395559115561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2237276226159077 / 5000000000000000 : ℝ)) (q := - (36241851835888241 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36241851835888241 / 80000000000000000 : ℚ)) + (r' := (36241851835888241 / 20000000000000000 : ℚ)) + (U := (-(7918120550604440884439 / 10000000000000000000000 : ℚ))) + (U' := (5944823055395559115561 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (2237276226159077 / 5000000000000000 : ℚ)) + (q := (36241851835888241 / 80000000000000000 : ℚ)) + (U := (-(7918120550604440884439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_9 : Uω (aρ 9) (bρ 9) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -651,25 +568,21 @@ lemma U_509_9 : have hlg : Real.log (33083492430225213 / 80000000000000000 : ℝ) ≤ (-(220748048573075527627 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33083492430225213 / 80000000000000000 : ℝ) = - (33083492430225213 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33083492430225213 / 20000000000000000 : ℚ)) - (U := (125825541576924472373 / 250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (33083492430225213 / 20000000000000000 : ℝ) ≤ - (125825541576924472373 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4025928229262397 / 10000000000000000 : ℝ)) (q := - (33083492430225213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33083492430225213 / 80000000000000000 : ℚ)) + (r' := (33083492430225213 / 20000000000000000 : ℚ)) + (U := (-(220748048573075527627 / 250000000000000000000 : ℚ))) + (U' := (125825541576924472373 / 250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (4025928229262397 / 10000000000000000 : ℚ)) + (q := (33083492430225213 / 80000000000000000 : ℚ)) + (U := (-(220748048573075527627 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_10 : Uω (aρ 10) (bρ 10) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -677,26 +590,21 @@ lemma U_509_10 : have hlg : Real.log (29202188279404597 / 80000000000000000 : ℝ) ≤ (-(157466091658155803863 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29202188279404597 / 80000000000000000 : ℝ) = - (29202188279404597 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29202188279404597 / 20000000000000000 : ℚ)) - (U := (59142402185594196137 / 156250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29202188279404597 / 20000000000000000 : ℝ) ≤ - (59142402185594196137 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3444161225052243 / 10000000000000000 : ℝ)) (q := - (29202188279404597 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29202188279404597 / 80000000000000000 : ℚ)) + (r' := (29202188279404597 / 20000000000000000 : ℚ)) + (U := (-(157466091658155803863 / 156250000000000000000 : ℚ))) + (U' := (59142402185594196137 / 156250000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (3444161225052243 / 10000000000000000 : ℚ)) + (q := (29202188279404597 / 80000000000000000 : ℚ)) + (U := (-(157466091658155803863 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_11 : Uω (aρ 11) (bρ 11) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -704,26 +612,21 @@ lemma U_509_11 : have hlg : Real.log (24471160217405897 / 80000000000000000 : ℝ) ≤ (-(11845313439531267758087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24471160217405897 / 80000000000000000 : ℝ) = - (24471160217405897 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24471160217405897 / 20000000000000000 : ℚ)) - (U := (2017630166468732241913 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24471160217405897 / 20000000000000000 : ℝ) ≤ - (2017630166468732241913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5234142257339 / 19531250000000 : ℝ)) (q := - (24471160217405897 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24471160217405897 / 80000000000000000 : ℚ)) + (r' := (24471160217405897 / 20000000000000000 : ℚ)) + (U := (-(11845313439531267758087 / 10000000000000000000000 : ℚ))) + (U' := (2017630166468732241913 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (5234142257339 / 19531250000000 : ℚ)) + (q := (24471160217405897 / 80000000000000000 : ℚ)) + (U := (-(11845313439531267758087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_12 : Uω (aρ 12) (bρ 12) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -731,26 +634,21 @@ lemma U_509_12 : have hlg : Real.log (18308669336300729 / 80000000000000000 : ℝ) ≤ (-(14746519519992178665709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18308669336300729 / 80000000000000000 : ℝ) = - (18308669336300729 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18308669336300729 / 10000000000000000 : ℚ)) - (U := (6047895889007821334291 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18308669336300729 / 10000000000000000 : ℝ) ≤ - (6047895889007821334291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (390739553041569 / 2500000000000000 : ℝ)) (q := - (18308669336300729 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18308669336300729 / 80000000000000000 : ℚ)) + (r' := (18308669336300729 / 10000000000000000 : ℚ)) + (U := (-(14746519519992178665709 / 10000000000000000000000 : ℚ))) + (U' := (6047895889007821334291 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35792002247929 / 64000000000000 : ℚ)) + (s := (390739553041569 / 2500000000000000 : ℚ)) + (q := (18308669336300729 / 80000000000000000 : ℚ)) + (U := (-(14746519519992178665709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_509_13 : Uω (aρ 13) (bρ 13) (35792002247929 / 64000000000000 : ℝ) ≤ @@ -861,25 +759,21 @@ lemma U_510_1 : have hlg : Real.log (11080912557893271 / 20000000000000000 : ℝ) ≤ (-(5905082345456817827057 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11080912557893271 / 20000000000000000 : ℝ) = - (11080912557893271 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11080912557893271 / 10000000000000000 : ℚ)) - (U := (1026389457543182172943 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11080912557893271 / 10000000000000000 : ℝ) ≤ - (1026389457543182172943 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1385106774855349 / 2500000000000000 : ℝ)) (q := - (11080912557893271 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11080912557893271 / 20000000000000000 : ℚ)) + (r' := (11080912557893271 / 10000000000000000 : ℚ)) + (U := (-(5905082345456817827057 / 10000000000000000000000 : ℚ))) + (U' := (1026389457543182172943 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (1385106774855349 / 2500000000000000 : ℚ)) + (q := (11080912557893271 / 20000000000000000 : ℚ)) + (U := (-(5905082345456817827057 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_2 : Uω (aρ 2) (bρ 2) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -887,25 +781,21 @@ lemma U_510_2 : have hlg : Real.log (11033048255892149 / 20000000000000000 : ℝ) ≤ (-(5948371177474891842903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11033048255892149 / 20000000000000000 : ℝ) = - (11033048255892149 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11033048255892149 / 10000000000000000 : ℚ)) - (U := (983100625525108157097 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11033048255892149 / 10000000000000000 : ℝ) ≤ - (983100625525108157097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2758165904965137 / 5000000000000000 : ℝ)) (q := - (11033048255892149 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11033048255892149 / 20000000000000000 : ℚ)) + (r' := (11033048255892149 / 10000000000000000 : ℚ)) + (U := (-(5948371177474891842903 / 10000000000000000000000 : ℚ))) + (U' := (983100625525108157097 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (2758165904965137 / 5000000000000000 : ℚ)) + (q := (11033048255892149 / 20000000000000000 : ℚ)) + (U := (-(5948371177474891842903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_3 : Uω (aρ 3) (bρ 3) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -913,25 +803,21 @@ lemma U_510_3 : have hlg : Real.log (10937287861146593 / 20000000000000000 : ℝ) ≤ (-(150888604337680130333 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10937287861146593 / 20000000000000000 : ℝ) = - (10937287861146593 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10937287861146593 / 10000000000000000 : ℚ)) - (U := (22398190737319869667 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10937287861146593 / 10000000000000000 : ℝ) ≤ - (22398190737319869667 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2733983760767359 / 5000000000000000 : ℝ)) (q := - (10937287861146593 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10937287861146593 / 20000000000000000 : ℚ)) + (r' := (10937287861146593 / 10000000000000000 : ℚ)) + (U := (-(150888604337680130333 / 250000000000000000000 : ℚ))) + (U' := (22398190737319869667 / 250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (2733983760767359 / 5000000000000000 : ℚ)) + (q := (10937287861146593 / 20000000000000000 : ℚ)) + (U := (-(150888604337680130333 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_4 : Uω (aρ 4) (bρ 4) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -939,25 +825,21 @@ lemma U_510_4 : have hlg : Real.log (1347268490598601 / 2500000000000000 : ℝ) ≤ (-(154552882294875529027 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1347268490598601 / 2500000000000000 : ℝ) = - (1347268490598601 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1347268490598601 / 1250000000000000 : ℚ)) - (U := (18733912780124470973 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1347268490598601 / 1250000000000000 : ℝ) ≤ - (18733912780124470973 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5387121766241933 / 10000000000000000 : ℝ)) (q := - (1347268490598601 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1347268490598601 / 2500000000000000 : ℚ)) + (r' := (1347268490598601 / 1250000000000000 : ℚ)) + (U := (-(154552882294875529027 / 250000000000000000000 : ℚ))) + (U' := (18733912780124470973 / 250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (5387121766241933 / 10000000000000000 : ℚ)) + (q := (1347268490598601 / 2500000000000000 : ℚ)) + (U := (-(154552882294875529027 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_5 : Uω (aρ 5) (bρ 5) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -965,24 +847,21 @@ lemma U_510_5 : have hlg : Real.log (13169453190309 / 25000000000000 : ℝ) ≤ (-(100152473289647147279 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13169453190309 / 25000000000000 : ℝ) = (13169453190309 / 12500000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13169453190309 / 12500000000000 : ℚ)) - (U := (8151773632227852721 / 156250000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (13169453190309 / 12500000000000 : ℝ) ≤ - (8151773632227852721 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (210509052521413 / 400000000000000 : ℝ)) (q := - (13169453190309 / 25000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13169453190309 / 25000000000000 : ℚ)) + (r' := (13169453190309 / 12500000000000 : ℚ)) + (U := (-(100152473289647147279 / 156250000000000000000 : ℚ))) + (U' := (8151773632227852721 / 156250000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (210509052521413 / 400000000000000 : ℚ)) + (q := (13169453190309 / 25000000000000 : ℚ)) + (U := (-(100152473289647147279 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_6 : Uω (aρ 6) (bρ 6) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -990,25 +869,21 @@ lemma U_510_6 : have hlg : Real.log (2037419612982103 / 4000000000000000 : ℝ) ≤ (-(843262811570624237493 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2037419612982103 / 4000000000000000 : ℝ) = - (2037419612982103 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2037419612982103 / 2000000000000000 : ℚ)) - (U := (23171163804375762507 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2037419612982103 / 2000000000000000 : ℝ) ≤ - (23171163804375762507 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63518777510483 / 125000000000000 : ℝ)) (q := - (2037419612982103 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2037419612982103 / 4000000000000000 : ℚ)) + (r' := (2037419612982103 / 2000000000000000 : ℚ)) + (U := (-(843262811570624237493 / 1250000000000000000000 : ℚ))) + (U' := (23171163804375762507 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (63518777510483 / 125000000000000 : ℚ)) + (q := (2037419612982103 / 4000000000000000 : ℚ)) + (U := (-(843262811570624237493 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_7 : Uω (aρ 7) (bρ 7) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1016,25 +891,21 @@ lemma U_510_7 : have hlg : Real.log (388418087329571 / 800000000000000 : ℝ) ≤ (-(7225294229954618860193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (388418087329571 / 800000000000000 : ℝ) = - (388418087329571 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (388418087329571 / 200000000000000 : ℚ)) - (U := (6637649376045381139807 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (388418087329571 / 200000000000000 : ℝ) ≤ - (6637649376045381139807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (24142588499637 / 50000000000000 : ℝ)) (q := - (388418087329571 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (388418087329571 / 800000000000000 : ℚ)) + (r' := (388418087329571 / 200000000000000 : ℚ)) + (U := (-(7225294229954618860193 / 10000000000000000000000 : ℚ))) + (U' := (6637649376045381139807 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (24142588499637 / 50000000000000 : ℚ)) + (q := (388418087329571 / 800000000000000 : ℚ)) + (U := (-(7225294229954618860193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_8 : Uω (aρ 8) (bρ 8) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1042,25 +913,21 @@ lemma U_510_8 : have hlg : Real.log (227143434549919 / 500000000000000 : ℝ) ≤ (-(1578052819405799303733 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (227143434549919 / 500000000000000 : ℝ) = - (227143434549919 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (227143434549919 / 125000000000000 : ℚ)) - (U := (1194535901794200696267 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (227143434549919 / 125000000000000 : ℝ) ≤ - (1194535901794200696267 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (897468910004977 / 2000000000000000 : ℝ)) (q := - (227143434549919 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (227143434549919 / 500000000000000 : ℚ)) + (r' := (227143434549919 / 125000000000000 : ℚ)) + (U := (-(1578052819405799303733 / 2000000000000000000000 : ℚ))) + (U' := (1194535901794200696267 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (897468910004977 / 2000000000000000 : ℚ)) + (q := (227143434549919 / 500000000000000 : ℚ)) + (U := (-(1578052819405799303733 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_9 : Uω (aρ 9) (bρ 9) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1068,25 +935,21 @@ lemma U_510_9 : have hlg : Real.log (518532166258671 / 1250000000000000 : ℝ) ≤ (-(2199741917220122414509 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (518532166258671 / 1250000000000000 : ℝ) = - (518532166258671 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (518532166258671 / 312500000000000 : ℚ)) - (U := (1265993984279877585491 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (518532166258671 / 312500000000000 : ℝ) ≤ - (1265993984279877585491 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4039087456526861 / 10000000000000000 : ℝ)) (q := - (518532166258671 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (518532166258671 / 1250000000000000 : ℚ)) + (r' := (518532166258671 / 312500000000000 : ℚ)) + (U := (-(2199741917220122414509 / 2500000000000000000000 : ℚ))) + (U' := (1265993984279877585491 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (4039087456526861 / 10000000000000000 : ℚ)) + (q := (518532166258671 / 1250000000000000 : ℚ)) + (U := (-(2199741917220122414509 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_10 : Uω (aρ 10) (bρ 10) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1094,25 +957,21 @@ lemma U_510_10 : have hlg : Real.log (366349999458383 / 1000000000000000 : ℝ) ≤ (-(2510415298336719111113 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (366349999458383 / 1000000000000000 : ℝ) = - (366349999458383 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (366349999458383 / 250000000000000 : ℚ)) - (U := (955320603163280888887 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (366349999458383 / 250000000000000 : ℝ) ≤ - (955320603163280888887 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (691626363810157 / 2000000000000000 : ℝ)) (q := - (366349999458383 / 1000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (366349999458383 / 1000000000000000 : ℚ)) + (r' := (366349999458383 / 250000000000000 : ℚ)) + (U := (-(2510415298336719111113 / 2500000000000000000000 : ℚ))) + (U' := (955320603163280888887 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (691626363810157 / 2000000000000000 : ℚ)) + (q := (366349999458383 / 1000000000000000 : ℚ)) + (U := (-(2510415298336719111113 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_11 : Uω (aρ 11) (bρ 11) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1120,26 +979,21 @@ lemma U_510_11 : have hlg : Real.log (1536566695756391 / 5000000000000000 : ℝ) ≤ (-(11798874026815627584347 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1536566695756391 / 5000000000000000 : ℝ) = - (1536566695756391 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1536566695756391 / 1250000000000000 : ℚ)) - (U := (2064069579184372415653 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1536566695756391 / 1250000000000000 : ℝ) ≤ - (2064069579184372415653 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2695875239113689 / 10000000000000000 : ℝ)) (q := - (1536566695756391 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1536566695756391 / 5000000000000000 : ℚ)) + (r' := (1536566695756391 / 1250000000000000 : ℚ)) + (U := (-(11798874026815627584347 / 10000000000000000000000 : ℚ))) + (U' := (2064069579184372415653 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (2695875239113689 / 10000000000000000 : ℚ)) + (q := (1536566695756391 / 5000000000000000 : ℚ)) + (U := (-(11798874026815627584347 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_12 : Uω (aρ 12) (bρ 12) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1147,26 +1001,21 @@ lemma U_510_12 : have hlg : Real.log (4613588689991969 / 20000000000000000 : ℝ) ≤ (-(57293994566708123539 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4613588689991969 / 20000000000000000 : ℝ) = - (4613588689991969 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4613588689991969 / 2500000000000000 : ℚ)) - (U := (23934190624698126461 / 39062500000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4613588689991969 / 2500000000000000 : ℝ) ≤ - (23934190624698126461 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (793448621382547 / 5000000000000000 : ℝ)) (q := - (4613588689991969 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4613588689991969 / 20000000000000000 : ℚ)) + (r' := (4613588689991969 / 2500000000000000 : ℚ)) + (U := (-(57293994566708123539 / 39062500000000000000 : ℚ))) + (U' := (23934190624698126461 / 39062500000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8967972282491 / 16000000000000 : ℚ)) + (s := (793448621382547 / 5000000000000000 : ℚ)) + (q := (4613588689991969 / 20000000000000000 : ℚ)) + (U := (-(57293994566708123539 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_510_13 : Uω (aρ 13) (bρ 13) (8967972282491 / 16000000000000 : ℝ) ≤ @@ -1276,25 +1125,21 @@ lemma U_511_1 : have hlg : Real.log (8884701871771111 / 16000000000000000 : ℝ) ≤ (-(5882578150418441128189 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8884701871771111 / 16000000000000000 : ℝ) = - (8884701871771111 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8884701871771111 / 8000000000000000 : ℚ)) - (U := (1048893652581558871811 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8884701871771111 / 8000000000000000 : ℝ) ≤ - (1048893652581558871811 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1110581911184809 / 2000000000000000 : ℝ)) (q := - (8884701871771111 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8884701871771111 / 16000000000000000 : ℚ)) + (r' := (8884701871771111 / 8000000000000000 : ℚ)) + (U := (-(5882578150418441128189 / 10000000000000000000000 : ℚ))) + (U' := (1048893652581558871811 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (1110581911184809 / 2000000000000000 : ℚ)) + (q := (8884701871771111 / 16000000000000000 : ℚ)) + (U := (-(5882578150418441128189 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_2 : Uω (aρ 2) (bρ 2) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1302,25 +1147,21 @@ lemma U_511_2 : have hlg : Real.log (44232055099661343 / 80000000000000000 : ℝ) ≤ (-(592576879682269358441 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44232055099661343 / 80000000000000000 : ℝ) = - (44232055099661343 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44232055099661343 / 40000000000000000 : ℚ)) - (U := (100570300617730641559 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44232055099661343 / 40000000000000000 : ℝ) ≤ - (100570300617730641559 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1382203750908873 / 2500000000000000 : ℝ)) (q := - (44232055099661343 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44232055099661343 / 80000000000000000 : ℚ)) + (r' := (44232055099661343 / 40000000000000000 : ℚ)) + (U := (-(592576879682269358441 / 1000000000000000000000 : ℚ))) + (U' := (100570300617730641559 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (1382203750908873 / 2500000000000000 : ℚ)) + (q := (44232055099661343 / 80000000000000000 : ℚ)) + (U := (-(592576879682269358441 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_3 : Uω (aρ 3) (bρ 3) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1328,25 +1169,21 @@ lemma U_511_3 : have hlg : Real.log (43849022371892547 / 80000000000000000 : ℝ) ≤ (-(300637105334994580849 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43849022371892547 / 80000000000000000 : ℝ) = - (43849022371892547 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43849022371892547 / 40000000000000000 : ℚ)) - (U := (45936484815005419151 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43849022371892547 / 40000000000000000 : ℝ) ≤ - (45936484815005419151 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5480452928043293 / 10000000000000000 : ℝ)) (q := - (43849022371892547 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43849022371892547 / 80000000000000000 : ℚ)) + (r' := (43849022371892547 / 40000000000000000 : ℚ)) + (U := (-(300637105334994580849 / 500000000000000000000 : ℚ))) + (U' := (45936484815005419151 / 500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (5480452928043293 / 10000000000000000 : ℚ)) + (q := (43849022371892547 / 80000000000000000 : ℚ)) + (U := (-(300637105334994580849 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_4 : Uω (aρ 4) (bρ 4) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1354,25 +1191,21 @@ lemma U_511_4 : have hlg : Real.log (1728499456199147 / 3200000000000000 : ℝ) ≤ (-(6158971437747780164537 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1728499456199147 / 3200000000000000 : ℝ) = - (1728499456199147 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1728499456199147 / 1600000000000000 : ℚ)) - (U := (772500365252219835463 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1728499456199147 / 1600000000000000 : ℝ) ≤ - (772500365252219835463 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (215984524695193 / 400000000000000 : ℝ)) (q := - (1728499456199147 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1728499456199147 / 3200000000000000 : ℚ)) + (r' := (1728499456199147 / 1600000000000000 : ℚ)) + (U := (-(6158971437747780164537 / 10000000000000000000000 : ℚ))) + (U' := (772500365252219835463 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (215984524695193 / 400000000000000 : ℚ)) + (q := (1728499456199147 / 3200000000000000 : ℚ)) + (U := (-(6158971437747780164537 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_5 : Uω (aρ 5) (bρ 5) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1380,25 +1213,21 @@ lemma U_511_5 : have hlg : Real.log (42242204500715663 / 80000000000000000 : ℝ) ≤ (-(1277213612986815760097 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42242204500715663 / 80000000000000000 : ℝ) = - (42242204500715663 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42242204500715663 / 40000000000000000 : ℚ)) - (U := (109080747613184239903 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42242204500715663 / 40000000000000000 : ℝ) ≤ - (109080747613184239903 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (329702035040567 / 625000000000000 : ℝ)) (q := - (42242204500715663 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42242204500715663 / 80000000000000000 : ℚ)) + (r' := (42242204500715663 / 40000000000000000 : ℚ)) + (U := (-(1277213612986815760097 / 2000000000000000000000 : ℚ))) + (U' := (109080747613184239903 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (329702035040567 / 625000000000000 : ℚ)) + (q := (42242204500715663 / 80000000000000000 : ℚ)) + (U := (-(1277213612986815760097 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_6 : Uω (aρ 6) (bρ 6) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1406,25 +1235,21 @@ lemma U_511_6 : have hlg : Real.log (40848487017751843 / 80000000000000000 : ℝ) ≤ (-(6721568513029647007487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40848487017751843 / 80000000000000000 : ℝ) = - (40848487017751843 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40848487017751843 / 40000000000000000 : ℚ)) - (U := (209903289970352992513 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40848487017751843 / 40000000000000000 : ℝ) ≤ - (209903289970352992513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5094043565048117 / 10000000000000000 : ℝ)) (q := - (40848487017751843 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40848487017751843 / 80000000000000000 : ℚ)) + (r' := (40848487017751843 / 40000000000000000 : ℚ)) + (U := (-(6721568513029647007487 / 10000000000000000000000 : ℚ))) + (U' := (209903289970352992513 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (5094043565048117 / 10000000000000000 : ℚ)) + (q := (40848487017751843 / 80000000000000000 : ℚ)) + (U := (-(6721568513029647007487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_7 : Uω (aρ 7) (bρ 7) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1432,25 +1257,21 @@ lemma U_511_7 : have hlg : Real.log (38942218259838171 / 80000000000000000 : ℝ) ≤ (-(359973834867452409587 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38942218259838171 / 80000000000000000 : ℝ) = - (38942218259838171 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38942218259838171 / 20000000000000000 : ℚ)) - (U := (333173345432547590413 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38942218259838171 / 20000000000000000 : ℝ) ≤ - (333173345432547590413 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4841137756329699 / 10000000000000000 : ℝ)) (q := - (38942218259838171 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38942218259838171 / 80000000000000000 : ℚ)) + (r' := (38942218259838171 / 20000000000000000 : ℚ)) + (U := (-(359973834867452409587 / 500000000000000000000 : ℚ))) + (U' := (333173345432547590413 / 500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (4841137756329699 / 10000000000000000 : ℚ)) + (q := (38942218259838171 / 80000000000000000 : ℚ)) + (U := (-(359973834867452409587 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_8 : Uω (aρ 8) (bρ 8) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1458,25 +1279,21 @@ lemma U_511_8 : have hlg : Real.log (36444040260901687 / 80000000000000000 : ℝ) ≤ (-(491405433481033414363 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36444040260901687 / 80000000000000000 : ℝ) = - (36444040260901687 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36444040260901687 / 20000000000000000 : ℚ)) - (U := (375028541893966585637 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36444040260901687 / 20000000000000000 : ℝ) ≤ - (375028541893966585637 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2250067453967789 / 5000000000000000 : ℝ)) (q := - (36444040260901687 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36444040260901687 / 80000000000000000 : ℚ)) + (r' := (36444040260901687 / 20000000000000000 : ℚ)) + (U := (-(491405433481033414363 / 625000000000000000000 : ℚ))) + (U' := (375028541893966585637 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (2250067453967789 / 5000000000000000 : ℚ)) + (q := (36444040260901687 / 80000000000000000 : ℚ)) + (U := (-(491405433481033414363 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_9 : Uω (aρ 9) (bρ 9) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1484,25 +1301,21 @@ lemma U_511_9 : have hlg : Real.log (1331544308713791 / 3200000000000000 : ℝ) ≤ (-(4384057031379989668599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1331544308713791 / 3200000000000000 : ℝ) = - (1331544308713791 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1331544308713791 / 800000000000000 : ℚ)) - (U := (2547414771620010331401 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1331544308713791 / 800000000000000 : ℝ) ≤ - (2547414771620010331401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (81044848010627 / 200000000000000 : ℝ)) (q := - (1331544308713791 / 3200000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1331544308713791 / 3200000000000000 : ℚ)) + (r' := (1331544308713791 / 800000000000000 : ℚ)) + (U := (-(4384057031379989668599 / 5000000000000000000000 : ℚ))) + (U' := (2547414771620010331401 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (81044848010627 / 200000000000000 : ℚ)) + (q := (1331544308713791 / 3200000000000000 : ℚ)) + (U := (-(4384057031379989668599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_10 : Uω (aρ 10) (bρ 10) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1510,26 +1323,21 @@ lemma U_511_10 : have hlg : Real.log (29413766279150527 / 80000000000000000 : ℝ) ≤ (-(10005638286124311866309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29413766279150527 / 80000000000000000 : ℝ) = - (29413766279150527 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29413766279150527 / 20000000000000000 : ℚ)) - (U := (3857305319875688133691 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29413766279150527 / 20000000000000000 : ℝ) ≤ - (3857305319875688133691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (868022768588197 / 2500000000000000 : ℝ)) (q := - (29413766279150527 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29413766279150527 / 80000000000000000 : ℚ)) + (r' := (29413766279150527 / 20000000000000000 : ℚ)) + (U := (-(10005638286124311866309 / 10000000000000000000000 : ℚ))) + (U' := (3857305319875688133691 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (868022768588197 / 2500000000000000 : ℚ)) + (q := (29413766279150527 / 80000000000000000 : ℚ)) + (U := (-(10005638286124311866309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_11 : Uω (aρ 11) (bρ 11) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1537,26 +1345,21 @@ lemma U_511_11 : have hlg : Real.log (24698826527652611 / 80000000000000000 : ℝ) ≤ (-(11752709006505664412089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24698826527652611 / 80000000000000000 : ℝ) = - (24698826527652611 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24698826527652611 / 20000000000000000 : ℚ)) - (U := (2110234599494335587911 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24698826527652611 / 20000000000000000 : ℝ) ≤ - (2110234599494335587911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2711832762683309 / 10000000000000000 : ℝ)) (q := - (24698826527652611 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24698826527652611 / 80000000000000000 : ℚ)) + (r' := (24698826527652611 / 20000000000000000 : ℚ)) + (U := (-(11752709006505664412089 / 10000000000000000000000 : ℚ))) + (U' := (2110234599494335587911 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (2711832762683309 / 10000000000000000 : ℚ)) + (q := (24698826527652611 / 80000000000000000 : ℚ)) + (U := (-(11752709006505664412089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_12 : Uω (aρ 12) (bρ 12) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1564,26 +1367,21 @@ lemma U_511_12 : have hlg : Real.log (18599003945990127 / 80000000000000000 : ℝ) ≤ (-(3647296514749162681049 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18599003945990127 / 80000000000000000 : ℝ) = - (18599003945990127 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18599003945990127 / 10000000000000000 : ℚ)) - (U := (1551307337500837318951 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18599003945990127 / 10000000000000000 : ℝ) ≤ - (1551307337500837318951 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100661075872043 / 625000000000000 : ℝ)) (q := - (18599003945990127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18599003945990127 / 80000000000000000 : ℚ)) + (r' := (18599003945990127 / 10000000000000000 : ℚ)) + (U := (-(3647296514749162681049 / 2500000000000000000000 : ℚ))) + (U' := (1551307337500837318951 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (35951776011999 / 64000000000000 : ℚ)) + (s := (100661075872043 / 625000000000000 : ℚ)) + (q := (18599003945990127 / 80000000000000000 : ℚ)) + (U := (-(3647296514749162681049 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_511_13 : Uω (aρ 13) (bρ 13) (35951776011999 / 64000000000000 : ℝ) ≤ @@ -1696,25 +1494,21 @@ lemma U_512_1 : have hlg : Real.log (22261684241892097 / 40000000000000000 : ℝ) ≤ (-(1465031121523832597231 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22261684241892097 / 40000000000000000 : ℝ) = - (22261684241892097 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22261684241892097 / 20000000000000000 : ℚ)) - (U := (267836829226167402769 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22261684241892097 / 20000000000000000 : ℝ) ≤ - (267836829226167402769 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1391348002959559 / 2500000000000000 : ℝ)) (q := - (22261684241892097 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22261684241892097 / 40000000000000000 : ℚ)) + (r' := (22261684241892097 / 20000000000000000 : ℚ)) + (U := (-(1465031121523832597231 / 2500000000000000000000 : ℚ))) + (U' := (267836829226167402769 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (1391348002959559 / 2500000000000000 : ℚ)) + (q := (22261684241892097 / 40000000000000000 : ℚ)) + (U := (-(1465031121523832597231 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_2 : Uω (aρ 2) (bρ 2) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1722,25 +1516,21 @@ lemma U_512_2 : have hlg : Real.log (22165958580052259 / 40000000000000000 : ℝ) ≤ (-(368951086954716155551 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22165958580052259 / 40000000000000000 : ℝ) = - (22165958580052259 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22165958580052259 / 20000000000000000 : ℚ)) - (U := (64265900732783844449 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22165958580052259 / 20000000000000000 : ℝ) ≤ - (64265900732783844449 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5541298193428317 / 10000000000000000 : ℝ)) (q := - (22165958580052259 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22165958580052259 / 40000000000000000 : ℚ)) + (r' := (22165958580052259 / 20000000000000000 : ℚ)) + (U := (-(368951086954716155551 / 625000000000000000000 : ℚ))) + (U' := (64265900732783844449 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (5541298193428317 / 10000000000000000 : ℚ)) + (q := (22165958580052259 / 40000000000000000 : ℚ)) + (U := (-(368951086954716155551 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_3 : Uω (aρ 3) (bρ 3) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1748,25 +1538,21 @@ lemma U_512_3 : have hlg : Real.log (21974446621588729 / 40000000000000000 : ℝ) ≤ (-(5989991927800893399251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21974446621588729 / 40000000000000000 : ℝ) = - (21974446621588729 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21974446621588729 / 20000000000000000 : ℚ)) - (U := (941479875199106600749 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21974446621588729 / 20000000000000000 : ℝ) ≤ - (941479875199106600749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (686617290068319 / 1250000000000000 : ℝ)) (q := - (21974446621588729 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21974446621588729 / 40000000000000000 : ℚ)) + (r' := (21974446621588729 / 20000000000000000 : ℚ)) + (U := (-(5989991927800893399251 / 10000000000000000000000 : ℚ))) + (U' := (941479875199106600749 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (686617290068319 / 1250000000000000 : ℚ)) + (q := (21974446621588729 / 40000000000000000 : ℚ)) + (U := (-(5989991927800893399251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_4 : Uω (aρ 4) (bρ 4) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1774,25 +1560,21 @@ lemma U_512_4 : have hlg : Real.log (21656190472103367 / 40000000000000000 : ℝ) ≤ (-(6135881062304958525311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21656190472103367 / 40000000000000000 : ℝ) = - (21656190472103367 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21656190472103367 / 20000000000000000 : ℚ)) - (U := (795590740695041474689 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21656190472103367 / 20000000000000000 : ℝ) ≤ - (795590740695041474689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5412104426868871 / 10000000000000000 : ℝ)) (q := - (21656190472103367 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21656190472103367 / 40000000000000000 : ℚ)) + (r' := (21656190472103367 / 20000000000000000 : ℚ)) + (U := (-(6135881062304958525311 / 10000000000000000000000 : ℚ))) + (U' := (795590740695041474689 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (5412104426868871 / 10000000000000000 : ℚ)) + (q := (21656190472103367 / 40000000000000000 : ℚ)) + (U := (-(6135881062304958525311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_5 : Uω (aρ 5) (bρ 5) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1800,25 +1582,21 @@ lemma U_512_5 : have hlg : Real.log (21171079170119309 / 40000000000000000 : ℝ) ≤ (-(318121696809580573499 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21171079170119309 / 40000000000000000 : ℝ) = - (21171079170119309 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21171079170119309 / 20000000000000000 : ℚ)) - (U := (28451893340419426501 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21171079170119309 / 20000000000000000 : ℝ) ≤ - (28451893340419426501 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2643869347605921 / 5000000000000000 : ℝ)) (q := - (21171079170119309 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21171079170119309 / 40000000000000000 : ℚ)) + (r' := (21171079170119309 / 20000000000000000 : ℚ)) + (U := (-(318121696809580573499 / 500000000000000000000 : ℚ))) + (U' := (28451893340419426501 / 500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (2643869347605921 / 5000000000000000 : ℚ)) + (q := (21171079170119309 / 40000000000000000 : ℚ)) + (U := (-(318121696809580573499 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_6 : Uω (aρ 6) (bρ 6) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1826,25 +1604,21 @@ lemma U_512_6 : have hlg : Real.log (20474290309316747 / 40000000000000000 : ℝ) ≤ (-(1674273715108017435577 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20474290309316747 / 40000000000000000 : ℝ) = - (20474290309316747 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20474290309316747 / 20000000000000000 : ℚ)) - (U := (58594235641982564423 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20474290309316747 / 20000000000000000 : ℝ) ≤ - (58594235641982564423 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5106584639950561 / 10000000000000000 : ℝ)) (q := - (20474290309316747 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20474290309316747 / 40000000000000000 : ℚ)) + (r' := (20474290309316747 / 20000000000000000 : ℚ)) + (U := (-(1674273715108017435577 / 2500000000000000000000 : ℚ))) + (U' := (58594235641982564423 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (5106584639950561 / 10000000000000000 : ℚ)) + (q := (20474290309316747 / 40000000000000000 : ℚ)) + (U := (-(1674273715108017435577 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_7 : Uω (aρ 7) (bρ 7) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1852,25 +1626,21 @@ lemma U_512_7 : have hlg : Real.log (19521312468740329 / 40000000000000000 : ℝ) ≤ (-(7173726377413230075053 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19521312468740329 / 40000000000000000 : ℝ) = - (19521312468740329 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19521312468740329 / 10000000000000000 : ℚ)) - (U := (6689217228586769924947 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19521312468740329 / 10000000000000000 : ℝ) ≤ - (6689217228586769924947 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (303359818776397 / 625000000000000 : ℝ)) (q := - (19521312468740329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19521312468740329 / 40000000000000000 : ℚ)) + (r' := (19521312468740329 / 10000000000000000 : ℚ)) + (U := (-(7173726377413230075053 / 10000000000000000000000 : ℚ))) + (U' := (6689217228586769924947 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (303359818776397 / 625000000000000 : ℚ)) + (q := (19521312468740329 / 40000000000000000 : ℚ)) + (U := (-(7173726377413230075053 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_8 : Uω (aρ 8) (bρ 8) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1878,25 +1648,21 @@ lemma U_512_8 : have hlg : Real.log (18272562046901279 / 40000000000000000 : ℝ) ≤ (-(1958697151459010594993 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18272562046901279 / 40000000000000000 : ℝ) = - (18272562046901279 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18272562046901279 / 10000000000000000 : ℚ)) - (U := (1507038750040989405007 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18272562046901279 / 10000000000000000 : ℝ) ≤ - (1507038750040989405007 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4512923540842827 / 10000000000000000 : ℝ)) (q := - (18272562046901279 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18272562046901279 / 40000000000000000 : ℚ)) + (r' := (18272562046901279 / 10000000000000000 : ℚ)) + (U := (-(1958697151459010594993 / 2500000000000000000000 : ℚ))) + (U' := (1507038750040989405007 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (4512923540842827 / 10000000000000000 : ℚ)) + (q := (18272562046901279 / 40000000000000000 : ℚ)) + (U := (-(1958697151459010594993 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_9 : Uω (aρ 9) (bρ 9) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1904,25 +1670,21 @@ lemma U_512_9 : have hlg : Real.log (3339113982841381 / 8000000000000000 : ℝ) ≤ (-(1747472087922510415983 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3339113982841381 / 8000000000000000 : ℝ) = - (3339113982841381 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3339113982841381 / 2000000000000000 : ℚ)) - (U := (1025116633277489584017 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3339113982841381 / 2000000000000000 : ℝ) ≤ - (1025116633277489584017 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101634827571391 / 250000000000000 : ℝ)) (q := - (3339113982841381 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3339113982841381 / 8000000000000000 : ℚ)) + (r' := (3339113982841381 / 2000000000000000 : ℚ)) + (U := (-(1747472087922510415983 / 2000000000000000000000 : ℚ))) + (U' := (1025116633277489584017 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (101634827571391 / 250000000000000 : ℚ)) + (q := (3339113982841381 / 8000000000000000 : ℚ)) + (U := (-(1747472087922510415983 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_10 : Uω (aρ 10) (bρ 10) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1930,26 +1692,21 @@ lemma U_512_10 : have hlg : Real.log (14759743895845517 / 40000000000000000 : ℝ) ≤ (-(9969759858022321014881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14759743895845517 / 40000000000000000 : ℝ) = - (14759743895845517 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14759743895845517 / 10000000000000000 : ℚ)) - (U := (3893183747977678985119 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14759743895845517 / 10000000000000000 : ℝ) ≤ - (3893183747977678985119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1743019563584973 / 5000000000000000 : ℝ)) (q := - (14759743895845517 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14759743895845517 / 40000000000000000 : ℚ)) + (r' := (14759743895845517 / 10000000000000000 : ℚ)) + (U := (-(9969759858022321014881 / 10000000000000000000000 : ℚ))) + (U' := (3893183747977678985119 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (1743019563584973 / 5000000000000000 : ℚ)) + (q := (14759743895845517 / 40000000000000000 : ℚ)) + (U := (-(9969759858022321014881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_11 : Uω (aρ 11) (bρ 11) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1957,26 +1714,21 @@ lemma U_512_11 : have hlg : Real.log (12406220496522309 / 40000000000000000 : ℝ) ≤ (-(2926703634558700865789 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12406220496522309 / 40000000000000000 : ℝ) = - (12406220496522309 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12406220496522309 / 10000000000000000 : ℚ)) - (U := (539032266941299134211 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12406220496522309 / 10000000000000000 : ℝ) ≤ - (539032266941299134211 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1363877026856671 / 5000000000000000 : ℝ)) (q := - (12406220496522309 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12406220496522309 / 40000000000000000 : ℚ)) + (r' := (12406220496522309 / 10000000000000000 : ℚ)) + (U := (-(2926703634558700865789 / 2500000000000000000000 : ℚ))) + (U' := (539032266941299134211 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (1363877026856671 / 5000000000000000 : ℚ)) + (q := (12406220496522309 / 40000000000000000 : ℚ)) + (U := (-(2926703634558700865789 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_12 : Uω (aρ 12) (bρ 12) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -1984,26 +1736,21 @@ lemma U_512_12 : have hlg : Real.log (9371330972906951 / 40000000000000000 : ℝ) ≤ (-(1814030401212492219359 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9371330972906951 / 40000000000000000 : ℝ) = - (9371330972906951 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9371330972906951 / 5000000000000000 : ℚ)) - (U := (785271524912507780641 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9371330972906951 / 5000000000000000 : ℝ) ≤ - (785271524912507780641 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1634009388590663 / 10000000000000000 : ℝ)) (q := - (9371330972906951 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9371330972906951 / 40000000000000000 : ℚ)) + (r' := (9371330972906951 / 5000000000000000 : ℚ)) + (U := (-(1814030401212492219359 / 1250000000000000000000 : ℚ))) + (U' := (785271524912507780641 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (18015831447017 / 32000000000000 : ℚ)) + (s := (1634009388590663 / 10000000000000000 : ℚ)) + (q := (9371330972906951 / 40000000000000000 : ℚ)) + (U := (-(1814030401212492219359 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_512_13 : Uω (aρ 13) (bρ 13) (18015831447017 / 32000000000000 : ℝ) ≤ @@ -2115,25 +1862,21 @@ lemma U_513_1 : have hlg : Real.log (8924645521274961 / 16000000000000000 : ℝ) ≤ (-(2918860563035500800487 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8924645521274961 / 16000000000000000 : ℝ) = - (8924645521274961 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8924645521274961 / 8000000000000000 : ℚ)) - (U := (546875338464499199513 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8924645521274961 / 8000000000000000 : ℝ) ≤ - (546875338464499199513 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (69723430839599 / 125000000000000 : ℝ)) (q := - (8924645521274961 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8924645521274961 / 16000000000000000 : ℚ)) + (r' := (8924645521274961 / 8000000000000000 : ℚ)) + (U := (-(2918860563035500800487 / 5000000000000000000000 : ℚ))) + (U' := (546875338464499199513 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (69723430839599 / 125000000000000 : ℚ)) + (q := (8924645521274961 / 16000000000000000 : ℚ)) + (U := (-(2918860563035500800487 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_2 : Uω (aρ 2) (bρ 2) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2141,25 +1884,21 @@ lemma U_513_2 : have hlg : Real.log (44431779205003641 / 80000000000000000 : ℝ) ≤ (-(2940358365703278109947 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44431779205003641 / 80000000000000000 : ℝ) = - (44431779205003641 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44431779205003641 / 40000000000000000 : ℚ)) - (U := (525377535796721890053 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44431779205003641 / 40000000000000000 : ℝ) ≤ - (525377535796721890053 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5553781379335129 / 10000000000000000 : ℝ)) (q := - (44431779205003641 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44431779205003641 / 80000000000000000 : ℚ)) + (r' := (44431779205003641 / 40000000000000000 : ℚ)) + (U := (-(2940358365703278109947 / 5000000000000000000000 : ℚ))) + (U' := (525377535796721890053 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (5553781379335129 / 10000000000000000 : ℚ)) + (q := (44431779205003641 / 80000000000000000 : ℚ)) + (U := (-(2940358365703278109947 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_3 : Uω (aρ 3) (bρ 3) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2167,25 +1906,21 @@ lemma U_513_3 : have hlg : Real.log (44048764058822241 / 80000000000000000 : ℝ) ≤ (-(18647791878558030403 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44048764058822241 / 80000000000000000 : ℝ) = - (44048764058822241 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44048764058822241 / 40000000000000000 : ℚ)) - (U := (3013057505816969597 / 31250000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44048764058822241 / 40000000000000000 : ℝ) ≤ - (3013057505816969597 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5505423699139779 / 10000000000000000 : ℝ)) (q := - (44048764058822241 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44048764058822241 / 80000000000000000 : ℚ)) + (r' := (44048764058822241 / 40000000000000000 : ℚ)) + (U := (-(18647791878558030403 / 31250000000000000000 : ℚ))) + (U' := (3013057505816969597 / 31250000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (5505423699139779 / 10000000000000000 : ℚ)) + (q := (44048764058822241 / 80000000000000000 : ℚ)) + (U := (-(18647791878558030403 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_4 : Uω (aρ 4) (bρ 4) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2193,25 +1928,21 @@ lemma U_513_4 : have hlg : Real.log (43412275317990269 / 80000000000000000 : ℝ) ≤ (-(1222568783742651878327 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43412275317990269 / 80000000000000000 : ℝ) = - (43412275317990269 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43412275317990269 / 40000000000000000 : ℚ)) - (U := (163725576857348121673 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43412275317990269 / 40000000000000000 : ℝ) ≤ - (163725576857348121673 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2712297847498393 / 5000000000000000 : ℝ)) (q := - (43412275317990269 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43412275317990269 / 80000000000000000 : ℚ)) + (r' := (43412275317990269 / 40000000000000000 : ℚ)) + (U := (-(1222568783742651878327 / 2000000000000000000000 : ℚ))) + (U' := (163725576857348121673 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (2712297847498393 / 5000000000000000 : ℚ)) + (q := (43412275317990269 / 80000000000000000 : ℚ)) + (U := (-(1222568783742651878327 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_5 : Uω (aρ 5) (bρ 5) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2219,25 +1950,21 @@ lemma U_513_5 : have hlg : Real.log (42442111730758641 / 80000000000000000 : ℝ) ≤ (-(396178477423036181643 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42442111730758641 / 80000000000000000 : ℝ) = - (42442111730758641 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42442111730758641 / 40000000000000000 : ℚ)) - (U := (37038510264463818357 / 625000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42442111730758641 / 40000000000000000 : ℝ) ≤ - (37038510264463818357 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5300244717523879 / 10000000000000000 : ℝ)) (q := - (42442111730758641 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42442111730758641 / 80000000000000000 : ℚ)) + (r' := (42442111730758641 / 40000000000000000 : ℚ)) + (U := (-(396178477423036181643 / 625000000000000000000 : ℚ))) + (U' := (37038510264463818357 / 625000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (5300244717523879 / 10000000000000000 : ℚ)) + (q := (42442111730758641 / 80000000000000000 : ℚ)) + (U := (-(396178477423036181643 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_6 : Uω (aρ 6) (bρ 6) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2245,25 +1972,21 @@ lemma U_513_6 : have hlg : Real.log (41048673070792113 / 80000000000000000 : ℝ) ≤ (-(133453624748920267399 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41048673070792113 / 80000000000000000 : ℝ) = - (41048673070792113 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41048673070792113 / 40000000000000000 : ℚ)) - (U := (5175811311079732601 / 200000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41048673070792113 / 40000000000000000 : ℝ) ≤ - (5175811311079732601 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5119125427672247 / 10000000000000000 : ℝ)) (q := - (41048673070792113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41048673070792113 / 80000000000000000 : ℚ)) + (r' := (41048673070792113 / 40000000000000000 : ℚ)) + (U := (-(133453624748920267399 / 200000000000000000000 : ℚ))) + (U' := (5175811311079732601 / 200000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (5119125427672247 / 10000000000000000 : ℚ)) + (q := (41048673070792113 / 80000000000000000 : ℚ)) + (U := (-(133453624748920267399 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_7 : Uω (aρ 7) (bρ 7) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2271,25 +1994,21 @@ lemma U_513_7 : have hlg : Real.log (39143028788050253 / 80000000000000000 : ℝ) ≤ (-(7148042917346742296531 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39143028788050253 / 80000000000000000 : ℝ) = - (39143028788050253 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39143028788050253 / 20000000000000000 : ℚ)) - (U := (6714900688653257703469 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39143028788050253 / 20000000000000000 : ℝ) ≤ - (6714900688653257703469 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2433187868873391 / 5000000000000000 : ℝ)) (q := - (39143028788050253 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39143028788050253 / 80000000000000000 : ℚ)) + (r' := (39143028788050253 / 20000000000000000 : ℚ)) + (U := (-(7148042917346742296531 / 10000000000000000000000 : ℚ))) + (U' := (6714900688653257703469 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (2433187868873391 / 5000000000000000 : ℚ)) + (q := (39143028788050253 / 80000000000000000 : ℚ)) + (U := (-(7148042917346742296531 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_8 : Uω (aρ 8) (bρ 8) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2297,25 +2016,21 @@ lemma U_513_8 : have hlg : Real.log (7329240217036657 / 16000000000000000 : ℝ) ≤ (-(1561433730153791004607 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7329240217036657 / 16000000000000000 : ℝ) = - (7329240217036657 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7329240217036657 / 4000000000000000 : ℚ)) - (U := (1211154991046208995393 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7329240217036657 / 4000000000000000 : ℝ) ≤ - (1211154991046208995393 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (113142761584251 / 250000000000000 : ℝ)) (q := - (7329240217036657 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7329240217036657 / 16000000000000000 : ℚ)) + (r' := (7329240217036657 / 4000000000000000 : ℚ)) + (U := (-(1561433730153791004607 / 2000000000000000000000 : ℚ))) + (U' := (1211154991046208995393 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (113142761584251 / 250000000000000 : ℚ)) + (q := (7329240217036657 / 16000000000000000 : ℚ)) + (U := (-(1561433730153791004607 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_9 : Uω (aρ 9) (bρ 9) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2323,25 +2038,21 @@ lemma U_513_9 : have hlg : Real.log (6698731027276557 / 16000000000000000 : ℝ) ≤ (-(8706706121751562856749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6698731027276557 / 16000000000000000 : ℝ) = - (6698731027276557 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6698731027276557 / 4000000000000000 : ℚ)) - (U := (5156237484248437143251 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6698731027276557 / 4000000000000000 : ℝ) ≤ - (5156237484248437143251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (815707920905983 / 2000000000000000 : ℝ)) (q := - (6698731027276557 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6698731027276557 / 16000000000000000 : ℚ)) + (r' := (6698731027276557 / 4000000000000000 : ℚ)) + (U := (-(8706706121751562856749 / 10000000000000000000000 : ℚ))) + (U' := (5156237484248437143251 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (815707920905983 / 2000000000000000 : ℚ)) + (q := (6698731027276557 / 16000000000000000 : ℚ)) + (U := (-(8706706121751562856749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_10 : Uω (aρ 10) (bρ 10) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2349,26 +2060,21 @@ lemma U_513_10 : have hlg : Real.log (29625165030019877 / 80000000000000000 : ℝ) ≤ (-(9934024640806293113911 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29625165030019877 / 80000000000000000 : ℝ) = - (29625165030019877 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29625165030019877 / 20000000000000000 : ℚ)) - (U := (3928918965193706886089 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29625165030019877 / 20000000000000000 : ℝ) ≤ - (3928918965193706886089 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (874994027858547 / 2500000000000000 : ℝ)) (q := - (29625165030019877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29625165030019877 / 80000000000000000 : ℚ)) + (r' := (29625165030019877 / 20000000000000000 : ℚ)) + (U := (-(9934024640806293113911 / 10000000000000000000000 : ℚ))) + (U' := (3928918965193706886089 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (874994027858547 / 2500000000000000 : ℚ)) + (q := (29625165030019877 / 80000000000000000 : ℚ)) + (U := (-(9934024640806293113911 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_11 : Uω (aρ 11) (bρ 11) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2376,26 +2082,21 @@ lemma U_513_11 : have hlg : Real.log (24925913051359713 / 80000000000000000 : ℝ) ≤ (-(5830593435133916158567 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24925913051359713 / 80000000000000000 : ℝ) = - (24925913051359713 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24925913051359713 / 20000000000000000 : ℚ)) - (U := (1100878367866083841433 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24925913051359713 / 20000000000000000 : ℝ) ≤ - (1100878367866083841433 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2743639742974147 / 10000000000000000 : ℝ)) (q := - (24925913051359713 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24925913051359713 / 80000000000000000 : ℚ)) + (r' := (24925913051359713 / 20000000000000000 : ℚ)) + (U := (-(5830593435133916158567 / 5000000000000000000000 : ℚ))) + (U' := (1100878367866083841433 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (2743639742974147 / 10000000000000000 : ℚ)) + (q := (24925913051359713 / 80000000000000000 : ℚ)) + (U := (-(5830593435133916158567 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_12 : Uω (aρ 12) (bρ 12) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2403,26 +2104,21 @@ lemma U_513_12 : have hlg : Real.log (18885370804446089 / 80000000000000000 : ℝ) ≤ (-(288727808611259611257 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18885370804446089 / 80000000000000000 : ℝ) = - (18885370804446089 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18885370804446089 / 10000000000000000 : ℚ)) - (U := (127160499568740388743 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18885370804446089 / 10000000000000000 : ℝ) ≤ - (127160499568740388743 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1657204277930741 / 10000000000000000 : ℝ)) (q := - (18885370804446089 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18885370804446089 / 80000000000000000 : ℚ)) + (r' := (18885370804446089 / 10000000000000000 : ℚ)) + (U := (-(288727808611259611257 / 200000000000000000000 : ℚ))) + (U' := (127160499568740388743 / 200000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (36111549776069 / 64000000000000 : ℚ)) + (s := (1657204277930741 / 10000000000000000 : ℚ)) + (q := (18885370804446089 / 80000000000000000 : ℚ)) + (U := (-(288727808611259611257 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_513_13 : Uω (aρ 13) (bρ 13) (36111549776069 / 64000000000000 : ℝ) ≤ @@ -2532,25 +2228,21 @@ lemma U_514_1 : have hlg : Real.log (5590385840830381 / 10000000000000000 : ℝ) ≤ (-(290768392272368305341 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5590385840830381 / 10000000000000000 : ℝ) = - (5590385840830381 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5590385840830381 / 5000000000000000 : ℚ)) - (U := (55805197877631694659 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5590385840830381 / 5000000000000000 : ℝ) ≤ - (55805197877631694659 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1397589230479253 / 2500000000000000 : ℝ)) (q := - (5590385840830381 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5590385840830381 / 10000000000000000 : ℚ)) + (r' := (5590385840830381 / 5000000000000000 : ℚ)) + (U := (-(290768392272368305341 / 500000000000000000000 : ℚ))) + (U' := (55805197877631694659 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (1397589230479253 / 2500000000000000 : ℚ)) + (q := (5590385840830381 / 10000000000000000 : ℚ)) + (U := (-(290768392272368305341 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_2 : Uω (aρ 2) (bρ 2) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2558,25 +2250,21 @@ lemma U_514_2 : have hlg : Real.log (445316412344633 / 800000000000000 : ℝ) ≤ (-(234330663573394913113 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (445316412344633 / 800000000000000 : ℝ) = - (445316412344633 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (445316412344633 / 400000000000000 : ℚ)) - (U := (42928208546605086887 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (445316412344633 / 400000000000000 : ℝ) ≤ - (42928208546605086887 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (222650582455283 / 400000000000000 : ℝ)) (q := - (445316412344633 / 800000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (445316412344633 / 800000000000000 : ℚ)) + (r' := (445316412344633 / 400000000000000 : ℚ)) + (U := (-(234330663573394913113 / 400000000000000000000 : ℚ))) + (U' := (42928208546605086887 / 400000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (222650582455283 / 400000000000000 : ℚ)) + (q := (445316412344633 / 800000000000000 : ℚ)) + (U := (-(234330663573394913113 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_3 : Uω (aρ 3) (bρ 3) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2584,25 +2272,21 @@ lemma U_514_3 : have hlg : Real.log (2759289676200287 / 5000000000000000 : ℝ) ≤ (-(2972323146321819319241 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2759289676200287 / 5000000000000000 : ℝ) = - (2759289676200287 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2759289676200287 / 2500000000000000 : ℚ)) - (U := (493412755178180680759 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2759289676200287 / 2500000000000000 : ℝ) ≤ - (493412755178180680759 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2758954531958699 / 5000000000000000 : ℝ)) (q := - (2759289676200287 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2759289676200287 / 5000000000000000 : ℚ)) + (r' := (2759289676200287 / 2500000000000000 : ℚ)) + (U := (-(2972323146321819319241 / 5000000000000000000000 : ℚ))) + (U' := (493412755178180680759 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (2758954531958699 / 5000000000000000 : ℚ)) + (q := (2759289676200287 / 5000000000000000 : ℚ)) + (U := (-(2972323146321819319241 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_4 : Uω (aρ 4) (bρ 4) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2610,25 +2294,21 @@ lemma U_514_4 : have hlg : Real.log (5439021190933697 / 10000000000000000 : ℝ) ≤ (-(3044929880962231886749 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5439021190933697 / 10000000000000000 : ℝ) = - (5439021190933697 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5439021190933697 / 5000000000000000 : ℚ)) - (U := (420806020537768113251 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5439021190933697 / 5000000000000000 : ℝ) ≤ - (420806020537768113251 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1359271730512161 / 2500000000000000 : ℝ)) (q := - (5439021190933697 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5439021190933697 / 10000000000000000 : ℚ)) + (r' := (5439021190933697 / 5000000000000000 : ℚ)) + (U := (-(3044929880962231886749 / 5000000000000000000000 : ℚ))) + (U' := (420806020537768113251 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (1359271730512161 / 2500000000000000 : ℚ)) + (q := (5439021190933697 / 10000000000000000 : ℚ)) + (U := (-(3044929880962231886749 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_5 : Uω (aρ 5) (bρ 5) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2636,25 +2316,21 @@ lemma U_514_5 : have hlg : Real.log (2658879042215409 / 5000000000000000 : ℝ) ≤ (-(6315332909008076166521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2658879042215409 / 5000000000000000 : ℝ) = - (2658879042215409 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2658879042215409 / 2500000000000000 : ℚ)) - (U := (616138893991923833479 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2658879042215409 / 2500000000000000 : ℝ) ≤ - (616138893991923833479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2656375314188943 / 5000000000000000 : ℝ)) (q := - (2658879042215409 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2658879042215409 / 5000000000000000 : ℚ)) + (r' := (2658879042215409 / 2500000000000000 : ℚ)) + (U := (-(6315332909008076166521 / 10000000000000000000000 : ℚ))) + (U' := (616138893991923833479 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (2656375314188943 / 5000000000000000 : ℚ)) + (q := (2658879042215409 / 5000000000000000 : ℚ)) + (U := (-(6315332909008076166521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_6 : Uω (aρ 6) (bρ 6) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2662,25 +2338,21 @@ lemma U_514_6 : have hlg : Real.log (2571797773915591 / 5000000000000000 : ℝ) ≤ (-(6648327348947931113759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2571797773915591 / 5000000000000000 : ℝ) = - (2571797773915591 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2571797773915591 / 2500000000000000 : ℚ)) - (U := (283144454052068886241 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2571797773915591 / 2500000000000000 : ℝ) ≤ - (283144454052068886241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2565832965159307 / 5000000000000000 : ℝ)) (q := - (2571797773915591 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2571797773915591 / 5000000000000000 : ℚ)) + (r' := (2571797773915591 / 2500000000000000 : ℚ)) + (U := (-(6648327348947931113759 / 10000000000000000000000 : ℚ))) + (U' := (283144454052068886241 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (2565832965159307 / 5000000000000000 : ℚ)) + (q := (2571797773915591 / 5000000000000000 : ℚ)) + (U := (-(6648327348947931113759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_7 : Uω (aρ 7) (bρ 7) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2688,25 +2360,21 @@ lemma U_514_7 : have hlg : Real.log (2452714364592631 / 5000000000000000 : ℝ) ≤ (-(7122425967148344153303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2452714364592631 / 5000000000000000 : ℝ) = - (2452714364592631 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2452714364592631 / 1250000000000000 : ℚ)) - (U := (6740517638851655846697 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2452714364592631 / 1250000000000000 : ℝ) ≤ - (6740517638851655846697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2439496836893387 / 5000000000000000 : ℝ)) (q := - (2452714364592631 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2452714364592631 / 5000000000000000 : ℚ)) + (r' := (2452714364592631 / 1250000000000000 : ℚ)) + (U := (-(7122425967148344153303 / 10000000000000000000000 : ℚ))) + (U' := (6740517638851655846697 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (2439496836893387 / 5000000000000000 : ℚ)) + (q := (2452714364592631 / 5000000000000000 : ℚ)) + (U := (-(7122425967148344153303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_8 : Uω (aρ 8) (bρ 8) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2714,24 +2382,21 @@ lemma U_514_8 : have hlg : Real.log (73494542585741 / 160000000000000 : ℝ) ≤ (-(3889813308929943655439 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (73494542585741 / 160000000000000 : ℝ) = (73494542585741 / 40000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (73494542585741 / 40000000000000 : ℚ)) - (U := (3041658494070056344561 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (73494542585741 / 40000000000000 : ℝ) ≤ - (3041658494070056344561 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (36307965519791 / 80000000000000 : ℝ)) (q := - (73494542585741 / 160000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (73494542585741 / 160000000000000 : ℚ)) + (r' := (73494542585741 / 40000000000000 : ℚ)) + (U := (-(3889813308929943655439 / 5000000000000000000000 : ℚ))) + (U' := (3041658494070056344561 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (36307965519791 / 80000000000000 : ℚ)) + (q := (73494542585741 / 160000000000000 : ℚ)) + (U := (-(3889813308929943655439 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_9 : Uω (aρ 9) (bρ 9) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2739,25 +2404,21 @@ lemma U_514_9 : have hlg : Real.log (4199519225463883 / 10000000000000000 : ℝ) ≤ (-(8676150438646844351813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4199519225463883 / 10000000000000000 : ℝ) = - (4199519225463883 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4199519225463883 / 2500000000000000 : ℚ)) - (U := (5186793167353155648187 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4199519225463883 / 2500000000000000 : ℝ) ≤ - (5186793167353155648187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (255730121627751 / 625000000000000 : ℝ)) (q := - (4199519225463883 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4199519225463883 / 10000000000000000 : ℚ)) + (r' := (4199519225463883 / 2500000000000000 : ℚ)) + (U := (-(8676150438646844351813 / 10000000000000000000000 : ℚ))) + (U' := (5186793167353155648187 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (255730121627751 / 625000000000000 : ℚ)) + (q := (4199519225463883 / 10000000000000000 : ℚ)) + (U := (-(8676150438646844351813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_10 : Uω (aρ 10) (bρ 10) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2765,26 +2426,21 @@ lemma U_514_10 : have hlg : Real.log (7432699630235927 / 20000000000000000 : ℝ) ≤ (-(395937255363209419699 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7432699630235927 / 20000000000000000 : ℝ) = - (7432699630235927 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7432699630235927 / 5000000000000000 : ℚ)) - (U := (158580488876790580301 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7432699630235927 / 5000000000000000 : ℝ) ≤ - (158580488876790580301 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3513902158847177 / 10000000000000000 : ℝ)) (q := - (7432699630235927 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7432699630235927 / 20000000000000000 : ℚ)) + (r' := (7432699630235927 / 5000000000000000 : ℚ)) + (U := (-(395937255363209419699 / 400000000000000000000 : ℚ))) + (U' := (158580488876790580301 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (3513902158847177 / 10000000000000000 : ℚ)) + (q := (7432699630235927 / 20000000000000000 : ℚ)) + (U := (-(395937255363209419699 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_11 : Uω (aρ 11) (bρ 11) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2792,26 +2448,21 @@ lemma U_514_11 : have hlg : Real.log (6259811290500711 / 20000000000000000 : ℝ) ≤ (-(5807911168319489409469 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6259811290500711 / 20000000000000000 : ℝ) = - (6259811290500711 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6259811290500711 / 5000000000000000 : ℚ)) - (U := (1123560634680510590531 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6259811290500711 / 5000000000000000 : ℝ) ≤ - (1123560634680510590531 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2759490445316961 / 10000000000000000 : ℝ)) (q := - (6259811290500711 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6259811290500711 / 20000000000000000 : ℚ)) + (r' := (6259811290500711 / 5000000000000000 : ℚ)) + (U := (-(5807911168319489409469 / 5000000000000000000000 : ℚ))) + (U' := (1123560634680510590531 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (2759490445316961 / 10000000000000000 : ℚ)) + (q := (6259811290500711 / 20000000000000000 : ℚ)) + (U := (-(5807911168319489409469 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_12 : Uω (aρ 12) (bρ 12) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2819,26 +2470,21 @@ lemma U_514_12 : have hlg : Real.log (4756792457721397 / 20000000000000000 : ℝ) ≤ (-(179519835636495302763 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4756792457721397 / 20000000000000000 : ℝ) = - (4756792457721397 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4756792457721397 / 2500000000000000 : ℚ)) - (U := (80410356976004697237 / 125000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4756792457721397 / 2500000000000000 : ℝ) ≤ - (80410356976004697237 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1680171709222647 / 10000000000000000 : ℝ)) (q := - (4756792457721397 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4756792457721397 / 20000000000000000 : ℚ)) + (r' := (4756792457721397 / 2500000000000000 : ℚ)) + (U := (-(179519835636495302763 / 125000000000000000000 : ℚ))) + (U' := (80410356976004697237 / 125000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4523929582263 / 8000000000000 : ℚ)) + (s := (1680171709222647 / 10000000000000000 : ℚ)) + (q := (4756792457721397 / 20000000000000000 : ℚ)) + (U := (-(179519835636495302763 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_514_13 : Uω (aρ 13) (bρ 13) (4523929582263 / 8000000000000 : ℝ) ≤ @@ -2949,25 +2595,21 @@ lemma U_515_1 : have hlg : Real.log (4492280496027439 / 8000000000000000 : ℝ) ≤ (-(2885405315160330269137 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4492280496027439 / 8000000000000000 : ℝ) = - (4492280496027439 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4492280496027439 / 4000000000000000 : ℚ)) - (U := (580330586339669730863 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4492280496027439 / 4000000000000000 : ℝ) ≤ - (580330586339669730863 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (561532182968891 / 1000000000000000 : ℝ)) (q := - (4492280496027439 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4492280496027439 / 8000000000000000 : ℚ)) + (r' := (4492280496027439 / 4000000000000000 : ℚ)) + (U := (-(2885405315160330269137 / 5000000000000000000000 : ℚ))) + (U' := (580330586339669730863 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (561532182968891 / 1000000000000000 : ℚ)) + (q := (4492280496027439 / 8000000000000000 : ℚ)) + (U := (-(2885405315160330269137 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_2 : Uω (aρ 2) (bρ 2) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -2975,25 +2617,21 @@ lemma U_515_2 : have hlg : Real.log (22365682623738931 / 40000000000000000 : ℝ) ≤ (-(1162703390940672187211 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22365682623738931 / 40000000000000000 : ℝ) = - (22365682623738931 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22365682623738931 / 20000000000000000 : ℚ)) - (U := (223590969659327812789 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22365682623738931 / 20000000000000000 : ℝ) ≤ - (223590969659327812789 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2795615456999889 / 5000000000000000 : ℝ)) (q := - (22365682623738931 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22365682623738931 / 40000000000000000 : ℚ)) + (r' := (22365682623738931 / 20000000000000000 : ℚ)) + (U := (-(1162703390940672187211 / 2000000000000000000000 : ℚ))) + (U' := (223590969659327812789 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (2795615456999889 / 5000000000000000 : ℚ)) + (q := (22365682623738931 / 40000000000000000 : ℚ)) + (U := (-(1162703390940672187211 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_3 : Uω (aρ 3) (bρ 3) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3001,25 +2639,21 @@ lemma U_515_3 : have hlg : Real.log (4434837617567573 / 8000000000000000 : ℝ) ≤ (-(5899505401803822401993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4434837617567573 / 8000000000000000 : ℝ) = - (4434837617567573 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4434837617567573 / 4000000000000000 : ℚ)) - (U := (1031966401196177598007 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4434837617567573 / 4000000000000000 : ℝ) ≤ - (1031966401196177598007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1108575950479849 / 2000000000000000 : ℝ)) (q := - (4434837617567573 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4434837617567573 / 8000000000000000 : ℚ)) + (r' := (4434837617567573 / 4000000000000000 : ℚ)) + (U := (-(5899505401803822401993 / 10000000000000000000000 : ℚ))) + (U' := (1031966401196177598007 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (1108575950479849 / 2000000000000000 : ℚ)) + (q := (4434837617567573 / 8000000000000000 : ℚ)) + (U := (-(5899505401803822401993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_4 : Uω (aρ 4) (bρ 4) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3027,25 +2661,21 @@ lemma U_515_4 : have hlg : Real.log (21855978729012229 / 40000000000000000 : ℝ) ≤ (-(6044049436994200835527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21855978729012229 / 40000000000000000 : ℝ) = - (21855978729012229 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21855978729012229 / 20000000000000000 : ℚ)) - (U := (887422366005799164473 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21855978729012229 / 20000000000000000 : ℝ) ≤ - (887422366005799164473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5462069254051427 / 10000000000000000 : ℝ)) (q := - (21855978729012229 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21855978729012229 / 40000000000000000 : ℚ)) + (r' := (21855978729012229 / 20000000000000000 : ℚ)) + (U := (-(6044049436994200835527 / 10000000000000000000000 : ℚ))) + (U' := (887422366005799164473 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (5462069254051427 / 10000000000000000 : ℚ)) + (q := (21855978729012229 / 40000000000000000 : ℚ)) + (U := (-(6044049436994200835527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_5 : Uω (aρ 5) (bρ 5) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3053,25 +2683,21 @@ lemma U_515_5 : have hlg : Real.log (4274196923986051 / 8000000000000000 : ℝ) ≤ (-(6268453107162976316631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4274196923986051 / 8000000000000000 : ℝ) = - (4274196923986051 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4274196923986051 / 4000000000000000 : ℚ)) - (U := (663018695837023683369 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4274196923986051 / 4000000000000000 : ℝ) ≤ - (663018695837023683369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1042531663837 / 1953125000000 : ℝ)) (q := - (4274196923986051 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4274196923986051 / 8000000000000000 : ℚ)) + (r' := (4274196923986051 / 4000000000000000 : ℚ)) + (U := (-(6268453107162976316631 / 10000000000000000000000 : ℚ))) + (U' := (663018695837023683369 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (1042531663837 / 1953125000000 : ℚ)) + (q := (4274196923986051 / 8000000000000000 : ℚ)) + (U := (-(6268453107162976316631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_6 : Uω (aρ 6) (bρ 6) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3079,25 +2705,21 @@ lemma U_515_6 : have hlg : Real.log (4134894361873683 / 8000000000000000 : ℝ) ≤ (-(6599797605804451610419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4134894361873683 / 8000000000000000 : ℝ) = - (4134894361873683 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4134894361873683 / 4000000000000000 : ℚ)) - (U := (331674197195548389581 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (4134894361873683 / 4000000000000000 : ℝ) ≤ - (331674197195548389581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128918652217613 / 250000000000000 : ℝ)) (q := - (4134894361873683 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4134894361873683 / 8000000000000000 : ℚ)) + (r' := (4134894361873683 / 4000000000000000 : ℚ)) + (U := (-(6599797605804451610419 / 10000000000000000000000 : ℚ))) + (U' := (331674197195548389581 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (128918652217613 / 250000000000000 : ℚ)) + (q := (4134894361873683 / 8000000000000000 : ℚ)) + (U := (-(6599797605804451610419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_7 : Uω (aρ 7) (bρ 7) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3105,25 +2727,21 @@ lemma U_515_7 : have hlg : Real.log (19722111797769177 / 40000000000000000 : ℝ) ≤ (-(7071390210168205466577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19722111797769177 / 40000000000000000 : ℝ) = - (19722111797769177 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19722111797769177 / 10000000000000000 : ℚ)) - (U := (6791553395831794533423 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19722111797769177 / 10000000000000000 : ℝ) ≤ - (6791553395831794533423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4904227463664901 / 10000000000000000 : ℝ)) (q := - (19722111797769177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19722111797769177 / 40000000000000000 : ℚ)) + (r' := (19722111797769177 / 10000000000000000 : ℚ)) + (U := (-(7071390210168205466577 / 10000000000000000000000 : ℚ))) + (U' := (6791553395831794533423 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (4904227463664901 / 10000000000000000 : ℚ)) + (q := (19722111797769177 / 40000000000000000 : ℚ)) + (U := (-(7071390210168205466577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_8 : Uω (aρ 8) (bρ 8) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3131,25 +2749,21 @@ lemma U_515_8 : have hlg : Real.log (18474695792596697 / 40000000000000000 : ℝ) ≤ (-(1544954905579950569431 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18474695792596697 / 40000000000000000 : ℝ) = - (18474695792596697 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18474695792596697 / 10000000000000000 : ℚ)) - (U := (1227633815620049430569 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18474695792596697 / 10000000000000000 : ℝ) ≤ - (1227633815620049430569 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4564061112418661 / 10000000000000000 : ℝ)) (q := - (18474695792596697 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18474695792596697 / 40000000000000000 : ℚ)) + (r' := (18474695792596697 / 10000000000000000 : ℚ)) + (U := (-(1544954905579950569431 / 2000000000000000000000 : ℚ))) + (U' := (1227633815620049430569 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (4564061112418661 / 10000000000000000 : ℚ)) + (q := (18474695792596697 / 40000000000000000 : ℚ)) + (U := (-(1544954905579950569431 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_9 : Uω (aρ 9) (bρ 9) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3157,25 +2771,21 @@ lemma U_515_9 : have hlg : Real.log (16900550926846531 / 40000000000000000 : ℝ) ≤ (-(1723066465949345500237 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16900550926846531 / 40000000000000000 : ℝ) = - (16900550926846531 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16900550926846531 / 10000000000000000 : ℚ)) - (U := (1049522255250654499763 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16900550926846531 / 10000000000000000 : ℝ) ≤ - (1049522255250654499763 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2058977153951789 / 5000000000000000 : ℝ)) (q := - (16900550926846531 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16900550926846531 / 40000000000000000 : ℚ)) + (r' := (16900550926846531 / 10000000000000000 : ℚ)) + (U := (-(1723066465949345500237 / 2000000000000000000000 : ℚ))) + (U' := (1049522255250654499763 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (2058977153951789 / 5000000000000000 : ℚ)) + (q := (16900550926846531 / 40000000000000000 : ℚ)) + (U := (-(1723066465949345500237 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_10 : Uω (aρ 10) (bρ 10) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3183,26 +2793,21 @@ lemma U_515_10 : have hlg : Real.log (14970968162174133 / 40000000000000000 : ℝ) ≤ (-(2456916459404556892093 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14970968162174133 / 40000000000000000 : ℝ) = - (14970968162174133 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14970968162174133 / 10000000000000000 : ℚ)) - (U := (1008819442095443107907 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14970968162174133 / 10000000000000000 : ℝ) ≤ - (1008819442095443107907 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3541721959062379 / 10000000000000000 : ℝ)) (q := - (14970968162174133 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14970968162174133 / 40000000000000000 : ℚ)) + (r' := (14970968162174133 / 10000000000000000 : ℚ)) + (U := (-(2456916459404556892093 / 2500000000000000000000 : ℚ))) + (U' := (1008819442095443107907 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (3541721959062379 / 10000000000000000 : ℚ)) + (q := (14970968162174133 / 40000000000000000 : ℚ)) + (U := (-(2456916459404556892093 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_11 : Uω (aρ 11) (bρ 11) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3210,26 +2815,21 @@ lemma U_515_11 : have hlg : Real.log (12632749536116209 / 40000000000000000 : ℝ) ≤ (-(11525868421030432666923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12632749536116209 / 40000000000000000 : ℝ) = - (12632749536116209 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12632749536116209 / 10000000000000000 : ℚ)) - (U := (2337075184969567333077 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12632749536116209 / 10000000000000000 : ℝ) ≤ - (2337075184969567333077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2791089272238417 / 10000000000000000 : ℝ)) (q := - (12632749536116209 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12632749536116209 / 40000000000000000 : ℚ)) + (r' := (12632749536116209 / 10000000000000000 : ℚ)) + (U := (-(11525868421030432666923 / 10000000000000000000000 : ℚ))) + (U' := (2337075184969567333077 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (2791089272238417 / 10000000000000000 : ℚ)) + (q := (12632749536116209 / 40000000000000000 : ℚ)) + (U := (-(11525868421030432666923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_12 : Uω (aρ 12) (bρ 12) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3237,26 +2837,21 @@ lemma U_515_12 : have hlg : Real.log (9654091678558937 / 40000000000000000 : ℝ) ≤ (-(14214976197084333418893 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9654091678558937 / 40000000000000000 : ℝ) = - (9654091678558937 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9654091678558937 / 5000000000000000 : ℚ)) - (U := (6579439211915666581107 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9654091678558937 / 5000000000000000 : ℝ) ≤ - (6579439211915666581107 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1725460440144781 / 10000000000000000 : ℝ)) (q := - (9654091678558937 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9654091678558937 / 40000000000000000 : ℚ)) + (r' := (9654091678558937 / 5000000000000000 : ℚ)) + (U := (-(14214976197084333418893 / 10000000000000000000000 : ℚ))) + (U' := (6579439211915666581107 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (18175605211087 / 32000000000000 : ℚ)) + (s := (1725460440144781 / 10000000000000000 : ℚ)) + (q := (9654091678558937 / 40000000000000000 : ℚ)) + (U := (-(14214976197084333418893 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_515_13 : Uω (aρ 13) (bρ 13) (18175605211087 / 32000000000000 : ℝ) ≤ @@ -3369,25 +2964,21 @@ lemma U_516_1 : have hlg : Real.log (5640315398100093 / 10000000000000000 : ℝ) ≤ (-(572645107138737305937 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5640315398100093 / 10000000000000000 : ℝ) = - (5640315398100093 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5640315398100093 / 5000000000000000 : ℚ)) - (U := (120502073161262694063 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5640315398100093 / 5000000000000000 : ℝ) ≤ - (120502073161262694063 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5640286735184561 / 10000000000000000 : ℝ)) (q := - (5640315398100093 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5640315398100093 / 10000000000000000 : ℚ)) + (r' := (5640315398100093 / 5000000000000000 : ℚ)) + (U := (-(572645107138737305937 / 1000000000000000000000 : ℚ))) + (U' := (120502073161262694063 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (5640286735184561 / 10000000000000000 : ℚ)) + (q := (5640315398100093 / 10000000000000000 : ℚ)) + (U := (-(572645107138737305937 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_2 : Uω (aρ 2) (bρ 2) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3395,25 +2986,21 @@ lemma U_516_2 : have hlg : Real.log (11232772299991577 / 20000000000000000 : ℝ) ≤ (-(5768966694719913615483 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11232772299991577 / 20000000000000000 : ℝ) = - (11232772299991577 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11232772299991577 / 10000000000000000 : ℚ)) - (U := (1162505108280086384517 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11232772299991577 / 10000000000000000 : ℝ) ≤ - (1162505108280086384517 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21938270513617 / 39062500000000 : ℝ)) (q := - (11232772299991577 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11232772299991577 / 20000000000000000 : ℚ)) + (r' := (11232772299991577 / 10000000000000000 : ℚ)) + (U := (-(5768966694719913615483 / 10000000000000000000000 : ℚ))) + (U' := (1162505108280086384517 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (21938270513617 / 39062500000000 : ℚ)) + (q := (11232772299991577 / 20000000000000000 : ℚ)) + (U := (-(5768966694719913615483 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_3 : Uω (aρ 3) (bρ 3) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3421,25 +3008,21 @@ lemma U_516_3 : have hlg : Real.log (5568514664443109 / 10000000000000000 : ℝ) ≤ (-(1170913482845522262301 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5568514664443109 / 10000000000000000 : ℝ) = - (5568514664443109 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5568514664443109 / 5000000000000000 : ℚ)) - (U := (215380877754477737699 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5568514664443109 / 5000000000000000 : ℝ) ≤ - (215380877754477737699 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5567850386730593 / 10000000000000000 : ℝ)) (q := - (5568514664443109 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5568514664443109 / 10000000000000000 : ℚ)) + (r' := (5568514664443109 / 5000000000000000 : ℚ)) + (U := (-(1170913482845522262301 / 2000000000000000000000 : ℚ))) + (U' := (215380877754477737699 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (5567850386730593 / 10000000000000000 : ℚ)) + (q := (5568514664443109 / 10000000000000000 : ℚ)) + (U := (-(1170913482845522262301 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_4 : Uω (aρ 4) (bρ 4) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3447,25 +3030,21 @@ lemma U_516_4 : have hlg : Real.log (10977936186196661 / 20000000000000000 : ℝ) ≤ (-(5998448160638532935769 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10977936186196661 / 20000000000000000 : ℝ) = - (10977936186196661 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10977936186196661 / 10000000000000000 : ℚ)) - (U := (933023642361467064231 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10977936186196661 / 10000000000000000 : ℝ) ≤ - (933023642361467064231 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1371762856276509 / 2500000000000000 : ℝ)) (q := - (10977936186196661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10977936186196661 / 20000000000000000 : ℚ)) + (r' := (10977936186196661 / 10000000000000000 : ℚ)) + (U := (-(5998448160638532935769 / 10000000000000000000000 : ℚ))) + (U' := (933023642361467064231 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (1371762856276509 / 2500000000000000 : ℚ)) + (q := (10977936186196661 / 20000000000000000 : ℚ)) + (U := (-(5998448160638532935769 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_5 : Uω (aρ 5) (bρ 5) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3473,25 +3052,21 @@ lemma U_516_5 : have hlg : Real.log (10735468014564247 / 20000000000000000 : ℝ) ≤ (-(6221792458419681924697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10735468014564247 / 20000000000000000 : ℝ) = - (10735468014564247 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10735468014564247 / 10000000000000000 : ℚ)) - (U := (709679344580318075303 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10735468014564247 / 10000000000000000 : ℝ) ≤ - (709679344580318075303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2681386586404311 / 5000000000000000 : ℝ)) (q := - (10735468014564247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10735468014564247 / 20000000000000000 : ℚ)) + (r' := (10735468014564247 / 10000000000000000 : ℚ)) + (U := (-(6221792458419681924697 / 10000000000000000000000 : ℚ))) + (U' := (709679344580318075303 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (2681386586404311 / 5000000000000000 : ℚ)) + (q := (10735468014564247 / 20000000000000000 : ℚ)) + (U := (-(6221792458419681924697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_6 : Uω (aρ 6) (bρ 6) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3499,25 +3074,21 @@ lemma U_516_6 : have hlg : Real.log (5193639799080183 / 10000000000000000 : ℝ) ≤ (-(6551503313245521501489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5193639799080183 / 10000000000000000 : ℝ) = - (5193639799080183 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5193639799080183 / 5000000000000000 : ℚ)) - (U := (379968489754478498511 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5193639799080183 / 5000000000000000 : ℝ) ≤ - (379968489754478498511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5181825131544741 / 10000000000000000 : ℝ)) (q := - (5193639799080183 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5193639799080183 / 10000000000000000 : ℚ)) + (r' := (5193639799080183 / 5000000000000000 : ℚ)) + (U := (-(6551503313245521501489 / 10000000000000000000000 : ℚ))) + (U' := (379968489754478498511 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (5181825131544741 / 10000000000000000 : ℚ)) + (q := (5193639799080183 / 10000000000000000 : ℚ)) + (U := (-(6551503313245521501489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_7 : Uω (aρ 7) (bρ 7) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3525,25 +3096,21 @@ lemma U_516_7 : have hlg : Real.log (4955625799329087 / 10000000000000000 : ℝ) ≤ (-(1755154090330776418639 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4955625799329087 / 10000000000000000 : ℝ) = - (4955625799329087 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4955625799329087 / 2500000000000000 : ℚ)) - (U := (1710581811169223581361 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4955625799329087 / 2500000000000000 : ℝ) ≤ - (1710581811169223581361 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4929458512802549 / 10000000000000000 : ℝ)) (q := - (4955625799329087 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4955625799329087 / 10000000000000000 : ℚ)) + (r' := (4955625799329087 / 2500000000000000 : ℚ)) + (U := (-(1755154090330776418639 / 2500000000000000000000 : ℚ))) + (U' := (1710581811169223581361 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (4929458512802549 / 10000000000000000 : ℚ)) + (q := (4955625799329087 / 10000000000000000 : ℚ)) + (U := (-(1755154090330776418639 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_8 : Uω (aρ 8) (bρ 8) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3551,25 +3118,21 @@ lemma U_516_8 : have hlg : Real.log (9287871355101189 / 20000000000000000 : ℝ) ≤ (-(7670228793910646247569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9287871355101189 / 20000000000000000 : ℝ) = - (9287871355101189 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9287871355101189 / 5000000000000000 : ℚ)) - (U := (6192714812089353752431 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9287871355101189 / 5000000000000000 : ℝ) ≤ - (6192714812089353752431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1147404980146391 / 2500000000000000 : ℝ)) (q := - (9287871355101189 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9287871355101189 / 20000000000000000 : ℚ)) + (r' := (9287871355101189 / 5000000000000000 : ℚ)) + (U := (-(7670228793910646247569 / 10000000000000000000000 : ℚ))) + (U' := (6192714812089353752431 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (1147404980146391 / 2500000000000000 : ℚ)) + (q := (9287871355101189 / 20000000000000000 : ℚ)) + (U := (-(7670228793910646247569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_9 : Uω (aρ 9) (bρ 9) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3577,25 +3140,21 @@ lemma U_516_9 : have hlg : Real.log (8501496308041777 / 20000000000000000 : ℝ) ≤ (-(34219603551607253439 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8501496308041777 / 20000000000000000 : ℝ) = - (8501496308041777 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8501496308041777 / 5000000000000000 : ℚ)) - (U := (21232170872392746561 / 40000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8501496308041777 / 5000000000000000 : ℝ) ≤ - (21232170872392746561 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (518026312735769 / 1250000000000000 : ℝ)) (q := - (8501496308041777 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8501496308041777 / 20000000000000000 : ℚ)) + (r' := (8501496308041777 / 5000000000000000 : ℚ)) + (U := (-(34219603551607253439 / 40000000000000000000 : ℚ))) + (U' := (21232170872392746561 / 40000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (518026312735769 / 1250000000000000 : ℚ)) + (q := (8501496308041777 / 20000000000000000 : ℚ)) + (U := (-(34219603551607253439 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_10 : Uω (aρ 10) (bρ 10) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3603,26 +3162,21 @@ lemma U_516_10 : have hlg : Real.log (7538226311282421 / 20000000000000000 : ℝ) ≤ (-(9757453559173009449761 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7538226311282421 / 20000000000000000 : ℝ) = - (7538226311282421 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7538226311282421 / 5000000000000000 : ℚ)) - (U := (4105490046826990550239 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7538226311282421 / 5000000000000000 : ℝ) ≤ - (4105490046826990550239 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (892374884655449 / 2500000000000000 : ℝ)) (q := - (7538226311282421 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7538226311282421 / 20000000000000000 : ℚ)) + (r' := (7538226311282421 / 5000000000000000 : ℚ)) + (U := (-(9757453559173009449761 / 10000000000000000000000 : ℚ))) + (U' := (4105490046826990550239 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (892374884655449 / 2500000000000000 : ℚ)) + (q := (7538226311282421 / 20000000000000000 : ℚ)) + (U := (-(9757453559173009449761 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_11 : Uω (aρ 11) (bρ 11) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3630,26 +3184,21 @@ lemma U_516_11 : have hlg : Real.log (6372805301094043 / 20000000000000000 : ℝ) ≤ (-(5718462538789883425289 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6372805301094043 / 20000000000000000 : ℝ) = - (6372805301094043 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6372805301094043 / 5000000000000000 : ℚ)) - (U := (1213009264210116574711 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6372805301094043 / 5000000000000000 : ℝ) ≤ - (1213009264210116574711 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1411277577319209 / 5000000000000000 : ℝ)) (q := - (6372805301094043 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6372805301094043 / 20000000000000000 : ℚ)) + (r' := (6372805301094043 / 5000000000000000 : ℚ)) + (U := (-(5718462538789883425289 / 5000000000000000000000 : ℚ))) + (U' := (1213009264210116574711 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (1411277577319209 / 5000000000000000 : ℚ)) + (q := (6372805301094043 / 20000000000000000 : ℚ)) + (U := (-(5718462538789883425289 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_12 : Uω (aρ 12) (bρ 12) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3657,26 +3206,21 @@ lemma U_516_12 : have hlg : Real.log (4896492691807321 / 20000000000000000 : ℝ) ≤ (-(7036065505652730763057 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4896492691807321 / 20000000000000000 : ℝ) = - (4896492691807321 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4896492691807321 / 2500000000000000 : ℚ)) - (U := (3361142198847269236943 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4896492691807321 / 2500000000000000 : ℝ) ≤ - (3361142198847269236943 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221242830254587 / 1250000000000000 : ℝ)) (q := - (4896492691807321 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4896492691807321 / 20000000000000000 : ℚ)) + (r' := (4896492691807321 / 2500000000000000 : ℚ)) + (U := (-(7036065505652730763057 / 5000000000000000000000 : ℚ))) + (U' := (3361142198847269236943 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9127746046561 / 16000000000000 : ℚ)) + (s := (221242830254587 / 1250000000000000 : ℚ)) + (q := (4896492691807321 / 20000000000000000 : ℚ)) + (U := (-(7036065505652730763057 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_516_13 : Uω (aρ 13) (bρ 13) (9127746046561 / 16000000000000 : ℝ) ≤ @@ -3789,25 +3333,21 @@ lemma U_517_1 : have hlg : Real.log (22661120700171239 / 40000000000000000 : ℝ) ≤ (-(568228742276248743139 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22661120700171239 / 40000000000000000 : ℝ) = - (22661120700171239 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22661120700171239 / 20000000000000000 : ℚ)) - (U := (124918438023751256861 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22661120700171239 / 20000000000000000 : ℝ) ≤ - (124918438023751256861 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5665251638434057 / 10000000000000000 : ℝ)) (q := - (22661120700171239 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22661120700171239 / 40000000000000000 : ℚ)) + (r' := (22661120700171239 / 20000000000000000 : ℚ)) + (U := (-(568228742276248743139 / 1000000000000000000000 : ℚ))) + (U' := (124918438023751256861 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (5665251638434057 / 10000000000000000 : ℚ)) + (q := (22661120700171239 / 40000000000000000 : ℚ)) + (U := (-(568228742276248743139 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_2 : Uω (aρ 2) (bρ 2) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3815,25 +3355,21 @@ lemma U_517_2 : have hlg : Real.log (22565406546366123 / 40000000000000000 : ℝ) ≤ (-(2862307020290630033483 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22565406546366123 / 40000000000000000 : ℝ) = - (22565406546366123 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22565406546366123 / 20000000000000000 : ℚ)) - (U := (603428881209369966517 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22565406546366123 / 20000000000000000 : ℝ) ≤ - (603428881209369966517 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5641163574041499 / 10000000000000000 : ℝ)) (q := - (22565406546366123 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22565406546366123 / 40000000000000000 : ℚ)) + (r' := (22565406546366123 / 20000000000000000 : ℚ)) + (U := (-(2862307020290630033483 / 5000000000000000000000 : ℚ))) + (U' := (603428881209369966517 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (5641163574041499 / 10000000000000000 : ℚ)) + (q := (22565406546366123 / 40000000000000000 : ℚ)) + (U := (-(2862307020290630033483 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_3 : Uω (aρ 3) (bρ 3) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3841,25 +3377,21 @@ lemma U_517_3 : have hlg : Real.log (22373929120856623 / 40000000000000000 : ℝ) ≤ (-(1161966102717595133409 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22373929120856623 / 40000000000000000 : ℝ) = - (22373929120856623 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22373929120856623 / 20000000000000000 : ℚ)) - (U := (224328257882404866591 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22373929120856623 / 20000000000000000 : ℝ) ≤ - (224328257882404866591 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5592820967636749 / 10000000000000000 : ℝ)) (q := - (22373929120856623 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22373929120856623 / 40000000000000000 : ℚ)) + (r' := (22373929120856623 / 20000000000000000 : ℚ)) + (U := (-(1161966102717595133409 / 2000000000000000000000 : ℚ))) + (U' := (224328257882404866591 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (5592820967636749 / 10000000000000000 : ℚ)) + (q := (22373929120856623 / 40000000000000000 : ℚ)) + (U := (-(1161966102717595133409 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_4 : Uω (aρ 4) (bρ 4) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3867,25 +3399,21 @@ lemma U_517_4 : have hlg : Real.log (4411153139650971 / 8000000000000000 : ℝ) ≤ (-(5953054032277824673143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4411153139650971 / 8000000000000000 : ℝ) = - (4411153139650971 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4411153139650971 / 4000000000000000 : ℚ)) - (U := (978417770722175326857 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4411153139650971 / 4000000000000000 : ℝ) ≤ - (978417770722175326857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1102406687480173 / 2000000000000000 : ℝ)) (q := - (4411153139650971 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4411153139650971 / 8000000000000000 : ℚ)) + (r' := (4411153139650971 / 4000000000000000 : ℚ)) + (U := (-(5953054032277824673143 / 10000000000000000000000 : ℚ))) + (U' := (978417770722175326857 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (1102406687480173 / 2000000000000000 : ℚ)) + (q := (4411153139650971 / 8000000000000000 : ℚ)) + (U := (-(5953054032277824673143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_5 : Uω (aρ 5) (bρ 5) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3893,25 +3421,21 @@ lemma U_517_5 : have hlg : Real.log (862835463099039 / 1600000000000000 : ℝ) ≤ (-(3087674459787515912569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (862835463099039 / 1600000000000000 : ℝ) = - (862835463099039 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (862835463099039 / 800000000000000 : ℚ)) - (U := (378061441712484087431 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (862835463099039 / 800000000000000 : ℝ) ≤ - (378061441712484087431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (215511351853857 / 400000000000000 : ℝ)) (q := - (862835463099039 / 1600000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (862835463099039 / 1600000000000000 : ℚ)) + (r' := (862835463099039 / 800000000000000 : ℚ)) + (U := (-(3087674459787515912569 / 5000000000000000000000 : ℚ))) + (U' := (378061441712484087431 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (215511351853857 / 400000000000000 : ℚ)) + (q := (862835463099039 / 1600000000000000 : ℚ)) + (U := (-(3087674459787515912569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_6 : Uω (aρ 6) (bρ 6) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3919,25 +3443,21 @@ lemma U_517_6 : have hlg : Real.log (834985775376793 / 1600000000000000 : ℝ) ≤ (-(1300688437478143619327 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (834985775376793 / 1600000000000000 : ℝ) = - (834985775376793 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (834985775376793 / 800000000000000 : ℚ)) - (U := (85605923121856380673 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (834985775376793 / 800000000000000 : ℝ) ≤ - (85605923121856380673 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (104138061499167 / 200000000000000 : ℝ)) (q := - (834985775376793 / 1600000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (834985775376793 / 1600000000000000 : ℚ)) + (r' := (834985775376793 / 800000000000000 : ℚ)) + (U := (-(1300688437478143619327 / 2000000000000000000000 : ℚ))) + (U' := (85605923121856380673 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (104138061499167 / 200000000000000 : ℚ)) + (q := (834985775376793 / 1600000000000000 : ℚ)) + (U := (-(1300688437478143619327 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_7 : Uω (aρ 7) (bρ 7) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3945,25 +3465,21 @@ lemma U_517_7 : have hlg : Real.log (19922889199123587 / 40000000000000000 : ℝ) ≤ (-(6970101718382483444987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19922889199123587 / 40000000000000000 : ℝ) = - (19922889199123587 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19922889199123587 / 10000000000000000 : ℚ)) - (U := (6892841887617516555013 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19922889199123587 / 10000000000000000 : ℝ) ≤ - (6892841887617516555013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4954686863070231 / 10000000000000000 : ℝ)) (q := - (19922889199123587 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19922889199123587 / 40000000000000000 : ℚ)) + (r' := (19922889199123587 / 10000000000000000 : ℚ)) + (U := (-(6970101718382483444987 / 10000000000000000000000 : ℚ))) + (U' := (6892841887617516555013 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (4954686863070231 / 10000000000000000 : ℚ)) + (q := (19922889199123587 / 40000000000000000 : ℚ)) + (U := (-(6970101718382483444987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_8 : Uω (aρ 8) (bρ 8) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3971,25 +3487,21 @@ lemma U_517_8 : have hlg : Real.log (18676776619031389 / 40000000000000000 : ℝ) ≤ (-(304639437420347823563 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18676776619031389 / 40000000000000000 : ℝ) = - (18676776619031389 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18676776619031389 / 10000000000000000 : ℚ)) - (U := (249878306819652176437 / 400000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18676776619031389 / 10000000000000000 : ℝ) ≤ - (249878306819652176437 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1153793056091033 / 2500000000000000 : ℝ)) (q := - (18676776619031389 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18676776619031389 / 40000000000000000 : ℚ)) + (r' := (18676776619031389 / 10000000000000000 : ℚ)) + (U := (-(304639437420347823563 / 400000000000000000000 : ℚ))) + (U' := (249878306819652176437 / 400000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (1153793056091033 / 2500000000000000 : ℚ)) + (q := (18676776619031389 / 40000000000000000 : ℚ)) + (U := (-(304639437420347823563 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_9 : Uω (aρ 9) (bρ 9) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -3997,25 +3509,21 @@ lemma U_517_9 : have hlg : Real.log (17105402580301911 / 40000000000000000 : ℝ) ≤ (-(1698970199231094459177 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17105402580301911 / 40000000000000000 : ℝ) = - (17105402580301911 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17105402580301911 / 10000000000000000 : ℚ)) - (U := (1073618521968905540823 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17105402580301911 / 10000000000000000 : ℝ) ≤ - (1073618521968905540823 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4170450833359393 / 10000000000000000 : ℝ)) (q := - (17105402580301911 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17105402580301911 / 40000000000000000 : ℚ)) + (r' := (17105402580301911 / 10000000000000000 : ℚ)) + (U := (-(1698970199231094459177 / 2000000000000000000000 : ℚ))) + (U' := (1073618521968905540823 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (4170450833359393 / 10000000000000000 : ℚ)) + (q := (17105402580301911 / 40000000000000000 : ℚ)) + (U := (-(1698970199231094459177 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_10 : Uω (aρ 10) (bρ 10) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -4023,26 +3531,21 @@ lemma U_517_10 : have hlg : Real.log (15181854597792241 / 40000000000000000 : ℝ) ≤ (-(4843892576607819671637 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15181854597792241 / 40000000000000000 : ℝ) = - (15181854597792241 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15181854597792241 / 10000000000000000 : ℚ)) - (U := (2087579226392180328363 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15181854597792241 / 10000000000000000 : ℝ) ≤ - (2087579226392180328363 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1798617937799779 / 5000000000000000 : ℝ)) (q := - (15181854597792241 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15181854597792241 / 40000000000000000 : ℚ)) + (r' := (15181854597792241 / 10000000000000000 : ℚ)) + (U := (-(4843892576607819671637 / 5000000000000000000000 : ℚ))) + (U' := (2087579226392180328363 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (1798617937799779 / 5000000000000000 : ℚ)) + (q := (15181854597792241 / 40000000000000000 : ℚ)) + (U := (-(4843892576607819671637 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_11 : Uω (aρ 11) (bρ 11) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -4050,26 +3553,21 @@ lemma U_517_11 : have hlg : Real.log (12858214573984021 / 40000000000000000 : ℝ) ≤ (-(2269793160077358042791 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12858214573984021 / 40000000000000000 : ℝ) = - (12858214573984021 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12858214573984021 / 10000000000000000 : ℚ)) - (U := (502795561122641957209 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12858214573984021 / 10000000000000000 : ℝ) ≤ - (502795561122641957209 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89184140309389 / 312500000000000 : ℝ)) (q := - (12858214573984021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12858214573984021 / 40000000000000000 : ℚ)) + (r' := (12858214573984021 / 10000000000000000 : ℚ)) + (U := (-(2269793160077358042791 / 2000000000000000000000 : ℚ))) + (U' := (502795561122641957209 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (89184140309389 / 312500000000000 : ℚ)) + (q := (12858214573984021 / 40000000000000000 : ℚ)) + (U := (-(2269793160077358042791 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_12 : Uω (aρ 12) (bρ 12) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -4077,26 +3575,21 @@ lemma U_517_12 : have hlg : Real.log (9930384717987227 / 40000000000000000 : ℝ) ≤ (-(13932802330277890281229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9930384717987227 / 40000000000000000 : ℝ) = - (9930384717987227 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9930384717987227 / 5000000000000000 : ℚ)) - (U := (6861613078722109718771 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9930384717987227 / 5000000000000000 : ℝ) ≤ - (6861613078722109718771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1813677658587051 / 10000000000000000 : ℝ)) (q := - (9930384717987227 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9930384717987227 / 40000000000000000 : ℚ)) + (r' := (9930384717987227 / 5000000000000000 : ℚ)) + (U := (-(13932802330277890281229 / 10000000000000000000000 : ℚ))) + (U' := (6861613078722109718771 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (18335378975157 / 32000000000000 : ℚ)) + (s := (1813677658587051 / 10000000000000000 : ℚ)) + (q := (9930384717987227 / 40000000000000000 : ℚ)) + (U := (-(13932802330277890281229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_517_13 : Uω (aρ 13) (bρ 13) (18335378975157 / 32000000000000 : ℝ) ≤ @@ -4209,25 +3702,21 @@ lemma U_518_1 : have hlg : Real.log (11380489901754463 / 20000000000000000 : ℝ) ≤ (-(704789745198935614057 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11380489901754463 / 20000000000000000 : ℝ) = - (11380489901754463 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11380489901754463 / 10000000000000000 : ℚ)) - (U := (161644230176064385943 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11380489901754463 / 10000000000000000 : ℝ) ≤ - (161644230176064385943 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5690216539466963 / 10000000000000000 : ℝ)) (q := - (11380489901754463 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11380489901754463 / 20000000000000000 : ℚ)) + (r' := (11380489901754463 / 10000000000000000 : ℚ)) + (U := (-(704789745198935614057 / 1250000000000000000000 : ℚ))) + (U' := (161644230176064385943 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (5690216539466963 / 10000000000000000 : ℚ)) + (q := (11380489901754463 / 20000000000000000 : ℚ)) + (U := (-(704789745198935614057 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_2 : Uω (aρ 2) (bρ 2) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4235,25 +3724,21 @@ lemma U_518_2 : have hlg : Real.log (5666317115820643 / 10000000000000000 : ℝ) ≤ (-(568045724692035134871 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5666317115820643 / 10000000000000000 : ℝ) = - (5666317115820643 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5666317115820643 / 5000000000000000 : ℚ)) - (U := (125101455607964865129 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5666317115820643 / 5000000000000000 : ℝ) ≤ - (125101455607964865129 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2833064940931893 / 5000000000000000 : ℝ)) (q := - (5666317115820643 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5666317115820643 / 10000000000000000 : ℚ)) + (r' := (5666317115820643 / 5000000000000000 : ℚ)) + (U := (-(568045724692035134871 / 1000000000000000000000 : ℚ))) + (U' := (125101455607964865129 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (2833064940931893 / 5000000000000000 : ℚ)) + (q := (5666317115820643 / 10000000000000000 : ℚ)) + (U := (-(568045724692035134871 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_3 : Uω (aρ 3) (bρ 3) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4261,25 +3746,21 @@ lemma U_518_3 : have hlg : Real.log (11236899739257623 / 20000000000000000 : ℝ) ≤ (-(5765292907843755640569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11236899739257623 / 20000000000000000 : ℝ) = - (11236899739257623 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11236899739257623 / 10000000000000000 : ℚ)) - (U := (1166178895156244359431 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11236899739257623 / 10000000000000000 : ℝ) ≤ - (1166178895156244359431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5617791495830123 / 10000000000000000 : ℝ)) (q := - (11236899739257623 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11236899739257623 / 20000000000000000 : ℚ)) + (r' := (11236899739257623 / 10000000000000000 : ℚ)) + (U := (-(5765292907843755640569 / 10000000000000000000000 : ℚ))) + (U' := (1166178895156244359431 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (5617791495830123 / 10000000000000000 : ℚ)) + (q := (11236899739257623 / 20000000000000000 : ℚ)) + (U := (-(5765292907843755640569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_4 : Uω (aρ 4) (bρ 4) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4287,25 +3768,21 @@ lemma U_518_4 : have hlg : Real.log (11077829355447301 / 20000000000000000 : ℝ) ≤ (-(184620786785993711109 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11077829355447301 / 20000000000000000 : ℝ) = - (11077829355447301 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11077829355447301 / 10000000000000000 : ℚ)) - (U := (31987707057756288891 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11077829355447301 / 10000000000000000 : ℝ) ≤ - (31987707057756288891 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5537015293084801 / 10000000000000000 : ℝ)) (q := - (11077829355447301 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11077829355447301 / 20000000000000000 : ℚ)) + (r' := (11077829355447301 / 10000000000000000 : ℚ)) + (U := (-(184620786785993711109 / 312500000000000000000 : ℚ))) + (U' := (31987707057756288891 / 312500000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (5537015293084801 / 10000000000000000 : ℚ)) + (q := (11077829355447301 / 20000000000000000 : ℚ)) + (U := (-(184620786785993711109 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_5 : Uω (aρ 5) (bρ 5) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4313,25 +3790,21 @@ lemma U_518_5 : have hlg : Real.log (10835418138452883 / 20000000000000000 : ℝ) ≤ (-(1225824095183702422711 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10835418138452883 / 20000000000000000 : ℝ) = - (10835418138452883 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10835418138452883 / 10000000000000000 : ℚ)) - (U := (160470265416297577289 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10835418138452883 / 10000000000000000 : ℝ) ≤ - (160470265416297577289 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5412793995425383 / 10000000000000000 : ℝ)) (q := - (10835418138452883 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10835418138452883 / 20000000000000000 : ℚ)) + (r' := (10835418138452883 / 10000000000000000 : ℚ)) + (U := (-(1225824095183702422711 / 2000000000000000000000 : ℚ))) + (U' := (160470265416297577289 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (5412793995425383 / 10000000000000000 : ℚ)) + (q := (10835418138452883 / 20000000000000000 : ℚ)) + (U := (-(1225824095183702422711 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_6 : Uω (aρ 6) (bρ 6) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4339,25 +3812,21 @@ lemma U_518_6 : have hlg : Real.log (5243681851321087 / 10000000000000000 : ℝ) ≤ (-(403475748598469510607 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5243681851321087 / 10000000000000000 : ℝ) = - (5243681851321087 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5243681851321087 / 5000000000000000 : ℚ)) - (U := (29741239089030489393 / 625000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5243681851321087 / 5000000000000000 : ℝ) ≤ - (29741239089030489393 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2615989967377337 / 5000000000000000 : ℝ)) (q := - (5243681851321087 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5243681851321087 / 10000000000000000 : ℚ)) + (r' := (5243681851321087 / 5000000000000000 : ℚ)) + (U := (-(403475748598469510607 / 625000000000000000000 : ℚ))) + (U' := (29741239089030489393 / 625000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (2615989967377337 / 5000000000000000 : ℚ)) + (q := (5243681851321087 / 10000000000000000 : ℚ)) + (U := (-(403475748598469510607 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_7 : Uω (aρ 7) (bρ 7) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4365,25 +3834,21 @@ lemma U_518_7 : have hlg : Real.log (156431795978329 / 312500000000000 : ℝ) ≤ (-(6919843623735854358829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (156431795978329 / 312500000000000 : ℝ) = - (156431795978329 / 156250000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (156431795978329 / 156250000000000 : ℚ)) - (U := (11628179264145641171 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (156431795978329 / 156250000000000 : ℝ) ≤ - (11628179264145641171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1244978138871389 / 2500000000000000 : ℝ)) (q := - (156431795978329 / 312500000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (156431795978329 / 312500000000000 : ℚ)) + (r' := (156431795978329 / 156250000000000 : ℚ)) + (U := (-(6919843623735854358829 / 10000000000000000000000 : ℚ))) + (U' := (11628179264145641171 / 10000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (1244978138871389 / 2500000000000000 : ℚ)) + (q := (156431795978329 / 312500000000000 : ℚ)) + (U := (-(6919843623735854358829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_8 : Uω (aρ 8) (bρ 8) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4391,25 +3856,21 @@ lemma U_518_8 : have hlg : Real.log (4694449433491747 / 10000000000000000 : ℝ) ≤ (-(7562042532521178980667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4694449433491747 / 10000000000000000 : ℝ) = - (4694449433491747 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4694449433491747 / 2500000000000000 : ℚ)) - (U := (6300901073478821019333 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4694449433491747 / 2500000000000000 : ℝ) ≤ - (6300901073478821019333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2320359065597997 / 5000000000000000 : ℝ)) (q := - (4694449433491747 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4694449433491747 / 10000000000000000 : ℚ)) + (r' := (4694449433491747 / 2500000000000000 : ℚ)) + (U := (-(7562042532521178980667 / 10000000000000000000000 : ℚ))) + (U' := (6300901073478821019333 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (2320359065597997 / 5000000000000000 : ℚ)) + (q := (4694449433491747 / 10000000000000000 : ℚ)) + (U := (-(7562042532521178980667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_9 : Uω (aρ 9) (bρ 9) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4417,25 +3878,21 @@ lemma U_518_9 : have hlg : Real.log (860389070729883 / 2000000000000000 : ℝ) ≤ (-(843517764254758507903 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (860389070729883 / 2000000000000000 : ℝ) = - (860389070729883 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (860389070729883 / 500000000000000 : ℚ)) - (U := (542776596345241492097 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (860389070729883 / 500000000000000 : ℝ) ≤ - (542776596345241492097 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (419667559987133 / 1000000000000000 : ℝ)) (q := - (860389070729883 / 2000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (860389070729883 / 2000000000000000 : ℚ)) + (r' := (860389070729883 / 500000000000000 : ℚ)) + (U := (-(843517764254758507903 / 1000000000000000000000 : ℚ))) + (U' := (542776596345241492097 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (419667559987133 / 1000000000000000 : ℚ)) + (q := (860389070729883 / 2000000000000000 : ℚ)) + (U := (-(843517764254758507903 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_10 : Uω (aρ 10) (bρ 10) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4443,26 +3900,21 @@ lemma U_518_10 : have hlg : Real.log (3821793995318473 / 10000000000000000 : ℝ) ≤ (-(9618651478160744289729 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3821793995318473 / 10000000000000000 : ℝ) = - (3821793995318473 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3821793995318473 / 2500000000000000 : ℚ)) - (U := (4244292127839255710271 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3821793995318473 / 2500000000000000 : ℝ) ≤ - (4244292127839255710271 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1812465958352223 / 5000000000000000 : ℝ)) (q := - (3821793995318473 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3821793995318473 / 10000000000000000 : ℚ)) + (r' := (3821793995318473 / 2500000000000000 : ℚ)) + (U := (-(9618651478160744289729 / 10000000000000000000000 : ℚ))) + (U' := (4244292127839255710271 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (1812465958352223 / 5000000000000000 : ℚ)) + (q := (3821793995318473 / 10000000000000000 : ℚ)) + (U := (-(9618651478160744289729 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_11 : Uω (aρ 11) (bρ 11) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4470,26 +3922,21 @@ lemma U_518_11 : have hlg : Real.log (6485284914501151 / 20000000000000000 : ℝ) ≤ (-(2252393043687111150489 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6485284914501151 / 20000000000000000 : ℝ) = - (6485284914501151 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6485284914501151 / 5000000000000000 : ℚ)) - (U := (520195677512888849511 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6485284914501151 / 5000000000000000 : ℝ) ≤ - (520195677512888849511 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2885105466773651 / 10000000000000000 : ℝ)) (q := - (6485284914501151 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6485284914501151 / 20000000000000000 : ℚ)) + (r' := (6485284914501151 / 5000000000000000 : ℚ)) + (U := (-(2252393043687111150489 / 2000000000000000000000 : ℚ))) + (U' := (520195677512888849511 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (2885105466773651 / 10000000000000000 : ℚ)) + (q := (6485284914501151 / 20000000000000000 : ℚ)) + (U := (-(2252393043687111150489 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_12 : Uω (aρ 12) (bρ 12) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4497,26 +3944,21 @@ lemma U_518_12 : have hlg : Real.log (2516598820731029 / 10000000000000000 : ℝ) ≤ (-(6898383884473223033613 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2516598820731029 / 10000000000000000 : ℝ) = - (2516598820731029 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2516598820731029 / 2500000000000000 : ℚ)) - (U := (33087918526776966387 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2516598820731029 / 2500000000000000 : ℝ) ≤ - (33087918526776966387 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (928359145209779 / 5000000000000000 : ℝ)) (q := - (2516598820731029 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2516598820731029 / 10000000000000000 : ℚ)) + (r' := (2516598820731029 / 2500000000000000 : ℚ)) + (U := (-(6898383884473223033613 / 5000000000000000000000 : ℚ))) + (U' := (33087918526776966387 / 5000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2301908232149 / 4000000000000 : ℚ)) + (s := (928359145209779 / 5000000000000000 : ℚ)) + (q := (2516598820731029 / 10000000000000000 : ℚ)) + (U := (-(6898383884473223033613 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_518_13 : Uω (aρ 13) (bρ 13) (2301908232149 / 4000000000000 : ℝ) ≤ @@ -4628,25 +4070,21 @@ lemma U_519_1 : have hlg : Real.log (22860838902471523 / 40000000000000000 : ℝ) ≤ (-(2797270493823523605897 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22860838902471523 / 40000000000000000 : ℝ) = - (22860838902471523 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22860838902471523 / 20000000000000000 : ℚ)) - (U := (668465407676476394103 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22860838902471523 / 20000000000000000 : ℝ) ≤ - (668465407676476394103 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1428795359578081 / 2500000000000000 : ℝ)) (q := - (22860838902471523 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22860838902471523 / 40000000000000000 : ℚ)) + (r' := (22860838902471523 / 20000000000000000 : ℚ)) + (U := (-(2797270493823523605897 / 5000000000000000000000 : ℚ))) + (U' := (668465407676476394103 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (1428795359578081 / 2500000000000000 : ℚ)) + (q := (22860838902471523 / 40000000000000000 : ℚ)) + (U := (-(2797270493823523605897 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_2 : Uω (aρ 2) (bρ 2) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4654,25 +4092,21 @@ lemma U_519_2 : have hlg : Real.log (22765130351120297 / 40000000000000000 : ℝ) ≤ (-(5636494591394130888957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22765130351120297 / 40000000000000000 : ℝ) = - (22765130351120297 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22765130351120297 / 20000000000000000 : ℚ)) - (U := (1294977211605869111043 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22765130351120297 / 20000000000000000 : ℝ) ≤ - (1294977211605869111043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5691096175146711 / 10000000000000000 : ℝ)) (q := - (22765130351120297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22765130351120297 / 40000000000000000 : ℚ)) + (r' := (22765130351120297 / 20000000000000000 : ℚ)) + (U := (-(5636494591394130888957 / 10000000000000000000000 : ℚ))) + (U' := (1294977211605869111043 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (5691096175146711 / 10000000000000000 : ℚ)) + (q := (22765130351120297 / 40000000000000000 : ℚ)) + (U := (-(5636494591394130888957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_3 : Uω (aρ 3) (bρ 3) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4680,25 +4114,21 @@ lemma U_519_3 : have hlg : Real.log (4514733946429581 / 8000000000000000 : ℝ) ≤ (-(178779775900266116243 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4514733946429581 / 8000000000000000 : ℝ) = - (4514733946429581 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4514733946429581 / 4000000000000000 : ℚ)) - (U := (37828717943483883757 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4514733946429581 / 4000000000000000 : ℝ) ≤ - (37828717943483883757 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1128552394402103 / 2000000000000000 : ℝ)) (q := - (4514733946429581 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4514733946429581 / 8000000000000000 : ℚ)) + (r' := (4514733946429581 / 4000000000000000 : ℚ)) + (U := (-(178779775900266116243 / 312500000000000000000 : ℚ))) + (U' := (37828717943483883757 / 312500000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (1128552394402103 / 2000000000000000 : ℚ)) + (q := (4514733946429581 / 8000000000000000 : ℚ)) + (U := (-(178779775900266116243 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_4 : Uω (aρ 4) (bρ 4) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4706,25 +4136,21 @@ lemma U_519_4 : have hlg : Real.log (22255551414533091 / 40000000000000000 : ℝ) ≤ (-(5862879745853656565577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22255551414533091 / 40000000000000000 : ℝ) = - (22255551414533091 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22255551414533091 / 20000000000000000 : ℚ)) - (U := (1068592057146343434423 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22255551414533091 / 20000000000000000 : ℝ) ≤ - (1068592057146343434423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1390499248567027 / 2500000000000000 : ℝ)) (q := - (22255551414533091 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22255551414533091 / 40000000000000000 : ℚ)) + (r' := (22255551414533091 / 20000000000000000 : ℚ)) + (U := (-(5862879745853656565577 / 10000000000000000000000 : ℚ))) + (U' := (1068592057146343434423 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (1390499248567027 / 2500000000000000 : ℚ)) + (q := (22255551414533091 / 40000000000000000 : ℚ)) + (U := (-(5862879745853656565577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_5 : Uω (aρ 5) (bρ 5) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4732,25 +4158,21 @@ lemma U_519_5 : have hlg : Real.log (21770785139131201 / 40000000000000000 : ℝ) ≤ (-(6083105140703991195419 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21770785139131201 / 40000000000000000 : ℝ) = - (21770785139131201 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21770785139131201 / 20000000000000000 : ℚ)) - (U := (848366662296008804581 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21770785139131201 / 20000000000000000 : ℝ) ≤ - (848366662296008804581 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5437803775902163 / 10000000000000000 : ℝ)) (q := - (21770785139131201 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21770785139131201 / 40000000000000000 : ℚ)) + (r' := (21770785139131201 / 20000000000000000 : ℚ)) + (U := (-(6083105140703991195419 / 10000000000000000000000 : ℚ))) + (U' := (848366662296008804581 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (5437803775902163 / 10000000000000000 : ℚ)) + (q := (21770785139131201 / 40000000000000000 : ℚ)) + (U := (-(6083105140703991195419 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_6 : Uω (aρ 6) (bρ 6) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4758,25 +4180,21 @@ lemma U_519_6 : have hlg : Real.log (21074808289928297 / 40000000000000000 : ℝ) ≤ (-(3204005232853766005531 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21074808289928297 / 40000000000000000 : ℝ) = - (21074808289928297 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21074808289928297 / 20000000000000000 : ℚ)) - (U := (261730668646233994469 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21074808289928297 / 20000000000000000 : ℝ) ≤ - (261730668646233994469 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5257055726440711 / 10000000000000000 : ℝ)) (q := - (21074808289928297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21074808289928297 / 40000000000000000 : ℚ)) + (r' := (21074808289928297 / 20000000000000000 : ℚ)) + (U := (-(3204005232853766005531 / 5000000000000000000000 : ℚ))) + (U' := (261730668646233994469 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (5257055726440711 / 10000000000000000 : ℚ)) + (q := (21074808289928297 / 40000000000000000 : ℚ)) + (U := (-(3204005232853766005531 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_7 : Uω (aρ 7) (bρ 7) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4784,25 +4202,21 @@ lemma U_519_7 : have hlg : Real.log (20123645335996769 / 40000000000000000 : ℝ) ≤ (-(214682482910002087813 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20123645335996769 / 40000000000000000 : ℝ) = - (20123645335996769 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20123645335996769 / 20000000000000000 : ℚ)) - (U := (1926010933747912187 / 312500000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20123645335996769 / 20000000000000000 : ℝ) ≤ - (1926010933747912187 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5005135630234947 / 10000000000000000 : ℝ)) (q := - (20123645335996769 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20123645335996769 / 40000000000000000 : ℚ)) + (r' := (20123645335996769 / 20000000000000000 : ℚ)) + (U := (-(214682482910002087813 / 312500000000000000000 : ℚ))) + (U' := (1926010933747912187 / 312500000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (5005135630234947 / 10000000000000000 : ℚ)) + (q := (20123645335996769 / 40000000000000000 : ℚ)) + (U := (-(214682482910002087813 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_8 : Uω (aρ 8) (bρ 8) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4810,25 +4224,21 @@ lemma U_519_8 : have hlg : Real.log (18878806265133627 / 40000000000000000 : ℝ) ≤ (-(3754197611789808260037 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18878806265133627 / 40000000000000000 : ℝ) = - (18878806265133627 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18878806265133627 / 10000000000000000 : ℚ)) - (U := (3177274191210191739963 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18878806265133627 / 10000000000000000 : ℝ) ≤ - (3177274191210191739963 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (291641109133961 / 625000000000000 : ℝ)) (q := - (18878806265133627 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18878806265133627 / 40000000000000000 : ℚ)) + (r' := (18878806265133627 / 10000000000000000 : ℚ)) + (U := (-(3754197611789808260037 / 5000000000000000000000 : ℚ))) + (U' := (3177274191210191739963 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (291641109133961 / 625000000000000 : ℚ)) + (q := (18878806265133627 / 40000000000000000 : ℚ)) + (U := (-(3754197611789808260037 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_9 : Uω (aρ 9) (bρ 9) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4836,25 +4246,21 @@ lemma U_519_9 : have hlg : Real.log (3462025939787131 / 8000000000000000 : ℝ) ≤ (-(1046984489645930925899 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3462025939787131 / 8000000000000000 : ℝ) = - (3462025939787131 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3462025939787131 / 2000000000000000 : ℚ)) - (U := (685883461104069074101 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3462025939787131 / 2000000000000000 : ℝ) ≤ - (685883461104069074101 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (422288509140439 / 1000000000000000 : ℝ)) (q := - (3462025939787131 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3462025939787131 / 8000000000000000 : ℚ)) + (r' := (3462025939787131 / 2000000000000000 : ℚ)) + (U := (-(1046984489645930925899 / 1250000000000000000000 : ℚ))) + (U' := (685883461104069074101 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (422288509140439 / 1000000000000000 : ℚ)) + (q := (3462025939787131 / 8000000000000000 : ℚ)) + (U := (-(1046984489645930925899 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_10 : Uω (aρ 10) (bρ 10) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4862,26 +4268,21 @@ lemma U_519_10 : have hlg : Real.log (15392418606289839 / 40000000000000000 : ℝ) ≤ (-(4775021818429599099321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15392418606289839 / 40000000000000000 : ℝ) = - (15392418606289839 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15392418606289839 / 10000000000000000 : ℚ)) - (U := (2156449984570400900679 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15392418606289839 / 10000000000000000 : ℝ) ≤ - (2156449984570400900679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1826294289288241 / 5000000000000000 : ℝ)) (q := - (15392418606289839 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15392418606289839 / 40000000000000000 : ℚ)) + (r' := (15392418606289839 / 10000000000000000 : ℚ)) + (U := (-(4775021818429599099321 / 5000000000000000000000 : ℚ))) + (U' := (2156449984570400900679 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (1826294289288241 / 5000000000000000 : ℚ)) + (q := (15392418606289839 / 40000000000000000 : ℚ)) + (U := (-(4775021818429599099321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_11 : Uω (aρ 11) (bρ 11) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4889,26 +4290,21 @@ lemma U_519_11 : have hlg : Real.log (13082684353527947 / 40000000000000000 : ℝ) ≤ (-(11175899028160388580739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13082684353527947 / 40000000000000000 : ℝ) = - (13082684353527947 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13082684353527947 / 10000000000000000 : ℚ)) - (U := (2687044577839611419261 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13082684353527947 / 10000000000000000 : ℝ) ≤ - (2687044577839611419261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (364524759800067 / 1250000000000000 : ℝ)) (q := - (13082684353527947 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13082684353527947 / 40000000000000000 : ℚ)) + (r' := (13082684353527947 / 10000000000000000 : ℚ)) + (U := (-(11175899028160388580739 / 10000000000000000000000 : ℚ))) + (U' := (2687044577839611419261 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (364524759800067 / 1250000000000000 : ℚ)) + (q := (13082684353527947 / 40000000000000000 : ℚ)) + (U := (-(11175899028160388580739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_12 : Uω (aρ 12) (bρ 12) (18495152739227 / 32000000000000 : ℝ) ≤ @@ -4916,26 +4312,21 @@ lemma U_519_12 : have hlg : Real.log (10201111502974553 / 40000000000000000 : ℝ) ≤ (-(13663827683608571830467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10201111502974553 / 40000000000000000 : ℝ) = - (10201111502974553 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10201111502974553 / 10000000000000000 : ℚ)) - (U := (199115922391428169533 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10201111502974553 / 10000000000000000 : ℝ) ≤ - (199115922391428169533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1899111749808839 / 10000000000000000 : ℝ)) (q := - (10201111502974553 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10201111502974553 / 40000000000000000 : ℚ)) + (r' := (10201111502974553 / 10000000000000000 : ℚ)) + (U := (-(13663827683608571830467 / 10000000000000000000000 : ℚ))) + (U' := (199115922391428169533 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (18495152739227 / 32000000000000 : ℚ)) + (s := (1899111749808839 / 10000000000000000 : ℚ)) + (q := (10201111502974553 / 40000000000000000 : ℚ)) + (U := (-(13663827683608571830467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_519_13 : Uω (aρ 13) (bρ 13) (18495152739227 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U43.lean b/LeanPool/Zeta5Irrational/Table/U43.lean index 55a30cc2d4..8462e69c12 100644 --- a/LeanPool/Zeta5Irrational/Table/U43.lean +++ b/LeanPool/Zeta5Irrational/Table/U43.lean @@ -24,25 +24,21 @@ lemma U_520_1 : have hlg : Real.log (11480348998558059 / 20000000000000000 : ℝ) ≤ (-(2775477411467269153561 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11480348998558059 / 20000000000000000 : ℝ) = - (11480348998558059 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11480348998558059 / 10000000000000000 : ℚ)) - (U := (690258490032730846439 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11480348998558059 / 10000000000000000 : ℝ) ≤ - (690258490032730846439 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1435036583749671 / 2500000000000000 : ℝ)) (q := - (11480348998558059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11480348998558059 / 20000000000000000 : ℚ)) + (r' := (11480348998558059 / 10000000000000000 : ℚ)) + (U := (-(2775477411467269153561 / 5000000000000000000000 : ℚ))) + (U' := (690258490032730846439 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (1435036583749671 / 2500000000000000 : ℚ)) + (q := (11480348998558059 / 20000000000000000 : ℚ)) + (U := (-(2775477411467269153561 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_2 : Uω (aρ 2) (bρ 2) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_520_2 : have hlg : Real.log (11432496105130163 / 20000000000000000 : ℝ) ≤ (-(5592724374280311294667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11432496105130163 / 20000000000000000 : ℝ) = - (11432496105130163 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11432496105130163 / 10000000000000000 : ℚ)) - (U := (1338747428719688705333 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11432496105130163 / 10000000000000000 : ℝ) ≤ - (1338747428719688705333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1429015613520197 / 2500000000000000 : ℝ)) (q := - (11432496105130163 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11432496105130163 / 20000000000000000 : ℚ)) + (r' := (11432496105130163 / 10000000000000000 : ℚ)) + (U := (-(5592724374280311294667 / 10000000000000000000000 : ℚ))) + (U' := (1338747428719688705333 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (1429015613520197 / 2500000000000000 : ℚ)) + (q := (11432496105130163 / 20000000000000000 : ℚ)) + (U := (-(5592724374280311294667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_3 : Uω (aρ 3) (bρ 3) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_520_3 : have hlg : Real.log (2834192485391191 / 5000000000000000 : ℝ) ≤ (-(5676808531728931494759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2834192485391191 / 5000000000000000 : ℝ) = - (2834192485391191 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2834192485391191 / 2500000000000000 : ℚ)) - (U := (1254663271271068505241 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2834192485391191 / 2500000000000000 : ℝ) ≤ - (1254663271271068505241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5667732396865389 / 10000000000000000 : ℝ)) (q := - (2834192485391191 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2834192485391191 / 5000000000000000 : ℚ)) + (r' := (2834192485391191 / 2500000000000000 : ℚ)) + (U := (-(5676808531728931494759 / 10000000000000000000000 : ℚ))) + (U' := (1254663271271068505241 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (5667732396865389 / 10000000000000000 : ℚ)) + (q := (2834192485391191 / 5000000000000000 : ℚ)) + (U := (-(5676808531728931494759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_4 : Uω (aρ 4) (bρ 4) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_520_4 : have hlg : Real.log (11177721906657673 / 20000000000000000 : ℝ) ≤ (-(5818095913874656755391 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11177721906657673 / 20000000000000000 : ℝ) = - (11177721906657673 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11177721906657673 / 10000000000000000 : ℚ)) - (U := (1113375889125343244609 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11177721906657673 / 10000000000000000 : ℝ) ≤ - (1113375889125343244609 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2793489271511649 / 5000000000000000 : ℝ)) (q := - (11177721906657673 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11177721906657673 / 20000000000000000 : ℚ)) + (r' := (11177721906657673 / 10000000000000000 : ℚ)) + (U := (-(5818095913874656755391 / 10000000000000000000000 : ℚ))) + (U' := (1113375889125343244609 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (2793489271511649 / 5000000000000000 : ℚ)) + (q := (11177721906657673 / 20000000000000000 : ℚ)) + (U := (-(5818095913874656755391 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_5 : Uω (aρ 5) (bρ 5) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_520_5 : have hlg : Real.log (683460411739091 / 1250000000000000 : ℝ) ≤ (-(3018650477316833315497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (683460411739091 / 1250000000000000 : ℝ) = - (683460411739091 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (683460411739091 / 625000000000000 : ℚ)) - (U := (447085424183166684503 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (683460411739091 / 625000000000000 : ℝ) ≤ - (447085424183166684503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5462813143526081 / 10000000000000000 : ℝ)) (q := - (683460411739091 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (683460411739091 / 1250000000000000 : ℚ)) + (r' := (683460411739091 / 625000000000000 : ℚ)) + (U := (-(3018650477316833315497 / 5000000000000000000000 : ℚ))) + (U' := (447085424183166684503 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (5462813143526081 / 10000000000000000 : ℚ)) + (q := (683460411739091 / 1250000000000000 : ℚ)) + (U := (-(3018650477316833315497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_6 : Uω (aρ 6) (bρ 6) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_520_6 : have hlg : Real.log (10587443534387717 / 20000000000000000 : ℝ) ≤ (-(795079433204800478269 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10587443534387717 / 20000000000000000 : ℝ) = - (10587443534387717 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10587443534387717 / 10000000000000000 : ℚ)) - (U := (71354542170199521731 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10587443534387717 / 10000000000000000 : ℝ) ≤ - (71354542170199521731 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2641065232614171 / 5000000000000000 : ℝ)) (q := - (10587443534387717 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10587443534387717 / 20000000000000000 : ℚ)) + (r' := (10587443534387717 / 10000000000000000 : ℚ)) + (U := (-(795079433204800478269 / 1250000000000000000000 : ℚ))) + (U' := (71354542170199521731 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (2641065232614171 / 5000000000000000 : ℚ)) + (q := (10587443534387717 / 20000000000000000 : ℚ)) + (U := (-(795079433204800478269 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_7 : Uω (aρ 7) (bρ 7) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_520_7 : have hlg : Real.log (10112007815094067 / 20000000000000000 : ℝ) ≤ (-(6820086630363946455629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10112007815094067 / 20000000000000000 : ℝ) = - (10112007815094067 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10112007815094067 / 10000000000000000 : ℚ)) - (U := (111385172636053544371 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10112007815094067 / 10000000000000000 : ℝ) ≤ - (111385172636053544371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1257589031673673 / 2500000000000000 : ℝ)) (q := - (10112007815094067 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10112007815094067 / 20000000000000000 : ℚ)) + (r' := (10112007815094067 / 10000000000000000 : ℚ)) + (U := (-(6820086630363946455629 / 10000000000000000000000 : ℚ))) + (U' := (111385172636053544371 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (1257589031673673 / 2500000000000000 : ℚ)) + (q := (10112007815094067 / 20000000000000000 : ℚ)) + (U := (-(6820086630363946455629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_8 : Uω (aρ 8) (bρ 8) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_520_8 : have hlg : Real.log (9489901209014669 / 20000000000000000 : ℝ) ≤ (-(7455040704754400716783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9489901209014669 / 20000000000000000 : ℝ) = - (9489901209014669 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9489901209014669 / 5000000000000000 : ℚ)) - (U := (6407902901245599283217 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9489901209014669 / 5000000000000000 : ℝ) ≤ - (6407902901245599283217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2345895585977647 / 5000000000000000 : ℝ)) (q := - (9489901209014669 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9489901209014669 / 20000000000000000 : ℚ)) + (r' := (9489901209014669 / 5000000000000000 : ℚ)) + (U := (-(7455040704754400716783 / 10000000000000000000000 : ℚ))) + (U' := (6407902901245599283217 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (2345895585977647 / 5000000000000000 : ℚ)) + (q := (9489901209014669 / 20000000000000000 : ℚ)) + (U := (-(7455040704754400716783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_9 : Uω (aρ 9) (bρ 9) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_520_9 : have hlg : Real.log (8706223999318771 / 20000000000000000 : ℝ) ≤ (-(8316941009312002770807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8706223999318771 / 20000000000000000 : ℝ) = - (8706223999318771 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8706223999318771 / 5000000000000000 : ℚ)) - (U := (5546002596687997229193 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8706223999318771 / 5000000000000000 : ℝ) ≤ - (5546002596687997229193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1062269897654849 / 2500000000000000 : ℝ)) (q := - (8706223999318771 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8706223999318771 / 20000000000000000 : ℚ)) + (r' := (8706223999318771 / 5000000000000000 : ℚ)) + (U := (-(8316941009312002770807 / 10000000000000000000000 : ℚ))) + (U' := (5546002596687997229193 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (1062269897654849 / 2500000000000000 : ℚ)) + (q := (8706223999318771 / 20000000000000000 : ℚ)) + (U := (-(8316941009312002770807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_10 : Uω (aρ 10) (bρ 10) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_520_10 : have hlg : Real.log (3874396062111003 / 10000000000000000 : ℝ) ≤ (-(4740976483772919301281 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3874396062111003 / 10000000000000000 : ℝ) = - (3874396062111003 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3874396062111003 / 2500000000000000 : ℚ)) - (U := (2190495319227080698719 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3874396062111003 / 2500000000000000 : ℝ) ≤ - (2190495319227080698719 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3680206749017631 / 10000000000000000 : ℝ)) (q := - (3874396062111003 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3874396062111003 / 10000000000000000 : ℚ)) + (r' := (3874396062111003 / 2500000000000000 : ℚ)) + (U := (-(4740976483772919301281 / 5000000000000000000000 : ℚ))) + (U' := (2190495319227080698719 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (3680206749017631 / 10000000000000000 : ℚ)) + (q := (3874396062111003 / 10000000000000000 : ℚ)) + (U := (-(4740976483772919301281 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_11 : Uω (aρ 11) (bρ 11) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_520_11 : have hlg : Real.log (3298641441666869 / 10000000000000000 : ℝ) ≤ (-(5545371965551789929277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3298641441666869 / 10000000000000000 : ℝ) = - (3298641441666869 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3298641441666869 / 2500000000000000 : ℚ)) - (U := (1386099837448210070723 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3298641441666869 / 2500000000000000 : ℝ) ≤ - (1386099837448210070723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2947174134334363 / 10000000000000000 : ℝ)) (q := - (3298641441666869 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3298641441666869 / 10000000000000000 : ℚ)) + (r' := (3298641441666869 / 2500000000000000 : ℚ)) + (U := (-(5545371965551789929277 / 5000000000000000000000 : ℚ))) + (U' := (1386099837448210070723 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (2947174134334363 / 10000000000000000 : ℚ)) + (q := (3298641441666869 / 10000000000000000 : ℚ)) + (U := (-(5545371965551789929277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_12 : Uω (aρ 12) (bρ 12) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_520_12 : have hlg : Real.log (5167309096466059 / 20000000000000000 : ℝ) ≤ (-(1353380204255246507751 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5167309096466059 / 20000000000000000 : ℝ) = - (5167309096466059 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5167309096466059 / 5000000000000000 : ℚ)) - (U := (32914156344753492249 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5167309096466059 / 5000000000000000 : ℝ) ≤ - (32914156344753492249 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (485225111037921 / 2500000000000000 : ℝ)) (q := - (5167309096466059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5167309096466059 / 20000000000000000 : ℚ)) + (r' := (5167309096466059 / 5000000000000000 : ℚ)) + (U := (-(1353380204255246507751 / 1000000000000000000000 : ℚ))) + (U' := (32914156344753492249 / 1000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9287519810631 / 16000000000000 : ℚ)) + (s := (485225111037921 / 2500000000000000 : ℚ)) + (q := (5167309096466059 / 20000000000000000 : ℚ)) + (U := (-(1353380204255246507751 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_520_13 : Uω (aρ 13) (bρ 13) (9287519810631 / 16000000000000 : ℝ) ≤ @@ -444,25 +393,21 @@ lemma U_521_1 : have hlg : Real.log (11580208086837357 / 20000000000000000 : ℝ) ≤ (-(218573932723313454971 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11580208086837357 / 20000000000000000 : ℝ) = - (11580208086837357 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11580208086837357 / 10000000000000000 : ℚ)) - (U := (58684939396686545029 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11580208086837357 / 10000000000000000 : ℝ) ≤ - (58684939396686545029 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5790076122006107 / 10000000000000000 : ℝ)) (q := - (11580208086837357 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11580208086837357 / 20000000000000000 : ℚ)) + (r' := (11580208086837357 / 10000000000000000 : ℚ)) + (U := (-(218573932723313454971 / 400000000000000000000 : ℚ))) + (U' := (58684939396686545029 / 400000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (5790076122006107 / 10000000000000000 : ℚ)) + (q := (11580208086837357 / 20000000000000000 : ℚ)) + (U := (-(218573932723313454971 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_2 : Uω (aρ 2) (bρ 2) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -470,25 +415,21 @@ lemma U_521_2 : have hlg : Real.log (5766178960984599 / 10000000000000000 : ℝ) ≤ (-(5505754567146598031943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5766178960984599 / 10000000000000000 : ℝ) = - (5766178960984599 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5766178960984599 / 5000000000000000 : ℚ)) - (U := (1425717235853401968057 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5766178960984599 / 5000000000000000 : ℝ) ≤ - (1425717235853401968057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1441498742411987 / 2500000000000000 : ℝ)) (q := - (5766178960984599 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5766178960984599 / 10000000000000000 : ℚ)) + (r' := (5766178960984599 / 5000000000000000 : ℚ)) + (U := (-(5505754567146598031943 / 10000000000000000000000 : ℚ))) + (U' := (1425717235853401968057 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (1441498742411987 / 2500000000000000 : ℚ)) + (q := (5766178960984599 / 10000000000000000 : ℚ)) + (U := (-(5505754567146598031943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_3 : Uω (aρ 3) (bρ 3) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -496,25 +437,21 @@ lemma U_521_3 : have hlg : Real.log (285915998531491 / 500000000000000 : ℝ) ≤ (-(698637552390495291897 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (285915998531491 / 500000000000000 : ℝ) = - (285915998531491 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (285915998531491 / 250000000000000 : ℚ)) - (U := (167796422984504708103 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (285915998531491 / 250000000000000 : ℝ) ≤ - (167796422984504708103 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (571767309528839 / 1000000000000000 : ℝ)) (q := - (285915998531491 / 500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (285915998531491 / 500000000000000 : ℚ)) + (r' := (285915998531491 / 250000000000000 : ℚ)) + (U := (-(698637552390495291897 / 1250000000000000000000 : ℚ))) + (U' := (167796422984504708103 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (571767309528839 / 1000000000000000 : ℚ)) + (q := (285915998531491 / 500000000000000 : ℚ)) + (U := (-(698637552390495291897 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_4 : Uω (aρ 4) (bρ 4) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -522,25 +459,21 @@ lemma U_521_4 : have hlg : Real.log (11277613856261851 / 20000000000000000 : ℝ) ≤ (-(5729125871667981875797 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11277613856261851 / 20000000000000000 : ℝ) = - (11277613856261851 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11277613856261851 / 10000000000000000 : ℚ)) - (U := (1202345931332018124203 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11277613856261851 / 10000000000000000 : ℝ) ≤ - (1202345931332018124203 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5636941191355601 / 10000000000000000 : ℝ)) (q := - (11277613856261851 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11277613856261851 / 20000000000000000 : ℚ)) + (r' := (11277613856261851 / 10000000000000000 : ℚ)) + (U := (-(5729125871667981875797 / 10000000000000000000000 : ℚ))) + (U' := (1202345931332018124203 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (5636941191355601 / 10000000000000000 : ℚ)) + (q := (11277613856261851 / 20000000000000000 : ℚ)) + (U := (-(5729125871667981875797 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_5 : Uω (aρ 5) (bρ 5) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -548,25 +481,21 @@ lemma U_521_5 : have hlg : Real.log (2207062681652349 / 4000000000000000 : ℝ) ≤ (-(2973159163481224856561 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2207062681652349 / 4000000000000000 : ℝ) = - (2207062681652349 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2207062681652349 / 2000000000000000 : ℚ)) - (U := (492576738018775143439 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2207062681652349 / 2000000000000000 : ℝ) ≤ - (492576738018775143439 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1102566132538099 / 2000000000000000 : ℝ)) (q := - (2207062681652349 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2207062681652349 / 4000000000000000 : ℚ)) + (r' := (2207062681652349 / 2000000000000000 : ℚ)) + (U := (-(2973159163481224856561 / 5000000000000000000000 : ℚ))) + (U' := (492576738018775143439 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (1102566132538099 / 2000000000000000 : ℚ)) + (q := (2207062681652349 / 4000000000000000 : ℚ)) + (U := (-(2973159163481224856561 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_6 : Uω (aρ 6) (bρ 6) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -574,25 +503,21 @@ lemma U_521_6 : have hlg : Real.log (1068751921395337 / 2000000000000000 : ℝ) ≤ (-(7833195515449707049 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1068751921395337 / 2000000000000000 : ℝ) = - (1068751921395337 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1068751921395337 / 1000000000000000 : ℚ)) - (U := (831144238300292951 / 12500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1068751921395337 / 1000000000000000 : ℝ) ≤ - (831144238300292951 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (133306921088053 / 250000000000000 : ℝ)) (q := - (1068751921395337 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1068751921395337 / 2000000000000000 : ℚ)) + (r' := (1068751921395337 / 1000000000000000 : ℚ)) + (U := (-(7833195515449707049 / 12500000000000000000 : ℚ))) + (U' := (831144238300292951 / 12500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (133306921088053 / 250000000000000 : ℚ)) + (q := (1068751921395337 / 2000000000000000 : ℚ)) + (U := (-(7833195515449707049 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_7 : Uω (aρ 7) (bρ 7) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -600,25 +525,21 @@ lemma U_521_7 : have hlg : Real.log (5106185263996413 / 10000000000000000 : ℝ) ≤ (-(6721324909858084649313 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5106185263996413 / 10000000000000000 : ℝ) = - (5106185263996413 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5106185263996413 / 5000000000000000 : ℚ)) - (U := (210146893141915350687 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5106185263996413 / 5000000000000000 : ℝ) ≤ - (210146893141915350687 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (635098692290197 / 1250000000000000 : ℝ)) (q := - (5106185263996413 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5106185263996413 / 10000000000000000 : ℚ)) + (r' := (5106185263996413 / 5000000000000000 : ℚ)) + (U := (-(6721324909858084649313 / 10000000000000000000000 : ℚ))) + (U' := (210146893141915350687 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (635098692290197 / 1250000000000000 : ℚ)) + (q := (5106185263996413 / 10000000000000000 : ℚ)) + (U := (-(6721324909858084649313 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_8 : Uω (aρ 8) (bρ 8) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -626,25 +547,21 @@ lemma U_521_8 : have hlg : Real.log (299714974822367 / 625000000000000 : ℝ) ≤ (-(1469839420203114228919 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (299714974822367 / 625000000000000 : ℝ) = - (299714974822367 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (299714974822367 / 156250000000000 : ℚ)) - (U := (1302749300996885771081 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (299714974822367 / 156250000000000 : ℝ) ≤ - (1302749300996885771081 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2371419927992247 / 5000000000000000 : ℝ)) (q := - (299714974822367 / 625000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (299714974822367 / 625000000000000 : ℚ)) + (r' := (299714974822367 / 156250000000000 : ℚ)) + (U := (-(1469839420203114228919 / 2000000000000000000000 : ℚ))) + (U' := (1302749300996885771081 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (2371419927992247 / 5000000000000000 : ℚ)) + (q := (299714974822367 / 625000000000000 : ℚ)) + (U := (-(1469839420203114228919 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_9 : Uω (aρ 9) (bρ 9) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -652,25 +569,21 @@ lemma U_521_9 : have hlg : Real.log (4404249208749617 / 10000000000000000 : ℝ) ≤ (-(6406369439884059803 / 7812500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4404249208749617 / 10000000000000000 : ℝ) = - (4404249208749617 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4404249208749617 / 2500000000000000 : ℚ)) - (U := (4424055252303440197 / 7812500000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4404249208749617 / 2500000000000000 : ℝ) ≤ - (4424055252303440197 / 7812500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268839044220499 / 625000000000000 : ℝ)) (q := - (4404249208749617 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4404249208749617 / 10000000000000000 : ℚ)) + (r' := (4404249208749617 / 2500000000000000 : ℚ)) + (U := (-(6406369439884059803 / 7812500000000000000 : ℚ))) + (U' := (4424055252303440197 / 7812500000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (268839044220499 / 625000000000000 : ℚ)) + (q := (4404249208749617 / 10000000000000000 : ℚ)) + (U := (-(6406369439884059803 / 7812500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_10 : Uω (aρ 10) (bρ 10) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -678,26 +591,21 @@ lemma U_521_10 : have hlg : Real.log (7853845706055591 / 20000000000000000 : ℝ) ≤ (-(9347289623404676103549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7853845706055591 / 20000000000000000 : ℝ) = - (7853845706055591 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7853845706055591 / 5000000000000000 : ℚ)) - (U := (4515653982595323896451 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7853845706055591 / 5000000000000000 : ℝ) ≤ - (4515653982595323896451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3735331029579341 / 10000000000000000 : ℝ)) (q := - (7853845706055591 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7853845706055591 / 20000000000000000 : ℚ)) + (r' := (7853845706055591 / 5000000000000000 : ℚ)) + (U := (-(9347289623404676103549 / 10000000000000000000000 : ℚ))) + (U' := (4515653982595323896451 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (3735331029579341 / 10000000000000000 : ℚ)) + (q := (7853845706055591 / 20000000000000000 : ℚ)) + (U := (-(9347289623404676103549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_11 : Uω (aρ 11) (bρ 11) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -705,26 +613,21 @@ lemma U_521_11 : have hlg : Real.log (6708829015430311 / 20000000000000000 : ℝ) ≤ (-(2730769626571057740701 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6708829015430311 / 20000000000000000 : ℝ) = - (6708829015430311 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6708829015430311 / 5000000000000000 : ℚ)) - (U := (734966274928942259299 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6708829015430311 / 5000000000000000 : ℝ) ≤ - (734966274928942259299 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3008790965159061 / 10000000000000000 : ℝ)) (q := - (6708829015430311 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6708829015430311 / 20000000000000000 : ℚ)) + (r' := (6708829015430311 / 5000000000000000 : ℚ)) + (U := (-(2730769626571057740701 / 2500000000000000000000 : ℚ))) + (U' := (734966274928942259299 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (3008790965159061 / 10000000000000000 : ℚ)) + (q := (6708829015430311 / 20000000000000000 : ℚ)) + (U := (-(2730769626571057740701 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_12 : Uω (aρ 12) (bρ 12) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -732,25 +635,21 @@ lemma U_521_12 : have hlg : Real.log (529915087832469 / 2000000000000000 : ℝ) ≤ (-(6640928384740651911177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (529915087832469 / 2000000000000000 : ℝ) = - (529915087832469 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (529915087832469 / 500000000000000 : ℚ)) - (U := (290543418259348088823 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (529915087832469 / 500000000000000 : ℝ) ≤ - (290543418259348088823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (50570323118461 / 250000000000000 : ℝ)) (q := - (529915087832469 / 2000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (529915087832469 / 2000000000000000 : ℚ)) + (r' := (529915087832469 / 500000000000000 : ℚ)) + (U := (-(6640928384740651911177 / 5000000000000000000000 : ℚ))) + (U' := (290543418259348088823 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4683703346333 / 8000000000000 : ℚ)) + (s := (50570323118461 / 250000000000000 : ℚ)) + (q := (529915087832469 / 2000000000000000 : ℚ)) + (U := (-(6640928384740651911177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_521_13 : Uω (aρ 13) (bρ 13) (4683703346333 / 8000000000000 : ℝ) ≤ @@ -862,25 +761,21 @@ lemma U_522_1 : have hlg : Real.log (11680067166810993 / 20000000000000000 : ℝ) ≤ (-(2689242726636831311537 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11680067166810993 / 20000000000000000 : ℝ) = - (11680067166810993 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11680067166810993 / 10000000000000000 : ℚ)) - (U := (776493174863168688463 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11680067166810993 / 10000000000000000 : ℝ) ≤ - (776493174863168688463 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1460001475176967 / 2500000000000000 : ℝ)) (q := - (11680067166810993 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11680067166810993 / 20000000000000000 : ℚ)) + (r' := (11680067166810993 / 10000000000000000 : ℚ)) + (U := (-(2689242726636831311537 / 5000000000000000000000 : ℚ))) + (U' := (776493174863168688463 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (1460001475176967 / 2500000000000000 : ℚ)) + (q := (11680067166810993 / 20000000000000000 : ℚ)) + (U := (-(2689242726636831311537 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_2 : Uω (aρ 2) (bρ 2) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -888,25 +783,21 @@ lemma U_522_2 : have hlg : Real.log (11632219683617487 / 20000000000000000 : ℝ) ≤ (-(2709767332690208033799 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11632219683617487 / 20000000000000000 : ℝ) = - (11632219683617487 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11632219683617487 / 10000000000000000 : ℚ)) - (U := (755968568809791966201 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11632219683617487 / 10000000000000000 : ℝ) ≤ - (755968568809791966201 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2907963715012181 / 5000000000000000 : ℝ)) (q := - (11632219683617487 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11632219683617487 / 20000000000000000 : ℚ)) + (r' := (11632219683617487 / 10000000000000000 : ℚ)) + (U := (-(2709767332690208033799 / 5000000000000000000000 : ℚ))) + (U' := (755968568809791966201 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (2907963715012181 / 5000000000000000 : ℚ)) + (q := (11632219683617487 / 20000000000000000 : ℚ)) + (U := (-(2709767332690208033799 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_3 : Uω (aρ 3) (bρ 3) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -914,25 +805,21 @@ lemma U_522_3 : have hlg : Real.log (11536509743605397 / 20000000000000000 : ℝ) ≤ (-(275107753260969971343 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11536509743605397 / 20000000000000000 : ℝ) = - (11536509743605397 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11536509743605397 / 10000000000000000 : ℚ)) - (U := (71465836889030028657 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11536509743605397 / 10000000000000000 : ℝ) ≤ - (71465836889030028657 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180237924886321 / 312500000000000 : ℝ)) (q := - (11536509743605397 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11536509743605397 / 20000000000000000 : ℚ)) + (r' := (11536509743605397 / 10000000000000000 : ℚ)) + (U := (-(275107753260969971343 / 500000000000000000000 : ℚ))) + (U' := (71465836889030028657 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (180237924886321 / 312500000000000 : ℚ)) + (q := (11536509743605397 / 20000000000000000 : ℚ)) + (U := (-(275107753260969971343 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_4 : Uω (aρ 4) (bρ 4) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -940,25 +827,21 @@ lemma U_522_4 : have hlg : Real.log (11377505220116183 / 20000000000000000 : ℝ) ≤ (-(5640940935750156606193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11377505220116183 / 20000000000000000 : ℝ) = - (11377505220116183 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11377505220116183 / 10000000000000000 : ℚ)) - (U := (1290530867249843393807 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11377505220116183 / 10000000000000000 : ℝ) ≤ - (1290530867249843393807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2843451626969029 / 5000000000000000 : ℝ)) (q := - (11377505220116183 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11377505220116183 / 20000000000000000 : ℚ)) + (r' := (11377505220116183 / 10000000000000000 : ℚ)) + (U := (-(5640940935750156606193 / 10000000000000000000000 : ℚ))) + (U' := (1290530867249843393807 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (2843451626969029 / 5000000000000000 : ℚ)) + (q := (11377505220116183 / 20000000000000000 : ℚ)) + (U := (-(5640940935750156606193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_5 : Uω (aρ 5) (bρ 5) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -966,25 +849,21 @@ lemma U_522_5 : have hlg : Real.log (445410345748031 / 800000000000000 : ℝ) ≤ (-(292807872430797669627 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (445410345748031 / 800000000000000 : ℝ) = - (445410345748031 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (445410345748031 / 400000000000000 : ℚ)) - (U := (53765717719202330373 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (445410345748031 / 400000000000000 : ℝ) ≤ - (53765717719202330373 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (111256931937153 / 200000000000000 : ℝ)) (q := - (445410345748031 / 800000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (445410345748031 / 800000000000000 : ℚ)) + (r' := (445410345748031 / 400000000000000 : ℚ)) + (U := (-(292807872430797669627 / 500000000000000000000 : ℚ))) + (U' := (53765717719202330373 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (111256931937153 / 200000000000000 : ℚ)) + (q := (445410345748031 / 800000000000000 : ℚ)) + (U := (-(292807872430797669627 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_6 : Uω (aρ 6) (bρ 6) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -992,25 +871,21 @@ lemma U_522_6 : have hlg : Real.log (10787590857392963 / 20000000000000000 : ℝ) ≤ (-(3086678972250842838001 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10787590857392963 / 20000000000000000 : ℝ) = - (10787590857392963 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10787590857392963 / 10000000000000000 : ℚ)) - (U := (379056929249157161999 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10787590857392963 / 10000000000000000 : ℝ) ≤ - (379056929249157161999 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2691209592844919 / 5000000000000000 : ℝ)) (q := - (10787590857392963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10787590857392963 / 20000000000000000 : ℚ)) + (r' := (10787590857392963 / 10000000000000000 : ℚ)) + (U := (-(3086678972250842838001 / 5000000000000000000000 : ℚ))) + (U' := (379056929249157161999 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (2691209592844919 / 5000000000000000 : ℚ)) + (q := (10787590857392963 / 20000000000000000 : ℚ)) + (U := (-(3086678972250842838001 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_7 : Uω (aρ 7) (bρ 7) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1018,25 +893,21 @@ lemma U_522_7 : have hlg : Real.log (10312723380877329 / 20000000000000000 : ℝ) ≤ (-(1655884651729656945347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10312723380877329 / 20000000000000000 : ℝ) = - (10312723380877329 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10312723380877329 / 10000000000000000 : ℚ)) - (U := (76983299020343054653 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10312723380877329 / 10000000000000000 : ℝ) ≤ - (76983299020343054653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1282803272483551 / 2500000000000000 : ℝ)) (q := - (10312723380877329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10312723380877329 / 20000000000000000 : ℚ)) + (r' := (10312723380877329 / 10000000000000000 : ℚ)) + (U := (-(1655884651729656945347 / 2500000000000000000000 : ℚ))) + (U' := (76983299020343054653 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (1282803272483551 / 2500000000000000 : ℚ)) + (q := (10312723380877329 / 20000000000000000 : ℚ)) + (U := (-(1655884651729656945347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_8 : Uω (aρ 8) (bρ 8) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1044,25 +915,21 @@ lemma U_522_8 : have hlg : Real.log (9691833600993193 / 20000000000000000 : ℝ) ≤ (-(3622243194618693881327 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9691833600993193 / 20000000000000000 : ℝ) = - (9691833600993193 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9691833600993193 / 5000000000000000 : ℚ)) - (U := (3309228608381306118673 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9691833600993193 / 5000000000000000 : ℝ) ≤ - (3309228608381306118673 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1198466240347517 / 2500000000000000 : ℝ)) (q := - (9691833600993193 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9691833600993193 / 20000000000000000 : ℚ)) + (r' := (9691833600993193 / 5000000000000000 : ℚ)) + (U := (-(3622243194618693881327 / 5000000000000000000000 : ℚ))) + (U' := (3309228608381306118673 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (1198466240347517 / 2500000000000000 : ℚ)) + (q := (9691833600993193 / 20000000000000000 : ℚ)) + (U := (-(3622243194618693881327 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_9 : Uω (aρ 9) (bρ 9) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1070,25 +937,21 @@ lemma U_522_9 : have hlg : Real.log (4455358042689239 / 10000000000000000 : ℝ) ≤ (-(1616955332102858313771 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4455358042689239 / 10000000000000000 : ℝ) = - (4455358042689239 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4455358042689239 / 2500000000000000 : ℚ)) - (U := (1155633389097141686229 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4455358042689239 / 2500000000000000 : ℝ) ≤ - (1155633389097141686229 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4353713074135353 / 10000000000000000 : ℝ)) (q := - (4455358042689239 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4455358042689239 / 10000000000000000 : ℚ)) + (r' := (4455358042689239 / 2500000000000000 : ℚ)) + (U := (-(1616955332102858313771 / 2000000000000000000000 : ℚ))) + (U' := (1155633389097141686229 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (4353713074135353 / 10000000000000000 : ℚ)) + (q := (4455358042689239 / 10000000000000000 : ℚ)) + (U := (-(1616955332102858313771 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_10 : Uω (aρ 10) (bρ 10) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1096,26 +959,21 @@ lemma U_522_10 : have hlg : Real.log (1591751060955643 / 4000000000000000 : ℝ) ≤ (-(9214596541511311802389 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1591751060955643 / 4000000000000000 : ℝ) = - (1591751060955643 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1591751060955643 / 1000000000000000 : ℚ)) - (U := (4648347064488688197611 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1591751060955643 / 1000000000000000 : ℝ) ≤ - (4648347064488688197611 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (379031132703009 / 1000000000000000 : ℝ)) (q := - (1591751060955643 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1591751060955643 / 4000000000000000 : ℚ)) + (r' := (1591751060955643 / 1000000000000000 : ℚ)) + (U := (-(9214596541511311802389 / 10000000000000000000000 : ℚ))) + (U' := (4648347064488688197611 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (379031132703009 / 1000000000000000 : ℚ)) + (q := (1591751060955643 / 4000000000000000 : ℚ)) + (U := (-(9214596541511311802389 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_11 : Uω (aρ 11) (bρ 11) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1123,26 +981,21 @@ lemma U_522_11 : have hlg : Real.log (6819950517003007 / 20000000000000000 : ℝ) ≤ (-(10758800567764580269163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6819950517003007 / 20000000000000000 : ℝ) = - (6819950517003007 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6819950517003007 / 5000000000000000 : ℚ)) - (U := (3104143038235419730837 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6819950517003007 / 5000000000000000 : ℝ) ≤ - (3104143038235419730837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1534991582729941 / 5000000000000000 : ℝ)) (q := - (6819950517003007 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6819950517003007 / 20000000000000000 : ℚ)) + (r' := (6819950517003007 / 5000000000000000 : ℚ)) + (U := (-(10758800567764580269163 / 10000000000000000000000 : ℚ))) + (U' := (3104143038235419730837 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (1534991582729941 / 5000000000000000 : ℚ)) + (q := (6819950517003007 / 20000000000000000 : ℚ)) + (U := (-(10758800567764580269163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_12 : Uω (aρ 12) (bρ 12) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1150,25 +1003,21 @@ lemma U_522_12 : have hlg : Real.log (271449412615447 / 1000000000000000 : ℝ) ≤ (-(1629974352488310309933 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (271449412615447 / 1000000000000000 : ℝ) = - (271449412615447 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (271449412615447 / 250000000000000 : ℚ)) - (U := (102893598261689690067 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (271449412615447 / 250000000000000 : ℝ) ≤ - (102893598261689690067 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (420544199490163 / 2000000000000000 : ℝ)) (q := - (271449412615447 / 1000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (271449412615447 / 1000000000000000 : ℚ)) + (r' := (271449412615447 / 250000000000000 : ℚ)) + (U := (-(1629974352488310309933 / 1250000000000000000000 : ℚ))) + (U' := (102893598261689690067 / 1250000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9447293574701 / 16000000000000 : ℚ)) + (s := (420544199490163 / 2000000000000000 : ℚ)) + (q := (271449412615447 / 1000000000000000 : ℚ)) + (U := (-(1629974352488310309933 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_522_13 : Uω (aρ 13) (bρ 13) (9447293574701 / 16000000000000 : ℝ) ≤ @@ -1280,25 +1129,21 @@ lemma U_523_1 : have hlg : Real.log (5889963119345097 / 10000000000000000 : ℝ) ≤ (-(1323338391653748969901 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5889963119345097 / 10000000000000000 : ℝ) = - (5889963119345097 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5889963119345097 / 5000000000000000 : ℚ)) - (U := (409529559096251030099 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5889963119345097 / 5000000000000000 : ℝ) ≤ - (409529559096251030099 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2944967835657597 / 5000000000000000 : ℝ)) (q := - (5889963119345097 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5889963119345097 / 10000000000000000 : ℚ)) + (r' := (5889963119345097 / 5000000000000000 : ℚ)) + (U := (-(1323338391653748969901 / 2500000000000000000000 : ℚ))) + (U' := (409529559096251030099 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (297724389273 / 500000000000 : ℚ)) + (s := (2944967835657597 / 5000000000000000 : ℚ)) + (q := (5889963119345097 / 10000000000000000 : ℚ)) + (U := (-(1323338391653748969901 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_2 : Uω (aρ 2) (bρ 2) (297724389273 / 500000000000 : ℝ) ≤ @@ -1306,25 +1151,21 @@ lemma U_523_2 : have hlg : Real.log (11732081391484447 / 20000000000000000 : ℝ) ≤ (-(2667025923201519139487 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11732081391484447 / 20000000000000000 : ℝ) = - (11732081391484447 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11732081391484447 / 10000000000000000 : ℚ)) - (U := (798709978298480860513 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11732081391484447 / 10000000000000000 : ℝ) ≤ - (798709978298480860513 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5865859836619447 / 10000000000000000 : ℝ)) (q := - (11732081391484447 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11732081391484447 / 20000000000000000 : ℚ)) + (r' := (11732081391484447 / 10000000000000000 : ℚ)) + (U := (-(2667025923201519139487 / 5000000000000000000000 : ℚ))) + (U' := (798709978298480860513 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (297724389273 / 500000000000 : ℚ)) + (s := (5865859836619447 / 10000000000000000 : ℚ)) + (q := (11732081391484447 / 20000000000000000 : ℚ)) + (U := (-(2667025923201519139487 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_3 : Uω (aρ 3) (bρ 3) (297724389273 / 500000000000 : ℝ) ≤ @@ -1332,25 +1173,21 @@ lemma U_523_3 : have hlg : Real.log (2909094838421109 / 5000000000000000 : ℝ) ≤ (-(5415959314664550473199 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2909094838421109 / 5000000000000000 : ℝ) = - (2909094838421109 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2909094838421109 / 2500000000000000 : ℚ)) - (U := (1515512488335449526801 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2909094838421109 / 2500000000000000 : ℝ) ≤ - (1515512488335449526801 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1454388476292359 / 2500000000000000 : ℝ)) (q := - (2909094838421109 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2909094838421109 / 5000000000000000 : ℚ)) + (r' := (2909094838421109 / 2500000000000000 : ℚ)) + (U := (-(5415959314664550473199 / 10000000000000000000000 : ℚ))) + (U' := (1515512488335449526801 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (297724389273 / 500000000000 : ℚ)) + (s := (1454388476292359 / 2500000000000000 : ℚ)) + (q := (2909094838421109 / 5000000000000000 : ℚ)) + (U := (-(5415959314664550473199 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_4 : Uω (aρ 4) (bρ 4) (297724389273 / 500000000000 : ℝ) ≤ @@ -1358,25 +1195,21 @@ lemma U_523_4 : have hlg : Real.log (2295479202704893 / 4000000000000000 : ℝ) ≤ (-(694190920277763514999 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2295479202704893 / 4000000000000000 : ℝ) = - (2295479202704893 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2295479202704893 / 2000000000000000 : ℚ)) - (U := (172243055097236485001 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2295479202704893 / 2000000000000000 : ℝ) ≤ - (172243055097236485001 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1147372949214893 / 2000000000000000 : ℝ)) (q := - (2295479202704893 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2295479202704893 / 4000000000000000 : ℚ)) + (r' := (2295479202704893 / 2000000000000000 : ℚ)) + (U := (-(694190920277763514999 / 1250000000000000000000 : ℚ))) + (U' := (172243055097236485001 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (297724389273 / 500000000000 : ℚ)) + (s := (1147372949214893 / 2000000000000000 : ℚ)) + (q := (2295479202704893 / 4000000000000000 : ℚ)) + (U := (-(694190920277763514999 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_5 : Uω (aρ 5) (bρ 5) (297724389273 / 500000000000 : ℝ) ≤ @@ -1384,25 +1217,21 @@ lemma U_523_5 : have hlg : Real.log (11235202336514049 / 20000000000000000 : ℝ) ≤ (-(1441700895845914328219 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11235202336514049 / 20000000000000000 : ℝ) = - (11235202336514049 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11235202336514049 / 10000000000000000 : ℚ)) - (U := (291167054904085671781 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11235202336514049 / 10000000000000000 : ℝ) ≤ - (291167054904085671781 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5612860988399049 / 10000000000000000 : ℝ)) (q := - (11235202336514049 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11235202336514049 / 20000000000000000 : ℚ)) + (r' := (11235202336514049 / 10000000000000000 : ℚ)) + (U := (-(1441700895845914328219 / 2500000000000000000000 : ℚ))) + (U' := (291167054904085671781 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (297724389273 / 500000000000 : ℚ)) + (s := (5612860988399049 / 10000000000000000 : ℚ)) + (q := (11235202336514049 / 20000000000000000 : ℚ)) + (U := (-(1441700895845914328219 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_6 : Uω (aρ 6) (bρ 6) (297724389273 / 500000000000 : ℝ) ≤ @@ -1410,25 +1239,21 @@ lemma U_523_6 : have hlg : Real.log (5443829288233231 / 10000000000000000 : ℝ) ≤ (-(1216204732437666014063 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5443829288233231 / 10000000000000000 : ℝ) = - (5443829288233231 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5443829288233231 / 5000000000000000 : ℚ)) - (U := (170089628162333985937 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5443829288233231 / 5000000000000000 : ℝ) ≤ - (170089628162333985937 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2716278801745731 / 5000000000000000 : ℝ)) (q := - (5443829288233231 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5443829288233231 / 10000000000000000 : ℚ)) + (r' := (5443829288233231 / 5000000000000000 : ℚ)) + (U := (-(1216204732437666014063 / 2000000000000000000000 : ℚ))) + (U' := (170089628162333985937 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (297724389273 / 500000000000 : ℚ)) + (s := (2716278801745731 / 5000000000000000 : ℚ)) + (q := (5443829288233231 / 10000000000000000 : ℚ)) + (U := (-(1216204732437666014063 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_7 : Uω (aρ 7) (bρ 7) (297724389273 / 500000000000 : ℝ) ≤ @@ -1436,25 +1261,21 @@ lemma U_523_7 : have hlg : Real.log (10413066661597479 / 20000000000000000 : ℝ) ≤ (-(326335422999999054939 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10413066661597479 / 20000000000000000 : ℝ) = - (10413066661597479 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10413066661597479 / 10000000000000000 : ℚ)) - (U := (20238167150000945061 / 500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10413066661597479 / 10000000000000000 : ℝ) ≤ - (20238167150000945061 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5181627069382479 / 10000000000000000 : ℝ)) (q := - (10413066661597479 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10413066661597479 / 20000000000000000 : ℚ)) + (r' := (10413066661597479 / 10000000000000000 : ℚ)) + (U := (-(326335422999999054939 / 500000000000000000000 : ℚ))) + (U' := (20238167150000945061 / 500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (297724389273 / 500000000000 : ℚ)) + (s := (5181627069382479 / 10000000000000000 : ℚ)) + (q := (10413066661597479 / 20000000000000000 : ℚ)) + (U := (-(326335422999999054939 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_8 : Uω (aρ 8) (bρ 8) (297724389273 / 500000000000 : ℝ) ≤ @@ -1462,25 +1283,21 @@ lemma U_523_8 : have hlg : Real.log (1224095646752767 / 2500000000000000 : ℝ) ≤ (-(7140884075452489921343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1224095646752767 / 2500000000000000 : ℝ) = - (1224095646752767 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1224095646752767 / 625000000000000 : ℚ)) - (U := (6722059530547510078657 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1224095646752767 / 625000000000000 : ℝ) ≤ - (6722059530547510078657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18925262629481 / 39062500000000 : ℝ)) (q := - (1224095646752767 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1224095646752767 / 2500000000000000 : ℚ)) + (r' := (1224095646752767 / 625000000000000 : ℚ)) + (U := (-(7140884075452489921343 / 10000000000000000000000 : ℚ))) + (U' := (6722059530547510078657 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (297724389273 / 500000000000 : ℚ)) + (s := (18925262629481 / 39062500000000 : ℚ)) + (q := (1224095646752767 / 2500000000000000 : ℚ)) + (U := (-(7140884075452489921343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_9 : Uω (aρ 9) (bρ 9) (297724389273 / 500000000000 : ℝ) ≤ @@ -1488,25 +1305,21 @@ lemma U_523_9 : have hlg : Real.log (9012879023440247 / 20000000000000000 : ℝ) ≤ (-(3985388580009479571857 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9012879023440247 / 20000000000000000 : ℝ) = - (9012879023440247 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9012879023440247 / 5000000000000000 : ℚ)) - (U := (2946083222990520428143 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9012879023440247 / 5000000000000000 : ℝ) ≤ - (2946083222990520428143 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4405946710925247 / 10000000000000000 : ℝ)) (q := - (9012879023440247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9012879023440247 / 20000000000000000 : ℚ)) + (r' := (9012879023440247 / 5000000000000000 : ℚ)) + (U := (-(3985388580009479571857 / 5000000000000000000000 : ℚ))) + (U' := (2946083222990520428143 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (297724389273 / 500000000000 : ℚ)) + (s := (4405946710925247 / 10000000000000000 : ℚ)) + (q := (9012879023440247 / 20000000000000000 : ℚ)) + (U := (-(3985388580009479571857 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_10 : Uω (aρ 10) (bρ 10) (297724389273 / 500000000000 : ℝ) ≤ @@ -1514,26 +1327,21 @@ lemma U_523_10 : have hlg : Real.log (4031763548331721 / 10000000000000000 : ℝ) ≤ (-(9083812071916347774149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4031763548331721 / 10000000000000000 : ℝ) = - (4031763548331721 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4031763548331721 / 2500000000000000 : ℚ)) - (U := (4779131534083652225851 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4031763548331721 / 2500000000000000 : ℝ) ≤ - (4779131534083652225851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1922576908821721 / 5000000000000000 : ℝ)) (q := - (4031763548331721 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4031763548331721 / 10000000000000000 : ℚ)) + (r' := (4031763548331721 / 2500000000000000 : ℚ)) + (U := (-(9083812071916347774149 / 10000000000000000000000 : ℚ))) + (U' := (4779131534083652225851 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (297724389273 / 500000000000 : ℚ)) + (s := (1922576908821721 / 5000000000000000 : ℚ)) + (q := (4031763548331721 / 10000000000000000 : ℚ)) + (U := (-(9083812071916347774149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_11 : Uω (aρ 11) (bρ 11) (297724389273 / 500000000000 : ℝ) ≤ @@ -1541,25 +1349,21 @@ lemma U_523_11 : have hlg : Real.log (866334035855753 / 2500000000000000 : ℝ) ≤ (-(10597754534486675358283 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (866334035855753 / 2500000000000000 : ℝ) = - (866334035855753 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (866334035855753 / 625000000000000 : ℚ)) - (U := (3265189071513324641717 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (866334035855753 / 625000000000000 : ℝ) ≤ - (3265189071513324641717 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (195673477126939 / 625000000000000 : ℝ)) (q := - (866334035855753 / 2500000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (866334035855753 / 2500000000000000 : ℚ)) + (r' := (866334035855753 / 625000000000000 : ℚ)) + (U := (-(10597754534486675358283 / 10000000000000000000000 : ℚ))) + (U' := (3265189071513324641717 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (297724389273 / 500000000000 : ℚ)) + (s := (195673477126939 / 625000000000000 : ℚ)) + (q := (866334035855753 / 2500000000000000 : ℚ)) + (U := (-(10597754534486675358283 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_12 : Uω (aρ 12) (bρ 12) (297724389273 / 500000000000 : ℝ) ≤ @@ -1567,26 +1371,21 @@ lemma U_523_12 : have hlg : Real.log (5557041559334771 / 20000000000000000 : ℝ) ≤ (-(12806664000284943041083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5557041559334771 / 20000000000000000 : ℝ) = - (5557041559334771 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5557041559334771 / 5000000000000000 : ℚ)) - (U := (1056279605715056958917 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5557041559334771 / 5000000000000000 : ℝ) ≤ - (1056279605715056958917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2180845003204771 / 10000000000000000 : ℝ)) (q := - (5557041559334771 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5557041559334771 / 20000000000000000 : ℚ)) + (r' := (5557041559334771 / 5000000000000000 : ℚ)) + (U := (-(12806664000284943041083 / 10000000000000000000000 : ℚ))) + (U' := (1056279605715056958917 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (297724389273 / 500000000000 : ℚ)) + (s := (2180845003204771 / 10000000000000000 : ℚ)) + (q := (5557041559334771 / 20000000000000000 : ℚ)) + (U := (-(12806664000284943041083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_523_13 : Uω (aρ 13) (bρ 13) (297724389273 / 500000000000 : ℝ) ≤ @@ -1699,25 +1498,21 @@ lemma U_524_1 : have hlg : Real.log (23645843632824819 / 40000000000000000 : ℝ) ≤ (-(1314230248183163826137 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23645843632824819 / 40000000000000000 : ℝ) = - (23645843632824819 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23645843632824819 / 20000000000000000 : ℚ)) - (U := (418637702566836173863 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23645843632824819 / 20000000000000000 : ℝ) ≤ - (418637702566836173863 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5911433559994597 / 10000000000000000 : ℝ)) (q := - (23645843632824819 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23645843632824819 / 40000000000000000 : ℚ)) + (r' := (23645843632824819 / 20000000000000000 : ℚ)) + (U := (-(1314230248183163826137 / 2500000000000000000000 : ℚ))) + (U' := (418637702566836173863 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (5911433559994597 / 10000000000000000 : ℚ)) + (q := (23645843632824819 / 40000000000000000 : ℚ)) + (U := (-(1314230248183163826137 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_2 : Uω (aρ 2) (bρ 2) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1725,25 +1520,21 @@ lemma U_524_2 : have hlg : Real.log (23550156180768569 / 40000000000000000 : ℝ) ≤ (-(5297470015337856711679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23550156180768569 / 40000000000000000 : ℝ) = - (23550156180768569 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23550156180768569 / 20000000000000000 : ℚ)) - (U := (1634001787662143288321 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23550156180768569 / 20000000000000000 : ℝ) ≤ - (1634001787662143288321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (735919855809559 / 1250000000000000 : ℝ)) (q := - (23550156180768569 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23550156180768569 / 40000000000000000 : ℚ)) + (r' := (23550156180768569 / 20000000000000000 : ℚ)) + (U := (-(5297470015337856711679 / 10000000000000000000000 : ℚ))) + (U' := (1634001787662143288321 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (735919855809559 / 1250000000000000 : ℚ)) + (q := (23550156180768569 / 40000000000000000 : ℚ)) + (U := (-(5297470015337856711679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_3 : Uω (aρ 3) (bρ 3) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1751,25 +1542,21 @@ lemma U_524_3 : have hlg : Real.log (23358758826441631 / 40000000000000000 : ℝ) ≤ (-(107581485947053385999 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23358758826441631 / 40000000000000000 : ℝ) = - (23358758826441631 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23358758826441631 / 20000000000000000 : ℚ)) - (U := (31047950112946614001 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23358758826441631 / 20000000000000000 : ℝ) ≤ - (31047950112946614001 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5839056275663003 / 10000000000000000 : ℝ)) (q := - (23358758826441631 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23358758826441631 / 40000000000000000 : ℚ)) + (r' := (23358758826441631 / 20000000000000000 : ℚ)) + (U := (-(107581485947053385999 / 200000000000000000000 : ℚ))) + (U' := (31047950112946614001 / 200000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (5839056275663003 / 10000000000000000 : ℚ)) + (q := (23358758826441631 / 40000000000000000 : ℚ)) + (U := (-(107581485947053385999 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_4 : Uω (aρ 4) (bρ 4) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1777,25 +1564,21 @@ lemma U_524_4 : have hlg : Real.log (23040810159629221 / 40000000000000000 : ℝ) ≤ (-(5516124554661589611093 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23040810159629221 / 40000000000000000 : ℝ) = - (23040810159629221 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23040810159629221 / 20000000000000000 : ℚ)) - (U := (1415347248338410388907 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23040810159629221 / 20000000000000000 : ℝ) ≤ - (1415347248338410388907 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2879188061660899 / 5000000000000000 : ℝ)) (q := - (23040810159629221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23040810159629221 / 40000000000000000 : ℚ)) + (r' := (23040810159629221 / 20000000000000000 : ℚ)) + (U := (-(5516124554661589611093 / 10000000000000000000000 : ℚ))) + (U' := (1415347248338410388907 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (2879188061660899 / 5000000000000000 : ℚ)) + (q := (23040810159629221 / 40000000000000000 : ℚ)) + (U := (-(5516124554661589611093 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_5 : Uω (aρ 5) (bρ 5) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1803,25 +1586,21 @@ lemma U_524_5 : have hlg : Real.log (22556467772897239 / 40000000000000000 : ℝ) ≤ (-(5728576098328493848859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22556467772897239 / 40000000000000000 : ℝ) = - (22556467772897239 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22556467772897239 / 20000000000000000 : ℚ)) - (U := (1202895704671506151141 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22556467772897239 / 20000000000000000 : ℝ) ≤ - (1202895704671506151141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5634394849290807 / 10000000000000000 : ℝ)) (q := - (22556467772897239 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22556467772897239 / 40000000000000000 : ℚ)) + (r' := (22556467772897239 / 20000000000000000 : ℚ)) + (U := (-(5728576098328493848859 / 10000000000000000000000 : ℚ))) + (U' := (1202895704671506151141 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (5634394849290807 / 10000000000000000 : ℚ)) + (q := (22556467772897239 / 40000000000000000 : ℚ)) + (U := (-(5728576098328493848859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_6 : Uω (aρ 6) (bρ 6) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1829,25 +1608,21 @@ lemma U_524_6 : have hlg : Real.log (21861485621420399 / 40000000000000000 : ℝ) ≤ (-(6041530126911093500149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21861485621420399 / 40000000000000000 : ℝ) = - (21861485621420399 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21861485621420399 / 20000000000000000 : ℚ)) - (U := (889941676088906499851 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21861485621420399 / 20000000000000000 : ℝ) ≤ - (889941676088906499851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5454144148692387 / 10000000000000000 : ℝ)) (q := - (21861485621420399 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21861485621420399 / 40000000000000000 : ℚ)) + (r' := (21861485621420399 / 20000000000000000 : ℚ)) + (U := (-(6041530126911093500149 / 10000000000000000000000 : ℚ))) + (U' := (889941676088906499851 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (5454144148692387 / 10000000000000000 : ℚ)) + (q := (21861485621420399 / 40000000000000000 : ℚ)) + (U := (-(6041530126911093500149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_7 : Uω (aρ 7) (bρ 7) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1855,25 +1630,21 @@ lemma U_524_7 : have hlg : Real.log (836501427633957 / 1600000000000000 : ℝ) ≤ (-(3242653404335615268931 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (836501427633957 / 1600000000000000 : ℝ) = - (836501427633957 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (836501427633957 / 800000000000000 : ℚ)) - (U := (223082497164384731069 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (836501427633957 / 800000000000000 : ℝ) ≤ - (223082497164384731069 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (104066611283333 / 200000000000000 : ℝ)) (q := - (836501427633957 / 1600000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (836501427633957 / 1600000000000000 : ℚ)) + (r' := (836501427633957 / 800000000000000 : ℚ)) + (U := (-(3242653404335615268931 / 5000000000000000000000 : ℚ))) + (U' := (223082497164384731069 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (104066611283333 / 200000000000000 : ℚ)) + (q := (836501427633957 / 1600000000000000 : ℚ)) + (U := (-(3242653404335615268931 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_8 : Uω (aρ 8) (bρ 8) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1881,25 +1652,21 @@ lemma U_524_8 : have hlg : Real.log (3934486272011177 / 8000000000000000 : ℝ) ≤ (-(7096612213048692962003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3934486272011177 / 8000000000000000 : ℝ) = - (3934486272011177 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3934486272011177 / 2000000000000000 : ℚ)) - (U := (6766331392951307037997 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3934486272011177 / 2000000000000000 : ℝ) ≤ - (6766331392951307037997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (486682005011013 / 1000000000000000 : ℝ)) (q := - (3934486272011177 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3934486272011177 / 8000000000000000 : ℚ)) + (r' := (3934486272011177 / 2000000000000000 : ℚ)) + (U := (-(7096612213048692962003 / 10000000000000000000000 : ℚ))) + (U' := (6766331392951307037997 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (486682005011013 / 1000000000000000 : ℚ)) + (q := (3934486272011177 / 8000000000000000 : ℚ)) + (U := (-(7096612213048692962003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_9 : Uω (aρ 9) (bρ 9) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1907,25 +1674,21 @@ lemma U_524_9 : have hlg : Real.log (18113700380301757 / 40000000000000000 : ℝ) ≤ (-(1584421749117207670283 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18113700380301757 / 40000000000000000 : ℝ) = - (18113700380301757 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18113700380301757 / 10000000000000000 : ℚ)) - (U := (1188166972082792329717 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18113700380301757 / 10000000000000000 : ℝ) ≤ - (1188166972082792329717 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2214210094296533 / 5000000000000000 : ℝ)) (q := - (18113700380301757 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18113700380301757 / 40000000000000000 : ℚ)) + (r' := (18113700380301757 / 10000000000000000 : ℚ)) + (U := (-(1584421749117207670283 / 2000000000000000000000 : ℚ))) + (U' := (1188166972082792329717 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (2214210094296533 / 5000000000000000 : ℚ)) + (q := (18113700380301757 / 40000000000000000 : ℚ)) + (U := (-(1584421749117207670283 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_10 : Uω (aρ 10) (bρ 10) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1933,26 +1696,21 @@ lemma U_524_10 : have hlg : Real.log (16217193864508737 / 40000000000000000 : ℝ) ≤ (-(72224593962241507771 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16217193864508737 / 40000000000000000 : ℝ) = - (16217193864508737 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16217193864508737 / 10000000000000000 : ℚ)) - (U := (38678954885758492229 / 80000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16217193864508737 / 10000000000000000 : ℝ) ≤ - (38678954885758492229 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (967181491047889 / 2500000000000000 : ℝ)) (q := - (16217193864508737 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16217193864508737 / 40000000000000000 : ℚ)) + (r' := (16217193864508737 / 10000000000000000 : ℚ)) + (U := (-(72224593962241507771 / 80000000000000000000 : ℚ))) + (U' := (38678954885758492229 / 80000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (967181491047889 / 2500000000000000 : ℚ)) + (q := (16217193864508737 / 40000000000000000 : ℚ)) + (U := (-(72224593962241507771 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_11 : Uω (aρ 11) (bρ 11) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1960,26 +1718,21 @@ lemma U_524_11 : have hlg : Real.log (13956455198364819 / 40000000000000000 : ℝ) ≤ (-(10529373141229537227421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13956455198364819 / 40000000000000000 : ℝ) = - (13956455198364819 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13956455198364819 / 10000000000000000 : ℚ)) - (U := (3333570464770462772579 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13956455198364819 / 10000000000000000 : ℝ) ≤ - (3333570464770462772579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3156833257324597 / 10000000000000000 : ℝ)) (q := - (13956455198364819 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13956455198364819 / 40000000000000000 : ℚ)) + (r' := (13956455198364819 / 10000000000000000 : ℚ)) + (U := (-(10529373141229537227421 / 10000000000000000000000 : ℚ))) + (U' := (3333570464770462772579 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (3156833257324597 / 10000000000000000 : ℚ)) + (q := (13956455198364819 / 40000000000000000 : ℚ)) + (U := (-(10529373141229537227421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_12 : Uω (aρ 12) (bρ 12) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -1987,26 +1740,21 @@ lemma U_524_12 : have hlg : Real.log (2244669741941209 / 8000000000000000 : ℝ) ≤ (-(2541766278107864221893 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2244669741941209 / 8000000000000000 : ℝ) = - (2244669741941209 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2244669741941209 / 2000000000000000 : ℚ)) - (U := (230822443092135778107 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2244669741941209 / 2000000000000000 : ℝ) ≤ - (230822443092135778107 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221398010968021 / 1000000000000000 : ℝ)) (q := - (2244669741941209 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2244669741941209 / 8000000000000000 : ℚ)) + (r' := (2244669741941209 / 2000000000000000 : ℚ)) + (U := (-(2541766278107864221893 / 2000000000000000000000 : ℚ))) + (U' := (230822443092135778107 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (221398010968021 / 1000000000000000 : ℚ)) + (q := (2244669741941209 / 8000000000000000 : ℚ)) + (U := (-(2541766278107864221893 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_13 : Uω (aρ 13) (bρ 13) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -2014,26 +1762,21 @@ lemma U_524_13 : have hlg : Real.log (6713427432028769 / 40000000000000000 : ℝ) ≤ (-(3569539676245047689691 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (6713427432028769 / 40000000000000000 : ℝ) = - (6713427432028769 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6713427432028769 / 5000000000000000 : ℚ)) - (U := (589343405554952310309 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6713427432028769 / 5000000000000000 : ℝ) ≤ - (589343405554952310309 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89600303109143 / 2500000000000000 : ℝ)) (q := - (6713427432028769 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6713427432028769 / 40000000000000000 : ℚ)) + (r' := (6713427432028769 / 5000000000000000 : ℚ)) + (U := (-(3569539676245047689691 / 2000000000000000000000 : ℚ))) + (U' := (589343405554952310309 / 2000000000000000000000 : ℚ)) + 3 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19123153518409 / 32000000000000 : ℚ)) + (s := (89600303109143 / 2500000000000000 : ℚ)) + (q := (6713427432028769 / 40000000000000000 : ℚ)) + (U := (-(3569539676245047689691 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_524_14 : Uω (aρ 14) (bρ 14) (19123153518409 / 32000000000000 : ℝ) ≤ @@ -2140,24 +1883,21 @@ lemma U_525_1 : have hlg : Real.log (46351239815187 / 78125000000000 : ℝ) ≤ (-(522062067163280364799 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46351239815187 / 78125000000000 : ℝ) = (46351239815187 / 39062500000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46351239815187 / 39062500000000 : ℚ)) - (U := (171085113136719635201 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (46351239815187 / 39062500000000 : ℝ) ≤ - (171085113136719635201 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5932931447227247 / 10000000000000000 : ℝ)) (q := - (46351239815187 / 78125000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46351239815187 / 78125000000000 : ℚ)) + (r' := (46351239815187 / 39062500000000 : ℚ)) + (U := (-(522062067163280364799 / 1000000000000000000000 : ℚ))) + (U' := (171085113136719635201 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (5932931447227247 / 10000000000000000 : ℚ)) + (q := (46351239815187 / 78125000000000 : ℚ)) + (U := (-(522062067163280364799 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_2 : Uω (aρ 2) (bρ 2) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2165,25 +1905,21 @@ lemma U_525_2 : have hlg : Real.log (11818074779673017 / 20000000000000000 : ℝ) ≤ (-(328813845489025310421 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11818074779673017 / 20000000000000000 : ℝ) = - (11818074779673017 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11818074779673017 / 10000000000000000 : ℚ)) - (U := (104403142198474689579 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11818074779673017 / 10000000000000000 : ℝ) ≤ - (104403142198474689579 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (738607230840299 / 1250000000000000 : ℝ)) (q := - (11818074779673017 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11818074779673017 / 20000000000000000 : ℚ)) + (r' := (11818074779673017 / 10000000000000000 : ℚ)) + (U := (-(328813845489025310421 / 625000000000000000000 : ℚ))) + (U' := (104403142198474689579 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (738607230840299 / 1250000000000000 : ℚ)) + (q := (11818074779673017 / 20000000000000000 : ℚ)) + (U := (-(328813845489025310421 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_3 : Uω (aρ 3) (bρ 3) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2191,25 +1927,21 @@ lemma U_525_3 : have hlg : Real.log (11722379438408479 / 20000000000000000 : ℝ) ≤ (-(5342324859967229659017 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11722379438408479 / 20000000000000000 : ℝ) = - (11722379438408479 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11722379438408479 / 10000000000000000 : ℚ)) - (U := (1589146943032770340983 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11722379438408479 / 10000000000000000 : ℝ) ≤ - (1589146943032770340983 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2930279305903927 / 5000000000000000 : ℝ)) (q := - (11722379438408479 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11722379438408479 / 20000000000000000 : ℚ)) + (r' := (11722379438408479 / 10000000000000000 : ℚ)) + (U := (-(5342324859967229659017 / 10000000000000000000000 : ℚ))) + (U' := (1589146943032770340983 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (2930279305903927 / 5000000000000000 : ℚ)) + (q := (11722379438408479 / 20000000000000000 : ℚ)) + (U := (-(5342324859967229659017 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_4 : Uω (aρ 4) (bρ 4) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2217,25 +1949,21 @@ lemma U_525_4 : have hlg : Real.log (11563414044248639 / 20000000000000000 : ℝ) ≤ (-(2739430605522132083087 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11563414044248639 / 20000000000000000 : ℝ) = - (11563414044248639 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11563414044248639 / 10000000000000000 : ℚ)) - (U := (726305295977867916913 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11563414044248639 / 10000000000000000 : ℝ) ≤ - (726305295977867916913 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2889943699356507 / 5000000000000000 : ℝ)) (q := - (11563414044248639 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11563414044248639 / 20000000000000000 : ℚ)) + (r' := (11563414044248639 / 10000000000000000 : ℚ)) + (U := (-(2739430605522132083087 / 5000000000000000000000 : ℚ))) + (U' := (726305295977867916913 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (2889943699356507 / 5000000000000000 : ℚ)) + (q := (11563414044248639 / 20000000000000000 : ℚ)) + (U := (-(2739430605522132083087 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_5 : Uω (aρ 5) (bρ 5) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2243,25 +1971,21 @@ lemma U_525_5 : have hlg : Real.log (11321265161179799 / 20000000000000000 : ℝ) ≤ (-(5690494434089613539713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11321265161179799 / 20000000000000000 : ℝ) = - (11321265161179799 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11321265161179799 / 10000000000000000 : ℚ)) - (U := (1240977368910386460287 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11321265161179799 / 10000000000000000 : ℝ) ≤ - (1240977368910386460287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2827964217489587 / 5000000000000000 : ℝ)) (q := - (11321265161179799 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11321265161179799 / 20000000000000000 : ℚ)) + (r' := (11321265161179799 / 10000000000000000 : ℚ)) + (U := (-(5690494434089613539713 / 10000000000000000000000 : ℚ))) + (U' := (1240977368910386460287 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (2827964217489587 / 5000000000000000 : ℚ)) + (q := (11321265161179799 / 20000000000000000 : ℚ)) + (U := (-(5690494434089613539713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_6 : Uω (aρ 6) (bρ 6) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2269,25 +1993,21 @@ lemma U_525_6 : have hlg : Real.log (1371728293226801 / 2500000000000000 : ℝ) ≤ (-(3001096294645691980019 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1371728293226801 / 2500000000000000 : ℝ) = - (1371728293226801 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1371728293226801 / 1250000000000000 : ℚ)) - (U := (464639606854308019981 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1371728293226801 / 1250000000000000 : ℝ) ≤ - (464639606854308019981 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5475729994753783 / 10000000000000000 : ℝ)) (q := - (1371728293226801 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1371728293226801 / 2500000000000000 : ℚ)) + (r' := (1371728293226801 / 1250000000000000 : ℚ)) + (U := (-(3001096294645691980019 / 5000000000000000000000 : ℚ))) + (U' := (464639606854308019981 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (5475729994753783 / 10000000000000000 : ℚ)) + (q := (1371728293226801 / 2500000000000000 : ℚ)) + (U := (-(3001096294645691980019 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_7 : Uω (aρ 7) (bρ 7) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2295,25 +2015,21 @@ lemma U_525_7 : have hlg : Real.log (10499467327625579 / 20000000000000000 : ℝ) ≤ (-(3222038740598697037627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10499467327625579 / 20000000000000000 : ℝ) = - (10499467327625579 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10499467327625579 / 10000000000000000 : ℚ)) - (U := (243697160901302962373 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10499467327625579 / 10000000000000000 : ℝ) ≤ - (243697160901302962373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2612516178662477 / 5000000000000000 : ℝ)) (q := - (10499467327625579 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10499467327625579 / 20000000000000000 : ℚ)) + (r' := (10499467327625579 / 10000000000000000 : ℚ)) + (U := (-(3222038740598697037627 / 5000000000000000000000 : ℚ))) + (U' := (243697160901302962373 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (2612516178662477 / 5000000000000000 : ℚ)) + (q := (10499467327625579 / 20000000000000000 : ℚ)) + (U := (-(3222038740598697037627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_8 : Uω (aρ 8) (bρ 8) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2321,25 +2037,21 @@ lemma U_525_8 : have hlg : Real.log (4939831070469791 / 10000000000000000 : ℝ) ≤ (-(1763134895300513255911 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4939831070469791 / 10000000000000000 : ℝ) = - (4939831070469791 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4939831070469791 / 2500000000000000 : ℚ)) - (U := (1702601006199486744089 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4939831070469791 / 2500000000000000 : ℝ) ≤ - (1702601006199486744089 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4888768821978957 / 10000000000000000 : ℝ)) (q := - (4939831070469791 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4939831070469791 / 10000000000000000 : ℚ)) + (r' := (4939831070469791 / 2500000000000000 : ℚ)) + (U := (-(1763134895300513255911 / 2500000000000000000000 : ℚ))) + (U' := (1702601006199486744089 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (4888768821978957 / 10000000000000000 : ℚ)) + (q := (4939831070469791 / 10000000000000000 : ℚ)) + (U := (-(1763134895300513255911 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_9 : Uω (aρ 9) (bρ 9) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2347,25 +2059,21 @@ lemma U_525_9 : have hlg : Real.log (568800732303903 / 1250000000000000 : ℝ) ≤ (-(1574737327668269272281 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (568800732303903 / 1250000000000000 : ℝ) = - (568800732303903 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (568800732303903 / 312500000000000 : ℚ)) - (U := (1197851393531730727719 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (568800732303903 / 312500000000000 : ℝ) ≤ - (1197851393531730727719 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4450884026261823 / 10000000000000000 : ℝ)) (q := - (568800732303903 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (568800732303903 / 1250000000000000 : ℚ)) + (r' := (568800732303903 / 312500000000000 : ℚ)) + (U := (-(1574737327668269272281 / 2000000000000000000000 : ℚ))) + (U' := (1197851393531730727719 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (4450884026261823 / 10000000000000000 : ℚ)) + (q := (568800732303903 / 1250000000000000 : ℚ)) + (U := (-(1574737327668269272281 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_10 : Uω (aρ 10) (bρ 10) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2373,26 +2081,21 @@ lemma U_525_10 : have hlg : Real.log (8153642747139649 / 20000000000000000 : ℝ) ≤ (-(8972674828002439749491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8153642747139649 / 20000000000000000 : ℝ) = - (8153642747139649 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8153642747139649 / 5000000000000000 : ℚ)) - (U := (4890268777997560250509 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8153642747139649 / 5000000000000000 : ℝ) ≤ - (4890268777997560250509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (486534261254253 / 1250000000000000 : ℝ)) (q := - (8153642747139649 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8153642747139649 / 20000000000000000 : ℚ)) + (r' := (8153642747139649 / 5000000000000000 : ℚ)) + (U := (-(8972674828002439749491 / 10000000000000000000000 : ℚ))) + (U' := (4890268777997560250509 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (486534261254253 / 1250000000000000 : ℚ)) + (q := (8153642747139649 / 20000000000000000 : ℚ)) + (U := (-(8972674828002439749491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_11 : Uω (aρ 11) (bρ 11) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2400,26 +2103,21 @@ lemma U_525_11 : have hlg : Real.log (1405142956236983 / 4000000000000000 : ℝ) ≤ (-(52307765738945663703 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1405142956236983 / 4000000000000000 : ℝ) = - (1405142956236983 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1405142956236983 / 1000000000000000 : ℚ)) - (U := (17006952291054336297 / 50000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1405142956236983 / 1000000000000000 : ℝ) ≤ - (17006952291054336297 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (318282275028429 / 1000000000000000 : ℝ)) (q := - (1405142956236983 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1405142956236983 / 4000000000000000 : ℚ)) + (r' := (1405142956236983 / 1000000000000000 : ℚ)) + (U := (-(52307765738945663703 / 50000000000000000000 : ℚ))) + (U' := (17006952291054336297 / 50000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (318282275028429 / 1000000000000000 : ℚ)) + (q := (1405142956236983 / 4000000000000000 : ℚ)) + (U := (-(52307765738945663703 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_12 : Uω (aρ 12) (bρ 12) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2427,26 +2125,21 @@ lemma U_525_12 : have hlg : Real.log (5666024198846061 / 20000000000000000 : ℝ) ≤ (-(12612446007478394770303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5666024198846061 / 20000000000000000 : ℝ) = - (5666024198846061 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5666024198846061 / 5000000000000000 : ℚ)) - (U := (1250497598521605229697 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5666024198846061 / 5000000000000000 : ℝ) ≤ - (1250497598521605229697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (561708066157609 / 2500000000000000 : ℝ)) (q := - (5666024198846061 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5666024198846061 / 20000000000000000 : ℚ)) + (r' := (5666024198846061 / 5000000000000000 : ℚ)) + (U := (-(12612446007478394770303 / 10000000000000000000000 : ℚ))) + (U' := (1250497598521605229697 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (561708066157609 / 2500000000000000 : ℚ)) + (q := (5666024198846061 / 20000000000000000 : ℚ)) + (U := (-(12612446007478394770303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_13 : Uω (aρ 13) (bρ 13) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2454,26 +2147,21 @@ lemma U_525_13 : have hlg : Real.log (3527577028304457 / 20000000000000000 : ℝ) ≤ (-(17351210317533614871703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3527577028304457 / 20000000000000000 : ℝ) = - (3527577028304457 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3527577028304457 / 2500000000000000 : ℚ)) - (U := (3443205091466385128297 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3527577028304457 / 2500000000000000 : ℝ) ≤ - (3443205091466385128297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63470854460479 / 1250000000000000 : ℝ)) (q := - (3527577028304457 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3527577028304457 / 20000000000000000 : ℚ)) + (r' := (3527577028304457 / 2500000000000000 : ℚ)) + (U := (-(17351210317533614871703 / 10000000000000000000000 : ℚ))) + (U' := (3443205091466385128297 / 10000000000000000000000 : ℚ)) + 3 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (9595973061673 / 16000000000000 : ℚ)) + (s := (63470854460479 / 1250000000000000 : ℚ)) + (q := (3527577028304457 / 20000000000000000 : ℚ)) + (U := (-(17351210317533614871703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_525_14 : Uω (aρ 14) (bρ 14) (9595973061673 / 16000000000000 : ℝ) ≤ @@ -2580,25 +2268,21 @@ lemma U_526_1 : have hlg : Real.log (23817825935064501 / 40000000000000000 : ℝ) ≤ (-(1296112911651224119971 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23817825935064501 / 40000000000000000 : ℝ) = - (23817825935064501 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23817825935064501 / 20000000000000000 : ℚ)) - (U := (436755039098775880029 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23817825935064501 / 20000000000000000 : ℝ) ≤ - (436755039098775880029 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5954429333028813 / 10000000000000000 : ℝ)) (q := - (23817825935064501 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23817825935064501 / 40000000000000000 : ℚ)) + (r' := (23817825935064501 / 20000000000000000 : ℚ)) + (U := (-(1296112911651224119971 / 2500000000000000000000 : ℚ))) + (U' := (436755039098775880029 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (5954429333028813 / 10000000000000000 : ℚ)) + (q := (23817825935064501 / 40000000000000000 : ℚ)) + (U := (-(1296112911651224119971 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_2 : Uω (aρ 2) (bρ 2) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2606,25 +2290,21 @@ lemma U_526_2 : have hlg : Real.log (4744428583782069 / 8000000000000000 : ℝ) ≤ (-(5224705415238725644339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4744428583782069 / 8000000000000000 : ℝ) = - (4744428583782069 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4744428583782069 / 4000000000000000 : ℚ)) - (U := (1706766387761274355661 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4744428583782069 / 4000000000000000 : ℝ) ≤ - (1706766387761274355661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1186071367492347 / 2000000000000000 : ℝ)) (q := - (4744428583782069 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4744428583782069 / 8000000000000000 : ℚ)) + (r' := (4744428583782069 / 4000000000000000 : ℚ)) + (U := (-(5224705415238725644339 / 10000000000000000000000 : ℚ))) + (U' := (1706766387761274355661 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (1186071367492347 / 2000000000000000 : ℚ)) + (q := (4744428583782069 / 8000000000000000 : ℚ)) + (U := (-(5224705415238725644339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_3 : Uω (aρ 3) (bρ 3) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2632,25 +2312,21 @@ lemma U_526_3 : have hlg : Real.log (23530758859248241 / 40000000000000000 : ℝ) ≤ (-(1326427502307451136827 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23530758859248241 / 40000000000000000 : ℝ) = - (23530758859248241 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23530758859248241 / 20000000000000000 : ℚ)) - (U := (406440448442548863173 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23530758859248241 / 20000000000000000 : ℝ) ≤ - (406440448442548863173 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5882060913980683 / 10000000000000000 : ℝ)) (q := - (23530758859248241 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23530758859248241 / 40000000000000000 : ℚ)) + (r' := (23530758859248241 / 20000000000000000 : ℚ)) + (U := (-(1326427502307451136827 / 2500000000000000000000 : ℚ))) + (U' := (406440448442548863173 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (5882060913980683 / 10000000000000000 : ℚ)) + (q := (23530758859248241 / 40000000000000000 : ℚ)) + (U := (-(1326427502307451136827 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_4 : Uω (aρ 4) (bρ 4) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2658,25 +2334,21 @@ lemma U_526_4 : have hlg : Real.log (23212845815919161 / 40000000000000000 : ℝ) ≤ (-(5441736294544028744673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23212845815919161 / 40000000000000000 : ℝ) = - (23212845815919161 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23212845815919161 / 20000000000000000 : ℚ)) - (U := (1489735508455971255327 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23212845815919161 / 20000000000000000 : ℝ) ≤ - (1489735508455971255327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5801398573381143 / 10000000000000000 : ℝ)) (q := - (23212845815919161 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23212845815919161 / 40000000000000000 : ℚ)) + (r' := (23212845815919161 / 20000000000000000 : ℚ)) + (U := (-(5441736294544028744673 / 10000000000000000000000 : ℚ))) + (U' := (1489735508455971255327 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (5801398573381143 / 10000000000000000 : ℚ)) + (q := (23212845815919161 / 40000000000000000 : ℚ)) + (U := (-(5441736294544028744673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_5 : Uω (aρ 5) (bρ 5) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2684,25 +2356,21 @@ lemma U_526_5 : have hlg : Real.log (4545718465535591 / 8000000000000000 : ℝ) ≤ (-(113051149611568404339 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4545718465535591 / 8000000000000000 : ℝ) = - (4545718465535591 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4545718465535591 / 4000000000000000 : ℚ)) - (U := (25578286448431595661 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4545718465535591 / 4000000000000000 : ℝ) ≤ - (25578286448431595661 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (283873087429777 / 500000000000000 : ℝ)) (q := - (4545718465535591 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4545718465535591 / 8000000000000000 : ℚ)) + (r' := (4545718465535591 / 4000000000000000 : ℚ)) + (U := (-(113051149611568404339 / 200000000000000000000 : ℚ))) + (U' := (25578286448431595661 / 200000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (283873087429777 / 500000000000000 : ℚ)) + (q := (4545718465535591 / 8000000000000000 : ℚ)) + (U := (-(113051149611568404339 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_6 : Uω (aρ 6) (bρ 6) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2710,25 +2378,21 @@ lemma U_526_6 : have hlg : Real.log (22033818380029693 / 40000000000000000 : ℝ) ≤ (-(1192601963369088836747 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22033818380029693 / 40000000000000000 : ℝ) = - (22033818380029693 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22033818380029693 / 20000000000000000 : ℚ)) - (U := (193692397230911163253 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22033818380029693 / 20000000000000000 : ℝ) ≤ - (193692397230911163253 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5497315149911409 / 10000000000000000 : ℝ)) (q := - (22033818380029693 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22033818380029693 / 40000000000000000 : ℚ)) + (r' := (22033818380029693 / 20000000000000000 : ℚ)) + (U := (-(1192601963369088836747 / 2000000000000000000000 : ℚ))) + (U' := (193692397230911163253 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (5497315149911409 / 10000000000000000 : ℚ)) + (q := (22033818380029693 / 40000000000000000 : ℚ)) + (U := (-(1192601963369088836747 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_7 : Uω (aρ 7) (bρ 7) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2736,25 +2400,21 @@ lemma U_526_7 : have hlg : Real.log (21085330258631749 / 40000000000000000 : ℝ) ≤ (-(6403019035753007704611 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21085330258631749 / 40000000000000000 : ℝ) = - (21085330258631749 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21085330258631749 / 20000000000000000 : ℚ)) - (U := (528452767246992295389 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21085330258631749 / 20000000000000000 : ℝ) ≤ - (528452767246992295389 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5246732469972437 / 10000000000000000 : ℝ)) (q := - (21085330258631749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21085330258631749 / 40000000000000000 : ℚ)) + (r' := (21085330258631749 / 20000000000000000 : ℚ)) + (U := (-(6403019035753007704611 / 10000000000000000000000 : ℚ))) + (U' := (528452767246992295389 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (5246732469972437 / 10000000000000000 : ℚ)) + (q := (21085330258631749 / 40000000000000000 : ℚ)) + (U := (-(6403019035753007704611 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_8 : Uω (aρ 8) (bρ 8) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2762,25 +2422,21 @@ lemma U_526_8 : have hlg : Real.log (19846209221993067 / 40000000000000000 : ℝ) ≤ (-(1752166089705982821403 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19846209221993067 / 40000000000000000 : ℝ) = - (19846209221993067 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19846209221993067 / 10000000000000000 : ℚ)) - (U := (1713569811794017178597 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19846209221993067 / 10000000000000000 : ℝ) ≤ - (1713569811794017178597 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (613839200374137 / 1250000000000000 : ℝ)) (q := - (19846209221993067 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19846209221993067 / 40000000000000000 : ℚ)) + (r' := (19846209221993067 / 10000000000000000 : ℚ)) + (U := (-(1752166089705982821403 / 2500000000000000000000 : ℚ))) + (U' := (1713569811794017178597 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (613839200374137 / 1250000000000000 : ℚ)) + (q := (19846209221993067 / 40000000000000000 : ℚ)) + (U := (-(1752166089705982821403 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_9 : Uω (aρ 9) (bρ 9) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2788,25 +2444,21 @@ lemma U_526_9 : have hlg : Real.log (18289527497605977 / 40000000000000000 : ℝ) ≤ (-(1565101650889641952791 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18289527497605977 / 40000000000000000 : ℝ) = - (18289527497605977 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18289527497605977 / 10000000000000000 : ℚ)) - (U := (1207487070310358047209 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18289527497605977 / 10000000000000000 : ℝ) ≤ - (1207487070310358047209 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4473338369159551 / 10000000000000000 : ℝ)) (q := - (18289527497605977 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18289527497605977 / 40000000000000000 : ℚ)) + (r' := (18289527497605977 / 10000000000000000 : ℚ)) + (U := (-(1565101650889641952791 / 2000000000000000000000 : ℚ))) + (U' := (1207487070310358047209 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (4473338369159551 / 10000000000000000 : ℚ)) + (q := (18289527497605977 / 40000000000000000 : ℚ)) + (U := (-(1565101650889641952791 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_10 : Uω (aρ 10) (bρ 10) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2814,25 +2466,21 @@ lemma U_526_10 : have hlg : Real.log (655893197973881 / 1600000000000000 : ℝ) ≤ (-(2229402349962983556549 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (655893197973881 / 1600000000000000 : ℝ) = - (655893197973881 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (655893197973881 / 400000000000000 : ℚ)) - (U := (1236333551537016443451 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (655893197973881 / 400000000000000 : ℝ) ≤ - (1236333551537016443451 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (156631945141003 / 400000000000000 : ℝ)) (q := - (655893197973881 / 1600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (655893197973881 / 1600000000000000 : ℚ)) + (r' := (655893197973881 / 400000000000000 : ℚ)) + (U := (-(2229402349962983556549 / 2500000000000000000000 : ℚ))) + (U' := (1236333551537016443451 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (156631945141003 / 400000000000000 : ℚ)) + (q := (655893197973881 / 1600000000000000 : ℚ)) + (U := (-(2229402349962983556549 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_11 : Uω (aρ 11) (bρ 11) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2840,26 +2488,21 @@ lemma U_526_11 : have hlg : Real.log (14146270976670461 / 40000000000000000 : ℝ) ≤ (-(5197141997269709507939 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14146270976670461 / 40000000000000000 : ℝ) = - (14146270976670461 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14146270976670461 / 10000000000000000 : ℚ)) - (U := (1734329805730290492061 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14146270976670461 / 10000000000000000 : ℝ) ≤ - (1734329805730290492061 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3208745768391793 / 10000000000000000 : ℝ)) (q := - (14146270976670461 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14146270976670461 / 40000000000000000 : ℚ)) + (r' := (14146270976670461 / 10000000000000000 : ℚ)) + (U := (-(5197141997269709507939 / 5000000000000000000000 : ℚ))) + (U' := (1734329805730290492061 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (3208745768391793 / 10000000000000000 : ℚ)) + (q := (14146270976670461 / 40000000000000000 : ℚ)) + (U := (-(5197141997269709507939 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_12 : Uω (aρ 12) (bρ 12) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2867,26 +2510,21 @@ lemma U_526_12 : have hlg : Real.log (11440206651004759 / 40000000000000000 : ℝ) ≤ (-(12517454039065267076341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11440206651004759 / 40000000000000000 : ℝ) = - (11440206651004759 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11440206651004759 / 10000000000000000 : ℚ)) - (U := (1345489566934732923659 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11440206651004759 / 10000000000000000 : ℝ) ≤ - (1345489566934732923659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1139706851121971 / 5000000000000000 : ℝ)) (q := - (11440206651004759 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11440206651004759 / 40000000000000000 : ℚ)) + (r' := (11440206651004759 / 10000000000000000 : ℚ)) + (U := (-(12517454039065267076341 / 10000000000000000000000 : ℚ))) + (U' := (1345489566934732923659 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (1139706851121971 / 5000000000000000 : ℚ)) + (q := (11440206651004759 / 40000000000000000 : ℚ)) + (U := (-(12517454039065267076341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_13 : Uω (aρ 13) (bρ 13) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -2894,26 +2532,21 @@ lemma U_526_13 : have hlg : Real.log (7328612859684809 / 40000000000000000 : ℝ) ≤ (-(16970931968603725312893 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7328612859684809 / 40000000000000000 : ℝ) = - (7328612859684809 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7328612859684809 / 5000000000000000 : ℚ)) - (U := (3823483440396274687107 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7328612859684809 / 5000000000000000 : ℝ) ≤ - (3823483440396274687107 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (622998548178967 / 10000000000000000 : ℝ)) (q := - (7328612859684809 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7328612859684809 / 40000000000000000 : ℚ)) + (r' := (7328612859684809 / 5000000000000000 : ℚ)) + (U := (-(16970931968603725312893 / 10000000000000000000000 : ℚ))) + (U' := (3823483440396274687107 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19260738728283 / 32000000000000 : ℚ)) + (s := (622998548178967 / 10000000000000000 : ℚ)) + (q := (7328612859684809 / 40000000000000000 : ℚ)) + (U := (-(16970931968603725312893 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_526_14 : Uω (aρ 14) (bρ 14) (19260738728283 / 32000000000000 : ℝ) ≤ @@ -3020,25 +2653,21 @@ lemma U_527_1 : have hlg : Real.log (1908865720707619 / 3200000000000000 : ℝ) ≤ (-(645802009247295681979 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1908865720707619 / 3200000000000000 : ℝ) = - (1908865720707619 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1908865720707619 / 1600000000000000 : ℚ)) - (U := (220631966127704318021 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1908865720707619 / 1600000000000000 : ℝ) ≤ - (220631966127704318021 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (238607131015911 / 400000000000000 : ℝ)) (q := - (1908865720707619 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1908865720707619 / 3200000000000000 : ℚ)) + (r' := (1908865720707619 / 1600000000000000 : ℚ)) + (U := (-(645802009247295681979 / 1250000000000000000000 : ℚ))) + (U' := (220631966127704318021 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (238607131015911 / 400000000000000 : ℚ)) + (q := (1908865720707619 / 3200000000000000 : ℚ)) + (U := (-(645802009247295681979 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_2 : Uω (aρ 2) (bρ 2) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3046,25 +2675,21 @@ lemma U_527_2 : have hlg : Real.log (47530279183254143 / 80000000000000000 : ℝ) ≤ (-(1301649174932163817053 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47530279183254143 / 80000000000000000 : ℝ) = - (47530279183254143 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47530279183254143 / 40000000000000000 : ℚ)) - (U := (431218775817836182947 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47530279183254143 / 40000000000000000 : ℝ) ≤ - (431218775817836182947 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1485276582324673 / 2500000000000000 : ℝ)) (q := - (47530279183254143 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47530279183254143 / 80000000000000000 : ℚ)) + (r' := (47530279183254143 / 40000000000000000 : ℚ)) + (U := (-(1301649174932163817053 / 2500000000000000000000 : ℚ))) + (U' := (431218775817836182947 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (1485276582324673 / 2500000000000000 : ℚ)) + (q := (47530279183254143 / 80000000000000000 : ℚ)) + (U := (-(1301649174932163817053 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_3 : Uω (aρ 3) (bρ 3) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3072,25 +2697,21 @@ lemma U_527_3 : have hlg : Real.log (47147517650434583 / 80000000000000000 : ℝ) ≤ (-(660931593304168506057 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47147517650434583 / 80000000000000000 : ℝ) = - (47147517650434583 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47147517650434583 / 40000000000000000 : ℚ)) - (U := (205502382070831493943 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47147517650434583 / 40000000000000000 : ℝ) ≤ - (205502382070831493943 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2946406026221901 / 5000000000000000 : ℝ)) (q := - (47147517650434583 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47147517650434583 / 80000000000000000 : ℚ)) + (r' := (47147517650434583 / 40000000000000000 : ℚ)) + (U := (-(660931593304168506057 / 1250000000000000000000 : ℚ))) + (U' := (205502382070831493943 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (2946406026221901 / 5000000000000000 : ℚ)) + (q := (47147517650434583 / 80000000000000000 : ℚ)) + (U := (-(660931593304168506057 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_4 : Uω (aρ 4) (bρ 4) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3098,25 +2719,21 @@ lemma U_527_4 : have hlg : Real.log (46511709209573511 / 80000000000000000 : ℝ) ≤ (-(1355806356402784096183 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46511709209573511 / 80000000000000000 : ℝ) = - (46511709209573511 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46511709209573511 / 40000000000000000 : ℚ)) - (U := (377061594347215903817 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46511709209573511 / 40000000000000000 : ℝ) ≤ - (377061594347215903817 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2906077061646767 / 5000000000000000 : ℝ)) (q := - (46511709209573511 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46511709209573511 / 80000000000000000 : ℚ)) + (r' := (46511709209573511 / 40000000000000000 : ℚ)) + (U := (-(1355806356402784096183 / 2500000000000000000000 : ℚ))) + (U' := (377061594347215903817 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (2906077061646767 / 5000000000000000 : ℚ)) + (q := (46511709209573511 / 80000000000000000 : ℚ)) + (U := (-(1355806356402784096183 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_5 : Uω (aρ 5) (bρ 5) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3124,25 +2741,21 @@ lemma U_527_5 : have hlg : Real.log (9108649251285719 / 16000000000000000 : ℝ) ≤ (-(352102682931682360927 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9108649251285719 / 16000000000000000 : ℝ) = - (9108649251285719 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9108649251285719 / 8000000000000000 : ℚ)) - (U := (81114304755817639073 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9108649251285719 / 8000000000000000 : ℝ) ≤ - (81114304755817639073 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1137645660868461 / 2000000000000000 : ℝ)) (q := - (9108649251285719 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9108649251285719 / 16000000000000000 : ℚ)) + (r' := (9108649251285719 / 8000000000000000 : ℚ)) + (U := (-(352102682931682360927 / 625000000000000000000 : ℚ))) + (U' := (81114304755817639073 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (1137645660868461 / 2000000000000000 : ℚ)) + (q := (9108649251285719 / 16000000000000000 : ℚ)) + (U := (-(352102682931682360927 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_6 : Uω (aρ 6) (bρ 6) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3150,25 +2763,21 @@ lemma U_527_6 : have hlg : Real.log (8830760284451563 / 16000000000000000 : ℝ) ≤ (-(46433406925091649199 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8830760284451563 / 16000000000000000 : ℝ) = - (8830760284451563 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8830760284451563 / 8000000000000000 : ℚ)) - (U := (7718716535845850801 / 78125000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8830760284451563 / 8000000000000000 : ℝ) ≤ - (7718716535845850801 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (550810747093961 / 1000000000000000 : ℝ)) (q := - (8830760284451563 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8830760284451563 / 16000000000000000 : ℚ)) + (r' := (8830760284451563 / 8000000000000000 : ℚ)) + (U := (-(46433406925091649199 / 78125000000000000000 : ℚ))) + (U' := (7718716535845850801 / 78125000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (550810747093961 / 1000000000000000 : ℚ)) + (q := (8830760284451563 / 16000000000000000 : ℚ)) + (U := (-(46433406925091649199 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_7 : Uω (aρ 7) (bρ 7) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3176,25 +2785,21 @@ lemma U_527_7 : have hlg : Real.log (8451410725177719 / 16000000000000000 : ℝ) ≤ (-(6382553448201340794523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8451410725177719 / 16000000000000000 : ℝ) = - (8451410725177719 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8451410725177719 / 8000000000000000 : ℚ)) - (U := (548918354798659205477 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8451410725177719 / 8000000000000000 : ℝ) ≤ - (548918354798659205477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1051516380521461 / 2000000000000000 : ℝ)) (q := - (8451410725177719 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8451410725177719 / 16000000000000000 : ℚ)) + (r' := (8451410725177719 / 8000000000000000 : ℚ)) + (U := (-(6382553448201340794523 / 10000000000000000000000 : ℚ))) + (U' := (548918354798659205477 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (1051516380521461 / 2000000000000000 : ℚ)) + (q := (8451410725177719 / 16000000000000000 : ℚ)) + (U := (-(6382553448201340794523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_8 : Uω (aρ 8) (bρ 8) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3202,25 +2807,21 @@ lemma U_527_8 : have hlg : Real.log (39779297464548527 / 80000000000000000 : ℝ) ≤ (-(3493400107016278783557 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39779297464548527 / 80000000000000000 : ℝ) = - (39779297464548527 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39779297464548527 / 20000000000000000 : ℚ)) - (U := (3438071695983721216443 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39779297464548527 / 20000000000000000 : ℝ) ≤ - (3438071695983721216443 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9612665065649 / 19531250000000 : ℝ)) (q := - (39779297464548527 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39779297464548527 / 80000000000000000 : ℚ)) + (r' := (39779297464548527 / 20000000000000000 : ℚ)) + (U := (-(3493400107016278783557 / 5000000000000000000000 : ℚ))) + (U' := (3438071695983721216443 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (9612665065649 / 19531250000000 : ℚ)) + (q := (39779297464548527 / 80000000000000000 : ℚ)) + (U := (-(3493400107016278783557 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_9 : Uω (aρ 9) (bρ 9) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3228,25 +2829,21 @@ lemma U_527_9 : have hlg : Real.log (36666944995223227 / 80000000000000000 : ℝ) ≤ (-(7801509662796789883127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36666944995223227 / 80000000000000000 : ℝ) = - (36666944995223227 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36666944995223227 / 20000000000000000 : ℚ)) - (U := (6061433943203210116873 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36666944995223227 / 20000000000000000 : ℝ) ≤ - (6061433943203210116873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4484562024640963 / 10000000000000000 : ℝ)) (q := - (36666944995223227 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36666944995223227 / 80000000000000000 : ℚ)) + (r' := (36666944995223227 / 20000000000000000 : ℚ)) + (U := (-(7801509662796789883127 / 10000000000000000000000 : ℚ))) + (U' := (6061433943203210116873 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (4484562024640963 / 10000000000000000 : ℚ)) + (q := (36666944995223227 / 80000000000000000 : ℚ)) + (U := (-(7801509662796789883127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_10 : Uω (aρ 10) (bρ 10) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3254,26 +2851,21 @@ lemma U_527_10 : have hlg : Real.log (32884669502598183 / 80000000000000000 : ℝ) ≤ (-(4445100287735114038913 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (32884669502598183 / 80000000000000000 : ℝ) = - (32884669502598183 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32884669502598183 / 20000000000000000 : ℚ)) - (U := (2486371515264885961087 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32884669502598183 / 20000000000000000 : ℝ) ≤ - (2486371515264885961087 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1963776092489851 / 5000000000000000 : ℝ)) (q := - (32884669502598183 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32884669502598183 / 80000000000000000 : ℚ)) + (r' := (32884669502598183 / 20000000000000000 : ℚ)) + (U := (-(4445100287735114038913 / 5000000000000000000000 : ℚ))) + (U' := (2486371515264885961087 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (1963776092489851 / 5000000000000000 : ℚ)) + (q := (32884669502598183 / 80000000000000000 : ℚ)) + (U := (-(4445100287735114038913 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_11 : Uω (aρ 11) (bρ 11) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3281,26 +2873,21 @@ lemma U_527_11 : have hlg : Real.log (5677457132364783 / 16000000000000000 : ℝ) ≤ (-(10360852771929530826219 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5677457132364783 / 16000000000000000 : ℝ) = - (5677457132364783 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5677457132364783 / 4000000000000000 : ℚ)) - (U := (3502090834070469173781 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5677457132364783 / 4000000000000000 : ℝ) ≤ - (3502090834070469173781 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (644336570198227 / 2000000000000000 : ℝ)) (q := - (5677457132364783 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5677457132364783 / 16000000000000000 : ℚ)) + (r' := (5677457132364783 / 4000000000000000 : ℚ)) + (U := (-(10360852771929530826219 / 10000000000000000000000 : ℚ))) + (U' := (3502090834070469173781 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (644336570198227 / 2000000000000000 : ℚ)) + (q := (5677457132364783 / 16000000000000000 : ℚ)) + (U := (-(10360852771929530826219 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_12 : Uω (aρ 12) (bρ 12) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3308,26 +2895,21 @@ lemma U_527_12 : have hlg : Real.log (22988179902838547 / 80000000000000000 : ℝ) ≤ (-(2494092935186941707943 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (22988179902838547 / 80000000000000000 : ℝ) = - (22988179902838547 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22988179902838547 / 20000000000000000 : ℚ)) - (U := (278495786013058292057 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22988179902838547 / 20000000000000000 : ℝ) ≤ - (278495786013058292057 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2295606507929793 / 10000000000000000 : ℝ)) (q := - (22988179902838547 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22988179902838547 / 80000000000000000 : ℚ)) + (r' := (22988179902838547 / 20000000000000000 : ℚ)) + (U := (-(2494092935186941707943 / 2000000000000000000000 : ℚ))) + (U' := (278495786013058292057 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (2295606507929793 / 10000000000000000 : ℚ)) + (q := (22988179902838547 / 80000000000000000 : ℚ)) + (U := (-(2494092935186941707943 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_13 : Uω (aρ 13) (bρ 13) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3335,26 +2917,21 @@ lemma U_527_13 : have hlg : Real.log (14902290956880979 / 80000000000000000 : ℝ) ≤ (-(16805116772664291941307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (14902290956880979 / 80000000000000000 : ℝ) = - (14902290956880979 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14902290956880979 / 10000000000000000 : ℚ)) - (U := (3989298636335708058693 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14902290956880979 / 10000000000000000 : ℝ) ≤ - (3989298636335708058693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (673516013035401 / 10000000000000000 : ℝ)) (q := - (14902290956880979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14902290956880979 / 80000000000000000 : ℚ)) + (r' := (14902290956880979 / 10000000000000000 : ℚ)) + (U := (-(16805116772664291941307 / 10000000000000000000000 : ℚ))) + (U' := (3989298636335708058693 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (38590270061503 / 64000000000000 : ℚ)) + (s := (673516013035401 / 10000000000000000 : ℚ)) + (q := (14902290956880979 / 80000000000000000 : ℚ)) + (U := (-(16805116772664291941307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_527_14 : Uω (aρ 14) (bρ 14) (38590270061503 / 64000000000000 : ℝ) ≤ @@ -3460,25 +3037,21 @@ lemma U_528_1 : have hlg : Real.log (1195190854096099 / 2000000000000000 : ℝ) ≤ (-(2574206485641140088087 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1195190854096099 / 2000000000000000 : ℝ) = - (1195190854096099 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1195190854096099 / 1000000000000000 : ℚ)) - (U := (891529415858859911913 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1195190854096099 / 1000000000000000 : ℝ) ≤ - (891529415858859911913 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (298796360870737 / 500000000000000 : ℝ)) (q := - (1195190854096099 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1195190854096099 / 2000000000000000 : ℚ)) + (r' := (1195190854096099 / 1000000000000000 : ℚ)) + (U := (-(2574206485641140088087 / 5000000000000000000000 : ℚ))) + (U' := (891529415858859911913 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (298796360870737 / 500000000000000 : ℚ)) + (q := (1195190854096099 / 2000000000000000 : ℚ)) + (U := (-(2574206485641140088087 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_2 : Uω (aρ 2) (bρ 2) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3486,25 +3059,21 @@ lemma U_528_2 : have hlg : Real.log (11904068129833769 / 20000000000000000 : ℝ) ≤ (-(1297130179868403671289 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11904068129833769 / 20000000000000000 : ℝ) = - (11904068129833769 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11904068129833769 / 10000000000000000 : ℚ)) - (U := (435737770881596328711 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11904068129833769 / 10000000000000000 : ℝ) ≤ - (435737770881596328711 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5951855818797519 / 10000000000000000 : ℝ)) (q := - (11904068129833769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11904068129833769 / 20000000000000000 : ℚ)) + (r' := (11904068129833769 / 10000000000000000 : ℚ)) + (U := (-(1297130179868403671289 / 2500000000000000000000 : ℚ))) + (U' := (435737770881596328711 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (5951855818797519 / 10000000000000000 : ℚ)) + (q := (11904068129833769 / 20000000000000000 : ℚ)) + (U := (-(1297130179868403671289 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_3 : Uω (aρ 3) (bρ 3) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3512,25 +3081,21 @@ lemma U_528_3 : have hlg : Real.log (2361675877447789 / 4000000000000000 : ℝ) ≤ (-(5269228762739811181977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2361675877447789 / 4000000000000000 : ℝ) = - (2361675877447789 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2361675877447789 / 2000000000000000 : ℚ)) - (U := (1662243040260188818023 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2361675877447789 / 2000000000000000 : ℝ) ≤ - (1662243040260188818023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1180712636510539 / 2000000000000000 : ℝ)) (q := - (2361675877447789 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2361675877447789 / 4000000000000000 : ℚ)) + (r' := (2361675877447789 / 2000000000000000 : ℚ)) + (U := (-(5269228762739811181977 / 10000000000000000000000 : ℚ))) + (U' := (1662243040260188818023 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (1180712636510539 / 2000000000000000 : ℚ)) + (q := (2361675877447789 / 4000000000000000 : ℚ)) + (U := (-(5269228762739811181977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_4 : Uω (aρ 4) (bρ 4) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3538,25 +3103,21 @@ lemma U_528_4 : have hlg : Real.log (11649431672063719 / 20000000000000000 : ℝ) ≤ (-(675593597482667857747 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11649431672063719 / 20000000000000000 : ℝ) = - (11649431672063719 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11649431672063719 / 10000000000000000 : ℚ)) - (U := (190840377892332142253 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11649431672063719 / 10000000000000000 : ℝ) ≤ - (190840377892332142253 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5822909648442469 / 10000000000000000 : ℝ)) (q := - (11649431672063719 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11649431672063719 / 20000000000000000 : ℚ)) + (r' := (11649431672063719 / 10000000000000000 : ℚ)) + (U := (-(675593597482667857747 / 1250000000000000000000 : ℚ))) + (U' := (190840377892332142253 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (5822909648442469 / 10000000000000000 : ℚ)) + (q := (11649431672063719 / 20000000000000000 : ℚ)) + (U := (-(675593597482667857747 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_5 : Uω (aρ 5) (bρ 5) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3564,25 +3125,21 @@ lemma U_528_5 : have hlg : Real.log (5703663448755089 / 10000000000000000 : ℝ) ≤ (-(5614764140355019561613 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5703663448755089 / 10000000000000000 : ℝ) = - (5703663448755089 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5703663448755089 / 5000000000000000 : ℚ)) - (U := (1316707662644980438387 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5703663448755089 / 5000000000000000 : ℝ) ≤ - (1316707662644980438387 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (712374349152991 / 1250000000000000 : ℝ)) (q := - (5703663448755089 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5703663448755089 / 10000000000000000 : ℚ)) + (r' := (5703663448755089 / 5000000000000000 : ℚ)) + (U := (-(5614764140355019561613 / 10000000000000000000000 : ℚ))) + (U' := (1316707662644980438387 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (712374349152991 / 1250000000000000 : ℚ)) + (q := (5703663448755089 / 10000000000000000 : ℚ)) + (U := (-(5614764140355019561613 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_6 : Uω (aρ 6) (bρ 6) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3590,25 +3147,21 @@ lemma U_528_6 : have hlg : Real.log (2211998270283633 / 4000000000000000 : ℝ) ≤ (-(5923980591695871839469 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2211998270283633 / 4000000000000000 : ℝ) = - (2211998270283633 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2211998270283633 / 2000000000000000 : ℚ)) - (U := (1007491211304128160531 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2211998270283633 / 2000000000000000 : ℝ) ≤ - (1007491211304128160531 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1103779924454383 / 2000000000000000 : ℝ)) (q := - (2211998270283633 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2211998270283633 / 4000000000000000 : ℚ)) + (r' := (2211998270283633 / 2000000000000000 : ℚ)) + (U := (-(5923980591695871839469 / 10000000000000000000000 : ℚ))) + (U' := (1007491211304128160531 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (1103779924454383 / 2000000000000000 : ℚ)) + (q := (2211998270283633 / 4000000000000000 : ℚ)) + (U := (-(5923980591695871839469 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_7 : Uω (aρ 7) (bρ 7) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3616,25 +3169,21 @@ lemma U_528_7 : have hlg : Real.log (1058586127126089 / 2000000000000000 : ℝ) ≤ (-(159053251217352304367 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1058586127126089 / 2000000000000000 : ℝ) = - (1058586127126089 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1058586127126089 / 1000000000000000 : ℚ)) - (U := (14233543857647695633 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1058586127126089 / 1000000000000000 : ℝ) ≤ - (14233543857647695633 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (65855386535933 / 125000000000000 : ℝ)) (q := - (1058586127126089 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1058586127126089 / 2000000000000000 : ℚ)) + (r' := (1058586127126089 / 1000000000000000 : ℚ)) + (U := (-(159053251217352304367 / 250000000000000000000 : ℚ))) + (U' := (14233543857647695633 / 250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (65855386535933 / 125000000000000 : ℚ)) + (q := (1058586127126089 / 2000000000000000 : ℚ)) + (U := (-(159053251217352304367 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_8 : Uω (aρ 8) (bρ 8) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3642,25 +3191,21 @@ lemma U_528_8 : have hlg : Real.log (9966543143463281 / 20000000000000000 : ℝ) ≤ (-(6964984750148177349421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9966543143463281 / 20000000000000000 : ℝ) = - (9966543143463281 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9966543143463281 / 5000000000000000 : ℚ)) - (U := (6897958855851822650579 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9966543143463281 / 5000000000000000 : ℝ) ≤ - (6897958855851822650579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4932654446417031 / 10000000000000000 : ℝ)) (q := - (9966543143463281 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9966543143463281 / 20000000000000000 : ℚ)) + (r' := (9966543143463281 / 5000000000000000 : ℚ)) + (U := (-(6964984750148177349421 / 10000000000000000000000 : ℚ))) + (U' := (6897958855851822650579 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (4932654446417031 / 10000000000000000 : ℚ)) + (q := (9966543143463281 / 20000000000000000 : ℚ)) + (U := (-(6964984750148177349421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_9 : Uω (aρ 9) (bρ 9) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3668,25 +3213,21 @@ lemma U_528_9 : have hlg : Real.log (2297176607059593 / 5000000000000000 : ℝ) ≤ (-(7777571051986987253239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2297176607059593 / 5000000000000000 : ℝ) = - (2297176607059593 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2297176607059593 / 1250000000000000 : ℚ)) - (U := (6085372554013012746761 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2297176607059593 / 1250000000000000 : ℝ) ≤ - (6085372554013012746761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2247891679776061 / 5000000000000000 : ℝ)) (q := - (2297176607059593 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2297176607059593 / 5000000000000000 : ℚ)) + (r' := (2297176607059593 / 1250000000000000 : ℚ)) + (U := (-(7777571051986987253239 / 10000000000000000000000 : ℚ))) + (U' := (6085372554013012746761 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (2247891679776061 / 5000000000000000 : ℚ)) + (q := (2297176607059593 / 5000000000000000 : ℚ)) + (U := (-(7777571051986987253239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_10 : Uω (aρ 10) (bρ 10) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3694,26 +3235,21 @@ lemma U_528_10 : have hlg : Real.log (1648732807485941 / 4000000000000000 : ℝ) ≤ (-(4431436816050858759941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1648732807485941 / 4000000000000000 : ℝ) = - (1648732807485941 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1648732807485941 / 1000000000000000 : ℚ)) - (U := (2500034986949141240059 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1648732807485941 / 1000000000000000 : ℝ) ≤ - (2500034986949141240059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (787860000447691 / 2000000000000000 : ℝ)) (q := - (1648732807485941 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1648732807485941 / 4000000000000000 : ℚ)) + (r' := (1648732807485941 / 1000000000000000 : ℚ)) + (U := (-(4431436816050858759941 / 5000000000000000000000 : ℚ))) + (U' := (2500034986949141240059 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (787860000447691 / 2000000000000000 : ℚ)) + (q := (1648732807485941 / 4000000000000000 : ℚ)) + (U := (-(4431436816050858759941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_11 : Uω (aρ 11) (bρ 11) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3721,26 +3257,21 @@ lemma U_528_11 : have hlg : Real.log (7120491318877783 / 20000000000000000 : ℝ) ≤ (-(5163777722653102252189 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7120491318877783 / 20000000000000000 : ℝ) = - (7120491318877783 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7120491318877783 / 5000000000000000 : ℚ)) - (U := (1767694080346897747811 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7120491318877783 / 5000000000000000 : ℝ) ≤ - (1767694080346897747811 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3234603909891533 / 10000000000000000 : ℝ)) (q := - (7120491318877783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7120491318877783 / 20000000000000000 : ℚ)) + (r' := (7120491318877783 / 5000000000000000 : ℚ)) + (U := (-(5163777722653102252189 / 5000000000000000000000 : ℚ))) + (U' := (1767694080346897747811 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (3234603909891533 / 10000000000000000 : ℚ)) + (q := (7120491318877783 / 20000000000000000 : ℚ)) + (U := (-(5163777722653102252189 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_12 : Uω (aρ 12) (bρ 12) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3748,23 +3279,21 @@ lemma U_528_12 : have hlg : Real.log (5638596856701 / 19531250000000 : ℝ) ≤ (-(2484760992263260070481 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show (5638596856701 / 19531250000000 : ℝ) = (5638596856701 / 4882812500000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5638596856701 / 4882812500000 : ℚ)) - (U := (287827728936739929519 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5638596856701 / 4882812500000 : ℝ) ≤ - (287827728936739929519 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1155867934480287 / 5000000000000000 : ℝ)) (q := - (5638596856701 / 19531250000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5638596856701 / 19531250000000 : ℚ)) + (r' := (5638596856701 / 4882812500000 : ℚ)) + (U := (-(2484760992263260070481 / 2000000000000000000000 : ℚ))) + (U' := (287827728936739929519 / 2000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (1155867934480287 / 5000000000000000 : ℚ)) + (q := (5638596856701 / 19531250000000 : ℚ)) + (U := (-(2484760992263260070481 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_13 : Uω (aρ 13) (bρ 13) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3772,26 +3301,21 @@ lemma U_528_13 : have hlg : Real.log (1891733024132149 / 10000000000000000 : ℝ) ≤ (-(260170584264644178209 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1891733024132149 / 10000000000000000 : ℝ) = - (1891733024132149 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1891733024132149 / 1250000000000000 : ℚ)) - (U := (64742156500980821791 / 156250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1891733024132149 / 1250000000000000 : ℝ) ≤ - (64742156500980821791 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (22520639923689 / 312500000000000 : ℝ)) (q := - (1891733024132149 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1891733024132149 / 10000000000000000 : ℚ)) + (r' := (1891733024132149 / 1250000000000000 : ℚ)) + (U := (-(260170584264644178209 / 156250000000000000000 : ℚ))) + (U' := (64742156500980821791 / 156250000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (966476566661 / 1600000000000 : ℚ)) + (s := (22520639923689 / 312500000000000 : ℚ)) + (q := (1891733024132149 / 10000000000000000 : ℚ)) + (U := (-(260170584264644178209 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_528_14 : Uω (aρ 14) (bρ 14) (966476566661 / 1600000000000 : ℝ) ≤ @@ -3898,25 +3422,21 @@ lemma U_529_1 : have hlg : Real.log (9578725061719409 / 16000000000000000 : ℝ) ≤ (-(5130442221812664608347 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9578725061719409 / 16000000000000000 : ℝ) = - (9578725061719409 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9578725061719409 / 8000000000000000 : ℚ)) - (U := (1801029581187335391653 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9578725061719409 / 8000000000000000 : ℝ) ≤ - (1801029581187335391653 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1197335231816321 / 2000000000000000 : ℝ)) (q := - (9578725061719409 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9578725061719409 / 16000000000000000 : ℚ)) + (r' := (9578725061719409 / 8000000000000000 : ℚ)) + (U := (-(5130442221812664608347 / 10000000000000000000000 : ℚ))) + (U' := (1801029581187335391653 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (1197335231816321 / 2000000000000000 : ℚ)) + (q := (9578725061719409 / 16000000000000000 : ℚ)) + (U := (-(5130442221812664608347 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_2 : Uω (aρ 2) (bρ 2) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -3924,25 +3444,21 @@ lemma U_529_2 : have hlg : Real.log (47702265846114077 / 80000000000000000 : ℝ) ≤ (-(5170477356328555880841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47702265846114077 / 80000000000000000 : ℝ) = - (47702265846114077 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47702265846114077 / 40000000000000000 : ℚ)) - (U := (1760994446671444119159 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47702265846114077 / 40000000000000000 : ℝ) ≤ - (1760994446671444119159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5962605305970863 / 10000000000000000 : ℝ)) (q := - (47702265846114077 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47702265846114077 / 80000000000000000 : ℚ)) + (r' := (47702265846114077 / 40000000000000000 : ℚ)) + (U := (-(5170477356328555880841 / 10000000000000000000000 : ℚ))) + (U' := (1760994446671444119159 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (5962605305970863 / 10000000000000000 : ℚ)) + (q := (47702265846114077 / 80000000000000000 : ℚ)) + (U := (-(5170477356328555880841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_3 : Uω (aρ 3) (bρ 3) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -3950,25 +3466,21 @@ lemma U_529_3 : have hlg : Real.log (47319517414242301 / 80000000000000000 : ℝ) ≤ (-(5251037937022816384007 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47319517414242301 / 80000000000000000 : ℝ) = - (47319517414242301 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47319517414242301 / 40000000000000000 : ℚ)) - (U := (1680433865977183615993 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47319517414242301 / 40000000000000000 : ℝ) ≤ - (1680433865977183615993 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5914314304352919 / 10000000000000000 : ℝ)) (q := - (47319517414242301 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47319517414242301 / 80000000000000000 : ℚ)) + (r' := (47319517414242301 / 40000000000000000 : ℚ)) + (U := (-(5251037937022816384007 / 10000000000000000000000 : ℚ))) + (U' := (1680433865977183615993 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (5914314304352919 / 10000000000000000 : ℚ)) + (q := (47319517414242301 / 80000000000000000 : ℚ)) + (U := (-(5251037937022816384007 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_4 : Uω (aρ 4) (bρ 4) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -3976,25 +3488,21 @@ lemma U_529_4 : have hlg : Real.log (46683744068430289 / 80000000000000000 : ℝ) ≤ (-(5386306230905287627101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46683744068430289 / 80000000000000000 : ℝ) = - (46683744068430289 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46683744068430289 / 40000000000000000 : ℚ)) - (U := (1545165572094712372899 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46683744068430289 / 40000000000000000 : ℝ) ≤ - (1545165572094712372899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1458416287241229 / 2500000000000000 : ℝ)) (q := - (46683744068430289 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46683744068430289 / 80000000000000000 : ℚ)) + (r' := (46683744068430289 / 40000000000000000 : ℚ)) + (U := (-(5386306230905287627101 / 10000000000000000000000 : ℚ))) + (U' := (1545165572094712372899 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (1458416287241229 / 2500000000000000 : ℚ)) + (q := (46683744068430289 / 80000000000000000 : ℚ)) + (U := (-(5386306230905287627101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_5 : Uω (aρ 5) (bρ 5) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4002,25 +3510,21 @@ lemma U_529_5 : have hlg : Real.log (45715368657705249 / 80000000000000000 : ℝ) ≤ (-(5595920985687641589971 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45715368657705249 / 80000000000000000 : ℝ) = - (45715368657705249 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45715368657705249 / 40000000000000000 : ℚ)) - (U := (1335550817312358410029 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45715368657705249 / 40000000000000000 : ℝ) ≤ - (1335550817312358410029 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (178430037988083 / 312500000000000 : ℝ)) (q := - (45715368657705249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45715368657705249 / 80000000000000000 : ℚ)) + (r' := (45715368657705249 / 40000000000000000 : ℚ)) + (U := (-(5595920985687641589971 / 10000000000000000000000 : ℚ))) + (U' := (1335550817312358410029 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (178430037988083 / 312500000000000 : ℚ)) + (q := (45715368657705249 / 80000000000000000 : ℚ)) + (U := (-(5595920985687641589971 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_6 : Uω (aρ 6) (bρ 6) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4028,25 +3532,21 @@ lemma U_529_6 : have hlg : Real.log (44326128714278213 / 80000000000000000 : ℝ) ≤ (-(738065397838446361183 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44326128714278213 / 80000000000000000 : ℝ) = - (44326128714278213 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44326128714278213 / 40000000000000000 : ℚ)) - (U := (128368577536553638817 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44326128714278213 / 40000000000000000 : ℝ) ≤ - (128368577536553638817 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5529691604901897 / 10000000000000000 : ℝ)) (q := - (44326128714278213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44326128714278213 / 80000000000000000 : ℚ)) + (r' := (44326128714278213 / 40000000000000000 : ℚ)) + (U := (-(738065397838446361183 / 1250000000000000000000 : ℚ))) + (U' := (128368577536553638817 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (5529691604901897 / 10000000000000000 : ℚ)) + (q := (44326128714278213 / 80000000000000000 : ℚ)) + (U := (-(738065397838446361183 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_7 : Uω (aρ 7) (bρ 7) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4054,25 +3554,21 @@ lemma U_529_7 : have hlg : Real.log (8485966980979493 / 16000000000000000 : ℝ) ≤ (-(792718582758281840787 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8485966980979493 / 16000000000000000 : ℝ) = - (8485966980979493 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8485966980979493 / 8000000000000000 : ℚ)) - (U := (73715392616718159213 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8485966980979493 / 8000000000000000 : ℝ) ≤ - (73715392616718159213 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (527927953331671 / 1000000000000000 : ℝ)) (q := - (8485966980979493 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8485966980979493 / 16000000000000000 : ℚ)) + (r' := (8485966980979493 / 8000000000000000 : ℚ)) + (U := (-(792718582758281840787 / 1250000000000000000000 : ℚ))) + (U' := (73715392616718159213 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (527927953331671 / 1000000000000000 : ℚ)) + (q := (8485966980979493 / 16000000000000000 : ℚ)) + (U := (-(792718582758281840787 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_8 : Uω (aρ 8) (bρ 8) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4080,25 +3576,21 @@ lemma U_529_8 : have hlg : Real.log (7990608759587449 / 16000000000000000 : ℝ) ≤ (-(6943217746578683048433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7990608759587449 / 16000000000000000 : ℝ) = - (7990608759587449 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7990608759587449 / 4000000000000000 : ℚ)) - (U := (6919725859421316951567 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (7990608759587449 / 4000000000000000 : ℝ) ≤ - (6919725859421316951567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (988724681583331 / 2000000000000000 : ℝ)) (q := - (7990608759587449 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7990608759587449 / 16000000000000000 : ℚ)) + (r' := (7990608759587449 / 4000000000000000 : ℚ)) + (U := (-(6943217746578683048433 / 10000000000000000000000 : ℚ))) + (U' := (6919725859421316951567 / 10000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (988724681583331 / 2000000000000000 : ℚ)) + (q := (7990608759587449 / 16000000000000000 : ℚ)) + (U := (-(6943217746578683048433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_9 : Uω (aρ 9) (bρ 9) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4106,25 +3598,21 @@ lemma U_529_9 : have hlg : Real.log (36842697217734573 / 80000000000000000 : ℝ) ≤ (-(7753692110675952395933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36842697217734573 / 80000000000000000 : ℝ) = - (36842697217734573 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36842697217734573 / 20000000000000000 : ℚ)) - (U := (6109251495324047604067 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36842697217734573 / 20000000000000000 : ℝ) ≤ - (6109251495324047604067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4507002391225987 / 10000000000000000 : ℝ)) (q := - (36842697217734573 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36842697217734573 / 80000000000000000 : ℚ)) + (r' := (36842697217734573 / 20000000000000000 : ℚ)) + (U := (-(7753692110675952395933 / 10000000000000000000000 : ℚ))) + (U' := (6109251495324047604067 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (4507002391225987 / 10000000000000000 : ℚ)) + (q := (36842697217734573 / 80000000000000000 : ℚ)) + (U := (-(7753692110675952395933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_10 : Uω (aρ 10) (bρ 10) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4132,26 +3620,21 @@ lemma U_529_10 : have hlg : Real.log (33064620044831381 / 80000000000000000 : ℝ) ≤ (-(4417814021261383902239 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33064620044831381 / 80000000000000000 : ℝ) = - (33064620044831381 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33064620044831381 / 20000000000000000 : ℚ)) - (U := (2513657781738616097761 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (33064620044831381 / 20000000000000000 : ℝ) ≤ - (2513657781738616097761 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3951042131495189 / 10000000000000000 : ℝ)) (q := - (33064620044831381 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33064620044831381 / 80000000000000000 : ℚ)) + (r' := (33064620044831381 / 20000000000000000 : ℚ)) + (U := (-(4417814021261383902239 / 5000000000000000000000 : ℚ))) + (U' := (2513657781738616097761 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (3951042131495189 / 10000000000000000 : ℚ)) + (q := (33064620044831381 / 80000000000000000 : ℚ)) + (U := (-(4417814021261383902239 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_11 : Uω (aρ 11) (bρ 11) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4159,26 +3642,21 @@ lemma U_529_11 : have hlg : Real.log (5715316311891197 / 16000000000000000 : ℝ) ≤ (-(10294390783422403344033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5715316311891197 / 16000000000000000 : ℝ) = - (5715316311891197 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5715316311891197 / 4000000000000000 : ℚ)) - (U := (3568552822577596655967 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5715316311891197 / 4000000000000000 : ℝ) ≤ - (3568552822577596655967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (162375456817817 / 500000000000000 : ℝ)) (q := - (5715316311891197 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5715316311891197 / 16000000000000000 : ℚ)) + (r' := (5715316311891197 / 4000000000000000 : ℚ)) + (U := (-(10294390783422403344033 / 10000000000000000000000 : ℚ))) + (U' := (3568552822577596655967 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (162375456817817 / 500000000000000 : ℚ)) + (q := (5715316311891197 / 16000000000000000 : ℚ)) + (U := (-(10294390783422403344033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_12 : Uω (aρ 12) (bρ 12) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4186,26 +3664,21 @@ lemma U_529_12 : have hlg : Real.log (4640591408787557 / 16000000000000000 : ℝ) ≤ (-(12377469048134864274801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4640591408787557 / 16000000000000000 : ℝ) = - (4640591408787557 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4640591408787557 / 4000000000000000 : ℚ)) - (U := (1485474557865135725199 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4640591408787557 / 4000000000000000 : ℝ) ≤ - (1485474557865135725199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (232780310416179 / 1000000000000000 : ℝ)) (q := - (4640591408787557 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4640591408787557 / 16000000000000000 : ℚ)) + (r' := (4640591408787557 / 4000000000000000 : ℚ)) + (U := (-(12377469048134864274801 / 10000000000000000000000 : ℚ))) + (U' := (1485474557865135725199 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (232780310416179 / 1000000000000000 : ℚ)) + (q := (4640591408787557 / 16000000000000000 : ℚ)) + (U := (-(12377469048134864274801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_13 : Uω (aρ 13) (bρ 13) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4213,26 +3686,21 @@ lemma U_529_13 : have hlg : Real.log (3070888133605453 / 16000000000000000 : ℝ) ≤ (-(8253109536821764390211 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3070888133605453 / 16000000000000000 : ℝ) = - (3070888133605453 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3070888133605453 / 2000000000000000 : ℚ)) - (U := (2144098167678235609789 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3070888133605453 / 2000000000000000 : ℝ) ≤ - (2144098167678235609789 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (19126393794479 / 250000000000000 : ℝ)) (q := - (3070888133605453 / 16000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3070888133605453 / 16000000000000000 : ℚ)) + (r' := (3070888133605453 / 2000000000000000 : ℚ)) + (U := (-(8253109536821764390211 / 5000000000000000000000 : ℚ))) + (U' := (2144098167678235609789 / 5000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (38727855271377 / 64000000000000 : ℚ)) + (s := (19126393794479 / 250000000000000 : ℚ)) + (q := (3070888133605453 / 16000000000000000 : ℚ)) + (U := (-(8253109536821764390211 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_529_14 : Uω (aρ 14) (bρ 14) (38727855271377 / 64000000000000 : ℝ) ≤ @@ -4340,25 +3808,21 @@ lemma U_530_1 : have hlg : Real.log (23989808225978627 / 40000000000000000 : ℝ) ≤ (-(102250074189872219547 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23989808225978627 / 40000000000000000 : ℝ) = - (23989808225978627 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23989808225978627 / 20000000000000000 : ℚ)) - (U := (36379361870127780453 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23989808225978627 / 20000000000000000 : ℝ) ≤ - (36379361870127780453 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5997425100400251 / 10000000000000000 : ℝ)) (q := - (23989808225978627 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23989808225978627 / 40000000000000000 : ℚ)) + (r' := (23989808225978627 / 20000000000000000 : ℚ)) + (U := (-(102250074189872219547 / 200000000000000000000 : ℚ))) + (U' := (36379361870127780453 / 200000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (5997425100400251 / 10000000000000000 : ℚ)) + (q := (23989808225978627 / 40000000000000000 : ℚ)) + (U := (-(102250074189872219547 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_2 : Uω (aρ 2) (bρ 2) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4366,25 +3830,21 @@ lemma U_530_2 : have hlg : Real.log (23894129581820681 / 40000000000000000 : ℝ) ≤ (-(1288116623196728951863 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23894129581820681 / 40000000000000000 : ℝ) = - (23894129581820681 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23894129581820681 / 20000000000000000 : ℚ)) - (U := (444751327553271048137 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23894129581820681 / 20000000000000000 : ℝ) ≤ - (444751327553271048137 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2986677395415639 / 5000000000000000 : ℝ)) (q := - (23894129581820681 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23894129581820681 / 40000000000000000 : ℚ)) + (r' := (23894129581820681 / 20000000000000000 : ℚ)) + (U := (-(1288116623196728951863 / 2500000000000000000000 : ℚ))) + (U' := (444751327553271048137 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (2986677395415639 / 5000000000000000 : ℚ)) + (q := (23894129581820681 / 40000000000000000 : ℚ)) + (U := (-(1288116623196728951863 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_3 : Uω (aρ 3) (bρ 3) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4392,25 +3852,21 @@ lemma U_530_3 : have hlg : Real.log (23702758623237533 / 40000000000000000 : ℝ) ≤ (-(1308220037204054730923 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23702758623237533 / 40000000000000000 : ℝ) = - (23702758623237533 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23702758623237533 / 20000000000000000 : ℚ)) - (U := (424647913545945269077 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23702758623237533 / 20000000000000000 : ℝ) ≤ - (424647913545945269077 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (740633177236213 / 1250000000000000 : ℝ)) (q := - (23702758623237533 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23702758623237533 / 40000000000000000 : ℚ)) + (r' := (23702758623237533 / 20000000000000000 : ℚ)) + (U := (-(1308220037204054730923 / 2500000000000000000000 : ℚ))) + (U' := (424647913545945269077 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (740633177236213 / 1250000000000000 : ℚ)) + (q := (23702758623237533 / 40000000000000000 : ℚ)) + (U := (-(1308220037204054730923 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_4 : Uω (aρ 4) (bρ 4) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4418,25 +3874,21 @@ lemma U_530_4 : have hlg : Real.log (4676976135064359 / 8000000000000000 : ℝ) ≤ (-(670987206631612576549 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4676976135064359 / 8000000000000000 : ℝ) = - (4676976135064359 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4676976135064359 / 4000000000000000 : ℚ)) - (U := (195446768743387423451 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4676976135064359 / 4000000000000000 : ℝ) ≤ - (195446768743387423451 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1168884124999367 / 2000000000000000 : ℝ)) (q := - (4676976135064359 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4676976135064359 / 8000000000000000 : ℚ)) + (r' := (4676976135064359 / 4000000000000000 : ℚ)) + (U := (-(670987206631612576549 / 1250000000000000000000 : ℚ))) + (U' := (195446768743387423451 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (1168884124999367 / 2000000000000000 : ℚ)) + (q := (4676976135064359 / 8000000000000000 : ℚ)) + (U := (-(670987206631612576549 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_5 : Uω (aρ 5) (bρ 5) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4444,25 +3896,21 @@ lemma U_530_5 : have hlg : Real.log (22900714730461903 / 40000000000000000 : ℝ) ≤ (-(5577113328436471908801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22900714730461903 / 40000000000000000 : ℝ) = - (22900714730461903 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22900714730461903 / 20000000000000000 : ℚ)) - (U := (1354358474563528091199 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22900714730461903 / 20000000000000000 : ℝ) ≤ - (1354358474563528091199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5720527571901889 / 10000000000000000 : ℝ)) (q := - (22900714730461903 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22900714730461903 / 40000000000000000 : ℚ)) + (r' := (22900714730461903 / 20000000000000000 : ℚ)) + (U := (-(5577113328436471908801 / 10000000000000000000000 : ℚ))) + (U' := (1354358474563528091199 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (5720527571901889 / 10000000000000000 : ℚ)) + (q := (22900714730461903 / 40000000000000000 : ℚ)) + (U := (-(5577113328436471908801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_6 : Uω (aρ 6) (bρ 6) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4470,25 +3918,21 @@ lemma U_530_6 : have hlg : Real.log (22206145676008869 / 40000000000000000 : ℝ) ≤ (-(5885103710340832165453 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22206145676008869 / 40000000000000000 : ℝ) = - (22206145676008869 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22206145676008869 / 20000000000000000 : ℚ)) - (U := (1046368092659167834547 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22206145676008869 / 20000000000000000 : ℝ) ≤ - (1046368092659167834547 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1385120854953843 / 2500000000000000 : ℝ)) (q := - (22206145676008869 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22206145676008869 / 40000000000000000 : ℚ)) + (r' := (22206145676008869 / 20000000000000000 : ℚ)) + (U := (-(5885103710340832165453 / 10000000000000000000000 : ℚ))) + (U' := (1046368092659167834547 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (1385120854953843 / 2500000000000000 : ℚ)) + (q := (22206145676008869 / 40000000000000000 : ℚ)) + (U := (-(5885103710340832165453 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_7 : Uω (aρ 7) (bρ 7) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4496,25 +3940,21 @@ lemma U_530_7 : have hlg : Real.log (4251622309553559 / 8000000000000000 : ℝ) ≤ (-(1264281822850228723667 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4251622309553559 / 8000000000000000 : ℝ) = - (4251622309553559 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4251622309553559 / 4000000000000000 : ℚ)) - (U := (122012537749771276333 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4251622309553559 / 4000000000000000 : ℝ) ≤ - (122012537749771276333 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1058025547290967 / 2000000000000000 : ℝ)) (q := - (4251622309553559 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4251622309553559 / 8000000000000000 : ℚ)) + (r' := (4251622309553559 / 4000000000000000 : ℚ)) + (U := (-(1264281822850228723667 / 2000000000000000000000 : ℚ))) + (U' := (122012537749771276333 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (1058025547290967 / 2000000000000000 : ℚ)) + (q := (4251622309553559 / 8000000000000000 : ℚ)) + (U := (-(1264281822850228723667 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_8 : Uω (aρ 8) (bρ 8) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4522,25 +3962,21 @@ lemma U_530_8 : have hlg : Real.log (20019955581302669 / 40000000000000000 : ℝ) ≤ (-(6921498986855282207523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20019955581302669 / 40000000000000000 : ℝ) = - (20019955581302669 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20019955581302669 / 20000000000000000 : ℚ)) - (U := (9972816144717792477 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (20019955581302669 / 20000000000000000 : ℝ) ≤ - (9972816144717792477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154830981392571 / 312500000000000 : ℝ)) (q := - (20019955581302669 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20019955581302669 / 40000000000000000 : ℚ)) + (r' := (20019955581302669 / 20000000000000000 : ℚ)) + (U := (-(6921498986855282207523 / 10000000000000000000000 : ℚ))) + (U' := (9972816144717792477 / 10000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (154830981392571 / 312500000000000 : ℚ)) + (q := (20019955581302669 / 40000000000000000 : ℚ)) + (U := (-(6921498986855282207523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_9 : Uω (aρ 9) (bρ 9) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4548,25 +3984,21 @@ lemma U_530_9 : have hlg : Real.log (18465279789097771 / 40000000000000000 : ℝ) ≤ (-(1932468132506487573157 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18465279789097771 / 40000000000000000 : ℝ) = - (18465279789097771 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18465279789097771 / 10000000000000000 : ℚ)) - (U := (1533267768993512426843 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18465279789097771 / 10000000000000000 : ℝ) ≤ - (1533267768993512426843 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4518219136819823 / 10000000000000000 : ℝ)) (q := - (18465279789097771 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18465279789097771 / 40000000000000000 : ℚ)) + (r' := (18465279789097771 / 10000000000000000 : ℚ)) + (U := (-(1932468132506487573157 / 2500000000000000000000 : ℚ))) + (U' := (1533267768993512426843 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (4518219136819823 / 10000000000000000 : ℚ)) + (q := (18465279789097771 / 40000000000000000 : ℚ)) + (U := (-(1932468132506487573157 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_10 : Uω (aρ 10) (bρ 10) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4574,26 +4006,21 @@ lemma U_530_10 : have hlg : Real.log (16577280695092817 / 40000000000000000 : ℝ) ≤ (-(8808463284906202056157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16577280695092817 / 40000000000000000 : ℝ) = - (16577280695092817 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16577280695092817 / 10000000000000000 : ℚ)) - (U := (5054480321093797943843 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16577280695092817 / 10000000000000000 : ℝ) ≤ - (5054480321093797943843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1981389311656173 / 5000000000000000 : ℝ)) (q := - (16577280695092817 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16577280695092817 / 40000000000000000 : ℚ)) + (r' := (16577280695092817 / 10000000000000000 : ℚ)) + (U := (-(8808463284906202056157 / 10000000000000000000000 : ℚ))) + (U' := (5054480321093797943843 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (1981389311656173 / 5000000000000000 : ℚ)) + (q := (16577280695092817 / 40000000000000000 : ℚ)) + (U := (-(8808463284906202056157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_11 : Uω (aρ 11) (bρ 11) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4601,26 +4028,21 @@ lemma U_530_11 : have hlg : Real.log (14335567632834491 / 40000000000000000 : ℝ) ≤ (-(513067878678141954839 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14335567632834491 / 40000000000000000 : ℝ) = - (14335567632834491 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14335567632834491 / 10000000000000000 : ℚ)) - (U := (180079301621858045161 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14335567632834491 / 10000000000000000 : ℝ) ≤ - (180079301621858045161 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3260398718388183 / 10000000000000000 : ℝ)) (q := - (14335567632834491 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14335567632834491 / 40000000000000000 : ℚ)) + (r' := (14335567632834491 / 10000000000000000 : ℚ)) + (U := (-(513067878678141954839 / 500000000000000000000 : ℚ))) + (U' := (180079301621858045161 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (3260398718388183 / 10000000000000000 : ℚ)) + (q := (14335567632834491 / 40000000000000000 : ℚ)) + (U := (-(513067878678141954839 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_12 : Uω (aρ 12) (bρ 12) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4628,26 +4050,21 @@ lemma U_530_12 : have hlg : Real.log (2330997797011611 / 8000000000000000 : ℝ) ≤ (-(1541431407737169729987 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2330997797011611 / 8000000000000000 : ℝ) = - (2330997797011611 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2330997797011611 / 2000000000000000 : ℚ)) - (U := (191436543012830270013 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2330997797011611 / 2000000000000000 : ℝ) ≤ - (191436543012830270013 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (468761898236993 / 2000000000000000 : ℝ)) (q := - (2330997797011611 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2330997797011611 / 8000000000000000 : ℚ)) + (r' := (2330997797011611 / 2000000000000000 : ℚ)) + (U := (-(1541431407737169729987 / 1250000000000000000000 : ℚ))) + (U' := (191436543012830270013 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (468761898236993 / 2000000000000000 : ℚ)) + (q := (2330997797011611 / 8000000000000000 : ℚ)) + (U := (-(1541431407737169729987 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_13 : Uω (aρ 13) (bρ 13) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4655,26 +4072,21 @@ lemma U_530_13 : have hlg : Real.log (7782917713863881 / 40000000000000000 : ℝ) ≤ (-(16369481579601011001041 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7782917713863881 / 40000000000000000 : ℝ) = - (7782917713863881 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7782917713863881 / 5000000000000000 : ℚ)) - (U := (4424933829398988998959 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7782917713863881 / 5000000000000000 : ℝ) ≤ - (4424933829398988998959 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (403577798591439 / 5000000000000000 : ℝ)) (q := - (7782917713863881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7782917713863881 / 40000000000000000 : ℚ)) + (r' := (7782917713863881 / 5000000000000000 : ℚ)) + (U := (-(16369481579601011001041 / 10000000000000000000000 : ℚ))) + (U' := (4424933829398988998959 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19398323938157 / 32000000000000 : ℚ)) + (s := (403577798591439 / 5000000000000000 : ℚ)) + (q := (7782917713863881 / 40000000000000000 : ℚ)) + (U := (-(16369481579601011001041 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_530_14 : Uω (aρ 14) (bρ 14) (19398323938157 / 32000000000000 : ℝ) ≤ @@ -4781,25 +4193,21 @@ lemma U_531_1 : have hlg : Real.log (48065607593932067 / 80000000000000000 : ℝ) ≤ (-(1273649329718194240281 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48065607593932067 / 80000000000000000 : ℝ) = - (48065607593932067 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48065607593932067 / 40000000000000000 : ℚ)) - (U := (459218621031805759719 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48065607593932067 / 40000000000000000 : ℝ) ≤ - (459218621031805759719 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1502043510343137 / 2500000000000000 : ℝ)) (q := - (48065607593932067 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48065607593932067 / 80000000000000000 : ℚ)) + (r' := (48065607593932067 / 40000000000000000 : ℚ)) + (U := (-(1273649329718194240281 / 2500000000000000000000 : ℚ))) + (U' := (459218621031805759719 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (1502043510343137 / 2500000000000000 : ℚ)) + (q := (48065607593932067 / 80000000000000000 : ℚ)) + (U := (-(1273649329718194240281 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_2 : Uω (aρ 2) (bρ 2) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4807,25 +4215,21 @@ lemma U_531_2 : have hlg : Real.log (47874252471966791 / 80000000000000000 : ℝ) ≤ (-(1026897602395204205191 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47874252471966791 / 80000000000000000 : ℝ) = - (47874252471966791 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47874252471966791 / 40000000000000000 : ℚ)) - (U := (359396758204795794809 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47874252471966791 / 40000000000000000 : ℝ) ≤ - (359396758204795794809 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5984104273391229 / 10000000000000000 : ℝ)) (q := - (47874252471966791 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47874252471966791 / 80000000000000000 : ℚ)) + (r' := (47874252471966791 / 40000000000000000 : ℚ)) + (U := (-(1026897602395204205191 / 2000000000000000000000 : ℚ))) + (U' := (359396758204795794809 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (5984104273391229 / 10000000000000000 : ℚ)) + (q := (47874252471966791 / 80000000000000000 : ℚ)) + (U := (-(1026897602395204205191 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_3 : Uω (aρ 3) (bρ 3) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4833,25 +4237,21 @@ lemma U_531_3 : have hlg : Real.log (47491517045833679 / 80000000000000000 : ℝ) ≤ (-(5214755278309320413741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47491517045833679 / 80000000000000000 : ℝ) = - (47491517045833679 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47491517045833679 / 40000000000000000 : ℚ)) - (U := (1716716524690679586259 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47491517045833679 / 40000000000000000 : ℝ) ≤ - (1716716524690679586259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5935816523207951 / 10000000000000000 : ℝ)) (q := - (47491517045833679 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47491517045833679 / 80000000000000000 : ℚ)) + (r' := (47491517045833679 / 40000000000000000 : ℚ)) + (U := (-(5214755278309320413741 / 10000000000000000000000 : ℚ))) + (U' := (1716716524690679586259 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (5935816523207951 / 10000000000000000 : ℚ)) + (q := (47491517045833679 / 80000000000000000 : ℚ)) + (U := (-(5214755278309320413741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_4 : Uω (aρ 4) (bρ 4) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4859,25 +4259,21 @@ lemma U_531_4 : have hlg : Real.log (46855778535434627 / 80000000000000000 : ℝ) ≤ (-(5349522921308249214813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46855778535434627 / 80000000000000000 : ℝ) = - (46855778535434627 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46855778535434627 / 40000000000000000 : ℚ)) - (U := (1581948881691750785187 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46855778535434627 / 40000000000000000 : ℝ) ≤ - (1581948881691750785187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1463794019168297 / 2500000000000000 : ℝ)) (q := - (46855778535434627 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46855778535434627 / 80000000000000000 : ℚ)) + (r' := (46855778535434627 / 40000000000000000 : ℚ)) + (U := (-(5349522921308249214813 / 10000000000000000000000 : ℚ))) + (U' := (1581948881691750785187 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (1463794019168297 / 2500000000000000 : ℚ)) + (q := (46855778535434627 / 80000000000000000 : ℚ)) + (U := (-(5349522921308249214813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_5 : Uω (aρ 5) (bρ 5) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4885,25 +4281,21 @@ lemma U_531_5 : have hlg : Real.log (45887490001186683 / 80000000000000000 : ℝ) ≤ (-(5558341034894179748239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45887490001186683 / 80000000000000000 : ℝ) = - (45887490001186683 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45887490001186683 / 40000000000000000 : ℚ)) - (U := (1373130768105820251761 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45887490001186683 / 40000000000000000 : ℝ) ≤ - (1373130768105820251761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2865646931223101 / 5000000000000000 : ℝ)) (q := - (45887490001186683 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45887490001186683 / 80000000000000000 : ℚ)) + (r' := (45887490001186683 / 40000000000000000 : ℚ)) + (U := (-(5558341034894179748239 / 10000000000000000000000 : ℚ))) + (U' := (1373130768105820251761 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (2865646931223101 / 5000000000000000 : ℚ)) + (q := (45887490001186683 / 80000000000000000 : ℚ)) + (U := (-(5558341034894179748239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_6 : Uω (aρ 6) (bρ 6) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4911,25 +4303,21 @@ lemma U_531_6 : have hlg : Real.log (1779938132912151 / 3200000000000000 : ℝ) ≤ (-(2932861013183497161807 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1779938132912151 / 3200000000000000 : ℝ) = - (1779938132912151 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1779938132912151 / 1600000000000000 : ℚ)) - (U := (532874888316502838193 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1779938132912151 / 1600000000000000 : ℝ) ≤ - (532874888316502838193 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (222051002719619 / 400000000000000 : ℝ)) (q := - (1779938132912151 / 3200000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1779938132912151 / 3200000000000000 : ℚ)) + (r' := (1779938132912151 / 1600000000000000 : ℚ)) + (U := (-(2932861013183497161807 / 5000000000000000000000 : ℚ))) + (U' := (532874888316502838193 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (222051002719619 / 400000000000000 : ℚ)) + (q := (1779938132912151 / 3200000000000000 : ℚ)) + (U := (-(2932861013183497161807 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_7 : Uω (aρ 7) (bρ 7) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4937,25 +4325,21 @@ lemma U_531_7 : have hlg : Real.log (42602609666960279 / 80000000000000000 : ℝ) ≤ (-(6301111232271157612451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42602609666960279 / 80000000000000000 : ℝ) = - (42602609666960279 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42602609666960279 / 40000000000000000 : ℚ)) - (U := (630360570728842387549 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42602609666960279 / 40000000000000000 : ℝ) ≤ - (630360570728842387549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5300975534789601 / 10000000000000000 : ℝ)) (q := - (42602609666960279 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42602609666960279 / 80000000000000000 : ℚ)) + (r' := (42602609666960279 / 40000000000000000 : ℚ)) + (U := (-(6301111232271157612451 / 10000000000000000000000 : ℚ))) + (U' := (630360570728842387549 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (5300975534789601 / 10000000000000000 : ℚ)) + (q := (42602609666960279 / 80000000000000000 : ℚ)) + (U := (-(6301111232271157612451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_8 : Uω (aρ 8) (bρ 8) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4963,25 +4347,21 @@ lemma U_531_8 : have hlg : Real.log (40126774693431603 / 80000000000000000 : ℝ) ≤ (-(6899828248220443165641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40126774693431603 / 80000000000000000 : ℝ) = - (40126774693431603 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40126774693431603 / 40000000000000000 : ℚ)) - (U := (31643554779556834359 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40126774693431603 / 40000000000000000 : ℝ) ≤ - (31643554779556834359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (620694805343429 / 1250000000000000 : ℝ)) (q := - (40126774693431603 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40126774693431603 / 80000000000000000 : ℚ)) + (r' := (40126774693431603 / 40000000000000000 : ℚ)) + (U := (-(6899828248220443165641 / 10000000000000000000000 : ℚ))) + (U' := (31643554779556834359 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (620694805343429 / 1250000000000000 : ℚ)) + (q := (40126774693431603 / 80000000000000000 : ℚ)) + (U := (-(6899828248220443165641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_9 : Uω (aρ 9) (bρ 9) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -4989,25 +4369,21 @@ lemma U_531_9 : have hlg : Real.log (37018412862271711 / 80000000000000000 : ℝ) ≤ (-(1926528000919187657291 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37018412862271711 / 80000000000000000 : ℝ) = - (37018412862271711 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37018412862271711 / 20000000000000000 : ℚ)) - (U := (1539207900580812342709 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37018412862271711 / 20000000000000000 : ℝ) ≤ - (1539207900580812342709 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4529433613317459 / 10000000000000000 : ℝ)) (q := - (37018412862271711 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37018412862271711 / 80000000000000000 : ℚ)) + (r' := (37018412862271711 / 20000000000000000 : ℚ)) + (U := (-(1926528000919187657291 / 2500000000000000000000 : ℚ))) + (U' := (1539207900580812342709 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (4529433613317459 / 10000000000000000 : ℚ)) + (q := (37018412862271711 / 80000000000000000 : ℚ)) + (U := (-(1926528000919187657291 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_10 : Uω (aρ 10) (bρ 10) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -5015,26 +4391,21 @@ lemma U_531_10 : have hlg : Real.log (33244480385545891 / 80000000000000000 : ℝ) ≤ (-(8781378842744531549129 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33244480385545891 / 80000000000000000 : ℝ) = - (33244480385545891 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33244480385545891 / 20000000000000000 : ℚ)) - (U := (5081564763255468450871 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33244480385545891 / 20000000000000000 : ℝ) ≤ - (5081564763255468450871 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (993627381907751 / 2500000000000000 : ℝ)) (q := - (33244480385545891 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33244480385545891 / 80000000000000000 : ℚ)) + (r' := (33244480385545891 / 20000000000000000 : ℚ)) + (U := (-(8781378842744531549129 / 10000000000000000000000 : ℚ))) + (U' := (5081564763255468450871 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (993627381907751 / 2500000000000000 : ℚ)) + (q := (33244480385545891 / 80000000000000000 : ℚ)) + (U := (-(8781378842744531549129 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_11 : Uω (aρ 11) (bρ 11) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -5042,26 +4413,21 @@ lemma U_531_11 : have hlg : Real.log (28765627133410979 / 80000000000000000 : ℝ) ≤ (-(1278556827644119619991 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28765627133410979 / 80000000000000000 : ℝ) = - (28765627133410979 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28765627133410979 / 20000000000000000 : ℚ)) - (U := (454311123105880380009 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28765627133410979 / 20000000000000000 : ℝ) ≤ - (454311123105880380009 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (818318210200569 / 2500000000000000 : ℝ)) (q := - (28765627133410979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28765627133410979 / 80000000000000000 : ℚ)) + (r' := (28765627133410979 / 20000000000000000 : ℚ)) + (U := (-(1278556827644119619991 / 1250000000000000000000 : ℚ))) + (U' := (454311123105880380009 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (818318210200569 / 2500000000000000 : ℚ)) + (q := (28765627133410979 / 80000000000000000 : ℚ)) + (U := (-(1278556827644119619991 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_12 : Uω (aρ 12) (bρ 12) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -5069,26 +4435,21 @@ lemma U_531_12 : have hlg : Real.log (4683352091286291 / 16000000000000000 : ℝ) ≤ (-(6142873046797036347843 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4683352091286291 / 16000000000000000 : ℝ) = - (4683352091286291 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4683352091286291 / 4000000000000000 : ℚ)) - (U := (788598756202963652157 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4683352091286291 / 4000000000000000 : ℝ) ≤ - (788598756202963652157 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (471951253648479 / 2000000000000000 : ℝ)) (q := - (4683352091286291 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4683352091286291 / 16000000000000000 : ℚ)) + (r' := (4683352091286291 / 4000000000000000 : ℚ)) + (U := (-(6142873046797036347843 / 5000000000000000000000 : ℚ))) + (U' := (788598756202963652157 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (471951253648479 / 2000000000000000 : ℚ)) + (q := (4683352091286291 / 16000000000000000 : ℚ)) + (U := (-(6142873046797036347843 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_13 : Uω (aρ 13) (bρ 13) (38865440481251 / 64000000000000 : ℝ) ≤ @@ -5096,26 +4457,21 @@ lemma U_531_13 : have hlg : Real.log (15769417382286619 / 80000000000000000 : ℝ) ≤ (-(16239541782885318070361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (15769417382286619 / 80000000000000000 : ℝ) = - (15769417382286619 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15769417382286619 / 10000000000000000 : ℚ)) - (U := (4554873626114681929639 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15769417382286619 / 10000000000000000 : ℝ) ≤ - (4554873626114681929639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (423651120650593 / 5000000000000000 : ℝ)) (q := - (15769417382286619 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15769417382286619 / 80000000000000000 : ℚ)) + (r' := (15769417382286619 / 10000000000000000 : ℚ)) + (U := (-(16239541782885318070361 / 10000000000000000000000 : ℚ))) + (U' := (4554873626114681929639 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (38865440481251 / 64000000000000 : ℚ)) + (s := (423651120650593 / 5000000000000000 : ℚ)) + (q := (15769417382286619 / 80000000000000000 : ℚ)) + (U := (-(16239541782885318070361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_531_14 : Uω (aρ 14) (bρ 14) (38865440481251 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U44.lean b/LeanPool/Zeta5Irrational/Table/U44.lean index 814618f121..dfc2c4a294 100644 --- a/LeanPool/Zeta5Irrational/Table/U44.lean +++ b/LeanPool/Zeta5Irrational/Table/U44.lean @@ -24,25 +24,21 @@ lemma U_532_1 : have hlg : Real.log (12037899683632227 / 20000000000000000 : ℝ) ≤ (-(1015344587023385956413 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12037899683632227 / 20000000000000000 : ℝ) = - (12037899683632227 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12037899683632227 / 10000000000000000 : ℚ)) - (U := (370949773576614043587 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12037899683632227 / 10000000000000000 : ℝ) ≤ - (370949773576614043587 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188091343187511 / 312500000000000 : ℝ)) (q := - (12037899683632227 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12037899683632227 / 20000000000000000 : ℚ)) + (r' := (12037899683632227 / 10000000000000000 : ℚ)) + (U := (-(1015344587023385956413 / 2000000000000000000000 : ℚ))) + (U' := (370949773576614043587 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (188091343187511 / 312500000000000 : ℚ)) + (q := (12037899683632227 / 20000000000000000 : ℚ)) + (U := (-(1015344587023385956413 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_2 : Uω (aρ 2) (bρ 2) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_532_2 : have hlg : Real.log (2398012288556993 / 4000000000000000 : ℝ) ≤ (-(2558270898826269298443 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2398012288556993 / 4000000000000000 : ℝ) = - (2398012288556993 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2398012288556993 / 2000000000000000 : ℚ)) - (U := (907465002673730701557 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2398012288556993 / 2000000000000000 : ℝ) ≤ - (907465002673730701557 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (599485375366309 / 1000000000000000 : ℝ)) (q := - (2398012288556993 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2398012288556993 / 4000000000000000 : ℚ)) + (r' := (2398012288556993 / 2000000000000000 : ℚ)) + (U := (-(2558270898826269298443 / 5000000000000000000000 : ℚ))) + (U' := (907465002673730701557 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (599485375366309 / 1000000000000000 : ℚ)) + (q := (2398012288556993 / 4000000000000000 : ℚ)) + (U := (-(2558270898826269298443 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_3 : Uω (aρ 3) (bρ 3) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_532_3 : have hlg : Real.log (1189437920312411 / 2000000000000000 : ℝ) ≤ (-(12991658015855303567 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1189437920312411 / 2000000000000000 : ℝ) = - (1189437920312411 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1189437920312411 / 1000000000000000 : ℚ)) - (U := (4337021491644696433 / 25000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1189437920312411 / 1000000000000000 : ℝ) ≤ - (4337021491644696433 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1189313524070447 / 2000000000000000 : ℝ)) (q := - (1189437920312411 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1189437920312411 / 2000000000000000 : ℚ)) + (r' := (1189437920312411 / 1000000000000000 : ℚ)) + (U := (-(12991658015855303567 / 25000000000000000000 : ℚ))) + (U' := (4337021491644696433 / 25000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (1189313524070447 / 2000000000000000 : ℚ)) + (q := (1189437920312411 / 2000000000000000 : ℚ)) + (U := (-(12991658015855303567 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_4 : Uω (aρ 4) (bρ 4) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_532_4 : have hlg : Real.log (5867724452917411 / 10000000000000000 : ℝ) ≤ (-(5331181911364434298457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5867724452917411 / 10000000000000000 : ℝ) = - (5867724452917411 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5867724452917411 / 5000000000000000 : ℚ)) - (U := (1600289891635565701543 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5867724452917411 / 5000000000000000 : ℝ) ≤ - (1600289891635565701543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5865931504127947 / 10000000000000000 : ℝ)) (q := - (5867724452917411 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5867724452917411 / 10000000000000000 : ℚ)) + (r' := (5867724452917411 / 5000000000000000 : ℚ)) + (U := (-(5331181911364434298457 / 10000000000000000000000 : ℚ))) + (U' := (1600289891635565701543 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (5865931504127947 / 10000000000000000 : ℚ)) + (q := (5867724452917411 / 10000000000000000 : ℚ)) + (U := (-(5331181911364434298457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_5 : Uω (aρ 5) (bρ 5) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_532_5 : have hlg : Real.log (359168361562289 / 625000000000000 : ℝ) ≤ (-(2769801986054336931911 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (359168361562289 / 625000000000000 : ℝ) = - (359168361562289 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (359168361562289 / 312500000000000 : ℚ)) - (U := (695933915445663068089 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (359168361562289 / 312500000000000 : ℝ) ≤ - (695933915445663068089 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5742060087621373 / 10000000000000000 : ℝ)) (q := - (359168361562289 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (359168361562289 / 625000000000000 : ℚ)) + (r' := (359168361562289 / 312500000000000 : ℚ)) + (U := (-(2769801986054336931911 / 5000000000000000000000 : ℚ))) + (U' := (695933915445663068089 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (5742060087621373 / 10000000000000000 : ℚ)) + (q := (359168361562289 / 625000000000000 : ℚ)) + (U := (-(2769801986054336931911 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_6 : Uω (aρ 6) (bρ 6) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_532_6 : have hlg : Real.log (1114615365762961 / 2000000000000000 : ℝ) ≤ (-(58463779834278348057 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1114615365762961 / 2000000000000000 : ℝ) = - (1114615365762961 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1114615365762961 / 1000000000000000 : ℚ)) - (U := (10850938195721651943 / 100000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1114615365762961 / 1000000000000000 : ℝ) ≤ - (10850938195721651943 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1112413310079547 / 2000000000000000 : ℝ)) (q := - (1114615365762961 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1114615365762961 / 2000000000000000 : ℚ)) + (r' := (1114615365762961 / 1000000000000000 : ℚ)) + (U := (-(58463779834278348057 / 100000000000000000000 : ℚ))) + (U' := (10850938195721651943 / 100000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (1112413310079547 / 2000000000000000 : ℚ)) + (q := (1114615365762961 / 2000000000000000 : ℚ)) + (U := (-(58463779834278348057 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_7 : Uω (aρ 7) (bρ 7) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_532_7 : have hlg : Real.log (1334031082159119 / 2500000000000000 : ℝ) ≤ (-(6280854844228632773047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1334031082159119 / 2500000000000000 : ℝ) = - (1334031082159119 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1334031082159119 / 1250000000000000 : ℚ)) - (U := (650616958771367226953 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1334031082159119 / 1250000000000000 : ℝ) ≤ - (650616958771367226953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5311822930801077 / 10000000000000000 : ℝ)) (q := - (1334031082159119 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1334031082159119 / 2500000000000000 : ℚ)) + (r' := (1334031082159119 / 1250000000000000 : ℚ)) + (U := (-(6280854844228632773047 / 10000000000000000000000 : ℚ))) + (U' := (650616958771367226953 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (5311822930801077 / 10000000000000000 : ℚ)) + (q := (1334031082159119 / 2500000000000000 : ℚ)) + (U := (-(6280854844228632773047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_8 : Uω (aρ 8) (bρ 8) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_532_8 : have hlg : Real.log (2010681720788129 / 4000000000000000 : ℝ) ≤ (-(343910265860526981271 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2010681720788129 / 4000000000000000 : ℝ) = - (2010681720788129 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2010681720788129 / 2000000000000000 : ℚ)) - (U := (2663324289473018729 / 500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2010681720788129 / 2000000000000000 : ℝ) ≤ - (2663324289473018729 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (497652452880877 / 1000000000000000 : ℝ)) (q := - (2010681720788129 / 4000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2010681720788129 / 4000000000000000 : ℚ)) + (r' := (2010681720788129 / 2000000000000000 : ℚ)) + (U := (-(343910265860526981271 / 500000000000000000000 : ℚ))) + (U' := (2663324289473018729 / 500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (497652452880877 / 1000000000000000 : ℚ)) + (q := (2010681720788129 / 4000000000000000 : ℚ)) + (U := (-(343910265860526981271 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_9 : Uω (aρ 9) (bρ 9) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_532_9 : have hlg : Real.log (2319141071075849 / 5000000000000000 : ℝ) ≤ (-(7682410227718395423797 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2319141071075849 / 5000000000000000 : ℝ) = - (2319141071075849 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2319141071075849 / 1250000000000000 : ℚ)) - (U := (6180533378281604576203 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2319141071075849 / 1250000000000000 : ℝ) ≤ - (6180533378281604576203 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4540645837531521 / 10000000000000000 : ℝ)) (q := - (2319141071075849 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2319141071075849 / 5000000000000000 : ℚ)) + (r' := (2319141071075849 / 1250000000000000 : ℚ)) + (U := (-(7682410227718395423797 / 10000000000000000000000 : ℚ))) + (U' := (6180533378281604576203 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (4540645837531521 / 10000000000000000 : ℚ)) + (q := (2319141071075849 / 5000000000000000 : ℚ)) + (U := (-(7682410227718395423797 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_10 : Uω (aρ 10) (bρ 10) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_532_10 : have hlg : Real.log (8333594307057603 / 20000000000000000 : ℝ) ≤ (-(1750874840954918337967 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8333594307057603 / 20000000000000000 : ℝ) = - (8333594307057603 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8333594307057603 / 5000000000000000 : ℚ)) - (U := (1021713880245081662033 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8333594307057603 / 5000000000000000 : ℝ) ≤ - (1021713880245081662033 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (498279361722591 / 1250000000000000 : ℝ)) (q := - (8333594307057603 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8333594307057603 / 20000000000000000 : ℚ)) + (r' := (8333594307057603 / 5000000000000000 : ℚ)) + (U := (-(1750874840954918337967 / 2000000000000000000000 : ℚ))) + (U' := (1021713880245081662033 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (498279361722591 / 1250000000000000 : ℚ)) + (q := (8333594307057603 / 20000000000000000 : ℚ)) + (U := (-(1750874840954918337967 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_11 : Uω (aρ 11) (bρ 11) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_532_11 : have hlg : Real.log (7215014472369557 / 20000000000000000 : ℝ) ≤ (-(2548920187344628660401 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7215014472369557 / 20000000000000000 : ℝ) = - (7215014472369557 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7215014472369557 / 5000000000000000 : ℚ)) - (U := (916815714155371339599 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7215014472369557 / 5000000000000000 : ℝ) ≤ - (916815714155371339599 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1643065842648841 / 5000000000000000 : ℝ)) (q := - (7215014472369557 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7215014472369557 / 20000000000000000 : ℚ)) + (r' := (7215014472369557 / 5000000000000000 : ℚ)) + (U := (-(2548920187344628660401 / 2500000000000000000000 : ℚ))) + (U' := (916815714155371339599 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (1643065842648841 / 5000000000000000 : ℚ)) + (q := (7215014472369557 / 20000000000000000 : ℚ)) + (U := (-(2548920187344628660401 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_12 : Uω (aρ 12) (bρ 12) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -312,24 +266,21 @@ lemma U_532_12 : have hlg : Real.log (58808273261367 / 200000000000000 : ℝ) ≤ (-(3060087048242988541479 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58808273261367 / 200000000000000 : ℝ) = (58808273261367 / 50000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58808273261367 / 50000000000000 : ℚ)) - (U := (405648853257011458521 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (58808273261367 / 50000000000000 : ℝ) ≤ - (405648853257011458521 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95025785429993 / 400000000000000 : ℝ)) (q := - (58808273261367 / 200000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58808273261367 / 200000000000000 : ℚ)) + (r' := (58808273261367 / 50000000000000 : ℚ)) + (U := (-(3060087048242988541479 / 2500000000000000000000 : ℚ))) + (U' := (405648853257011458521 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (95025785429993 / 400000000000000 : ℚ)) + (q := (58808273261367 / 200000000000000 : ℚ)) + (U := (-(3060087048242988541479 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_13 : Uω (aρ 13) (bρ 13) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -337,26 +288,21 @@ lemma U_532_13 : have hlg : Real.log (3991562256075879 / 20000000000000000 : ℝ) ≤ (-(16115495756291320341457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3991562256075879 / 20000000000000000 : ℝ) = - (3991562256075879 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3991562256075879 / 2500000000000000 : ℚ)) - (U := (4678919652708679658543 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3991562256075879 / 2500000000000000 : ℝ) ≤ - (4678919652708679658543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (221440326821001 / 2500000000000000 : ℝ)) (q := - (3991562256075879 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3991562256075879 / 20000000000000000 : ℚ)) + (r' := (3991562256075879 / 2500000000000000 : ℚ)) + (U := (-(16115495756291320341457 / 10000000000000000000000 : ℚ))) + (U' := (4678919652708679658543 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (9733558271547 / 16000000000000 : ℚ)) + (s := (221440326821001 / 2500000000000000 : ℚ)) + (q := (3991562256075879 / 20000000000000000 : ℚ)) + (U := (-(16115495756291320341457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_532_14 : Uω (aρ 14) (bρ 14) (9733558271547 / 16000000000000 : ℝ) ≤ @@ -462,25 +408,21 @@ lemma U_533_1 : have hlg : Real.log (9647517974751029 / 16000000000000000 : ℝ) ≤ (-(2529440222003763779621 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9647517974751029 / 16000000000000000 : ℝ) = - (9647517974751029 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9647517974751029 / 8000000000000000 : ℚ)) - (U := (936295679496236220379 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9647517974751029 / 8000000000000000 : ℝ) ≤ - (936295679496236220379 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1205934384457101 / 2000000000000000 : ℝ)) (q := - (9647517974751029 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9647517974751029 / 16000000000000000 : ℚ)) + (r' := (9647517974751029 / 8000000000000000 : ℚ)) + (U := (-(2529440222003763779621 / 5000000000000000000000 : ℚ))) + (U' := (936295679496236220379 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (312024205529 / 512000000000 : ℚ)) + (s := (1205934384457101 / 2000000000000000 : ℚ)) + (q := (9647517974751029 / 16000000000000000 : ℚ)) + (U := (-(2529440222003763779621 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_2 : Uω (aρ 2) (bρ 2) (312024205529 / 512000000000 : ℝ) ≤ @@ -488,25 +430,21 @@ lemma U_533_2 : have hlg : Real.log (48046239061209721 / 80000000000000000 : ℝ) ≤ (-(5098627734197961890647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48046239061209721 / 80000000000000000 : ℝ) = - (48046239061209721 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48046239061209721 / 40000000000000000 : ℚ)) - (U := (1832844068802038109353 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48046239061209721 / 40000000000000000 : ℝ) ≤ - (1832844068802038109353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6005603231659149 / 10000000000000000 : ℝ)) (q := - (48046239061209721 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48046239061209721 / 80000000000000000 : ℚ)) + (r' := (48046239061209721 / 40000000000000000 : ℚ)) + (U := (-(5098627734197961890647 / 10000000000000000000000 : ℚ))) + (U' := (1832844068802038109353 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (312024205529 / 512000000000 : ℚ)) + (s := (6005603231659149 / 10000000000000000 : ℚ)) + (q := (48046239061209721 / 80000000000000000 : ℚ)) + (U := (-(5098627734197961890647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_3 : Uω (aρ 3) (bρ 3) (312024205529 / 512000000000 : ℝ) ≤ @@ -514,25 +452,21 @@ lemma U_533_3 : have hlg : Real.log (47663516546640373 / 80000000000000000 : ℝ) ≤ (-(5178603814400613640559 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47663516546640373 / 80000000000000000 : ℝ) = - (47663516546640373 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47663516546640373 / 40000000000000000 : ℚ)) - (U := (1752867988599386359441 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47663516546640373 / 40000000000000000 : ℝ) ≤ - (1752867988599386359441 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1489329677341703 / 2500000000000000 : ℝ)) (q := - (47663516546640373 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47663516546640373 / 80000000000000000 : ℚ)) + (r' := (47663516546640373 / 40000000000000000 : ℚ)) + (U := (-(5178603814400613640559 / 10000000000000000000000 : ℚ))) + (U' := (1752867988599386359441 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (312024205529 / 512000000000 : ℚ)) + (s := (1489329677341703 / 2500000000000000 : ℚ)) + (q := (47663516546640373 / 80000000000000000 : ℚ)) + (U := (-(5178603814400613640559 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_4 : Uω (aρ 4) (bρ 4) (312024205529 / 512000000000 : ℝ) ≤ @@ -540,25 +474,21 @@ lemma U_533_4 : have hlg : Real.log (1881112504595581 / 3200000000000000 : ℝ) ≤ (-(5312874499598534674163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1881112504595581 / 3200000000000000 : ℝ) = - (1881112504595581 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1881112504595581 / 1600000000000000 : ℚ)) - (U := (1618597303401465325837 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1881112504595581 / 1600000000000000 : ℝ) ≤ - (1618597303401465325837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58766869074941 / 100000000000000 : ℝ)) (q := - (1881112504595581 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1881112504595581 / 3200000000000000 : ℚ)) + (r' := (1881112504595581 / 1600000000000000 : ℚ)) + (U := (-(5312874499598534674163 / 10000000000000000000000 : ℚ))) + (U' := (1618597303401465325837 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (312024205529 / 512000000000 : ℚ)) + (s := (58766869074941 / 100000000000000 : ℚ)) + (q := (1881112504595581 / 3200000000000000 : ℚ)) + (U := (-(5312874499598534674163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_5 : Uω (aρ 5) (bρ 5) (312024205529 / 512000000000 : ℝ) ≤ @@ -566,25 +496,21 @@ lemma U_533_5 : have hlg : Real.log (46059610298750769 / 80000000000000000 : ℝ) ≤ (-(5520902007877414746151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46059610298750769 / 80000000000000000 : ℝ) = - (46059610298750769 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46059610298750769 / 40000000000000000 : ℚ)) - (U := (1410569795122585253849 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46059610298750769 / 40000000000000000 : ℝ) ≤ - (1410569795122585253849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5752826247794411 / 10000000000000000 : ℝ)) (q := - (46059610298750769 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46059610298750769 / 80000000000000000 : ℚ)) + (r' := (46059610298750769 / 40000000000000000 : ℚ)) + (U := (-(5520902007877414746151 / 10000000000000000000000 : ℚ))) + (U' := (1410569795122585253849 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (312024205529 / 512000000000 : ℚ)) + (s := (5752826247794411 / 10000000000000000 : ℚ)) + (q := (46059610298750769 / 80000000000000000 : ℚ)) + (U := (-(5520902007877414746151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_6 : Uω (aρ 6) (bρ 6) (312024205529 / 512000000000 : ℝ) ≤ @@ -592,25 +518,21 @@ lemma U_533_6 : have hlg : Real.log (44670775279013717 / 80000000000000000 : ℝ) ≤ (-(2913535717514371392481 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44670775279013717 / 80000000000000000 : ℝ) = - (44670775279013717 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44670775279013717 / 40000000000000000 : ℚ)) - (U := (552200183985628607519 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44670775279013717 / 40000000000000000 : ℝ) ≤ - (552200183985628607519 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1393214467000037 / 2500000000000000 : ℝ)) (q := - (44670775279013717 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44670775279013717 / 80000000000000000 : ℚ)) + (r' := (44670775279013717 / 40000000000000000 : ℚ)) + (U := (-(2913535717514371392481 / 5000000000000000000000 : ℚ))) + (U' := (552200183985628607519 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (312024205529 / 512000000000 : ℚ)) + (s := (1393214467000037 / 2500000000000000 : ℚ)) + (q := (44670775279013717 / 80000000000000000 : ℚ)) + (U := (-(2913535717514371392481 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_7 : Uω (aρ 7) (bρ 7) (312024205529 / 512000000000 : ℝ) ≤ @@ -618,25 +540,21 @@ lemma U_533_7 : have hlg : Real.log (42775377991769201 / 80000000000000000 : ℝ) ≤ (-(6260639779296802408789 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42775377991769201 / 80000000000000000 : ℝ) = - (42775377991769201 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42775377991769201 / 40000000000000000 : ℚ)) - (U := (670832023703197591211 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42775377991769201 / 40000000000000000 : ℝ) ≤ - (670832023703197591211 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5322669926949019 / 10000000000000000 : ℝ)) (q := - (42775377991769201 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42775377991769201 / 80000000000000000 : ℚ)) + (r' := (42775377991769201 / 40000000000000000 : ℚ)) + (U := (-(6260639779296802408789 / 10000000000000000000000 : ℚ))) + (U' := (670832023703197591211 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (312024205529 / 512000000000 : ℚ)) + (s := (5322669926949019 / 10000000000000000 : ℚ)) + (q := (42775377991769201 / 80000000000000000 : ℚ)) + (U := (-(6260639779296802408789 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_8 : Uω (aρ 8) (bρ 8) (312024205529 / 512000000000 : ℝ) ≤ @@ -644,25 +562,21 @@ lemma U_533_8 : have hlg : Real.log (40300490354719693 / 80000000000000000 : ℝ) ≤ (-(6856629979244132857753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40300490354719693 / 80000000000000000 : ℝ) = - (40300490354719693 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40300490354719693 / 40000000000000000 : ℚ)) - (U := (74841823755867142247 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40300490354719693 / 40000000000000000 : ℝ) ≤ - (74841823755867142247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2493744834513321 / 5000000000000000 : ℝ)) (q := - (40300490354719693 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40300490354719693 / 80000000000000000 : ℚ)) + (r' := (40300490354719693 / 40000000000000000 : ℚ)) + (U := (-(6856629979244132857753 / 10000000000000000000000 : ℚ))) + (U' := (74841823755867142247 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (312024205529 / 512000000000 : ℚ)) + (s := (2493744834513321 / 5000000000000000 : ℚ)) + (q := (40300490354719693 / 80000000000000000 : ℚ)) + (U := (-(6856629979244132857753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_9 : Uω (aρ 9) (bρ 9) (312024205529 / 512000000000 : ℝ) ≤ @@ -670,25 +584,21 @@ lemma U_533_9 : have hlg : Real.log (37194092469595613 / 80000000000000000 : ℝ) ≤ (-(3829383450332178808059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37194092469595613 / 80000000000000000 : ℝ) = - (37194092469595613 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37194092469595613 / 20000000000000000 : ℚ)) - (U := (3102088352667821191941 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37194092469595613 / 20000000000000000 : ℝ) ≤ - (3102088352667821191941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2275927913052811 / 5000000000000000 : ℝ)) (q := - (37194092469595613 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37194092469595613 / 80000000000000000 : ℚ)) + (r' := (37194092469595613 / 20000000000000000 : ℚ)) + (U := (-(3829383450332178808059 / 5000000000000000000000 : ℚ))) + (U' := (3102088352667821191941 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (312024205529 / 512000000000 : ℚ)) + (s := (2275927913052811 / 5000000000000000 : ℚ)) + (q := (37194092469595613 / 80000000000000000 : ℚ)) + (U := (-(3829383450332178808059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_10 : Uω (aρ 10) (bρ 10) (312024205529 / 512000000000 : ℝ) ≤ @@ -696,26 +606,21 @@ lemma U_533_10 : have hlg : Real.log (33424252113150029 / 80000000000000000 : ℝ) ≤ (-(272732777028236039401 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33424252113150029 / 80000000000000000 : ℝ) = - (33424252113150029 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33424252113150029 / 20000000000000000 : ℚ)) - (U := (160484210659263960599 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33424252113150029 / 20000000000000000 : ℝ) ≤ - (160484210659263960599 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1998977385244613 / 5000000000000000 : ℝ)) (q := - (33424252113150029 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33424252113150029 / 80000000000000000 : ℚ)) + (r' := (33424252113150029 / 20000000000000000 : ℚ)) + (U := (-(272732777028236039401 / 312500000000000000000 : ℚ))) + (U' := (160484210659263960599 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (312024205529 / 512000000000 : ℚ)) + (s := (1998977385244613 / 5000000000000000 : ℚ)) + (q := (33424252113150029 / 80000000000000000 : ℚ)) + (U := (-(272732777028236039401 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_11 : Uω (aρ 11) (bρ 11) (312024205529 / 512000000000 : ℝ) ≤ @@ -723,26 +628,21 @@ lemma U_533_11 : have hlg : Real.log (28954428248479461 / 80000000000000000 : ℝ) ≤ (-(10163034798815418328541 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28954428248479461 / 80000000000000000 : ℝ) = - (28954428248479461 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28954428248479461 / 20000000000000000 : ℚ)) - (U := (3699908807184581671459 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28954428248479461 / 20000000000000000 : ℝ) ≤ - (3699908807184581671459 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (412371928815823 / 1250000000000000 : ℝ)) (q := - (28954428248479461 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28954428248479461 / 80000000000000000 : ℚ)) + (r' := (28954428248479461 / 20000000000000000 : ℚ)) + (U := (-(10163034798815418328541 / 10000000000000000000000 : ℚ))) + (U' := (3699908807184581671459 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (312024205529 / 512000000000 : ℚ)) + (s := (412371928815823 / 1250000000000000 : ℚ)) + (q := (28954428248479461 / 80000000000000000 : ℚ)) + (U := (-(10163034798815418328541 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_12 : Uω (aρ 12) (bρ 12) (312024205529 / 512000000000 : ℝ) ≤ @@ -750,26 +650,21 @@ lemma U_533_12 : have hlg : Real.log (23629629171164773 / 80000000000000000 : ℝ) ≤ (-(12195252362156481322259 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23629629171164773 / 80000000000000000 : ℝ) = - (23629629171164773 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23629629171164773 / 20000000000000000 : ℚ)) - (U := (1667691243843518677741 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23629629171164773 / 20000000000000000 : ℝ) ≤ - (1667691243843518677741 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (74733617433841 / 312500000000000 : ℝ)) (q := - (23629629171164773 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23629629171164773 / 80000000000000000 : ℚ)) + (r' := (23629629171164773 / 20000000000000000 : ℚ)) + (U := (-(12195252362156481322259 / 10000000000000000000000 : ℚ))) + (U' := (1667691243843518677741 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (312024205529 / 512000000000 : ℚ)) + (s := (74733617433841 / 312500000000000 : ℚ)) + (q := (23629629171164773 / 80000000000000000 : ℚ)) + (U := (-(12195252362156481322259 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_13 : Uω (aρ 13) (bρ 13) (312024205529 / 512000000000 : ℝ) ≤ @@ -777,26 +672,21 @@ lemma U_533_13 : have hlg : Real.log (16157174489704889 / 80000000000000000 : ℝ) ≤ (-(3999156105056330198967 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16157174489704889 / 80000000000000000 : ℝ) = - (16157174489704889 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16157174489704889 / 10000000000000000 : ℚ)) - (U := (1199447747193669801033 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16157174489704889 / 10000000000000000 : ℝ) ≤ - (1199447747193669801033 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (922743829112941 / 10000000000000000 : ℝ)) (q := - (16157174489704889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16157174489704889 / 80000000000000000 : ℚ)) + (r' := (16157174489704889 / 10000000000000000 : ℚ)) + (U := (-(3999156105056330198967 / 2500000000000000000000 : ℚ))) + (U' := (1199447747193669801033 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (312024205529 / 512000000000 : ℚ)) + (s := (922743829112941 / 10000000000000000 : ℚ)) + (q := (16157174489704889 / 80000000000000000 : ℚ)) + (U := (-(3999156105056330198967 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_533_14 : Uω (aρ 14) (bρ 14) (312024205529 / 512000000000 : ℝ) ≤ @@ -903,25 +793,21 @@ lemma U_534_1 : have hlg : Real.log (4832358101161809 / 8000000000000000 : ℝ) ≤ (-(2520534865968170005413 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4832358101161809 / 8000000000000000 : ℝ) = - (4832358101161809 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4832358101161809 / 4000000000000000 : ℚ)) - (U := (945201035531829994587 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4832358101161809 / 4000000000000000 : ℝ) ≤ - (945201035531829994587 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1208084172445967 / 2000000000000000 : ℝ)) (q := - (4832358101161809 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4832358101161809 / 8000000000000000 : ℚ)) + (r' := (4832358101161809 / 4000000000000000 : ℚ)) + (U := (-(2520534865968170005413 / 5000000000000000000000 : ℚ))) + (U' := (945201035531829994587 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (1208084172445967 / 2000000000000000 : ℚ)) + (q := (4832358101161809 / 8000000000000000 : ℚ)) + (U := (-(2520534865968170005413 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_2 : Uω (aρ 2) (bρ 2) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -929,25 +815,21 @@ lemma U_534_2 : have hlg : Real.log (24066116171112581 / 40000000000000000 : ℝ) ≤ (-(5080745706614145080733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24066116171112581 / 40000000000000000 : ℝ) = - (24066116171112581 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24066116171112581 / 20000000000000000 : ℚ)) - (U := (1850726096385854919267 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24066116171112581 / 20000000000000000 : ℝ) ≤ - (1850726096385854919267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6016352707391603 / 10000000000000000 : ℝ)) (q := - (24066116171112581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24066116171112581 / 40000000000000000 : ℚ)) + (r' := (24066116171112581 / 20000000000000000 : ℚ)) + (U := (-(5080745706614145080733 / 10000000000000000000000 : ℚ))) + (U' := (1850726096385854919267 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (6016352707391603 / 10000000000000000 : ℚ)) + (q := (24066116171112581 / 40000000000000000 : ℚ)) + (U := (-(5080745706614145080733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_3 : Uω (aρ 3) (bρ 3) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -955,25 +837,21 @@ lemma U_534_3 : have hlg : Real.log (23874758124220609 / 40000000000000000 : ℝ) ≤ (-(258028849230606099 / 500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23874758124220609 / 40000000000000000 : ℝ) = - (23874758124220609 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23874758124220609 / 20000000000000000 : ℚ)) - (U := (88544740919393901 / 500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23874758124220609 / 20000000000000000 : ℝ) ≤ - (88544740919393901 / 500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5968069790295617 / 10000000000000000 : ℝ)) (q := - (23874758124220609 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23874758124220609 / 40000000000000000 : ℚ)) + (r' := (23874758124220609 / 20000000000000000 : ℚ)) + (U := (-(258028849230606099 / 500000000000000000 : ℚ))) + (U' := (88544740919393901 / 500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (5968069790295617 / 10000000000000000 : ℚ)) + (q := (23874758124220609 / 40000000000000000 : ℚ)) + (U := (-(258028849230606099 / 500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_4 : Uω (aρ 4) (bρ 4) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -981,25 +859,21 @@ lemma U_534_4 : have hlg : Real.log (23556914755306709 / 40000000000000000 : ℝ) ≤ (-(5294600563066589342857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23556914755306709 / 40000000000000000 : ℝ) = - (23556914755306709 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23556914755306709 / 20000000000000000 : ℚ)) - (U := (1636871239933410657143 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23556914755306709 / 20000000000000000 : ℝ) ≤ - (1636871239933410657143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5887442286903667 / 10000000000000000 : ℝ)) (q := - (23556914755306709 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23556914755306709 / 40000000000000000 : ℚ)) + (r' := (23556914755306709 / 20000000000000000 : ℚ)) + (U := (-(5294600563066589342857 / 10000000000000000000000 : ℚ))) + (U' := (1636871239933410657143 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (5887442286903667 / 10000000000000000 : ℚ)) + (q := (23556914755306709 / 40000000000000000 : ℚ)) + (U := (-(5294600563066589342857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_5 : Uω (aρ 5) (bρ 5) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1007,25 +881,21 @@ lemma U_534_5 : have hlg : Real.log (23072835029488537 / 40000000000000000 : ℝ) ≤ (-(1100447002148356538251 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23072835029488537 / 40000000000000000 : ℝ) = - (23072835029488537 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23072835029488537 / 20000000000000000 : ℚ)) - (U := (285847358451643461749 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23072835029488537 / 20000000000000000 : ℝ) ≤ - (285847358451643461749 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5763592343329581 / 10000000000000000 : ℝ)) (q := - (23072835029488537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23072835029488537 / 40000000000000000 : ℚ)) + (r' := (23072835029488537 / 20000000000000000 : ℚ)) + (U := (-(1100447002148356538251 / 2000000000000000000000 : ℚ))) + (U' := (285847358451643461749 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (5763592343329581 / 10000000000000000 : ℚ)) + (q := (23072835029488537 / 40000000000000000 : ℚ)) + (U := (-(1100447002148356538251 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_6 : Uω (aρ 6) (bρ 6) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1033,25 +903,21 @@ lemma U_534_6 : have hlg : Real.log (22378467636055877 / 40000000000000000 : ℝ) ≤ (-(1161560447106391500073 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22378467636055877 / 40000000000000000 : ℝ) = - (22378467636055877 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22378467636055877 / 20000000000000000 : ℚ)) - (U := (224733913493608499927 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22378467636055877 / 20000000000000000 : ℝ) ≤ - (224733913493608499927 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5583649021753251 / 10000000000000000 : ℝ)) (q := - (22378467636055877 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22378467636055877 / 40000000000000000 : ℚ)) + (r' := (22378467636055877 / 20000000000000000 : ℚ)) + (U := (-(1161560447106391500073 / 2000000000000000000000 : ℚ))) + (U' := (224733913493608499927 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (5583649021753251 / 10000000000000000 : ℚ)) + (q := (22378467636055877 / 40000000000000000 : ℚ)) + (U := (-(1161560447106391500073 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_7 : Uω (aρ 7) (bρ 7) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1059,25 +925,21 @@ lemma U_534_7 : have hlg : Real.log (4286175976475109 / 8000000000000000 : ℝ) ≤ (-(1560116466927709879407 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4286175976475109 / 8000000000000000 : ℝ) = - (4286175976475109 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4286175976475109 / 4000000000000000 : ℚ)) - (U := (172751483822290120593 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4286175976475109 / 4000000000000000 : ℝ) ≤ - (172751483822290120593 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1066703305134617 / 2000000000000000 : ℝ)) (q := - (4286175976475109 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4286175976475109 / 8000000000000000 : ℚ)) + (r' := (4286175976475109 / 4000000000000000 : ℚ)) + (U := (-(1560116466927709879407 / 2500000000000000000000 : ℚ))) + (U' := (172751483822290120593 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (1066703305134617 / 2000000000000000 : ℚ)) + (q := (4286175976475109 / 8000000000000000 : ℚ)) + (U := (-(1560116466927709879407 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_8 : Uω (aρ 8) (bρ 8) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1085,25 +947,21 @@ lemma U_534_8 : have hlg : Real.log (20193671267600891 / 40000000000000000 : ℝ) ≤ (-(3417551010603838729737 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20193671267600891 / 40000000000000000 : ℝ) = - (20193671267600891 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20193671267600891 / 20000000000000000 : ℚ)) - (U := (48184890896161270263 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20193671267600891 / 20000000000000000 : ℝ) ≤ - (48184890896161270263 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2499226934812879 / 5000000000000000 : ℝ)) (q := - (20193671267600891 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20193671267600891 / 40000000000000000 : ℚ)) + (r' := (20193671267600891 / 20000000000000000 : ℚ)) + (U := (-(3417551010603838729737 / 5000000000000000000000 : ℚ))) + (U' := (48184890896161270263 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (2499226934812879 / 5000000000000000 : ℚ)) + (q := (20193671267600891 / 40000000000000000 : ℚ)) + (U := (-(3417551010603838729737 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_9 : Uω (aρ 9) (bρ 9) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1111,25 +969,21 @@ lemma U_534_9 : have hlg : Real.log (3728191892532483 / 8000000000000000 : ℝ) ≤ (-(7635181723425072818701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3728191892532483 / 8000000000000000 : ℝ) = - (3728191892532483 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3728191892532483 / 2000000000000000 : ℚ)) - (U := (6227761882574927181299 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3728191892532483 / 2000000000000000 : ℝ) ≤ - (6227761882574927181299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114076589887913 / 250000000000000 : ℝ)) (q := - (3728191892532483 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3728191892532483 / 8000000000000000 : ℚ)) + (r' := (3728191892532483 / 2000000000000000 : ℚ)) + (U := (-(7635181723425072818701 / 10000000000000000000000 : ℚ))) + (U' := (6227761882574927181299 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (114076589887913 / 250000000000000 : ℚ)) + (q := (3728191892532483 / 8000000000000000 : ℚ)) + (U := (-(7635181723425072818701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_10 : Uω (aρ 10) (bρ 10) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1137,26 +991,21 @@ lemma U_534_10 : have hlg : Real.log (16757052616423023 / 40000000000000000 : ℝ) ≤ (-(8700602322136267647359 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16757052616423023 / 40000000000000000 : ℝ) = - (16757052616423023 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16757052616423023 / 10000000000000000 : ℚ)) - (U := (5162341283863732352641 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16757052616423023 / 10000000000000000 : ℝ) ≤ - (5162341283863732352641 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (250604325368239 / 625000000000000 : ℝ)) (q := - (16757052616423023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16757052616423023 / 40000000000000000 : ℚ)) + (r' := (16757052616423023 / 10000000000000000 : ℚ)) + (U := (-(8700602322136267647359 / 10000000000000000000000 : ℚ))) + (U' := (5162341283863732352641 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (250604325368239 / 625000000000000 : ℚ)) + (q := (16757052616423023 / 40000000000000000 : ℚ)) + (U := (-(8700602322136267647359 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_11 : Uω (aρ 11) (bρ 11) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1164,26 +1013,21 @@ lemma U_534_11 : have hlg : Real.log (14524369456552627 / 40000000000000000 : ℝ) ≤ (-(10130515627069486294957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14524369456552627 / 40000000000000000 : ℝ) = - (14524369456552627 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14524369456552627 / 10000000000000000 : ℚ)) - (U := (3732427978930513705043 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14524369456552627 / 10000000000000000 : ℝ) ≤ - (3732427978930513705043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1655902126080813 / 5000000000000000 : ℝ)) (q := - (14524369456552627 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14524369456552627 / 40000000000000000 : ℚ)) + (r' := (14524369456552627 / 10000000000000000 : ℚ)) + (U := (-(10130515627069486294957 / 10000000000000000000000 : ℚ))) + (U' := (3732427978930513705043 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (1655902126080813 / 5000000000000000 : ℚ)) + (q := (14524369456552627 / 40000000000000000 : ℚ)) + (U := (-(10130515627069486294957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_12 : Uω (aρ 12) (bρ 12) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1191,26 +1035,21 @@ lemma U_534_12 : have hlg : Real.log (11867862286965257 / 40000000000000000 : ℝ) ≤ (-(6075226774800110837489 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11867862286965257 / 40000000000000000 : ℝ) = - (11867862286965257 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11867862286965257 / 10000000000000000 : ℚ)) - (U := (856245028199889162511 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11867862286965257 / 10000000000000000 : ℝ) ≤ - (856245028199889162511 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2407250764052941 / 10000000000000000 : ℝ)) (q := - (11867862286965257 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11867862286965257 / 40000000000000000 : ℚ)) + (r' := (11867862286965257 / 10000000000000000 : ℚ)) + (U := (-(6075226774800110837489 / 5000000000000000000000 : ℚ))) + (U' := (856245028199889162511 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (2407250764052941 / 10000000000000000 : ℚ)) + (q := (11867862286965257 / 40000000000000000 : ℚ)) + (U := (-(6075226774800110837489 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_13 : Uω (aρ 13) (bρ 13) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1218,24 +1057,21 @@ lemma U_534_13 : have hlg : Real.log (65371510173111 / 320000000000000 : ℝ) ≤ (-(3970586139317389642427 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (65371510173111 / 320000000000000 : ℝ) = (65371510173111 / 40000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65371510173111 / 40000000000000 : ℚ)) - (U := (1228017712932610357573 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (65371510173111 / 40000000000000 : ℝ) ≤ - (1228017712932610357573 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3833682991939 / 40000000000000 : ℝ)) (q := - (65371510173111 / 320000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65371510173111 / 320000000000000 : ℚ)) + (r' := (65371510173111 / 40000000000000 : ℚ)) + (U := (-(3970586139317389642427 / 2500000000000000000000 : ℚ))) + (U' := (1228017712932610357573 / 2500000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19535909148031 / 32000000000000 : ℚ)) + (s := (3833682991939 / 40000000000000 : ℚ)) + (q := (65371510173111 / 320000000000000 : ℚ)) + (U := (-(3970586139317389642427 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_534_14 : Uω (aρ 14) (bρ 14) (19535909148031 / 32000000000000 : ℝ) ≤ @@ -1342,25 +1178,21 @@ lemma U_535_1 : have hlg : Real.log (9681914429625003 / 16000000000000000 : ℝ) ≤ (-(2511645342950552390927 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9681914429625003 / 16000000000000000 : ℝ) = - (9681914429625003 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9681914429625003 / 8000000000000000 : ℚ)) - (U := (954090558549447609073 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9681914429625003 / 8000000000000000 : ℝ) ≤ - (954090558549447609073 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (151279245045879 / 250000000000000 : ℝ)) (q := - (9681914429625003 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9681914429625003 / 16000000000000000 : ℚ)) + (r' := (9681914429625003 / 8000000000000000 : ℚ)) + (U := (-(2511645342950552390927 / 5000000000000000000000 : ℚ))) + (U' := (954090558549447609073 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (151279245045879 / 250000000000000 : ℚ)) + (q := (9681914429625003 / 16000000000000000 : ℚ)) + (U := (-(2511645342950552390927 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_2 : Uω (aρ 2) (bρ 2) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1368,25 +1200,21 @@ lemma U_535_2 : have hlg : Real.log (48218225614234631 / 80000000000000000 : ℝ) ≤ (-(5062895600518868362853 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48218225614234631 / 80000000000000000 : ℝ) = - (48218225614234631 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48218225614234631 / 40000000000000000 : ℚ)) - (U := (1868576202481131637147 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48218225614234631 / 40000000000000000 : ℝ) ≤ - (1868576202481131637147 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1506775545218141 / 2500000000000000 : ℝ)) (q := - (48218225614234631 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48218225614234631 / 80000000000000000 : ℚ)) + (r' := (48218225614234631 / 40000000000000000 : ℚ)) + (U := (-(5062895600518868362853 / 10000000000000000000000 : ℚ))) + (U' := (1868576202481131637147 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (1506775545218141 / 2500000000000000 : ℚ)) + (q := (48218225614234631 / 80000000000000000 : ℚ)) + (U := (-(5062895600518868362853 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_3 : Uω (aρ 3) (bρ 3) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1394,25 +1222,21 @@ lemma U_535_3 : have hlg : Real.log (47835515918073447 / 80000000000000000 : ℝ) ≤ (-(1028516519948136732061 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47835515918073447 / 80000000000000000 : ℝ) = - (47835515918073447 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47835515918073447 / 40000000000000000 : ℚ)) - (U := (357777840651863267939 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47835515918073447 / 40000000000000000 : ℝ) ≤ - (357777840651863267939 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1494705215795567 / 2500000000000000 : ℝ)) (q := - (47835515918073447 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47835515918073447 / 80000000000000000 : ℚ)) + (r' := (47835515918073447 / 40000000000000000 : ℚ)) + (U := (-(1028516519948136732061 / 2000000000000000000000 : ℚ))) + (U' := (357777840651863267939 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (1494705215795567 / 2500000000000000 : ℚ)) + (q := (47835515918073447 / 80000000000000000 : ℚ)) + (U := (-(1028516519948136732061 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_4 : Uω (aρ 4) (bρ 4) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1420,25 +1244,21 @@ lemma U_535_4 : have hlg : Real.log (47199846311035179 / 80000000000000000 : ℝ) ≤ (-(263817998974931911661 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47199846311035179 / 80000000000000000 : ℝ) = - (47199846311035179 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47199846311035179 / 40000000000000000 : ℚ)) - (U := (82755591175068088339 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47199846311035179 / 40000000000000000 : ℝ) ≤ - (82755591175068088339 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5898197642487701 / 10000000000000000 : ℝ)) (q := - (47199846311035179 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47199846311035179 / 80000000000000000 : ℚ)) + (r' := (47199846311035179 / 40000000000000000 : ℚ)) + (U := (-(263817998974931911661 / 500000000000000000000 : ℚ))) + (U' := (82755591175068088339 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (5898197642487701 / 10000000000000000 : ℚ)) + (q := (47199846311035179 / 80000000000000000 : ℚ)) + (U := (-(263817998974931911661 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_5 : Uω (aρ 5) (bρ 5) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1446,25 +1266,21 @@ lemma U_535_5 : have hlg : Real.log (46231729562098087 / 80000000000000000 : ℝ) ≤ (-(685450356247687421249 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46231729562098087 / 80000000000000000 : ℝ) = - (46231729562098087 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46231729562098087 / 40000000000000000 : ℚ)) - (U := (180983619127312578751 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46231729562098087 / 40000000000000000 : ℝ) ≤ - (180983619127312578751 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1443589593647107 / 2500000000000000 : ℝ)) (q := - (46231729562098087 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46231729562098087 / 80000000000000000 : ℚ)) + (r' := (46231729562098087 / 40000000000000000 : ℚ)) + (U := (-(685450356247687421249 / 1250000000000000000000 : ℚ))) + (U' := (180983619127312578751 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (1443589593647107 / 2500000000000000 : ℚ)) + (q := (46231729562098087 / 80000000000000000 : ℚ)) + (U := (-(685450356247687421249 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_6 : Uω (aρ 6) (bρ 6) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1472,25 +1288,21 @@ lemma U_535_6 : have hlg : Real.log (8968618922721031 / 16000000000000000 : ℝ) ≤ (-(5788570240149873008043 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8968618922721031 / 16000000000000000 : ℝ) = - (8968618922721031 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8968618922721031 / 8000000000000000 : ℚ)) - (U := (1142901562850126991957 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8968618922721031 / 8000000000000000 : ℝ) ≤ - (1142901562850126991957 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1118888002521039 / 2000000000000000 : ℝ)) (q := - (8968618922721031 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8968618922721031 / 16000000000000000 : ℚ)) + (r' := (8968618922721031 / 8000000000000000 : ℚ)) + (U := (-(5788570240149873008043 / 10000000000000000000000 : ℚ))) + (U' := (1142901562850126991957 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (1118888002521039 / 2000000000000000 : ℚ)) + (q := (8968618922721031 / 16000000000000000 : ℚ)) + (U := (-(5788570240149873008043 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_7 : Uω (aρ 7) (bρ 7) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1498,25 +1310,21 @@ lemma U_535_7 : have hlg : Real.log (42948139957716527 / 80000000000000000 : ℝ) ≤ (-(3110166470379501080453 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42948139957716527 / 80000000000000000 : ℝ) = - (42948139957716527 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42948139957716527 / 40000000000000000 : ℚ)) - (U := (355569431120498919547 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42948139957716527 / 40000000000000000 : ℝ) ≤ - (355569431120498919547 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2672181364696519 / 5000000000000000 : ℝ)) (q := - (42948139957716527 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42948139957716527 / 80000000000000000 : ℚ)) + (r' := (42948139957716527 / 40000000000000000 : ℚ)) + (U := (-(3110166470379501080453 / 5000000000000000000000 : ℚ))) + (U' := (355569431120498919547 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (2672181364696519 / 5000000000000000 : ℚ)) + (q := (42948139957716527 / 80000000000000000 : ℚ)) + (U := (-(3110166470379501080453 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_8 : Uω (aρ 8) (bρ 8) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1524,25 +1332,21 @@ lemma U_535_8 : have hlg : Real.log (40474190981887567 / 80000000000000000 : ℝ) ≤ (-(6813621231441943836873 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40474190981887567 / 80000000000000000 : ℝ) = - (40474190981887567 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40474190981887567 / 40000000000000000 : ℚ)) - (U := (117850571558056163127 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40474190981887567 / 40000000000000000 : ℝ) ≤ - (117850571558056163127 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2504708568387899 / 5000000000000000 : ℝ)) (q := - (40474190981887567 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40474190981887567 / 80000000000000000 : ℚ)) + (r' := (40474190981887567 / 40000000000000000 : ℚ)) + (U := (-(6813621231441943836873 / 10000000000000000000000 : ℚ))) + (U' := (117850571558056163127 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (2504708568387899 / 5000000000000000 : ℚ)) + (q := (40474190981887567 / 80000000000000000 : ℚ)) + (U := (-(6813621231441943836873 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_9 : Uω (aρ 9) (bρ 9) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1550,25 +1354,21 @@ lemma U_535_9 : have hlg : Real.log (37369736569649347 / 80000000000000000 : ℝ) ≤ (-(190291359982045990177 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37369736569649347 / 80000000000000000 : ℝ) = - (37369736569649347 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37369736569649347 / 20000000000000000 : ℚ)) - (U := (156282230167954009823 / 250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37369736569649347 / 20000000000000000 : ℝ) ≤ - (156282230167954009823 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4574269162076243 / 10000000000000000 : ℝ)) (q := - (37369736569649347 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37369736569649347 / 80000000000000000 : ℚ)) + (r' := (37369736569649347 / 20000000000000000 : ℚ)) + (U := (-(190291359982045990177 / 250000000000000000000 : ℚ))) + (U' := (156282230167954009823 / 250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (4574269162076243 / 10000000000000000 : ℚ)) + (q := (37369736569649347 / 80000000000000000 : ℚ)) + (U := (-(190291359982045990177 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_10 : Uω (aρ 10) (bρ 10) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1576,26 +1376,21 @@ lemma U_535_10 : have hlg : Real.log (33603936777527351 / 80000000000000000 : ℝ) ≤ (-(4336917040251970202751 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33603936777527351 / 80000000000000000 : ℝ) = - (33603936777527351 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33603936777527351 / 20000000000000000 : ℚ)) - (U := (2594554762748029797249 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33603936777527351 / 20000000000000000 : ℝ) ≤ - (2594554762748029797249 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (502672280942593 / 1250000000000000 : ℝ)) (q := - (33603936777527351 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33603936777527351 / 80000000000000000 : ℚ)) + (r' := (33603936777527351 / 20000000000000000 : ℚ)) + (U := (-(4336917040251970202751 / 5000000000000000000000 : ℚ))) + (U' := (2594554762748029797249 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (502672280942593 / 1250000000000000 : ℚ)) + (q := (33603936777527351 / 80000000000000000 : ℚ)) + (U := (-(4336917040251970202751 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_11 : Uω (aρ 11) (bρ 11) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1603,26 +1398,21 @@ lemma U_535_11 : have hlg : Real.log (29142990574389979 / 80000000000000000 : ℝ) ≤ (-(5049061054212899413027 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29142990574389979 / 80000000000000000 : ℝ) = - (29142990574389979 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29142990574389979 / 20000000000000000 : ℚ)) - (U := (1882410748787100586973 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29142990574389979 / 20000000000000000 : ℝ) ≤ - (1882410748787100586973 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3324618322961401 / 10000000000000000 : ℝ)) (q := - (29142990574389979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29142990574389979 / 80000000000000000 : ℚ)) + (r' := (29142990574389979 / 20000000000000000 : ℚ)) + (U := (-(5049061054212899413027 / 5000000000000000000000 : ℚ))) + (U' := (1882410748787100586973 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (3324618322961401 / 10000000000000000 : ℚ)) + (q := (29142990574389979 / 80000000000000000 : ℚ)) + (U := (-(5049061054212899413027 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_12 : Uω (aρ 12) (bρ 12) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1630,26 +1420,21 @@ lemma U_535_12 : have hlg : Real.log (23841599897031647 / 80000000000000000 : ℝ) ≤ (-(12105946844337847702467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23841599897031647 / 80000000000000000 : ℝ) = - (23841599897031647 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23841599897031647 / 20000000000000000 : ℚ)) - (U := (1756996761662152297533 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23841599897031647 / 20000000000000000 : ℝ) ≤ - (1756996761662152297533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1211485375153409 / 5000000000000000 : ℝ)) (q := - (23841599897031647 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23841599897031647 / 80000000000000000 : ℚ)) + (r' := (23841599897031647 / 20000000000000000 : ℚ)) + (U := (-(12105946844337847702467 / 10000000000000000000000 : ℚ))) + (U' := (1756996761662152297533 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (1211485375153409 / 5000000000000000 : ℚ)) + (q := (23841599897031647 / 80000000000000000 : ℚ)) + (U := (-(12105946844337847702467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_13 : Uω (aρ 13) (bρ 13) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1657,26 +1442,21 @@ lemma U_535_13 : have hlg : Real.log (16523921161995631 / 80000000000000000 : ℝ) ≤ (-(7886087677459839047893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16523921161995631 / 80000000000000000 : ℝ) = - (16523921161995631 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16523921161995631 / 10000000000000000 : ℚ)) - (U := (2511120027040160952107 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16523921161995631 / 10000000000000000 : ℝ) ≤ - (2511120027040160952107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (496466404071407 / 5000000000000000 : ℝ)) (q := - (16523921161995631 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16523921161995631 / 80000000000000000 : ℚ)) + (r' := (16523921161995631 / 10000000000000000 : ℚ)) + (U := (-(7886087677459839047893 / 5000000000000000000000 : ℚ))) + (U' := (2511120027040160952107 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39140610900999 / 64000000000000 : ℚ)) + (s := (496466404071407 / 5000000000000000 : ℚ)) + (q := (16523921161995631 / 80000000000000000 : ℚ)) + (U := (-(7886087677459839047893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_535_14 : Uω (aρ 14) (bρ 14) (39140610900999 / 64000000000000 : ℝ) ≤ @@ -1782,25 +1562,21 @@ lemma U_536_1 : have hlg : Real.log (6061945410410391 / 10000000000000000 : ℝ) ≤ (-(1251385798375307642803 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6061945410410391 / 10000000000000000 : ℝ) = - (6061945410410391 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6061945410410391 / 5000000000000000 : ℚ)) - (U := (481482152374692357197 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6061945410410391 / 5000000000000000 : ℝ) ≤ - (481482152374692357197 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3030959370551641 / 5000000000000000 : ℝ)) (q := - (6061945410410391 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6061945410410391 / 10000000000000000 : ℚ)) + (r' := (6061945410410391 / 5000000000000000 : ℚ)) + (U := (-(1251385798375307642803 / 2500000000000000000000 : ℚ))) + (U' := (481482152374692357197 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (3030959370551641 / 5000000000000000 : ℚ)) + (q := (6061945410410391 / 10000000000000000 : ℚ)) + (U := (-(1251385798375307642803 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_2 : Uω (aρ 2) (bρ 2) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1808,25 +1584,21 @@ lemma U_536_2 : have hlg : Real.log (6038027359660779 / 10000000000000000 : ℝ) ≤ (-(5045077302141448493163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6038027359660779 / 10000000000000000 : ℝ) = - (6038027359660779 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6038027359660779 / 5000000000000000 : ℚ)) - (U := (1886394500858551506837 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6038027359660779 / 5000000000000000 : ℝ) ≤ - (1886394500858551506837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3018925826057029 / 5000000000000000 : ℝ)) (q := - (6038027359660779 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6038027359660779 / 10000000000000000 : ℚ)) + (r' := (6038027359660779 / 5000000000000000 : ℚ)) + (U := (-(5045077302141448493163 / 10000000000000000000000 : ℚ))) + (U' := (1886394500858551506837 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (3018925826057029 / 5000000000000000 : ℚ)) + (q := (6038027359660779 / 10000000000000000 : ℚ)) + (U := (-(5045077302141448493163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_3 : Uω (aρ 3) (bρ 3) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1834,25 +1606,21 @@ lemma U_536_3 : have hlg : Real.log (2995094722231893 / 5000000000000000 : ℝ) ≤ (-(640577567897808385041 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2995094722231893 / 5000000000000000 : ℝ) = - (2995094722231893 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2995094722231893 / 2500000000000000 : ℚ)) - (U := (225856407477191614959 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2995094722231893 / 2500000000000000 : ℝ) ≤ - (225856407477191614959 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (748696491008759 / 1250000000000000 : ℝ)) (q := - (2995094722231893 / 5000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2995094722231893 / 5000000000000000 : ℚ)) + (r' := (2995094722231893 / 2500000000000000 : ℚ)) + (U := (-(640577567897808385041 / 1250000000000000000000 : ℚ))) + (U' := (225856407477191614959 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (748696491008759 / 1250000000000000 : ℚ)) + (q := (2995094722231893 / 5000000000000000 : ℚ)) + (U := (-(640577567897808385041 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_4 : Uω (aρ 4) (bρ 4) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1860,25 +1628,21 @@ lemma U_536_4 : have hlg : Real.log (2955366438542201 / 5000000000000000 : ℝ) ≤ (-(164317269602931110393 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2955366438542201 / 5000000000000000 : ℝ) = - (2955366438542201 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2955366438542201 / 2500000000000000 : ℚ)) - (U := (52291224240818889607 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2955366438542201 / 2500000000000000 : ℝ) ≤ - (52291224240818889607 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (369309560898519 / 625000000000000 : ℝ)) (q := - (2955366438542201 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2955366438542201 / 5000000000000000 : ℚ)) + (r' := (2955366438542201 / 2500000000000000 : ℚ)) + (U := (-(164317269602931110393 / 312500000000000000000 : ℚ))) + (U' := (52291224240818889607 / 312500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (369309560898519 / 625000000000000 : ℚ)) + (q := (2955366438542201 / 5000000000000000 : ℚ)) + (U := (-(164317269602931110393 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_5 : Uω (aρ 5) (bρ 5) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1886,25 +1650,21 @@ lemma U_536_5 : have hlg : Real.log (11579447202387303 / 20000000000000000 : ℝ) ≤ (-(5465005395609099705269 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11579447202387303 / 20000000000000000 : ℝ) = - (11579447202387303 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11579447202387303 / 10000000000000000 : ℚ)) - (U := (1466466407390900294731 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11579447202387303 / 10000000000000000 : ℝ) ≤ - (1466466407390900294731 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5785124341929803 / 10000000000000000 : ℝ)) (q := - (11579447202387303 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11579447202387303 / 20000000000000000 : ℚ)) + (r' := (11579447202387303 / 10000000000000000 : ℚ)) + (U := (-(5465005395609099705269 / 10000000000000000000000 : ℚ))) + (U' := (1466466407390900294731 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (5785124341929803 / 10000000000000000 : ℚ)) + (q := (11579447202387303 / 20000000000000000 : ℚ)) + (U := (-(5465005395609099705269 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_6 : Uω (aρ 6) (bρ 6) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1912,25 +1672,21 @@ lemma U_536_6 : have hlg : Real.log (5616156663407157 / 10000000000000000 : ℝ) ≤ (-(1442343826234602812091 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5616156663407157 / 10000000000000000 : ℝ) = - (5616156663407157 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5616156663407157 / 5000000000000000 : ℚ)) - (U := (290524124515397187909 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5616156663407157 / 5000000000000000 : ℝ) ≤ - (290524124515397187909 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2802615420748407 / 5000000000000000 : ℝ)) (q := - (5616156663407157 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5616156663407157 / 10000000000000000 : ℚ)) + (r' := (5616156663407157 / 5000000000000000 : ℚ)) + (U := (-(1442343826234602812091 / 2500000000000000000000 : ℚ))) + (U' := (290524124515397187909 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (2802615420748407 / 5000000000000000 : ℚ)) + (q := (5616156663407157 / 10000000000000000 : ℚ)) + (U := (-(1442343826234602812091 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_7 : Uω (aρ 7) (bρ 7) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1938,25 +1694,21 @@ lemma U_536_7 : have hlg : Real.log (10758629645066451 / 20000000000000000 : ℝ) ≤ (-(620024083077386747109 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10758629645066451 / 20000000000000000 : ℝ) = - (10758629645066451 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10758629645066451 / 10000000000000000 : ℚ)) - (U := (73123097222613252891 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10758629645066451 / 10000000000000000 : ℝ) ≤ - (73123097222613252891 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5355208540508951 / 10000000000000000 : ℝ)) (q := - (10758629645066451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10758629645066451 / 20000000000000000 : ℚ)) + (r' := (10758629645066451 / 10000000000000000 : ℚ)) + (U := (-(620024083077386747109 / 1000000000000000000000 : ℚ))) + (U' := (73123097222613252891 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (5355208540508951 / 10000000000000000 : ℚ)) + (q := (10758629645066451 / 20000000000000000 : ℚ)) + (U := (-(620024083077386747109 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_8 : Uω (aρ 8) (bρ 8) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1964,25 +1716,21 @@ lemma U_536_8 : have hlg : Real.log (1267532366226191 / 2500000000000000 : ℝ) ≤ (-(6792187399728591460427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1267532366226191 / 2500000000000000 : ℝ) = - (1267532366226191 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1267532366226191 / 1250000000000000 : ℚ)) - (U := (139284403271408539573 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1267532366226191 / 1250000000000000 : ℝ) ≤ - (139284403271408539573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1255094869148007 / 2500000000000000 : ℝ)) (q := - (1267532366226191 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1267532366226191 / 2500000000000000 : ℚ)) + (r' := (1267532366226191 / 1250000000000000 : ℚ)) + (U := (-(6792187399728591460427 / 10000000000000000000000 : ℚ))) + (U' := (139284403271408539573 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (1255094869148007 / 2500000000000000 : ℚ)) + (q := (1267532366226191 / 2500000000000000 : ℚ)) + (U := (-(6792187399728591460427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_9 : Uω (aρ 9) (bρ 9) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -1990,25 +1738,21 @@ lemma U_536_9 : have hlg : Real.log (9364386366791683 / 20000000000000000 : ℝ) ≤ (-(7588184633861080601369 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9364386366791683 / 20000000000000000 : ℝ) = - (9364386366791683 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9364386366791683 / 5000000000000000 : ℚ)) - (U := (6274758972138919398631 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9364386366791683 / 5000000000000000 : ℝ) ≤ - (6274758972138919398631 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4585472541934183 / 10000000000000000 : ℝ)) (q := - (9364386366791683 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9364386366791683 / 20000000000000000 : ℚ)) + (r' := (9364386366791683 / 5000000000000000 : ℚ)) + (U := (-(7588184633861080601369 / 10000000000000000000000 : ℚ))) + (U' := (6274758972138919398631 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (4585472541934183 / 10000000000000000 : ℚ)) + (q := (9364386366791683 / 20000000000000000 : ℚ)) + (U := (-(7588184633861080601369 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_10 : Uω (aρ 10) (bρ 10) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -2016,24 +1760,21 @@ lemma U_536_10 : have hlg : Real.log (105292959172209 / 250000000000000 : ℝ) ≤ (-(1080892956124258428013 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (105292959172209 / 250000000000000 : ℝ) = (105292959172209 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (105292959172209 / 62500000000000 : ℚ)) - (U := (651974994625741571987 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (105292959172209 / 62500000000000 : ℝ) ≤ - (651974994625741571987 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (201654097120711 / 500000000000000 : ℝ)) (q := - (105292959172209 / 250000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (105292959172209 / 250000000000000 : ℚ)) + (r' := (105292959172209 / 62500000000000 : ℚ)) + (U := (-(1080892956124258428013 / 1250000000000000000000 : ℚ))) + (U' := (651974994625741571987 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (201654097120711 / 500000000000000 : ℚ)) + (q := (105292959172209 / 250000000000000 : ℚ)) + (U := (-(1080892956124258428013 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_11 : Uω (aρ 11) (bρ 11) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -2041,26 +1782,21 @@ lemma U_536_11 : have hlg : Real.log (3654647988995821 / 10000000000000000 : ℝ) ≤ (-(314557910422104071209 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3654647988995821 / 10000000000000000 : ℝ) = - (3654647988995821 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3654647988995821 / 2500000000000000 : ℚ)) - (U := (118659077265395928791 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3654647988995821 / 2500000000000000 : ℝ) ≤ - (118659077265395928791 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1668708906417071 / 5000000000000000 : ℝ)) (q := - (3654647988995821 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3654647988995821 / 10000000000000000 : ℚ)) + (r' := (3654647988995821 / 2500000000000000 : ℚ)) + (U := (-(314557910422104071209 / 312500000000000000000 : ℚ))) + (U' := (118659077265395928791 / 312500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (1668708906417071 / 5000000000000000 : ℚ)) + (q := (3654647988995821 / 10000000000000000 : ℚ)) + (U := (-(314557910422104071209 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_12 : Uω (aρ 12) (bρ 12) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -2068,26 +1804,21 @@ lemma U_536_12 : have hlg : Real.log (2993407424564263 / 10000000000000000 : ℝ) ≤ (-(6030863735264409501953 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2993407424564263 / 10000000000000000 : ℝ) = - (2993407424564263 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2993407424564263 / 2500000000000000 : ℚ)) - (U := (900608067735590498047 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2993407424564263 / 2500000000000000 : ℝ) ≤ - (900608067735590498047 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1219318390328013 / 5000000000000000 : ℝ)) (q := - (2993407424564263 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2993407424564263 / 10000000000000000 : ℚ)) + (r' := (2993407424564263 / 2500000000000000 : ℚ)) + (U := (-(6030863735264409501953 / 5000000000000000000000 : ℚ))) + (U' := (900608067735590498047 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (1219318390328013 / 5000000000000000 : ℚ)) + (q := (2993407424564263 / 10000000000000000 : ℚ)) + (U := (-(6030863735264409501953 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_13 : Uω (aρ 13) (bρ 13) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -2095,25 +1826,21 @@ lemma U_536_13 : have hlg : Real.log (521899230802451 / 2500000000000000 : ℝ) ≤ (-(3133142970538085451271 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (521899230802451 / 2500000000000000 : ℝ) = - (521899230802451 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (521899230802451 / 312500000000000 : ℚ)) - (U := (1025740111261914548729 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (521899230802451 / 312500000000000 : ℝ) ≤ - (1025740111261914548729 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256599379885527 / 2500000000000000 : ℝ)) (q := - (521899230802451 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (521899230802451 / 2500000000000000 : ℚ)) + (r' := (521899230802451 / 312500000000000 : ℚ)) + (U := (-(3133142970538085451271 / 2000000000000000000000 : ℚ))) + (U' := (1025740111261914548729 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2450587719121 / 4000000000000 : ℚ)) + (s := (256599379885527 / 2500000000000000 : ℚ)) + (q := (521899230802451 / 2500000000000000 : ℚ)) + (U := (-(3133142970538085451271 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_536_14 : Uω (aρ 14) (bρ 14) (2450587719121 / 4000000000000 : ℝ) ≤ @@ -2219,25 +1946,21 @@ lemma U_537_1 : have hlg : Real.log (48581554417099593 / 80000000000000000 : ℝ) ≤ (-(2493913571466764627649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48581554417099593 / 80000000000000000 : ℝ) = - (48581554417099593 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48581554417099593 / 40000000000000000 : ℚ)) - (U := (971822330033235372351 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48581554417099593 / 40000000000000000 : ℝ) ≤ - (971822330033235372351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (759083460004499 / 1250000000000000 : ℝ)) (q := - (48581554417099593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48581554417099593 / 80000000000000000 : ℚ)) + (r' := (48581554417099593 / 40000000000000000 : ℚ)) + (U := (-(2493913571466764627649 / 5000000000000000000000 : ℚ))) + (U' := (971822330033235372351 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (759083460004499 / 1250000000000000 : ℚ)) + (q := (48581554417099593 / 80000000000000000 : ℚ)) + (U := (-(2493913571466764627649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_2 : Uω (aρ 2) (bρ 2) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2245,25 +1968,21 @@ lemma U_537_2 : have hlg : Real.log (48390212131427721 / 80000000000000000 : ℝ) ≤ (-(1005458139663677673063 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48390212131427721 / 80000000000000000 : ℝ) = - (48390212131427721 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48390212131427721 / 40000000000000000 : ℚ)) - (U := (380836220936322326937 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48390212131427721 / 40000000000000000 : ℝ) ≤ - (380836220936322326937 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (756075140141003 / 1250000000000000 : ℝ)) (q := - (48390212131427721 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48390212131427721 / 80000000000000000 : ℚ)) + (r' := (48390212131427721 / 40000000000000000 : ℚ)) + (U := (-(1005458139663677673063 / 2000000000000000000000 : ℚ))) + (U' := (380836220936322326937 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (756075140141003 / 1250000000000000 : ℚ)) + (q := (48390212131427721 / 80000000000000000 : ℚ)) + (U := (-(1005458139663677673063 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_3 : Uω (aρ 3) (bρ 3) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2271,25 +1990,21 @@ lemma U_537_3 : have hlg : Real.log (48007515161523729 / 80000000000000000 : ℝ) ≤ (-(5106690698961235973153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48007515161523729 / 80000000000000000 : ℝ) = - (48007515161523729 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48007515161523729 / 40000000000000000 : ℚ)) - (U := (1824781104038764026847 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48007515161523729 / 40000000000000000 : ℝ) ≤ - (1824781104038764026847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3000161492501013 / 5000000000000000 : ℝ)) (q := - (48007515161523729 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48007515161523729 / 80000000000000000 : ℚ)) + (r' := (48007515161523729 / 40000000000000000 : ℚ)) + (U := (-(5106690698961235973153 / 10000000000000000000000 : ℚ))) + (U' := (1824781104038764026847 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (3000161492501013 / 5000000000000000 : ℚ)) + (q := (48007515161523729 / 80000000000000000 : ℚ)) + (U := (-(5106690698961235973153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_4 : Uω (aρ 4) (bρ 4) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2297,25 +2012,21 @@ lemma U_537_4 : have hlg : Real.log (47371879628050141 / 80000000000000000 : ℝ) ≤ (-(5239978385515379585033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47371879628050141 / 80000000000000000 : ℝ) = - (47371879628050141 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47371879628050141 / 40000000000000000 : ℚ)) - (U := (1691493417484620414967 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47371879628050141 / 40000000000000000 : ℝ) ≤ - (1691493417484620414967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5919708282698629 / 10000000000000000 : ℝ)) (q := - (47371879628050141 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47371879628050141 / 80000000000000000 : ℚ)) + (r' := (47371879628050141 / 40000000000000000 : ℚ)) + (U := (-(5239978385515379585033 / 10000000000000000000000 : ℚ))) + (U' := (1691493417484620414967 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (5919708282698629 / 10000000000000000 : ℚ)) + (q := (47371879628050141 / 80000000000000000 : ℚ)) + (U := (-(5239978385515379585033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_5 : Uω (aρ 5) (bρ 5) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2323,25 +2034,21 @@ lemma U_537_5 : have hlg : Real.log (46403847802755189 / 80000000000000000 : ℝ) ≤ (-(5446442518364453498131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46403847802755189 / 80000000000000000 : ℝ) = - (46403847802755189 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46403847802755189 / 40000000000000000 : ℚ)) - (U := (1485029284635546501869 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46403847802755189 / 40000000000000000 : ℝ) ≤ - (1485029284635546501869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5795890245709891 / 10000000000000000 : ℝ)) (q := - (46403847802755189 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46403847802755189 / 80000000000000000 : ℚ)) + (r' := (46403847802755189 / 40000000000000000 : ℚ)) + (U := (-(5446442518364453498131 / 10000000000000000000000 : ℚ))) + (U' := (1485029284635546501869 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (5795890245709891 / 10000000000000000 : ℚ)) + (q := (46403847802755189 / 80000000000000000 : ℚ)) + (U := (-(5446442518364453498131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_6 : Uω (aρ 6) (bρ 6) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2349,25 +2056,21 @@ lemma U_537_6 : have hlg : Real.log (45015411356802417 / 80000000000000000 : ℝ) ≤ (-(5750217286790455522099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45015411356802417 / 80000000000000000 : ℝ) = - (45015411356802417 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45015411356802417 / 40000000000000000 : ℚ)) - (U := (1181254516209544477901 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45015411356802417 / 40000000000000000 : ℝ) ≤ - (1181254516209544477901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2808010754680849 / 5000000000000000 : ℝ)) (q := - (45015411356802417 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45015411356802417 / 80000000000000000 : ℚ)) + (r' := (45015411356802417 / 40000000000000000 : ℚ)) + (U := (-(5750217286790455522099 / 10000000000000000000000 : ℚ))) + (U' := (1181254516209544477901 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (2808010754680849 / 5000000000000000 : ℚ)) + (q := (45015411356802417 / 80000000000000000 : ℚ)) + (U := (-(5750217286790455522099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_7 : Uω (aρ 7) (bρ 7) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2375,25 +2078,21 @@ lemma U_537_7 : have hlg : Real.log (43120895641921241 / 80000000000000000 : ℝ) ≤ (-(6180189371123662487857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43120895641921241 / 80000000000000000 : ℝ) = - (43120895641921241 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43120895641921241 / 40000000000000000 : ℚ)) - (U := (751282431876337512143 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43120895641921241 / 40000000000000000 : ℝ) ≤ - (751282431876337512143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1341513490350351 / 2500000000000000 : ℝ)) (q := - (43120895641921241 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43120895641921241 / 80000000000000000 : ℚ)) + (r' := (43120895641921241 / 40000000000000000 : ℚ)) + (U := (-(6180189371123662487857 / 10000000000000000000000 : ℚ))) + (U' := (751282431876337512143 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (1341513490350351 / 2500000000000000 : ℚ)) + (q := (43120895641921241 / 80000000000000000 : ℚ)) + (U := (-(6180189371123662487857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_8 : Uω (aρ 8) (bρ 8) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2401,25 +2100,21 @@ lemma U_537_8 : have hlg : Real.log (40647876771499233 / 80000000000000000 : ℝ) ≤ (-(1692700079319226165529 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40647876771499233 / 80000000000000000 : ℝ) = - (40647876771499233 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40647876771499233 / 40000000000000000 : ℚ)) - (U := (40167871430773834471 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40647876771499233 / 40000000000000000 : ℝ) ≤ - (40167871430773834471 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2515670447567951 / 5000000000000000 : ℝ)) (q := - (40647876771499233 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40647876771499233 / 80000000000000000 : ℚ)) + (r' := (40647876771499233 / 40000000000000000 : ℚ)) + (U := (-(1692700079319226165529 / 2500000000000000000000 : ℚ))) + (U' := (40167871430773834471 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (2515670447567951 / 5000000000000000 : ℚ)) + (q := (40647876771499233 / 80000000000000000 : ℚ)) + (U := (-(1692700079319226165529 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_9 : Uω (aρ 9) (bρ 9) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2427,25 +2122,21 @@ lemma U_537_9 : have hlg : Real.log (1501813827273289 / 3200000000000000 : ℝ) ≤ (-(3782386067554484225809 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1501813827273289 / 3200000000000000 : ℝ) = - (1501813827273289 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1501813827273289 / 800000000000000 : ℚ)) - (U := (3149085735445515774191 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1501813827273289 / 800000000000000 : ℝ) ≤ - (3149085735445515774191 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (91933475021583 / 200000000000000 : ℝ)) (q := - (1501813827273289 / 3200000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1501813827273289 / 3200000000000000 : ℚ)) + (r' := (1501813827273289 / 800000000000000 : ℚ)) + (U := (-(3782386067554484225809 / 5000000000000000000000 : ℚ))) + (U' := (3149085735445515774191 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (91933475021583 / 200000000000000 : ℚ)) + (q := (1501813827273289 / 3200000000000000 : ℚ)) + (U := (-(3782386067554484225809 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_10 : Uω (aρ 10) (bρ 10) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2453,26 +2144,21 @@ lemma U_537_10 : have hlg : Real.log (33783535891237313 / 80000000000000000 : ℝ) ≤ (-(8620530541481646251921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33783535891237313 / 80000000000000000 : ℝ) = - (33783535891237313 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33783535891237313 / 20000000000000000 : ℚ)) - (U := (5242413064518353748079 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33783535891237313 / 20000000000000000 : ℝ) ≤ - (5242413064518353748079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2022390168462711 / 5000000000000000 : ℝ)) (q := - (33783535891237313 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33783535891237313 / 80000000000000000 : ℚ)) + (r' := (33783535891237313 / 20000000000000000 : ℚ)) + (U := (-(8620530541481646251921 / 10000000000000000000000 : ℚ))) + (U' := (5242413064518353748079 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (2022390168462711 / 5000000000000000 : ℚ)) + (q := (33783535891237313 / 80000000000000000 : ℚ)) + (U := (-(8620530541481646251921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_11 : Uω (aρ 11) (bρ 11) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2480,26 +2166,21 @@ lemma U_537_11 : have hlg : Real.log (29331319594314289 / 80000000000000000 : ℝ) ≤ (-(2508426902235644193011 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29331319594314289 / 80000000000000000 : ℝ) = - (29331319594314289 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29331319594314289 / 20000000000000000 : ℚ)) - (U := (957308999264355806989 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29331319594314289 / 20000000000000000 : ℝ) ≤ - (957308999264355806989 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1675101444449833 / 5000000000000000 : ℝ)) (q := - (29331319594314289 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29331319594314289 / 80000000000000000 : ℚ)) + (r' := (29331319594314289 / 20000000000000000 : ℚ)) + (U := (-(2508426902235644193011 / 2500000000000000000000 : ℚ))) + (U' := (957308999264355806989 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (1675101444449833 / 5000000000000000 : ℚ)) + (q := (29331319594314289 / 80000000000000000 : ℚ)) + (U := (-(2508426902235644193011 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_12 : Uω (aρ 12) (bρ 12) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2507,26 +2188,21 @@ lemma U_537_12 : have hlg : Real.log (4810541441066241 / 16000000000000000 : ℝ) ≤ (-(1502223847783784689383 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4810541441066241 / 16000000000000000 : ℝ) = - (4810541441066241 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4810541441066241 / 4000000000000000 : ℚ)) - (U := (230644102966215310617 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4810541441066241 / 4000000000000000 : ℝ) ≤ - (230644102966215310617 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (490849977667779 / 2000000000000000 : ℝ)) (q := - (4810541441066241 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4810541441066241 / 16000000000000000 : ℚ)) + (r' := (4810541441066241 / 4000000000000000 : ℚ)) + (U := (-(1502223847783784689383 / 1250000000000000000000 : ℚ))) + (U' := (230644102966215310617 / 1250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (490849977667779 / 2000000000000000 : ℚ)) + (q := (4810541441066241 / 16000000000000000 : ℚ)) + (U := (-(1502223847783784689383 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_13 : Uω (aρ 13) (bρ 13) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2534,25 +2210,21 @@ lemma U_537_13 : have hlg : Real.log (674953496939277 / 3200000000000000 : ℝ) ≤ (-(15562622929320063846659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (674953496939277 / 3200000000000000 : ℝ) = - (674953496939277 / 400000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (674953496939277 / 400000000000000 : ℚ)) - (U := (5231792479679936153341 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (674953496939277 / 400000000000000 : ℝ) ≤ - (5231792479679936153341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (42356567378863 / 400000000000000 : ℝ)) (q := - (674953496939277 / 3200000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (674953496939277 / 3200000000000000 : ℚ)) + (r' := (674953496939277 / 400000000000000 : ℚ)) + (U := (-(15562622929320063846659 / 10000000000000000000000 : ℚ))) + (U' := (5231792479679936153341 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39278196110873 / 64000000000000 : ℚ)) + (s := (42356567378863 / 400000000000000 : ℚ)) + (q := (674953496939277 / 3200000000000000 : ℚ)) + (U := (-(15562622929320063846659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_537_14 : Uω (aρ 14) (bρ 14) (39278196110873 / 64000000000000 : ℝ) ≤ @@ -2660,25 +2332,21 @@ lemma U_538_1 : have hlg : Real.log (24333772774790763 / 40000000000000000 : ℝ) ≤ (-(4970142422987990689033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24333772774790763 / 40000000000000000 : ℝ) = - (24333772774790763 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24333772774790763 / 20000000000000000 : ℚ)) - (U := (1961329380012009310967 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24333772774790763 / 20000000000000000 : ℝ) ≤ - (1961329380012009310967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6083416618635069 / 10000000000000000 : ℝ)) (q := - (24333772774790763 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24333772774790763 / 40000000000000000 : ℚ)) + (r' := (24333772774790763 / 20000000000000000 : ℚ)) + (U := (-(4970142422987990689033 / 10000000000000000000000 : ℚ))) + (U' := (1961329380012009310967 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (6083416618635069 / 10000000000000000 : ℚ)) + (q := (24333772774790763 / 40000000000000000 : ℚ)) + (U := (-(4970142422987990689033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_2 : Uω (aρ 2) (bρ 2) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2686,25 +2354,21 @@ lemma U_538_2 : have hlg : Real.log (24238102688353259 / 40000000000000000 : ℝ) ≤ (-(626191959561132738727 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24238102688353259 / 40000000000000000 : ℝ) = - (24238102688353259 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24238102688353259 / 20000000000000000 : ℚ)) - (U := (240242015813867261273 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24238102688353259 / 20000000000000000 : ℝ) ≤ - (240242015813867261273 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6059350587926317 / 10000000000000000 : ℝ)) (q := - (24238102688353259 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24238102688353259 / 40000000000000000 : ℚ)) + (r' := (24238102688353259 / 20000000000000000 : ℚ)) + (U := (-(626191959561132738727 / 1250000000000000000000 : ℚ))) + (U' := (240242015813867261273 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (6059350587926317 / 10000000000000000 : ℚ)) + (q := (24238102688353259 / 40000000000000000 : ℚ)) + (U := (-(626191959561132738727 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_3 : Uω (aρ 3) (bρ 3) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2712,25 +2376,21 @@ lemma U_538_3 : have hlg : Real.log (24046757367842257 / 40000000000000000 : ℝ) ≤ (-(5088792951723855824927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24046757367842257 / 40000000000000000 : ℝ) = - (24046757367842257 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24046757367842257 / 20000000000000000 : ℚ)) - (U := (1842678851276144175073 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24046757367842257 / 20000000000000000 : ℝ) ≤ - (1842678851276144175073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (375692127126301 / 625000000000000 : ℝ)) (q := - (24046757367842257 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24046757367842257 / 40000000000000000 : ℚ)) + (r' := (24046757367842257 / 20000000000000000 : ℚ)) + (U := (-(5088792951723855824927 / 10000000000000000000000 : ℚ))) + (U' := (1842678851276144175073 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (375692127126301 / 625000000000000 : ℚ)) + (q := (24046757367842257 / 40000000000000000 : ℚ)) + (U := (-(5088792951723855824927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_4 : Uω (aρ 4) (bρ 4) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2738,25 +2398,21 @@ lemma U_538_4 : have hlg : Real.log (23728948072836411 / 40000000000000000 : ℝ) ≤ (-(1305459283471519444757 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23728948072836411 / 40000000000000000 : ℝ) = - (23728948072836411 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23728948072836411 / 20000000000000000 : ℚ)) - (U := (427408667278480555243 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23728948072836411 / 20000000000000000 : ℝ) ≤ - (427408667278480555243 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5930463567582893 / 10000000000000000 : ℝ)) (q := - (23728948072836411 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23728948072836411 / 40000000000000000 : ℚ)) + (r' := (23728948072836411 / 20000000000000000 : ℚ)) + (U := (-(1305459283471519444757 / 2500000000000000000000 : ℚ))) + (U' := (427408667278480555243 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (5930463567582893 / 10000000000000000 : ℚ)) + (q := (23728948072836411 / 40000000000000000 : ℚ)) + (U := (-(1305459283471519444757 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_5 : Uω (aρ 5) (bρ 5) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2764,25 +2420,21 @@ lemma U_538_5 : have hlg : Real.log (23244953271565087 / 40000000000000000 : ℝ) ≤ (-(339244630606834053439 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23244953271565087 / 40000000000000000 : ℝ) = - (23244953271565087 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23244953271565087 / 20000000000000000 : ℚ)) - (U := (93972357080665946561 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23244953271565087 / 20000000000000000 : ℝ) ≤ - (93972357080665946561 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5806656086282231 / 10000000000000000 : ℝ)) (q := - (23244953271565087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23244953271565087 / 40000000000000000 : ℚ)) + (r' := (23244953271565087 / 20000000000000000 : ℚ)) + (U := (-(339244630606834053439 / 625000000000000000000 : ℚ))) + (U' := (93972357080665946561 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (5806656086282231 / 10000000000000000 : ℚ)) + (q := (23244953271565087 / 40000000000000000 : ℚ)) + (U := (-(339244630606834053439 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_6 : Uω (aρ 6) (bρ 6) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2790,25 +2442,21 @@ lemma U_538_6 : have hlg : Real.log (4510156876594629 / 8000000000000000 : ℝ) ≤ (-(2865548021714676276341 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4510156876594629 / 8000000000000000 : ℝ) = - (4510156876594629 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4510156876594629 / 4000000000000000 : ℚ)) - (U := (600187879785323723659 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4510156876594629 / 4000000000000000 : ℝ) ≤ - (600187879785323723659 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (281340600856313 / 500000000000000 : ℝ)) (q := - (4510156876594629 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4510156876594629 / 8000000000000000 : ℚ)) + (r' := (4510156876594629 / 4000000000000000 : ℚ)) + (U := (-(2865548021714676276341 / 5000000000000000000000 : ℚ))) + (U' := (600187879785323723659 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (281340600856313 / 500000000000000 : ℚ)) + (q := (4510156876594629 / 8000000000000000 : ℚ)) + (U := (-(2865548021714676276341 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_7 : Uω (aρ 7) (bρ 7) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2816,25 +2464,21 @@ lemma U_538_7 : have hlg : Real.log (21603635576063999 / 40000000000000000 : ℝ) ≤ (-(24640713584814710663 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21603635576063999 / 40000000000000000 : ℝ) = - (21603635576063999 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21603635576063999 / 20000000000000000 : ℚ)) - (U := (3085173627185289337 / 40000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21603635576063999 / 20000000000000000 : ℝ) ≤ - (3085173627185289337 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5376898994431687 / 10000000000000000 : ℝ)) (q := - (21603635576063999 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21603635576063999 / 40000000000000000 : ℚ)) + (r' := (21603635576063999 / 20000000000000000 : ℚ)) + (U := (-(24640713584814710663 / 40000000000000000000 : ℚ))) + (U' := (3085173627185289337 / 40000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (5376898994431687 / 10000000000000000 : ℚ)) + (q := (21603635576063999 / 40000000000000000 : ℚ)) + (U := (-(24640713584814710663 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_8 : Uω (aρ 8) (bρ 8) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2842,25 +2486,21 @@ lemma U_538_8 : have hlg : Real.log (20367357081351947 / 40000000000000000 : ℝ) ≤ (-(6749459776710677993977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20367357081351947 / 40000000000000000 : ℝ) = - (20367357081351947 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20367357081351947 / 20000000000000000 : ℚ)) - (U := (182012026289322006023 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20367357081351947 / 20000000000000000 : ℝ) ≤ - (182012026289322006023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5042301398415661 / 10000000000000000 : ℝ)) (q := - (20367357081351947 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20367357081351947 / 40000000000000000 : ℚ)) + (r' := (20367357081351947 / 20000000000000000 : ℚ)) + (U := (-(6749459776710677993977 / 10000000000000000000000 : ℚ))) + (U' := (182012026289322006023 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (5042301398415661 / 10000000000000000 : ℚ)) + (q := (20367357081351947 / 40000000000000000 : ℚ)) + (U := (-(6749459776710677993977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_9 : Uω (aρ 9) (bρ 9) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2868,25 +2508,21 @@ lemma U_538_9 : have hlg : Real.log (18816568638483439 / 40000000000000000 : ℝ) ≤ (-(3770708306633194469347 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18816568638483439 / 40000000000000000 : ℝ) = - (18816568638483439 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18816568638483439 / 10000000000000000 : ℚ)) - (U := (3160763496366805530653 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18816568638483439 / 10000000000000000 : ℝ) ≤ - (3160763496366805530653 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4607872805341407 / 10000000000000000 : ℝ)) (q := - (18816568638483439 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18816568638483439 / 40000000000000000 : ℚ)) + (r' := (18816568638483439 / 10000000000000000 : ℚ)) + (U := (-(3770708306633194469347 / 5000000000000000000000 : ℚ))) + (U' := (3160763496366805530653 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (4607872805341407 / 10000000000000000 : ℚ)) + (q := (18816568638483439 / 40000000000000000 : ℚ)) + (U := (-(3770708306633194469347 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_10 : Uω (aρ 10) (bρ 10) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2894,25 +2530,21 @@ lemma U_538_10 : have hlg : Real.log (677466076586923 / 1600000000000000 : ℝ) ≤ (-(8593994276661595780249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (677466076586923 / 1600000000000000 : ℝ) = - (677466076586923 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (677466076586923 / 400000000000000 : ℚ)) - (U := (5268949329338404219751 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (677466076586923 / 400000000000000 : ℝ) ≤ - (5268949329338404219751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (162258939077249 / 400000000000000 : ℝ)) (q := - (677466076586923 / 1600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (677466076586923 / 1600000000000000 : ℚ)) + (r' := (677466076586923 / 400000000000000 : ℚ)) + (U := (-(8593994276661595780249 / 10000000000000000000000 : ℚ))) + (U' := (5268949329338404219751 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (162258939077249 / 400000000000000 : ℚ)) + (q := (677466076586923 / 1600000000000000 : ℚ)) + (U := (-(8593994276661595780249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_11 : Uω (aρ 11) (bρ 11) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2920,26 +2552,21 @@ lemma U_538_11 : have hlg : Real.log (14712699139499919 / 40000000000000000 : ℝ) ≤ (-(10001684457041864999147 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14712699139499919 / 40000000000000000 : ℝ) = - (14712699139499919 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14712699139499919 / 10000000000000000 : ℚ)) - (U := (3861259148958135000853 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14712699139499919 / 10000000000000000 : ℝ) ≤ - (3861259148958135000853 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3362973715549647 / 10000000000000000 : ℝ)) (q := - (14712699139499919 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14712699139499919 / 40000000000000000 : ℚ)) + (r' := (14712699139499919 / 10000000000000000 : ℚ)) + (U := (-(10001684457041864999147 / 10000000000000000000000 : ℚ))) + (U' := (3861259148958135000853 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (3362973715549647 / 10000000000000000 : ℚ)) + (q := (14712699139499919 / 40000000000000000 : ℚ)) + (U := (-(10001684457041864999147 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_12 : Uω (aρ 12) (bρ 12) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2947,26 +2574,21 @@ lemma U_538_12 : have hlg : Real.log (12078973669071019 / 40000000000000000 : ℝ) ≤ (-(5987066129331995198681 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12078973669071019 / 40000000000000000 : ℝ) = - (12078973669071019 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12078973669071019 / 10000000000000000 : ℚ)) - (U := (944405673668004801319 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12078973669071019 / 10000000000000000 : ℝ) ≤ - (944405673668004801319 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2469811077020197 / 10000000000000000 : ℝ)) (q := - (12078973669071019 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12078973669071019 / 40000000000000000 : ℚ)) + (r' := (12078973669071019 / 10000000000000000 : ℚ)) + (U := (-(5987066129331995198681 / 5000000000000000000000 : ℚ))) + (U' := (944405673668004801319 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (2469811077020197 / 10000000000000000 : ℚ)) + (q := (12078973669071019 / 40000000000000000 : ℚ)) + (U := (-(5987066129331995198681 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_13 : Uω (aρ 13) (bρ 13) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -2974,26 +2596,21 @@ lemma U_538_13 : have hlg : Real.log (8521723247589617 / 40000000000000000 : ℝ) ≤ (-(3092521747675457896549 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8521723247589617 / 40000000000000000 : ℝ) = - (8521723247589617 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8521723247589617 / 5000000000000000 : ℚ)) - (U := (1066361334124542103451 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8521723247589617 / 5000000000000000 : ℝ) ≤ - (1066361334124542103451 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17040118873039 / 156250000000000 : ℝ)) (q := - (8521723247589617 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8521723247589617 / 40000000000000000 : ℚ)) + (r' := (8521723247589617 / 5000000000000000 : ℚ)) + (U := (-(3092521747675457896549 / 2000000000000000000000 : ℚ))) + (U' := (1066361334124542103451 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (3934698871581 / 6400000000000 : ℚ)) + (s := (17040118873039 / 156250000000000 : ℚ)) + (q := (8521723247589617 / 40000000000000000 : ℚ)) + (U := (-(3092521747675457896549 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_538_14 : Uω (aρ 14) (bρ 14) (3934698871581 / 6400000000000 : ℝ) ≤ @@ -3099,25 +2716,21 @@ lemma U_539_1 : have hlg : Real.log (48753536680735983 / 80000000000000000 : ℝ) ≤ (-(39619911384348771533 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48753536680735983 / 80000000000000000 : ℝ) = - (48753536680735983 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48753536680735983 / 40000000000000000 : ℚ)) - (U := (15831863039651228467 / 80000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48753536680735983 / 40000000000000000 : ℝ) ≤ - (15831863039651228467 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6094165556902277 / 10000000000000000 : ℝ)) (q := - (48753536680735983 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48753536680735983 / 80000000000000000 : ℚ)) + (r' := (48753536680735983 / 40000000000000000 : ℚ)) + (U := (-(39619911384348771533 / 80000000000000000000 : ℚ))) + (U' := (15831863039651228467 / 80000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (6094165556902277 / 10000000000000000 : ℚ)) + (q := (48753536680735983 / 80000000000000000 : ℚ)) + (U := (-(39619911384348771533 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_2 : Uω (aρ 2) (bρ 2) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3125,25 +2738,21 @@ lemma U_539_2 : have hlg : Real.log (48562198613169711 / 80000000000000000 : ℝ) ≤ (-(4991812124691438887987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48562198613169711 / 80000000000000000 : ℝ) = - (48562198613169711 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48562198613169711 / 40000000000000000 : ℚ)) - (U := (1939659678308561112013 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48562198613169711 / 40000000000000000 : ℝ) ≤ - (1939659678308561112013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6070100052520709 / 10000000000000000 : ℝ)) (q := - (48562198613169711 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48562198613169711 / 80000000000000000 : ℚ)) + (r' := (48562198613169711 / 40000000000000000 : ℚ)) + (U := (-(4991812124691438887987 / 10000000000000000000000 : ℚ))) + (U' := (1939659678308561112013 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (6070100052520709 / 10000000000000000 : ℚ)) + (q := (48562198613169711 / 80000000000000000 : ℚ)) + (U := (-(4991812124691438887987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_3 : Uω (aρ 3) (bρ 3) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3151,25 +2760,21 @@ lemma U_539_3 : have hlg : Real.log (48179514278362183 / 80000000000000000 : ℝ) ≤ (-(2535463593367915656409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48179514278362183 / 80000000000000000 : ℝ) = - (48179514278362183 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48179514278362183 / 40000000000000000 : ℚ)) - (U := (930272308132084343591 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48179514278362183 / 40000000000000000 : ℝ) ≤ - (930272308132084343591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6021825075168827 / 10000000000000000 : ℝ)) (q := - (48179514278362183 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48179514278362183 / 80000000000000000 : ℚ)) + (r' := (48179514278362183 / 40000000000000000 : ℚ)) + (U := (-(2535463593367915656409 / 5000000000000000000000 : ℚ))) + (U' := (930272308132084343591 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (6021825075168827 / 10000000000000000 : ℚ)) + (q := (48179514278362183 / 80000000000000000 : ℚ)) + (U := (-(2535463593367915656409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_4 : Uω (aρ 4) (bρ 4) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3177,25 +2782,21 @@ lemma U_539_4 : have hlg : Real.log (47543912570052419 / 80000000000000000 : ℝ) ≤ (-(162616523524473707163 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47543912570052419 / 80000000000000000 : ℝ) = - (47543912570052419 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47543912570052419 / 40000000000000000 : ℚ)) - (U := (53991970319276292837 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47543912570052419 / 40000000000000000 : ℝ) ≤ - (53991970319276292837 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2970609414578193 / 5000000000000000 : ℝ)) (q := - (47543912570052419 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47543912570052419 / 80000000000000000 : ℚ)) + (r' := (47543912570052419 / 40000000000000000 : ℚ)) + (U := (-(162616523524473707163 / 312500000000000000000 : ℚ))) + (U' := (53991970319276292837 / 312500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (2970609414578193 / 5000000000000000 : ℚ)) + (q := (47543912570052419 / 80000000000000000 : ℚ)) + (U := (-(162616523524473707163 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_5 : Uω (aρ 5) (bρ 5) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3203,25 +2804,21 @@ lemma U_539_5 : have hlg : Real.log (46575965032077847 / 80000000000000000 : ℝ) ≤ (-(5409419981822095878167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46575965032077847 / 80000000000000000 : ℝ) = - (46575965032077847 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46575965032077847 / 40000000000000000 : ℚ)) - (U := (1522051821177904121833 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46575965032077847 / 40000000000000000 : ℝ) ≤ - (1522051821177904121833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5817421863997743 / 10000000000000000 : ℝ)) (q := - (46575965032077847 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46575965032077847 / 80000000000000000 : ℚ)) + (r' := (46575965032077847 / 40000000000000000 : ℚ)) + (U := (-(5409419981822095878167 / 10000000000000000000000 : ℚ))) + (U' := (1522051821177904121833 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (5817421863997743 / 10000000000000000 : ℚ)) + (q := (46575965032077847 / 80000000000000000 : ℚ)) + (U := (-(5409419981822095878167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_6 : Uω (aρ 6) (bρ 6) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3229,25 +2826,21 @@ lemma U_539_6 : have hlg : Real.log (45187725538366107 / 80000000000000000 : ℝ) ≤ (-(2856005716701236298161 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45187725538366107 / 80000000000000000 : ℝ) = - (45187725538366107 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45187725538366107 / 40000000000000000 : ℚ)) - (U := (609730184798763701839 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45187725538366107 / 40000000000000000 : ℝ) ≤ - (609730184798763701839 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (352350147856863 / 625000000000000 : ℝ)) (q := - (45187725538366107 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45187725538366107 / 80000000000000000 : ℚ)) + (r' := (45187725538366107 / 40000000000000000 : ℚ)) + (U := (-(2856005716701236298161 / 5000000000000000000000 : ℚ))) + (U' := (609730184798763701839 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (352350147856863 / 625000000000000 : ℚ)) + (q := (45187725538366107 / 80000000000000000 : ℚ)) + (U := (-(2856005716701236298161 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_7 : Uω (aρ 7) (bρ 7) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3255,25 +2848,21 @@ lemma U_539_7 : have hlg : Real.log (43293645120254843 / 80000000000000000 : ℝ) ≤ (-(614020774142777776231 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43293645120254843 / 80000000000000000 : ℝ) = - (43293645120254843 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43293645120254843 / 40000000000000000 : ℚ)) - (U := (79126406157222223769 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43293645120254843 / 40000000000000000 : ℝ) ≤ - (79126406157222223769 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (673467955242749 / 1250000000000000 : ℝ)) (q := - (43293645120254843 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43293645120254843 / 80000000000000000 : ℚ)) + (r' := (43293645120254843 / 40000000000000000 : ℚ)) + (U := (-(614020774142777776231 / 1000000000000000000000 : ℚ))) + (U' := (79126406157222223769 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (673467955242749 / 1250000000000000 : ℚ)) + (q := (43293645120254843 / 80000000000000000 : ℚ)) + (U := (-(614020774142777776231 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_8 : Uω (aρ 8) (bρ 8) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3281,25 +2870,21 @@ lemma U_539_8 : have hlg : Real.log (40821547916674547 / 80000000000000000 : ℝ) ≤ (-(6728165572055259940237 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40821547916674547 / 80000000000000000 : ℝ) = - (40821547916674547 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40821547916674547 / 40000000000000000 : ℚ)) - (U := (203306230944740059763 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40821547916674547 / 40000000000000000 : ℝ) ≤ - (203306230944740059763 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2526630496193459 / 5000000000000000 : ℝ)) (q := - (40821547916674547 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40821547916674547 / 80000000000000000 : ℚ)) + (r' := (40821547916674547 / 40000000000000000 : ℚ)) + (U := (-(6728165572055259940237 / 10000000000000000000000 : ℚ))) + (U' := (203306230944740059763 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (2526630496193459 / 5000000000000000 : ℚ)) + (q := (40821547916674547 / 80000000000000000 : ℚ)) + (U := (-(6728165572055259940237 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_9 : Uω (aρ 9) (bρ 9) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3307,25 +2892,21 @@ lemma U_539_9 : have hlg : Real.log (37720920315265511 / 80000000000000000 : ℝ) ≤ (-(7518117780844264344539 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (37720920315265511 / 80000000000000000 : ℝ) = - (37720920315265511 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37720920315265511 / 20000000000000000 : ℚ)) - (U := (6344825825155735655461 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (37720920315265511 / 20000000000000000 : ℝ) ≤ - (6344825825155735655461 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4619069720394659 / 10000000000000000 : ℝ)) (q := - (37720920315265511 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37720920315265511 / 80000000000000000 : ℚ)) + (r' := (37720920315265511 / 20000000000000000 : ℚ)) + (U := (-(7518117780844264344539 / 10000000000000000000000 : ℚ))) + (U' := (6344825825155735655461 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (4619069720394659 / 10000000000000000 : ℚ)) + (q := (37720920315265511 / 80000000000000000 : ℚ)) + (U := (-(7518117780844264344539 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_10 : Uω (aρ 10) (bρ 10) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3333,26 +2914,21 @@ lemma U_539_10 : have hlg : Real.log (33963050930670051 / 80000000000000000 : ℝ) ≤ (-(8567534377982396619123 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33963050930670051 / 80000000000000000 : ℝ) = - (33963050930670051 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33963050930670051 / 20000000000000000 : ℚ)) - (U := (5295409228017603380877 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33963050930670051 / 20000000000000000 : ℝ) ≤ - (5295409228017603380877 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2034080703870397 / 5000000000000000 : ℝ)) (q := - (33963050930670051 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33963050930670051 / 80000000000000000 : ℚ)) + (r' := (33963050930670051 / 20000000000000000 : ℚ)) + (U := (-(8567534377982396619123 / 10000000000000000000000 : ℚ))) + (U' := (5295409228017603380877 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (2034080703870397 / 5000000000000000 : ℚ)) + (q := (33963050930670051 / 80000000000000000 : ℚ)) + (U := (-(8567534377982396619123 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_11 : Uω (aρ 11) (bρ 11) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3360,26 +2936,21 @@ lemma U_539_11 : have hlg : Real.log (29519420612911899 / 80000000000000000 : ℝ) ≤ (-(1993956523096417586819 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29519420612911899 / 80000000000000000 : ℝ) = - (29519420612911899 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29519420612911899 / 20000000000000000 : ℚ)) - (U := (778632198103582413181 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29519420612911899 / 20000000000000000 : ℝ) ≤ - (778632198103582413181 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (210983153406641 / 625000000000000 : ℝ)) (q := - (29519420612911899 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29519420612911899 / 80000000000000000 : ℚ)) + (r' := (29519420612911899 / 20000000000000000 : ℚ)) + (U := (-(1993956523096417586819 / 2000000000000000000000 : ℚ))) + (U' := (778632198103582413181 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (210983153406641 / 625000000000000 : ℚ)) + (q := (29519420612911899 / 80000000000000000 : ℚ)) + (U := (-(1993956523096417586819 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_12 : Uω (aρ 12) (bρ 12) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3387,26 +2958,21 @@ lemma U_539_12 : have hlg : Real.log (24262983695874167 / 80000000000000000 : ℝ) ≤ (-(745671718695141265711 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24262983695874167 / 80000000000000000 : ℝ) = - (24262983695874167 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24262983695874167 / 20000000000000000 : ℚ)) - (U := (120762256679858734289 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24262983695874167 / 20000000000000000 : ℝ) ≤ - (120762256679858734289 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2485321321931823 / 10000000000000000 : ℝ)) (q := - (24262983695874167 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24262983695874167 / 80000000000000000 : ℚ)) + (r' := (24262983695874167 / 20000000000000000 : ℚ)) + (U := (-(745671718695141265711 / 625000000000000000000 : ℚ))) + (U' := (120762256679858734289 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (2485321321931823 / 10000000000000000 : ℚ)) + (q := (24262983695874167 / 80000000000000000 : ℚ)) + (U := (-(745671718695141265711 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_13 : Uω (aρ 13) (bρ 13) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3414,26 +2980,21 @@ lemma U_539_13 : have hlg : Real.log (17209894999780123 / 80000000000000000 : ℝ) ≤ (-(7682710624029974679527 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17209894999780123 / 80000000000000000 : ℝ) = - (17209894999780123 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17209894999780123 / 10000000000000000 : ℚ)) - (U := (2714497080470025320473 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17209894999780123 / 10000000000000000 : ℝ) ≤ - (2714497080470025320473 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (70089430593957 / 625000000000000 : ℝ)) (q := - (17209894999780123 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17209894999780123 / 80000000000000000 : ℚ)) + (r' := (17209894999780123 / 10000000000000000 : ℚ)) + (U := (-(7682710624029974679527 / 5000000000000000000000 : ℚ))) + (U' := (2714497080470025320473 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39415781320747 / 64000000000000 : ℚ)) + (s := (70089430593957 / 625000000000000 : ℚ)) + (q := (17209894999780123 / 80000000000000000 : ℚ)) + (U := (-(7682710624029974679527 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_539_14 : Uω (aρ 14) (bρ 14) (39415781320747 / 64000000000000 : ℝ) ≤ @@ -3539,25 +3100,21 @@ lemma U_540_1 : have hlg : Real.log (2441976390528499 / 4000000000000000 : ℝ) ≤ (-(4934866533064163862467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2441976390528499 / 4000000000000000 : ℝ) = - (2441976390528499 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2441976390528499 / 2000000000000000 : ℚ)) - (U := (1996605269935836137533 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2441976390528499 / 2000000000000000 : ℝ) ≤ - (1996605269935836137533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (610491449483937 / 1000000000000000 : ℝ)) (q := - (2441976390528499 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2441976390528499 / 4000000000000000 : ℚ)) + (r' := (2441976390528499 / 2000000000000000 : ℚ)) + (U := (-(4934866533064163862467 / 10000000000000000000000 : ℚ))) + (U' := (1996605269935836137533 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (610491449483937 / 1000000000000000 : ℚ)) + (q := (2441976390528499 / 4000000000000000 : ℚ)) + (U := (-(4934866533064163862467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_2 : Uω (aρ 2) (bρ 2) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3565,25 +3122,21 @@ lemma U_540_2 : have hlg : Real.log (3040511990054003 / 5000000000000000 : ℝ) ≤ (-(497411993155784997629 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3040511990054003 / 5000000000000000 : ℝ) = - (3040511990054003 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3040511990054003 / 2500000000000000 : ℚ)) - (U := (195735187144215002371 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3040511990054003 / 2500000000000000 : ℝ) ≤ - (195735187144215002371 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6080849514922887 / 10000000000000000 : ℝ)) (q := - (3040511990054003 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3040511990054003 / 5000000000000000 : ℚ)) + (r' := (3040511990054003 / 2500000000000000 : ℚ)) + (U := (-(497411993155784997629 / 1000000000000000000000 : ℚ))) + (U' := (195735187144215002371 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (6080849514922887 / 10000000000000000 : ℚ)) + (q := (3040511990054003 / 5000000000000000 : ℚ)) + (U := (-(497411993155784997629 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_3 : Uω (aρ 3) (bρ 3) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3591,25 +3144,21 @@ lemma U_540_3 : have hlg : Real.log (377074326482227 / 625000000000000 : ℝ) ≤ (-(631636661234611895621 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (377074326482227 / 625000000000000 : ℝ) = - (377074326482227 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (377074326482227 / 312500000000000 : ℚ)) - (U := (234797314140388104379 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (377074326482227 / 312500000000000 : ℝ) ≤ - (234797314140388104379 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6032576108488139 / 10000000000000000 : ℝ)) (q := - (377074326482227 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (377074326482227 / 625000000000000 : ℚ)) + (r' := (377074326482227 / 312500000000000 : ℚ)) + (U := (-(631636661234611895621 / 1250000000000000000000 : ℚ))) + (U' := (234797314140388104379 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (6032576108488139 / 10000000000000000 : ℚ)) + (q := (377074326482227 / 625000000000000 : ℚ)) + (U := (-(631636661234611895621 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_4 : Uω (aρ 4) (bρ 4) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3617,24 +3166,21 @@ lemma U_540_4 : have hlg : Real.log (29768705563559 / 50000000000000 : ℝ) ≤ (-(648206640404216422783 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29768705563559 / 50000000000000 : ℝ) = (29768705563559 / 25000000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29768705563559 / 25000000000000 : ℚ)) - (U := (218227334970783577217 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (29768705563559 / 25000000000000 : ℝ) ≤ - (218227334970783577217 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (238078962701819 / 400000000000000 : ℝ)) (q := - (29768705563559 / 50000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29768705563559 / 50000000000000 : ℚ)) + (r' := (29768705563559 / 25000000000000 : ℚ)) + (U := (-(648206640404216422783 / 1250000000000000000000 : ℚ))) + (U' := (218227334970783577217 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (238078962701819 / 400000000000000 : ℚ)) + (q := (29768705563559 / 50000000000000 : ℚ)) + (U := (-(648206640404216422783 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_5 : Uω (aρ 5) (bρ 5) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3642,25 +3188,21 @@ lemma U_540_5 : have hlg : Real.log (11665505817747879 / 20000000000000000 : ℝ) ≤ (-(5390960067592240995977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11665505817747879 / 20000000000000000 : ℝ) = - (11665505817747879 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11665505817747879 / 10000000000000000 : ℚ)) - (U := (1540511735407759004023 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11665505817747879 / 10000000000000000 : ℝ) ≤ - (1540511735407759004023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2914093789602377 / 5000000000000000 : ℝ)) (q := - (11665505817747879 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11665505817747879 / 20000000000000000 : ℚ)) + (r' := (11665505817747879 / 10000000000000000 : ℚ)) + (U := (-(5390960067592240995977 / 10000000000000000000000 : ℚ))) + (U' := (1540511735407759004023 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (2914093789602377 / 5000000000000000 : ℚ)) + (q := (11665505817747879 / 20000000000000000 : ℚ)) + (U := (-(5390960067592240995977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_6 : Uω (aρ 6) (bρ 6) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3668,25 +3210,21 @@ lemma U_540_6 : have hlg : Real.log (5659235209713869 / 10000000000000000 : ℝ) ≤ (-(2846481658037417445579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5659235209713869 / 10000000000000000 : ℝ) = - (5659235209713869 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5659235209713869 / 5000000000000000 : ℚ)) - (U := (619254243462582554421 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5659235209713869 / 5000000000000000 : ℝ) ≤ - (619254243462582554421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5648392556024613 / 10000000000000000 : ℝ)) (q := - (5659235209713869 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5659235209713869 / 10000000000000000 : ℚ)) + (r' := (5659235209713869 / 5000000000000000 : ℚ)) + (U := (-(2846481658037417445579 / 5000000000000000000000 : ℚ))) + (U' := (619254243462582554421 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (5648392556024613 / 10000000000000000 : ℚ)) + (q := (5659235209713869 / 10000000000000000 : ℚ)) + (U := (-(2846481658037417445579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_7 : Uω (aρ 7) (bρ 7) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3694,25 +3232,21 @@ lemma U_540_7 : have hlg : Real.log (5422502194449367 / 10000000000000000 : ℝ) ≤ (-(6120277243219995072763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5422502194449367 / 10000000000000000 : ℝ) = - (5422502194449367 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5422502194449367 / 5000000000000000 : ℚ)) - (U := (811194559780004927237 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5422502194449367 / 5000000000000000 : ℝ) ≤ - (811194559780004927237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5398587906255609 / 10000000000000000 : ℝ)) (q := - (5422502194449367 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5422502194449367 / 10000000000000000 : ℚ)) + (r' := (5422502194449367 / 5000000000000000 : ℚ)) + (U := (-(6120277243219995072763 / 10000000000000000000000 : ℚ))) + (U' := (811194559780004927237 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (5398587906255609 / 10000000000000000 : ℚ)) + (q := (5422502194449367 / 10000000000000000 : ℚ)) + (U := (-(6120277243219995072763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_8 : Uω (aρ 8) (bρ 8) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3720,25 +3254,21 @@ lemma U_540_8 : have hlg : Real.log (5113547257128181 / 10000000000000000 : ℝ) ≤ (-(670691749872474504841 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5113547257128181 / 10000000000000000 : ℝ) = - (5113547257128181 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5113547257128181 / 5000000000000000 : ℚ)) - (U := (22455430427525495159 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5113547257128181 / 5000000000000000 : ℝ) ≤ - (22455430427525495159 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5064219682953237 / 10000000000000000 : ℝ)) (q := - (5113547257128181 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5113547257128181 / 10000000000000000 : ℚ)) + (r' := (5113547257128181 / 5000000000000000 : ℚ)) + (U := (-(670691749872474504841 / 1000000000000000000000 : ℚ))) + (U' := (22455430427525495159 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (5064219682953237 / 10000000000000000 : ℚ)) + (q := (5113547257128181 / 10000000000000000 : ℚ)) + (U := (-(670691749872474504841 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_9 : Uω (aρ 9) (bρ 9) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3746,25 +3276,21 @@ lemma U_540_9 : have hlg : Real.log (295380428584411 / 625000000000000 : ℝ) ≤ (-(7494875352599199835211 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (295380428584411 / 625000000000000 : ℝ) = - (295380428584411 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (295380428584411 / 156250000000000 : ℚ)) - (U := (6368068253400800164789 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (295380428584411 / 156250000000000 : ℝ) ≤ - (6368068253400800164789 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4630264511758027 / 10000000000000000 : ℝ)) (q := - (295380428584411 / 625000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (295380428584411 / 625000000000000 : ℚ)) + (r' := (295380428584411 / 156250000000000 : ℚ)) + (U := (-(7494875352599199835211 / 10000000000000000000000 : ℚ))) + (U' := (6368068253400800164789 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (4630264511758027 / 10000000000000000 : ℚ)) + (q := (295380428584411 / 625000000000000 : ℚ)) + (U := (-(7494875352599199835211 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_10 : Uω (aρ 10) (bρ 10) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3772,26 +3298,21 @@ lemma U_540_10 : have hlg : Real.log (4256597171786073 / 10000000000000000 : ℝ) ≤ (-(8541150373580887895981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4256597171786073 / 10000000000000000 : ℝ) = - (4256597171786073 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4256597171786073 / 2500000000000000 : ℚ)) - (U := (5321793232419112104019 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4256597171786073 / 2500000000000000 : ℝ) ≤ - (5321793232419112104019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4079844174124021 / 10000000000000000 : ℝ)) (q := - (4256597171786073 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4256597171786073 / 10000000000000000 : ℚ)) + (r' := (4256597171786073 / 2500000000000000 : ℚ)) + (U := (-(8541150373580887895981 / 10000000000000000000000 : ℚ))) + (U' := (5321793232419112104019 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (4079844174124021 / 10000000000000000 : ℚ)) + (q := (4256597171786073 / 10000000000000000 : ℚ)) + (U := (-(8541150373580887895981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_11 : Uω (aρ 11) (bρ 11) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3799,26 +3320,21 @@ lemma U_540_11 : have hlg : Real.log (7403346808122357 / 20000000000000000 : ℝ) ≤ (-(397520041479983402797 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7403346808122357 / 20000000000000000 : ℝ) = - (7403346808122357 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7403346808122357 / 5000000000000000 : ℚ)) - (U := (156997702760016597203 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7403346808122357 / 5000000000000000 : ℝ) ≤ - (156997702760016597203 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (26472447381869 / 78125000000000 : ℝ)) (q := - (7403346808122357 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7403346808122357 / 20000000000000000 : ℚ)) + (r' := (7403346808122357 / 5000000000000000 : ℚ)) + (U := (-(397520041479983402797 / 400000000000000000000 : ℚ))) + (U' := (156997702760016597203 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (26472447381869 / 78125000000000 : ℚ)) + (q := (7403346808122357 / 20000000000000000 : ℚ)) + (U := (-(397520041479983402797 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_12 : Uω (aρ 12) (bρ 12) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3826,26 +3342,21 @@ lemma U_540_12 : have hlg : Real.log (3045977508758077 / 10000000000000000 : ℝ) ≤ (-(475505288755951282507 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3045977508758077 / 10000000000000000 : ℝ) = - (3045977508758077 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3045977508758077 / 2500000000000000 : ℚ)) - (U := (79012455484048717493 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3045977508758077 / 2500000000000000 : ℝ) ≤ - (79012455484048717493 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2500781570958029 / 10000000000000000 : ℝ)) (q := - (3045977508758077 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3045977508758077 / 10000000000000000 : ℚ)) + (r' := (3045977508758077 / 2500000000000000 : ℚ)) + (U := (-(475505288755951282507 / 400000000000000000000 : ℚ))) + (U' := (79012455484048717493 / 400000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (2500781570958029 / 10000000000000000 : ℚ)) + (q := (3045977508758077 / 10000000000000000 : ℚ)) + (U := (-(475505288755951282507 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_13 : Uω (aρ 13) (bρ 13) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3853,26 +3364,21 @@ lemma U_540_13 : have hlg : Real.log (2171679633044277 / 10000000000000000 : ℝ) ≤ (-(7635420998099539770937 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2171679633044277 / 10000000000000000 : ℝ) = - (2171679633044277 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2171679633044277 / 1250000000000000 : ℚ)) - (U := (2761786706400460229063 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2171679633044277 / 1250000000000000 : ℝ) ≤ - (2761786706400460229063 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1151567561125429 / 10000000000000000 : ℝ)) (q := - (2171679633044277 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2171679633044277 / 10000000000000000 : ℚ)) + (r' := (2171679633044277 / 1250000000000000 : ℚ)) + (U := (-(7635420998099539770937 / 5000000000000000000000 : ℚ))) + (U' := (2761786706400460229063 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (9871143481421 / 16000000000000 : ℚ)) + (s := (1151567561125429 / 10000000000000000 : ℚ)) + (q := (2171679633044277 / 10000000000000000 : ℚ)) + (U := (-(7635420998099539770937 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_540_14 : Uω (aρ 14) (bρ 14) (9871143481421 / 16000000000000 : ℝ) ≤ @@ -3978,25 +3484,21 @@ lemma U_541_1 : have hlg : Real.log (48925518939090473 / 80000000000000000 : ℝ) ≤ (-(4917275143594234884783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48925518939090473 / 80000000000000000 : ℝ) = - (48925518939090473 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48925518939090473 / 40000000000000000 : ℚ)) - (U := (2014196659405765115217 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48925518939090473 / 40000000000000000 : ℝ) ≤ - (2014196659405765115217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6115663432448087 / 10000000000000000 : ℝ)) (q := - (48925518939090473 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48925518939090473 / 80000000000000000 : ℚ)) + (r' := (48925518939090473 / 40000000000000000 : ℚ)) + (U := (-(4917275143594234884783 / 10000000000000000000000 : ℚ))) + (U' := (2014196659405765115217 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (6115663432448087 / 10000000000000000 : ℚ)) + (q := (48925518939090473 / 80000000000000000 : ℚ)) + (U := (-(4917275143594234884783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_2 : Uω (aρ 2) (bρ 2) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4004,25 +3506,21 @@ lemma U_541_2 : have hlg : Real.log (48734185059835957 / 80000000000000000 : ℝ) ≤ (-(77444671661105992217 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48734185059835957 / 80000000000000000 : ℝ) = - (48734185059835957 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48734185059835957 / 40000000000000000 : ℚ)) - (U := (30859575260769007783 / 156250000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48734185059835957 / 40000000000000000 : ℝ) ≤ - (30859575260769007783 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3045799487572229 / 5000000000000000 : ℝ)) (q := - (48734185059835957 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48734185059835957 / 80000000000000000 : ℚ)) + (r' := (48734185059835957 / 40000000000000000 : ℚ)) + (U := (-(77444671661105992217 / 156250000000000000000 : ℚ))) + (U' := (30859575260769007783 / 156250000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (3045799487572229 / 5000000000000000 : ℚ)) + (q := (48734185059835957 / 80000000000000000 : ℚ)) + (U := (-(77444671661105992217 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_3 : Uω (aρ 3) (bρ 3) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4030,25 +3528,21 @@ lemma U_541_3 : have hlg : Real.log (48351513269940257 / 80000000000000000 : ℝ) ≤ (-(2517645573818314008889 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48351513269940257 / 80000000000000000 : ℝ) = - (48351513269940257 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48351513269940257 / 40000000000000000 : ℚ)) - (U := (948090327681685991111 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48351513269940257 / 40000000000000000 : ℝ) ≤ - (948090327681685991111 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6043327134020533 / 10000000000000000 : ℝ)) (q := - (48351513269940257 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48351513269940257 / 80000000000000000 : ℚ)) + (r' := (48351513269940257 / 40000000000000000 : ℚ)) + (U := (-(2517645573818314008889 / 5000000000000000000000 : ℚ))) + (U' := (948090327681685991111 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (6043327134020533 / 10000000000000000 : ℚ)) + (q := (48351513269940257 / 80000000000000000 : ℚ)) + (U := (-(2517645573818314008889 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_4 : Uω (aρ 4) (bρ 4) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4056,25 +3550,21 @@ lemma U_541_4 : have hlg : Real.log (47715945141100593 / 80000000000000000 : ℝ) ≤ (-(2583805063455020443923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47715945141100593 / 80000000000000000 : ℝ) = - (47715945141100593 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47715945141100593 / 40000000000000000 : ℚ)) - (U := (881930838044979556077 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47715945141100593 / 40000000000000000 : ℝ) ≤ - (881930838044979556077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5962729282875617 / 10000000000000000 : ℝ)) (q := - (47715945141100593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47715945141100593 / 80000000000000000 : ℚ)) + (r' := (47715945141100593 / 40000000000000000 : ℚ)) + (U := (-(2583805063455020443923 / 5000000000000000000000 : ℚ))) + (U' := (881930838044979556077 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (5962729282875617 / 10000000000000000 : ℚ)) + (q := (47715945141100593 / 80000000000000000 : ℚ)) + (U := (-(2583805063455020443923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_5 : Uω (aρ 5) (bρ 5) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4082,25 +3572,21 @@ lemma U_541_5 : have hlg : Real.log (46748081261254197 / 80000000000000000 : ℝ) ≤ (-(83945847197113369509 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46748081261254197 / 80000000000000000 : ℝ) = - (46748081261254197 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46748081261254197 / 40000000000000000 : ℚ)) - (U := (24358399724761630491 / 156250000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46748081261254197 / 40000000000000000 : ℝ) ≤ - (24358399724761630491 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2919476616124509 / 5000000000000000 : ℝ)) (q := - (46748081261254197 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46748081261254197 / 80000000000000000 : ℚ)) + (r' := (46748081261254197 / 40000000000000000 : ℚ)) + (U := (-(83945847197113369509 / 156250000000000000000 : ℚ))) + (U' := (24358399724761630491 / 156250000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (2919476616124509 / 5000000000000000 : ℚ)) + (q := (46748081261254197 / 80000000000000000 : ℚ)) + (U := (-(83945847197113369509 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_6 : Uω (aρ 6) (bρ 6) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4108,25 +3594,21 @@ lemma U_541_6 : have hlg : Real.log (45360037187602009 / 80000000000000000 : ℝ) ≤ (-(354621971976424965729 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45360037187602009 / 80000000000000000 : ℝ) = - (45360037187602009 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45360037187602009 / 40000000000000000 : ℚ)) - (U := (78595015711075034271 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45360037187602009 / 40000000000000000 : ℝ) ≤ - (78595015711075034271 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5659182588975971 / 10000000000000000 : ℝ)) (q := - (45360037187602009 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45360037187602009 / 80000000000000000 : ℚ)) + (r' := (45360037187602009 / 40000000000000000 : ℚ)) + (U := (-(354621971976424965729 / 625000000000000000000 : ℚ))) + (U' := (78595015711075034271 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (5659182588975971 / 10000000000000000 : ℚ)) + (q := (45360037187602009 / 80000000000000000 : ℚ)) + (U := (-(354621971976424965729 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_7 : Uω (aρ 7) (bρ 7) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4134,25 +3616,21 @@ lemma U_541_7 : have hlg : Real.log (43466388467366593 / 80000000000000000 : ℝ) ≤ (-(3050193369503106150261 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43466388467366593 / 80000000000000000 : ℝ) = - (43466388467366593 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43466388467366593 / 40000000000000000 : ℚ)) - (U := (415542531996893849739 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43466388467366593 / 40000000000000000 : ℝ) ≤ - (415542531996893849739 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5409431789677117 / 10000000000000000 : ℝ)) (q := - (43466388467366593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43466388467366593 / 80000000000000000 : ℚ)) + (r' := (43466388467366593 / 40000000000000000 : ℚ)) + (U := (-(3050193369503106150261 / 5000000000000000000000 : ℚ))) + (U' := (415542531996893849739 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (5409431789677117 / 10000000000000000 : ℚ)) + (q := (43466388467366593 / 80000000000000000 : ℚ)) + (U := (-(3050193369503106150261 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_8 : Uω (aρ 8) (bρ 8) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4160,25 +3638,21 @@ lemma U_541_8 : have hlg : Real.log (40995204607164973 / 80000000000000000 : ℝ) ≤ (-(3342857676754653328359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40995204607164973 / 80000000000000000 : ℝ) = - (40995204607164973 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40995204607164973 / 40000000000000000 : ℚ)) - (U := (122878224745346671641 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (40995204607164973 / 40000000000000000 : ℝ) ≤ - (122878224745346671641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (634397184495839 / 1250000000000000 : ℝ)) (q := - (40995204607164973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40995204607164973 / 80000000000000000 : ℚ)) + (r' := (40995204607164973 / 40000000000000000 : ℚ)) + (U := (-(3342857676754653328359 / 5000000000000000000000 : ℚ))) + (U' := (122878224745346671641 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (634397184495839 / 1250000000000000 : ℚ)) + (q := (40995204607164973 / 80000000000000000 : ℚ)) + (U := (-(3342857676754653328359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_9 : Uω (aρ 9) (bρ 9) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4186,25 +3660,21 @@ lemma U_541_9 : have hlg : Real.log (1515858438762001 / 3200000000000000 : ℝ) ≤ (-(116745141336085632999 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1515858438762001 / 3200000000000000 : ℝ) = - (1515858438762001 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1515858438762001 / 800000000000000 : ℚ)) - (U := (99863352507664367001 / 156250000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1515858438762001 / 800000000000000 : ℝ) ≤ - (99863352507664367001 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (185658287791919 / 400000000000000 : ℝ)) (q := - (1515858438762001 / 3200000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1515858438762001 / 3200000000000000 : ℚ)) + (r' := (1515858438762001 / 800000000000000 : ℚ)) + (U := (-(116745141336085632999 / 156250000000000000000 : ℚ))) + (U' := (99863352507664367001 / 156250000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (185658287791919 / 400000000000000 : ℚ)) + (q := (1515858438762001 / 3200000000000000 : ℚ)) + (U := (-(116745141336085632999 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_10 : Uω (aρ 10) (bρ 10) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4212,26 +3682,21 @@ lemma U_541_10 : have hlg : Real.log (34142483337157277 / 80000000000000000 : ℝ) ≤ (-(8514841796218230196619 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34142483337157277 / 80000000000000000 : ℝ) = - (34142483337157277 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34142483337157277 / 20000000000000000 : ℚ)) - (U := (5348101809781769803381 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34142483337157277 / 20000000000000000 : ℝ) ≤ - (5348101809781769803381 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1022880455079947 / 2500000000000000 : ℝ)) (q := - (34142483337157277 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34142483337157277 / 80000000000000000 : ℚ)) + (r' := (34142483337157277 / 20000000000000000 : ℚ)) + (U := (-(8514841796218230196619 / 10000000000000000000000 : ℚ))) + (U' := (5348101809781769803381 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (1022880455079947 / 2500000000000000 : ℚ)) + (q := (34142483337157277 / 80000000000000000 : ℚ)) + (U := (-(8514841796218230196619 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_11 : Uω (aρ 11) (bρ 11) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4239,26 +3704,21 @@ lemma U_541_11 : have hlg : Real.log (1188291950557753 / 3200000000000000 : ℝ) ≤ (-(9906338689090923457797 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1188291950557753 / 3200000000000000 : ℝ) = - (1188291950557753 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1188291950557753 / 800000000000000 : ℚ)) - (U := (3956604916909076542203 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1188291950557753 / 800000000000000 : ℝ) ≤ - (3956604916909076542203 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (136048092128857 / 400000000000000 : ℝ)) (q := - (1188291950557753 / 3200000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1188291950557753 / 3200000000000000 : ℚ)) + (r' := (1188291950557753 / 800000000000000 : ℚ)) + (U := (-(9906338689090923457797 / 10000000000000000000000 : ℚ))) + (U' := (3956604916909076542203 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (136048092128857 / 400000000000000 : ℚ)) + (q := (1188291950557753 / 3200000000000000 : ℚ)) + (U := (-(9906338689090923457797 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_12 : Uω (aρ 12) (bρ 12) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4266,26 +3726,21 @@ lemma U_541_12 : have hlg : Real.log (24472460146992109 / 80000000000000000 : ℝ) ≤ (-(2368956448966278179891 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24472460146992109 / 80000000000000000 : ℝ) = - (24472460146992109 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24472460146992109 / 20000000000000000 : ℚ)) - (U := (403632272233721820109 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24472460146992109 / 20000000000000000 : ℝ) ≤ - (403632272233721820109 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (157262046604281 / 625000000000000 : ℝ)) (q := - (24472460146992109 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24472460146992109 / 80000000000000000 : ℚ)) + (r' := (24472460146992109 / 20000000000000000 : ℚ)) + (U := (-(2368956448966278179891 / 2000000000000000000000 : ℚ))) + (U' := (403632272233721820109 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (157262046604281 / 625000000000000 : ℚ)) + (q := (24472460146992109 / 80000000000000000 : ℚ)) + (U := (-(2368956448966278179891 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_13 : Uω (aρ 13) (bρ 13) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4293,26 +3748,21 @@ lemma U_541_13 : have hlg : Real.log (17534295186849661 / 80000000000000000 : ℝ) ≤ (-(15178679457575972544311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17534295186849661 / 80000000000000000 : ℝ) = - (17534295186849661 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17534295186849661 / 10000000000000000 : ℚ)) - (U := (5615735951424027455689 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17534295186849661 / 10000000000000000 : ℝ) ≤ - (5615735951424027455689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (295258311806971 / 2500000000000000 : ℝ)) (q := - (17534295186849661 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17534295186849661 / 80000000000000000 : ℚ)) + (r' := (17534295186849661 / 10000000000000000 : ℚ)) + (U := (-(15178679457575972544311 / 10000000000000000000000 : ℚ))) + (U' := (5615735951424027455689 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39553366530621 / 64000000000000 : ℚ)) + (s := (295258311806971 / 2500000000000000 : ℚ)) + (q := (17534295186849661 / 80000000000000000 : ℚ)) + (U := (-(15178679457575972544311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_541_14 : Uω (aρ 14) (bρ 14) (39553366530621 / 64000000000000 : ℝ) ≤ @@ -4418,25 +3868,21 @@ lemma U_542_1 : have hlg : Real.log (24505755033152193 / 40000000000000000 : ℝ) ≤ (-(195988585830199645053 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24505755033152193 / 40000000000000000 : ℝ) = - (24505755033152193 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24505755033152193 / 20000000000000000 : ℚ)) - (U := (81270286289800354947 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24505755033152193 / 20000000000000000 : ℝ) ≤ - (81270286289800354947 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6126412369730159 / 10000000000000000 : ℝ)) (q := - (24505755033152193 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24505755033152193 / 40000000000000000 : ℚ)) + (r' := (24505755033152193 / 20000000000000000 : ℚ)) + (U := (-(195988585830199645053 / 400000000000000000000 : ℚ))) + (U' := (81270286289800354947 / 400000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (6126412369730159 / 10000000000000000 : ℚ)) + (q := (24505755033152193 / 40000000000000000 : ℚ)) + (U := (-(195988585830199645053 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_2 : Uω (aρ 2) (bρ 2) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4444,25 +3890,21 @@ lemma U_542_2 : have hlg : Real.log (24410089135065761 / 40000000000000000 : ℝ) ≤ (-(617353647344841031591 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24410089135065761 / 40000000000000000 : ℝ) = - (24410089135065761 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24410089135065761 / 20000000000000000 : ℚ)) - (U := (249080328030158968409 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24410089135065761 / 20000000000000000 : ℝ) ≤ - (249080328030158968409 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6102348433196943 / 10000000000000000 : ℝ)) (q := - (24410089135065761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24410089135065761 / 40000000000000000 : ℚ)) + (r' := (24410089135065761 / 20000000000000000 : ℚ)) + (U := (-(617353647344841031591 / 1250000000000000000000 : ℚ))) + (U' := (249080328030158968409 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (6102348433196943 / 10000000000000000 : ℚ)) + (q := (24410089135065761 / 40000000000000000 : ℚ)) + (U := (-(617353647344841031591 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_3 : Uω (aρ 3) (bρ 3) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4470,25 +3912,21 @@ lemma U_542_3 : have hlg : Real.log (24218756359586867 / 40000000000000000 : ℝ) ≤ (-(5017520647110118038431 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24218756359586867 / 40000000000000000 : ℝ) = - (24218756359586867 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24218756359586867 / 20000000000000000 : ℚ)) - (U := (1913951155889881961569 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24218756359586867 / 20000000000000000 : ℝ) ≤ - (1913951155889881961569 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (756759768975937 / 1250000000000000 : ℝ)) (q := - (24218756359586867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24218756359586867 / 40000000000000000 : ℚ)) + (r' := (24218756359586867 / 20000000000000000 : ℚ)) + (U := (-(5017520647110118038431 / 10000000000000000000000 : ℚ))) + (U' := (1913951155889881961569 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (756759768975937 / 1250000000000000 : ℚ)) + (q := (24218756359586867 / 40000000000000000 : ℚ)) + (U := (-(5017520647110118038431 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_4 : Uω (aρ 4) (bρ 4) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4496,25 +3934,21 @@ lemma U_542_4 : have hlg : Real.log (23900980644384603 / 40000000000000000 : ℝ) ≤ (-(514959964612481159213 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23900980644384603 / 40000000000000000 : ℝ) = - (23900980644384603 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23900980644384603 / 20000000000000000 : ℚ)) - (U := (178187215687518840787 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23900980644384603 / 20000000000000000 : ℝ) ≤ - (178187215687518840787 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1493371118817841 / 2500000000000000 : ℝ)) (q := - (23900980644384603 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23900980644384603 / 40000000000000000 : ℚ)) + (r' := (23900980644384603 / 20000000000000000 : ℚ)) + (U := (-(514959964612481159213 / 1000000000000000000000 : ℚ))) + (U' := (178187215687518840787 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (1493371118817841 / 2500000000000000 : ℚ)) + (q := (23900980644384603 / 40000000000000000 : ℚ)) + (U := (-(514959964612481159213 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_5 : Uω (aρ 5) (bρ 5) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4522,25 +3956,21 @@ lemma U_542_5 : have hlg : Real.log (23417069502119359 / 40000000000000000 : ℝ) ≤ (-(1070828463037465693711 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23417069502119359 / 40000000000000000 : ℝ) = - (23417069502119359 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23417069502119359 / 20000000000000000 : ℚ)) - (U := (315465897562534306289 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23417069502119359 / 20000000000000000 : ℝ) ≤ - (315465897562534306289 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2924859411736871 / 5000000000000000 : ℝ)) (q := - (23417069502119359 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23417069502119359 / 40000000000000000 : ℚ)) + (r' := (23417069502119359 / 20000000000000000 : ℚ)) + (U := (-(1070828463037465693711 / 2000000000000000000000 : ℚ))) + (U' := (315465897562534306289 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (2924859411736871 / 5000000000000000 : ℚ)) + (q := (23417069502119359 / 40000000000000000 : ℚ)) + (U := (-(1070828463037465693711 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_6 : Uω (aρ 6) (bρ 6) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4548,25 +3978,21 @@ lemma U_542_6 : have hlg : Real.log (22723096035816431 / 40000000000000000 : ℝ) ≤ (-(565497600102780771467 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22723096035816431 / 40000000000000000 : ℝ) = - (22723096035816431 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22723096035816431 / 20000000000000000 : ℚ)) - (U := (127649580197219228533 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22723096035816431 / 20000000000000000 : ℝ) ≤ - (127649580197219228533 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2834986232731139 / 5000000000000000 : ℝ)) (q := - (22723096035816431 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22723096035816431 / 40000000000000000 : ℚ)) + (r' := (22723096035816431 / 20000000000000000 : ℚ)) + (U := (-(565497600102780771467 / 1000000000000000000000 : ℚ))) + (U' := (127649580197219228533 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (2834986232731139 / 5000000000000000 : ℚ)) + (q := (22723096035816431 / 40000000000000000 : ℚ)) + (U := (-(565497600102780771467 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_7 : Uω (aρ 7) (bρ 7) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4574,25 +4000,21 @@ lemma U_542_7 : have hlg : Real.log (21776378932357017 / 40000000000000000 : ℝ) ≤ (-(6080536067205933051063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21776378932357017 / 40000000000000000 : ℝ) = - (21776378932357017 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21776378932357017 / 20000000000000000 : ℚ)) - (U := (850935735794066948937 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21776378932357017 / 20000000000000000 : ℝ) ≤ - (850935735794066948937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5420275294492571 / 10000000000000000 : ℝ)) (q := - (21776378932357017 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21776378932357017 / 40000000000000000 : ℚ)) + (r' := (21776378932357017 / 20000000000000000 : ℚ)) + (U := (-(6080536067205933051063 / 10000000000000000000000 : ℚ))) + (U' := (850935735794066948937 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (5420275294492571 / 10000000000000000 : ℚ)) + (q := (21776378932357017 / 40000000000000000 : ℚ)) + (U := (-(6080536067205933051063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_8 : Uω (aρ 8) (bρ 8) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4600,25 +4022,21 @@ lemma U_542_8 : have hlg : Real.log (20541013795148927 / 40000000000000000 : ℝ) ≤ (-(6664558934562687843943 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20541013795148927 / 40000000000000000 : ℝ) = - (20541013795148927 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20541013795148927 / 20000000000000000 : ℚ)) - (U := (266912868437312156057 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20541013795148927 / 20000000000000000 : ℝ) ≤ - (266912868437312156057 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2543067188614263 / 5000000000000000 : ℝ)) (q := - (20541013795148927 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20541013795148927 / 40000000000000000 : ℚ)) + (r' := (20541013795148927 / 20000000000000000 : ℚ)) + (U := (-(6664558934562687843943 / 10000000000000000000000 : ℚ))) + (U' := (266912868437312156057 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (2543067188614263 / 5000000000000000 : ℚ)) + (q := (20541013795148927 / 40000000000000000 : ℚ)) + (U := (-(6664558934562687843943 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_9 : Uω (aρ 9) (bρ 9) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4626,25 +4044,21 @@ lemma U_542_9 : have hlg : Real.log (18992109353432327 / 40000000000000000 : ℝ) ≤ (-(1862139644687844223167 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18992109353432327 / 40000000000000000 : ℝ) = - (18992109353432327 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18992109353432327 / 10000000000000000 : ℚ)) - (U := (1603596256812155776833 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18992109353432327 / 10000000000000000 : ℝ) ≤ - (1603596256812155776833 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2326323892365113 / 5000000000000000 : ℝ)) (q := - (18992109353432327 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18992109353432327 / 40000000000000000 : ℚ)) + (r' := (18992109353432327 / 10000000000000000 : ℚ)) + (U := (-(1862139644687844223167 / 2500000000000000000000 : ℚ))) + (U' := (1603596256812155776833 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (2326323892365113 / 5000000000000000 : ℚ)) + (q := (18992109353432327 / 40000000000000000 : ℚ)) + (U := (-(1862139644687844223167 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_10 : Uω (aρ 10) (bρ 10) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4652,26 +4066,21 @@ lemma U_542_10 : have hlg : Real.log (17116084497070053 / 40000000000000000 : ℝ) ≤ (-(8488608183216975225863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17116084497070053 / 40000000000000000 : ℝ) = - (17116084497070053 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17116084497070053 / 10000000000000000 : ℚ)) - (U := (5374335422783024774137 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17116084497070053 / 10000000000000000 : ℝ) ≤ - (5374335422783024774137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4103194390044089 / 10000000000000000 : ℝ)) (q := - (17116084497070053 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17116084497070053 / 40000000000000000 : ℚ)) + (r' := (17116084497070053 / 10000000000000000 : ℚ)) + (U := (-(8488608183216975225863 / 10000000000000000000000 : ℚ))) + (U' := (5374335422783024774137 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (4103194390044089 / 10000000000000000 : ℚ)) + (q := (17116084497070053 / 40000000000000000 : ℚ)) + (U := (-(8488608183216975225863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_11 : Uω (aρ 11) (bρ 11) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4679,26 +4088,21 @@ lemma U_542_11 : have hlg : Real.log (14900577911737607 / 40000000000000000 : ℝ) ≤ (-(4937397276860661833359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14900577911737607 / 40000000000000000 : ℝ) = - (14900577911737607 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14900577911737607 / 10000000000000000 : ℚ)) - (U := (1994074526139338166641 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14900577911737607 / 10000000000000000 : ℝ) ≤ - (1994074526139338166641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1706958861791433 / 5000000000000000 : ℝ)) (q := - (14900577911737607 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14900577911737607 / 40000000000000000 : ℚ)) + (r' := (14900577911737607 / 10000000000000000 : ℚ)) + (U := (-(4937397276860661833359 / 5000000000000000000000 : ℚ))) + (U' := (1994074526139338166641 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (1706958861791433 / 5000000000000000 : ℚ)) + (q := (14900577911737607 / 40000000000000000 : ℚ)) + (U := (-(4937397276860661833359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_12 : Uω (aρ 12) (bρ 12) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4706,26 +4110,21 @@ lemma U_542_12 : have hlg : Real.log (12288453755806303 / 40000000000000000 : ℝ) ≤ (-(2950548377821138222619 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12288453755806303 / 40000000000000000 : ℝ) = - (12288453755806303 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12288453755806303 / 10000000000000000 : ℚ)) - (U := (515187523678861777381 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12288453755806303 / 10000000000000000 : ℝ) ≤ - (515187523678861777381 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1265777871151107 / 5000000000000000 : ℝ)) (q := - (12288453755806303 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12288453755806303 / 40000000000000000 : ℚ)) + (r' := (12288453755806303 / 10000000000000000 : ℚ)) + (U := (-(2950548377821138222619 / 2500000000000000000000 : ℚ))) + (U' := (515187523678861777381 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (1265777871151107 / 5000000000000000 : ℚ)) + (q := (12288453755806303 / 40000000000000000 : ℚ)) + (U := (-(2950548377821138222619 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_13 : Uω (aρ 13) (bρ 13) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4733,26 +4132,21 @@ lemma U_542_13 : have hlg : Real.log (8846332733846867 / 40000000000000000 : ℝ) ≤ (-(15088764605498135512977 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8846332733846867 / 40000000000000000 : ℝ) = - (8846332733846867 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8846332733846867 / 5000000000000000 : ℚ)) - (U := (5705650803501864487023 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8846332733846867 / 5000000000000000 : ℝ) ≤ - (5705650803501864487023 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (151234621614687 / 1250000000000000 : ℝ)) (q := - (8846332733846867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8846332733846867 / 40000000000000000 : ℚ)) + (r' := (8846332733846867 / 5000000000000000 : ℚ)) + (U := (-(15088764605498135512977 / 10000000000000000000000 : ℚ))) + (U' := (5705650803501864487023 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19811079567779 / 32000000000000 : ℚ)) + (s := (151234621614687 / 1250000000000000 : ℚ)) + (q := (8846332733846867 / 40000000000000000 : ℚ)) + (U := (-(15088764605498135512977 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_542_14 : Uω (aρ 14) (bρ 14) (19811079567779 / 32000000000000 : ℝ) ≤ @@ -4860,25 +4254,21 @@ lemma U_543_1 : have hlg : Real.log (1963900047688743 / 3200000000000000 : ℝ) ≤ (-(195287397249608713577 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1963900047688743 / 3200000000000000 : ℝ) = - (1963900047688743 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1963900047688743 / 1600000000000000 : ℚ)) - (U := (81971474870391286423 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1963900047688743 / 1600000000000000 : ℝ) ≤ - (81971474870391286423 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61371613066873 / 100000000000000 : ℝ)) (q := - (1963900047688743 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1963900047688743 / 3200000000000000 : ℚ)) + (r' := (1963900047688743 / 1600000000000000 : ℚ)) + (U := (-(195287397249608713577 / 400000000000000000000 : ℚ))) + (U' := (81971474870391286423 / 400000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (61371613066873 / 100000000000000 : ℚ)) + (q := (1963900047688743 / 3200000000000000 : ℚ)) + (U := (-(195287397249608713577 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_2 : Uω (aρ 2) (bρ 2) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -4886,25 +4276,21 @@ lemma U_543_2 : have hlg : Real.log (48906171471796523 / 80000000000000000 : ℝ) ≤ (-(492123039929203977663 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48906171471796523 / 80000000000000000 : ℝ) = - (48906171471796523 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48906171471796523 / 40000000000000000 : ℚ)) - (U := (201024140370796022337 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48906171471796523 / 40000000000000000 : ℝ) ≤ - (201024140370796022337 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6113097889091787 / 10000000000000000 : ℝ)) (q := - (48906171471796523 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48906171471796523 / 80000000000000000 : ℚ)) + (r' := (48906171471796523 / 40000000000000000 : ℚ)) + (U := (-(492123039929203977663 / 1000000000000000000000 : ℚ))) + (U' := (201024140370796022337 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (6113097889091787 / 10000000000000000 : ℚ)) + (q := (48906171471796523 / 80000000000000000 : ℚ)) + (U := (-(492123039929203977663 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_3 : Uω (aρ 3) (bρ 3) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -4912,25 +4298,21 @@ lemma U_543_3 : have hlg : Real.log (48523512137590243 / 80000000000000000 : ℝ) ≤ (-(4999781675993666482479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48523512137590243 / 80000000000000000 : ℝ) = - (48523512137590243 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48523512137590243 / 40000000000000000 : ℚ)) - (U := (1931690127006333517521 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48523512137590243 / 40000000000000000 : ℝ) ≤ - (1931690127006333517521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6064829161890217 / 10000000000000000 : ℝ)) (q := - (48523512137590243 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48523512137590243 / 80000000000000000 : ℚ)) + (r' := (48523512137590243 / 40000000000000000 : ℚ)) + (U := (-(4999781675993666482479 / 10000000000000000000000 : ℚ))) + (U' := (1931690127006333517521 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (6064829161890217 / 10000000000000000 : ℚ)) + (q := (48523512137590243 / 80000000000000000 : ℚ)) + (U := (-(4999781675993666482479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_4 : Uω (aρ 4) (bρ 4) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -4938,25 +4320,21 @@ lemma U_543_4 : have hlg : Real.log (47887977345194867 / 80000000000000000 : ℝ) ≤ (-(2565810781913314626317 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47887977345194867 / 80000000000000000 : ℝ) = - (47887977345194867 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47887977345194867 / 40000000000000000 : ℚ)) - (U := (899925119586685373683 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47887977345194867 / 40000000000000000 : ℝ) ≤ - (899925119586685373683 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5984239644856373 / 10000000000000000 : ℝ)) (q := - (47887977345194867 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47887977345194867 / 80000000000000000 : ℚ)) + (r' := (47887977345194867 / 40000000000000000 : ℚ)) + (U := (-(2565810781913314626317 / 5000000000000000000000 : ℚ))) + (U' := (899925119586685373683 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (5984239644856373 / 10000000000000000 : ℚ)) + (q := (47887977345194867 / 80000000000000000 : ℚ)) + (U := (-(2565810781913314626317 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_5 : Uω (aρ 5) (bρ 5) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -4964,25 +4342,21 @@ lemma U_543_5 : have hlg : Real.log (46920196501307823 / 80000000000000000 : ℝ) ≤ (-(5335784226300181600677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46920196501307823 / 80000000000000000 : ℝ) = - (46920196501307823 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46920196501307823 / 40000000000000000 : ℚ)) - (U := (1595687576699818399323 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46920196501307823 / 40000000000000000 : ℝ) ≤ - (1595687576699818399323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1465121088304903 / 2500000000000000 : ℝ)) (q := - (46920196501307823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46920196501307823 / 80000000000000000 : ℚ)) + (r' := (46920196501307823 / 40000000000000000 : ℚ)) + (U := (-(5335784226300181600677 / 10000000000000000000000 : ℚ))) + (U' := (1595687576699818399323 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (1465121088304903 / 2500000000000000 : ℚ)) + (q := (46920196501307823 / 80000000000000000 : ℚ)) + (U := (-(5335784226300181600677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_6 : Uω (aρ 6) (bρ 6) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -4990,25 +4364,21 @@ lemma U_543_6 : have hlg : Real.log (9106469266673947 / 16000000000000000 : ℝ) ≤ (-(2818018263035098048087 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9106469266673947 / 16000000000000000 : ℝ) = - (9106469266673947 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9106469266673947 / 8000000000000000 : ℚ)) - (U := (647717638464901951913 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9106469266673947 / 8000000000000000 : ℝ) ≤ - (647717638464901951913 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (568076218637509 / 1000000000000000 : ℝ)) (q := - (9106469266673947 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9106469266673947 / 16000000000000000 : ℚ)) + (r' := (9106469266673947 / 8000000000000000 : ℚ)) + (U := (-(2818018263035098048087 / 5000000000000000000000 : ℚ))) + (U' := (647717638464901951913 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (568076218637509 / 1000000000000000 : ℚ)) + (q := (9106469266673947 / 16000000000000000 : ℚ)) + (U := (-(2818018263035098048087 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_7 : Uω (aρ 7) (bρ 7) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5016,25 +4386,21 @@ lemma U_543_7 : have hlg : Real.log (43639125756708131 / 80000000000000000 : ℝ) ≤ (-(1515181266806033804241 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43639125756708131 / 80000000000000000 : ℝ) = - (43639125756708131 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43639125756708131 / 40000000000000000 : ℚ)) - (U := (217686683943966195759 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43639125756708131 / 40000000000000000 : ℝ) ≤ - (217686683943966195759 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5431118422969689 / 10000000000000000 : ℝ)) (q := - (43639125756708131 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43639125756708131 / 80000000000000000 : ℚ)) + (r' := (43639125756708131 / 40000000000000000 : ℚ)) + (U := (-(1515181266806033804241 / 2500000000000000000000 : ℚ))) + (U' := (217686683943966195759 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (5431118422969689 / 10000000000000000 : ℚ)) + (q := (43639125756708131 / 80000000000000000 : ℚ)) + (U := (-(1515181266806033804241 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_8 : Uω (aρ 8) (bρ 8) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5042,25 +4408,21 @@ lemma U_543_8 : have hlg : Real.log (41168847029427407 / 80000000000000000 : ℝ) ≤ (-(830431005173728875531 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41168847029427407 / 80000000000000000 : ℝ) = - (41168847029427407 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41168847029427407 / 40000000000000000 : ℚ)) - (U := (36002970201271124469 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41168847029427407 / 40000000000000000 : ℝ) ≤ - (36002970201271124469 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1274272598122377 / 2500000000000000 : ℝ)) (q := - (41168847029427407 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41168847029427407 / 80000000000000000 : ℚ)) + (r' := (41168847029427407 / 40000000000000000 : ℚ)) + (U := (-(830431005173728875531 / 1250000000000000000000 : ℚ))) + (U' := (36002970201271124469 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (1274272598122377 / 2500000000000000 : ℚ)) + (q := (41168847029427407 / 80000000000000000 : ℚ)) + (U := (-(830431005173728875531 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_9 : Uω (aρ 9) (bρ 9) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5068,25 +4430,21 @@ lemma U_543_9 : have hlg : Real.log (38071968132515891 / 80000000000000000 : ℝ) ≤ (-(3712741836837896895691 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38071968132515891 / 80000000000000000 : ℝ) = - (38071968132515891 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38071968132515891 / 20000000000000000 : ℚ)) - (U := (3218729966162103104309 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38071968132515891 / 20000000000000000 : ℝ) ≤ - (3218729966162103104309 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4663836296621629 / 10000000000000000 : ℝ)) (q := - (38071968132515891 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38071968132515891 / 80000000000000000 : ℚ)) + (r' := (38071968132515891 / 20000000000000000 : ℚ)) + (U := (-(3712741836837896895691 / 5000000000000000000000 : ℚ))) + (U' := (3218729966162103104309 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (4663836296621629 / 10000000000000000 : ℚ)) + (q := (38071968132515891 / 80000000000000000 : ℚ)) + (U := (-(3712741836837896895691 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_10 : Uω (aρ 10) (bρ 10) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5094,26 +4452,21 @@ lemma U_543_10 : have hlg : Real.log (6864366903608263 / 16000000000000000 : ℝ) ≤ (-(2115612269099813192683 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6864366903608263 / 16000000000000000 : ℝ) = - (6864366903608263 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6864366903608263 / 4000000000000000 : ℚ)) - (U := (1350123632400186807317 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6864366903608263 / 4000000000000000 : ℝ) ≤ - (1350123632400186807317 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (822972385299597 / 2000000000000000 : ℝ)) (q := - (6864366903608263 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6864366903608263 / 16000000000000000 : ℚ)) + (r' := (6864366903608263 / 4000000000000000 : ℚ)) + (U := (-(2115612269099813192683 / 2500000000000000000000 : ℚ))) + (U' := (1350123632400186807317 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (822972385299597 / 2000000000000000 : ℚ)) + (q := (6864366903608263 / 16000000000000000 : ℚ)) + (U := (-(2115612269099813192683 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_11 : Uω (aρ 11) (bρ 11) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5121,26 +4474,21 @@ lemma U_543_11 : have hlg : Real.log (5978991803496607 / 16000000000000000 : ℝ) ≤ (-(4921683813520243516333 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5978991803496607 / 16000000000000000 : ℝ) = - (5978991803496607 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5978991803496607 / 4000000000000000 : ℚ)) - (U := (2009787989479756483667 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5978991803496607 / 4000000000000000 : ℝ) ≤ - (2009787989479756483667 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (685323935512683 / 2000000000000000 : ℝ)) (q := - (5978991803496607 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5978991803496607 / 16000000000000000 : ℚ)) + (r' := (5978991803496607 / 4000000000000000 : ℚ)) + (U := (-(4921683813520243516333 / 5000000000000000000000 : ℚ))) + (U' := (2009787989479756483667 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (685323935512683 / 2000000000000000 : ℚ)) + (q := (5978991803496607 / 16000000000000000 : ℚ)) + (U := (-(4921683813520243516333 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_12 : Uω (aρ 12) (bρ 12) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5148,26 +4496,21 @@ lemma U_543_12 : have hlg : Real.log (24681165651309479 / 80000000000000000 : ℝ) ≤ (-(11759862056280220014139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24681165651309479 / 80000000000000000 : ℝ) = - (24681165651309479 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24681165651309479 / 20000000000000000 : ℚ)) - (U := (2103081549719779985861 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24681165651309479 / 20000000000000000 : ℝ) ≤ - (2103081549719779985861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1273435716352513 / 5000000000000000 : ℝ)) (q := - (24681165651309479 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24681165651309479 / 80000000000000000 : ℚ)) + (r' := (24681165651309479 / 20000000000000000 : ℚ)) + (U := (-(11759862056280220014139 / 10000000000000000000000 : ℚ))) + (U' := (2103081549719779985861 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (1273435716352513 / 5000000000000000 : ℚ)) + (q := (24681165651309479 / 80000000000000000 : ℚ)) + (U := (-(11759862056280220014139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_13 : Uω (aρ 13) (bρ 13) (7938190348099 / 12800000000000 : ℝ) ≤ @@ -5175,26 +4518,21 @@ lemma U_543_13 : have hlg : Real.log (17848721780004003 / 80000000000000000 : ℝ) ≤ (-(7500473685979014998829 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17848721780004003 / 80000000000000000 : ℝ) = - (17848721780004003 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17848721780004003 / 10000000000000000 : ℚ)) - (U := (2896734018520985001171 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17848721780004003 / 10000000000000000 : ℝ) ≤ - (2896734018520985001171 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1238142206473657 / 10000000000000000 : ℝ)) (q := - (17848721780004003 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17848721780004003 / 80000000000000000 : ℚ)) + (r' := (17848721780004003 / 10000000000000000 : ℚ)) + (U := (-(7500473685979014998829 / 5000000000000000000000 : ℚ))) + (U' := (2896734018520985001171 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (7938190348099 / 12800000000000 : ℚ)) + (s := (1238142206473657 / 10000000000000000 : ℚ)) + (q := (17848721780004003 / 80000000000000000 : ℚ)) + (U := (-(7500473685979014998829 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_543_14 : Uω (aρ 14) (bρ 14) (7938190348099 / 12800000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U45.lean b/LeanPool/Zeta5Irrational/Table/U45.lean index a6712daf2c..851a576c47 100644 --- a/LeanPool/Zeta5Irrational/Table/U45.lean +++ b/LeanPool/Zeta5Irrational/Table/U45.lean @@ -24,25 +24,21 @@ lemma U_544_1 : have hlg : Real.log (2459174615841993 / 4000000000000000 : ℝ) ≤ (-(243234294615614466823 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2459174615841993 / 4000000000000000 : ℝ) = - (2459174615841993 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2459174615841993 / 2000000000000000 : ℚ)) - (U := (103339295534385533177 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2459174615841993 / 2000000000000000 : ℝ) ≤ - (103339295534385533177 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1229582048664243 / 2000000000000000 : ℝ)) (q := - (2459174615841993 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2459174615841993 / 4000000000000000 : ℚ)) + (r' := (2459174615841993 / 2000000000000000 : ℚ)) + (U := (-(243234294615614466823 / 500000000000000000000 : ℚ))) + (U' := (103339295534385533177 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (1229582048664243 / 2000000000000000 : ℚ)) + (q := (2459174615841993 / 4000000000000000 : ℚ)) + (U := (-(243234294615614466823 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_2 : Uω (aρ 2) (bρ 2) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_544_2 : have hlg : Real.log (12248041166219101 / 20000000000000000 : ℝ) ≤ (-(980732507775771540851 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12248041166219101 / 20000000000000000 : ℝ) = - (12248041166219101 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12248041166219101 / 10000000000000000 : ℚ)) - (U := (405561852824228459149 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12248041166219101 / 10000000000000000 : ℝ) ≤ - (405561852824228459149 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6123847342840351 / 10000000000000000 : ℝ)) (q := - (12248041166219101 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12248041166219101 / 20000000000000000 : ℚ)) + (r' := (12248041166219101 / 10000000000000000 : ℚ)) + (U := (-(980732507775771540851 / 2000000000000000000000 : ℚ))) + (U' := (405561852824228459149 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (6123847342840351 / 10000000000000000 : ℚ)) + (q := (12248041166219101 / 20000000000000000 : ℚ)) + (U := (-(980732507775771540851 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_3 : Uω (aρ 3) (bρ 3) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_544_3 : have hlg : Real.log (1519047235167293 / 2500000000000000 : ℝ) ≤ (-(2491037061290261113757 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1519047235167293 / 2500000000000000 : ℝ) = - (1519047235167293 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1519047235167293 / 1250000000000000 : ℚ)) - (U := (974698840209738886243 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1519047235167293 / 1250000000000000 : ℝ) ≤ - (974698840209738886243 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3037790082154797 / 5000000000000000 : ℝ)) (q := - (1519047235167293 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1519047235167293 / 2500000000000000 : ℚ)) + (r' := (1519047235167293 / 1250000000000000 : ℚ)) + (U := (-(2491037061290261113757 / 5000000000000000000000 : ℚ))) + (U' := (974698840209738886243 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (3037790082154797 / 5000000000000000 : ℚ)) + (q := (1519047235167293 / 2500000000000000 : ℚ)) + (U := (-(2491037061290261113757 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_4 : Uω (aρ 4) (bρ 4) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_544_4 : have hlg : Real.log (11993498327717163 / 20000000000000000 : ℝ) ≤ (-(5113675763595366645521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11993498327717163 / 20000000000000000 : ℝ) = - (11993498327717163 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11993498327717163 / 10000000000000000 : ℚ)) - (U := (1817796039404633354479 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11993498327717163 / 10000000000000000 : ℝ) ≤ - (1817796039404633354479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5994994791753413 / 10000000000000000 : ℝ)) (q := - (11993498327717163 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11993498327717163 / 20000000000000000 : ℚ)) + (r' := (11993498327717163 / 10000000000000000 : ℚ)) + (U := (-(5113675763595366645521 / 10000000000000000000000 : ℚ))) + (U' := (1817796039404633354479 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (5994994791753413 / 10000000000000000 : ℚ)) + (q := (11993498327717163 / 20000000000000000 : ℚ)) + (U := (-(5113675763595366645521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_5 : Uω (aρ 5) (bρ 5) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_544_5 : have hlg : Real.log (11751563438453559 / 20000000000000000 : ℝ) ≤ (-(166170619676123348097 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11751563438453559 / 20000000000000000 : ℝ) = - (11751563438453559 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11751563438453559 / 10000000000000000 : ℚ)) - (U := (50437874167626651903 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11751563438453559 / 10000000000000000 : ℝ) ≤ - (50437874167626651903 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5871249821824809 / 10000000000000000 : ℝ)) (q := - (11751563438453559 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11751563438453559 / 20000000000000000 : ℚ)) + (r' := (11751563438453559 / 10000000000000000 : ℚ)) + (U := (-(166170619676123348097 / 312500000000000000000 : ℚ))) + (U' := (50437874167626651903 / 312500000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (5871249821824809 / 10000000000000000 : ℚ)) + (q := (11751563438453559 / 20000000000000000 : ℚ)) + (U := (-(166170619676123348097 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_6 : Uω (aρ 6) (bρ 6) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_544_6 : have hlg : Real.log (5702312497043969 / 10000000000000000 : ℝ) ≤ (-(2808566494661532032637 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5702312497043969 / 10000000000000000 : ℝ) = - (5702312497043969 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5702312497043969 / 5000000000000000 : ℚ)) - (U := (657169406838467967363 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5702312497043969 / 5000000000000000 : ℝ) ≤ - (657169406838467967363 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1422887938149797 / 2500000000000000 : ℝ)) (q := - (5702312497043969 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5702312497043969 / 10000000000000000 : ℚ)) + (r' := (5702312497043969 / 5000000000000000 : ℚ)) + (U := (-(2808566494661532032637 / 5000000000000000000000 : ℚ))) + (U' := (657169406838467967363 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (1422887938149797 / 2500000000000000 : ℚ)) + (q := (5702312497043969 / 10000000000000000 : ℚ)) + (U := (-(2808566494661532032637 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_7 : Uω (aρ 7) (bρ 7) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_544_7 : have hlg : Real.log (10931373038086789 / 20000000000000000 : ℝ) ≤ (-(755119197430400781771 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10931373038086789 / 20000000000000000 : ℝ) = - (10931373038086789 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10931373038086789 / 10000000000000000 : ℚ)) - (U := (111314777944599218229 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10931373038086789 / 10000000000000000 : ℝ) ≤ - (111314777944599218229 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5441961177358039 / 10000000000000000 : ℝ)) (q := - (10931373038086789 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10931373038086789 / 20000000000000000 : ℚ)) + (r' := (10931373038086789 / 10000000000000000 : ℚ)) + (U := (-(755119197430400781771 / 1250000000000000000000 : ℚ))) + (U' := (111314777944599218229 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (5441961177358039 / 10000000000000000 : ℚ)) + (q := (10931373038086789 / 20000000000000000 : ℚ)) + (U := (-(755119197430400781771 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_8 : Uω (aρ 8) (bρ 8) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_544_8 : have hlg : Real.log (10313915736839439 / 20000000000000000 : ℝ) ≤ (-(1655595618708660814971 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10313915736839439 / 20000000000000000 : ℝ) = - (10313915736839439 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10313915736839439 / 10000000000000000 : ℚ)) - (U := (77272332041339185029 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10313915736839439 / 10000000000000000 : ℝ) ≤ - (77272332041339185029 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5108045527450689 / 10000000000000000 : ℝ)) (q := - (10313915736839439 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10313915736839439 / 20000000000000000 : ℚ)) + (r' := (10313915736839439 / 10000000000000000 : ℚ)) + (U := (-(1655595618708660814971 / 2500000000000000000000 : ℚ))) + (U' := (77272332041339185029 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (5108045527450689 / 10000000000000000 : ℚ)) + (q := (10313915736839439 / 20000000000000000 : ℚ)) + (U := (-(1655595618708660814971 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_9 : Uω (aρ 9) (bρ 9) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_544_9 : have hlg : Real.log (9539927326420767 / 20000000000000000 : ℝ) ≤ (-(7402464053785215584387 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9539927326420767 / 20000000000000000 : ℝ) = - (9539927326420767 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9539927326420767 / 5000000000000000 : ℚ)) - (U := (6460479552214784415613 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9539927326420767 / 5000000000000000 : ℝ) ≤ - (6460479552214784415613 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4675022745392017 / 10000000000000000 : ℝ)) (q := - (9539927326420767 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9539927326420767 / 20000000000000000 : ℚ)) + (r' := (9539927326420767 / 5000000000000000 : ℚ)) + (U := (-(7402464053785215584387 / 10000000000000000000000 : ℚ))) + (U' := (6460479552214784415613 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (4675022745392017 / 10000000000000000 : ℚ)) + (q := (9539927326420767 / 20000000000000000 : ℚ)) + (U := (-(7402464053785215584387 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_10 : Uω (aρ 10) (bρ 10) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -258,25 +222,21 @@ lemma U_544_10 : have hlg : Real.log (537679376244323 / 1250000000000000 : ℝ) ≤ (-(4218182011013012442561 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (537679376244323 / 1250000000000000 : ℝ) = - (537679376244323 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (537679376244323 / 312500000000000 : ℚ)) - (U := (2713289791986987557439 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (537679376244323 / 312500000000000 : ℝ) ≤ - (2713289791986987557439 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2063262236187709 / 5000000000000000 : ℝ)) (q := - (537679376244323 / 1250000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (537679376244323 / 1250000000000000 : ℚ)) + (r' := (537679376244323 / 312500000000000 : ℚ)) + (U := (-(4218182011013012442561 / 5000000000000000000000 : ℚ))) + (U' := (2713289791986987557439 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (2063262236187709 / 5000000000000000 : ℚ)) + (q := (537679376244323 / 1250000000000000 : ℚ)) + (U := (-(4218182011013012442561 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_11 : Uω (aρ 11) (bρ 11) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -284,26 +244,21 @@ lemma U_544_11 : have hlg : Real.log (7497177235692769 / 20000000000000000 : ℝ) ≤ (-(981205691910561245223 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7497177235692769 / 20000000000000000 : ℝ) = - (7497177235692769 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7497177235692769 / 5000000000000000 : ℚ)) - (U := (405088668689438754777 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7497177235692769 / 5000000000000000 : ℝ) ≤ - (405088668689438754777 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3439308314364019 / 10000000000000000 : ℝ)) (q := - (7497177235692769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7497177235692769 / 20000000000000000 : ℚ)) + (r' := (7497177235692769 / 5000000000000000 : ℚ)) + (U := (-(981205691910561245223 / 1000000000000000000000 : ℚ))) + (U' := (405088668689438754777 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (3439308314364019 / 10000000000000000 : ℚ)) + (q := (7497177235692769 / 20000000000000000 : ℚ)) + (U := (-(981205691910561245223 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_12 : Uω (aρ 12) (bρ 12) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -311,26 +266,21 @@ lemma U_544_12 : have hlg : Real.log (1549077372466801 / 5000000000000000 : ℝ) ≤ (-(292944600445161657491 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1549077372466801 / 5000000000000000 : ℝ) = - (1549077372466801 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1549077372466801 / 1250000000000000 : ℚ)) - (U := (53628989704838342509 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1549077372466801 / 1250000000000000 : ℝ) ≤ - (53628989704838342509 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1281070332611727 / 5000000000000000 : ℝ)) (q := - (1549077372466801 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1549077372466801 / 5000000000000000 : ℚ)) + (r' := (1549077372466801 / 1250000000000000 : ℚ)) + (U := (-(292944600445161657491 / 250000000000000000000 : ℚ))) + (U' := (53628989704838342509 / 250000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (1281070332611727 / 5000000000000000 : ℚ)) + (q := (1549077372466801 / 5000000000000000 : ℚ)) + (U := (-(292944600445161657491 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_13 : Uω (aρ 13) (bρ 13) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -338,25 +288,21 @@ lemma U_544_13 : have hlg : Real.log (562581847817931 / 2500000000000000 : ℝ) ≤ (-(1864386724188942654493 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (562581847817931 / 2500000000000000 : ℝ) = - (562581847817931 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (562581847817931 / 312500000000000 : ℚ)) - (U := (734915201936057345507 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (562581847817931 / 312500000000000 : ℝ) ≤ - (734915201936057345507 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (632933849747349 / 5000000000000000 : ℝ)) (q := - (562581847817931 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (562581847817931 / 2500000000000000 : ℚ)) + (r' := (562581847817931 / 312500000000000 : ℚ)) + (U := (-(1864386724188942654493 / 1250000000000000000000 : ℚ))) + (U' := (734915201936057345507 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4969968043179 / 8000000000000 : ℚ)) + (s := (632933849747349 / 5000000000000000 : ℚ)) + (q := (562581847817931 / 2500000000000000 : ℚ)) + (U := (-(1864386724188942654493 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_544_14 : Uω (aρ 14) (bρ 14) (4969968043179 / 8000000000000 : ℝ) ≤ @@ -462,25 +408,21 @@ lemma U_545_1 : have hlg : Real.log (49269483440175017 / 80000000000000000 : ℝ) ≤ (-(4847217421798197610027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49269483440175017 / 80000000000000000 : ℝ) = - (49269483440175017 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49269483440175017 / 40000000000000000 : ℚ)) - (U := (2084254381201802389973 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49269483440175017 / 40000000000000000 : ℝ) ≤ - (2084254381201802389973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3079329589816799 / 5000000000000000 : ℝ)) (q := - (49269483440175017 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49269483440175017 / 80000000000000000 : ℚ)) + (r' := (49269483440175017 / 40000000000000000 : ℚ)) + (U := (-(4847217421798197610027 / 10000000000000000000000 : ℚ))) + (U' := (2084254381201802389973 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (3079329589816799 / 5000000000000000 : ℚ)) + (q := (49269483440175017 / 80000000000000000 : ℚ)) + (U := (-(4847217421798197610027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_2 : Uω (aρ 2) (bρ 2) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -488,25 +430,21 @@ lemma U_545_2 : have hlg : Real.log (49078157849416297 / 80000000000000000 : ℝ) ≤ (-(2443062744530523726207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49078157849416297 / 80000000000000000 : ℝ) = - (49078157849416297 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49078157849416297 / 40000000000000000 : ℚ)) - (U := (1022673156969476273793 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49078157849416297 / 40000000000000000 : ℝ) ≤ - (1022673156969476273793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3067298397226959 / 5000000000000000 : ℝ)) (q := - (49078157849416297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49078157849416297 / 80000000000000000 : ℚ)) + (r' := (49078157849416297 / 40000000000000000 : ℚ)) + (U := (-(2443062744530523726207 / 5000000000000000000000 : ℚ))) + (U' := (1022673156969476273793 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (3067298397226959 / 5000000000000000 : ℚ)) + (q := (49078157849416297 / 80000000000000000 : ℚ)) + (U := (-(2443062744530523726207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_3 : Uω (aρ 3) (bρ 3) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -514,25 +452,21 @@ lemma U_545_3 : have hlg : Real.log (48695510882625581 / 80000000000000000 : ℝ) ≤ (-(992879575151331134011 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48695510882625581 / 80000000000000000 : ℝ) = - (48695510882625581 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48695510882625581 / 40000000000000000 : ℚ)) - (U := (393414785448668865989 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48695510882625581 / 40000000000000000 : ℝ) ≤ - (393414785448668865989 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6086331159106239 / 10000000000000000 : ℝ)) (q := - (48695510882625581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48695510882625581 / 80000000000000000 : ℚ)) + (r' := (48695510882625581 / 40000000000000000 : ℚ)) + (U := (-(992879575151331134011 / 2000000000000000000000 : ℚ))) + (U' := (393414785448668865989 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (6086331159106239 / 10000000000000000 : ℚ)) + (q := (48695510882625581 / 80000000000000000 : ℚ)) + (U := (-(992879575151331134011 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_4 : Uω (aρ 4) (bρ 4) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -540,25 +474,21 @@ lemma U_545_4 : have hlg : Real.log (48060009186278117 / 80000000000000000 : ℝ) ≤ (-(1273940532409412364583 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48060009186278117 / 80000000000000000 : ℝ) = - (48060009186278117 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48060009186278117 / 40000000000000000 : ℚ)) - (U := (458927418340587635417 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48060009186278117 / 40000000000000000 : ℝ) ≤ - (458927418340587635417 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6005749916084373 / 10000000000000000 : ℝ)) (q := - (48060009186278117 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48060009186278117 / 80000000000000000 : ℚ)) + (r' := (48060009186278117 / 40000000000000000 : ℚ)) + (U := (-(1273940532409412364583 / 2500000000000000000000 : ℚ))) + (U' := (458927418340587635417 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (6005749916084373 / 10000000000000000 : ℚ)) + (q := (48060009186278117 / 80000000000000000 : ℚ)) + (U := (-(1273940532409412364583 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_5 : Uω (aρ 5) (bρ 5) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -566,25 +496,21 @@ lemma U_545_5 : have hlg : Real.log (47092310763100777 / 80000000000000000 : ℝ) ≤ (-(2649584500781039761267 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47092310763100777 / 80000000000000000 : ℝ) = - (47092310763100777 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47092310763100777 / 40000000000000000 : ℚ)) - (U := (816151400718960238733 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47092310763100777 / 40000000000000000 : ℝ) ≤ - (816151400718960238733 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2941007614812519 / 5000000000000000 : ℝ)) (q := - (47092310763100777 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47092310763100777 / 80000000000000000 : ℚ)) + (r' := (47092310763100777 / 40000000000000000 : ℚ)) + (U := (-(2649584500781039761267 / 5000000000000000000000 : ℚ))) + (U' := (816151400718960238733 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (2941007614812519 / 5000000000000000 : ℚ)) + (q := (47092310763100777 / 80000000000000000 : ℚ)) + (U := (-(2649584500781039761267 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_6 : Uω (aρ 6) (bρ 6) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -592,25 +518,21 @@ lemma U_545_6 : have hlg : Real.log (9140930600818241 / 16000000000000000 : ℝ) ≤ (-(559826525414619874691 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9140930600818241 / 16000000000000000 : ℝ) = - (9140930600818241 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9140930600818241 / 8000000000000000 : ℚ)) - (U := (133320654885380125309 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9140930600818241 / 8000000000000000 : ℝ) ≤ - (133320654885380125309 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1140468233002529 / 2000000000000000 : ℝ)) (q := - (9140930600818241 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9140930600818241 / 16000000000000000 : ℚ)) + (r' := (9140930600818241 / 8000000000000000 : ℚ)) + (U := (-(559826525414619874691 / 1000000000000000000000 : ℚ))) + (U' := (133320654885380125309 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (1140468233002529 / 2000000000000000 : ℚ)) + (q := (9140930600818241 / 16000000000000000 : ℚ)) + (U := (-(559826525414619874691 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_7 : Uω (aρ 7) (bρ 7) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -618,25 +540,21 @@ lemma U_545_7 : have hlg : Real.log (43811857060557489 / 80000000000000000 : ℝ) ≤ (-(240848857808598739739 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43811857060557489 / 80000000000000000 : ℝ) = - (43811857060557489 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43811857060557489 / 40000000000000000 : ℚ)) - (U := (36410014311401260261 / 400000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43811857060557489 / 40000000000000000 : ℝ) ≤ - (36410014311401260261 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85200055623269 / 156250000000000 : ℝ)) (q := - (43811857060557489 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43811857060557489 / 80000000000000000 : ℚ)) + (r' := (43811857060557489 / 40000000000000000 : ℚ)) + (U := (-(240848857808598739739 / 400000000000000000000 : ℚ))) + (U' := (36410014311401260261 / 400000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (85200055623269 / 156250000000000 : ℚ)) + (q := (43811857060557489 / 80000000000000000 : ℚ)) + (U := (-(240848857808598739739 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_8 : Uω (aρ 8) (bρ 8) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -644,25 +562,21 @@ lemma U_545_8 : have hlg : Real.log (41342475366695973 / 80000000000000000 : ℝ) ≤ (-(3300681018533957643367 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41342475366695973 / 80000000000000000 : ℝ) = - (41342475366695973 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41342475366695973 / 40000000000000000 : ℚ)) - (U := (165054882966042356633 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (41342475366695973 / 40000000000000000 : ℝ) ≤ - (165054882966042356633 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5118999787763837 / 10000000000000000 : ℝ)) (q := - (41342475366695973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41342475366695973 / 80000000000000000 : ℚ)) + (r' := (41342475366695973 / 40000000000000000 : ℚ)) + (U := (-(3300681018533957643367 / 5000000000000000000000 : ℚ))) + (U' := (165054882966042356633 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (5118999787763837 / 10000000000000000 : ℚ)) + (q := (41342475366695973 / 80000000000000000 : ℚ)) + (U := (-(3300681018533957643367 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_9 : Uω (aρ 9) (bρ 9) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -670,25 +584,21 @@ lemma U_545_9 : have hlg : Real.log (38247442285464721 / 80000000000000000 : ℝ) ≤ (-(1844874861177744237403 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38247442285464721 / 80000000000000000 : ℝ) = - (38247442285464721 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38247442285464721 / 20000000000000000 : ℚ)) - (U := (1620861040322255762597 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38247442285464721 / 20000000000000000 : ℝ) ≤ - (1620861040322255762597 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (585775893227003 / 1250000000000000 : ℝ)) (q := - (38247442285464721 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38247442285464721 / 80000000000000000 : ℚ)) + (r' := (38247442285464721 / 20000000000000000 : ℚ)) + (U := (-(1844874861177744237403 / 2500000000000000000000 : ℚ))) + (U' := (1620861040322255762597 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (585775893227003 / 1250000000000000 : ℚ)) + (q := (38247442285464721 / 80000000000000000 : ℚ)) + (U := (-(1844874861177744237403 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_10 : Uω (aρ 10) (bρ 10) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -696,26 +606,21 @@ lemma U_545_10 : have hlg : Real.log (34501105847704137 / 80000000000000000 : ℝ) ≤ (-(336414102829495814321 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34501105847704137 / 80000000000000000 : ℝ) = - (34501105847704137 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34501105847704137 / 20000000000000000 : ℚ)) - (U := (218103641410504185679 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34501105847704137 / 20000000000000000 : ℝ) ≤ - (218103641410504185679 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2069091034935439 / 5000000000000000 : ℝ)) (q := - (34501105847704137 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34501105847704137 / 80000000000000000 : ℚ)) + (r' := (34501105847704137 / 20000000000000000 : ℚ)) + (U := (-(336414102829495814321 / 400000000000000000000 : ℚ))) + (U' := (218103641410504185679 / 400000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (2069091034935439 / 5000000000000000 : ℚ)) + (q := (34501105847704137 / 80000000000000000 : ℚ)) + (U := (-(336414102829495814321 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_11 : Uω (aρ 11) (bρ 11) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -723,26 +628,21 @@ lemma U_545_11 : have hlg : Real.log (30082406186747193 / 80000000000000000 : ℝ) ≤ (-(1956172290722271357863 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30082406186747193 / 80000000000000000 : ℝ) = - (30082406186747193 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30082406186747193 / 20000000000000000 : ℚ)) - (U := (816416430477728642137 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30082406186747193 / 20000000000000000 : ℝ) ≤ - (816416430477728642137 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1725991890418321 / 5000000000000000 : ℝ)) (q := - (30082406186747193 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30082406186747193 / 80000000000000000 : ℚ)) + (r' := (30082406186747193 / 20000000000000000 : ℚ)) + (U := (-(1956172290722271357863 / 2000000000000000000000 : ℚ))) + (U' := (816416430477728642137 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (1725991890418321 / 5000000000000000 : ℚ)) + (q := (30082406186747193 / 80000000000000000 : ℚ)) + (U := (-(1956172290722271357863 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_12 : Uω (aρ 12) (bρ 12) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -750,26 +650,21 @@ lemma U_545_12 : have hlg : Real.log (24889127738889657 / 80000000000000000 : ℝ) ≤ (-(11675955630294015158997 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24889127738889657 / 80000000000000000 : ℝ) = - (24889127738889657 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24889127738889657 / 20000000000000000 : ℚ)) - (U := (2186987975705984841003 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24889127738889657 / 20000000000000000 : ℝ) ≤ - (2186987975705984841003 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1288682132778629 / 5000000000000000 : ℝ)) (q := - (24889127738889657 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24889127738889657 / 80000000000000000 : ℚ)) + (r' := (24889127738889657 / 20000000000000000 : ℚ)) + (U := (-(11675955630294015158997 / 10000000000000000000000 : ℚ))) + (U' := (2186987975705984841003 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (1288682132778629 / 5000000000000000 : ℚ)) + (q := (24889127738889657 / 80000000000000000 : ℚ)) + (U := (-(11675955630294015158997 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_13 : Uω (aρ 13) (bρ 13) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -777,26 +672,21 @@ lemma U_545_13 : have hlg : Real.log (18154496392940433 / 80000000000000000 : ℝ) ≤ (-(14831083687162373912247 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18154496392940433 / 80000000000000000 : ℝ) = - (18154496392940433 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18154496392940433 / 10000000000000000 : ℚ)) - (U := (5963331721837626087753 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18154496392940433 / 10000000000000000 : ℝ) ≤ - (5963331721837626087753 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (161636021333119 / 1250000000000000 : ℝ)) (q := - (18154496392940433 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18154496392940433 / 80000000000000000 : ℚ)) + (r' := (18154496392940433 / 10000000000000000 : ℚ)) + (U := (-(14831083687162373912247 / 10000000000000000000000 : ℚ))) + (U' := (5963331721837626087753 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39828536950369 / 64000000000000 : ℚ)) + (s := (161636021333119 / 1250000000000000 : ℚ)) + (q := (18154496392940433 / 80000000000000000 : ℚ)) + (U := (-(14831083687162373912247 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_545_14 : Uω (aρ 14) (bρ 14) (39828536950369 / 64000000000000 : ℝ) ≤ @@ -903,25 +793,21 @@ lemma U_546_1 : have hlg : Real.log (24677737281115379 / 40000000000000000 : ℝ) ≤ (-(4829779413085618008589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24677737281115379 / 40000000000000000 : ℝ) = - (24677737281115379 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24677737281115379 / 20000000000000000 : ℚ)) - (U := (2101692389914381991411 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24677737281115379 / 20000000000000000 : ℝ) ≤ - (2101692389914381991411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6169408115626127 / 10000000000000000 : ℝ)) (q := - (24677737281115379 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24677737281115379 / 40000000000000000 : ℚ)) + (r' := (24677737281115379 / 20000000000000000 : ℚ)) + (U := (-(4829779413085618008589 / 10000000000000000000000 : ℚ))) + (U' := (2101692389914381991411 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (6169408115626127 / 10000000000000000 : ℚ)) + (q := (24677737281115379 / 40000000000000000 : ℚ)) + (U := (-(4829779413085618008589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_2 : Uω (aρ 2) (bρ 2) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -929,25 +815,21 @@ lemma U_546_2 : have hlg : Real.log (24582075512730507 / 40000000000000000 : ℝ) ≤ (-(2434309570975091985393 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24582075512730507 / 40000000000000000 : ℝ) = - (24582075512730507 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24582075512730507 / 20000000000000000 : ℚ)) - (U := (1031426330524908014607 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24582075512730507 / 20000000000000000 : ℝ) ≤ - (1031426330524908014607 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6145346243943691 / 10000000000000000 : ℝ)) (q := - (24582075512730507 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24582075512730507 / 40000000000000000 : ℚ)) + (r' := (24582075512730507 / 20000000000000000 : ℚ)) + (U := (-(2434309570975091985393 / 5000000000000000000000 : ℚ))) + (U' := (1031426330524908014607 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (6145346243943691 / 10000000000000000 : ℚ)) + (q := (24582075512730507 / 40000000000000000 : ℚ)) + (U := (-(2434309570975091985393 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_3 : Uω (aρ 3) (bρ 3) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -955,25 +837,21 @@ lemma U_546_3 : have hlg : Real.log (975630204191363 / 1600000000000000 : ℝ) ≤ (-(4946752824996576485697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (975630204191363 / 1600000000000000 : ℝ) = - (975630204191363 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (975630204191363 / 800000000000000 : ℚ)) - (U := (1984718978003423514303 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (975630204191363 / 800000000000000 : ℝ) ≤ - (1984718978003423514303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (243883285852819 / 400000000000000 : ℝ)) (q := - (975630204191363 / 1600000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (975630204191363 / 1600000000000000 : ℚ)) + (r' := (975630204191363 / 800000000000000 : ℚ)) + (U := (-(4946752824996576485697 / 10000000000000000000000 : ℚ))) + (U' := (1984718978003423514303 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (243883285852819 / 400000000000000 : ℚ)) + (q := (975630204191363 / 1600000000000000 : ℚ)) + (U := (-(4946752824996576485697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_4 : Uω (aρ 4) (bρ 4) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -981,25 +859,21 @@ lemma U_546_4 : have hlg : Real.log (4814602497190733 / 8000000000000000 : ℝ) ≤ (-(1269470136695590692193 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4814602497190733 / 8000000000000000 : ℝ) = - (4814602497190733 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4814602497190733 / 4000000000000000 : ℚ)) - (U := (463397814054409307807 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4814602497190733 / 4000000000000000 : ℝ) ≤ - (463397814054409307807 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (601650501797027 / 1000000000000000 : ℝ)) (q := - (4814602497190733 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4814602497190733 / 8000000000000000 : ℚ)) + (r' := (4814602497190733 / 4000000000000000 : ℚ)) + (U := (-(1269470136695590692193 / 2500000000000000000000 : ℚ))) + (U' := (463397814054409307807 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (601650501797027 / 1000000000000000 : ℚ)) + (q := (4814602497190733 / 8000000000000000 : ℚ)) + (U := (-(1269470136695590692193 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_5 : Uω (aρ 5) (bρ 5) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1007,25 +881,21 @@ lemma U_546_5 : have hlg : Real.log (23589183765250227 / 40000000000000000 : ℝ) ≤ (-(1056182323825263913179 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23589183765250227 / 40000000000000000 : ℝ) = - (23589183765250227 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23589183765250227 / 20000000000000000 : ℚ)) - (U := (330112036774736086821 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23589183765250227 / 20000000000000000 : ℝ) ≤ - (330112036774736086821 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5892780576953551 / 10000000000000000 : ℝ)) (q := - (23589183765250227 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23589183765250227 / 40000000000000000 : ℚ)) + (r' := (23589183765250227 / 20000000000000000 : ℚ)) + (U := (-(1056182323825263913179 / 2000000000000000000000 : ℚ))) + (U' := (330112036774736086821 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (5892780576953551 / 10000000000000000 : ℚ)) + (q := (23589183765250227 / 40000000000000000 : ℚ)) + (U := (-(1056182323825263913179 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_6 : Uω (aρ 6) (bρ 6) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1033,25 +903,21 @@ lemma U_546_6 : have hlg : Real.log (22895402710036903 / 40000000000000000 : ℝ) ≤ (-(1394858296170015163569 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22895402710036903 / 40000000000000000 : ℝ) = - (22895402710036903 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22895402710036903 / 20000000000000000 : ℚ)) - (U := (338009654579984836431 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22895402710036903 / 20000000000000000 : ℝ) ≤ - (338009654579984836431 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5713130424486889 / 10000000000000000 : ℝ)) (q := - (22895402710036903 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22895402710036903 / 40000000000000000 : ℚ)) + (r' := (22895402710036903 / 20000000000000000 : ℚ)) + (U := (-(1394858296170015163569 / 2500000000000000000000 : ℚ))) + (U' := (338009654579984836431 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (5713130424486889 / 10000000000000000 : ℚ)) + (q := (22895402710036903 / 40000000000000000 : ℚ)) + (U := (-(1394858296170015163569 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_7 : Uω (aρ 7) (bρ 7) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1059,25 +925,21 @@ lemma U_546_7 : have hlg : Real.log (21949110245097181 / 40000000000000000 : ℝ) ≤ (-(6001528506852776076673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21949110245097181 / 40000000000000000 : ℝ) = - (21949110245097181 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21949110245097181 / 20000000000000000 : ℚ)) - (U := (929943296147223923327 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21949110245097181 / 20000000000000000 : ℝ) ≤ - (929943296147223923327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1365911393194257 / 2500000000000000 : ℝ)) (q := - (21949110245097181 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21949110245097181 / 40000000000000000 : ℚ)) + (r' := (21949110245097181 / 20000000000000000 : ℚ)) + (U := (-(6001528506852776076673 / 10000000000000000000000 : ℚ))) + (U' := (929943296147223923327 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (1365911393194257 / 2500000000000000 : ℚ)) + (q := (21949110245097181 / 40000000000000000 : ℚ)) + (U := (-(6001528506852776076673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_8 : Uω (aρ 8) (bρ 8) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1085,25 +947,21 @@ lemma U_546_8 : have hlg : Real.log (165717137239417 / 320000000000000 : ℝ) ≤ (-(1316077306315072704157 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (165717137239417 / 320000000000000 : ℝ) = - (165717137239417 / 160000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (165717137239417 / 160000000000000 : ℚ)) - (U := (70217054284927295843 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (165717137239417 / 160000000000000 : ℝ) ≤ - (70217054284927295843 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (641244147379 / 1250000000000 : ℝ)) (q := - (165717137239417 / 320000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (165717137239417 / 320000000000000 : ℚ)) + (r' := (165717137239417 / 160000000000000 : ℚ)) + (U := (-(1316077306315072704157 / 2000000000000000000000 : ℚ))) + (U' := (70217054284927295843 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (641244147379 / 1250000000000 : ℚ)) + (q := (165717137239417 / 320000000000000 : ℚ)) + (U := (-(1316077306315072704157 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_9 : Uω (aρ 9) (bρ 9) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1111,25 +969,21 @@ lemma U_546_9 : have hlg : Real.log (19167583565192881 / 40000000000000000 : ℝ) ≤ (-(1839147393547709124913 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19167583565192881 / 40000000000000000 : ℝ) = - (19167583565192881 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19167583565192881 / 10000000000000000 : ℚ)) - (U := (1626588507952290875087 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19167583565192881 / 10000000000000000 : ℝ) ≤ - (1626588507952290875087 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2348694756262439 / 5000000000000000 : ℝ)) (q := - (19167583565192881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19167583565192881 / 40000000000000000 : ℚ)) + (r' := (19167583565192881 / 10000000000000000 : ℚ)) + (U := (-(1839147393547709124913 / 2500000000000000000000 : ℚ))) + (U' := (1626588507952290875087 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (2348694756262439 / 5000000000000000 : ℚ)) + (q := (19167583565192881 / 40000000000000000 : ℚ)) + (U := (-(1839147393547709124913 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_10 : Uω (aρ 10) (bρ 10) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1137,26 +991,21 @@ lemma U_546_10 : have hlg : Real.log (17295355994526979 / 40000000000000000 : ℝ) ≤ (-(8384414277493951212261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17295355994526979 / 40000000000000000 : ℝ) = - (17295355994526979 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17295355994526979 / 10000000000000000 : ℚ)) - (U := (5478529328506048787739 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17295355994526979 / 10000000000000000 : ℝ) ≤ - (5478529328506048787739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4149834760686927 / 10000000000000000 : ℝ)) (q := - (17295355994526979 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17295355994526979 / 40000000000000000 : ℚ)) + (r' := (17295355994526979 / 10000000000000000 : ℚ)) + (U := (-(8384414277493951212261 / 10000000000000000000000 : ℚ))) + (U' := (5478529328506048787739 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (4149834760686927 / 10000000000000000 : ℚ)) + (q := (17295355994526979 / 40000000000000000 : ℚ)) + (U := (-(8384414277493951212261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_11 : Uω (aρ 11) (bρ 11) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1164,26 +1013,21 @@ lemma U_546_11 : have hlg : Real.log (15088025663808893 / 40000000000000000 : ℝ) ≤ (-(9749780267626559126277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15088025663808893 / 40000000000000000 : ℝ) = - (15088025663808893 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15088025663808893 / 10000000000000000 : ℚ)) - (U := (4113163338373440873723 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15088025663808893 / 10000000000000000 : ℝ) ≤ - (4113163338373440873723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (866161555383221 / 2500000000000000 : ℝ)) (q := - (15088025663808893 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15088025663808893 / 40000000000000000 : ℚ)) + (r' := (15088025663808893 / 10000000000000000 : ℚ)) + (U := (-(9749780267626559126277 / 10000000000000000000000 : ℚ))) + (U' := (4113163338373440873723 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (866161555383221 / 2500000000000000 : ℚ)) + (q := (15088025663808893 / 40000000000000000 : ℚ)) + (U := (-(9749780267626559126277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_12 : Uω (aρ 12) (bρ 12) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1191,26 +1035,21 @@ lemma U_546_12 : have hlg : Real.log (12496419102519193 / 40000000000000000 : ℝ) ≤ (-(2326874644250277370813 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12496419102519193 / 40000000000000000 : ℝ) = - (12496419102519193 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12496419102519193 / 10000000000000000 : ℚ)) - (U := (445714076949722629187 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12496419102519193 / 10000000000000000 : ℝ) ≤ - (445714076949722629187 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1296271518786517 / 5000000000000000 : ℝ)) (q := - (12496419102519193 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12496419102519193 / 40000000000000000 : ℚ)) + (r' := (12496419102519193 / 10000000000000000 : ℚ)) + (U := (-(2326874644250277370813 / 2000000000000000000000 : ℚ))) + (U' := (445714076949722629187 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (1296271518786517 / 5000000000000000 : ℚ)) + (q := (12496419102519193 / 40000000000000000 : ℚ)) + (U := (-(2326874644250277370813 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_13 : Uω (aρ 13) (bρ 13) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1218,26 +1057,21 @@ lemma U_546_13 : have hlg : Real.log (9152239278767629 / 40000000000000000 : ℝ) ≤ (-(14748808740681928824749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9152239278767629 / 40000000000000000 : ℝ) = - (9152239278767629 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9152239278767629 / 5000000000000000 : ℚ)) - (U := (6045606668318071175251 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9152239278767629 / 5000000000000000 : ℝ) ≤ - (6045606668318071175251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (329958716823063 / 2500000000000000 : ℝ)) (q := - (9152239278767629 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9152239278767629 / 40000000000000000 : ℚ)) + (r' := (9152239278767629 / 5000000000000000 : ℚ)) + (U := (-(14748808740681928824749 / 10000000000000000000000 : ℚ))) + (U' := (6045606668318071175251 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (19948664777653 / 32000000000000 : ℚ)) + (s := (329958716823063 / 2500000000000000 : ℚ)) + (q := (9152239278767629 / 40000000000000000 : ℚ)) + (U := (-(14748808740681928824749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_546_14 : Uω (aρ 14) (bρ 14) (19948664777653 / 32000000000000 : ℝ) ≤ @@ -1345,25 +1179,21 @@ lemma U_547_1 : have hlg : Real.log (49441465683013763 / 80000000000000000 : ℝ) ≤ (-(4812371760118998631747 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49441465683013763 / 80000000000000000 : ℝ) = - (49441465683013763 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49441465683013763 / 40000000000000000 : ℚ)) - (U := (2119100042881001368253 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49441465683013763 / 40000000000000000 : ℝ) ≤ - (2119100042881001368253 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (772519631412559 / 1250000000000000 : ℝ)) (q := - (49441465683013763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49441465683013763 / 80000000000000000 : ℚ)) + (r' := (49441465683013763 / 40000000000000000 : ℚ)) + (U := (-(4812371760118998631747 / 10000000000000000000000 : ℚ))) + (U' := (2119100042881001368253 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (772519631412559 / 1250000000000000 : ℚ)) + (q := (49441465683013763 / 80000000000000000 : ℚ)) + (U := (-(4812371760118998631747 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_2 : Uω (aρ 2) (bρ 2) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1371,25 +1201,21 @@ lemma U_547_2 : have hlg : Real.log (9850028838611011 / 16000000000000000 : ℝ) ≤ (-(1212785847555891833407 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9850028838611011 / 16000000000000000 : ℝ) = - (9850028838611011 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9850028838611011 / 8000000000000000 : ℚ)) - (U := (520082103194108166593 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9850028838611011 / 8000000000000000 : ℝ) ≤ - (520082103194108166593 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1231219138264159 / 2000000000000000 : ℝ)) (q := - (9850028838611011 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9850028838611011 / 16000000000000000 : ℚ)) + (r' := (9850028838611011 / 8000000000000000 : ℚ)) + (U := (-(1212785847555891833407 / 2500000000000000000000 : ℚ))) + (U' := (520082103194108166593 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (1231219138264159 / 2000000000000000 : ℚ)) + (q := (9850028838611011 / 16000000000000000 : ℚ)) + (U := (-(1212785847555891833407 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_3 : Uω (aρ 3) (bρ 3) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1397,25 +1223,21 @@ lemma U_547_3 : have hlg : Real.log (48867509506341239 / 80000000000000000 : ℝ) ≤ (-(2464569430179590840317 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48867509506341239 / 80000000000000000 : ℝ) = - (48867509506341239 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48867509506341239 / 40000000000000000 : ℚ)) - (U := (1001166471320409159683 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48867509506341239 / 40000000000000000 : ℝ) ≤ - (1001166471320409159683 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6107833125992341 / 10000000000000000 : ℝ)) (q := - (48867509506341239 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48867509506341239 / 80000000000000000 : ℚ)) + (r' := (48867509506341239 / 40000000000000000 : ℚ)) + (U := (-(2464569430179590840317 / 5000000000000000000000 : ℚ))) + (U' := (1001166471320409159683 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (6107833125992341 / 10000000000000000 : ℚ)) + (q := (48867509506341239 / 80000000000000000 : ℚ)) + (U := (-(2464569430179590840317 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_4 : Uω (aρ 4) (bρ 4) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1423,25 +1245,21 @@ lemma U_547_4 : have hlg : Real.log (9646408133647383 / 16000000000000000 : ℝ) ≤ (-(316251931279762199151 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9646408133647383 / 16000000000000000 : ℝ) = - (9646408133647383 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9646408133647383 / 8000000000000000 : ℚ)) - (U := (116965056407737800849 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9646408133647383 / 8000000000000000 : ℝ) ≤ - (116965056407737800849 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (301363004876563 / 500000000000000 : ℝ)) (q := - (9646408133647383 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9646408133647383 / 16000000000000000 : ℚ)) + (r' := (9646408133647383 / 8000000000000000 : ℚ)) + (U := (-(316251931279762199151 / 625000000000000000000 : ℚ))) + (U' := (116965056407737800849 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (301363004876563 / 500000000000000 : ℚ)) + (q := (9646408133647383 / 16000000000000000 : ℚ)) + (U := (-(316251931279762199151 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_5 : Uω (aρ 5) (bρ 5) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1449,25 +1267,21 @@ lemma U_547_5 : have hlg : Real.log (9452884811467307 / 16000000000000000 : ℝ) ≤ (-(5262687560051708840297 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9452884811467307 / 16000000000000000 : ℝ) = - (9452884811467307 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9452884811467307 / 8000000000000000 : ℚ)) - (U := (1668784242948291159703 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9452884811467307 / 8000000000000000 : ℝ) ≤ - (1668784242948291159703 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1180709172828233 / 2000000000000000 : ℝ)) (q := - (9452884811467307 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9452884811467307 / 16000000000000000 : ℚ)) + (r' := (9452884811467307 / 8000000000000000 : ℚ)) + (U := (-(5262687560051708840297 / 10000000000000000000000 : ℚ))) + (U' := (1668784242948291159703 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (1180709172828233 / 2000000000000000 : ℚ)) + (q := (9452884811467307 / 16000000000000000 : ℚ)) + (U := (-(5262687560051708840297 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_6 : Uω (aρ 6) (bρ 6) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1475,25 +1289,21 @@ lemma U_547_6 : have hlg : Real.log (9175391445551787 / 16000000000000000 : ℝ) ≤ (-(5560636645839827234383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9175391445551787 / 16000000000000000 : ℝ) = - (9175391445551787 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9175391445551787 / 8000000000000000 : ℚ)) - (U := (1370835157160172765617 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9175391445551787 / 8000000000000000 : ℝ) ≤ - (1370835157160172765617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1144783906377353 / 2000000000000000 : ℝ)) (q := - (9175391445551787 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9175391445551787 / 16000000000000000 : ℚ)) + (r' := (9175391445551787 / 8000000000000000 : ℚ)) + (U := (-(5560636645839827234383 / 10000000000000000000000 : ℚ))) + (U' := (1370835157160172765617 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (1144783906377353 / 2000000000000000 : ℚ)) + (q := (9175391445551787 / 16000000000000000 : ℚ)) + (U := (-(5560636645839827234383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_7 : Uω (aρ 7) (bρ 7) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1501,25 +1311,21 @@ lemma U_547_7 : have hlg : Real.log (43984582450042547 / 80000000000000000 : ℝ) ≤ (-(2990937303811851794713 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43984582450042547 / 80000000000000000 : ℝ) = - (43984582450042547 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43984582450042547 / 40000000000000000 : ℚ)) - (U := (474798597688148205287 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43984582450042547 / 40000000000000000 : ℝ) ≤ - (474798597688148205287 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1368621804554417 / 2500000000000000 : ℝ)) (q := - (43984582450042547 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43984582450042547 / 80000000000000000 : ℚ)) + (r' := (43984582450042547 / 40000000000000000 : ℚ)) + (U := (-(2990937303811851794713 / 5000000000000000000000 : ℚ))) + (U' := (474798597688148205287 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (1368621804554417 / 2500000000000000 : ℚ)) + (q := (43984582450042547 / 80000000000000000 : ℚ)) + (U := (-(2990937303811851794713 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_8 : Uω (aρ 8) (bρ 8) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1527,25 +1333,21 @@ lemma U_547_8 : have hlg : Real.log (8303217959810399 / 16000000000000000 : ℝ) ≤ (-(3279727881572910084163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8303217959810399 / 16000000000000000 : ℝ) = - (8303217959810399 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8303217959810399 / 8000000000000000 : ℚ)) - (U := (186008019927089915837 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8303217959810399 / 8000000000000000 : ℝ) ≤ - (186008019927089915837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (514090570681003 / 1000000000000000 : ℝ)) (q := - (8303217959810399 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8303217959810399 / 16000000000000000 : ℚ)) + (r' := (8303217959810399 / 8000000000000000 : ℚ)) + (U := (-(3279727881572910084163 / 5000000000000000000000 : ℚ))) + (U' := (186008019927089915837 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (514090570681003 / 1000000000000000 : ℚ)) + (q := (8303217959810399 / 16000000000000000 : ℚ)) + (U := (-(3279727881572910084163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_9 : Uω (aρ 9) (bρ 9) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1553,25 +1355,21 @@ lemma U_547_9 : have hlg : Real.log (38422883898404551 / 80000000000000000 : ℝ) ≤ (-(7333734172046849876191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38422883898404551 / 80000000000000000 : ℝ) = - (38422883898404551 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38422883898404551 / 20000000000000000 : ℚ)) - (U := (6529209433953150123809 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38422883898404551 / 20000000000000000 : ℝ) ≤ - (6529209433953150123809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4708569860008169 / 10000000000000000 : ℝ)) (q := - (38422883898404551 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38422883898404551 / 80000000000000000 : ℚ)) + (r' := (38422883898404551 / 20000000000000000 : ℚ)) + (U := (-(7333734172046849876191 / 10000000000000000000000 : ℚ))) + (U' := (6529209433953150123809 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (4708569860008169 / 10000000000000000 : ℚ)) + (q := (38422883898404551 / 80000000000000000 : ℚ)) + (U := (-(7333734172046849876191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_10 : Uω (aρ 10) (bρ 10) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1579,26 +1377,21 @@ lemma U_547_10 : have hlg : Real.log (34680298668558191 / 80000000000000000 : ℝ) ≤ (-(417927435075955961471 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34680298668558191 / 80000000000000000 : ℝ) = - (34680298668558191 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34680298668558191 / 20000000000000000 : ℚ)) - (U := (275219745224044038529 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34680298668558191 / 20000000000000000 : ℝ) ≤ - (275219745224044038529 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4161482586041579 / 10000000000000000 : ℝ)) (q := - (34680298668558191 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34680298668558191 / 80000000000000000 : ℚ)) + (r' := (34680298668558191 / 20000000000000000 : ℚ)) + (U := (-(417927435075955961471 / 500000000000000000000 : ℚ))) + (U' := (275219745224044038529 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (4161482586041579 / 10000000000000000 : ℚ)) + (q := (34680298668558191 / 80000000000000000 : ℚ)) + (U := (-(417927435075955961471 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_11 : Uω (aρ 11) (bρ 11) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1606,26 +1399,21 @@ lemma U_547_11 : have hlg : Real.log (30269644934577319 / 80000000000000000 : ℝ) ≤ (-(4859406205668740621801 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30269644934577319 / 80000000000000000 : ℝ) = - (30269644934577319 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30269644934577319 / 20000000000000000 : ℚ)) - (U := (2072065597331259378199 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30269644934577319 / 20000000000000000 : ℝ) ≤ - (2072065597331259378199 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3477295778751361 / 10000000000000000 : ℝ)) (q := - (30269644934577319 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30269644934577319 / 80000000000000000 : ℚ)) + (r' := (30269644934577319 / 20000000000000000 : ℚ)) + (U := (-(4859406205668740621801 / 5000000000000000000000 : ℚ))) + (U' := (2072065597331259378199 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (3477295778751361 / 10000000000000000 : ℚ)) + (q := (30269644934577319 / 80000000000000000 : ℚ)) + (U := (-(4859406205668740621801 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_12 : Uω (aρ 12) (bρ 12) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1633,26 +1421,21 @@ lemma U_547_12 : have hlg : Real.log (25096372489155823 / 80000000000000000 : ℝ) ≤ (-(11593033208050026335313 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25096372489155823 / 80000000000000000 : ℝ) = - (25096372489155823 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25096372489155823 / 20000000000000000 : ℚ)) - (U := (2269910397949973664687 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25096372489155823 / 20000000000000000 : ℝ) ≤ - (2269910397949973664687 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2607677764080987 / 10000000000000000 : ℝ)) (q := - (25096372489155823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25096372489155823 / 80000000000000000 : ℚ)) + (r' := (25096372489155823 / 20000000000000000 : ℚ)) + (U := (-(11593033208050026335313 / 10000000000000000000000 : ℚ))) + (U' := (2269910397949973664687 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (2607677764080987 / 10000000000000000 : ℚ)) + (q := (25096372489155823 / 80000000000000000 : ℚ)) + (U := (-(11593033208050026335313 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_13 : Uω (aρ 13) (bρ 13) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1660,26 +1443,21 @@ lemma U_547_13 : have hlg : Real.log (18452678587610763 / 80000000000000000 : ℝ) ≤ (-(183352136630615516529 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18452678587610763 / 80000000000000000 : ℝ) = - (18452678587610763 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18452678587610763 / 10000000000000000 : ℚ)) - (U := (76578055981884483471 / 125000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18452678587610763 / 10000000000000000 : ℝ) ≤ - (76578055981884483471 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (673068015144861 / 5000000000000000 : ℝ)) (q := - (18452678587610763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18452678587610763 / 80000000000000000 : ℚ)) + (r' := (18452678587610763 / 10000000000000000 : ℚ)) + (U := (-(183352136630615516529 / 125000000000000000000 : ℚ))) + (U' := (76578055981884483471 / 125000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (39966122160243 / 64000000000000 : ℚ)) + (s := (673068015144861 / 5000000000000000 : ℚ)) + (q := (18452678587610763 / 80000000000000000 : ℚ)) + (U := (-(183352136630615516529 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_547_14 : Uω (aρ 14) (bρ 14) (39966122160243 / 64000000000000 : ℝ) ≤ @@ -1784,25 +1562,21 @@ lemma U_548_1 : have hlg : Real.log (6190932100316333 / 10000000000000000 : ℝ) ≤ (-(2397497178697846703457 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6190932100316333 / 10000000000000000 : ℝ) = - (6190932100316333 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6190932100316333 / 5000000000000000 : ℚ)) - (U := (1068238722802153296543 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6190932100316333 / 5000000000000000 : ℝ) ≤ - (1068238722802153296543 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6190905986658291 / 10000000000000000 : ℝ)) (q := - (6190932100316333 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6190932100316333 / 10000000000000000 : ℚ)) + (r' := (6190932100316333 / 5000000000000000 : ℚ)) + (U := (-(2397497178697846703457 / 5000000000000000000000 : ℚ))) + (U' := (1068238722802153296543 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (6190905986658291 / 10000000000000000 : ℚ)) + (q := (6190932100316333 / 10000000000000000 : ℚ)) + (U := (-(2397497178697846703457 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_2 : Uω (aρ 2) (bρ 2) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1810,25 +1584,21 @@ lemma U_548_2 : have hlg : Real.log (2466806867612131 / 4000000000000000 : ℝ) ≤ (-(1208424531780068070263 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2466806867612131 / 4000000000000000 : ℝ) = - (2466806867612131 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2466806867612131 / 2000000000000000 : ℚ)) - (U := (524443418969931929737 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2466806867612131 / 2000000000000000 : ℝ) ≤ - (524443418969931929737 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154171128414907 / 250000000000000 : ℝ)) (q := - (2466806867612131 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2466806867612131 / 4000000000000000 : ℚ)) + (r' := (2466806867612131 / 2000000000000000 : ℚ)) + (U := (-(1208424531780068070263 / 2500000000000000000000 : ℚ))) + (U' := (524443418969931929737 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (154171128414907 / 250000000000000 : ℚ)) + (q := (2466806867612131 / 4000000000000000 : ℚ)) + (U := (-(1208424531780068070263 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_3 : Uω (aρ 3) (bρ 3) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1836,25 +1606,21 @@ lemma U_548_3 : have hlg : Real.log (12238377193275971 / 20000000000000000 : ℝ) ≤ (-(613944484060455122537 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12238377193275971 / 20000000000000000 : ℝ) = - (12238377193275971 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12238377193275971 / 10000000000000000 : ℚ)) - (U := (252489491314544877463 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12238377193275971 / 10000000000000000 : ℝ) ≤ - (252489491314544877463 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1529646024540399 / 2500000000000000 : ℝ)) (q := - (12238377193275971 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12238377193275971 / 20000000000000000 : ℚ)) + (r' := (12238377193275971 / 10000000000000000 : ℚ)) + (U := (-(613944484060455122537 / 1250000000000000000000 : ℚ))) + (U' := (252489491314544877463 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (1529646024540399 / 2500000000000000 : ℚ)) + (q := (12238377193275971 / 20000000000000000 : ℚ)) + (U := (-(613944484060455122537 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_4 : Uω (aρ 4) (bρ 4) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1862,25 +1628,21 @@ lemma U_548_4 : have hlg : Real.log (12079514068936013 / 20000000000000000 : ℝ) ≤ (-(252110653838961592423 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12079514068936013 / 20000000000000000 : ℝ) = - (12079514068936013 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12079514068936013 / 10000000000000000 : ℚ)) - (U := (94462936311038407577 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12079514068936013 / 10000000000000000 : ℝ) ≤ - (94462936311038407577 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3019007577443319 / 5000000000000000 : ℝ)) (q := - (12079514068936013 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12079514068936013 / 20000000000000000 : ℚ)) + (r' := (12079514068936013 / 10000000000000000 : ℚ)) + (U := (-(252110653838961592423 / 500000000000000000000 : ℚ))) + (U' := (94462936311038407577 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (3019007577443319 / 5000000000000000 : ℚ)) + (q := (12079514068936013 / 20000000000000000 : ℚ)) + (U := (-(252110653838961592423 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_5 : Uω (aρ 5) (bρ 5) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1888,25 +1650,21 @@ lemma U_548_5 : have hlg : Real.log (5918810043115331 / 10000000000000000 : ℝ) ≤ (-(5244496702731643532673 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5918810043115331 / 10000000000000000 : ℝ) = - (5918810043115331 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5918810043115331 / 5000000000000000 : ℚ)) - (U := (1686975100268356467327 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5918810043115331 / 5000000000000000 : ℝ) ≤ - (1686975100268356467327 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5914311091516287 / 10000000000000000 : ℝ)) (q := - (5918810043115331 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5918810043115331 / 10000000000000000 : ℚ)) + (r' := (5918810043115331 / 5000000000000000 : ℚ)) + (U := (-(5244496702731643532673 / 10000000000000000000000 : ℚ))) + (U' := (1686975100268356467327 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (5914311091516287 / 10000000000000000 : ℚ)) + (q := (5918810043115331 / 10000000000000000 : ℚ)) + (U := (-(5244496702731643532673 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_6 : Uω (aρ 6) (bρ 6) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1914,25 +1672,21 @@ lemma U_548_6 : have hlg : Real.log (11490777107644973 / 20000000000000000 : ℝ) ≤ (-(55418755033094918291 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11490777107644973 / 20000000000000000 : ℝ) = - (11490777107644973 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11490777107644973 / 10000000000000000 : ℚ)) - (U := (13895962996905081709 / 100000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11490777107644973 / 10000000000000000 : ℝ) ≤ - (13895962996905081709 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2867354244035299 / 5000000000000000 : ℝ)) (q := - (11490777107644973 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11490777107644973 / 20000000000000000 : ℚ)) + (r' := (11490777107644973 / 10000000000000000 : ℚ)) + (U := (-(55418755033094918291 / 100000000000000000000 : ℚ))) + (U' := (13895962996905081709 / 100000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (2867354244035299 / 5000000000000000 : ℚ)) + (q := (11490777107644973 / 20000000000000000 : ℚ)) + (U := (-(55418755033094918291 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_7 : Uω (aρ 7) (bρ 7) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1940,25 +1694,21 @@ lemma U_548_7 : have hlg : Real.log (11017735737204267 / 20000000000000000 : ℝ) ≤ (-(953961534678529139 / 1600000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11017735737204267 / 20000000000000000 : ℝ) = - (11017735737204267 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11017735737204267 / 10000000000000000 : ℚ)) - (U := (155073953801470861 / 1600000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11017735737204267 / 10000000000000000 : ℝ) ≤ - (155073953801470861 / 1600000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1371332124597473 / 2500000000000000 : ℝ)) (q := - (11017735737204267 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11017735737204267 / 20000000000000000 : ℚ)) + (r' := (11017735737204267 / 10000000000000000 : ℚ)) + (U := (-(953961534678529139 / 1600000000000000000 : ℚ))) + (U' := (155073953801470861 / 1600000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (1371332124597473 / 2500000000000000 : ℚ)) + (q := (11017735737204267 / 20000000000000000 : ℚ)) + (U := (-(953961534678529139 / 1600000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_8 : Uω (aρ 8) (bρ 8) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1966,25 +1716,21 @@ lemma U_548_8 : have hlg : Real.log (260018074101987 / 500000000000000 : ℝ) ≤ (-(1634642384464888181893 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (260018074101987 / 500000000000000 : ℝ) = - (260018074101987 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (260018074101987 / 250000000000000 : ℚ)) - (U := (98225566285111818107 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (260018074101987 / 250000000000000 : ℝ) ≤ - (98225566285111818107 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1030371475321021 / 2000000000000000 : ℝ)) (q := - (260018074101987 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (260018074101987 / 500000000000000 : ℚ)) + (r' := (260018074101987 / 250000000000000 : ℚ)) + (U := (-(1634642384464888181893 / 2500000000000000000000 : ℚ))) + (U' := (98225566285111818107 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (1030371475321021 / 2000000000000000 : ℚ)) + (q := (260018074101987 / 500000000000000 : ℚ)) + (U := (-(1634642384464888181893 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_9 : Uω (aρ 9) (bρ 9) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -1992,25 +1738,21 @@ lemma U_548_9 : have hlg : Real.log (2406912040432491 / 5000000000000000 : ℝ) ≤ (-(3655466485081770504419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2406912040432491 / 5000000000000000 : ℝ) = - (2406912040432491 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2406912040432491 / 1250000000000000 : ℚ)) - (U := (3276005317918229495581 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2406912040432491 / 1250000000000000 : ℝ) ≤ - (3276005317918229495581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4719748202615589 / 10000000000000000 : ℝ)) (q := - (2406912040432491 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2406912040432491 / 5000000000000000 : ℚ)) + (r' := (2406912040432491 / 1250000000000000 : ℚ)) + (U := (-(3655466485081770504419 / 5000000000000000000000 : ℚ))) + (U' := (3276005317918229495581 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (4719748202615589 / 10000000000000000 : ℚ)) + (q := (2406912040432491 / 5000000000000000 : ℚ)) + (U := (-(3655466485081770504419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_10 : Uω (aρ 10) (bρ 10) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -2018,26 +1760,21 @@ lemma U_548_10 : have hlg : Real.log (8692466512294929 / 20000000000000000 : ℝ) ≤ (-(4166377703121249495059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8692466512294929 / 20000000000000000 : ℝ) = - (8692466512294929 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8692466512294929 / 5000000000000000 : ℚ)) - (U := (2765094099878750504941 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8692466512294929 / 5000000000000000 : ℝ) ≤ - (2765094099878750504941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2086562793337777 / 5000000000000000 : ℝ)) (q := - (8692466512294929 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8692466512294929 / 20000000000000000 : ℚ)) + (r' := (8692466512294929 / 5000000000000000 : ℚ)) + (U := (-(4166377703121249495059 / 5000000000000000000000 : ℚ))) + (U' := (2765094099878750504941 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (2086562793337777 / 5000000000000000 : ℚ)) + (q := (8692466512294929 / 20000000000000000 : ℚ)) + (U := (-(4166377703121249495059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_11 : Uω (aρ 11) (bρ 11) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -2045,26 +1782,21 @@ lemma U_548_11 : have hlg : Real.log (7590796891998231 / 20000000000000000 : ℝ) ≤ (-(121099461847467560769 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7590796891998231 / 20000000000000000 : ℝ) = - (7590796891998231 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7590796891998231 / 5000000000000000 : ℚ)) - (U := (52187333227532439231 / 125000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7590796891998231 / 5000000000000000 : ℝ) ≤ - (52187333227532439231 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (218120787036491 / 625000000000000 : ℝ)) (q := - (7590796891998231 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7590796891998231 / 20000000000000000 : ℚ)) + (r' := (7590796891998231 / 5000000000000000 : ℚ)) + (U := (-(121099461847467560769 / 125000000000000000000 : ℚ))) + (U' := (52187333227532439231 / 125000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (218120787036491 / 625000000000000 : ℚ)) + (q := (7590796891998231 / 20000000000000000 : ℚ)) + (U := (-(121099461847467560769 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_12 : Uω (aρ 12) (bρ 12) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -2072,26 +1804,21 @@ lemma U_548_12 : have hlg : Real.log (1259986682061253 / 4000000000000000 : ℝ) ≤ (-(5775966047425651859671 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1259986682061253 / 4000000000000000 : ℝ) = - (1259986682061253 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1259986682061253 / 1000000000000000 : ℚ)) - (U := (1155505755574348140329 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1259986682061253 / 1000000000000000 : ℝ) ≤ - (1155505755574348140329 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (262276920757689 / 1000000000000000 : ℝ)) (q := - (1259986682061253 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1259986682061253 / 4000000000000000 : ℚ)) + (r' := (1259986682061253 / 1000000000000000 : ℚ)) + (U := (-(5775966047425651859671 / 5000000000000000000000 : ℚ))) + (U' := (1155505755574348140329 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (262276920757689 / 1000000000000000 : ℚ)) + (q := (1259986682061253 / 4000000000000000 : ℚ)) + (U := (-(5775966047425651859671 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_13 : Uω (aρ 13) (bρ 13) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -2099,26 +1826,21 @@ lemma U_548_13 : have hlg : Real.log (2324899871636139 / 10000000000000000 : ℝ) ≤ (-(3647270300163015730903 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2324899871636139 / 10000000000000000 : ℝ) = - (2324899871636139 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2324899871636139 / 1250000000000000 : ℚ)) - (U := (1551333552086984269097 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2324899871636139 / 1250000000000000 : ℝ) ≤ - (1551333552086984269097 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1372017282137903 / 10000000000000000 : ℝ)) (q := - (2324899871636139 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2324899871636139 / 10000000000000000 : ℚ)) + (r' := (2324899871636139 / 1250000000000000 : ℚ)) + (U := (-(3647270300163015730903 / 2500000000000000000000 : ℚ))) + (U' := (1551333552086984269097 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2001745738259 / 3200000000000 : ℚ)) + (s := (1372017282137903 / 10000000000000000 : ℚ)) + (q := (2324899871636139 / 10000000000000000 : ℚ)) + (U := (-(3647270300163015730903 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_548_14 : Uω (aρ 14) (bρ 14) (2001745738259 / 3200000000000 : ℝ) ≤ @@ -2222,25 +1944,21 @@ lemma U_549_1 : have hlg : Real.log (49613447920788041 / 80000000000000000 : ℝ) ≤ (-(1194411774990531570599 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49613447920788041 / 80000000000000000 : ℝ) = - (49613447920788041 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49613447920788041 / 40000000000000000 : ℚ)) - (U := (538456175759468429401 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49613447920788041 / 40000000000000000 : ℝ) ≤ - (538456175759468429401 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6201654921701229 / 10000000000000000 : ℝ)) (q := - (49613447920788041 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49613447920788041 / 80000000000000000 : ℚ)) + (r' := (49613447920788041 / 40000000000000000 : ℚ)) + (U := (-(1194411774990531570599 / 2500000000000000000000 : ℚ))) + (U' := (538456175759468429401 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (6201654921701229 / 10000000000000000 : ℚ)) + (q := (49613447920788041 / 80000000000000000 : ℚ)) + (U := (-(1194411774990531570599 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_2 : Uω (aρ 2) (bρ 2) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2248,25 +1966,21 @@ lemma U_549_2 : have hlg : Real.log (9884426100613517 / 16000000000000000 : ℝ) ≤ (-(4816283246437239450033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9884426100613517 / 16000000000000000 : ℝ) = - (9884426100613517 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9884426100613517 / 8000000000000000 : ℚ)) - (U := (2115188556562760549967 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9884426100613517 / 8000000000000000 : ℝ) ≤ - (2115188556562760549967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1235518915956223 / 2000000000000000 : ℝ)) (q := - (9884426100613517 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9884426100613517 / 16000000000000000 : ℚ)) + (r' := (9884426100613517 / 8000000000000000 : ℚ)) + (U := (-(4816283246437239450033 / 10000000000000000000000 : ℚ))) + (U' := (2115188556562760549967 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (1235518915956223 / 2000000000000000 : ℚ)) + (q := (9884426100613517 / 16000000000000000 : ℚ)) + (U := (-(4816283246437239450033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_3 : Uω (aρ 3) (bρ 3) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2274,25 +1988,21 @@ lemma U_549_3 : have hlg : Real.log (49039508010013997 / 80000000000000000 : ℝ) ≤ (-(195760150103412896917 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49039508010013997 / 80000000000000000 : ℝ) = - (49039508010013997 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49039508010013997 / 40000000000000000 : ℚ)) - (U := (81498722016587103083 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49039508010013997 / 40000000000000000 : ℝ) ≤ - (81498722016587103083 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3064667531433859 / 5000000000000000 : ℝ)) (q := - (49039508010013997 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49039508010013997 / 80000000000000000 : ℚ)) + (r' := (49039508010013997 / 40000000000000000 : ℚ)) + (U := (-(195760150103412896917 / 400000000000000000000 : ℚ))) + (U' := (81498722016587103083 / 400000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (3064667531433859 / 5000000000000000 : ℚ)) + (q := (49039508010013997 / 80000000000000000 : ℚ)) + (U := (-(195760150103412896917 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_4 : Uω (aρ 4) (bρ 4) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2300,25 +2010,21 @@ lemma U_549_4 : have hlg : Real.log (48404071794902537 / 80000000000000000 : ℝ) ≤ (-(1256106740590143561431 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48404071794902537 / 80000000000000000 : ℝ) = - (48404071794902537 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48404071794902537 / 40000000000000000 : ℚ)) - (U := (476761210159856438569 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48404071794902537 / 40000000000000000 : ℝ) ≤ - (476761210159856438569 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6048770190154853 / 10000000000000000 : ℝ)) (q := - (48404071794902537 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48404071794902537 / 80000000000000000 : ℚ)) + (r' := (48404071794902537 / 40000000000000000 : ℚ)) + (U := (-(1256106740590143561431 / 2500000000000000000000 : ℚ))) + (U' := (476761210159856438569 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (6048770190154853 / 10000000000000000 : ℚ)) + (q := (48404071794902537 / 80000000000000000 : ℚ)) + (U := (-(1256106740590143561431 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_5 : Uω (aρ 5) (bρ 5) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2326,25 +2032,21 @@ lemma U_549_5 : have hlg : Real.log (47436536394562869 / 80000000000000000 : ℝ) ≤ (-(653292365778121990287 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47436536394562869 / 80000000000000000 : ℝ) = - (47436536394562869 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47436536394562869 / 40000000000000000 : ℚ)) - (U := (213141609596878009713 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47436536394562869 / 40000000000000000 : ℝ) ≤ - (213141609596878009713 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (740634532425617 / 1250000000000000 : ℝ)) (q := - (47436536394562869 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47436536394562869 / 80000000000000000 : ℚ)) + (r' := (47436536394562869 / 40000000000000000 : ℚ)) + (U := (-(653292365778121990287 / 1250000000000000000000 : ℚ))) + (U' := (213141609596878009713 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (740634532425617 / 1250000000000000 : ℚ)) + (q := (47436536394562869 / 80000000000000000 : ℚ)) + (U := (-(653292365778121990287 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_6 : Uω (aρ 6) (bρ 6) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2352,25 +2054,21 @@ lemma U_549_6 : have hlg : Real.log (46049259031944133 / 80000000000000000 : ℝ) ≤ (-(690393702942002721149 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46049259031944133 / 80000000000000000 : ℝ) = - (46049259031944133 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46049259031944133 / 40000000000000000 : ℚ)) - (U := (176040272432997278851 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46049259031944133 / 40000000000000000 : ℝ) ≤ - (176040272432997278851 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1436374323472563 / 2500000000000000 : ℝ)) (q := - (46049259031944133 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46049259031944133 / 80000000000000000 : ℚ)) + (r' := (46049259031944133 / 40000000000000000 : ℚ)) + (U := (-(690393702942002721149 / 1250000000000000000000 : ℚ))) + (U' := (176040272432997278851 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (1436374323472563 / 2500000000000000 : ℚ)) + (q := (46049259031944133 / 80000000000000000 : ℚ)) + (U := (-(690393702942002721149 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_7 : Uω (aρ 7) (bρ 7) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2378,25 +2076,21 @@ lemma U_549_7 : have hlg : Real.log (44157301995163901 / 80000000000000000 : ℝ) ≤ (-(185708853261108282267 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44157301995163901 / 80000000000000000 : ℝ) = - (44157301995163901 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44157301995163901 / 40000000000000000 : ℚ)) - (U := (30899640582641717733 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44157301995163901 / 40000000000000000 : ℝ) ≤ - (30899640582641717733 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2748084707727597 / 5000000000000000 : ℝ)) (q := - (44157301995163901 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44157301995163901 / 80000000000000000 : ℚ)) + (r' := (44157301995163901 / 40000000000000000 : ℚ)) + (U := (-(185708853261108282267 / 312500000000000000000 : ℚ))) + (U' := (30899640582641717733 / 312500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (2748084707727597 / 5000000000000000 : ℚ)) + (q := (44157301995163901 / 80000000000000000 : ℚ)) + (U := (-(185708853261108282267 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_8 : Uω (aρ 8) (bρ 8) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2404,25 +2098,21 @@ lemma U_549_8 : have hlg : Real.log (8337938100698421 / 16000000000000000 : ℝ) ≤ (-(6517727663076715180429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8337938100698421 / 16000000000000000 : ℝ) = - (8337938100698421 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8337938100698421 / 8000000000000000 : ℚ)) - (U := (413744139923284819571 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8337938100698421 / 8000000000000000 : ℝ) ≤ - (413744139923284819571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1032561638775449 / 2000000000000000 : ℝ)) (q := - (8337938100698421 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8337938100698421 / 16000000000000000 : ℚ)) + (r' := (8337938100698421 / 8000000000000000 : ℚ)) + (U := (-(6517727663076715180429 / 10000000000000000000000 : ℚ))) + (U' := (413744139923284819571 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (1032561638775449 / 2000000000000000 : ℚ)) + (q := (8337938100698421 / 16000000000000000 : ℚ)) + (U := (-(6517727663076715180429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_9 : Uω (aρ 9) (bρ 9) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2430,25 +2120,21 @@ lemma U_549_9 : have hlg : Real.log (38598293432777697 / 80000000000000000 : ℝ) ≤ (-(7288185702466368188041 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38598293432777697 / 80000000000000000 : ℝ) = - (38598293432777697 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38598293432777697 / 20000000000000000 : ℚ)) - (U := (6574757903533631811959 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38598293432777697 / 20000000000000000 : ℝ) ≤ - (6574757903533631811959 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4730924554558643 / 10000000000000000 : ℝ)) (q := - (38598293432777697 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38598293432777697 / 80000000000000000 : ℚ)) + (r' := (38598293432777697 / 20000000000000000 : ℚ)) + (U := (-(7288185702466368188041 / 10000000000000000000000 : ℚ))) + (U' := (6574757903533631811959 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (4730924554558643 / 10000000000000000 : ℚ)) + (q := (38598293432777697 / 80000000000000000 : ℚ)) + (U := (-(7288185702466368188041 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_10 : Uω (aρ 10) (bρ 10) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2456,26 +2142,21 @@ lemma U_549_10 : have hlg : Real.log (34859414292000669 / 80000000000000000 : ℝ) ≤ (-(8307033959244178314683 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34859414292000669 / 80000000000000000 : ℝ) = - (34859414292000669 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34859414292000669 / 20000000000000000 : ℚ)) - (U := (5555909646755821685317 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34859414292000669 / 20000000000000000 : ℝ) ≤ - (5555909646755821685317 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2092381901429693 / 5000000000000000 : ℝ)) (q := - (34859414292000669 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34859414292000669 / 80000000000000000 : ℚ)) + (r' := (34859414292000669 / 20000000000000000 : ℚ)) + (U := (-(8307033959244178314683 / 10000000000000000000000 : ℚ))) + (U' := (5555909646755821685317 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (2092381901429693 / 5000000000000000 : ℚ)) + (q := (34859414292000669 / 80000000000000000 : ℚ)) + (U := (-(8307033959244178314683 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_11 : Uω (aρ 11) (bρ 11) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2483,26 +2164,21 @@ lemma U_549_11 : have hlg : Real.log (30456679779584297 / 80000000000000000 : ℝ) ≤ (-(603575809542648455083 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30456679779584297 / 80000000000000000 : ℝ) = - (30456679779584297 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30456679779584297 / 20000000000000000 : ℚ)) - (U := (262858165832351544917 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30456679779584297 / 20000000000000000 : ℝ) ≤ - (262858165832351544917 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3502556800960293 / 10000000000000000 : ℝ)) (q := - (30456679779584297 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30456679779584297 / 80000000000000000 : ℚ)) + (r' := (30456679779584297 / 20000000000000000 : ℚ)) + (U := (-(603575809542648455083 / 625000000000000000000 : ℚ))) + (U' := (262858165832351544917 / 625000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (3502556800960293 / 10000000000000000 : ℚ)) + (q := (30456679779584297 / 80000000000000000 : ℚ)) + (U := (-(603575809542648455083 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_12 : Uω (aρ 12) (bρ 12) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2510,26 +2186,21 @@ lemma U_549_12 : have hlg : Real.log (25302924632807569 / 80000000000000000 : ℝ) ≤ (-(5755533234833897135403 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25302924632807569 / 80000000000000000 : ℝ) = - (25302924632807569 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25302924632807569 / 20000000000000000 : ℚ)) - (U := (1175938568166102864597 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25302924632807569 / 20000000000000000 : ℝ) ≤ - (1175938568166102864597 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2637818110951111 / 10000000000000000 : ℝ)) (q := - (25302924632807569 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25302924632807569 / 80000000000000000 : ℚ)) + (r' := (25302924632807569 / 20000000000000000 : ℚ)) + (U := (-(5755533234833897135403 / 5000000000000000000000 : ℚ))) + (U' := (1175938568166102864597 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (2637818110951111 / 10000000000000000 : ℚ)) + (q := (25302924632807569 / 80000000000000000 : ℚ)) + (U := (-(5755533234833897135403 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_13 : Uω (aρ 13) (bρ 13) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2537,26 +2208,21 @@ lemma U_549_13 : have hlg : Real.log (18744133034056773 / 80000000000000000 : ℝ) ≤ (-(14511458352928684789089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18744133034056773 / 80000000000000000 : ℝ) = - (18744133034056773 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18744133034056773 / 10000000000000000 : ℚ)) - (U := (6282957056071315210911 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18744133034056773 / 10000000000000000 : ℝ) ≤ - (6282957056071315210911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (349375488214603 / 2500000000000000 : ℝ)) (q := - (18744133034056773 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18744133034056773 / 80000000000000000 : ℚ)) + (r' := (18744133034056773 / 10000000000000000 : ℚ)) + (U := (-(14511458352928684789089 / 10000000000000000000000 : ℚ))) + (U' := (6282957056071315210911 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40103707370117 / 64000000000000 : ℚ)) + (s := (349375488214603 / 2500000000000000 : ℚ)) + (q := (18744133034056773 / 80000000000000000 : ℚ)) + (U := (-(14511458352928684789089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_549_14 : Uω (aρ 14) (bρ 14) (40103707370117 / 64000000000000 : ℝ) ≤ @@ -2662,25 +2328,21 @@ lemma U_550_1 : have hlg : Real.log (24849719518896217 / 40000000000000000 : ℝ) ≤ (-(4760329883409985412941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24849719518896217 / 40000000000000000 : ℝ) = - (24849719518896217 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24849719518896217 / 20000000000000000 : ℚ)) - (U := (2171141919590014587059 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24849719518896217 / 20000000000000000 : ℝ) ≤ - (2171141919590014587059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6212403856430921 / 10000000000000000 : ℝ)) (q := - (24849719518896217 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24849719518896217 / 40000000000000000 : ℚ)) + (r' := (24849719518896217 / 20000000000000000 : ℚ)) + (U := (-(4760329883409985412941 / 10000000000000000000000 : ℚ))) + (U' := (2171141919590014587059 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (6212403856430921 / 10000000000000000 : ℚ)) + (q := (24849719518896217 / 40000000000000000 : ℚ)) + (U := (-(4760329883409985412941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_2 : Uω (aρ 2) (bρ 2) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2688,25 +2350,21 @@ lemma U_550_2 : have hlg : Real.log (4950812364557353 / 8000000000000000 : ℝ) ≤ (-(959779728505078014553 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4950812364557353 / 8000000000000000 : ℝ) = - (4950812364557353 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4950812364557353 / 4000000000000000 : ℚ)) - (U := (426514632094921985447 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4950812364557353 / 4000000000000000 : ℝ) ≤ - (426514632094921985447 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1237668804177239 / 2000000000000000 : ℝ)) (q := - (4950812364557353 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4950812364557353 / 8000000000000000 : ℚ)) + (r' := (4950812364557353 / 4000000000000000 : ℚ)) + (U := (-(959779728505078014553 / 2000000000000000000000 : ℚ))) + (U' := (426514632094921985447 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (1237668804177239 / 2000000000000000 : ℚ)) + (q := (4950812364557353 / 8000000000000000 : ℚ)) + (U := (-(959779728505078014553 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_3 : Uω (aρ 3) (bρ 3) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2714,25 +2372,21 @@ lemma U_550_3 : have hlg : Real.log (24562753608614197 / 40000000000000000 : ℝ) ≤ (-(2438241196225873571523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24562753608614197 / 40000000000000000 : ℝ) = - (24562753608614197 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24562753608614197 / 20000000000000000 : ℚ)) - (U := (1027494705274126428477 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24562753608614197 / 20000000000000000 : ℝ) ≤ - (1027494705274126428477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6140086020149911 / 10000000000000000 : ℝ)) (q := - (24562753608614197 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24562753608614197 / 40000000000000000 : ℚ)) + (r' := (24562753608614197 / 20000000000000000 : ℚ)) + (U := (-(2438241196225873571523 / 5000000000000000000000 : ℚ))) + (U' := (1027494705274126428477 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (6140086020149911 / 10000000000000000 : ℚ)) + (q := (24562753608614197 / 40000000000000000 : ℚ)) + (U := (-(2438241196225873571523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_4 : Uω (aρ 4) (bρ 4) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2740,25 +2394,21 @@ lemma U_550_4 : have hlg : Real.log (24245043613091401 / 40000000000000000 : ℝ) ≤ (-(19557314236304715771 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24245043613091401 / 40000000000000000 : ℝ) = - (24245043613091401 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24245043613091401 / 20000000000000000 : ℚ)) - (U := (7518747494164034229 / 39062500000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24245043613091401 / 20000000000000000 : ℝ) ≤ - (7518747494164034229 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6059525203453513 / 10000000000000000 : ℝ)) (q := - (24245043613091401 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24245043613091401 / 40000000000000000 : ℚ)) + (r' := (24245043613091401 / 20000000000000000 : ℚ)) + (U := (-(19557314236304715771 / 39062500000000000000 : ℚ))) + (U' := (7518747494164034229 / 39062500000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (6059525203453513 / 10000000000000000 : ℚ)) + (q := (24245043613091401 / 40000000000000000 : ℚ)) + (U := (-(19557314236304715771 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_5 : Uω (aρ 5) (bρ 5) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2766,25 +2416,21 @@ lemma U_550_5 : have hlg : Real.log (23761296103775901 / 40000000000000000 : ℝ) ≤ (-(520821411025116205967 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23761296103775901 / 40000000000000000 : ℝ) = - (23761296103775901 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23761296103775901 / 20000000000000000 : ℚ)) - (U := (172325769274883794033 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23761296103775901 / 20000000000000000 : ℝ) ≤ - (172325769274883794033 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5935841368130763 / 10000000000000000 : ℝ)) (q := - (23761296103775901 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23761296103775901 / 40000000000000000 : ℚ)) + (r' := (23761296103775901 / 20000000000000000 : ℚ)) + (U := (-(520821411025116205967 / 1000000000000000000000 : ℚ))) + (U' := (172325769274883794033 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (5935841368130763 / 10000000000000000 : ℚ)) + (q := (23761296103775901 / 40000000000000000 : ℚ)) + (U := (-(520821411025116205967 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_6 : Uω (aρ 6) (bρ 6) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2792,25 +2438,21 @@ lemma U_550_6 : have hlg : Real.log (4613540903523353 / 8000000000000000 : ℝ) ≤ (-(5504458873723566257013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4613540903523353 / 8000000000000000 : ℝ) = - (4613540903523353 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4613540903523353 / 4000000000000000 : ℚ)) - (U := (1427012929276433742987 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4613540903523353 / 4000000000000000 : ℝ) ≤ - (1427012929276433742987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1151257190038239 / 2000000000000000 : ℝ)) (q := - (4613540903523353 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4613540903523353 / 8000000000000000 : ℚ)) + (r' := (4613540903523353 / 4000000000000000 : ℚ)) + (U := (-(5504458873723566257013 / 10000000000000000000000 : ℚ))) + (U' := (1427012929276433742987 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (1151257190038239 / 2000000000000000 : ℚ)) + (q := (4613540903523353 / 8000000000000000 : ℚ)) + (U := (-(5504458873723566257013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_7 : Uω (aρ 7) (bρ 7) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2818,25 +2460,21 @@ lemma U_550_7 : have hlg : Real.log (22121829798830323 / 40000000000000000 : ℝ) ≤ (-(1184629118309960228537 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22121829798830323 / 40000000000000000 : ℝ) = - (22121829798830323 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22121829798830323 / 20000000000000000 : ℚ)) - (U := (201665242290039771463 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22121829798830323 / 20000000000000000 : ℝ) ≤ - (201665242290039771463 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2753504985778987 / 5000000000000000 : ℝ)) (q := - (22121829798830323 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22121829798830323 / 40000000000000000 : ℚ)) + (r' := (22121829798830323 / 20000000000000000 : ℚ)) + (U := (-(1184629118309960228537 / 2000000000000000000000 : ℚ))) + (U' := (201665242290039771463 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (2753504985778987 / 5000000000000000 : ℚ)) + (q := (22121829798830323 / 40000000000000000 : ℚ)) + (U := (-(1184629118309960228537 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_8 : Uω (aρ 8) (bρ 8) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2844,25 +2482,21 @@ lemma U_550_8 : have hlg : Real.log (20888242881114017 / 40000000000000000 : ℝ) ≤ (-(6496929947425930102249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20888242881114017 / 40000000000000000 : ℝ) = - (20888242881114017 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20888242881114017 / 20000000000000000 : ℚ)) - (U := (434541855574069897751 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20888242881114017 / 20000000000000000 : ℝ) ≤ - (434541855574069897751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5173758164039821 / 10000000000000000 : ℝ)) (q := - (20888242881114017 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20888242881114017 / 40000000000000000 : ℚ)) + (r' := (20888242881114017 / 20000000000000000 : ℚ)) + (U := (-(6496929947425930102249 / 10000000000000000000000 : ℚ))) + (U' := (434541855574069897751 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (5173758164039821 / 10000000000000000 : ℚ)) + (q := (20888242881114017 / 40000000000000000 : ℚ)) + (U := (-(6496929947425930102249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_9 : Uω (aρ 9) (bρ 9) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2870,25 +2504,21 @@ lemma U_550_9 : have hlg : Real.log (3868598631227813 / 8000000000000000 : ℝ) ≤ (-(3632746052450233074369 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3868598631227813 / 8000000000000000 : ℝ) = - (3868598631227813 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3868598631227813 / 2000000000000000 : ℚ)) - (U := (3298725750549766925631 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3868598631227813 / 2000000000000000 : ℝ) ≤ - (3298725750549766925631 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (948419785982469 / 2000000000000000 : ℝ)) (q := - (3868598631227813 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3868598631227813 / 8000000000000000 : ℚ)) + (r' := (3868598631227813 / 2000000000000000 : ℚ)) + (U := (-(3632746052450233074369 / 5000000000000000000000 : ℚ))) + (U' := (3298725750549766925631 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (948419785982469 / 2000000000000000 : ℚ)) + (q := (3868598631227813 / 8000000000000000 : ℚ)) + (U := (-(3632746052450233074369 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_10 : Uω (aρ 10) (bρ 10) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2896,26 +2526,21 @@ lemma U_550_10 : have hlg : Real.log (17474471778125199 / 40000000000000000 : ℝ) ≤ (-(8281383932199983076381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17474471778125199 / 40000000000000000 : ℝ) = - (17474471778125199 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17474471778125199 / 10000000000000000 : ℚ)) - (U := (5581559673800016923619 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17474471778125199 / 10000000000000000 : ℝ) ≤ - (5581559673800016923619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1049099318600103 / 2500000000000000 : ℝ)) (q := - (17474471778125199 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17474471778125199 / 40000000000000000 : ℚ)) + (r' := (17474471778125199 / 10000000000000000 : ℚ)) + (U := (-(8281383932199983076381 / 10000000000000000000000 : ℚ))) + (U' := (5581559673800016923619 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (1049099318600103 / 2500000000000000 : ℚ)) + (q := (17474471778125199 / 40000000000000000 : ℚ)) + (U := (-(8281383932199983076381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_11 : Uω (aρ 11) (bρ 11) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2923,26 +2548,21 @@ lemma U_550_11 : have hlg : Real.log (15275061056299521 / 40000000000000000 : ℝ) ≤ (-(9626579514052903566141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15275061056299521 / 40000000000000000 : ℝ) = - (15275061056299521 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15275061056299521 / 10000000000000000 : ℚ)) - (U := (4236364091947096433859 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15275061056299521 / 10000000000000000 : ℝ) ≤ - (4236364091947096433859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3515168539692573 / 10000000000000000 : ℝ)) (q := - (15275061056299521 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15275061056299521 / 40000000000000000 : ℚ)) + (r' := (15275061056299521 / 10000000000000000 : ℚ)) + (U := (-(9626579514052903566141 / 10000000000000000000000 : ℚ))) + (U' := (4236364091947096433859 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (3515168539692573 / 10000000000000000 : ℚ)) + (q := (15275061056299521 / 40000000000000000 : ℚ)) + (U := (-(9626579514052903566141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_12 : Uω (aρ 12) (bρ 12) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2950,26 +2570,21 @@ lemma U_550_12 : have hlg : Real.log (12702974179877313 / 40000000000000000 : ℝ) ≤ (-(11470433001551724661083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12702974179877313 / 40000000000000000 : ℝ) = - (12702974179877313 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12702974179877313 / 10000000000000000 : ℚ)) - (U := (2392510604448275338917 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12702974179877313 / 10000000000000000 : ℝ) ≤ - (2392510604448275338917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2652825198166469 / 10000000000000000 : ℝ)) (q := - (12702974179877313 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12702974179877313 / 40000000000000000 : ℚ)) + (r' := (12702974179877313 / 10000000000000000 : ℚ)) + (U := (-(11470433001551724661083 / 10000000000000000000000 : ℚ))) + (U' := (2392510604448275338917 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (2652825198166469 / 10000000000000000 : ℚ)) + (q := (12702974179877313 / 40000000000000000 : ℚ)) + (U := (-(11470433001551724661083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_13 : Uω (aρ 13) (bρ 13) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -2977,26 +2592,21 @@ lemma U_550_13 : have hlg : Real.log (9443783011720333 / 40000000000000000 : ℝ) ≤ (-(7217614053428216597823 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9443783011720333 / 40000000000000000 : ℝ) = - (9443783011720333 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9443783011720333 / 5000000000000000 : ℚ)) - (U := (3179593651071783402177 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9443783011720333 / 5000000000000000 : ℝ) ≤ - (3179593651071783402177 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1422611355682979 / 10000000000000000 : ℝ)) (q := - (9443783011720333 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9443783011720333 / 40000000000000000 : ℚ)) + (r' := (9443783011720333 / 5000000000000000 : ℚ)) + (U := (-(7217614053428216597823 / 5000000000000000000000 : ℚ))) + (U' := (3179593651071783402177 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20086249987527 / 32000000000000 : ℚ)) + (s := (1422611355682979 / 10000000000000000 : ℚ)) + (q := (9443783011720333 / 40000000000000000 : ℚ)) + (U := (-(7217614053428216597823 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_550_14 : Uω (aρ 14) (bρ 14) (20086249987527 / 32000000000000 : ℝ) ≤ @@ -3102,25 +2712,21 @@ lemma U_551_1 : have hlg : Real.log (9957086030710067 / 16000000000000000 : ℝ) ≤ (-(4743042603872454263259 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9957086030710067 / 16000000000000000 : ℝ) = - (9957086030710067 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9957086030710067 / 8000000000000000 : ℚ)) - (U := (2188429199127545736741 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9957086030710067 / 8000000000000000 : ℝ) ≤ - (2188429199127545736741 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (622315279084899 / 1000000000000000 : ℝ)) (q := - (9957086030710067 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9957086030710067 / 16000000000000000 : ℚ)) + (r' := (9957086030710067 / 8000000000000000 : ℚ)) + (U := (-(4743042603872454263259 / 10000000000000000000000 : ℚ))) + (U' := (2188429199127545736741 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (622315279084899 / 1000000000000000 : ℚ)) + (q := (9957086030710067 / 16000000000000000 : ℚ)) + (U := (-(4743042603872454263259 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_2 : Uω (aρ 2) (bρ 2) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3128,25 +2734,21 @@ lemma U_551_2 : have hlg : Real.log (49594116779803731 / 80000000000000000 : ℝ) ≤ (-(2390772105142890830111 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49594116779803731 / 80000000000000000 : ℝ) = - (49594116779803731 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49594116779803731 / 40000000000000000 : ℚ)) - (U := (1074963796357109169889 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49594116779803731 / 40000000000000000 : ℝ) ≤ - (1074963796357109169889 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6199093459922339 / 10000000000000000 : ℝ)) (q := - (49594116779803731 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49594116779803731 / 80000000000000000 : ℚ)) + (r' := (49594116779803731 / 40000000000000000 : ℚ)) + (U := (-(2390772105142890830111 / 5000000000000000000000 : ℚ))) + (U' := (1074963796357109169889 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (6199093459922339 / 10000000000000000 : ℚ)) + (q := (49594116779803731 / 80000000000000000 : ℚ)) + (U := (-(2390772105142890830111 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_3 : Uω (aρ 3) (bρ 3) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3154,25 +2756,21 @@ lemma U_551_3 : have hlg : Real.log (49211506394902783 / 80000000000000000 : ℝ) ≤ (-(2429495842219293840209 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49211506394902783 / 80000000000000000 : ℝ) = - (49211506394902783 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49211506394902783 / 40000000000000000 : ℚ)) - (U := (1036240059280706159791 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49211506394902783 / 40000000000000000 : ℝ) ≤ - (1036240059280706159791 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3075418485023551 / 5000000000000000 : ℝ)) (q := - (49211506394902783 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49211506394902783 / 80000000000000000 : ℚ)) + (r' := (49211506394902783 / 40000000000000000 : ℚ)) + (U := (-(2429495842219293840209 / 5000000000000000000000 : ℚ))) + (U' := (1036240059280706159791 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (3075418485023551 / 5000000000000000 : ℚ)) + (q := (49211506394902783 / 80000000000000000 : ℚ)) + (U := (-(2429495842219293840209 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_4 : Uω (aρ 4) (bρ 4) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3180,25 +2778,21 @@ lemma U_551_4 : have hlg : Real.log (48576102570051939 / 80000000000000000 : ℝ) ≤ (-(2494474705526851839749 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48576102570051939 / 80000000000000000 : ℝ) = - (48576102570051939 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48576102570051939 / 40000000000000000 : ℚ)) - (U := (971261195973148160251 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48576102570051939 / 40000000000000000 : ℝ) ≤ - (971261195973148160251 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6070280194899391 / 10000000000000000 : ℝ)) (q := - (48576102570051939 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48576102570051939 / 80000000000000000 : ℚ)) + (r' := (48576102570051939 / 40000000000000000 : ℚ)) + (U := (-(2494474705526851839749 / 5000000000000000000000 : ℚ))) + (U' := (971261195973148160251 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (6070280194899391 / 10000000000000000 : ℚ)) + (q := (48576102570051939 / 80000000000000000 : ℚ)) + (U := (-(2494474705526851839749 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_5 : Uω (aρ 5) (bρ 5) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3206,25 +2800,21 @@ lemma U_551_5 : have hlg : Real.log (1904345911406987 / 3200000000000000 : ℝ) ≤ (-(259506106759272505429 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1904345911406987 / 3200000000000000 : ℝ) = - (1904345911406987 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1904345911406987 / 1600000000000000 : ℚ)) - (U := (87067483390727494571 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1904345911406987 / 1600000000000000 : ℝ) ≤ - (87067483390727494571 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (237864256720603 / 400000000000000 : ℝ)) (q := - (1904345911406987 / 3200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1904345911406987 / 3200000000000000 : ℚ)) + (r' := (1904345911406987 / 1600000000000000 : ℚ)) + (U := (-(259506106759272505429 / 500000000000000000000 : ℚ))) + (U' := (87067483390727494571 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (237864256720603 / 400000000000000 : ℚ)) + (q := (1904345911406987 / 3200000000000000 : ℚ)) + (U := (-(259506106759272505429 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_6 : Uω (aρ 6) (bρ 6) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3232,25 +2822,21 @@ lemma U_551_6 : have hlg : Real.log (9244311688760919 / 16000000000000000 : ℝ) ≤ (-(5485803121827726466689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9244311688760919 / 16000000000000000 : ℝ) = - (9244311688760919 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9244311688760919 / 8000000000000000 : ℚ)) - (U := (1445668681172273533311 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9244311688760919 / 8000000000000000 : ℝ) ≤ - (1445668681172273533311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1153414891562511 / 2000000000000000 : ℝ)) (q := - (9244311688760919 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9244311688760919 / 16000000000000000 : ℚ)) + (r' := (9244311688760919 / 8000000000000000 : ℚ)) + (U := (-(5485803121827726466689 / 10000000000000000000000 : ℚ))) + (U' := (1445668681172273533311 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (1153414891562511 / 2000000000000000 : ℚ)) + (q := (9244311688760919 / 16000000000000000 : ℚ)) + (U := (-(5485803121827726466689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_7 : Uω (aρ 7) (bρ 7) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3258,25 +2844,21 @@ lemma U_551_7 : have hlg : Real.log (44330015764817219 / 80000000000000000 : ℝ) ≤ (-(5903646300329178437817 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44330015764817219 / 80000000000000000 : ℝ) = - (44330015764817219 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44330015764817219 / 40000000000000000 : ℚ)) - (U := (1027825502670821562183 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44330015764817219 / 40000000000000000 : ℝ) ≤ - (1027825502670821562183 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5517850168825711 / 10000000000000000 : ℝ)) (q := - (44330015764817219 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44330015764817219 / 80000000000000000 : ℚ)) + (r' := (44330015764817219 / 40000000000000000 : ℚ)) + (U := (-(5903646300329178437817 / 10000000000000000000000 : ℚ))) + (U' := (1027825502670821562183 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (5517850168825711 / 10000000000000000 : ℚ)) + (q := (44330015764817219 / 80000000000000000 : ℚ)) + (U := (-(5903646300329178437817 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_8 : Uω (aρ 8) (bρ 8) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3284,25 +2866,21 @@ lemma U_551_8 : have hlg : Real.log (8372655530798919 / 16000000000000000 : ℝ) ≤ (-(6476176200793001902877 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8372655530798919 / 16000000000000000 : ℝ) = - (8372655530798919 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8372655530798919 / 8000000000000000 : ℚ)) - (U := (455295602206998097123 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (8372655530798919 / 8000000000000000 : ℝ) ≤ - (455295602206998097123 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1036941458492011 / 2000000000000000 : ℝ)) (q := - (8372655530798919 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8372655530798919 / 16000000000000000 : ℚ)) + (r' := (8372655530798919 / 8000000000000000 : ℚ)) + (U := (-(6476176200793001902877 / 10000000000000000000000 : ℚ))) + (U' := (455295602206998097123 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (1036941458492011 / 2000000000000000 : ℚ)) + (q := (8372655530798919 / 16000000000000000 : ℚ)) + (U := (-(6476176200793001902877 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_9 : Uω (aρ 9) (bρ 9) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3310,25 +2888,21 @@ lemma U_551_9 : have hlg : Real.log (38773671341181867 / 80000000000000000 : ℝ) ≤ (-(905356489426210870313 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38773671341181867 / 80000000000000000 : ℝ) = - (38773671341181867 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38773671341181867 / 20000000000000000 : ℚ)) - (U := (827511461323789129687 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38773671341181867 / 20000000000000000 : ℝ) ≤ - (827511461323789129687 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4753271342616873 / 10000000000000000 : ℝ)) (q := - (38773671341181867 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38773671341181867 / 80000000000000000 : ℚ)) + (r' := (38773671341181867 / 20000000000000000 : ℚ)) + (U := (-(905356489426210870313 / 1250000000000000000000 : ℚ))) + (U' := (827511461323789129687 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (4753271342616873 / 10000000000000000 : ℚ)) + (q := (38773671341181867 / 80000000000000000 : ℚ)) + (U := (-(905356489426210870313 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_10 : Uω (aρ 10) (bρ 10) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3336,25 +2910,21 @@ lemma U_551_10 : have hlg : Real.log (280307631994663 / 640000000000000 : ℝ) ≤ (-(412790245041383228599 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (280307631994663 / 640000000000000 : ℝ) = - (280307631994663 / 160000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (280307631994663 / 160000000000000 : ℚ)) - (U := (280356935258616771401 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (280307631994663 / 160000000000000 : ℝ) ≤ - (280356935258616771401 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33664208325197 / 80000000000000 : ℝ)) (q := - (280307631994663 / 640000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (280307631994663 / 640000000000000 : ℚ)) + (r' := (280307631994663 / 160000000000000 : ℚ)) + (U := (-(412790245041383228599 / 500000000000000000000 : ℚ))) + (U' := (280356935258616771401 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (33664208325197 / 80000000000000 : ℚ)) + (q := (280307631994663 / 640000000000000 : ℚ)) + (U := (-(412790245041383228599 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_11 : Uω (aρ 11) (bρ 11) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3362,26 +2932,21 @@ lemma U_551_11 : have hlg : Real.log (30643515101983563 / 80000000000000000 : ℝ) ≤ (-(2399013933030365643021 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30643515101983563 / 80000000000000000 : ℝ) = - (30643515101983563 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30643515101983563 / 20000000000000000 : ℚ)) - (U := (1066721968469634356979 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30643515101983563 / 20000000000000000 : ℝ) ≤ - (1066721968469634356979 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3527767942517297 / 10000000000000000 : ℝ)) (q := - (30643515101983563 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30643515101983563 / 80000000000000000 : ℚ)) + (r' := (30643515101983563 / 20000000000000000 : ℚ)) + (U := (-(2399013933030365643021 / 2500000000000000000000 : ℚ))) + (U' := (1066721968469634356979 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (3527767942517297 / 10000000000000000 : ℚ)) + (q := (30643515101983563 / 80000000000000000 : ℚ)) + (U := (-(2399013933030365643021 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_12 : Uω (aρ 12) (bρ 12) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3389,26 +2954,21 @@ lemma U_551_12 : have hlg : Real.log (25508807644800619 / 80000000000000000 : ℝ) ≤ (-(11430028437903927354641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25508807644800619 / 80000000000000000 : ℝ) = - (25508807644800619 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25508807644800619 / 20000000000000000 : ℚ)) - (U := (2432915168096072645359 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25508807644800619 / 20000000000000000 : ℝ) ≤ - (2432915168096072645359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2667791174906561 / 10000000000000000 : ℝ)) (q := - (25508807644800619 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25508807644800619 / 80000000000000000 : ℚ)) + (r' := (25508807644800619 / 20000000000000000 : ℚ)) + (U := (-(11430028437903927354641 / 10000000000000000000000 : ℚ))) + (U' := (2432915168096072645359 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (2667791174906561 / 10000000000000000 : ℚ)) + (q := (25508807644800619 / 80000000000000000 : ℚ)) + (U := (-(11430028437903927354641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_13 : Uω (aρ 13) (bρ 13) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3416,26 +2976,21 @@ lemma U_551_13 : have hlg : Real.log (19029576065137959 / 80000000000000000 : ℝ) ≤ (-(1436032230020782576113 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19029576065137959 / 80000000000000000 : ℝ) = - (19029576065137959 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19029576065137959 / 10000000000000000 : ℚ)) - (U := (643409310879217423887 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19029576065137959 / 10000000000000000 : ℝ) ≤ - (643409310879217423887 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (180920627698237 / 1250000000000000 : ℝ)) (q := - (19029576065137959 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19029576065137959 / 80000000000000000 : ℚ)) + (r' := (19029576065137959 / 10000000000000000 : ℚ)) + (U := (-(1436032230020782576113 / 1000000000000000000000 : ℚ))) + (U' := (643409310879217423887 / 1000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40241292579991 / 64000000000000 : ℚ)) + (s := (180920627698237 / 1250000000000000 : ℚ)) + (q := (19029576065137959 / 80000000000000000 : ℚ)) + (U := (-(1436032230020782576113 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_551_14 : Uω (aρ 14) (bρ 14) (40241292579991 / 64000000000000 : ℝ) ≤ @@ -3541,25 +3096,21 @@ lemma U_552_1 : have hlg : Real.log (1558481914627131 / 2500000000000000 : ℝ) ≤ (-(4725785158020472823779 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1558481914627131 / 2500000000000000 : ℝ) = - (1558481914627131 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1558481914627131 / 1250000000000000 : ℚ)) - (U := (2205686644979527176221 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1558481914627131 / 1250000000000000 : ℝ) ≤ - (2205686644979527176221 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (779237715619631 / 1250000000000000 : ℝ)) (q := - (1558481914627131 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1558481914627131 / 2500000000000000 : ℚ)) + (r' := (1558481914627131 / 1250000000000000 : ℚ)) + (U := (-(4725785158020472823779 / 10000000000000000000000 : ℚ))) + (U' := (2205686644979527176221 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (779237715619631 / 1250000000000000 : ℚ)) + (q := (1558481914627131 / 2500000000000000 : ℚ)) + (U := (-(4725785158020472823779 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_2 : Uω (aρ 2) (bρ 2) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3567,25 +3118,21 @@ lemma U_552_2 : have hlg : Real.log (12420027476450291 / 20000000000000000 : ℝ) ≤ (-(4764219845165794570447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12420027476450291 / 20000000000000000 : ℝ) = - (12420027476450291 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12420027476450291 / 10000000000000000 : ℚ)) - (U := (2167251957834205429553 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12420027476450291 / 10000000000000000 : ℝ) ≤ - (2167251957834205429553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6209842896900291 / 10000000000000000 : ℝ)) (q := - (12420027476450291 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12420027476450291 / 20000000000000000 : ℚ)) + (r' := (12420027476450291 / 10000000000000000 : ℚ)) + (U := (-(4764219845165794570447 / 10000000000000000000000 : ℚ))) + (U' := (2167251957834205429553 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (6209842896900291 / 10000000000000000 : ℚ)) + (q := (12420027476450291 / 20000000000000000 : ℚ)) + (U := (-(4764219845165794570447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_3 : Uω (aρ 3) (bρ 3) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3593,25 +3140,21 @@ lemma U_552_3 : have hlg : Real.log (246487527715959 / 400000000000000 : ℝ) ≤ (-(2420765760732845746699 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (246487527715959 / 400000000000000 : ℝ) = - (246487527715959 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (246487527715959 / 200000000000000 : ℚ)) - (U := (1044970140767154253301 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (246487527715959 / 200000000000000 : ℝ) ≤ - (1044970140767154253301 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (123231758251959 / 200000000000000 : ℝ)) (q := - (246487527715959 / 400000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (246487527715959 / 400000000000000 : ℚ)) + (r' := (246487527715959 / 200000000000000 : ℚ)) + (U := (-(2420765760732845746699 / 5000000000000000000000 : ℚ))) + (U' := (1044970140767154253301 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (123231758251959 / 200000000000000 : ℚ)) + (q := (246487527715959 / 400000000000000 : ℚ)) + (U := (-(2420765760732845746699 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_4 : Uω (aρ 4) (bρ 4) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3619,25 +3162,21 @@ lemma U_552_4 : have hlg : Real.log (6082764728371717 / 10000000000000000 : ℝ) ≤ (-(1242814437627491156317 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6082764728371717 / 10000000000000000 : ℝ) = - (6082764728371717 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6082764728371717 / 5000000000000000 : ℚ)) - (U := (490053513122508843683 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6082764728371717 / 5000000000000000 : ℝ) ≤ - (490053513122508843683 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3040517582304217 / 5000000000000000 : ℝ)) (q := - (6082764728371717 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6082764728371717 / 10000000000000000 : ℚ)) + (r' := (6082764728371717 / 5000000000000000 : ℚ)) + (U := (-(1242814437627491156317 / 2500000000000000000000 : ℚ))) + (U' := (490053513122508843683 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (3040517582304217 / 5000000000000000 : ℚ)) + (q := (6082764728371717 / 10000000000000000 : ℚ)) + (U := (-(1242814437627491156317 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_5 : Uω (aρ 5) (bρ 5) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3645,25 +3184,21 @@ lemma U_552_5 : have hlg : Real.log (11923675782176853 / 20000000000000000 : ℝ) ≤ (-(5172062882054117301997 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11923675782176853 / 20000000000000000 : ℝ) = - (11923675782176853 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11923675782176853 / 10000000000000000 : ℚ)) - (U := (1759408920945882698003 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11923675782176853 / 10000000000000000 : ℝ) ≤ - (1759408920945882698003 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5957371409376853 / 10000000000000000 : ℝ)) (q := - (11923675782176853 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11923675782176853 / 20000000000000000 : ℚ)) + (r' := (11923675782176853 / 10000000000000000 : ℚ)) + (U := (-(5172062882054117301997 / 10000000000000000000000 : ℚ))) + (U' := (1759408920945882698003 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (5957371409376853 / 10000000000000000 : ℚ)) + (q := (11923675782176853 / 20000000000000000 : ℚ)) + (U := (-(5172062882054117301997 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_6 : Uω (aρ 6) (bρ 6) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3671,25 +3206,21 @@ lemma U_552_6 : have hlg : Real.log (5788463407623591 / 10000000000000000 : ℝ) ≤ (-(136679555913746854773 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5788463407623591 / 10000000000000000 : ℝ) = - (5788463407623591 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5788463407623591 / 5000000000000000 : ℚ)) - (U := (36607239161253145227 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5788463407623591 / 5000000000000000 : ℝ) ≤ - (36607239161253145227 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2888931408793591 / 5000000000000000 : ℝ)) (q := - (5788463407623591 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5788463407623591 / 10000000000000000 : ℚ)) + (r' := (5788463407623591 / 5000000000000000 : ℚ)) + (U := (-(136679555913746854773 / 250000000000000000000 : ℚ))) + (U' := (36607239161253145227 / 250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (2888931408793591 / 5000000000000000 : ℚ)) + (q := (5788463407623591 / 10000000000000000 : ℚ)) + (U := (-(136679555913746854773 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_7 : Uω (aρ 7) (bρ 7) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3697,24 +3228,21 @@ lemma U_552_7 : have hlg : Real.log (88832741010153 / 160000000000000 : ℝ) ≤ (-(5884185278614776937653 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (88832741010153 / 160000000000000 : ℝ) = (88832741010153 / 80000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (88832741010153 / 80000000000000 : ℚ)) - (U := (1047286524385223062347 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (88832741010153 / 80000000000000 : ℝ) ≤ - (1047286524385223062347 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44229520074953 / 80000000000000 : ℝ)) (q := - (88832741010153 / 160000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (88832741010153 / 160000000000000 : ℚ)) + (r' := (88832741010153 / 80000000000000 : ℚ)) + (U := (-(5884185278614776937653 / 10000000000000000000000 : ℚ))) + (U' := (1047286524385223062347 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (44229520074953 / 80000000000000 : ℚ)) + (q := (88832741010153 / 160000000000000 : ℚ)) + (U := (-(5884185278614776937653 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_8 : Uω (aρ 8) (bρ 8) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3722,25 +3250,21 @@ lemma U_552_8 : have hlg : Real.log (5243758275009757 / 10000000000000000 : ℝ) ≤ (-(5164372987447805311 / 8000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5243758275009757 / 10000000000000000 : ℝ) = - (5243758275009757 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5243758275009757 / 5000000000000000 : ℚ)) - (U := (380804454952194689 / 8000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5243758275009757 / 5000000000000000 : ℝ) ≤ - (380804454952194689 / 8000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2597827792229757 / 5000000000000000 : ℝ)) (q := - (5243758275009757 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5243758275009757 / 10000000000000000 : ℚ)) + (r' := (5243758275009757 / 5000000000000000 : ℚ)) + (U := (-(5164372987447805311 / 8000000000000000000 : ℚ))) + (U' := (380804454952194689 / 8000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (2597827792229757 / 5000000000000000 : ℚ)) + (q := (5243758275009757 / 10000000000000000 : ℚ)) + (U := (-(5164372987447805311 / 8000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_9 : Uω (aρ 9) (bρ 9) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3748,25 +3272,21 @@ lemma U_552_9 : have hlg : Real.log (2428834285919803 / 5000000000000000 : ℝ) ≤ (-(3610132436957952754391 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2428834285919803 / 5000000000000000 : ℝ) = - (2428834285919803 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2428834285919803 / 1250000000000000 : ℚ)) - (U := (3321339366042047245609 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2428834285919803 / 1250000000000000 : ℝ) ≤ - (3321339366042047245609 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1191110451619803 / 2500000000000000 : ℝ)) (q := - (2428834285919803 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2428834285919803 / 5000000000000000 : ℚ)) + (r' := (2428834285919803 / 1250000000000000 : ℚ)) + (U := (-(3610132436957952754391 / 5000000000000000000000 : ℚ))) + (U' := (3321339366042047245609 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (1191110451619803 / 2500000000000000 : ℚ)) + (q := (2428834285919803 / 5000000000000000 : ℚ)) + (U := (-(3610132436957952754391 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_10 : Uω (aρ 10) (bρ 10) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3774,26 +3294,21 @@ lemma U_552_10 : have hlg : Real.log (2195496611053351 / 5000000000000000 : ℝ) ≤ (-(8230296444833993408677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2195496611053351 / 5000000000000000 : ℝ) = - (2195496611053351 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2195496611053351 / 1250000000000000 : ℚ)) - (U := (5632647161166006591323 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2195496611053351 / 1250000000000000 : ℝ) ≤ - (5632647161166006591323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1054912535127101 / 2500000000000000 : ℝ)) (q := - (2195496611053351 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2195496611053351 / 5000000000000000 : ℚ)) + (r' := (2195496611053351 / 1250000000000000 : ℚ)) + (U := (-(8230296444833993408677 / 10000000000000000000000 : ℚ))) + (U' := (5632647161166006591323 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (1054912535127101 / 2500000000000000 : ℚ)) + (q := (2195496611053351 / 5000000000000000 : ℚ)) + (U := (-(8230296444833993408677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_11 : Uω (aρ 11) (bρ 11) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3801,26 +3316,21 @@ lemma U_552_11 : have hlg : Real.log (1536842963727483 / 4000000000000000 : ℝ) ≤ (-(2391410179756399555909 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1536842963727483 / 4000000000000000 : ℝ) = - (1536842963727483 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1536842963727483 / 1000000000000000 : ℚ)) - (U := (1074325721743600444091 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1536842963727483 / 1000000000000000 : ℝ) ≤ - (1074325721743600444091 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (708071028227483 / 2000000000000000 : ℝ)) (q := - (1536842963727483 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1536842963727483 / 4000000000000000 : ℚ)) + (r' := (1536842963727483 / 1000000000000000 : ℚ)) + (U := (-(2391410179756399555909 / 2500000000000000000000 : ℚ))) + (U' := (1074325721743600444091 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (708071028227483 / 2000000000000000 : ℚ)) + (q := (1536842963727483 / 4000000000000000 : ℚ)) + (U := (-(2391410179756399555909 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_12 : Uω (aρ 12) (bρ 12) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3828,25 +3338,21 @@ lemma U_552_12 : have hlg : Real.log (640287631001113 / 2000000000000000 : ℝ) ≤ (-(11389849601897008077703 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (640287631001113 / 2000000000000000 : ℝ) = - (640287631001113 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (640287631001113 / 500000000000000 : ℚ)) - (U := (2473094004102991922297 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (640287631001113 / 500000000000000 : ℝ) ≤ - (2473094004102991922297 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268271672919613 / 1000000000000000 : ℝ)) (q := - (640287631001113 / 2000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (640287631001113 / 2000000000000000 : ℚ)) + (r' := (640287631001113 / 500000000000000 : ℚ)) + (U := (-(11389849601897008077703 / 10000000000000000000000 : ℚ))) + (U' := (2473094004102991922297 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (268271672919613 / 1000000000000000 : ℚ)) + (q := (640287631001113 / 2000000000000000 : ℚ)) + (U := (-(11389849601897008077703 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_13 : Uω (aρ 13) (bρ 13) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3854,26 +3360,21 @@ lemma U_552_13 : have hlg : Real.log (4792558739157083 / 20000000000000000 : ℝ) ≤ (-(1428667820436467843137 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4792558739157083 / 20000000000000000 : ℝ) = - (4792558739157083 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4792558739157083 / 2500000000000000 : ℚ)) - (U := (650773720463532156863 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4792558739157083 / 2500000000000000 : ℝ) ≤ - (650773720463532156863 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1471780899937083 / 10000000000000000 : ℝ)) (q := - (4792558739157083 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4792558739157083 / 20000000000000000 : ℚ)) + (r' := (4792558739157083 / 2500000000000000 : ℚ)) + (U := (-(1428667820436467843137 / 1000000000000000000000 : ℚ))) + (U' := (650773720463532156863 / 1000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (1259690162029 / 2000000000000 : ℚ)) + (s := (1471780899937083 / 10000000000000000 : ℚ)) + (q := (4792558739157083 / 20000000000000000 : ℚ)) + (U := (-(1428667820436467843137 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_552_14 : Uω (aρ 14) (bρ 14) (1259690162029 / 2000000000000 : ℝ) ≤ @@ -3980,25 +3481,21 @@ lemma U_553_1 : have hlg : Real.log (49957412381352409 / 80000000000000000 : ℝ) ≤ (-(294284840191189489643 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49957412381352409 / 80000000000000000 : ℝ) = - (49957412381352409 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49957412381352409 / 40000000000000000 : ℚ)) - (U := (138932147496310510357 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49957412381352409 / 40000000000000000 : ℝ) ≤ - (138932147496310510357 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (780581332344587 / 1250000000000000 : ℝ)) (q := - (49957412381352409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49957412381352409 / 80000000000000000 : ℚ)) + (r' := (49957412381352409 / 40000000000000000 : ℚ)) + (U := (-(294284840191189489643 / 625000000000000000000 : ℚ))) + (U' := (138932147496310510357 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (780581332344587 / 1250000000000000 : ℚ)) + (q := (49957412381352409 / 80000000000000000 : ℚ)) + (U := (-(294284840191189489643 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_2 : Uω (aρ 2) (bρ 2) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4006,25 +3503,21 @@ lemma U_553_2 : have hlg : Real.log (49766103023608513 / 80000000000000000 : ℝ) ≤ (-(593365680394418844097 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49766103023608513 / 80000000000000000 : ℝ) = - (49766103023608513 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49766103023608513 / 40000000000000000 : ℚ)) - (U := (273068294980581155903 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49766103023608513 / 40000000000000000 : ℝ) ≤ - (273068294980581155903 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3110296165915361 / 5000000000000000 : ℝ)) (q := - (49766103023608513 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49766103023608513 / 80000000000000000 : ℚ)) + (r' := (49766103023608513 / 40000000000000000 : ℚ)) + (U := (-(593365680394418844097 / 1250000000000000000000 : ℚ))) + (U' := (273068294980581155903 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (3110296165915361 / 5000000000000000 : ℚ)) + (q := (49766103023608513 / 80000000000000000 : ℚ)) + (U := (-(593365680394418844097 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_3 : Uω (aρ 3) (bρ 3) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4032,25 +3525,21 @@ lemma U_553_3 : have hlg : Real.log (9876700932449797 / 16000000000000000 : ℝ) ≤ (-(4824101797013151299569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9876700932449797 / 16000000000000000 : ℝ) = - (9876700932449797 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9876700932449797 / 8000000000000000 : ℚ)) - (U := (2107370005986848700431 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9876700932449797 / 8000000000000000 : ℝ) ≤ - (2107370005986848700431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154308471196021 / 250000000000000 : ℝ)) (q := - (9876700932449797 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9876700932449797 / 16000000000000000 : ℚ)) + (r' := (9876700932449797 / 8000000000000000 : ℚ)) + (U := (-(4824101797013151299569 / 10000000000000000000000 : ℚ))) + (U' := (2107370005986848700431 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (154308471196021 / 250000000000000 : ℚ)) + (q := (9876700932449797 / 16000000000000000 : ℚ)) + (U := (-(4824101797013151299569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_4 : Uω (aρ 4) (bρ 4) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4058,25 +3547,21 @@ lemma U_553_4 : have hlg : Real.log (48748132997408709 / 80000000000000000 : ℝ) ≤ (-(990719470384999601177 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48748132997408709 / 80000000000000000 : ℝ) = - (48748132997408709 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48748132997408709 / 40000000000000000 : ℚ)) - (U := (395574890215000398823 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48748132997408709 / 40000000000000000 : ℝ) ≤ - (395574890215000398823 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6091790112695771 / 10000000000000000 : ℝ)) (q := - (48748132997408709 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48748132997408709 / 80000000000000000 : ℚ)) + (r' := (48748132997408709 / 40000000000000000 : ℚ)) + (U := (-(990719470384999601177 / 2000000000000000000000 : ℚ))) + (U' := (395574890215000398823 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (6091790112695771 / 10000000000000000 : ℚ)) + (q := (48748132997408709 / 80000000000000000 : ℚ)) + (U := (-(990719470384999601177 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_5 : Uω (aρ 5) (bρ 5) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4084,25 +3569,21 @@ lemma U_553_5 : have hlg : Real.log (47780758239416737 / 80000000000000000 : ℝ) ≤ (-(16106363226655447673 / 31250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47780758239416737 / 80000000000000000 : ℝ) = - (47780758239416737 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47780758239416737 / 40000000000000000 : ℚ)) - (U := (5554486157719552327 / 31250000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47780758239416737 / 40000000000000000 : ℝ) ≤ - (5554486157719552327 / 31250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2984068171266389 / 5000000000000000 : ℝ)) (q := - (47780758239416737 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47780758239416737 / 80000000000000000 : ℚ)) + (r' := (47780758239416737 / 40000000000000000 : ℚ)) + (U := (-(16106363226655447673 / 31250000000000000000 : ℚ))) + (U' := (5554486157719552327 / 31250000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (2984068171266389 / 5000000000000000 : ℚ)) + (q := (47780758239416737 / 80000000000000000 : ℚ)) + (U := (-(16106363226655447673 / 31250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_6 : Uω (aρ 6) (bρ 6) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4110,25 +3591,21 @@ lemma U_553_6 : have hlg : Real.log (46393855490092449 / 80000000000000000 : ℝ) ≤ (-(2724298043665763560073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46393855490092449 / 80000000000000000 : ℝ) = - (46393855490092449 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46393855490092449 / 40000000000000000 : ℚ)) - (U := (741437857834236439927 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46393855490092449 / 40000000000000000 : ℝ) ≤ - (741437857834236439927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2894325515170853 / 5000000000000000 : ℝ)) (q := - (46393855490092449 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46393855490092449 / 80000000000000000 : ℚ)) + (r' := (46393855490092449 / 40000000000000000 : ℚ)) + (U := (-(2724298043665763560073 / 5000000000000000000000 : ℚ))) + (U' := (741437857834236439927 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (2894325515170853 / 5000000000000000 : ℚ)) + (q := (46393855490092449 / 80000000000000000 : ℚ)) + (U := (-(2724298043665763560073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_7 : Uω (aρ 7) (bρ 7) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4136,25 +3613,21 @@ lemma U_553_7 : have hlg : Real.log (1780108953072601 / 3200000000000000 : ℝ) ≤ (-(183273824226132342093 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1780108953072601 / 3200000000000000 : ℝ) = - (1780108953072601 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1780108953072601 / 1600000000000000 : ℚ)) - (U := (33334669617617657907 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1780108953072601 / 1600000000000000 : ℝ) ≤ - (33334669617617657907 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110790589905647 / 200000000000000 : ℝ)) (q := - (1780108953072601 / 3200000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1780108953072601 / 3200000000000000 : ℚ)) + (r' := (1780108953072601 / 1600000000000000 : ℚ)) + (U := (-(183273824226132342093 / 312500000000000000000 : ℚ))) + (U' := (33334669617617657907 / 312500000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (110790589905647 / 200000000000000 : ℚ)) + (q := (1780108953072601 / 3200000000000000 : ℚ)) + (U := (-(183273824226132342093 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_8 : Uω (aρ 8) (bρ 8) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4162,25 +3635,21 @@ lemma U_553_8 : have hlg : Real.log (42036851421584033 / 80000000000000000 : ℝ) ≤ (-(3217399930171501478579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42036851421584033 / 80000000000000000 : ℝ) = - (42036851421584033 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42036851421584033 / 40000000000000000 : ℚ)) - (U := (248335971328498521421 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (42036851421584033 / 40000000000000000 : ℝ) ≤ - (248335971328498521421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2603301522657301 / 5000000000000000 : ℝ)) (q := - (42036851421584033 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42036851421584033 / 80000000000000000 : ℚ)) + (r' := (42036851421584033 / 40000000000000000 : ℚ)) + (U := (-(3217399930171501478579 / 5000000000000000000000 : ℚ))) + (U' := (248335971328498521421 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (2603301522657301 / 5000000000000000 : ℚ)) + (q := (42036851421584033 / 80000000000000000 : ℚ)) + (U := (-(3217399930171501478579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_9 : Uω (aρ 9) (bρ 9) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4188,25 +3657,21 @@ lemma U_553_9 : have hlg : Real.log (7789803613516941 / 16000000000000000 : ℝ) ≤ (-(143954614445972021909 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7789803613516941 / 16000000000000000 : ℝ) = - (7789803613516941 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7789803613516941 / 4000000000000000 : ℚ)) - (U := (133304257674027978091 / 200000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7789803613516941 / 4000000000000000 : ℝ) ≤ - (133304257674027978091 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (477561033517477 / 1000000000000000 : ℝ)) (q := - (7789803613516941 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7789803613516941 / 16000000000000000 : ℚ)) + (r' := (7789803613516941 / 4000000000000000 : ℚ)) + (U := (-(143954614445972021909 / 200000000000000000000 : ℚ))) + (U' := (133304257674027978091 / 200000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (477561033517477 / 1000000000000000 : ℚ)) + (q := (7789803613516941 / 16000000000000000 : ℚ)) + (U := (-(143954614445972021909 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_10 : Uω (aρ 10) (bρ 10) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4214,26 +3679,21 @@ lemma U_553_10 : have hlg : Real.log (35217419042646141 / 80000000000000000 : ℝ) ≤ (-(4102429073931367588247 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35217419042646141 / 80000000000000000 : ℝ) = - (35217419042646141 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35217419042646141 / 20000000000000000 : ℚ)) - (U := (2829042729068632411753 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35217419042646141 / 20000000000000000 : ℝ) ≤ - (2829042729068632411753 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4231269612435129 / 10000000000000000 : ℝ)) (q := - (35217419042646141 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35217419042646141 / 80000000000000000 : ℚ)) + (r' := (35217419042646141 / 20000000000000000 : ℚ)) + (U := (-(4102429073931367588247 / 5000000000000000000000 : ℚ))) + (U' := (2829042729068632411753 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (4231269612435129 / 10000000000000000 : ℚ)) + (q := (35217419042646141 / 80000000000000000 : ℚ)) + (U := (-(4102429073931367588247 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_11 : Uω (aρ 11) (bρ 11) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4241,26 +3701,21 @@ lemma U_553_11 : have hlg : Real.log (30830155149136949 / 80000000000000000 : ℝ) ≤ (-(9535333598606493714421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30830155149136949 / 80000000000000000 : ℝ) = - (30830155149136949 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30830155149136949 / 20000000000000000 : ℚ)) - (U := (4327610007393506285579 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30830155149136949 / 20000000000000000 : ℝ) ≤ - (4327610007393506285579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3552930265262831 / 10000000000000000 : ℝ)) (q := - (30830155149136949 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30830155149136949 / 80000000000000000 : ℚ)) + (r' := (30830155149136949 / 20000000000000000 : ℚ)) + (U := (-(9535333598606493714421 / 10000000000000000000000 : ℚ))) + (U' := (4327610007393506285579 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (3552930265262831 / 10000000000000000 : ℚ)) + (q := (30830155149136949 / 80000000000000000 : ℚ)) + (U := (-(9535333598606493714421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_12 : Uω (aρ 12) (bρ 12) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4268,26 +3723,21 @@ lemma U_553_12 : have hlg : Real.log (25714043829325249 / 80000000000000000 : ℝ) ≤ (-(11349893390006880405851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25714043829325249 / 80000000000000000 : ℝ) = - (25714043829325249 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25714043829325249 / 20000000000000000 : ℚ)) - (U := (2513050215993119594149 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25714043829325249 / 20000000000000000 : ℝ) ≤ - (2513050215993119594149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1348801265997453 / 5000000000000000 : ℝ)) (q := - (25714043829325249 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25714043829325249 / 80000000000000000 : ℚ)) + (r' := (25714043829325249 / 20000000000000000 : ℚ)) + (U := (-(11349893390006880405851 / 10000000000000000000000 : ℚ))) + (U' := (2513050215993119594149 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (1348801265997453 / 5000000000000000 : ℚ)) + (q := (25714043829325249 / 80000000000000000 : ℚ)) + (U := (-(11349893390006880405851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_13 : Uω (aρ 13) (bρ 13) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4295,26 +3745,21 @@ lemma U_553_13 : have hlg : Real.log (19309608859234949 / 80000000000000000 : ℝ) ≤ (-(7107118967621958687121 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19309608859234949 / 80000000000000000 : ℝ) = - (19309608859234949 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19309608859234949 / 10000000000000000 : ℚ)) - (U := (3290088736878041312879 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19309608859234949 / 10000000000000000 : ℝ) ≤ - (3290088736878041312879 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1495875531067331 / 10000000000000000 : ℝ)) (q := - (19309608859234949 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19309608859234949 / 80000000000000000 : ℚ)) + (r' := (19309608859234949 / 10000000000000000 : ℚ)) + (U := (-(7107118967621958687121 / 5000000000000000000000 : ℚ))) + (U' := (3290088736878041312879 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (8075775557973 / 12800000000000 : ℚ)) + (s := (1495875531067331 / 10000000000000000 : ℚ)) + (q := (19309608859234949 / 80000000000000000 : ℚ)) + (U := (-(7107118967621958687121 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_553_14 : Uω (aρ 14) (bρ 14) (8075775557973 / 12800000000000 : ℝ) ≤ @@ -4421,25 +3866,21 @@ lemma U_554_1 : have hlg : Real.log (25021701746704671 / 40000000000000000 : ℝ) ≤ (-(293209959795218729589 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25021701746704671 / 40000000000000000 : ℝ) = - (25021701746704671 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25021701746704671 / 20000000000000000 : ℚ)) - (U := (140007027892281270411 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25021701746704671 / 20000000000000000 : ℝ) ≤ - (140007027892281270411 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6255399592249523 / 10000000000000000 : ℝ)) (q := - (25021701746704671 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25021701746704671 / 40000000000000000 : ℚ)) + (r' := (25021701746704671 / 20000000000000000 : ℚ)) + (U := (-(293209959795218729589 / 625000000000000000000 : ℚ))) + (U' := (140007027892281270411 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (6255399592249523 / 10000000000000000 : ℚ)) + (q := (25021701746704671 / 40000000000000000 : ℚ)) + (U := (-(293209959795218729589 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_2 : Uω (aρ 2) (bρ 2) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4447,25 +3888,21 @@ lemma U_554_2 : have hlg : Real.log (24926048066634081 / 40000000000000000 : ℝ) ≤ (-(4729660900783168347879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24926048066634081 / 40000000000000000 : ℝ) = - (24926048066634081 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24926048066634081 / 20000000000000000 : ℚ)) - (U := (2201810902216831652121 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24926048066634081 / 20000000000000000 : ℝ) ≤ - (2201810902216831652121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1557835441181057 / 2500000000000000 : ℝ)) (q := - (24926048066634081 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24926048066634081 / 40000000000000000 : ℚ)) + (r' := (24926048066634081 / 20000000000000000 : ℚ)) + (U := (-(4729660900783168347879 / 10000000000000000000000 : ℚ))) + (U' := (2201810902216831652121 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (1557835441181057 / 2500000000000000 : ℚ)) + (q := (24926048066634081 / 40000000000000000 : ℚ)) + (U := (-(4729660900783168347879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_3 : Uω (aρ 3) (bρ 3) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4473,25 +3910,21 @@ lemma U_554_3 : have hlg : Real.log (24734751876113413 / 40000000000000000 : ℝ) ≤ (-(2403351202558697929501 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24734751876113413 / 40000000000000000 : ℝ) = - (24734751876113413 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24734751876113413 / 20000000000000000 : ℚ)) - (U := (1062384698941302070499 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24734751876113413 / 20000000000000000 : ℝ) ≤ - (1062384698941302070499 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3091544887906947 / 5000000000000000 : ℝ)) (q := - (24734751876113413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24734751876113413 / 40000000000000000 : ℚ)) + (r' := (24734751876113413 / 20000000000000000 : ℚ)) + (U := (-(2403351202558697929501 / 5000000000000000000000 : ℚ))) + (U' := (1062384698941302070499 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (3091544887906947 / 5000000000000000 : ℚ)) + (q := (24734751876113413 / 40000000000000000 : ℚ)) + (U := (-(2403351202558697929501 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_4 : Uω (aρ 4) (bρ 4) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4499,25 +3932,21 @@ lemma U_554_4 : have hlg : Real.log (24417074040907061 / 40000000000000000 : ℝ) ≤ (-(123399202623718425537 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24417074040907061 / 40000000000000000 : ℝ) = - (24417074040907061 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24417074040907061 / 20000000000000000 : ℚ)) - (U := (49887592451281574463 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24417074040907061 / 20000000000000000 : ℝ) ≤ - (49887592451281574463 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3051272519637859 / 5000000000000000 : ℝ)) (q := - (24417074040907061 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24417074040907061 / 40000000000000000 : ℚ)) + (r' := (24417074040907061 / 20000000000000000 : ℚ)) + (U := (-(123399202623718425537 / 250000000000000000000 : ℚ))) + (U' := (49887592451281574463 / 250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (3051272519637859 / 5000000000000000 : ℚ)) + (q := (24417074040907061 / 40000000000000000 : ℚ)) + (U := (-(123399202623718425537 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_5 : Uω (aρ 5) (bρ 5) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4525,25 +3954,21 @@ lemma U_554_5 : have hlg : Real.log (23933406559280117 / 40000000000000000 : ℝ) ≤ (-(1284010517231633783179 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23933406559280117 / 40000000000000000 : ℝ) = - (23933406559280117 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23933406559280117 / 20000000000000000 : ℚ)) - (U := (448857433518366216821 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23933406559280117 / 20000000000000000 : ℝ) ≤ - (448857433518366216821 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2989450608898623 / 5000000000000000 : ℝ)) (q := - (23933406559280117 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23933406559280117 / 40000000000000000 : ℚ)) + (r' := (23933406559280117 / 20000000000000000 : ℚ)) + (U := (-(1284010517231633783179 / 2500000000000000000000 : ℚ))) + (U' := (448857433518366216821 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (2989450608898623 / 5000000000000000 : ℚ)) + (q := (23933406559280117 / 40000000000000000 : ℚ)) + (U := (-(1284010517231633783179 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_6 : Uω (aρ 6) (bρ 6) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4551,25 +3976,21 @@ lemma U_554_6 : have hlg : Real.log (23240001567198817 / 40000000000000000 : ℝ) ≤ (-(1357511136087193952523 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23240001567198817 / 40000000000000000 : ℝ) = - (23240001567198817 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23240001567198817 / 20000000000000000 : ℚ)) - (U := (375356814662806047477 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23240001567198817 / 20000000000000000 : ℝ) ≤ - (375356814662806047477 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1449859774224149 / 2500000000000000 : ℝ)) (q := - (23240001567198817 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23240001567198817 / 40000000000000000 : ℚ)) + (r' := (23240001567198817 / 20000000000000000 : ℚ)) + (U := (-(1357511136087193952523 / 2500000000000000000000 : ℚ))) + (U' := (375356814662806047477 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (1449859774224149 / 2500000000000000 : ℚ)) + (q := (23240001567198817 / 40000000000000000 : ℚ)) + (U := (-(1357511136087193952523 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_7 : Uω (aρ 7) (bρ 7) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4577,25 +3998,21 @@ lemma U_554_7 : have hlg : Real.log (22294537869171803 / 40000000000000000 : ℝ) ≤ (-(5845377439924378908381 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22294537869171803 / 40000000000000000 : ℝ) = - (22294537869171803 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22294537869171803 / 20000000000000000 : ℚ)) - (U := (1086094363075621091619 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22294537869171803 / 20000000000000000 : ℝ) ≤ - (1086094363075621091619 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5550368628643089 / 10000000000000000 : ℝ)) (q := - (22294537869171803 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22294537869171803 / 40000000000000000 : ℚ)) + (r' := (22294537869171803 / 20000000000000000 : ℚ)) + (U := (-(5845377439924378908381 / 10000000000000000000000 : ℚ))) + (U' := (1086094363075621091619 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (5550368628643089 / 10000000000000000 : ℚ)) + (q := (22294537869171803 / 40000000000000000 : ℚ)) + (U := (-(5845377439924378908381 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_8 : Uω (aρ 8) (bρ 8) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4603,25 +4020,21 @@ lemma U_554_8 : have hlg : Real.log (21061816669719703 / 40000000000000000 : ℝ) ≤ (-(3207088446241811533109 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21061816669719703 / 40000000000000000 : ℝ) = - (21061816669719703 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21061816669719703 / 20000000000000000 : ℚ)) - (U := (258647455258188466891 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21061816669719703 / 20000000000000000 : ℝ) ≤ - (258647455258188466891 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5217549680257039 / 10000000000000000 : ℝ)) (q := - (21061816669719703 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21061816669719703 / 40000000000000000 : ℚ)) + (r' := (21061816669719703 / 20000000000000000 : ℚ)) + (U := (-(3207088446241811533109 / 5000000000000000000000 : ℚ))) + (U' := (258647455258188466891 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (5217549680257039 / 10000000000000000 : ℚ)) + (q := (21061816669719703 / 40000000000000000 : ℚ)) + (U := (-(3207088446241811533109 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_9 : Uω (aρ 9) (bρ 9) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4629,25 +4042,21 @@ lemma U_554_9 : have hlg : Real.log (3903667987396711 / 8000000000000000 : ℝ) ≤ (-(1793812301093678316561 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3903667987396711 / 8000000000000000 : ℝ) = - (3903667987396711 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3903667987396711 / 2000000000000000 : ℚ)) - (U := (1671923600406321683439 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3903667987396711 / 2000000000000000 : ℝ) ≤ - (1671923600406321683439 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (957355388449793 / 2000000000000000 : ℝ)) (q := - (3903667987396711 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3903667987396711 / 8000000000000000 : ℚ)) + (r' := (3903667987396711 / 2000000000000000 : ℚ)) + (U := (-(1793812301093678316561 / 2500000000000000000000 : ℚ))) + (U' := (1671923600406321683439 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (957355388449793 / 2000000000000000 : ℚ)) + (q := (3903667987396711 / 8000000000000000 : ℚ)) + (U := (-(1793812301093678316561 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_10 : Uω (aρ 10) (bρ 10) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4655,26 +4064,21 @@ lemma U_554_10 : have hlg : Real.log (17653436974398951 / 40000000000000000 : ℝ) ≤ (-(4089744798721756566173 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17653436974398951 / 40000000000000000 : ℝ) = - (17653436974398951 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17653436974398951 / 10000000000000000 : ℚ)) - (U := (2841727004278243433827 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17653436974398951 / 10000000000000000 : ℝ) ≤ - (2841727004278243433827 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4242884494451663 / 10000000000000000 : ℝ)) (q := - (17653436974398951 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17653436974398951 / 40000000000000000 : ℚ)) + (r' := (17653436974398951 / 10000000000000000 : ℚ)) + (U := (-(4089744798721756566173 / 5000000000000000000000 : ℚ))) + (U' := (2841727004278243433827 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (4242884494451663 / 10000000000000000 : ℚ)) + (q := (17653436974398951 / 40000000000000000 : ℚ)) + (U := (-(4089744798721756566173 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_11 : Uω (aρ 11) (bρ 11) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4682,26 +4086,21 @@ lemma U_554_11 : have hlg : Real.log (15461701618385637 / 40000000000000000 : ℝ) ≤ (-(190102670123856259617 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15461701618385637 / 40000000000000000 : ℝ) = - (15461701618385637 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15461701618385637 / 10000000000000000 : ℚ)) - (U := (87156201996143740383 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15461701618385637 / 10000000000000000 : ℝ) ≤ - (87156201996143740383 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1782746721325003 / 5000000000000000 : ℝ)) (q := - (15461701618385637 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15461701618385637 / 40000000000000000 : ℚ)) + (r' := (15461701618385637 / 10000000000000000 : ℚ)) + (U := (-(190102670123856259617 / 200000000000000000000 : ℚ))) + (U' := (87156201996143740383 / 200000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (1782746721325003 / 5000000000000000 : ℚ)) + (q := (15461701618385637 / 40000000000000000 : ℚ)) + (U := (-(190102670123856259617 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_12 : Uω (aρ 12) (bρ 12) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4709,26 +4108,21 @@ lemma U_554_12 : have hlg : Real.log (12908213015248219 / 40000000000000000 : ℝ) ≤ (-(113101567696471236689 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12908213015248219 / 40000000000000000 : ℝ) = - (12908213015248219 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12908213015248219 / 10000000000000000 : ℚ)) - (U := (25527868363528763311 / 100000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12908213015248219 / 10000000000000000 : ℝ) ≤ - (25527868363528763311 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2712449237766297 / 10000000000000000 : ℝ)) (q := - (12908213015248219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12908213015248219 / 40000000000000000 : ℚ)) + (r' := (12908213015248219 / 10000000000000000 : ℚ)) + (U := (-(113101567696471236689 / 100000000000000000000 : ℚ))) + (U' := (25527868363528763311 / 100000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (2712449237766297 / 10000000000000000 : ℚ)) + (q := (12908213015248219 / 40000000000000000 : ℚ)) + (U := (-(113101567696471236689 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_13 : Uω (aρ 13) (bρ 13) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4736,26 +4130,21 @@ lemma U_554_13 : have hlg : Real.log (1944775889466269 / 8000000000000000 : ℝ) ≤ (-(7071473971965871018263 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1944775889466269 / 8000000000000000 : ℝ) = - (1944775889466269 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1944775889466269 / 1000000000000000 : ℚ)) - (U := (3325733732534128981737 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1944775889466269 / 1000000000000000 : ℝ) ≤ - (3325733732534128981737 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (75983209770143 / 500000000000000 : ℝ)) (q := - (1944775889466269 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1944775889466269 / 8000000000000000 : ℚ)) + (r' := (1944775889466269 / 1000000000000000 : ℚ)) + (U := (-(7071473971965871018263 / 5000000000000000000000 : ℚ))) + (U' := (3325733732534128981737 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20223835197401 / 32000000000000 : ℚ)) + (s := (75983209770143 / 500000000000000 : ℚ)) + (q := (1944775889466269 / 8000000000000000 : ℚ)) + (U := (-(7071473971965871018263 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_554_14 : Uω (aρ 14) (bρ 14) (20223835197401 / 32000000000000 : ℝ) ≤ @@ -4860,25 +4249,21 @@ lemma U_555_1 : have hlg : Real.log (50129394604245311 / 80000000000000000 : ℝ) ≤ (-(1168547699318994396631 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50129394604245311 / 80000000000000000 : ℝ) = - (50129394604245311 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50129394604245311 / 40000000000000000 : ℚ)) - (U := (564320251431005603369 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50129394604245311 / 40000000000000000 : ℝ) ≤ - (564320251431005603369 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6266148525437109 / 10000000000000000 : ℝ)) (q := - (50129394604245311 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50129394604245311 / 80000000000000000 : ℚ)) + (r' := (50129394604245311 / 40000000000000000 : ℚ)) + (U := (-(1168547699318994396631 / 2500000000000000000000 : ℚ))) + (U' := (564320251431005603369 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (6266148525437109 / 10000000000000000 : ℚ)) + (q := (50129394604245311 / 80000000000000000 : ℚ)) + (U := (-(1168547699318994396631 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_2 : Uω (aρ 2) (bρ 2) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -4886,25 +4271,21 @@ lemma U_555_2 : have hlg : Real.log (49938089234822199 / 80000000000000000 : ℝ) ≤ (-(1178106528778261540091 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49938089234822199 / 80000000000000000 : ℝ) = - (49938089234822199 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49938089234822199 / 40000000000000000 : ℚ)) - (U := (554761421971738459909 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49938089234822199 / 40000000000000000 : ℝ) ≤ - (554761421971738459909 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6242091195591331 / 10000000000000000 : ℝ)) (q := - (49938089234822199 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49938089234822199 / 80000000000000000 : ℚ)) + (r' := (49938089234822199 / 40000000000000000 : ℚ)) + (U := (-(1178106528778261540091 / 2500000000000000000000 : ℚ))) + (U' := (554761421971738459909 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (6242091195591331 / 10000000000000000 : ℚ)) + (q := (49938089234822199 / 80000000000000000 : ℚ)) + (U := (-(1178106528778261540091 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_3 : Uω (aρ 3) (bρ 3) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -4912,25 +4293,21 @@ lemma U_555_3 : have hlg : Real.log (49555502813276743 / 80000000000000000 : ℝ) ≤ (-(4789333240367326840447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49555502813276743 / 80000000000000000 : ℝ) = - (49555502813276743 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49555502813276743 / 40000000000000000 : ℚ)) - (U := (2142138562632673159553 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49555502813276743 / 40000000000000000 : ℝ) ≤ - (2142138562632673159553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6193840696554967 / 10000000000000000 : ℝ)) (q := - (49555502813276743 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49555502813276743 / 80000000000000000 : ℚ)) + (r' := (49555502813276743 / 40000000000000000 : ℚ)) + (U := (-(4789333240367326840447 / 10000000000000000000000 : ℚ))) + (U' := (2142138562632673159553 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (6193840696554967 / 10000000000000000 : ℚ)) + (q := (49555502813276743 / 80000000000000000 : ℚ)) + (U := (-(4789333240367326840447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_4 : Uω (aρ 4) (bρ 4) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -4938,25 +4315,21 @@ lemma U_555_4 : have hlg : Real.log (48920163080644023 / 80000000000000000 : ℝ) ≤ (-(2459184949907346047189 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48920163080644023 / 80000000000000000 : ℝ) = - (48920163080644023 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48920163080644023 / 40000000000000000 : ℚ)) - (U := (1006550951592653952811 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48920163080644023 / 40000000000000000 : ℝ) ≤ - (1006550951592653952811 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6113299944461787 / 10000000000000000 : ℝ)) (q := - (48920163080644023 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48920163080644023 / 80000000000000000 : ℚ)) + (r' := (48920163080644023 / 40000000000000000 : ℚ)) + (U := (-(2459184949907346047189 / 5000000000000000000000 : ℚ))) + (U' := (1006550951592653952811 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (6113299944461787 / 10000000000000000 : ℚ)) + (q := (48920163080644023 / 80000000000000000 : ℚ)) + (U := (-(2459184949907346047189 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_5 : Uω (aρ 5) (bρ 5) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -4964,25 +4337,21 @@ lemma U_555_5 : have hlg : Real.log (47952867767386439 / 80000000000000000 : ℝ) ≤ (-(5118080274195688240163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47952867767386439 / 80000000000000000 : ℝ) = - (47952867767386439 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47952867767386439 / 40000000000000000 : ℚ)) - (U := (1813391528804311759837 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47952867767386439 / 40000000000000000 : ℝ) ≤ - (1813391528804311759837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5989666035482391 / 10000000000000000 : ℝ)) (q := - (47952867767386439 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47952867767386439 / 80000000000000000 : ℚ)) + (r' := (47952867767386439 / 40000000000000000 : ℚ)) + (U := (-(5118080274195688240163 / 10000000000000000000000 : ℚ))) + (U' := (1813391528804311759837 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (5989666035482391 / 10000000000000000 : ℚ)) + (q := (47952867767386439 / 80000000000000000 : ℚ)) + (U := (-(5118080274195688240163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_6 : Uω (aρ 6) (bρ 6) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -4990,25 +4359,21 @@ lemma U_555_6 : have hlg : Real.log (46566150197161723 / 80000000000000000 : ℝ) ≤ (-(1352881869626692158181 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46566150197161723 / 80000000000000000 : ℝ) = - (46566150197161723 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46566150197161723 / 40000000000000000 : ℚ)) - (U := (379986081123307841819 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46566150197161723 / 40000000000000000 : ℝ) ≤ - (379986081123307841819 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1452556754516553 / 2500000000000000 : ℝ)) (q := - (46566150197161723 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46566150197161723 / 80000000000000000 : ℚ)) + (r' := (46566150197161723 / 40000000000000000 : ℚ)) + (U := (-(1352881869626692158181 / 2500000000000000000000 : ℚ))) + (U' := (379986081123307841819 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (1452556754516553 / 2500000000000000 : ℚ)) + (q := (46566150197161723 / 80000000000000000 : ℚ)) + (U := (-(1352881869626692158181 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_7 : Uω (aρ 7) (bρ 7) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5016,25 +4381,21 @@ lemma U_555_7 : have hlg : Real.log (44675426247907999 / 80000000000000000 : ℝ) ≤ (-(1165206064660802796103 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44675426247907999 / 80000000000000000 : ℝ) = - (44675426247907999 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44675426247907999 / 40000000000000000 : ℚ)) - (U := (221088295939197203897 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44675426247907999 / 40000000000000000 : ℝ) ≤ - (221088295939197203897 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5561207411512781 / 10000000000000000 : ℝ)) (q := - (44675426247907999 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44675426247907999 / 80000000000000000 : ℚ)) + (r' := (44675426247907999 / 40000000000000000 : ℚ)) + (U := (-(1165206064660802796103 / 2000000000000000000000 : ℚ))) + (U' := (221088295939197203897 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (5561207411512781 / 10000000000000000 : ℚ)) + (q := (44675426247907999 / 80000000000000000 : ℚ)) + (U := (-(1165206064660802796103 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_8 : Uω (aρ 8) (bρ 8) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5042,25 +4403,21 @@ lemma U_555_8 : have hlg : Real.log (42210411974394231 / 80000000000000000 : ℝ) ≤ (-(6393597145535780670923 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42210411974394231 / 80000000000000000 : ℝ) = - (42210411974394231 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42210411974394231 / 40000000000000000 : ℚ)) - (U := (537874657464219329077 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42210411974394231 / 40000000000000000 : ℝ) ≤ - (537874657464219329077 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5228495494474339 / 10000000000000000 : ℝ)) (q := - (42210411974394231 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42210411974394231 / 80000000000000000 : ℚ)) + (r' := (42210411974394231 / 40000000000000000 : ℚ)) + (U := (-(6393597145535780670923 / 10000000000000000000000 : ℚ))) + (U' := (537874657464219329077 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (5228495494474339 / 10000000000000000 : ℚ)) + (q := (42210411974394231 / 80000000000000000 : ℚ)) + (U := (-(6393597145535780670923 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_9 : Uω (aρ 9) (bρ 9) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5068,25 +4425,21 @@ lemma U_555_9 : have hlg : Real.log (7824866809506411 / 16000000000000000 : ℝ) ≤ (-(7152820065878755550463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7824866809506411 / 16000000000000000 : ℝ) = - (7824866809506411 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7824866809506411 / 4000000000000000 : ℚ)) - (U := (6710123540121244449537 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7824866809506411 / 4000000000000000 : ℝ) ≤ - (6710123540121244449537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (959588328223759 / 2000000000000000 : ℝ)) (q := - (7824866809506411 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7824866809506411 / 16000000000000000 : ℚ)) + (r' := (7824866809506411 / 4000000000000000 : ℚ)) + (U := (-(7152820065878755550463 / 10000000000000000000000 : ℚ))) + (U' := (6710123540121244449537 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (959588328223759 / 2000000000000000 : ℚ)) + (q := (7824866809506411 / 16000000000000000 : ℚ)) + (U := (-(7152820065878755550463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_10 : Uω (aρ 10) (bρ 10) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5094,26 +4447,21 @@ lemma U_555_10 : have hlg : Real.log (35396310645675803 / 80000000000000000 : ℝ) ≤ (-(1630838076988301541033 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35396310645675803 / 80000000000000000 : ℝ) = - (35396310645675803 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35396310645675803 / 20000000000000000 : ℚ)) - (U := (1141750644211698458967 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35396310645675803 / 20000000000000000 : ℝ) ≤ - (1141750644211698458967 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1063623706037433 / 2500000000000000 : ℝ)) (q := - (35396310645675803 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35396310645675803 / 80000000000000000 : ℚ)) + (r' := (35396310645675803 / 20000000000000000 : ℚ)) + (U := (-(1630838076988301541033 / 2000000000000000000000 : ℚ))) + (U' := (1141750644211698458967 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (1063623706037433 / 2500000000000000 : ℚ)) + (q := (35396310645675803 / 80000000000000000 : ℚ)) + (U := (-(1630838076988301541033 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_11 : Uω (aρ 11) (bρ 11) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5121,26 +4469,21 @@ lemma U_555_11 : have hlg : Real.log (31016604040819147 / 80000000000000000 : ℝ) ≤ (-(2368759897097424207653 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31016604040819147 / 80000000000000000 : ℝ) = - (31016604040819147 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31016604040819147 / 20000000000000000 : ℚ)) - (U := (1096976004402575792347 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31016604040819147 / 20000000000000000 : ℝ) ≤ - (1096976004402575792347 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (447255599892571 / 1250000000000000 : ℝ)) (q := - (31016604040819147 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31016604040819147 / 80000000000000000 : ℚ)) + (r' := (31016604040819147 / 20000000000000000 : ℚ)) + (U := (-(2368759897097424207653 / 2500000000000000000000 : ℚ))) + (U' := (1096976004402575792347 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (447255599892571 / 1250000000000000 : ℚ)) + (q := (31016604040819147 / 80000000000000000 : ℚ)) + (U := (-(2368759897097424207653 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_12 : Uω (aρ 12) (bρ 12) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5148,26 +4491,21 @@ lemma U_555_12 : have hlg : Real.log (25918654397605731 / 80000000000000000 : ℝ) ≤ (-(5635318388450483959479 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25918654397605731 / 80000000000000000 : ℝ) = - (25918654397605731 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25918654397605731 / 20000000000000000 : ℚ)) - (U := (1296153414549516040521 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25918654397605731 / 20000000000000000 : ℝ) ≤ - (1296153414549516040521 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1363628742511107 / 5000000000000000 : ℝ)) (q := - (25918654397605731 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25918654397605731 / 80000000000000000 : ℚ)) + (r' := (25918654397605731 / 20000000000000000 : ℚ)) + (U := (-(5635318388450483959479 / 5000000000000000000000 : ℚ))) + (U' := (1296153414549516040521 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (1363628742511107 / 5000000000000000 : ℚ)) + (q := (25918654397605731 / 80000000000000000 : ℚ)) + (U := (-(5635318388450483959479 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_13 : Uω (aρ 13) (bρ 13) (40516462999739 / 64000000000000 : ℝ) ≤ @@ -5175,26 +4513,21 @@ lemma U_555_13 : have hlg : Real.log (19584741662899847 / 80000000000000000 : ℝ) ≤ (-(7036379287111782039099 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19584741662899847 / 80000000000000000 : ℝ) = - (19584741662899847 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19584741662899847 / 10000000000000000 : ℚ)) - (U := (3360828417388217960901 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19584741662899847 / 10000000000000000 : ℝ) ≤ - (3360828417388217960901 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1543161042940743 / 10000000000000000 : ℝ)) (q := - (19584741662899847 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19584741662899847 / 80000000000000000 : ℚ)) + (r' := (19584741662899847 / 10000000000000000 : ℚ)) + (U := (-(7036379287111782039099 / 5000000000000000000000 : ℚ))) + (U' := (3360828417388217960901 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40516462999739 / 64000000000000 : ℚ)) + (s := (1543161042940743 / 10000000000000000 : ℚ)) + (q := (19584741662899847 / 80000000000000000 : ℚ)) + (U := (-(7036379287111782039099 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_555_14 : Uω (aρ 14) (bρ 14) (40516462999739 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U46.lean b/LeanPool/Zeta5Irrational/Table/U46.lean index d6b1f1fcab..a44d009567 100644 --- a/LeanPool/Zeta5Irrational/Table/U46.lean +++ b/LeanPool/Zeta5Irrational/Table/U46.lean @@ -24,25 +24,21 @@ lemma U_556_1 : have hlg : Real.log (12553846428466647 / 20000000000000000 : ℝ) ≤ (-(291065728968855683219 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12553846428466647 / 20000000000000000 : ℝ) = - (12553846428466647 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12553846428466647 / 10000000000000000 : ℚ)) - (U := (142151258718644316781 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12553846428466647 / 10000000000000000 : ℝ) ≤ - (142151258718644316781 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3138448729160511 / 5000000000000000 : ℝ)) (q := - (12553846428466647 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12553846428466647 / 20000000000000000 : ℚ)) + (r' := (12553846428466647 / 10000000000000000 : ℚ)) + (U := (-(291065728968855683219 / 625000000000000000000 : ℚ))) + (U' := (142151258718644316781 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (3138448729160511 / 5000000000000000 : ℚ)) + (q := (12553846428466647 / 20000000000000000 : ℚ)) + (U := (-(291065728968855683219 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_2 : Uω (aρ 2) (bρ 2) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_556_2 : have hlg : Real.log (12506020582078109 / 20000000000000000 : ℝ) ≤ (-(2347610491870088450017 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12506020582078109 / 20000000000000000 : ℝ) = - (12506020582078109 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12506020582078109 / 10000000000000000 : ℚ)) - (U := (1118125409629911549983 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12506020582078109 / 10000000000000000 : ℝ) ≤ - (1118125409629911549983 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1563210156110621 / 2500000000000000 : ℝ)) (q := - (12506020582078109 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12506020582078109 / 20000000000000000 : ℚ)) + (r' := (12506020582078109 / 10000000000000000 : ℚ)) + (U := (-(2347610491870088450017 / 5000000000000000000000 : ℚ))) + (U' := (1118125409629911549983 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (1563210156110621 / 2500000000000000 : ℚ)) + (q := (12506020582078109 / 20000000000000000 : ℚ)) + (U := (-(2347610491870088450017 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_3 : Uω (aρ 3) (bρ 3) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_556_3 : have hlg : Real.log (12410375461387277 / 20000000000000000 : ℝ) ≤ (-(4771994197900481931239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12410375461387277 / 20000000000000000 : ℝ) = - (12410375461387277 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12410375461387277 / 10000000000000000 : ℚ)) - (U := (2159477605099518068761 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12410375461387277 / 10000000000000000 : ℝ) ≤ - (2159477605099518068761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1551147902525413 / 2500000000000000 : ℝ)) (q := - (12410375461387277 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12410375461387277 / 20000000000000000 : ℚ)) + (r' := (12410375461387277 / 10000000000000000 : ℚ)) + (U := (-(4771994197900481931239 / 10000000000000000000000 : ℚ))) + (U' := (2159477605099518068761 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (1551147902525413 / 2500000000000000 : ℚ)) + (q := (12410375461387277 / 20000000000000000 : ℚ)) + (U := (-(4771994197900481931239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_4 : Uω (aρ 4) (bρ 4) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_556_4 : have hlg : Real.log (12251544498587317 / 20000000000000000 : ℝ) ≤ (-(2450401313667920874891 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12251544498587317 / 20000000000000000 : ℝ) = - (12251544498587317 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12251544498587317 / 10000000000000000 : ℚ)) - (U := (1015334587832079125109 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12251544498587317 / 10000000000000000 : ℝ) ≤ - (1015334587832079125109 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1531013707091673 / 2500000000000000 : ℝ)) (q := - (12251544498587317 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12251544498587317 / 20000000000000000 : ℚ)) + (r' := (12251544498587317 / 10000000000000000 : ℚ)) + (U := (-(2450401313667920874891 / 5000000000000000000000 : ℚ))) + (U' := (1015334587832079125109 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (1531013707091673 / 2500000000000000 : ℚ)) + (q := (12251544498587317 / 20000000000000000 : ℚ)) + (U := (-(2450401313667920874891 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_5 : Uω (aρ 5) (bρ 5) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_556_5 : have hlg : Real.log (3002432636695933 / 5000000000000000 : ℝ) ≤ (-(1275037682980197292503 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3002432636695933 / 5000000000000000 : ℝ) = - (3002432636695933 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3002432636695933 / 2500000000000000 : ℚ)) - (U := (457830267769802707497 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3002432636695933 / 2500000000000000 : ℝ) ≤ - (457830267769802707497 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6000430795898107 / 10000000000000000 : ℝ)) (q := - (3002432636695933 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3002432636695933 / 5000000000000000 : ℚ)) + (r' := (3002432636695933 / 2500000000000000 : ℚ)) + (U := (-(1275037682980197292503 / 2500000000000000000000 : ℚ))) + (U' := (457830267769802707497 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (6000430795898107 / 10000000000000000 : ℚ)) + (q := (3002432636695933 / 5000000000000000 : ℚ)) + (U := (-(1275037682980197292503 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_6 : Uω (aρ 6) (bρ 6) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_556_6 : have hlg : Real.log (11663074170404497 / 20000000000000000 : ℝ) ≤ (-(5393044761434235189473 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11663074170404497 / 20000000000000000 : ℝ) = - (11663074170404497 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11663074170404497 / 10000000000000000 : ℚ)) - (U := (1538427041565764810527 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11663074170404497 / 10000000000000000 : ℝ) ≤ - (1538427041565764810527 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (727626849332359 / 1250000000000000 : ℝ)) (q := - (11663074170404497 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11663074170404497 / 20000000000000000 : ℚ)) + (r' := (11663074170404497 / 10000000000000000 : ℚ)) + (U := (-(5393044761434235189473 / 10000000000000000000000 : ℚ))) + (U' := (1538427041565764810527 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (727626849332359 / 1250000000000000 : ℚ)) + (q := (11663074170404497 / 20000000000000000 : ℚ)) + (U := (-(5393044761434235189473 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_7 : Uω (aρ 7) (bρ 7) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_556_7 : have hlg : Real.log (2238088768184477 / 4000000000000000 : ℝ) ≤ (-(362920054805424530923 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2238088768184477 / 4000000000000000 : ℝ) = - (2238088768184477 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2238088768184477 / 2000000000000000 : ℚ)) - (U := (70296932882075469077 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2238088768184477 / 2000000000000000 : ℝ) ≤ - (70296932882075469077 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (139301146148419 / 250000000000000 : ℝ)) (q := - (2238088768184477 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2238088768184477 / 4000000000000000 : ℚ)) + (r' := (2238088768184477 / 2000000000000000 : ℚ)) + (U := (-(362920054805424530923 / 625000000000000000000 : ℚ))) + (U' := (70296932882075469077 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (139301146148419 / 250000000000000 : ℚ)) + (q := (2238088768184477 / 4000000000000000 : ℚ)) + (U := (-(362920054805424530923 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_8 : Uω (aρ 8) (bρ 8) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_556_8 : have hlg : Real.log (165223388074311 / 312500000000000 : ℝ) ≤ (-(6373060435506251966543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (165223388074311 / 312500000000000 : ℝ) = - (165223388074311 / 156250000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (165223388074311 / 156250000000000 : ℚ)) - (U := (558411367493748033457 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (165223388074311 / 156250000000000 : ℝ) ≤ - (558411367493748033457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5239440493110279 / 10000000000000000 : ℝ)) (q := - (165223388074311 / 312500000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (165223388074311 / 312500000000000 : ℚ)) + (r' := (165223388074311 / 156250000000000 : ℚ)) + (U := (-(6373060435506251966543 / 10000000000000000000000 : ℚ))) + (U' := (558411367493748033457 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (5239440493110279 / 10000000000000000 : ℚ)) + (q := (165223388074311 / 312500000000000 : ℚ)) + (U := (-(6373060435506251966543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_9 : Uω (aρ 9) (bρ 9) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_556_9 : have hlg : Real.log (4901497580180003 / 10000000000000000 : ℝ) ≤ (-(1426088610888638727831 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4901497580180003 / 10000000000000000 : ℝ) = - (4901497580180003 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4901497580180003 / 2500000000000000 : ℚ)) - (U := (1346500110311361272169 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4901497580180003 / 2500000000000000 : ℝ) ≤ - (1346500110311361272169 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4809104445074381 / 10000000000000000 : ℝ)) (q := - (4901497580180003 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4901497580180003 / 10000000000000000 : ℚ)) + (r' := (4901497580180003 / 2500000000000000 : ℚ)) + (U := (-(1426088610888638727831 / 2000000000000000000000 : ℚ))) + (U' := (1346500110311361272169 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (4809104445074381 / 10000000000000000 : ℚ)) + (q := (4901497580180003 / 10000000000000000 : ℚ)) + (U := (-(1426088610888638727831 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_10 : Uω (aρ 10) (bρ 10) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_556_10 : have hlg : Real.log (4435716160243901 / 10000000000000000 : ℝ) ≤ (-(508060006594250466711 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4435716160243901 / 10000000000000000 : ℝ) = - (4435716160243901 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4435716160243901 / 2500000000000000 : ℚ)) - (U := (358373968780749533289 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4435716160243901 / 2500000000000000 : ℝ) ≤ - (358373968780749533289 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4266100638697177 / 10000000000000000 : ℝ)) (q := - (4435716160243901 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4435716160243901 / 10000000000000000 : ℚ)) + (r' := (4435716160243901 / 2500000000000000 : ℚ)) + (U := (-(508060006594250466711 / 625000000000000000000 : ℚ))) + (U' := (358373968780749533289 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (4266100638697177 / 10000000000000000 : ℚ)) + (q := (4435716160243901 / 10000000000000000 : ℚ)) + (U := (-(508060006594250466711 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_11 : Uω (aρ 11) (bρ 11) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_556_11 : have hlg : Real.log (3888719757142301 / 10000000000000000 : ℝ) ≤ (-(1180631375359092244143 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3888719757142301 / 10000000000000000 : ℝ) = - (3888719757142301 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3888719757142301 / 2500000000000000 : ℚ)) - (U := (552236575390907755857 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3888719757142301 / 2500000000000000 : ℝ) ≤ - (552236575390907755857 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3590584458698977 / 10000000000000000 : ℝ)) (q := - (3888719757142301 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3888719757142301 / 10000000000000000 : ℚ)) + (r' := (3888719757142301 / 2500000000000000 : ℚ)) + (U := (-(1180631375359092244143 / 1250000000000000000000 : ℚ))) + (U' := (552236575390907755857 / 1250000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (3590584458698977 / 10000000000000000 : ℚ)) + (q := (3888719757142301 / 10000000000000000 : ℚ)) + (U := (-(1180631375359092244143 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_12 : Uω (aρ 12) (bρ 12) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_556_12 : have hlg : Real.log (3252591427872931 / 10000000000000000 : ℝ) ≤ (-(11231330514346018154391 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3252591427872931 / 10000000000000000 : ℝ) = - (3252591427872931 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3252591427872931 / 2500000000000000 : ℚ)) - (U := (2631613091653981845609 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3252591427872931 / 2500000000000000 : ℝ) ≤ - (2631613091653981845609 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2742027896845237 / 10000000000000000 : ℝ)) (q := - (3252591427872931 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3252591427872931 / 10000000000000000 : ℚ)) + (r' := (3252591427872931 / 2500000000000000 : ℚ)) + (U := (-(11231330514346018154391 / 10000000000000000000000 : ℚ))) + (U' := (2631613091653981845609 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (2742027896845237 / 10000000000000000 : ℚ)) + (q := (3252591427872931 / 10000000000000000 : ℚ)) + (U := (-(11231330514346018154391 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_13 : Uω (aρ 13) (bρ 13) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -339,26 +288,21 @@ lemma U_556_13 : have hlg : Real.log (4930152423445567 / 20000000000000000 : ℝ) ≤ (-(14003623676628956738161 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4930152423445567 / 20000000000000000 : ℝ) = - (4930152423445567 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4930152423445567 / 2500000000000000 : ℚ)) - (U := (6790791732371043261839 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4930152423445567 / 2500000000000000 : ℝ) ≤ - (6790791732371043261839 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (783189603069971 / 5000000000000000 : ℝ)) (q := - (4930152423445567 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4930152423445567 / 20000000000000000 : ℚ)) + (r' := (4930152423445567 / 2500000000000000 : ℚ)) + (U := (-(14003623676628956738161 / 10000000000000000000000 : ℚ))) + (U' := (6790791732371043261839 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10146313901169 / 16000000000000 : ℚ)) + (s := (783189603069971 / 5000000000000000 : ℚ)) + (q := (4930152423445567 / 20000000000000000 : ℚ)) + (U := (-(14003623676628956738161 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_556_14 : Uω (aρ 14) (bρ 14) (10146313901169 / 16000000000000 : ℝ) ≤ @@ -465,25 +409,21 @@ lemma U_557_1 : have hlg : Real.log (50301376822279401 / 80000000000000000 : ℝ) ≤ (-(2319970927352704056403 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50301376822279401 / 80000000000000000 : ℝ) = - (50301376822279401 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50301376822279401 / 40000000000000000 : ℚ)) - (U := (1145764974147295943597 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50301376822279401 / 40000000000000000 : ℝ) ≤ - (1145764974147295943597 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6287646390902819 / 10000000000000000 : ℝ)) (q := - (50301376822279401 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50301376822279401 / 80000000000000000 : ℚ)) + (r' := (50301376822279401 / 40000000000000000 : ℚ)) + (U := (-(2319970927352704056403 / 5000000000000000000000 : ℚ))) + (U' := (1145764974147295943597 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (6287646390902819 / 10000000000000000 : ℚ)) + (q := (50301376822279401 / 80000000000000000 : ℚ)) + (U := (-(2319970927352704056403 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_2 : Uω (aρ 2) (bρ 2) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -491,25 +431,21 @@ lemma U_557_2 : have hlg : Real.log (50110075413780381 / 80000000000000000 : ℝ) ≤ (-(1169511351196875418163 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50110075413780381 / 80000000000000000 : ℝ) = - (50110075413780381 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50110075413780381 / 40000000000000000 : ℚ)) - (U := (563356599553124581837 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50110075413780381 / 40000000000000000 : ℝ) ≤ - (563356599553124581837 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6116787159461 / 9765625000000 : ℝ)) (q := - (50110075413780381 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50110075413780381 / 80000000000000000 : ℚ)) + (r' := (50110075413780381 / 40000000000000000 : ℚ)) + (U := (-(1169511351196875418163 / 2500000000000000000000 : ℚ))) + (U' := (563356599553124581837 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (6116787159461 / 9765625000000 : ℚ)) + (q := (50110075413780381 / 80000000000000000 : ℚ)) + (U := (-(1169511351196875418163 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_3 : Uω (aρ 3) (bρ 3) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -517,25 +453,21 @@ lemma U_557_3 : have hlg : Real.log (49727500849193261 / 80000000000000000 : ℝ) ≤ (-(4754685173399231974649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49727500849193261 / 80000000000000000 : ℝ) = - (49727500849193261 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49727500849193261 / 40000000000000000 : ℚ)) - (U := (2176786629600768025351 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49727500849193261 / 40000000000000000 : ℝ) ≤ - (2176786629600768025351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1553835629122821 / 2500000000000000 : ℝ)) (q := - (49727500849193261 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49727500849193261 / 80000000000000000 : ℚ)) + (r' := (49727500849193261 / 40000000000000000 : ℚ)) + (U := (-(4754685173399231974649 / 10000000000000000000000 : ℚ))) + (U' := (2176786629600768025351 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (1553835629122821 / 2500000000000000 : ℚ)) + (q := (49727500849193261 / 80000000000000000 : ℚ)) + (U := (-(4754685173399231974649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_4 : Uω (aρ 4) (bρ 4) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -543,25 +475,21 @@ lemma U_557_4 : have hlg : Real.log (49092192823377549 / 80000000000000000 : ℝ) ≤ (-(2441633089450279375213 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49092192823377549 / 80000000000000000 : ℝ) = - (49092192823377549 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49092192823377549 / 40000000000000000 : ℚ)) - (U := (1024102812049720624787 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49092192823377549 / 40000000000000000 : ℝ) ≤ - (1024102812049720624787 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1533702422775589 / 2500000000000000 : ℝ)) (q := - (49092192823377549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49092192823377549 / 80000000000000000 : ℚ)) + (r' := (49092192823377549 / 40000000000000000 : ℚ)) + (U := (-(2441633089450279375213 / 5000000000000000000000 : ℚ))) + (U' := (1024102812049720624787 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (1533702422775589 / 2500000000000000 : ℚ)) + (q := (49092192823377549 / 80000000000000000 : ℚ)) + (U := (-(2441633089450279375213 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_5 : Uω (aρ 5) (bρ 5) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -569,25 +497,21 @@ lemma U_557_5 : have hlg : Real.log (9624995275807277 / 16000000000000000 : ℝ) ≤ (-(5082253326313264360587 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9624995275807277 / 16000000000000000 : ℝ) = - (9624995275807277 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9624995275807277 / 8000000000000000 : ℚ)) - (U := (1849218476686735639413 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9624995275807277 / 8000000000000000 : ℝ) ≤ - (1849218476686735639413 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1202239099870413 / 2000000000000000 : ℝ)) (q := - (9624995275807277 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9624995275807277 / 16000000000000000 : ℚ)) + (r' := (9624995275807277 / 8000000000000000 : ℚ)) + (U := (-(5082253326313264360587 / 10000000000000000000000 : ℚ))) + (U' := (1849218476686735639413 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (1202239099870413 / 2000000000000000 : ℚ)) + (q := (9624995275807277 / 16000000000000000 : ℚ)) + (U := (-(5082253326313264360587 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_6 : Uω (aρ 6) (bρ 6) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -595,25 +519,21 @@ lemma U_557_6 : have hlg : Real.log (46738442590975717 / 80000000000000000 : ℝ) ≤ (-(5374596265478078590309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46738442590975717 / 80000000000000000 : ℝ) = - (46738442590975717 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46738442590975717 / 40000000000000000 : ℚ)) - (U := (1556875537521921409691 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46738442590975717 / 40000000000000000 : ℝ) ≤ - (1556875537521921409691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2915901213738449 / 5000000000000000 : ℝ)) (q := - (46738442590975717 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46738442590975717 / 80000000000000000 : ℚ)) + (r' := (46738442590975717 / 40000000000000000 : ℚ)) + (U := (-(5374596265478078590309 / 10000000000000000000000 : ℚ))) + (U' := (1556875537521921409691 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (2915901213738449 / 5000000000000000 : ℚ)) + (q := (46738442590975717 / 80000000000000000 : ℚ)) + (U := (-(5374596265478078590309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_7 : Uω (aρ 7) (bρ 7) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -621,25 +541,21 @@ lemma U_557_7 : have hlg : Real.log (8969624618761153 / 16000000000000000 : ℝ) ≤ (-(2893724476532077899517 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8969624618761153 / 16000000000000000 : ℝ) = - (8969624618761153 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8969624618761153 / 8000000000000000 : ℚ)) - (U := (572011424967922100483 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (8969624618761153 / 8000000000000000 : ℝ) ≤ - (572011424967922100483 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (558288393394441 / 1000000000000000 : ℝ)) (q := - (8969624618761153 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8969624618761153 / 16000000000000000 : ℚ)) + (r' := (8969624618761153 / 8000000000000000 : ℚ)) + (U := (-(2893724476532077899517 / 5000000000000000000000 : ℚ))) + (U' := (572011424967922100483 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (558288393394441 / 1000000000000000 : ℚ)) + (q := (8969624618761153 / 16000000000000000 : ℚ)) + (U := (-(2893724476532077899517 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_8 : Uω (aρ 8) (bρ 8) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -647,25 +563,21 @@ lemma U_557_8 : have hlg : Real.log (42383959477729581 / 80000000000000000 : ℝ) ≤ (-(6352566579593873370831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42383959477729581 / 80000000000000000 : ℝ) = - (42383959477729581 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42383959477729581 / 40000000000000000 : ℚ)) - (U := (578905223406126629169 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42383959477729581 / 40000000000000000 : ℝ) ≤ - (578905223406126629169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1312596170316341 / 2500000000000000 : ℝ)) (q := - (42383959477729581 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42383959477729581 / 80000000000000000 : ℚ)) + (r' := (42383959477729581 / 40000000000000000 : ℚ)) + (U := (-(6352566579593873370831 / 10000000000000000000000 : ℚ))) + (U' := (578905223406126629169 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (1312596170316341 / 2500000000000000 : ℚ)) + (q := (42383959477729581 / 80000000000000000 : ℚ)) + (U := (-(6352566579593873370831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_9 : Uω (aρ 9) (bρ 9) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -673,25 +585,21 @@ lemma U_557_9 : have hlg : Real.log (39299619708350081 / 80000000000000000 : ℝ) ≤ (-(177702947989476951683 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39299619708350081 / 80000000000000000 : ℝ) = - (39299619708350081 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39299619708350081 / 20000000000000000 : ℚ)) - (U := (168870642160523048317 / 250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39299619708350081 / 20000000000000000 : ℝ) ≤ - (168870642160523048317 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4820265367280489 / 10000000000000000 : ℝ)) (q := - (39299619708350081 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39299619708350081 / 80000000000000000 : ℚ)) + (r' := (39299619708350081 / 20000000000000000 : ℚ)) + (U := (-(177702947989476951683 / 250000000000000000000 : ℚ))) + (U' := (168870642160523048317 / 250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (4820265367280489 / 10000000000000000 : ℚ)) + (q := (39299619708350081 / 80000000000000000 : ℚ)) + (U := (-(177702947989476951683 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_10 : Uω (aρ 10) (bρ 10) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -699,26 +607,21 @@ lemma U_557_10 : have hlg : Real.log (7115026000924909 / 16000000000000000 : ℝ) ≤ (-(253243698688492737057 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7115026000924909 / 16000000000000000 : ℝ) = - (7115026000924909 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7115026000924909 / 4000000000000000 : ℚ)) - (U := (179973288999007262943 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7115026000924909 / 4000000000000000 : ℝ) ≤ - (179973288999007262943 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (855540394968821 / 2000000000000000 : ℝ)) (q := - (7115026000924909 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7115026000924909 / 16000000000000000 : ℚ)) + (r' := (7115026000924909 / 4000000000000000 : ℚ)) + (U := (-(253243698688492737057 / 312500000000000000000 : ℚ))) + (U' := (179973288999007262943 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (855540394968821 / 2000000000000000 : ℚ)) + (q := (7115026000924909 / 16000000000000000 : ℚ)) + (U := (-(253243698688492737057 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_11 : Uω (aρ 11) (bρ 11) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -726,26 +629,21 @@ lemma U_557_11 : have hlg : Real.log (31202865774225213 / 80000000000000000 : ℝ) ≤ (-(9415166918186793190237 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31202865774225213 / 80000000000000000 : ℝ) = - (31202865774225213 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31202865774225213 / 20000000000000000 : ℚ)) - (U := (4447776687813206809763 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31202865774225213 / 20000000000000000 : ℝ) ≤ - (4447776687813206809763 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (450389067931159 / 1250000000000000 : ℝ)) (q := - (31202865774225213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31202865774225213 / 80000000000000000 : ℚ)) + (r' := (31202865774225213 / 20000000000000000 : ℚ)) + (U := (-(9415166918186793190237 / 10000000000000000000000 : ℚ))) + (U' := (4447776687813206809763 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (450389067931159 / 1250000000000000 : ℚ)) + (q := (31202865774225213 / 80000000000000000 : ℚ)) + (U := (-(9415166918186793190237 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_12 : Uω (aρ 12) (bρ 12) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -753,26 +651,21 @@ lemma U_557_12 : have hlg : Real.log (26122659539245121 / 80000000000000000 : ℝ) ≤ (-(11192235148967130137221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26122659539245121 / 80000000000000000 : ℝ) = - (26122659539245121 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26122659539245121 / 20000000000000000 : ℚ)) - (U := (2670708457032869862779 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26122659539245121 / 20000000000000000 : ℝ) ≤ - (2670708457032869862779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2756761081389249 / 10000000000000000 : ℝ)) (q := - (26122659539245121 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26122659539245121 / 80000000000000000 : ℚ)) + (r' := (26122659539245121 / 20000000000000000 : ℚ)) + (U := (-(11192235148967130137221 / 10000000000000000000000 : ℚ))) + (U' := (2670708457032869862779 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (2756761081389249 / 10000000000000000 : ℚ)) + (q := (26122659539245121 / 80000000000000000 : ℚ)) + (U := (-(11192235148967130137221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_13 : Uω (aρ 13) (bρ 13) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -780,26 +673,21 @@ lemma U_557_13 : have hlg : Real.log (19855411842309173 / 80000000000000000 : ℝ) ≤ (-(6967750135136901165281 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19855411842309173 / 80000000000000000 : ℝ) = - (19855411842309173 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19855411842309173 / 10000000000000000 : ℚ)) - (U := (3429457569363098834719 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19855411842309173 / 10000000000000000 : ℝ) ≤ - (3429457569363098834719 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (794665449375131 / 5000000000000000 : ℝ)) (q := - (19855411842309173 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19855411842309173 / 80000000000000000 : ℚ)) + (r' := (19855411842309173 / 10000000000000000 : ℚ)) + (U := (-(6967750135136901165281 / 5000000000000000000000 : ℚ))) + (U' := (3429457569363098834719 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40654048209613 / 64000000000000 : ℚ)) + (s := (794665449375131 / 5000000000000000 : ℚ)) + (q := (19855411842309173 / 80000000000000000 : ℚ)) + (U := (-(6967750135136901165281 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_557_14 : Uω (aρ 14) (bρ 14) (40654048209613 / 64000000000000 : ℝ) ≤ @@ -906,25 +794,21 @@ lemma U_558_1 : have hlg : Real.log (25193683964744969 / 40000000000000000 : ℝ) ≤ (-(4622861270707890117367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25193683964744969 / 40000000000000000 : ℝ) = - (25193683964744969 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25193683964744969 / 20000000000000000 : ℚ)) - (U := (2308610532292109882633 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25193683964744969 / 20000000000000000 : ℝ) ≤ - (2308610532292109882633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6298395323184047 / 10000000000000000 : ℝ)) (q := - (25193683964744969 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25193683964744969 / 40000000000000000 : ℚ)) + (r' := (25193683964744969 / 20000000000000000 : ℚ)) + (U := (-(4622861270707890117367 / 10000000000000000000000 : ℚ))) + (U' := (2308610532292109882633 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (6298395323184047 / 10000000000000000 : ℚ)) + (q := (25193683964744969 / 40000000000000000 : ℚ)) + (U := (-(4622861270707890117367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_2 : Uω (aρ 2) (bρ 2) (814456816291 / 1280000000000 : ℝ) ≤ @@ -932,25 +816,21 @@ lemma U_558_2 : have hlg : Real.log (25098034245633637 / 40000000000000000 : ℝ) ≤ (-(4660899276902082966911 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25098034245633637 / 40000000000000000 : ℝ) = - (25098034245633637 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25098034245633637 / 20000000000000000 : ℚ)) - (U := (2270572526097917033089 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25098034245633637 / 20000000000000000 : ℝ) ≤ - (2270572526097917033089 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6274339476138381 / 10000000000000000 : ℝ)) (q := - (25098034245633637 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25098034245633637 / 40000000000000000 : ℚ)) + (r' := (25098034245633637 / 20000000000000000 : ℚ)) + (U := (-(4660899276902082966911 / 10000000000000000000000 : ℚ))) + (U' := (2270572526097917033089 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (6274339476138381 / 10000000000000000 : ℚ)) + (q := (25098034245633637 / 40000000000000000 : ℚ)) + (U := (-(4660899276902082966911 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_3 : Uω (aρ 3) (bρ 3) (814456816291 / 1280000000000 : ℝ) ≤ @@ -958,25 +838,21 @@ lemma U_558_3 : have hlg : Real.log (24906749912178749 / 40000000000000000 : ℝ) ≤ (-(4737406063087016598307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24906749912178749 / 40000000000000000 : ℝ) = - (24906749912178749 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24906749912178749 / 20000000000000000 : ℚ)) - (U := (2194065739912983401693 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24906749912178749 / 20000000000000000 : ℝ) ≤ - (2194065739912983401693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6226093415760937 / 10000000000000000 : ℝ)) (q := - (24906749912178749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24906749912178749 / 40000000000000000 : ℚ)) + (r' := (24906749912178749 / 20000000000000000 : ℚ)) + (U := (-(4737406063087016598307 / 10000000000000000000000 : ℚ))) + (U' := (2194065739912983401693 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (6226093415760937 / 10000000000000000 : ℚ)) + (q := (24906749912178749 / 40000000000000000 : ℚ)) + (U := (-(4737406063087016598307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_4 : Uω (aρ 4) (bρ 4) (814456816291 / 1280000000000 : ℝ) ≤ @@ -984,25 +860,21 @@ lemma U_558_4 : have hlg : Real.log (4917820756817343 / 8000000000000000 : ℝ) ≤ (-(4865760446468570302513 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4917820756817343 / 8000000000000000 : ℝ) = - (4917820756817343 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4917820756817343 / 4000000000000000 : ℚ)) - (U := (2065711356531429697487 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4917820756817343 / 4000000000000000 : ℝ) ≤ - (2065711356531429697487 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (76819556659749 / 125000000000000 : ℝ)) (q := - (4917820756817343 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4917820756817343 / 8000000000000000 : ℚ)) + (r' := (4917820756817343 / 4000000000000000 : ℚ)) + (U := (-(4865760446468570302513 / 10000000000000000000000 : ℚ))) + (U' := (2065711356531429697487 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (76819556659749 / 125000000000000 : ℚ)) + (q := (4917820756817343 / 8000000000000000 : ℚ)) + (U := (-(4865760446468570302513 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_5 : Uω (aρ 5) (bρ 5) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1010,25 +882,21 @@ lemma U_558_5 : have hlg : Real.log (24105515172156347 / 40000000000000000 : ℝ) ≤ (-(2532193971103932224791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24105515172156347 / 40000000000000000 : ℝ) = - (24105515172156347 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24105515172156347 / 20000000000000000 : ℚ)) - (U := (933541930396067775209 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24105515172156347 / 20000000000000000 : ℝ) ≤ - (933541930396067775209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (752745018268717 / 1250000000000000 : ℝ)) (q := - (24105515172156347 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24105515172156347 / 40000000000000000 : ℚ)) + (r' := (24105515172156347 / 20000000000000000 : ℚ)) + (U := (-(2532193971103932224791 / 5000000000000000000000 : ℚ))) + (U' := (933541930396067775209 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (752745018268717 / 1250000000000000 : ℚ)) + (q := (24105515172156347 / 40000000000000000 : ℚ)) + (U := (-(2532193971103932224791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_6 : Uω (aρ 6) (bρ 6) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1036,25 +904,21 @@ lemma U_558_6 : have hlg : Real.log (23412293964210231 / 40000000000000000 : ℝ) ≤ (-(1339045465924501048353 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23412293964210231 / 40000000000000000 : ℝ) = - (23412293964210231 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23412293964210231 / 20000000000000000 : ℚ)) - (U := (393822484825498951647 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23412293964210231 / 20000000000000000 : ℝ) ≤ - (393822484825498951647 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2921294958658339 / 5000000000000000 : ℝ)) (q := - (23412293964210231 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23412293964210231 / 40000000000000000 : ℚ)) + (r' := (23412293964210231 / 20000000000000000 : ℚ)) + (U := (-(1339045465924501048353 / 2500000000000000000000 : ℚ))) + (U' := (393822484825498951647 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (2921294958658339 / 5000000000000000 : ℚ)) + (q := (23412293964210231 / 40000000000000000 : ℚ)) + (U := (-(1339045465924501048353 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_7 : Uω (aρ 7) (bρ 7) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1062,25 +926,21 @@ lemma U_558_7 : have hlg : Real.log (22467234723155521 / 40000000000000000 : ℝ) ≤ (-(2884107202550171195271 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22467234723155521 / 40000000000000000 : ℝ) = - (22467234723155521 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22467234723155521 / 20000000000000000 : ℚ)) - (U := (581628698949828804729 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22467234723155521 / 20000000000000000 : ℝ) ≤ - (581628698949828804729 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5593721677549323 / 10000000000000000 : ℝ)) (q := - (22467234723155521 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22467234723155521 / 40000000000000000 : ℚ)) + (r' := (22467234723155521 / 20000000000000000 : ℚ)) + (U := (-(2884107202550171195271 / 5000000000000000000000 : ℚ))) + (U' := (581628698949828804729 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (5593721677549323 / 10000000000000000 : ℚ)) + (q := (22467234723155521 / 40000000000000000 : ℚ)) + (U := (-(2884107202550171195271 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_8 : Uω (aρ 8) (bρ 8) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1088,25 +948,21 @@ lemma U_558_8 : have hlg : Real.log (21235364193371443 / 40000000000000000 : ℝ) ≤ (-(633211539617910829051 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21235364193371443 / 40000000000000000 : ℝ) = - (21235364193371443 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21235364193371443 / 20000000000000000 : ℚ)) - (U := (59935640682089170949 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21235364193371443 / 20000000000000000 : ℝ) ≤ - (59935640682089170949 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1315332015999321 / 2500000000000000 : ℝ)) (q := - (21235364193371443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21235364193371443 / 40000000000000000 : ℚ)) + (r' := (21235364193371443 / 20000000000000000 : ℚ)) + (U := (-(633211539617910829051 / 1000000000000000000000 : ℚ))) + (U' := (59935640682089170949 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (1315332015999321 / 2500000000000000 : ℚ)) + (q := (21235364193371443 / 40000000000000000 : ℚ)) + (U := (-(633211539617910829051 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_9 : Uω (aρ 9) (bρ 9) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1114,25 +970,21 @@ lemma U_558_9 : have hlg : Real.log (19693625650212941 / 40000000000000000 : ℝ) ≤ (-(3542922206328462858359 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19693625650212941 / 40000000000000000 : ℝ) = - (19693625650212941 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19693625650212941 / 10000000000000000 : ℚ)) - (U := (3388549596671537141641 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19693625650212941 / 10000000000000000 : ℝ) ≤ - (3388549596671537141641 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4831424420778033 / 10000000000000000 : ℝ)) (q := - (19693625650212941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19693625650212941 / 40000000000000000 : ℚ)) + (r' := (19693625650212941 / 10000000000000000 : ℚ)) + (U := (-(3542922206328462858359 / 5000000000000000000000 : ℚ))) + (U' := (3388549596671537141641 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (4831424420778033 / 10000000000000000 : ℚ)) + (q := (19693625650212941 / 40000000000000000 : ℚ)) + (U := (-(3542922206328462858359 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_10 : Uω (aρ 10) (bρ 10) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1140,26 +992,21 @@ lemma U_558_10 : have hlg : Real.log (17832256479524721 / 40000000000000000 : ℝ) ≤ (-(1009838093136397352783 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17832256479524721 / 40000000000000000 : ℝ) = - (17832256479524721 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17832256479524721 / 10000000000000000 : ℚ)) - (U := (723029857613602647217 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17832256479524721 / 10000000000000000 : ℝ) ≤ - (723029857613602647217 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4289298868928923 / 10000000000000000 : ℝ)) (q := - (17832256479524721 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17832256479524721 / 40000000000000000 : ℚ)) + (r' := (17832256479524721 / 10000000000000000 : ℚ)) + (U := (-(1009838093136397352783 / 1250000000000000000000 : ℚ))) + (U' := (723029857613602647217 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (4289298868928923 / 10000000000000000 : ℚ)) + (q := (17832256479524721 / 40000000000000000 : ℚ)) + (U := (-(1009838093136397352783 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_11 : Uω (aρ 11) (bρ 11) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1167,26 +1014,21 @@ lemma U_558_11 : have hlg : Real.log (15647963836678691 / 40000000000000000 : ℝ) ≤ (-(9385386513549517948139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15647963836678691 / 40000000000000000 : ℝ) = - (15647963836678691 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15647963836678691 / 10000000000000000 : ℚ)) - (U := (4477557092450482051861 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15647963836678691 / 10000000000000000 : ℝ) ≤ - (4477557092450482051861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (903907293427727 / 2500000000000000 : ℝ)) (q := - (15647963836678691 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15647963836678691 / 40000000000000000 : ℚ)) + (r' := (15647963836678691 / 10000000000000000 : ℚ)) + (U := (-(9385386513549517948139 / 10000000000000000000000 : ℚ))) + (U' := (4477557092450482051861 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (903907293427727 / 2500000000000000 : ℚ)) + (q := (15647963836678691 / 40000000000000000 : ℚ)) + (U := (-(9385386513549517948139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_12 : Uω (aρ 12) (bρ 12) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1194,24 +1036,21 @@ lemma U_558_12 : have hlg : Real.log (104897764484849 / 320000000000000 : ℝ) ≤ (-(11153347910153076889553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (104897764484849 / 320000000000000 : ℝ) = (104897764484849 / 80000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (104897764484849 / 80000000000000 : ℚ)) - (U := (2709595695846923110447 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (104897764484849 / 80000000000000 : ℝ) ≤ - (2709595695846923110447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (22171661058877 / 80000000000000 : ℝ)) (q := - (104897764484849 / 320000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (104897764484849 / 320000000000000 : ℚ)) + (r' := (104897764484849 / 80000000000000 : ℚ)) + (U := (-(11153347910153076889553 / 10000000000000000000000 : ℚ))) + (U' := (2709595695846923110447 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (22171661058877 / 80000000000000 : ℚ)) + (q := (104897764484849 / 320000000000000 : ℚ)) + (U := (-(11153347910153076889553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_13 : Uω (aρ 13) (bρ 13) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1219,26 +1058,21 @@ lemma U_558_13 : have hlg : Real.log (9994596818018049 / 40000000000000000 : ℝ) ≤ (-(13868348245627295984087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9994596818018049 / 40000000000000000 : ℝ) = - (9994596818018049 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9994596818018049 / 5000000000000000 : ℚ)) - (U := (6926067163372704015913 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9994596818018049 / 5000000000000000 : ℝ) ≤ - (6926067163372704015913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1612027502660587 / 10000000000000000 : ℝ)) (q := - (9994596818018049 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9994596818018049 / 40000000000000000 : ℚ)) + (r' := (9994596818018049 / 5000000000000000 : ℚ)) + (U := (-(13868348245627295984087 / 10000000000000000000000 : ℚ))) + (U' := (6926067163372704015913 / 10000000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (814456816291 / 1280000000000 : ℚ)) + (s := (1612027502660587 / 10000000000000000 : ℚ)) + (q := (9994596818018049 / 40000000000000000 : ℚ)) + (U := (-(13868348245627295984087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_558_14 : Uω (aρ 14) (bρ 14) (814456816291 / 1280000000000 : ℝ) ≤ @@ -1346,25 +1180,21 @@ lemma U_559_1 : have hlg : Real.log (50473359035504343 / 80000000000000000 : ℝ) ≤ (-(2302904905921185912749 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50473359035504343 / 80000000000000000 : ℝ) = - (50473359035504343 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50473359035504343 / 40000000000000000 : ℚ)) - (U := (1162830995578814087251 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50473359035504343 / 40000000000000000 : ℝ) ≤ - (1162830995578814087251 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3154572127583121 / 5000000000000000 : ℝ)) (q := - (50473359035504343 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50473359035504343 / 80000000000000000 : ℚ)) + (r' := (50473359035504343 / 40000000000000000 : ℚ)) + (U := (-(2302904905921185912749 / 5000000000000000000000 : ℚ))) + (U' := (1162830995578814087251 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (3154572127583121 / 5000000000000000 : ℚ)) + (q := (50473359035504343 / 80000000000000000 : ℚ)) + (U := (-(2302904905921185912749 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_2 : Uω (aρ 2) (bρ 2) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1372,25 +1202,21 @@ lemma U_559_2 : have hlg : Real.log (50282061560814059 / 80000000000000000 : ℝ) ≤ (-(580472812406440178227 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50282061560814059 / 80000000000000000 : ℝ) = - (50282061560814059 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50282061560814059 / 40000000000000000 : ℚ)) - (U := (285961162968559821773 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50282061560814059 / 40000000000000000 : ℝ) ≤ - (285961162968559821773 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6285088899003671 / 10000000000000000 : ℝ)) (q := - (50282061560814059 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50282061560814059 / 80000000000000000 : ℚ)) + (r' := (50282061560814059 / 40000000000000000 : ℚ)) + (U := (-(580472812406440178227 / 1250000000000000000000 : ℚ))) + (U' := (285961162968559821773 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (6285088899003671 / 10000000000000000 : ℚ)) + (q := (50282061560814059 / 80000000000000000 : ℚ)) + (U := (-(580472812406440178227 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_3 : Uω (aρ 3) (bρ 3) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1398,25 +1224,21 @@ lemma U_559_3 : have hlg : Real.log (9979899754237819 / 16000000000000000 : ℝ) ≤ (-(472015676372460509977 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9979899754237819 / 16000000000000000 : ℝ) = - (9979899754237819 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9979899754237819 / 8000000000000000 : ℚ)) - (U := (221131503927539490023 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9979899754237819 / 8000000000000000 : ℝ) ≤ - (221131503927539490023 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (623684430794743 / 1000000000000000 : ℝ)) (q := - (9979899754237819 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9979899754237819 / 16000000000000000 : ℚ)) + (r' := (9979899754237819 / 8000000000000000 : ℚ)) + (U := (-(472015676372460509977 / 1000000000000000000000 : ℚ))) + (U' := (221131503927539490023 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (623684430794743 / 1000000000000000 : ℚ)) + (q := (9979899754237819 / 16000000000000000 : ℚ)) + (U := (-(472015676372460509977 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_4 : Uω (aρ 4) (bρ 4) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1424,25 +1246,21 @@ lemma U_559_4 : have hlg : Real.log (9852844445835671 / 16000000000000000 : ℝ) ≤ (-(151508916330217477677 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9852844445835671 / 16000000000000000 : ℝ) = - (9852844445835671 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9852844445835671 / 8000000000000000 : ℚ)) - (U := (65099577513532522323 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9852844445835671 / 8000000000000000 : ℝ) ≤ - (65099577513532522323 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1231263870701949 / 2000000000000000 : ℝ)) (q := - (9852844445835671 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9852844445835671 / 16000000000000000 : ℚ)) + (r' := (9852844445835671 / 8000000000000000 : ℚ)) + (U := (-(151508916330217477677 / 312500000000000000000 : ℚ))) + (U' := (65099577513532522323 / 312500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (1231263870701949 / 2000000000000000 : ℚ)) + (q := (9852844445835671 / 16000000000000000 : ℚ)) + (U := (-(151508916330217477677 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_5 : Uω (aρ 5) (bρ 5) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1450,25 +1268,21 @@ lemma U_559_5 : have hlg : Real.log (48297084084177007 / 80000000000000000 : ℝ) ≤ (-(5046554465058193984063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48297084084177007 / 80000000000000000 : ℝ) = - (48297084084177007 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48297084084177007 / 40000000000000000 : ℚ)) - (U := (1884917337941806015937 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48297084084177007 / 40000000000000000 : ℝ) ≤ - (1884917337941806015937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (754090592074301 / 1250000000000000 : ℝ)) (q := - (48297084084177007 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48297084084177007 / 80000000000000000 : ℚ)) + (r' := (48297084084177007 / 40000000000000000 : ℚ)) + (U := (-(5046554465058193984063 / 10000000000000000000000 : ℚ))) + (U' := (1884917337941806015937 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (754090592074301 / 1250000000000000 : ℚ)) + (q := (48297084084177007 / 80000000000000000 : ℚ)) + (U := (-(5046554465058193984063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_6 : Uω (aρ 6) (bρ 6) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1476,25 +1290,21 @@ lemma U_559_6 : have hlg : Real.log (46910732697114243 / 80000000000000000 : ℝ) ≤ (-(533780142986120744697 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46910732697114243 / 80000000000000000 : ℝ) = - (46910732697114243 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46910732697114243 / 40000000000000000 : ℚ)) - (U := (159367037313879255303 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46910732697114243 / 40000000000000000 : ℝ) ≤ - (159367037313879255303 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5853377264968717 / 10000000000000000 : ℝ)) (q := - (46910732697114243 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46910732697114243 / 80000000000000000 : ℚ)) + (r' := (46910732697114243 / 40000000000000000 : ℚ)) + (U := (-(533780142986120744697 / 1000000000000000000000 : ℚ))) + (U' := (159367037313879255303 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (5853377264968717 / 10000000000000000 : ℚ)) + (q := (46910732697114243 / 80000000000000000 : ℚ)) + (U := (-(533780142986120744697 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_7 : Uω (aρ 7) (bρ 7) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1502,25 +1312,21 @@ lemma U_559_7 : have hlg : Real.log (45020814429197179 / 80000000000000000 : ℝ) ≤ (-(5749017087125469562931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45020814429197179 / 80000000000000000 : ℝ) = - (45020814429197179 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45020814429197179 / 40000000000000000 : ℚ)) - (U := (1182454715874530437069 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45020814429197179 / 40000000000000000 : ℝ) ≤ - (1182454715874530437069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5604559078749451 / 10000000000000000 : ℝ)) (q := - (45020814429197179 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45020814429197179 / 80000000000000000 : ℚ)) + (r' := (45020814429197179 / 40000000000000000 : ℚ)) + (U := (-(5749017087125469562931 / 10000000000000000000000 : ℚ))) + (U' := (1182454715874530437069 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (5604559078749451 / 10000000000000000 : ℚ)) + (q := (45020814429197179 / 80000000000000000 : ℚ)) + (U := (-(5749017087125469562931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_8 : Uω (aρ 8) (bρ 8) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1528,25 +1334,21 @@ lemma U_559_8 : have hlg : Real.log (8511498818824967 / 16000000000000000 : ℝ) ≤ (-(631170670481372951783 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8511498818824967 / 16000000000000000 : ℝ) = - (8511498818824967 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8511498818824967 / 8000000000000000 : ℚ)) - (U := (61976509818627048217 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8511498818824967 / 8000000000000000 : ℝ) ≤ - (61976509818627048217 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1054454129264273 / 2000000000000000 : ℝ)) (q := - (8511498818824967 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8511498818824967 / 16000000000000000 : ℚ)) + (r' := (8511498818824967 / 8000000000000000 : ℚ)) + (U := (-(631170670481372951783 / 1000000000000000000000 : ℚ))) + (U' := (61976509818627048217 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (1054454129264273 / 2000000000000000 : ℚ)) + (q := (8511498818824967 / 16000000000000000 : ℚ)) + (U := (-(631170670481372951783 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_9 : Uω (aρ 9) (bρ 9) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1554,25 +1356,21 @@ lemma U_559_9 : have hlg : Real.log (39474875469341551 / 80000000000000000 : ℝ) ≤ (-(353181114344393088867 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39474875469341551 / 80000000000000000 : ℝ) = - (39474875469341551 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39474875469341551 / 20000000000000000 : ℚ)) - (U := (339966065955606911133 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39474875469341551 / 20000000000000000 : ℝ) ≤ - (339966065955606911133 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (605322702310693 / 1250000000000000 : ℝ)) (q := - (39474875469341551 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39474875469341551 / 80000000000000000 : ℚ)) + (r' := (39474875469341551 / 20000000000000000 : ℚ)) + (U := (-(353181114344393088867 / 500000000000000000000 : ℚ))) + (U' := (339966065955606911133 / 500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (605322702310693 / 1250000000000000 : ℚ)) + (q := (39474875469341551 / 80000000000000000 : ℚ)) + (U := (-(353181114344393088867 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_10 : Uω (aρ 10) (bρ 10) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1580,26 +1378,21 @@ lemma U_559_10 : have hlg : Real.log (35753878288956451 / 80000000000000000 : ℝ) ≤ (-(402683943645360927051 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35753878288956451 / 80000000000000000 : ℝ) = - (35753878288956451 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35753878288956451 / 20000000000000000 : ℚ)) - (U := (290463236654639072949 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35753878288956451 / 20000000000000000 : ℝ) ≤ - (290463236654639072949 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4300891356884269 / 10000000000000000 : ℝ)) (q := - (35753878288956451 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35753878288956451 / 80000000000000000 : ℚ)) + (r' := (35753878288956451 / 20000000000000000 : ℚ)) + (U := (-(402683943645360927051 / 500000000000000000000 : ℚ))) + (U' := (290463236654639072949 / 500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (4300891356884269 / 10000000000000000 : ℚ)) + (q := (35753878288956451 / 80000000000000000 : ℚ)) + (U := (-(402683943645360927051 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_11 : Uω (aρ 11) (bρ 11) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1607,26 +1400,21 @@ lemma U_559_11 : have hlg : Real.log (31388944228734327 / 80000000000000000 : ℝ) ≤ (-(146182952791553937827 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31388944228734327 / 80000000000000000 : ℝ) = - (31388944228734327 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31388944228734327 / 20000000000000000 : ℚ)) - (U := (70425541052196062173 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31388944228734327 / 20000000000000000 : ℝ) ≤ - (70425541052196062173 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1814067234016869 / 5000000000000000 : ℝ)) (q := - (31388944228734327 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31388944228734327 / 80000000000000000 : ℚ)) + (r' := (31388944228734327 / 20000000000000000 : ℚ)) + (U := (-(146182952791553937827 / 156250000000000000000 : ℚ))) + (U' := (70425541052196062173 / 156250000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (1814067234016869 / 5000000000000000 : ℚ)) + (q := (31388944228734327 / 80000000000000000 : ℚ)) + (U := (-(146182952791553937827 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_12 : Uω (aρ 12) (bρ 12) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1634,26 +1422,21 @@ lemma U_559_12 : have hlg : Real.log (26326078487755239 / 80000000000000000 : ℝ) ≤ (-(11114666087772948681293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26326078487755239 / 80000000000000000 : ℝ) = - (26326078487755239 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26326078487755239 / 20000000000000000 : ℚ)) - (U := (2748277518227051318707 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26326078487755239 / 20000000000000000 : ℝ) ≤ - (2748277518227051318707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1393059064736983 / 5000000000000000 : ℝ)) (q := - (26326078487755239 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26326078487755239 / 80000000000000000 : ℚ)) + (r' := (26326078487755239 / 20000000000000000 : ℚ)) + (U := (-(11114666087772948681293 / 10000000000000000000000 : ℚ))) + (U' := (2748277518227051318707 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (1393059064736983 / 5000000000000000 : ℚ)) + (q := (26326078487755239 / 80000000000000000 : ℚ)) + (U := (-(11114666087772948681293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_13 : Uω (aρ 13) (bρ 13) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1661,26 +1444,21 @@ lemma U_559_13 : have hlg : Real.log (20121997581452683 / 80000000000000000 : ℝ) ≤ (-(13802130104783206082597 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20121997581452683 / 80000000000000000 : ℝ) = - (20121997581452683 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20121997581452683 / 20000000000000000 : ℚ)) - (U := (60813501216793917403 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20121997581452683 / 20000000000000000 : ℝ) ≤ - (60813501216793917403 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1634479644493327 / 10000000000000000 : ℝ)) (q := - (20121997581452683 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20121997581452683 / 80000000000000000 : ℚ)) + (r' := (20121997581452683 / 20000000000000000 : ℚ)) + (U := (-(13802130104783206082597 / 10000000000000000000000 : ℚ))) + (U' := (60813501216793917403 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40791633419487 / 64000000000000 : ℚ)) + (s := (1634479644493327 / 10000000000000000 : ℚ)) + (q := (20121997581452683 / 80000000000000000 : ℚ)) + (U := (-(13802130104783206082597 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_559_14 : Uω (aρ 14) (bρ 14) (40791633419487 / 64000000000000 : ℝ) ≤ @@ -1785,25 +1563,21 @@ lemma U_560_1 : have hlg : Real.log (631991876754109 / 1000000000000000 : ℝ) ≤ (-(2294393689475535923337 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (631991876754109 / 1000000000000000 : ℝ) = - (631991876754109 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (631991876754109 / 500000000000000 : ℚ)) - (U := (1171342212024464076663 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (631991876754109 / 500000000000000 : ℝ) ≤ - (1171342212024464076663 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (631989318685093 / 1000000000000000 : ℝ)) (q := - (631991876754109 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (631991876754109 / 1000000000000000 : ℚ)) + (r' := (631991876754109 / 500000000000000 : ℚ)) + (U := (-(2294393689475535923337 / 5000000000000000000000 : ℚ))) + (U' := (1171342212024464076663 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (631989318685093 / 1000000000000000 : ℚ)) + (q := (631991876754109 / 1000000000000000 : ℚ)) + (U := (-(2294393689475535923337 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_2 : Uω (aρ 2) (bρ 2) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1811,25 +1585,21 @@ lemma U_560_2 : have hlg : Real.log (1574001706951919 / 2500000000000000 : ℝ) ≤ (-(4626694971520392917771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1574001706951919 / 2500000000000000 : ℝ) = - (1574001706951919 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1574001706951919 / 1250000000000000 : ℚ)) - (U := (2304776831479607082229 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1574001706951919 / 1250000000000000 : ℝ) ≤ - (2304776831479607082229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3147919159947051 / 5000000000000000 : ℝ)) (q := - (1574001706951919 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1574001706951919 / 2500000000000000 : ℚ)) + (r' := (1574001706951919 / 1250000000000000 : ℚ)) + (U := (-(4626694971520392917771 / 10000000000000000000000 : ℚ))) + (U' := (2304776831479607082229 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (3147919159947051 / 5000000000000000 : ℚ)) + (q := (1574001706951919 / 2500000000000000 : ℚ)) + (U := (-(4626694971520392917771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_3 : Uω (aρ 3) (bρ 3) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1837,25 +1607,21 @@ lemma U_560_3 : have hlg : Real.log (12496374422458581 / 20000000000000000 : ℝ) ≤ (-(940587434521278228623 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12496374422458581 / 20000000000000000 : ℝ) = - (12496374422458581 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12496374422458581 / 10000000000000000 : ℚ)) - (U := (445706926078721771377 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12496374422458581 / 10000000000000000 : ℝ) ≤ - (445706926078721771377 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6247595193087331 / 10000000000000000 : ℝ)) (q := - (12496374422458581 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12496374422458581 / 20000000000000000 : ℚ)) + (r' := (12496374422458581 / 10000000000000000 : ℚ)) + (U := (-(940587434521278228623 / 2000000000000000000000 : ℚ))) + (U' := (445706926078721771377 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (6247595193087331 / 10000000000000000 : ℚ)) + (q := (12496374422458581 / 20000000000000000 : ℚ)) + (U := (-(940587434521278228623 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_4 : Uω (aρ 4) (bρ 4) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1863,25 +1629,21 @@ lemma U_560_4 : have hlg : Real.log (3084389800426919 / 5000000000000000 : ℝ) ≤ (-(1207710175071547666761 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3084389800426919 / 5000000000000000 : ℝ) = - (3084389800426919 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3084389800426919 / 2500000000000000 : ℚ)) - (U := (525157775678452333239 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3084389800426919 / 2500000000000000 : ℝ) ≤ - (525157775678452333239 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3083537076700713 / 5000000000000000 : ℝ)) (q := - (3084389800426919 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3084389800426919 / 5000000000000000 : ℚ)) + (r' := (3084389800426919 / 2500000000000000 : ℚ)) + (U := (-(1207710175071547666761 / 2500000000000000000000 : ℚ))) + (U' := (525157775678452333239 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (3083537076700713 / 5000000000000000 : ℚ)) + (q := (3084389800426919 / 5000000000000000 : ℚ)) + (U := (-(1207710175071547666761 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_5 : Uω (aρ 5) (bρ 5) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1889,25 +1651,21 @@ lemma U_560_5 : have hlg : Real.log (1511973049994807 / 2500000000000000 : ℝ) ≤ (-(251437639046613927597 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1511973049994807 / 2500000000000000 : ℝ) = - (1511973049994807 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1511973049994807 / 1250000000000000 : ℚ)) - (U := (95135951103386072403 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1511973049994807 / 1250000000000000 : ℝ) ≤ - (95135951103386072403 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3021744635493603 / 5000000000000000 : ℝ)) (q := - (1511973049994807 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1511973049994807 / 2500000000000000 : ℚ)) + (r' := (1511973049994807 / 1250000000000000 : ℚ)) + (U := (-(251437639046613927597 / 500000000000000000000 : ℚ))) + (U' := (95135951103386072403 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (3021744635493603 / 5000000000000000 : ℚ)) + (q := (1511973049994807 / 2500000000000000 : ℚ)) + (U := (-(251437639046613927597 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_6 : Uω (aρ 6) (bρ 6) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1915,25 +1673,21 @@ lemma U_560_6 : have hlg : Real.log (2349843845009789 / 4000000000000000 : ℝ) ≤ (-(5319454838437104841271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2349843845009789 / 4000000000000000 : ℝ) = - (2349843845009789 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2349843845009789 / 2000000000000000 : ℚ)) - (U := (1612016964562895158729 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2349843845009789 / 2000000000000000 : ℝ) ≤ - (1612016964562895158729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1172832894243539 / 2000000000000000 : ℝ)) (q := - (2349843845009789 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2349843845009789 / 4000000000000000 : ℚ)) + (r' := (2349843845009789 / 2000000000000000 : ℚ)) + (U := (-(5319454838437104841271 / 10000000000000000000000 : ℚ))) + (U' := (1612016964562895158729 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (1172832894243539 / 2000000000000000 : ℚ)) + (q := (2349843845009789 / 4000000000000000 : ℚ)) + (U := (-(5319454838437104841271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_7 : Uω (aρ 7) (bρ 7) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1941,25 +1695,21 @@ lemma U_560_7 : have hlg : Real.log (704799344537407 / 1250000000000000 : ℝ) ≤ (-(2864928427064339415983 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (704799344537407 / 1250000000000000 : ℝ) = - (704799344537407 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (704799344537407 / 625000000000000 : ℚ)) - (U := (600807474435660584017 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (704799344537407 / 625000000000000 : ℝ) ≤ - (600807474435660584017 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2807698069763631 / 5000000000000000 : ℝ)) (q := - (704799344537407 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (704799344537407 / 1250000000000000 : ℚ)) + (r' := (704799344537407 / 625000000000000 : ℚ)) + (U := (-(2864928427064339415983 / 5000000000000000000000 : ℚ))) + (U' := (600807474435660584017 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (2807698069763631 / 5000000000000000 : ℚ)) + (q := (704799344537407 / 1250000000000000 : ℚ)) + (U := (-(2864928427064339415983 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_8 : Uω (aρ 8) (bρ 8) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1967,25 +1717,21 @@ lemma U_560_8 : have hlg : Real.log (2665266038735567 / 5000000000000000 : ℝ) ≤ (-(6291340326210612036741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2665266038735567 / 5000000000000000 : ℝ) = - (2665266038735567 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2665266038735567 / 2500000000000000 : ℚ)) - (U := (640131476789387963259 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2665266038735567 / 2500000000000000 : ℝ) ≤ - (640131476789387963259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2641606216605509 / 5000000000000000 : ℝ)) (q := - (2665266038735567 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2665266038735567 / 5000000000000000 : ℚ)) + (r' := (2665266038735567 / 2500000000000000 : ℚ)) + (U := (-(6291340326210612036741 / 10000000000000000000000 : ℚ))) + (U' := (640131476789387963259 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (2641606216605509 / 5000000000000000 : ℚ)) + (q := (2665266038735567 / 5000000000000000 : ℚ)) + (U := (-(6291340326210612036741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_9 : Uω (aρ 9) (bρ 9) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -1993,25 +1739,21 @@ lemma U_560_9 : have hlg : Real.log (618163941660743 / 1250000000000000 : ℝ) ≤ (-(7041451297304985064883 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (618163941660743 / 1250000000000000 : ℝ) = - (618163941660743 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (618163941660743 / 312500000000000 : ℚ)) - (U := (6821492308695014935117 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (618163941660743 / 312500000000000 : ℝ) ≤ - (6821492308695014935117 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2426868486600319 / 5000000000000000 : ℝ)) (q := - (618163941660743 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (618163941660743 / 1250000000000000 : ℚ)) + (r' := (618163941660743 / 312500000000000 : ℚ)) + (U := (-(7041451297304985064883 / 10000000000000000000000 : ℚ))) + (U' := (6821492308695014935117 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (2426868486600319 / 5000000000000000 : ℚ)) + (q := (618163941660743 / 1250000000000000 : ℚ)) + (U := (-(7041451297304985064883 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_10 : Uω (aρ 10) (bρ 10) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -2019,26 +1761,21 @@ lemma U_560_10 : have hlg : Real.log (8960806534119087 / 20000000000000000 : ℝ) ≤ (-(4014360175648586768127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8960806534119087 / 20000000000000000 : ℝ) = - (8960806534119087 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8960806534119087 / 5000000000000000 : ℚ)) - (U := (2917111627351413231873 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8960806534119087 / 5000000000000000 : ℝ) ≤ - (2917111627351413231873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4312479474242837 / 10000000000000000 : ℝ)) (q := - (8960806534119087 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8960806534119087 / 20000000000000000 : ℚ)) + (r' := (8960806534119087 / 5000000000000000 : ℚ)) + (U := (-(4014360175648586768127 / 5000000000000000000000 : ℚ))) + (U' := (2917111627351413231873 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (4312479474242837 / 10000000000000000 : ℚ)) + (q := (8960806534119087 / 20000000000000000 : ℚ)) + (U := (-(4014360175648586768127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_11 : Uω (aρ 11) (bρ 11) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -2046,26 +1783,21 @@ lemma U_560_11 : have hlg : Real.log (7870478976903391 / 20000000000000000 : ℝ) ≤ (-(932613351350855815937 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7870478976903391 / 20000000000000000 : ℝ) = - (7870478976903391 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7870478976903391 / 5000000000000000 : ℚ)) - (U := (453681009249144184063 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7870478976903391 / 5000000000000000 : ℝ) ≤ - (453681009249144184063 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3640628543232141 / 10000000000000000 : ℝ)) (q := - (7870478976903391 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7870478976903391 / 20000000000000000 : ℚ)) + (r' := (7870478976903391 / 5000000000000000 : ℚ)) + (U := (-(932613351350855815937 / 1000000000000000000000 : ℚ))) + (U' := (453681009249144184063 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (3640628543232141 / 10000000000000000 : ℚ)) + (q := (7870478976903391 / 20000000000000000 : ℚ)) + (U := (-(932613351350855815937 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_12 : Uω (aρ 12) (bρ 12) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -2073,26 +1805,21 @@ lemma U_560_12 : have hlg : Real.log (3303446737945291 / 10000000000000000 : ℝ) ≤ (-(2769046757582107150309 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3303446737945291 / 10000000000000000 : ℝ) = - (3303446737945291 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3303446737945291 / 2500000000000000 : ℚ)) - (U := (696689143917892849691 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3303446737945291 / 2500000000000000 : ℝ) ≤ - (696689143917892849691 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (700185784726083 / 2500000000000000 : ℝ)) (q := - (3303446737945291 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3303446737945291 / 10000000000000000 : ℚ)) + (r' := (3303446737945291 / 2500000000000000 : ℚ)) + (U := (-(2769046757582107150309 / 2500000000000000000000 : ℚ))) + (U' := (696689143917892849691 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (700185784726083 / 2500000000000000 : ℚ)) + (q := (3303446737945291 / 10000000000000000 : ℚ)) + (U := (-(2769046757582107150309 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_13 : Uω (aρ 13) (bρ 13) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -2100,26 +1827,21 @@ lemma U_560_13 : have hlg : Real.log (5063465858776757 / 20000000000000000 : ℝ) ≤ (-(13736810718800869438119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5063465858776757 / 20000000000000000 : ℝ) = - (5063465858776757 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5063465858776757 / 5000000000000000 : ℚ)) - (U := (126132887199130561881 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5063465858776757 / 5000000000000000 : ℝ) ≤ - (126132887199130561881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1656697263385507 / 10000000000000000 : ℝ)) (q := - (5063465858776757 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5063465858776757 / 20000000000000000 : ℚ)) + (r' := (5063465858776757 / 5000000000000000 : ℚ)) + (U := (-(13736810718800869438119 / 10000000000000000000000 : ℚ))) + (U' := (126132887199130561881 / 10000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5107553253053 / 8000000000000 : ℚ)) + (s := (1656697263385507 / 10000000000000000 : ℚ)) + (q := (5063465858776757 / 20000000000000000 : ℚ)) + (U := (-(13736810718800869438119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_560_14 : Uω (aρ 14) (bρ 14) (5107553253053 / 8000000000000 : ℝ) ≤ @@ -2226,25 +1948,21 @@ lemma U_561_1 : have hlg : Real.log (25365666173215799 / 40000000000000000 : ℝ) ≤ (-(2277414598492095836739 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25365666173215799 / 40000000000000000 : ℝ) = - (25365666173215799 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25365666173215799 / 20000000000000000 : ℚ)) - (U := (1188321303007904163261 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25365666173215799 / 20000000000000000 : ℝ) ≤ - (1188321303007904163261 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6341391049333837 / 10000000000000000 : ℝ)) (q := - (25365666173215799 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25365666173215799 / 40000000000000000 : ℚ)) + (r' := (25365666173215799 / 20000000000000000 : ℚ)) + (U := (-(2277414598492095836739 / 5000000000000000000000 : ℚ))) + (U' := (1188321303007904163261 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (6341391049333837 / 10000000000000000 : ℚ)) + (q := (25365666173215799 / 40000000000000000 : ℚ)) + (U := (-(2277414598492095836739 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_2 : Uω (aρ 2) (bρ 2) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2252,25 +1970,21 @@ lemma U_561_2 : have hlg : Real.log (25270020361109551 / 40000000000000000 : ℝ) ≤ (-(4592607267118482431659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25270020361109551 / 40000000000000000 : ℝ) = - (25270020361109551 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25270020361109551 / 20000000000000000 : ℚ)) - (U := (2338864535881517568341 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25270020361109551 / 20000000000000000 : ℝ) ≤ - (2338864535881517568341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6317337155790713 / 10000000000000000 : ℝ)) (q := - (25270020361109551 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25270020361109551 / 40000000000000000 : ℚ)) + (r' := (25270020361109551 / 20000000000000000 : ℚ)) + (U := (-(4592607267118482431659 / 10000000000000000000000 : ℚ))) + (U' := (2338864535881517568341 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (6317337155790713 / 10000000000000000 : ℚ)) + (q := (25270020361109551 / 40000000000000000 : ℚ)) + (U := (-(4592607267118482431659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_3 : Uω (aρ 3) (bρ 3) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2278,25 +1992,21 @@ lemma U_561_3 : have hlg : Real.log (25078747721572853 / 40000000000000000 : ℝ) ≤ (-(4668586706926270342089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25078747721572853 / 40000000000000000 : ℝ) = - (25078747721572853 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25078747721572853 / 20000000000000000 : ℚ)) - (U := (2262885096073729657911 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25078747721572853 / 20000000000000000 : ℝ) ≤ - (2262885096073729657911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1567274235593091 / 2500000000000000 : ℝ)) (q := - (25078747721572853 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25078747721572853 / 40000000000000000 : ℚ)) + (r' := (25078747721572853 / 20000000000000000 : ℚ)) + (U := (-(4668586706926270342089 / 10000000000000000000000 : ℚ))) + (U' := (2262885096073729657911 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (1567274235593091 / 2500000000000000 : ℚ)) + (q := (25078747721572853 / 40000000000000000 : ℚ)) + (U := (-(4668586706926270342089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_4 : Uω (aρ 4) (bρ 4) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2304,25 +2014,21 @@ lemma U_561_4 : have hlg : Real.log (24761132856907953 / 40000000000000000 : ℝ) ≤ (-(479604253574241296943 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24761132856907953 / 40000000000000000 : ℝ) = - (24761132856907953 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24761132856907953 / 20000000000000000 : ℚ)) - (U := (213542926725758703057 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24761132856907953 / 20000000000000000 : ℝ) ≤ - (213542926725758703057 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3094291845552457 / 5000000000000000 : ℝ)) (q := - (24761132856907953 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24761132856907953 / 40000000000000000 : ℚ)) + (r' := (24761132856907953 / 20000000000000000 : ℚ)) + (U := (-(479604253574241296943 / 1000000000000000000000 : ℚ))) + (U' := (213542926725758703057 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (3094291845552457 / 5000000000000000 : ℚ)) + (q := (24761132856907953 / 40000000000000000 : ℚ)) + (U := (-(479604253574241296943 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_5 : Uω (aρ 5) (bρ 5) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2330,25 +2036,21 @@ lemma U_561_5 : have hlg : Real.log (4855524396330021 / 8000000000000000 : ℝ) ≤ (-(4993244339069595102151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4855524396330021 / 8000000000000000 : ℝ) = - (4855524396330021 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4855524396330021 / 4000000000000000 : ℚ)) - (U := (1938227463930404897849 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4855524396330021 / 4000000000000000 : ℝ) ≤ - (1938227463930404897849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (606501817281099 / 1000000000000000 : ℝ)) (q := - (4855524396330021 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4855524396330021 / 8000000000000000 : ℚ)) + (r' := (4855524396330021 / 4000000000000000 : ℚ)) + (U := (-(4993244339069595102151 / 10000000000000000000000 : ℚ))) + (U' := (1938227463930404897849 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (606501817281099 / 1000000000000000 : ℚ)) + (q := (4855524396330021 / 8000000000000000 : ℚ)) + (U := (-(4993244339069595102151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_6 : Uω (aρ 6) (bρ 6) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2356,25 +2058,21 @@ lemma U_561_6 : have hlg : Real.log (23584581810980857 / 40000000000000000 : ℝ) ≤ (-(5282862684184516705617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23584581810980857 / 40000000000000000 : ℝ) = - (23584581810980857 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23584581810980857 / 20000000000000000 : ℚ)) - (U := (1648609118815483294383 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23584581810980857 / 20000000000000000 : ℝ) ≤ - (1648609118815483294383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2942869231308183 / 5000000000000000 : ℝ)) (q := - (23584581810980857 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23584581810980857 / 40000000000000000 : ℚ)) + (r' := (23584581810980857 / 20000000000000000 : ℚ)) + (U := (-(5282862684184516705617 / 10000000000000000000000 : ℚ))) + (U' := (1648609118815483294383 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (2942869231308183 / 5000000000000000 : ℚ)) + (q := (23584581810980857 / 40000000000000000 : ℚ)) + (U := (-(5282862684184516705617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_7 : Uω (aρ 7) (bρ 7) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2382,25 +2080,21 @@ lemma U_561_7 : have hlg : Real.log (22639920619566651 / 40000000000000000 : ℝ) ≤ (-(1138329413456083984391 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22639920619566651 / 40000000000000000 : ℝ) = - (22639920619566651 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22639920619566651 / 20000000000000000 : ℚ)) - (U := (247964947143916015609 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22639920619566651 / 20000000000000000 : ℝ) ≤ - (247964947143916015609 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5637069247669263 / 10000000000000000 : ℝ)) (q := - (22639920619566651 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22639920619566651 / 40000000000000000 : ℚ)) + (r' := (22639920619566651 / 20000000000000000 : ℚ)) + (U := (-(1138329413456083984391 / 2000000000000000000000 : ℚ))) + (U' := (247964947143916015609 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (5637069247669263 / 10000000000000000 : ℚ)) + (q := (22639920619566651 / 40000000000000000 : ℚ)) + (U := (-(1138329413456083984391 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_8 : Uω (aρ 8) (bρ 8) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2408,25 +2102,21 @@ lemma U_561_8 : have hlg : Real.log (21408886102295611 / 40000000000000000 : ℝ) ≤ (-(6250733795887733386939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21408886102295611 / 40000000000000000 : ℝ) = - (21408886102295611 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21408886102295611 / 20000000000000000 : ℚ)) - (U := (680738007112266613061 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21408886102295611 / 20000000000000000 : ℝ) ≤ - (680738007112266613061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5305093640373743 / 10000000000000000 : ℝ)) (q := - (21408886102295611 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21408886102295611 / 40000000000000000 : ℚ)) + (r' := (21408886102295611 / 20000000000000000 : ℚ)) + (U := (-(6250733795887733386939 / 10000000000000000000000 : ℚ))) + (U' := (680738007112266613061 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (5305093640373743 / 10000000000000000 : ℚ)) + (q := (21408886102295611 / 40000000000000000 : ℚ)) + (U := (-(6250733795887733386939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_9 : Uω (aρ 9) (bρ 9) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2434,25 +2124,21 @@ lemma U_561_9 : have hlg : Real.log (3973770394664829 / 8000000000000000 : ℝ) ≤ (-(3498630877915021785957 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3973770394664829 / 8000000000000000 : ℝ) = - (3973770394664829 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3973770394664829 / 2000000000000000 : ℚ)) - (U := (3432840925084978214043 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3973770394664829 / 2000000000000000 : ℝ) ≤ - (3432840925084978214043 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (487604220424801 / 1000000000000000 : ℝ)) (q := - (3973770394664829 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3973770394664829 / 8000000000000000 : ℚ)) + (r' := (3973770394664829 / 2000000000000000 : ℚ)) + (U := (-(3498630877915021785957 / 5000000000000000000000 : ℚ))) + (U' := (3432840925084978214043 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (487604220424801 / 1000000000000000 : ℚ)) + (q := (3973770394664829 / 8000000000000000 : ℚ)) + (U := (-(3498630877915021785957 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_10 : Uω (aρ 10) (bρ 10) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2460,26 +2146,21 @@ lemma U_561_10 : have hlg : Real.log (18010934972507951 / 40000000000000000 : ℝ) ≤ (-(3989501908388574488219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18010934972507951 / 40000000000000000 : ℝ) = - (18010934972507951 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18010934972507951 / 10000000000000000 : ℚ)) - (U := (2941969894611425511781 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18010934972507951 / 10000000000000000 : ℝ) ≤ - (2941969894611425511781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4335642737334913 / 10000000000000000 : ℝ)) (q := - (18010934972507951 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18010934972507951 / 40000000000000000 : ℚ)) + (r' := (18010934972507951 / 10000000000000000 : ℚ)) + (U := (-(3989501908388574488219 / 5000000000000000000000 : ℚ))) + (U' := (2941969894611425511781 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (4335642737334913 / 10000000000000000 : ℚ)) + (q := (18010934972507951 / 40000000000000000 : ℚ)) + (U := (-(3989501908388574488219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_11 : Uω (aρ 11) (bρ 11) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2487,26 +2168,21 @@ lemma U_561_11 : have hlg : Real.log (15833863235497879 / 40000000000000000 : ℝ) ≤ (-(4633642821382275522129 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15833863235497879 / 40000000000000000 : ℝ) = - (15833863235497879 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15833863235497879 / 10000000000000000 : ℚ)) - (U := (2297828981617724477871 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15833863235497879 / 10000000000000000 : ℝ) ≤ - (2297828981617724477871 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3665583495034877 / 10000000000000000 : ℝ)) (q := - (15833863235497879 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15833863235497879 / 40000000000000000 : ℚ)) + (r' := (15833863235497879 / 10000000000000000 : ℚ)) + (U := (-(4633642821382275522129 / 5000000000000000000000 : ℚ))) + (U' := (2297828981617724477871 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (3665583495034877 / 10000000000000000 : ℚ)) + (q := (15833863235497879 / 40000000000000000 : ℚ)) + (U := (-(4633642821382275522129 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_12 : Uω (aρ 12) (bρ 12) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2514,26 +2190,21 @@ lemma U_561_12 : have hlg : Real.log (2663014768093521 / 8000000000000000 : ℝ) ≤ (-(10999826886831738863463 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2663014768093521 / 8000000000000000 : ℝ) = - (2663014768093521 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2663014768093521 / 2000000000000000 : ℚ)) - (U := (2863116719168261136537 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2663014768093521 / 2000000000000000 : ℝ) ≤ - (2863116719168261136537 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (141494444710237 / 500000000000000 : ℝ)) (q := - (2663014768093521 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2663014768093521 / 8000000000000000 : ℚ)) + (r' := (2663014768093521 / 2000000000000000 : ℚ)) + (U := (-(10999826886831738863463 / 10000000000000000000000 : ℚ))) + (U' := (2863116719168261136537 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (141494444710237 / 500000000000000 : ℚ)) + (q := (2663014768093521 / 8000000000000000 : ℚ)) + (U := (-(10999826886831738863463 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_13 : Uω (aρ 13) (bρ 13) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2541,26 +2212,21 @@ lemma U_561_13 : have hlg : Real.log (10257463780728953 / 40000000000000000 : ℝ) ≤ (-(1701092299087291908943 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10257463780728953 / 40000000000000000 : ℝ) = - (10257463780728953 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10257463780728953 / 10000000000000000 : ℚ)) - (U := (31775651662708091057 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10257463780728953 / 10000000000000000 : ℝ) ≤ - (31775651662708091057 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (850232802965207 / 5000000000000000 : ℝ)) (q := - (10257463780728953 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10257463780728953 / 40000000000000000 : ℚ)) + (r' := (10257463780728953 / 10000000000000000 : ℚ)) + (U := (-(1701092299087291908943 / 1250000000000000000000 : ℚ))) + (U' := (31775651662708091057 / 1250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20499005617149 / 32000000000000 : ℚ)) + (s := (850232802965207 / 5000000000000000 : ℚ)) + (q := (10257463780728953 / 40000000000000000 : ℚ)) + (U := (-(1701092299087291908943 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_561_14 : Uω (aρ 14) (bρ 14) (20499005617149 / 32000000000000 : ℝ) ≤ @@ -2668,25 +2334,21 @@ lemma U_562_1 : have hlg : Real.log (6362914318480821 / 10000000000000000 : ℝ) ≤ (-(565123242699242190631 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6362914318480821 / 10000000000000000 : ℝ) = - (6362914318480821 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6362914318480821 / 5000000000000000 : ℚ)) - (U := (301310732675757809369 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6362914318480821 / 5000000000000000 : ℝ) ≤ - (301310732675757809369 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6362888910644767 / 10000000000000000 : ℝ)) (q := - (6362914318480821 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6362914318480821 / 10000000000000000 : ℚ)) + (r' := (6362914318480821 / 5000000000000000 : ℚ)) + (U := (-(565123242699242190631 / 1250000000000000000000 : ℚ))) + (U' := (301310732675757809369 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (6362888910644767 / 10000000000000000 : ℚ)) + (q := (6362914318480821 / 10000000000000000 : ℚ)) + (U := (-(565123242699242190631 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_2 : Uω (aρ 2) (bρ 2) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2694,25 +2356,21 @@ lemma U_562_2 : have hlg : Real.log (12678006697715053 / 20000000000000000 : ℝ) ≤ (-(227931768568958541353 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12678006697715053 / 20000000000000000 : ℝ) = - (12678006697715053 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12678006697715053 / 10000000000000000 : ℚ)) - (U := (118641821581041458647 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12678006697715053 / 10000000000000000 : ℝ) ≤ - (118641821581041458647 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3169417991954089 / 5000000000000000 : ℝ)) (q := - (12678006697715053 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12678006697715053 / 20000000000000000 : ℚ)) + (r' := (12678006697715053 / 10000000000000000 : ℚ)) + (U := (-(227931768568958541353 / 500000000000000000000 : ℚ))) + (U' := (118641821581041458647 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (3169417991954089 / 5000000000000000 : ℚ)) + (q := (12678006697715053 / 20000000000000000 : ℚ)) + (U := (-(227931768568958541353 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_3 : Uω (aρ 3) (bρ 3) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2720,25 +2378,21 @@ lemma U_562_3 : have hlg : Real.log (12582373271360453 / 20000000000000000 : ℝ) ≤ (-(4634353854935592034951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12582373271360453 / 20000000000000000 : ℝ) = - (12582373271360453 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12582373271360453 / 10000000000000000 : ℚ)) - (U := (2297117948064407965049 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12582373271360453 / 10000000000000000 : ℝ) ≤ - (2297117948064407965049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3145299331951789 / 5000000000000000 : ℝ)) (q := - (12582373271360453 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12582373271360453 / 20000000000000000 : ℚ)) + (r' := (12582373271360453 / 10000000000000000 : ℚ)) + (U := (-(4634353854935592034951 / 10000000000000000000000 : ℚ))) + (U' := (2297117948064407965049 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (3145299331951789 / 5000000000000000 : ℚ)) + (q := (12582373271360453 / 20000000000000000 : ℚ)) + (U := (-(4634353854935592034951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_4 : Uω (aρ 4) (bρ 4) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2746,25 +2400,21 @@ lemma U_562_4 : have hlg : Real.log (12423573573143853 / 20000000000000000 : ℝ) ≤ (-(74396329823126201829 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12423573573143853 / 20000000000000000 : ℝ) = - (12423573573143853 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12423573573143853 / 10000000000000000 : ℚ)) - (U := (33907917098748798171 / 156250000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12423573573143853 / 10000000000000000 : ℝ) ≤ - (33907917098748798171 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3105046573375989 / 5000000000000000 : ℝ)) (q := - (12423573573143853 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12423573573143853 / 20000000000000000 : ℚ)) + (r' := (12423573573143853 / 10000000000000000 : ℚ)) + (U := (-(74396329823126201829 / 156250000000000000000 : ℚ))) + (U' := (33907917098748798171 / 156250000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (3105046573375989 / 5000000000000000 : ℚ)) + (q := (12423573573143853 / 20000000000000000 : ℚ)) + (U := (-(74396329823126201829 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_5 : Uω (aρ 5) (bρ 5) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2772,25 +2422,21 @@ lemma U_562_5 : have hlg : Real.log (12181837361044447 / 20000000000000000 : ℝ) ≤ (-(4957861717286478519223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12181837361044447 / 20000000000000000 : ℝ) = - (12181837361044447 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12181837361044447 / 10000000000000000 : ℚ)) - (U := (1973610085713521480777 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12181837361044447 / 10000000000000000 : ℝ) ≤ - (1973610085713521480777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1521636713496893 / 2500000000000000 : ℝ)) (q := - (12181837361044447 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12181837361044447 / 20000000000000000 : ℚ)) + (r' := (12181837361044447 / 10000000000000000 : ℚ)) + (U := (-(4957861717286478519223 / 10000000000000000000000 : ℚ))) + (U' := (1973610085713521480777 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (1521636713496893 / 2500000000000000 : ℚ)) + (q := (12181837361044447 / 20000000000000000 : ℚ)) + (U := (-(4957861717286478519223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_6 : Uω (aρ 6) (bρ 6) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2798,25 +2444,21 @@ lemma U_562_6 : have hlg : Real.log (11835362029592483 / 20000000000000000 : ℝ) ≤ (-(5246404410543003654287 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11835362029592483 / 20000000000000000 : ℝ) = - (11835362029592483 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11835362029592483 / 10000000000000000 : ℚ)) - (U := (1685067392456996345713 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11835362029592483 / 10000000000000000 : ℝ) ≤ - (1685067392456996345713 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (738413987209451 / 1250000000000000 : ℝ)) (q := - (11835362029592483 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11835362029592483 / 20000000000000000 : ℚ)) + (r' := (11835362029592483 / 10000000000000000 : ℚ)) + (U := (-(5246404410543003654287 / 10000000000000000000000 : ℚ))) + (U' := (1685067392456996345713 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (738413987209451 / 1250000000000000 : ℚ)) + (q := (11835362029592483 / 20000000000000000 : ℚ)) + (U := (-(5246404410543003654287 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_7 : Uω (aρ 7) (bρ 7) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2824,25 +2466,21 @@ lemma U_562_7 : have hlg : Real.log (11363129768687869 / 20000000000000000 : ℝ) ≤ (-(282679195069658106583 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11363129768687869 / 20000000000000000 : ℝ) = - (11363129768687869 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11363129768687869 / 10000000000000000 : ℚ)) - (U := (63894395080341893417 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11363129768687869 / 10000000000000000 : ℝ) ≤ - (63894395080341893417 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2829370508765497 / 5000000000000000 : ℝ)) (q := - (11363129768687869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11363129768687869 / 20000000000000000 : ℚ)) + (r' := (11363129768687869 / 10000000000000000 : ℚ)) + (U := (-(282679195069658106583 / 500000000000000000000 : ℚ))) + (U' := (63894395080341893417 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (2829370508765497 / 5000000000000000 : ℚ)) + (q := (11363129768687869 / 20000000000000000 : ℚ)) + (U := (-(282679195069658106583 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_8 : Uω (aρ 8) (bρ 8) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2850,25 +2488,21 @@ lemma U_562_8 : have hlg : Real.log (10747818824267901 / 20000000000000000 : ℝ) ≤ (-(621029439375479713257 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10747818824267901 / 20000000000000000 : ℝ) = - (10747818824267901 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10747818824267901 / 10000000000000000 : ℚ)) - (U := (72117740924520286743 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10747818824267901 / 10000000000000000 : ℝ) ≤ - (72117740924520286743 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2663485862225513 / 5000000000000000 : ℝ)) (q := - (10747818824267901 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10747818824267901 / 20000000000000000 : ℚ)) + (r' := (10747818824267901 / 10000000000000000 : ℚ)) + (U := (-(621029439375479713257 / 1000000000000000000000 : ℚ))) + (U' := (72117740924520286743 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (2663485862225513 / 5000000000000000 : ℚ)) + (q := (10747818824267901 / 20000000000000000 : ℚ)) + (U := (-(621029439375479713257 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_9 : Uω (aρ 9) (bρ 9) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2876,25 +2510,21 @@ lemma U_562_9 : have hlg : Real.log (9978221685393537 / 20000000000000000 : ℝ) ≤ (-(6953273864243853381139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9978221685393537 / 20000000000000000 : ℝ) = - (9978221685393537 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9978221685393537 / 5000000000000000 : ℚ)) - (U := (6909669741756146618861 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9978221685393537 / 5000000000000000 : ℝ) ≤ - (6909669741756146618861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2449170106968331 / 5000000000000000 : ℝ)) (q := - (9978221685393537 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9978221685393537 / 20000000000000000 : ℚ)) + (r' := (9978221685393537 / 5000000000000000 : ℚ)) + (U := (-(6953273864243853381139 / 10000000000000000000000 : ℚ))) + (U' := (6909669741756146618861 / 10000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (2449170106968331 / 5000000000000000 : ℚ)) + (q := (9978221685393537 / 20000000000000000 : ℚ)) + (U := (-(6953273864243853381139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_10 : Uω (aρ 10) (bρ 10) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2902,26 +2532,21 @@ lemma U_562_10 : have hlg : Real.log (4525055686322299 / 10000000000000000 : ℝ) ≤ (-(7929552090284195248573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4525055686322299 / 10000000000000000 : ℝ) = - (4525055686322299 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4525055686322299 / 2500000000000000 : ℚ)) - (U := (5933391515715804751427 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4525055686322299 / 2500000000000000 : ℝ) ≤ - (5933391515715804751427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4358788934682723 / 10000000000000000 : ℝ)) (q := - (4525055686322299 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4525055686322299 / 10000000000000000 : ℚ)) + (r' := (4525055686322299 / 2500000000000000 : ℚ)) + (U := (-(7929552090284195248573 / 10000000000000000000000 : ℚ))) + (U' := (5933391515715804751427 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (4358788934682723 / 10000000000000000 : ℚ)) + (q := (4525055686322299 / 10000000000000000 : ℚ)) + (U := (-(7929552090284195248573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_11 : Uω (aρ 11) (bρ 11) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2929,26 +2554,21 @@ lemma U_562_11 : have hlg : Real.log (3981670370963811 / 10000000000000000 : ℝ) ≤ (-(92088367002658787047 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3981670370963811 / 10000000000000000 : ℝ) = - (3981670370963811 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3981670370963811 / 2500000000000000 : ℚ)) - (U := (46541069057341212953 / 100000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3981670370963811 / 2500000000000000 : ℝ) ≤ - (46541069057341212953 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3690494930170747 / 10000000000000000 : ℝ)) (q := - (3981670370963811 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3981670370963811 / 10000000000000000 : ℚ)) + (r' := (3981670370963811 / 2500000000000000 : ℚ)) + (U := (-(92088367002658787047 / 100000000000000000000 : ℚ))) + (U' := (46541069057341212953 / 100000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (3690494930170747 / 10000000000000000 : ℚ)) + (q := (3981670370963811 / 10000000000000000 : ℚ)) + (U := (-(92088367002658787047 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_12 : Uω (aρ 12) (bρ 12) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2956,25 +2576,21 @@ lemma U_562_12 : have hlg : Real.log (167701122188047 / 500000000000000 : ℝ) ≤ (-(5462123687277067907423 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (167701122188047 / 500000000000000 : ℝ) = - (167701122188047 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (167701122188047 / 125000000000000 : ℚ)) - (U := (1469348115722932092577 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (167701122188047 / 125000000000000 : ℝ) ≤ - (1469348115722932092577 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (571779834490001 / 2000000000000000 : ℝ)) (q := - (167701122188047 / 500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (167701122188047 / 500000000000000 : ℚ)) + (r' := (167701122188047 / 125000000000000 : ℚ)) + (U := (-(5462123687277067907423 / 5000000000000000000000 : ℚ))) + (U' := (1469348115722932092577 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (571779834490001 / 2000000000000000 : ℚ)) + (q := (167701122188047 / 500000000000000 : ℚ)) + (U := (-(5462123687277067907423 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_13 : Uω (aρ 13) (bρ 13) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -2982,26 +2598,21 @@ lemma U_562_13 : have hlg : Real.log (5193164395830821 / 20000000000000000 : ℝ) ≤ (-(13483890514746875546159 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5193164395830821 / 20000000000000000 : ℝ) = - (5193164395830821 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5193164395830821 / 5000000000000000 : ℚ)) - (U := (379053091253124453841 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5193164395830821 / 5000000000000000 : ℝ) ≤ - (379053091253124453841 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (871700211176973 / 5000000000000000 : ℝ)) (q := - (5193164395830821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5193164395830821 / 20000000000000000 : ℚ)) + (r' := (5193164395830821 / 5000000000000000 : ℚ)) + (U := (-(13483890514746875546159 / 10000000000000000000000 : ℚ))) + (U' := (379053091253124453841 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10283899111043 / 16000000000000 : ℚ)) + (s := (871700211176973 / 5000000000000000 : ℚ)) + (q := (5193164395830821 / 20000000000000000 : ℚ)) + (U := (-(13483890514746875546159 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_562_14 : Uω (aρ 14) (bρ 14) (10283899111043 / 16000000000000 : ℝ) ≤ @@ -3107,25 +2718,21 @@ lemma U_563_1 : have hlg : Real.log (25537648372310497 / 40000000000000000 : ℝ) ≤ (-(1121814209373083173601 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25537648372310497 / 40000000000000000 : ℝ) = - (25537648372310497 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25537648372310497 / 20000000000000000 : ℚ)) - (U := (611053741376916826399 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25537648372310497 / 20000000000000000 : ℝ) ≤ - (611053741376916826399 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6384386770795561 / 10000000000000000 : ℝ)) (q := - (25537648372310497 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25537648372310497 / 40000000000000000 : ℚ)) + (r' := (25537648372310497 / 20000000000000000 : ℚ)) + (U := (-(1121814209373083173601 / 2500000000000000000000 : ℚ))) + (U' := (611053741376916826399 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (6384386770795561 / 10000000000000000 : ℚ)) + (q := (25537648372310497 / 40000000000000000 : ℚ)) + (U := (-(1121814209373083173601 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_2 : Uω (aρ 2) (bρ 2) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3133,25 +2740,21 @@ lemma U_563_2 : have hlg : Real.log (25442006414350139 / 40000000000000000 : ℝ) ≤ (-(565597312504274044621 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25442006414350139 / 40000000000000000 : ℝ) = - (25442006414350139 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25442006414350139 / 20000000000000000 : ℚ)) - (U := (300836662870725955379 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25442006414350139 / 20000000000000000 : ℝ) ≤ - (300836662870725955379 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3180167402162691 / 5000000000000000 : ℝ)) (q := - (25442006414350139 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25442006414350139 / 40000000000000000 : ℚ)) + (r' := (25442006414350139 / 20000000000000000 : ℚ)) + (U := (-(565597312504274044621 / 1250000000000000000000 : ℚ))) + (U' := (300836662870725955379 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (3180167402162691 / 5000000000000000 : ℚ)) + (q := (25442006414350139 / 40000000000000000 : ℚ)) + (U := (-(565597312504274044621 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_3 : Uω (aρ 3) (bρ 3) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3159,25 +2762,21 @@ lemma U_563_3 : have hlg : Real.log (25250745308928571 / 40000000000000000 : ℝ) ≤ (-(184009512553182304903 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25250745308928571 / 40000000000000000 : ℝ) = - (25250745308928571 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25250745308928571 / 20000000000000000 : ℚ)) - (U := (93249359566817695097 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25250745308928571 / 20000000000000000 : ℝ) ≤ - (93249359566817695097 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3156050178982299 / 5000000000000000 : ℝ)) (q := - (25250745308928571 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25250745308928571 / 40000000000000000 : ℚ)) + (r' := (25250745308928571 / 20000000000000000 : ℚ)) + (U := (-(184009512553182304903 / 400000000000000000000 : ℚ))) + (U' := (93249359566817695097 / 400000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (3156050178982299 / 5000000000000000 : ℚ)) + (q := (25250745308928571 / 40000000000000000 : ℚ)) + (U := (-(184009512553182304903 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_4 : Uω (aρ 4) (bρ 4) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3185,25 +2784,21 @@ lemma U_563_4 : have hlg : Real.log (4986632254650801 / 8000000000000000 : ℝ) ≤ (-(1181701895927001116443 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4986632254650801 / 8000000000000000 : ℝ) = - (4986632254650801 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4986632254650801 / 4000000000000000 : ℚ)) - (U := (551166054822998883557 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4986632254650801 / 4000000000000000 : ℝ) ≤ - (551166054822998883557 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1246320504238463 / 2000000000000000 : ℝ)) (q := - (4986632254650801 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4986632254650801 / 8000000000000000 : ℚ)) + (r' := (4986632254650801 / 4000000000000000 : ℚ)) + (U := (-(1181701895927001116443 / 2500000000000000000000 : ℚ))) + (U' := (551166054822998883557 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (1246320504238463 / 2000000000000000 : ℚ)) + (q := (4986632254650801 / 8000000000000000 : ℚ)) + (U := (-(1181701895927001116443 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_5 : Uω (aρ 5) (bρ 5) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3211,25 +2806,21 @@ lemma U_563_5 : have hlg : Real.log (24449727025899473 / 40000000000000000 : ℝ) ≤ (-(4922604025803230328569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24449727025899473 / 40000000000000000 : ℝ) = - (24449727025899473 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24449727025899473 / 20000000000000000 : ℚ)) - (U := (2008867777196769671431 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24449727025899473 / 20000000000000000 : ℝ) ≤ - (2008867777196769671431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6108075316850049 / 10000000000000000 : ℝ)) (q := - (24449727025899473 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24449727025899473 / 40000000000000000 : ℚ)) + (r' := (24449727025899473 / 20000000000000000 : ℚ)) + (U := (-(4922604025803230328569 / 10000000000000000000000 : ℚ))) + (U' := (2008867777196769671431 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (6108075316850049 / 10000000000000000 : ℚ)) + (q := (24449727025899473 / 40000000000000000 : ℚ)) + (U := (-(4922604025803230328569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_6 : Uω (aρ 6) (bρ 6) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3237,25 +2828,21 @@ lemma U_563_6 : have hlg : Real.log (23756865206856329 / 40000000000000000 : ℝ) ≤ (-(2605039519011009743847 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23756865206856329 / 40000000000000000 : ℝ) = - (23756865206856329 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23756865206856329 / 20000000000000000 : ℚ)) - (U := (860696382488990256153 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23756865206856329 / 20000000000000000 : ℝ) ≤ - (860696382488990256153 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5928884782468477 / 10000000000000000 : ℝ)) (q := - (23756865206856329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23756865206856329 / 40000000000000000 : ℚ)) + (r' := (23756865206856329 / 20000000000000000 : ℚ)) + (U := (-(2605039519011009743847 / 5000000000000000000000 : ℚ))) + (U' := (860696382488990256153 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (5928884782468477 / 10000000000000000 : ℚ)) + (q := (23756865206856329 / 40000000000000000 : ℚ)) + (U := (-(2605039519011009743847 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_7 : Uω (aρ 7) (bρ 7) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3263,25 +2850,21 @@ lemma U_563_7 : have hlg : Real.log (22812595809258933 / 40000000000000000 : ℝ) ≤ (-(1123133245324348551683 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22812595809258933 / 40000000000000000 : ℝ) = - (22812595809258933 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22812595809258933 / 20000000000000000 : ℚ)) - (U := (263161115275651448317 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22812595809258933 / 20000000000000000 : ℝ) ≤ - (263161115275651448317 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5680411464429779 / 10000000000000000 : ℝ)) (q := - (22812595809258933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22812595809258933 / 40000000000000000 : ℚ)) + (r' := (22812595809258933 / 20000000000000000 : ℚ)) + (U := (-(1123133245324348551683 / 2000000000000000000000 : ℚ))) + (U' := (263161115275651448317 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (5680411464429779 / 10000000000000000 : ℚ)) + (q := (22812595809258933 / 40000000000000000 : ℚ)) + (U := (-(1123133245324348551683 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_8 : Uω (aρ 8) (bρ 8) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3289,25 +2872,21 @@ lemma U_563_8 : have hlg : Real.log (21582383025250187 / 40000000000000000 : ℝ) ≤ (-(6170020726299281010733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21582383025250187 / 40000000000000000 : ℝ) = - (21582383025250187 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21582383025250187 / 20000000000000000 : ℚ)) - (U := (761451076700718989267 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21582383025250187 / 20000000000000000 : ℝ) ≤ - (761451076700718989267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2674423361882703 / 5000000000000000 : ℝ)) (q := - (21582383025250187 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21582383025250187 / 40000000000000000 : ℚ)) + (r' := (21582383025250187 / 20000000000000000 : ℚ)) + (U := (-(6170020726299281010733 / 10000000000000000000000 : ℚ))) + (U' := (761451076700718989267 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (2674423361882703 / 5000000000000000 : ℚ)) + (q := (21582383025250187 / 40000000000000000 : ℚ)) + (U := (-(6170020726299281010733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_9 : Uω (aρ 9) (bρ 9) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3315,25 +2894,21 @@ lemma U_563_9 : have hlg : Real.log (20044020521875581 / 40000000000000000 : ℝ) ≤ (-(3454742864578543876601 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20044020521875581 / 40000000000000000 : ℝ) = - (20044020521875581 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20044020521875581 / 20000000000000000 : ℚ)) - (U := (10993036921456123399 / 5000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (20044020521875581 / 20000000000000000 : ℝ) ≤ - (10993036921456123399 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4920631100438103 / 10000000000000000 : ℝ)) (q := - (20044020521875581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20044020521875581 / 40000000000000000 : ℚ)) + (r' := (20044020521875581 / 20000000000000000 : ℚ)) + (U := (-(3454742864578543876601 / 5000000000000000000000 : ℚ))) + (U' := (10993036921456123399 / 5000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (4920631100438103 / 10000000000000000 : ℚ)) + (q := (20044020521875581 / 40000000000000000 : ℚ)) + (U := (-(3454742864578543876601 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_10 : Uω (aρ 10) (bρ 10) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3341,26 +2916,21 @@ lemma U_563_10 : have hlg : Real.log (18189476927450631 / 40000000000000000 : ℝ) ≤ (-(1576072435054941454207 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18189476927450631 / 40000000000000000 : ℝ) = - (18189476927450631 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18189476927450631 / 10000000000000000 : ℚ)) - (U := (1196516286145058545793 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18189476927450631 / 10000000000000000 : ℝ) ≤ - (1196516286145058545793 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1095479584180157 / 2500000000000000 : ℝ)) (q := - (18189476927450631 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18189476927450631 / 40000000000000000 : ℚ)) + (r' := (18189476927450631 / 10000000000000000 : ℚ)) + (U := (-(1576072435054941454207 / 2000000000000000000000 : ℚ))) + (U' := (1196516286145058545793 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (1095479584180157 / 2500000000000000 : ℚ)) + (q := (18189476927450631 / 40000000000000000 : ℚ)) + (U := (-(1576072435054941454207 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_11 : Uω (aρ 11) (bρ 11) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3368,26 +2938,21 @@ lemma U_563_11 : have hlg : Real.log (16019414449549067 / 40000000000000000 : ℝ) ≤ (-(9150780638360100323413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16019414449549067 / 40000000000000000 : ℝ) = - (16019414449549067 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16019414449549067 / 10000000000000000 : ℚ)) - (U := (4712162967639899676587 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16019414449549067 / 10000000000000000 : ℝ) ≤ - (4712162967639899676587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1857681861987423 / 5000000000000000 : ℝ)) (q := - (16019414449549067 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16019414449549067 / 40000000000000000 : ℚ)) + (r' := (16019414449549067 / 10000000000000000 : ℚ)) + (U := (-(9150780638360100323413 / 10000000000000000000000 : ℚ))) + (U' := (4712162967639899676587 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (1857681861987423 / 5000000000000000 : ℚ)) + (q := (16019414449549067 / 40000000000000000 : ℚ)) + (U := (-(9150780638360100323413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_12 : Uω (aρ 12) (bρ 12) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3395,26 +2960,21 @@ lemma U_563_12 : have hlg : Real.log (13516842921434643 / 40000000000000000 : ℝ) ≤ (-(542471460987771583411 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13516842921434643 / 40000000000000000 : ℝ) = - (13516842921434643 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13516842921434643 / 10000000000000000 : ℚ)) - (U := (150675719312228416589 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13516842921434643 / 10000000000000000 : ℝ) ≤ - (150675719312228416589 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1443889028301317 / 5000000000000000 : ℝ)) (q := - (13516842921434643 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13516842921434643 / 40000000000000000 : ℚ)) + (r' := (13516842921434643 / 10000000000000000 : ℚ)) + (U := (-(542471460987771583411 / 500000000000000000000 : ℚ))) + (U' := (150675719312228416589 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (1443889028301317 / 5000000000000000 : ℚ)) + (q := (13516842921434643 / 40000000000000000 : ℚ)) + (U := (-(542471460987771583411 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_13 : Uω (aρ 13) (bρ 13) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3422,26 +2982,21 @@ lemma U_563_13 : have hlg : Real.log (2102729401588053 / 8000000000000000 : ℝ) ≤ (-(2672410650574187809643 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2102729401588053 / 8000000000000000 : ℝ) = - (2102729401588053 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2102729401588053 / 2000000000000000 : ℚ)) - (U := (100178070625812190357 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (2102729401588053 / 2000000000000000 : ℝ) ≤ - (100178070625812190357 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (357112368290089 / 2000000000000000 : ℝ)) (q := - (2102729401588053 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2102729401588053 / 8000000000000000 : ℚ)) + (r' := (2102729401588053 / 2000000000000000 : ℚ)) + (U := (-(2672410650574187809643 / 2000000000000000000000 : ℚ))) + (U' := (100178070625812190357 / 2000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20636590827023 / 32000000000000 : ℚ)) + (s := (357112368290089 / 2000000000000000 : ℚ)) + (q := (2102729401588053 / 8000000000000000 : ℚ)) + (U := (-(2672410650574187809643 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_563_14 : Uω (aρ 14) (bρ 14) (20636590827023 / 32000000000000 : ℝ) ≤ @@ -3548,25 +3103,21 @@ lemma U_564_1 : have hlg : Real.log (6405909867100199 / 10000000000000000 : ℝ) ≤ (-(4453641117210170942821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6405909867100199 / 10000000000000000 : ℝ) = - (6405909867100199 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6405909867100199 / 5000000000000000 : ℚ)) - (U := (2477830685789829057179 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6405909867100199 / 5000000000000000 : ℝ) ≤ - (2477830685789829057179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3202942314898949 / 5000000000000000 : ℝ)) (q := - (6405909867100199 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6405909867100199 / 10000000000000000 : ℚ)) + (r' := (6405909867100199 / 5000000000000000 : ℚ)) + (U := (-(4453641117210170942821 / 10000000000000000000000 : ℚ))) + (U' := (2477830685789829057179 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (517634585799 / 800000000000 : ℚ)) + (s := (3202942314898949 / 5000000000000000 : ℚ)) + (q := (6405909867100199 / 10000000000000000 : ℚ)) + (U := (-(4453641117210170942821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_2 : Uω (aρ 2) (bρ 2) (517634585799 / 800000000000 : ℝ) ≤ @@ -3574,25 +3125,21 @@ lemma U_564_2 : have hlg : Real.log (3190999927253161 / 5000000000000000 : ℝ) ≤ (-(4491035876755540387069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3190999927253161 / 5000000000000000 : ℝ) = - (3190999927253161 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3190999927253161 / 2500000000000000 : ℚ)) - (U := (2440435926244459612931 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3190999927253161 / 2500000000000000 : ℝ) ≤ - (2440435926244459612931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (398864601070009 / 625000000000000 : ℝ)) (q := - (3190999927253161 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3190999927253161 / 5000000000000000 : ℚ)) + (r' := (3190999927253161 / 2500000000000000 : ℚ)) + (U := (-(4491035876755540387069 / 10000000000000000000000 : ℚ))) + (U' := (2440435926244459612931 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (517634585799 / 800000000000 : ℚ)) + (s := (398864601070009 / 625000000000000 : ℚ)) + (q := (3190999927253161 / 5000000000000000 : ℚ)) + (U := (-(4491035876755540387069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_3 : Uω (aρ 3) (bρ 3) (517634585799 / 800000000000 : ℝ) ≤ @@ -3600,25 +3147,21 @@ lemma U_564_3 : have hlg : Real.log (395886625324303 / 625000000000000 : ℝ) ≤ (-(4566237788996584143217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (395886625324303 / 625000000000000 : ℝ) = - (395886625324303 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (395886625324303 / 312500000000000 : ℚ)) - (U := (2365234014003415856783 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (395886625324303 / 312500000000000 : ℝ) ≤ - (2365234014003415856783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1583400506208799 / 2500000000000000 : ℝ)) (q := - (395886625324303 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (395886625324303 / 625000000000000 : ℚ)) + (r' := (395886625324303 / 312500000000000 : ℚ)) + (U := (-(4566237788996584143217 / 10000000000000000000000 : ℚ))) + (U' := (2365234014003415856783 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (517634585799 / 800000000000 : ℚ)) + (s := (1583400506208799 / 2500000000000000 : ℚ)) + (q := (395886625324303 / 625000000000000 : ℚ)) + (U := (-(4566237788996584143217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_4 : Uω (aρ 4) (bρ 4) (517634585799 / 800000000000 : ℝ) ≤ @@ -3626,25 +3169,21 @@ lemma U_564_4 : have hlg : Real.log (6254793809870713 / 10000000000000000 : ℝ) ≤ (-(58654614175999811513 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6254793809870713 / 10000000000000000 : ℝ) = - (6254793809870713 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6254793809870713 / 5000000000000000 : ℚ)) - (U := (27988783361500188487 / 125000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6254793809870713 / 5000000000000000 : ℝ) ≤ - (27988783361500188487 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3126555907631963 / 5000000000000000 : ℝ)) (q := - (6254793809870713 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6254793809870713 / 10000000000000000 : ℚ)) + (r' := (6254793809870713 / 5000000000000000 : ℚ)) + (U := (-(58654614175999811513 / 125000000000000000000 : ℚ))) + (U' := (27988783361500188487 / 125000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (517634585799 / 800000000000 : ℚ)) + (s := (3126555907631963 / 5000000000000000 : ℚ)) + (q := (6254793809870713 / 10000000000000000 : ℚ)) + (U := (-(58654614175999811513 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_5 : Uω (aρ 5) (bρ 5) (517634585799 / 800000000000 : ℝ) ≤ @@ -3652,23 +3191,21 @@ lemma U_564_5 : have hlg : Real.log (2995090197471 / 4882812500000 : ℝ) ≤ (-(977494076851752214137 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show (2995090197471 / 4882812500000 : ℝ) = (2995090197471 / 2441406250000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2995090197471 / 2441406250000 : ℚ)) - (U := (408800283748247785863 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2995090197471 / 2441406250000 : ℝ) ≤ - (408800283748247785863 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1532400890924679 / 2500000000000000 : ℝ)) (q := - (2995090197471 / 4882812500000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2995090197471 / 4882812500000 : ℚ)) + (r' := (2995090197471 / 2441406250000 : ℚ)) + (U := (-(977494076851752214137 / 2000000000000000000000 : ℚ))) + (U' := (408800283748247785863 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (517634585799 / 800000000000 : ℚ)) + (s := (1532400890924679 / 2500000000000000 : ℚ)) + (q := (2995090197471 / 4882812500000 : ℚ)) + (U := (-(977494076851752214137 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_6 : Uω (aρ 6) (bρ 6) (517634585799 / 800000000000 : ℝ) ≤ @@ -3676,25 +3213,21 @@ lemma U_564_6 : have hlg : Real.log (11921502632982307 / 20000000000000000 : ℝ) ≤ (-(5173885597877607211283 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11921502632982307 / 20000000000000000 : ℝ) = - (11921502632982307 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11921502632982307 / 10000000000000000 : ℚ)) - (U := (1757586205122392788717 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11921502632982307 / 10000000000000000 : ℝ) ≤ - (1757586205122392788717 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5950457122979807 / 10000000000000000 : ℝ)) (q := - (11921502632982307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11921502632982307 / 20000000000000000 : ℚ)) + (r' := (11921502632982307 / 10000000000000000 : ℚ)) + (U := (-(5173885597877607211283 / 10000000000000000000000 : ℚ))) + (U' := (1757586205122392788717 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (517634585799 / 800000000000 : ℚ)) + (s := (5950457122979807 / 10000000000000000 : ℚ)) + (q := (11921502632982307 / 20000000000000000 : ℚ)) + (U := (-(5173885597877607211283 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_7 : Uω (aρ 7) (bρ 7) (517634585799 / 800000000000 : ℝ) ≤ @@ -3702,25 +3235,21 @@ lemma U_564_7 : have hlg : Real.log (715591545793229 / 1250000000000000 : ℝ) ≤ (-(1394473231557664473619 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (715591545793229 / 1250000000000000 : ℝ) = - (715591545793229 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (715591545793229 / 625000000000000 : ℚ)) - (U := (338394719192335526381 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (715591545793229 / 625000000000000 : ℝ) ≤ - (338394719192335526381 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1425520150862291 / 2500000000000000 : ℝ)) (q := - (715591545793229 / 1250000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (715591545793229 / 1250000000000000 : ℚ)) + (r' := (715591545793229 / 625000000000000 : ℚ)) + (U := (-(1394473231557664473619 / 2500000000000000000000 : ℚ))) + (U' := (338394719192335526381 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (517634585799 / 800000000000 : ℚ)) + (s := (1425520150862291 / 2500000000000000 : ℚ)) + (q := (715591545793229 / 1250000000000000 : ℚ)) + (U := (-(1394473231557664473619 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_8 : Uω (aρ 8) (bρ 8) (517634585799 / 800000000000 : ℝ) ≤ @@ -3728,25 +3257,21 @@ lemma U_564_8 : have hlg : Real.log (5417280576956103 / 10000000000000000 : ℝ) ≤ (-(766238927205555868307 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5417280576956103 / 10000000000000000 : ℝ) = - (5417280576956103 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5417280576956103 / 5000000000000000 : ℚ)) - (U := (100195048169444131693 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5417280576956103 / 5000000000000000 : ℝ) ≤ - (100195048169444131693 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2685359338004853 / 5000000000000000 : ℝ)) (q := - (5417280576956103 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5417280576956103 / 10000000000000000 : ℚ)) + (r' := (5417280576956103 / 5000000000000000 : ℚ)) + (U := (-(766238927205555868307 / 1250000000000000000000 : ℚ))) + (U' := (100195048169444131693 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (517634585799 / 800000000000 : ℚ)) + (s := (2685359338004853 / 5000000000000000 : ℚ)) + (q := (5417280576956103 / 10000000000000000 : ℚ)) + (U := (-(766238927205555868307 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_9 : Uω (aρ 9) (bρ 9) (517634585799 / 800000000000 : ℝ) ≤ @@ -3754,25 +3279,21 @@ lemma U_564_9 : have hlg : Real.log (503289590483219 / 1000000000000000 : ℝ) ≤ (-(6865895476826353308691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (503289590483219 / 1000000000000000 : ℝ) = - (503289590483219 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (503289590483219 / 500000000000000 : ℚ)) - (U := (65576326173646691309 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (503289590483219 / 500000000000000 : ℝ) ≤ - (65576326173646691309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (123572874003047 / 250000000000000 : ℝ)) (q := - (503289590483219 / 1000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (503289590483219 / 1000000000000000 : ℚ)) + (r' := (503289590483219 / 500000000000000 : ℚ)) + (U := (-(6865895476826353308691 / 10000000000000000000000 : ℚ))) + (U' := (65576326173646691309 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (517634585799 / 800000000000 : ℚ)) + (s := (123572874003047 / 250000000000000 : ℚ)) + (q := (503289590483219 / 1000000000000000 : ℚ)) + (U := (-(6865895476826353308691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_10 : Uω (aρ 10) (bρ 10) (517634585799 / 800000000000 : ℝ) ≤ @@ -3780,26 +3301,21 @@ lemma U_564_10 : have hlg : Real.log (9139349024056447 / 20000000000000000 : ℝ) ≤ (-(7831431128554380707361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9139349024056447 / 20000000000000000 : ℝ) = - (9139349024056447 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9139349024056447 / 5000000000000000 : ℚ)) - (U := (6031512477445619292639 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9139349024056447 / 5000000000000000 : ℝ) ≤ - (6031512477445619292639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4405031208008947 / 10000000000000000 : ℝ)) (q := - (9139349024056447 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9139349024056447 / 20000000000000000 : ℚ)) + (r' := (9139349024056447 / 5000000000000000 : ℚ)) + (U := (-(7831431128554380707361 / 10000000000000000000000 : ℚ))) + (U' := (6031512477445619292639 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (517634585799 / 800000000000 : ℚ)) + (s := (4405031208008947 / 10000000000000000 : ℚ)) + (q := (9139349024056447 / 20000000000000000 : ℚ)) + (U := (-(7831431128554380707361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_11 : Uω (aρ 11) (bρ 11) (517634585799 / 800000000000 : ℝ) ≤ @@ -3807,26 +3323,21 @@ lemma U_564_11 : have hlg : Real.log (8056031916865501 / 20000000000000000 : ℝ) ≤ (-(9093111557506252195301 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8056031916865501 / 20000000000000000 : ℝ) = - (8056031916865501 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8056031916865501 / 5000000000000000 : ℚ)) - (U := (4769832048493747804699 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8056031916865501 / 5000000000000000 : ℝ) ≤ - (4769832048493747804699 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3740190727023001 / 10000000000000000 : ℝ)) (q := - (8056031916865501 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8056031916865501 / 20000000000000000 : ℚ)) + (r' := (8056031916865501 / 5000000000000000 : ℚ)) + (U := (-(9093111557506252195301 / 10000000000000000000000 : ℚ))) + (U' := (4769832048493747804699 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (517634585799 / 800000000000 : ℚ)) + (s := (3740190727023001 / 10000000000000000 : ℚ)) + (q := (8056031916865501 / 20000000000000000 : ℚ)) + (U := (-(9093111557506252195301 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_12 : Uω (aρ 12) (bρ 12) (517634585799 / 800000000000 : ℝ) ≤ @@ -3834,25 +3345,21 @@ lemma U_564_12 : have hlg : Real.log (136173410858717 / 400000000000000 : ℝ) ≤ (-(5387676966162376967213 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (136173410858717 / 400000000000000 : ℝ) = - (136173410858717 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (136173410858717 / 100000000000000 : ℚ)) - (U := (1543794836837623032787 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (136173410858717 / 100000000000000 : ℝ) ≤ - (1543794836837623032787 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (58330588995567 / 200000000000000 : ℝ)) (q := - (136173410858717 / 400000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (136173410858717 / 400000000000000 : ℚ)) + (r' := (136173410858717 / 100000000000000 : ℚ)) + (U := (-(5387676966162376967213 / 5000000000000000000000 : ℚ))) + (U' := (1543794836837623032787 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (517634585799 / 800000000000 : ℚ)) + (s := (58330588995567 / 200000000000000 : ℚ)) + (q := (136173410858717 / 400000000000000 : ℚ)) + (U := (-(5387676966162376967213 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_13 : Uω (aρ 13) (bρ 13) (517634585799 / 800000000000 : ℝ) ≤ @@ -3860,26 +3367,21 @@ lemma U_564_13 : have hlg : Real.log (5319762758207451 / 20000000000000000 : ℝ) ≤ (-(3310758912492028501331 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5319762758207451 / 20000000000000000 : ℝ) = - (5319762758207451 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5319762758207451 / 5000000000000000 : ℚ)) - (U := (154976989007971498669 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5319762758207451 / 5000000000000000 : ℝ) ≤ - (154976989007971498669 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1827003406644951 / 10000000000000000 : ℝ)) (q := - (5319762758207451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5319762758207451 / 20000000000000000 : ℚ)) + (r' := (5319762758207451 / 5000000000000000 : ℚ)) + (U := (-(3310758912492028501331 / 2500000000000000000000 : ℚ))) + (U' := (154976989007971498669 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (517634585799 / 800000000000 : ℚ)) + (s := (1827003406644951 / 10000000000000000 : ℚ)) + (q := (5319762758207451 / 20000000000000000 : ℚ)) + (U := (-(3310758912492028501331 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_564_14 : Uω (aρ 14) (bρ 14) (517634585799 / 800000000000 : ℝ) ≤ @@ -3985,25 +3487,21 @@ lemma U_565_1 : have hlg : Real.log (25709630562217229 / 40000000000000000 : ℝ) ≤ (-(11050345052480570479 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25709630562217229 / 40000000000000000 : ℝ) = - (25709630562217229 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25709630562217229 / 20000000000000000 : ℚ)) - (U := (6278334455019429521 / 25000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25709630562217229 / 20000000000000000 : ℝ) ≤ - (6278334455019429521 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3213691243831651 / 5000000000000000 : ℝ)) (q := - (25709630562217229 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25709630562217229 / 40000000000000000 : ℚ)) + (r' := (25709630562217229 / 20000000000000000 : ℚ)) + (U := (-(11050345052480570479 / 25000000000000000000 : ℚ))) + (U' := (6278334455019429521 / 25000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (3213691243831651 / 5000000000000000 : ℚ)) + (q := (25709630562217229 / 40000000000000000 : ℚ)) + (U := (-(11050345052480570479 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_2 : Uω (aρ 2) (bρ 2) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4011,25 +3509,21 @@ lemma U_565_2 : have hlg : Real.log (25613992406609107 / 40000000000000000 : ℝ) ≤ (-(4457406733048630161033 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25613992406609107 / 40000000000000000 : ℝ) = - (25613992406609107 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25613992406609107 / 20000000000000000 : ℚ)) - (U := (2474065069951369838967 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25613992406609107 / 20000000000000000 : ℝ) ≤ - (2474065069951369838967 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6403332422369241 / 10000000000000000 : ℝ)) (q := - (25613992406609107 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25613992406609107 / 40000000000000000 : ℚ)) + (r' := (25613992406609107 / 20000000000000000 : ℚ)) + (U := (-(4457406733048630161033 / 10000000000000000000000 : ℚ))) + (U' := (2474065069951369838967 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (6403332422369241 / 10000000000000000 : ℚ)) + (q := (25613992406609107 / 40000000000000000 : ℚ)) + (U := (-(4457406733048630161033 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_3 : Uω (aρ 3) (bρ 3) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4037,25 +3531,21 @@ lemma U_565_3 : have hlg : Real.log (25422742678753341 / 40000000000000000 : ℝ) ≤ (-(4532352993907169877393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25422742678753341 / 40000000000000000 : ℝ) = - (25422742678753341 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25422742678753341 / 20000000000000000 : ℚ)) - (U := (2399118809092830122607 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25422742678753341 / 20000000000000000 : ℝ) ≤ - (2399118809092830122607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3177551832395679 / 5000000000000000 : ℝ)) (q := - (25422742678753341 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25422742678753341 / 40000000000000000 : ℚ)) + (r' := (25422742678753341 / 20000000000000000 : ℚ)) + (U := (-(4532352993907169877393 / 10000000000000000000000 : ℚ))) + (U' := (2399118809092830122607 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (3177551832395679 / 5000000000000000 : ℚ)) + (q := (25422742678753341 / 40000000000000000 : ℚ)) + (U := (-(4532352993907169877393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_4 : Uω (aρ 4) (bρ 4) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4063,25 +3553,21 @@ lemma U_565_4 : have hlg : Real.log (25105189046627263 / 40000000000000000 : ℝ) ≤ (-(232902447078791866397 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25105189046627263 / 40000000000000000 : ℝ) = - (25105189046627263 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25105189046627263 / 20000000000000000 : ℚ)) - (U := (113671143071208133603 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25105189046627263 / 20000000000000000 : ℝ) ≤ - (113671143071208133603 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6274621029793319 / 10000000000000000 : ℝ)) (q := - (25105189046627263 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25105189046627263 / 40000000000000000 : ℚ)) + (r' := (25105189046627263 / 20000000000000000 : ℚ)) + (U := (-(232902447078791866397 / 500000000000000000000 : ℚ))) + (U' := (113671143071208133603 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (6274621029793319 / 10000000000000000 : ℚ)) + (q := (25105189046627263 / 40000000000000000 : ℚ)) + (U := (-(232902447078791866397 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_5 : Uω (aρ 5) (bρ 5) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4089,25 +3575,21 @@ lemma U_565_5 : have hlg : Real.log (24621830341973913 / 40000000000000000 : ℝ) ≤ (-(4852459921577938326357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24621830341973913 / 40000000000000000 : ℝ) = - (24621830341973913 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24621830341973913 / 20000000000000000 : ℚ)) - (U := (2079011881422061673643 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24621830341973913 / 20000000000000000 : ℝ) ≤ - (2079011881422061673643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1537782899200411 / 2500000000000000 : ℝ)) (q := - (24621830341973913 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24621830341973913 / 40000000000000000 : ℚ)) + (r' := (24621830341973913 / 20000000000000000 : ℚ)) + (U := (-(4852459921577938326357 / 10000000000000000000000 : ℚ))) + (U' := (2079011881422061673643 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (1537782899200411 / 2500000000000000 : ℚ)) + (q := (24621830341973913 / 40000000000000000 : ℚ)) + (U := (-(4852459921577938326357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_6 : Uω (aρ 6) (bρ 6) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4115,25 +3597,21 @@ lemma U_565_6 : have hlg : Real.log (4785828849661249 / 8000000000000000 : ℝ) ≤ (-(64222789149440470487 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4785828849661249 / 8000000000000000 : ℝ) = - (4785828849661249 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4785828849661249 / 4000000000000000 : ℚ)) - (U := (22420608388059529513 / 125000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4785828849661249 / 4000000000000000 : ℝ) ≤ - (22420608388059529513 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (597202892510781 / 1000000000000000 : ℝ)) (q := - (4785828849661249 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4785828849661249 / 8000000000000000 : ℚ)) + (r' := (4785828849661249 / 4000000000000000 : ℚ)) + (U := (-(64222789149440470487 / 125000000000000000000 : ℚ))) + (U' := (22420608388059529513 / 125000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (597202892510781 / 1000000000000000 : ℚ)) + (q := (4785828849661249 / 8000000000000000 : ℚ)) + (U := (-(64222789149440470487 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_7 : Uω (aρ 7) (bρ 7) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4141,25 +3619,21 @@ lemma U_565_7 : have hlg : Real.log (22985260535457379 / 40000000000000000 : ℝ) ≤ (-(5540262896390538563607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22985260535457379 / 40000000000000000 : ℝ) = - (22985260535457379 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22985260535457379 / 20000000000000000 : ℚ)) - (U := (1391208906609461436393 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22985260535457379 / 20000000000000000 : ℝ) ≤ - (1391208906609461436393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5723748449443377 / 10000000000000000 : ℝ)) (q := - (22985260535457379 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22985260535457379 / 40000000000000000 : ℚ)) + (r' := (22985260535457379 / 20000000000000000 : ℚ)) + (U := (-(5540262896390538563607 / 10000000000000000000000 : ℚ))) + (U' := (1391208906609461436393 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (5723748449443377 / 10000000000000000 : ℚ)) + (q := (22985260535457379 / 40000000000000000 : ℚ)) + (U := (-(5540262896390538563607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_8 : Uω (aρ 8) (bρ 8) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4167,25 +3641,21 @@ lemma U_565_8 : have hlg : Real.log (21755855570410679 / 40000000000000000 : ℝ) ≤ (-(6089965109248601034731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21755855570410679 / 40000000000000000 : ℝ) = - (21755855570410679 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21755855570410679 / 20000000000000000 : ℚ)) - (U := (841506693751398965269 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21755855570410679 / 20000000000000000 : ℝ) ≤ - (841506693751398965269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5392587618260027 / 10000000000000000 : ℝ)) (q := - (21755855570410679 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21755855570410679 / 40000000000000000 : ℚ)) + (r' := (21755855570410679 / 20000000000000000 : ℚ)) + (U := (-(6089965109248601034731 / 10000000000000000000000 : ℚ))) + (U' := (841506693751398965269 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (5392587618260027 / 10000000000000000 : ℚ)) + (q := (21755855570410679 / 40000000000000000 : ℚ)) + (U := (-(6089965109248601034731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_9 : Uω (aρ 9) (bρ 9) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4193,25 +3663,21 @@ lemma U_565_9 : have hlg : Real.log (20219132852365427 / 40000000000000000 : ℝ) ≤ (-(213203164631554066227 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20219132852365427 / 40000000000000000 : ℝ) = - (20219132852365427 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20219132852365427 / 20000000000000000 : ℚ)) - (U := (3405329212195933773 / 312500000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20219132852365427 / 20000000000000000 : ℝ) ≤ - (3405329212195933773 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4965191887597401 / 10000000000000000 : ℝ)) (q := - (20219132852365427 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20219132852365427 / 40000000000000000 : ℚ)) + (r' := (20219132852365427 / 20000000000000000 : ℚ)) + (U := (-(213203164631554066227 / 312500000000000000000 : ℚ))) + (U' := (3405329212195933773 / 312500000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (4965191887597401 / 10000000000000000 : ℚ)) + (q := (20219132852365427 / 40000000000000000 : ℚ)) + (U := (-(213203164631554066227 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_10 : Uω (aρ 10) (bρ 10) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4219,26 +3685,21 @@ lemma U_565_10 : have hlg : Real.log (18367886624975269 / 40000000000000000 : ℝ) ≤ (-(3891378029483553701593 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18367886624975269 / 40000000000000000 : ℝ) = - (18367886624975269 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18367886624975269 / 10000000000000000 : ℚ)) - (U := (3040093773516446298407 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18367886624975269 / 10000000000000000 : ℝ) ≤ - (3040093773516446298407 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2214063903698661 / 5000000000000000 : ℝ)) (q := - (18367886624975269 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18367886624975269 / 40000000000000000 : ℚ)) + (r' := (18367886624975269 / 10000000000000000 : ℚ)) + (U := (-(3891378029483553701593 / 5000000000000000000000 : ℚ))) + (U' := (3040093773516446298407 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (2214063903698661 / 5000000000000000 : ℚ)) + (q := (18367886624975269 / 40000000000000000 : ℚ)) + (U := (-(3891378029483553701593 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_11 : Uω (aρ 11) (bρ 11) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4246,26 +3707,21 @@ lemma U_565_11 : have hlg : Real.log (16204631289860401 / 40000000000000000 : ℝ) ≤ (-(9035823701220572399023 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16204631289860401 / 40000000000000000 : ℝ) = - (16204631289860401 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16204631289860401 / 10000000000000000 : ℚ)) - (U := (4827119904779427600977 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16204631289860401 / 10000000000000000 : ℝ) ≤ - (4827119904779427600977 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (470622095755611 / 1250000000000000 : ℝ)) (q := - (16204631289860401 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16204631289860401 / 40000000000000000 : ℚ)) + (r' := (16204631289860401 / 10000000000000000 : ℚ)) + (U := (-(9035823701220572399023 / 10000000000000000000000 : ℚ))) + (U' := (4827119904779427600977 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (470622095755611 / 1250000000000000 : ℚ)) + (q := (16204631289860401 / 40000000000000000 : ℚ)) + (U := (-(9035823701220572399023 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_12 : Uω (aρ 12) (bρ 12) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4273,26 +3729,21 @@ lemma U_565_12 : have hlg : Real.log (13717591735961083 / 40000000000000000 : ℝ) ≤ (-(5351001880761519242997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13717591735961083 / 40000000000000000 : ℝ) = - (13717591735961083 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13717591735961083 / 10000000000000000 : ℚ)) - (U := (1580469922238480757003 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13717591735961083 / 10000000000000000 : ℝ) ≤ - (1580469922238480757003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2945157085780229 / 10000000000000000 : ℝ)) (q := - (13717591735961083 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13717591735961083 / 40000000000000000 : ℚ)) + (r' := (13717591735961083 / 10000000000000000 : ℚ)) + (U := (-(5351001880761519242997 / 5000000000000000000000 : ℚ))) + (U' := (1580469922238480757003 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (2945157085780229 / 10000000000000000 : ℚ)) + (q := (13717591735961083 / 40000000000000000 : ℚ)) + (U := (-(5351001880761519242997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_13 : Uω (aρ 13) (bρ 13) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4300,26 +3751,21 @@ lemma U_565_13 : have hlg : Real.log (10764060149677171 / 40000000000000000 : ℝ) ≤ (-(13126666327036419575017 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10764060149677171 / 40000000000000000 : ℝ) = - (10764060149677171 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10764060149677171 / 10000000000000000 : ℚ)) - (U := (736277278963580424983 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10764060149677171 / 10000000000000000 : ℝ) ≤ - (736277278963580424983 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1867773034233273 / 10000000000000000 : ℝ)) (q := - (10764060149677171 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10764060149677171 / 40000000000000000 : ℚ)) + (r' := (10764060149677171 / 10000000000000000 : ℚ)) + (U := (-(13126666327036419575017 / 10000000000000000000000 : ℚ))) + (U' := (736277278963580424983 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20774176036897 / 32000000000000 : ℚ)) + (s := (1867773034233273 / 10000000000000000 : ℚ)) + (q := (10764060149677171 / 40000000000000000 : ℚ)) + (U := (-(13126666327036419575017 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_565_14 : Uω (aρ 14) (bρ 14) (20774176036897 / 32000000000000 : ℝ) ≤ @@ -4425,25 +3871,21 @@ lemma U_566_1 : have hlg : Real.log (12897810826891269 / 20000000000000000 : ℝ) ≤ (-(438674679669422764263 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12897810826891269 / 20000000000000000 : ℝ) = - (12897810826891269 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12897810826891269 / 10000000000000000 : ℚ)) - (U := (254472500630577235737 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12897810826891269 / 10000000000000000 : ℝ) ≤ - (254472500630577235737 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (806110043050393 / 1250000000000000 : ℝ)) (q := - (12897810826891269 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12897810826891269 / 20000000000000000 : ℚ)) + (r' := (12897810826891269 / 10000000000000000 : ℚ)) + (U := (-(438674679669422764263 / 1000000000000000000000 : ℚ))) + (U' := (254472500630577235737 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (806110043050393 / 1250000000000000 : ℚ)) + (q := (12897810826891269 / 20000000000000000 : ℚ)) + (U := (-(438674679669422764263 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_2 : Uω (aρ 2) (bρ 2) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4451,25 +3893,21 @@ lemma U_566_2 : have hlg : Real.log (12849992690126547 / 20000000000000000 : ℝ) ≤ (-(552986288518407495121 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12849992690126547 / 20000000000000000 : ℝ) = - (12849992690126547 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12849992690126547 / 10000000000000000 : ℚ)) - (U := (313447686856592504879 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12849992690126547 / 10000000000000000 : ℝ) ≤ - (313447686856592504879 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3212415610074211 / 5000000000000000 : ℝ)) (q := - (12849992690126547 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12849992690126547 / 20000000000000000 : ℚ)) + (r' := (12849992690126547 / 10000000000000000 : ℚ)) + (U := (-(552986288518407495121 / 1250000000000000000000 : ℚ))) + (U' := (313447686856592504879 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (3212415610074211 / 5000000000000000 : ℚ)) + (q := (12849992690126547 / 20000000000000000 : ℚ)) + (U := (-(552986288518407495121 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_3 : Uω (aρ 3) (bρ 3) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4477,25 +3915,21 @@ lemma U_566_3 : have hlg : Real.log (12754370641733471 / 20000000000000000 : ℝ) ≤ (-(1124645662501160291839 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12754370641733471 / 20000000000000000 : ℝ) = - (12754370641733471 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12754370641733471 / 10000000000000000 : ℚ)) - (U := (608222288248839708161 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12754370641733471 / 10000000000000000 : ℝ) ≤ - (608222288248839708161 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3188302639052673 / 5000000000000000 : ℝ)) (q := - (12754370641733471 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12754370641733471 / 20000000000000000 : ℚ)) + (r' := (12754370641733471 / 10000000000000000 : ℚ)) + (U := (-(1124645662501160291839 / 2500000000000000000000 : ℚ))) + (U' := (608222288248839708161 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (3188302639052673 / 5000000000000000 : ℚ)) + (q := (12754370641733471 / 20000000000000000 : ℚ)) + (U := (-(1124645662501160291839 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_4 : Uω (aρ 4) (bρ 4) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4503,25 +3937,21 @@ lemma U_566_4 : have hlg : Real.log (12595601348158829 / 20000000000000000 : ℝ) ≤ (-(4623846196384515435809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12595601348158829 / 20000000000000000 : ℝ) = - (12595601348158829 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12595601348158829 / 10000000000000000 : ℚ)) - (U := (2307625606615484564191 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12595601348158829 / 10000000000000000 : ℝ) ≤ - (2307625606615484564191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (787016270699463 / 1250000000000000 : ℝ)) (q := - (12595601348158829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12595601348158829 / 20000000000000000 : ℚ)) + (r' := (12595601348158829 / 10000000000000000 : ℚ)) + (U := (-(4623846196384515435809 / 10000000000000000000000 : ℚ))) + (U' := (2307625606615484564191 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (787016270699463 / 1250000000000000 : ℚ)) + (q := (12595601348158829 / 20000000000000000 : ℚ)) + (U := (-(4623846196384515435809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_5 : Uω (aρ 5) (bρ 5) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4529,25 +3959,21 @@ lemma U_566_5 : have hlg : Real.log (12353940681623363 / 20000000000000000 : ℝ) ≤ (-(963514355168254296311 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12353940681623363 / 20000000000000000 : ℝ) = - (12353940681623363 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12353940681623363 / 10000000000000000 : ℚ)) - (U := (422780005431745703689 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12353940681623363 / 10000000000000000 : ℝ) ≤ - (422780005431745703689 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3086329709197619 / 5000000000000000 : ℝ)) (q := - (12353940681623363 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12353940681623363 / 20000000000000000 : ℚ)) + (r' := (12353940681623363 / 10000000000000000 : ℚ)) + (U := (-(963514355168254296311 / 2000000000000000000000 : ℚ))) + (U' := (422780005431745703689 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (3086329709197619 / 5000000000000000 : ℚ)) + (q := (12353940681623363 / 20000000000000000 : ℚ)) + (U := (-(963514355168254296311 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_6 : Uω (aρ 6) (bρ 6) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4555,25 +3981,21 @@ lemma U_566_6 : have hlg : Real.log (6003820541376879 / 10000000000000000 : ℝ) ≤ (-(5101890692535526692447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6003820541376879 / 10000000000000000 : ℝ) = - (6003820541376879 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6003820541376879 / 5000000000000000 : ℚ)) - (U := (1829581110464473307553 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6003820541376879 / 5000000000000000 : ℝ) ≤ - (1829581110464473307553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5993600194665633 / 10000000000000000 : ℝ)) (q := - (6003820541376879 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6003820541376879 / 10000000000000000 : ℚ)) + (r' := (6003820541376879 / 5000000000000000 : ℚ)) + (U := (-(5101890692535526692447 / 10000000000000000000000 : ℚ))) + (U' := (1829581110464473307553 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (5993600194665633 / 10000000000000000 : ℚ)) + (q := (6003820541376879 / 10000000000000000 : ℚ)) + (U := (-(5101890692535526692447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_7 : Uω (aρ 7) (bρ 7) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4581,25 +4003,21 @@ lemma U_566_7 : have hlg : Real.log (11535794524369811 / 20000000000000000 : ℝ) ≤ (-(1375693761494647139359 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11535794524369811 / 20000000000000000 : ℝ) = - (11535794524369811 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11535794524369811 / 10000000000000000 : ℚ)) - (U := (357174189255352860641 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11535794524369811 / 10000000000000000 : ℝ) ≤ - (357174189255352860641 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2872707508520843 / 5000000000000000 : ℝ)) (q := - (11535794524369811 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11535794524369811 / 20000000000000000 : ℚ)) + (r' := (11535794524369811 / 10000000000000000 : ℚ)) + (U := (-(1375693761494647139359 / 2500000000000000000000 : ℚ))) + (U' := (357174189255352860641 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (2872707508520843 / 5000000000000000 : ℚ)) + (q := (11535794524369811 / 20000000000000000 : ℚ)) + (U := (-(1375693761494647139359 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_8 : Uω (aρ 8) (bρ 8) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4607,25 +4025,21 @@ lemma U_566_8 : have hlg : Real.log (1092129144297653 / 2000000000000000 : ℝ) ≤ (-(3025090229805417688551 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1092129144297653 / 2000000000000000 : ℝ) = - (1092129144297653 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1092129144297653 / 1000000000000000 : ℚ)) - (U := (440645671694582311449 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1092129144297653 / 1000000000000000 : ℝ) ≤ - (440645671694582311449 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1082890717397681 / 2000000000000000 : ℝ)) (q := - (1092129144297653 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1092129144297653 / 2000000000000000 : ℚ)) + (r' := (1092129144297653 / 1000000000000000 : ℚ)) + (U := (-(3025090229805417688551 / 5000000000000000000000 : ℚ))) + (U' := (440645671694582311449 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (1082890717397681 / 2000000000000000 : ℚ)) + (q := (1092129144297653 / 2000000000000000 : ℚ)) + (U := (-(3025090229805417688551 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_9 : Uω (aρ 9) (bρ 9) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4633,25 +4047,21 @@ lemma U_566_9 : have hlg : Real.log (10153334203382703 / 20000000000000000 : ℝ) ≤ (-(1355860257608270240147 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10153334203382703 / 20000000000000000 : ℝ) = - (10153334203382703 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10153334203382703 / 10000000000000000 : ℚ)) - (U := (30434102991729759853 / 2000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10153334203382703 / 10000000000000000 : ℝ) ≤ - (30434102991729759853 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2493730987877289 / 5000000000000000 : ℝ)) (q := - (10153334203382703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10153334203382703 / 20000000000000000 : ℚ)) + (r' := (10153334203382703 / 10000000000000000 : ℚ)) + (U := (-(1355860257608270240147 / 2000000000000000000000 : ℚ))) + (U' := (30434102991729759853 / 2000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (2493730987877289 / 5000000000000000 : ℚ)) + (q := (10153334203382703 / 20000000000000000 : ℚ)) + (U := (-(1355860257608270240147 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_10 : Uω (aρ 10) (bρ 10) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4659,26 +4069,21 @@ lemma U_566_10 : have hlg : Real.log (4614260791157823 / 10000000000000000 : ℝ) ≤ (-(1933583531531276978283 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4614260791157823 / 10000000000000000 : ℝ) = - (4614260791157823 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4614260791157823 / 2500000000000000 : ℚ)) - (U := (1532152369968723021717 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4614260791157823 / 2500000000000000 : ℝ) ≤ - (1532152369968723021717 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4451208388182521 / 10000000000000000 : ℝ)) (q := - (4614260791157823 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4614260791157823 / 10000000000000000 : ℚ)) + (r' := (4614260791157823 / 2500000000000000 : ℚ)) + (U := (-(1933583531531276978283 / 2500000000000000000000 : ℚ))) + (U' := (1532152369968723021717 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (4451208388182521 / 10000000000000000 : ℚ)) + (q := (4614260791157823 / 10000000000000000 : ℚ)) + (U := (-(1933583531531276978283 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_11 : Uω (aρ 11) (bρ 11) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4686,25 +4091,21 @@ lemma U_566_11 : have hlg : Real.log (407427960636177 / 1000000000000000 : ℝ) ≤ (-(140295491425674205323 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (407427960636177 / 1000000000000000 : ℝ) = - (407427960636177 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (407427960636177 / 250000000000000 : ℚ)) - (U := (76313002418075794677 / 156250000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (407427960636177 / 250000000000000 : ℝ) ≤ - (76313002418075794677 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (757944528959083 / 2000000000000000 : ℝ)) (q := - (407427960636177 / 1000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (407427960636177 / 1000000000000000 : ℚ)) + (r' := (407427960636177 / 250000000000000 : ℚ)) + (U := (-(140295491425674205323 / 156250000000000000000 : ℚ))) + (U' := (76313002418075794677 / 156250000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (757944528959083 / 2000000000000000 : ℚ)) + (q := (407427960636177 / 1000000000000000 : ℚ)) + (U := (-(140295491425674205323 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_12 : Uω (aρ 12) (bρ 12) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4712,25 +4113,21 @@ lemma U_566_12 : have hlg : Real.log (431800063131587 / 1250000000000000 : ℝ) ≤ (-(10629361654901392404073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (431800063131587 / 1250000000000000 : ℝ) = - (431800063131587 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (431800063131587 / 312500000000000 : ℚ)) - (U := (3233581951098607595927 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (431800063131587 / 312500000000000 : ℝ) ≤ - (3233581951098607595927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2973664538862267 / 10000000000000000 : ℝ)) (q := - (431800063131587 / 1250000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (431800063131587 / 1250000000000000 : ℚ)) + (r' := (431800063131587 / 312500000000000 : ℚ)) + (U := (-(10629361654901392404073 / 10000000000000000000000 : ℚ))) + (U' := (3233581951098607595927 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (2973664538862267 / 10000000000000000 : ℚ)) + (q := (431800063131587 / 1250000000000000 : ℚ)) + (U := (-(10629361654901392404073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_13 : Uω (aρ 13) (bρ 13) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4738,26 +4135,21 @@ lemma U_566_13 : have hlg : Real.log (5443668529638587 / 20000000000000000 : ℝ) ≤ (-(13012790773802567949037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5443668529638587 / 20000000000000000 : ℝ) = - (5443668529638587 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5443668529638587 / 5000000000000000 : ℚ)) - (U := (850152832197432050963 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5443668529638587 / 5000000000000000 : ℝ) ≤ - (850152832197432050963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (953956899995231 / 5000000000000000 : ℝ)) (q := - (5443668529638587 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5443668529638587 / 20000000000000000 : ℚ)) + (r' := (5443668529638587 / 5000000000000000 : ℚ)) + (U := (-(13012790773802567949037 / 10000000000000000000000 : ℚ))) + (U' := (850152832197432050963 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10421484320917 / 16000000000000 : ℚ)) + (s := (953956899995231 / 5000000000000000 : ℚ)) + (q := (5443668529638587 / 20000000000000000 : ℚ)) + (U := (-(13012790773802567949037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_566_14 : Uω (aρ 14) (bρ 14) (10421484320917 / 16000000000000 : ℝ) ≤ @@ -4863,25 +4255,21 @@ lemma U_567_1 : have hlg : Real.log (25881612743119157 / 40000000000000000 : ℝ) ≤ (-(4353466699681521755969 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25881612743119157 / 40000000000000000 : ℝ) = - (25881612743119157 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25881612743119157 / 20000000000000000 : ℚ)) - (U := (2578005103318478244031 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25881612743119157 / 20000000000000000 : ℝ) ≤ - (2578005103318478244031 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6470378200028641 / 10000000000000000 : ℝ)) (q := - (25881612743119157 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25881612743119157 / 40000000000000000 : ℚ)) + (r' := (25881612743119157 / 20000000000000000 : ℚ)) + (U := (-(4353466699681521755969 / 10000000000000000000000 : ℚ))) + (U' := (2578005103318478244031 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (6470378200028641 / 10000000000000000 : ℚ)) + (q := (25881612743119157 / 40000000000000000 : ℚ)) + (U := (-(4353466699681521755969 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_2 : Uω (aρ 2) (bρ 2) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -4889,25 +4277,21 @@ lemma U_567_2 : have hlg : Real.log (25785978339106719 / 40000000000000000 : ℝ) ≤ (-(4390485848910326832271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25785978339106719 / 40000000000000000 : ℝ) = - (25785978339106719 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25785978339106719 / 20000000000000000 : ℚ)) - (U := (2540985954089673167729 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25785978339106719 / 20000000000000000 : ℝ) ≤ - (2540985954089673167729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3223165005266211 / 5000000000000000 : ℝ)) (q := - (25785978339106719 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25785978339106719 / 40000000000000000 : ℚ)) + (r' := (25785978339106719 / 20000000000000000 : ℚ)) + (U := (-(4390485848910326832271 / 10000000000000000000000 : ℚ))) + (U' := (2540985954089673167729 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (3223165005266211 / 5000000000000000 : ℚ)) + (q := (25785978339106719 / 40000000000000000 : ℚ)) + (U := (-(4390485848910326832271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_3 : Uω (aρ 3) (bρ 3) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -4915,25 +4299,21 @@ lemma U_567_3 : have hlg : Real.log (25594739835433403 / 40000000000000000 : ℝ) ≤ (-(558115748324716916001 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25594739835433403 / 40000000000000000 : ℝ) = - (25594739835433403 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25594739835433403 / 20000000000000000 : ℚ)) - (U := (308318227050283083999 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25594739835433403 / 20000000000000000 : ℝ) ≤ - (308318227050283083999 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1599526716261441 / 2500000000000000 : ℝ)) (q := - (25594739835433403 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25594739835433403 / 40000000000000000 : ℚ)) + (r' := (25594739835433403 / 20000000000000000 : ℚ)) + (U := (-(558115748324716916001 / 1250000000000000000000 : ℚ))) + (U' := (308318227050283083999 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (1599526716261441 / 2500000000000000 : ℚ)) + (q := (25594739835433403 / 40000000000000000 : ℚ)) + (U := (-(558115748324716916001 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_4 : Uω (aρ 4) (bρ 4) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -4941,25 +4321,21 @@ lemma U_567_4 : have hlg : Real.log (25277216190162251 / 40000000000000000 : ℝ) ≤ (-(1147440024247301742847 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25277216190162251 / 40000000000000000 : ℝ) = - (25277216190162251 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25277216190162251 / 20000000000000000 : ℚ)) - (U := (585427926502698257153 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25277216190162251 / 20000000000000000 : ℝ) ≤ - (585427926502698257153 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1579409805868797 / 2500000000000000 : ℝ)) (q := - (25277216190162251 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25277216190162251 / 40000000000000000 : ℚ)) + (r' := (25277216190162251 / 20000000000000000 : ℚ)) + (U := (-(1147440024247301742847 / 2500000000000000000000 : ℚ))) + (U' := (585427926502698257153 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (1579409805868797 / 2500000000000000 : ℚ)) + (q := (25277216190162251 / 40000000000000000 : ℚ)) + (U := (-(1147440024247301742847 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_5 : Uω (aρ 5) (bρ 5) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -4967,25 +4343,21 @@ lemma U_567_5 : have hlg : Real.log (24793931965911463 / 40000000000000000 : ℝ) ≤ (-(239140254707843448427 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24793931965911463 / 40000000000000000 : ℝ) = - (24793931965911463 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24793931965911463 / 20000000000000000 : ℚ)) - (U := (107433335442156551573 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24793931965911463 / 20000000000000000 : ℝ) ≤ - (107433335442156551573 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3097093515342397 / 5000000000000000 : ℝ)) (q := - (24793931965911463 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24793931965911463 / 40000000000000000 : ℚ)) + (r' := (24793931965911463 / 20000000000000000 : ℚ)) + (U := (-(239140254707843448427 / 500000000000000000000 : ℚ))) + (U' := (107433335442156551573 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (3097093515342397 / 5000000000000000 : ℚ)) + (q := (24793931965911463 / 40000000000000000 : ℚ)) + (U := (-(239140254707843448427 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_6 : Uω (aρ 6) (bρ 6) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -4993,25 +4365,21 @@ lemma U_567_6 : have hlg : Real.log (24101419029027671 / 40000000000000000 : ℝ) ≤ (-(5066087342182747444541 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24101419029027671 / 40000000000000000 : ℝ) = - (24101419029027671 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24101419029027671 / 20000000000000000 : ℚ)) - (U := (1865384460817252555459 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24101419029027671 / 20000000000000000 : ℝ) ≤ - (1865384460817252555459 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3007585468691449 / 5000000000000000 : ℝ)) (q := - (24101419029027671 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24101419029027671 / 40000000000000000 : ℚ)) + (r' := (24101419029027671 / 20000000000000000 : ℚ)) + (U := (-(5066087342182747444541 / 10000000000000000000000 : ℚ))) + (U' := (1865384460817252555459 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (3007585468691449 / 5000000000000000 : ℚ)) + (q := (24101419029027671 / 40000000000000000 : ℚ)) + (U := (-(5066087342182747444541 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_7 : Uω (aρ 7) (bρ 7) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5019,25 +4387,21 @@ lemma U_567_7 : have hlg : Real.log (23157915034047183 / 40000000000000000 : ℝ) ≤ (-(2732714148191447201139 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23157915034047183 / 40000000000000000 : ℝ) = - (23157915034047183 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23157915034047183 / 20000000000000000 : ℚ)) - (U := (733021753308552798861 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23157915034047183 / 20000000000000000 : ℝ) ≤ - (733021753308552798861 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2883540160326327 / 5000000000000000 : ℝ)) (q := - (23157915034047183 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23157915034047183 / 40000000000000000 : ℚ)) + (r' := (23157915034047183 / 20000000000000000 : ℚ)) + (U := (-(2732714148191447201139 / 5000000000000000000000 : ℚ))) + (U' := (733021753308552798861 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (2883540160326327 / 5000000000000000 : ℚ)) + (q := (23157915034047183 / 40000000000000000 : ℚ)) + (U := (-(2732714148191447201139 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_8 : Uω (aρ 8) (bρ 8) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5045,25 +4409,21 @@ lemma U_567_8 : have hlg : Real.log (21929304326212211 / 40000000000000000 : ℝ) ≤ (-(6010556143983057996553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21929304326212211 / 40000000000000000 : ℝ) = - (21929304326212211 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21929304326212211 / 20000000000000000 : ℚ)) - (U := (920915659016942003447 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21929304326212211 / 20000000000000000 : ℝ) ≤ - (920915659016942003447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (169884894314849 / 312500000000000 : ℝ)) (q := - (21929304326212211 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21929304326212211 / 40000000000000000 : ℚ)) + (r' := (21929304326212211 / 20000000000000000 : ℚ)) + (U := (-(6010556143983057996553 / 10000000000000000000000 : ℚ))) + (U' := (920915659016942003447 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (169884894314849 / 312500000000000 : ℚ)) + (q := (21929304326212211 / 40000000000000000 : ℚ)) + (U := (-(6010556143983057996553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_9 : Uω (aρ 9) (bρ 9) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5071,25 +4431,21 @@ lemma U_567_9 : have hlg : Real.log (20394190464948549 / 40000000000000000 : ℝ) ≤ (-(168407343672909906301 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20394190464948549 / 40000000000000000 : ℝ) = - (20394190464948549 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20394190464948549 / 20000000000000000 : ℚ)) - (U := (4879451402090093699 / 250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20394190464948549 / 20000000000000000 : ℝ) ≤ - (4879451402090093699 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5009725315803337 / 10000000000000000 : ℝ)) (q := - (20394190464948549 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20394190464948549 / 40000000000000000 : ℚ)) + (r' := (20394190464948549 / 20000000000000000 : ℚ)) + (U := (-(168407343672909906301 / 250000000000000000000 : ℚ))) + (U' := (4879451402090093699 / 250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (5009725315803337 / 10000000000000000 : ℚ)) + (q := (20394190464948549 / 40000000000000000 : ℚ)) + (U := (-(168407343672909906301 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_10 : Uω (aρ 10) (bρ 10) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5097,26 +4453,21 @@ lemma U_567_10 : have hlg : Real.log (18546168162873673 / 40000000000000000 : ℝ) ≤ (-(1921540634794681486427 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18546168162873673 / 40000000000000000 : ℝ) = - (18546168162873673 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18546168162873673 / 10000000000000000 : ℚ)) - (U := (1544195266705318513573 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18546168162873673 / 10000000000000000 : ℝ) ≤ - (1544195266705318513573 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4474273198260899 / 10000000000000000 : ℝ)) (q := - (18546168162873673 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18546168162873673 / 40000000000000000 : ℚ)) + (r' := (18546168162873673 / 10000000000000000 : ℚ)) + (U := (-(1921540634794681486427 / 2500000000000000000000 : ℚ))) + (U' := (1544195266705318513573 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (4474273198260899 / 10000000000000000 : ℚ)) + (q := (18546168162873673 / 40000000000000000 : ℚ)) + (U := (-(1921540634794681486427 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_11 : Uω (aρ 11) (bρ 11) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5124,26 +4475,21 @@ lemma U_567_11 : have hlg : Real.log (3277905360743043 / 8000000000000000 : ℝ) ≤ (-(892236932291373259771 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3277905360743043 / 8000000000000000 : ℝ) = - (3277905360743043 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3277905360743043 / 2000000000000000 : ℚ)) - (U := (494057428308626740229 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3277905360743043 / 2000000000000000 : ℝ) ≤ - (494057428308626740229 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (381442914488667 / 1000000000000000 : ℝ)) (q := - (3277905360743043 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3277905360743043 / 8000000000000000 : ℚ)) + (r' := (3277905360743043 / 2000000000000000 : ℚ)) + (U := (-(892236932291373259771 / 1000000000000000000000 : ℚ))) + (U' := (494057428308626740229 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (381442914488667 / 1000000000000000 : ℚ)) + (q := (3277905360743043 / 8000000000000000 : ℚ)) + (U := (-(892236932291373259771 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_12 : Uω (aρ 12) (bρ 12) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5151,26 +4497,21 @@ lemma U_567_12 : have hlg : Real.log (13917378786151519 / 40000000000000000 : ℝ) ≤ (-(10557411220120595044881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13917378786151519 / 40000000000000000 : ℝ) = - (13917378786151519 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13917378786151519 / 10000000000000000 : ℚ)) - (U := (3305532385879404955119 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13917378786151519 / 10000000000000000 : ℝ) ≤ - (3305532385879404955119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1501027616394911 / 5000000000000000 : ℝ)) (q := - (13917378786151519 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13917378786151519 / 40000000000000000 : ℚ)) + (r' := (13917378786151519 / 10000000000000000 : ℚ)) + (U := (-(10557411220120595044881 / 10000000000000000000000 : ℚ))) + (U' := (3305532385879404955119 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (1501027616394911 / 5000000000000000 : ℚ)) + (q := (13917378786151519 / 40000000000000000 : ℚ)) + (U := (-(10557411220120595044881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_13 : Uω (aρ 13) (bρ 13) (20911761246771 / 32000000000000 : ℝ) ≤ @@ -5178,26 +4519,21 @@ lemma U_567_13 : have hlg : Real.log (11009434017866411 / 40000000000000000 : ℝ) ≤ (-(3225317275922843369361 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11009434017866411 / 40000000000000000 : ℝ) = - (11009434017866411 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11009434017866411 / 10000000000000000 : ℚ)) - (U := (240418625577156630639 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11009434017866411 / 10000000000000000 : ℝ) ≤ - (240418625577156630639 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (486866147560567 / 2500000000000000 : ℝ)) (q := - (11009434017866411 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11009434017866411 / 40000000000000000 : ℚ)) + (r' := (11009434017866411 / 10000000000000000 : ℚ)) + (U := (-(3225317275922843369361 / 2500000000000000000000 : ℚ))) + (U' := (240418625577156630639 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (20911761246771 / 32000000000000 : ℚ)) + (s := (486866147560567 / 2500000000000000 : ℚ)) + (q := (11009434017866411 / 40000000000000000 : ℚ)) + (U := (-(3225317275922843369361 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_567_14 : Uω (aρ 14) (bρ 14) (20911761246771 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U47.lean b/LeanPool/Zeta5Irrational/Table/U47.lean index 864feb9ea6..00f1b9397e 100644 --- a/LeanPool/Zeta5Irrational/Table/U47.lean +++ b/LeanPool/Zeta5Irrational/Table/U47.lean @@ -24,25 +24,21 @@ lemma U_568_1 : have hlg : Real.log (2596760383024923 / 4000000000000000 : ℝ) ≤ (-(4320296992729446895061 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2596760383024923 / 4000000000000000 : ℝ) = - (2596760383024923 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2596760383024923 / 2000000000000000 : ℚ)) - (U := (2611174810270553104939 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2596760383024923 / 2000000000000000 : ℝ) ≤ - (2611174810270553104939 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1298375210910173 / 2000000000000000 : ℝ)) (q := - (2596760383024923 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2596760383024923 / 4000000000000000 : ℚ)) + (r' := (2596760383024923 / 2000000000000000 : ℚ)) + (U := (-(4320296992729446895061 / 10000000000000000000000 : ℚ))) + (U' := (2611174810270553104939 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (1298375210910173 / 2000000000000000 : ℚ)) + (q := (2596760383024923 / 4000000000000000 : ℚ)) + (U := (-(4320296992729446895061 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_2 : Uω (aρ 2) (bρ 2) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_568_2 : have hlg : Real.log (12935985641658737 / 20000000000000000 : ℝ) ≤ (-(2178596304860126658363 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12935985641658737 / 20000000000000000 : ℝ) = - (12935985641658737 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12935985641658737 / 10000000000000000 : ℚ)) - (U := (1287139596639873341637 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12935985641658737 / 10000000000000000 : ℝ) ≤ - (1287139596639873341637 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6467828793594987 / 10000000000000000 : ℝ)) (q := - (12935985641658737 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12935985641658737 / 20000000000000000 : ℚ)) + (r' := (12935985641658737 / 10000000000000000 : ℚ)) + (U := (-(2178596304860126658363 / 5000000000000000000000 : ℚ))) + (U' := (1287139596639873341637 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (6467828793594987 / 10000000000000000 : ℚ)) + (q := (12935985641658737 / 20000000000000000 : ℚ)) + (U := (-(2178596304860126658363 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_3 : Uω (aρ 3) (bρ 3) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_568_3 : have hlg : Real.log (2568073833518273 / 4000000000000000 : ℝ) ≤ (-(553922780094374103553 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2568073833518273 / 4000000000000000 : ℝ) = - (2568073833518273 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2568073833518273 / 2000000000000000 : ℚ)) - (U := (312511195280625896447 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2568073833518273 / 2000000000000000 : ℝ) ≤ - (312511195280625896447 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1283921685175523 / 2000000000000000 : ℝ)) (q := - (2568073833518273 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2568073833518273 / 4000000000000000 : ℚ)) + (r' := (2568073833518273 / 2000000000000000 : ℚ)) + (U := (-(553922780094374103553 / 1250000000000000000000 : ℚ))) + (U' := (312511195280625896447 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (1283921685175523 / 2000000000000000 : ℚ)) + (q := (2568073833518273 / 4000000000000000 : ℚ)) + (U := (-(553922780094374103553 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_4 : Uω (aρ 4) (bρ 4) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_568_4 : have hlg : Real.log (3170403691218427 / 5000000000000000 : ℝ) ≤ (-(36446318800435169751 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3170403691218427 / 5000000000000000 : ℝ) = - (3170403691218427 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3170403691218427 / 2500000000000000 : ℚ)) - (U := (19005455623564830249 / 80000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3170403691218427 / 2500000000000000 : ℝ) ≤ - (19005455623564830249 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3169574102112479 / 5000000000000000 : ℝ)) (q := - (3170403691218427 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3170403691218427 / 5000000000000000 : ℚ)) + (r' := (3170403691218427 / 2500000000000000 : ℚ)) + (U := (-(36446318800435169751 / 80000000000000000000 : ℚ))) + (U' := (19005455623564830249 / 80000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (3169574102112479 / 5000000000000000 : ℚ)) + (q := (3170403691218427 / 5000000000000000 : ℚ)) + (U := (-(36446318800435169751 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_5 : Uω (aρ 5) (bρ 5) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_568_5 : have hlg : Real.log (12439991077158783 / 20000000000000000 : ℝ) ≤ (-(1187039758133659573379 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12439991077158783 / 20000000000000000 : ℝ) = - (12439991077158783 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12439991077158783 / 10000000000000000 : ℚ)) - (U := (545828192616340426621 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12439991077158783 / 10000000000000000 : ℝ) ≤ - (545828192616340426621 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6215714435845033 / 10000000000000000 : ℝ)) (q := - (12439991077158783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12439991077158783 / 20000000000000000 : ℚ)) + (r' := (12439991077158783 / 10000000000000000 : ℚ)) + (U := (-(1187039758133659573379 / 2500000000000000000000 : ℚ))) + (U' := (545828192616340426621 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (6215714435845033 / 10000000000000000 : ℚ)) + (q := (12439991077158783 / 20000000000000000 : ℚ)) + (U := (-(1187039758133659573379 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_6 : Uω (aρ 6) (bρ 6) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_568_6 : have hlg : Real.log (12093777425080943 / 20000000000000000 : ℝ) ≤ (-(5030412153596103091251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12093777425080943 / 20000000000000000 : ℝ) = - (12093777425080943 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12093777425080943 / 10000000000000000 : ℚ)) - (U := (1901059649403896908749 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12093777425080943 / 10000000000000000 : ℝ) ≤ - (1901059649403896908749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6036741158907193 / 10000000000000000 : ℝ)) (q := - (12093777425080943 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12093777425080943 / 20000000000000000 : ℚ)) + (r' := (12093777425080943 / 10000000000000000 : ℚ)) + (U := (-(5030412153596103091251 / 10000000000000000000000 : ℚ))) + (U' := (1901059649403896908749 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (6036741158907193 / 10000000000000000 : ℚ)) + (q := (12093777425080943 / 20000000000000000 : ℚ)) + (U := (-(5030412153596103091251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_7 : Uω (aρ 7) (bρ 7) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_568_7 : have hlg : Real.log (11622119259882059 / 20000000000000000 : ℝ) ≤ (-(5428221581310503912809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11622119259882059 / 20000000000000000 : ℝ) = - (11622119259882059 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11622119259882059 / 10000000000000000 : ℚ)) - (U := (1503250221689496087191 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11622119259882059 / 10000000000000000 : ℝ) ≤ - (1503250221689496087191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5788744374468309 / 10000000000000000 : ℝ)) (q := - (11622119259882059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11622119259882059 / 20000000000000000 : ℚ)) + (r' := (11622119259882059 / 10000000000000000 : ℚ)) + (U := (-(5428221581310503912809 / 10000000000000000000000 : ℚ))) + (U' := (1503250221689496087191 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (5788744374468309 / 10000000000000000 : ℚ)) + (q := (11622119259882059 / 20000000000000000 : ℚ)) + (U := (-(5428221581310503912809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_8 : Uω (aρ 8) (bρ 8) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_568_8 : have hlg : Real.log (5504004990447363 / 10000000000000000 : ℝ) ≤ (-(597109085408817176559 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5504004990447363 / 10000000000000000 : ℝ) = - (5504004990447363 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5504004990447363 / 5000000000000000 : ℚ)) - (U := (96038094891182823441 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5504004990447363 / 5000000000000000 : ℝ) ≤ - (96038094891182823441 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (341136046676311 / 625000000000000 : ℝ)) (q := - (5504004990447363 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5504004990447363 / 10000000000000000 : ℚ)) + (r' := (5504004990447363 / 5000000000000000 : ℚ)) + (U := (-(597109085408817176559 / 1000000000000000000000 : ℚ))) + (U' := (96038094891182823441 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (341136046676311 / 625000000000000 : ℚ)) + (q := (5504004990447363 / 10000000000000000 : ℚ)) + (U := (-(597109085408817176559 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_9 : Uω (aρ 9) (bρ 9) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_568_9 : have hlg : Real.log (10240849603025773 / 20000000000000000 : ℝ) ≤ (-(3346738440394695985477 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10240849603025773 / 20000000000000000 : ℝ) = - (10240849603025773 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10240849603025773 / 10000000000000000 : ℚ)) - (U := (118997461105304014523 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10240849603025773 / 10000000000000000 : ℝ) ≤ - (118997461105304014523 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5031981997312023 / 10000000000000000 : ℝ)) (q := - (10240849603025773 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10240849603025773 / 20000000000000000 : ℚ)) + (r' := (10240849603025773 / 10000000000000000 : ℚ)) + (U := (-(3346738440394695985477 / 5000000000000000000000 : ℚ))) + (U' := (118997461105304014523 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (5031981997312023 / 10000000000000000 : ℚ)) + (q := (10240849603025773 / 20000000000000000 : ℚ)) + (U := (-(3346738440394695985477 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_10 : Uω (aρ 10) (bρ 10) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_568_10 : have hlg : Real.log (9317631052494493 / 20000000000000000 : ℝ) ≤ (-(7638238555624362940643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9317631052494493 / 20000000000000000 : ℝ) = - (9317631052494493 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9317631052494493 / 5000000000000000 : ℚ)) - (U := (6224705050375637059357 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9317631052494493 / 5000000000000000 : ℝ) ≤ - (6224705050375637059357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4497322480275743 / 10000000000000000 : ℝ)) (q := - (9317631052494493 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9317631052494493 / 20000000000000000 : ℚ)) + (r' := (9317631052494493 / 5000000000000000 : ℚ)) + (U := (-(7638238555624362940643 / 10000000000000000000000 : ℚ))) + (U' := (6224705050375637059357 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (4497322480275743 / 10000000000000000 : ℚ)) + (q := (9317631052494493 / 20000000000000000 : ℚ)) + (U := (-(7638238555624362940643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_11 : Uω (aρ 11) (bρ 11) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_568_11 : have hlg : Real.log (2060232243149073 / 5000000000000000 : ℝ) ≤ (-(2216547990186434725099 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2060232243149073 / 5000000000000000 : ℝ) = - (2060232243149073 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2060232243149073 / 1250000000000000 : ℚ)) - (U := (1249187911313565274901 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (2060232243149073 / 1250000000000000 : ℝ) ≤ - (1249187911313565274901 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1919548513291271 / 5000000000000000 : ℝ)) (q := - (2060232243149073 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2060232243149073 / 5000000000000000 : ℚ)) + (r' := (2060232243149073 / 1250000000000000 : ℚ)) + (U := (-(2216547990186434725099 / 2500000000000000000000 : ℚ))) + (U' := (1249187911313565274901 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (1919548513291271 / 5000000000000000 : ℚ)) + (q := (2060232243149073 / 5000000000000000 : ℚ)) + (U := (-(2216547990186434725099 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_12 : Uω (aρ 12) (bρ 12) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_568_12 : have hlg : Real.log (1401692859717249 / 4000000000000000 : ℝ) ≤ (-(2621534172356183131653 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1401692859717249 / 4000000000000000 : ℝ) = - (1401692859717249 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1401692859717249 / 1000000000000000 : ℚ)) - (U := (844201729143816868347 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1401692859717249 / 1000000000000000 : ℝ) ≤ - (844201729143816868347 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (606066489851499 / 2000000000000000 : ℝ)) (q := - (1401692859717249 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1401692859717249 / 4000000000000000 : ℚ)) + (r' := (1401692859717249 / 1000000000000000 : ℚ)) + (U := (-(2621534172356183131653 / 2500000000000000000000 : ℚ))) + (U' := (844201729143816868347 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (606066489851499 / 2000000000000000 : ℚ)) + (q := (1401692859717249 / 4000000000000000 : ℚ)) + (U := (-(2621534172356183131653 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_13 : Uω (aρ 13) (bρ 13) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -339,25 +288,21 @@ lemma U_568_13 : have hlg : Real.log (695651344073957 / 2500000000000000 : ℝ) ≤ (-(12791974179380312102249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (695651344073957 / 2500000000000000 : ℝ) = - (695651344073957 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (695651344073957 / 625000000000000 : ℚ)) - (U := (1070969426619687897751 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (695651344073957 / 625000000000000 : ℝ) ≤ - (1070969426619687897751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (993230322428953 / 5000000000000000 : ℝ)) (q := - (695651344073957 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (695651344073957 / 2500000000000000 : ℚ)) + (r' := (695651344073957 / 625000000000000 : ℚ)) + (U := (-(12791974179380312102249 / 10000000000000000000000 : ℚ))) + (U' := (1070969426619687897751 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5245138462927 / 8000000000000 : ℚ)) + (s := (993230322428953 / 5000000000000000 : ℚ)) + (q := (695651344073957 / 2500000000000000 : ℚ)) + (U := (-(12791974179380312102249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_568_14 : Uω (aρ 14) (bρ 14) (5245138462927 / 8000000000000 : ℝ) ≤ @@ -464,25 +409,21 @@ lemma U_569_1 : have hlg : Real.log (13069792998988423 / 20000000000000000 : ℝ) ≤ (-(4254285836572129056119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13069792998988423 / 20000000000000000 : ℝ) = - (13069792998988423 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13069792998988423 / 10000000000000000 : ℚ)) - (U := (2677185966427870943881 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13069792998988423 / 10000000000000000 : ℝ) ≤ - (2677185966427870943881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (816858970041131 / 1250000000000000 : ℝ)) (q := - (13069792998988423 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13069792998988423 / 20000000000000000 : ℚ)) + (r' := (13069792998988423 / 10000000000000000 : ℚ)) + (U := (-(4254285836572129056119 / 10000000000000000000000 : ℚ))) + (U' := (2677185966427870943881 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (816858970041131 / 1250000000000000 : ℚ)) + (q := (13069792998988423 / 20000000000000000 : ℚ)) + (U := (-(4254285836572129056119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_2 : Uω (aρ 2) (bρ 2) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -490,25 +431,21 @@ lemma U_569_2 : have hlg : Real.log (1627747320524411 / 2500000000000000 : ℝ) ≤ (-(4290936846030395396877 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1627747320524411 / 2500000000000000 : ℝ) = - (1627747320524411 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1627747320524411 / 1250000000000000 : ℚ)) - (U := (2640534956969604603123 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1627747320524411 / 1250000000000000 : ℝ) ≤ - (2640534956969604603123 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6510826338045913 / 10000000000000000 : ℝ)) (q := - (1627747320524411 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1627747320524411 / 2500000000000000 : ℚ)) + (r' := (1627747320524411 / 1250000000000000 : ℚ)) + (U := (-(4290936846030395396877 / 10000000000000000000000 : ℚ))) + (U' := (2640534956969604603123 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (6510826338045913 / 10000000000000000 : ℚ)) + (q := (1627747320524411 / 2500000000000000 : ℚ)) + (U := (-(4290936846030395396877 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_3 : Uω (aρ 3) (bρ 3) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -516,25 +453,21 @@ lemma U_569_3 : have hlg : Real.log (12926367590057373 / 20000000000000000 : ℝ) ≤ (-(4364630488213829430073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12926367590057373 / 20000000000000000 : ℝ) = - (12926367590057373 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12926367590057373 / 10000000000000000 : ℚ)) - (U := (2566841314786170569927 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12926367590057373 / 10000000000000000 : ℝ) ≤ - (2566841314786170569927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3231305735128999 / 5000000000000000 : ℝ)) (q := - (12926367590057373 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12926367590057373 / 20000000000000000 : ℚ)) + (r' := (12926367590057373 / 10000000000000000 : ℚ)) + (U := (-(4364630488213829430073 / 10000000000000000000000 : ℚ))) + (U' := (2566841314786170569927 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (3231305735128999 / 5000000000000000 : ℚ)) + (q := (12926367590057373 / 20000000000000000 : ℚ)) + (U := (-(4364630488213829430073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_4 : Uω (aρ 4) (bρ 4) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -542,25 +475,21 @@ lemma U_569_4 : have hlg : Real.log (12767627876189017 / 20000000000000000 : ℝ) ≤ (-(448819378046638877049 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12767627876189017 / 20000000000000000 : ℝ) = - (12767627876189017 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12767627876189017 / 10000000000000000 : ℚ)) - (U := (244327802253361122951 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12767627876189017 / 10000000000000000 : ℝ) ≤ - (244327802253361122951 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3191082968727321 / 5000000000000000 : ℝ)) (q := - (12767627876189017 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12767627876189017 / 20000000000000000 : ℚ)) + (r' := (12767627876189017 / 10000000000000000 : ℚ)) + (U := (-(448819378046638877049 / 1000000000000000000000 : ℚ))) + (U' := (244327802253361122951 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (3191082968727321 / 5000000000000000 : ℚ)) + (q := (12767627876189017 / 20000000000000000 : ℚ)) + (U := (-(448819378046638877049 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_5 : Uω (aρ 5) (bρ 5) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -568,25 +497,21 @@ lemma U_569_5 : have hlg : Real.log (3131510163181529 / 5000000000000000 : ℝ) ≤ (-(935845087457148488507 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3131510163181529 / 5000000000000000 : ℝ) = - (3131510163181529 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3131510163181529 / 2500000000000000 : ℚ)) - (U := (450449273142851511493 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3131510163181529 / 2500000000000000 : ℝ) ≤ - (450449273142851511493 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6258768633326741 / 10000000000000000 : ℝ)) (q := - (3131510163181529 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3131510163181529 / 5000000000000000 : ℚ)) + (r' := (3131510163181529 / 2500000000000000 : ℚ)) + (U := (-(935845087457148488507 / 2000000000000000000000 : ℚ))) + (U' := (450449273142851511493 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (6258768633326741 / 10000000000000000 : ℚ)) + (q := (3131510163181529 / 5000000000000000 : ℚ)) + (U := (-(935845087457148488507 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_6 : Uω (aρ 6) (bρ 6) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -594,25 +519,21 @@ lemma U_569_6 : have hlg : Real.log (3044977926206299 / 5000000000000000 : ℝ) ≤ (-(1239860650579759773883 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3044977926206299 / 5000000000000000 : ℝ) = - (3044977926206299 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3044977926206299 / 2500000000000000 : ℚ)) - (U := (493007300170240226117 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3044977926206299 / 2500000000000000 : ℝ) ≤ - (493007300170240226117 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6079880060565821 / 10000000000000000 : ℝ)) (q := - (3044977926206299 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3044977926206299 / 5000000000000000 : ℚ)) + (r' := (3044977926206299 / 2500000000000000 : ℚ)) + (U := (-(1239860650579759773883 / 2500000000000000000000 : ℚ))) + (U' := (493007300170240226117 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (6079880060565821 / 10000000000000000 : ℚ)) + (q := (3044977926206299 / 5000000000000000 : ℚ)) + (U := (-(1239860650579759773883 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_7 : Uω (aρ 7) (bρ 7) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -620,25 +541,21 @@ lemma U_569_7 : have hlg : Real.log (1170843905192277 / 2000000000000000 : ℝ) ≤ (-(535422405003292823967 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1170843905192277 / 2000000000000000 : ℝ) = - (1170843905192277 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1170843905192277 / 1000000000000000 : ℚ)) - (U := (157724775296707176033 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1170843905192277 / 1000000000000000 : ℝ) ≤ - (157724775296707176033 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1166413757684679 / 2000000000000000 : ℝ)) (q := - (1170843905192277 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1170843905192277 / 2000000000000000 : ℚ)) + (r' := (1170843905192277 / 1000000000000000 : ℚ)) + (U := (-(535422405003292823967 / 1000000000000000000000 : ℚ))) + (U' := (157724775296707176033 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (1166413757684679 / 2000000000000000 : ℚ)) + (q := (1170843905192277 / 2000000000000000 : ℚ)) + (U := (-(535422405003292823967 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_8 : Uω (aρ 8) (bρ 8) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -646,25 +563,21 @@ lemma U_569_8 : have hlg : Real.log (221894340956473 / 400000000000000 : ℝ) ≤ (-(589263219909437068171 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (221894340956473 / 400000000000000 : ℝ) = - (221894340956473 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (221894340956473 / 200000000000000 : ℚ)) - (U := (103883960390562931829 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (221894340956473 / 200000000000000 : ℝ) ≤ - (103883960390562931829 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (220075537426571 / 400000000000000 : ℝ)) (q := - (221894340956473 / 400000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (221894340956473 / 400000000000000 : ℚ)) + (r' := (221894340956473 / 200000000000000 : ℚ)) + (U := (-(589263219909437068171 / 1000000000000000000000 : ℚ))) + (U' := (103883960390562931829 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (220075537426571 / 400000000000000 : ℚ)) + (q := (221894340956473 / 400000000000000 : ℚ)) + (U := (-(589263219909437068171 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_9 : Uω (aρ 9) (bρ 9) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -672,25 +585,21 @@ lemma U_569_9 : have hlg : Real.log (10328338718797059 / 20000000000000000 : ℝ) ≤ (-(826051030152510713157 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10328338718797059 / 20000000000000000 : ℝ) = - (10328338718797059 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10328338718797059 / 10000000000000000 : ℚ)) - (U := (40382945222489286843 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10328338718797059 / 10000000000000000 : ℝ) ≤ - (40382945222489286843 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1269118933749421 / 2500000000000000 : ℝ)) (q := - (10328338718797059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10328338718797059 / 20000000000000000 : ℚ)) + (r' := (10328338718797059 / 10000000000000000 : ℚ)) + (U := (-(826051030152510713157 / 1250000000000000000000 : ℚ))) + (U' := (40382945222489286843 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (1269118933749421 / 2500000000000000 : ℚ)) + (q := (10328338718797059 / 20000000000000000 : ℚ)) + (U := (-(826051030152510713157 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_10 : Uω (aρ 10) (bρ 10) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -698,26 +607,21 @@ lemma U_569_10 : have hlg : Real.log (4703339677788387 / 10000000000000000 : ℝ) ≤ (-(7543122663510840268807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4703339677788387 / 10000000000000000 : ℝ) = - (4703339677788387 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4703339677788387 / 2500000000000000 : ℚ)) - (U := (6319820942489159731193 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4703339677788387 / 2500000000000000 : ℝ) ≤ - (6319820942489159731193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4543375405272399 / 10000000000000000 : ℝ)) (q := - (4703339677788387 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4703339677788387 / 10000000000000000 : ℚ)) + (r' := (4703339677788387 / 2500000000000000 : ℚ)) + (U := (-(7543122663510840268807 / 10000000000000000000000 : ℚ))) + (U' := (6319820942489159731193 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (4543375405272399 / 10000000000000000 : ℚ)) + (q := (4703339677788387 / 10000000000000000 : ℚ)) + (U := (-(7543122663510840268807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_11 : Uω (aρ 11) (bρ 11) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -725,26 +629,21 @@ lemma U_569_11 : have hlg : Real.log (8333147197724503 / 20000000000000000 : ℝ) ≤ (-(1750982146713054436347 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8333147197724503 / 20000000000000000 : ℝ) = - (8333147197724503 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8333147197724503 / 5000000000000000 : ℚ)) - (U := (1021606574486945563653 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8333147197724503 / 5000000000000000 : ℝ) ≤ - (1021606574486945563653 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (486039984203141 / 1250000000000000 : ℝ)) (q := - (8333147197724503 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8333147197724503 / 20000000000000000 : ℚ)) + (r' := (8333147197724503 / 5000000000000000 : ℚ)) + (U := (-(1750982146713054436347 / 2000000000000000000000 : ℚ))) + (U' := (1021606574486945563653 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (486039984203141 / 1250000000000000 : ℚ)) + (q := (8333147197724503 / 20000000000000000 : ℚ)) + (U := (-(1750982146713054436347 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_12 : Uω (aρ 12) (bρ 12) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -752,26 +651,21 @@ lemma U_569_12 : have hlg : Real.log (1421537228018487 / 4000000000000000 : ℝ) ≤ (-(5172777597921439708851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1421537228018487 / 4000000000000000 : ℝ) = - (1421537228018487 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1421537228018487 / 1000000000000000 : ℚ)) - (U := (1758694205078560291149 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1421537228018487 / 1000000000000000 : ℝ) ≤ - (1758694205078560291149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (154327945633903 / 500000000000000 : ℝ)) (q := - (1421537228018487 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1421537228018487 / 4000000000000000 : ℚ)) + (r' := (1421537228018487 / 1000000000000000 : ℚ)) + (U := (-(5172777597921439708851 / 5000000000000000000000 : ℚ))) + (U' := (1758694205078560291149 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (154327945633903 / 500000000000000 : ℚ)) + (q := (1421537228018487 / 4000000000000000 : ℚ)) + (U := (-(5172777597921439708851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_13 : Uω (aρ 13) (bρ 13) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -779,25 +673,21 @@ lemma U_569_13 : have hlg : Real.log (284232971293049 / 1000000000000000 : ℝ) ≤ (-(393112829726998233739 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (284232971293049 / 1000000000000000 : ℝ) = - (284232971293049 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (284232971293049 / 250000000000000 : ℚ)) - (U := (40104157960501766261 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (284232971293049 / 250000000000000 : ℝ) ≤ - (40104157960501766261 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (412582788008321 / 2000000000000000 : ℝ)) (q := - (284232971293049 / 1000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (284232971293049 / 1000000000000000 : ℚ)) + (r' := (284232971293049 / 250000000000000 : ℚ)) + (U := (-(393112829726998233739 / 312500000000000000000 : ℚ))) + (U' := (40104157960501766261 / 312500000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10559069530791 / 16000000000000 : ℚ)) + (s := (412582788008321 / 2000000000000000 : ℚ)) + (q := (284232971293049 / 1000000000000000 : ℚ)) + (U := (-(393112829726998233739 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_569_14 : Uω (aρ 14) (bρ 14) (10559069530791 / 16000000000000 : ℝ) ≤ @@ -903,25 +793,21 @@ lemma U_570_1 : have hlg : Real.log (6577892039284187 / 10000000000000000 : ℝ) ≤ (-(4188707574941079792709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6577892039284187 / 10000000000000000 : ℝ) = - (6577892039284187 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6577892039284187 / 5000000000000000 : ℚ)) - (U := (2742764228058920207291 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6577892039284187 / 5000000000000000 : ℝ) ≤ - (2742764228058920207291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3288933730911687 / 5000000000000000 : ℝ)) (q := - (6577892039284187 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6577892039284187 / 10000000000000000 : ℚ)) + (r' := (6577892039284187 / 5000000000000000 : ℚ)) + (U := (-(4188707574941079792709 / 10000000000000000000000 : ℚ))) + (U' := (2742764228058920207291 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (3288933730911687 / 5000000000000000 : ℚ)) + (q := (6577892039284187 / 10000000000000000 : ℚ)) + (U := (-(4188707574941079792709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_2 : Uω (aρ 2) (bρ 2) (664241383483 / 1000000000000 : ℝ) ≤ @@ -929,25 +815,21 @@ lemma U_570_2 : have hlg : Real.log (2621594291661379 / 4000000000000000 : ℝ) ≤ (-(4225117198853214904403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2621594291661379 / 4000000000000000 : ℝ) = - (2621594291661379 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2621594291661379 / 2000000000000000 : ℚ)) - (U := (2706354604146785095597 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2621594291661379 / 2000000000000000 : ℝ) ≤ - (2706354604146785095597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1310764770814379 / 2000000000000000 : ℝ)) (q := - (2621594291661379 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2621594291661379 / 4000000000000000 : ℚ)) + (r' := (2621594291661379 / 2000000000000000 : ℚ)) + (U := (-(4225117198853214904403 / 10000000000000000000000 : ℚ))) + (U' := (2706354604146785095597 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (1310764770814379 / 2000000000000000 : ℚ)) + (q := (2621594291661379 / 4000000000000000 : ℚ)) + (U := (-(4225117198853214904403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_3 : Uω (aρ 3) (bρ 3) (664241383483 / 1000000000000 : ℝ) ≤ @@ -955,24 +837,21 @@ lemma U_570_3 : have hlg : Real.log (65061829555909 / 100000000000000 : ℝ) ≤ (-(429832144022243457453 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (65061829555909 / 100000000000000 : ℝ) = (65061829555909 / 50000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65061829555909 / 50000000000000 : ℚ)) - (U := (263315036277756542547 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (65061829555909 / 50000000000000 : ℝ) ≤ - (263315036277756542547 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8132018016621 / 12500000000000 : ℝ)) (q := - (65061829555909 / 100000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65061829555909 / 100000000000000 : ℚ)) + (r' := (65061829555909 / 50000000000000 : ℚ)) + (U := (-(429832144022243457453 / 1000000000000000000000 : ℚ))) + (U' := (263315036277756542547 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (8132018016621 / 12500000000000 : ℚ)) + (q := (65061829555909 / 100000000000000 : ℚ)) + (U := (-(429832144022243457453 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_4 : Uω (aρ 4) (bρ 4) (664241383483 / 1000000000000 : ℝ) ≤ @@ -980,25 +859,21 @@ lemma U_570_4 : have hlg : Real.log (3213410172059717 / 5000000000000000 : ℝ) ≤ (-(552631475048740095093 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3213410172059717 / 5000000000000000 : ℝ) = - (3213410172059717 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3213410172059717 / 2500000000000000 : ℚ)) - (U := (313802500326259904907 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3213410172059717 / 2500000000000000 : ℝ) ≤ - (313802500326259904907 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1606295842854717 / 2500000000000000 : ℝ)) (q := - (3213410172059717 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3213410172059717 / 5000000000000000 : ℚ)) + (r' := (3213410172059717 / 2500000000000000 : ℚ)) + (U := (-(552631475048740095093 / 1250000000000000000000 : ℚ))) + (U' := (313802500326259904907 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (1606295842854717 / 2500000000000000 : ℚ)) + (q := (3213410172059717 / 5000000000000000 : ℚ)) + (U := (-(552631475048740095093 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_5 : Uω (aρ 5) (bρ 5) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1006,25 +881,21 @@ lemma U_570_5 : have hlg : Real.log (6306044712565743 / 10000000000000000 : ℝ) ≤ (-(4610764411565489378927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6306044712565743 / 10000000000000000 : ℝ) = - (6306044712565743 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6306044712565743 / 5000000000000000 : ℚ)) - (U := (2320707391434510621073 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6306044712565743 / 5000000000000000 : ℝ) ≤ - (2320707391434510621073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3150911013823243 / 5000000000000000 : ℝ)) (q := - (6306044712565743 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6306044712565743 / 10000000000000000 : ℚ)) + (r' := (6306044712565743 / 5000000000000000 : ℚ)) + (U := (-(4610764411565489378927 / 10000000000000000000000 : ℚ))) + (U' := (2320707391434510621073 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (3150911013823243 / 5000000000000000 : ℚ)) + (q := (6306044712565743 / 10000000000000000 : ℚ)) + (U := (-(4610764411565489378927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_6 : Uω (aρ 6) (bρ 6) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1032,25 +903,21 @@ lemma U_570_6 : have hlg : Real.log (6133021982790739 / 10000000000000000 : ℝ) ≤ (-(2444487408756060489599 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6133021982790739 / 10000000000000000 : ℝ) = - (6133021982790739 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6133021982790739 / 5000000000000000 : ℚ)) - (U := (1021248492743939510401 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6133021982790739 / 5000000000000000 : ℝ) ≤ - (1021248492743939510401 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3061508471618239 / 5000000000000000 : ℝ)) (q := - (6133021982790739 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6133021982790739 / 10000000000000000 : ℚ)) + (r' := (6133021982790739 / 5000000000000000 : ℚ)) + (U := (-(2444487408756060489599 / 5000000000000000000000 : ℚ))) + (U' := (1021248492743939510401 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (3061508471618239 / 5000000000000000 : ℚ)) + (q := (6133021982790739 / 10000000000000000 : ℚ)) + (U := (-(2444487408756060489599 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_7 : Uω (aρ 7) (bρ 7) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1058,25 +925,21 @@ lemma U_570_7 : have hlg : Real.log (1474344251231207 / 2500000000000000 : ℝ) ≤ (-(5280774161118552785937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1474344251231207 / 2500000000000000 : ℝ) = - (1474344251231207 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1474344251231207 / 1250000000000000 : ℚ)) - (U := (1650697641881447214063 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1474344251231207 / 1250000000000000 : ℝ) ≤ - (1650697641881447214063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (367211773016541 / 625000000000000 : ℝ)) (q := - (1474344251231207 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1474344251231207 / 2500000000000000 : ℚ)) + (r' := (1474344251231207 / 1250000000000000 : ℚ)) + (U := (-(5280774161118552785937 / 10000000000000000000000 : ℚ))) + (U' := (1650697641881447214063 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (367211773016541 / 625000000000000 : ℚ)) + (q := (1474344251231207 / 2500000000000000 : ℚ)) + (U := (-(5280774161118552785937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_8 : Uω (aρ 8) (bρ 8) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1084,25 +947,21 @@ lemma U_570_8 : have hlg : Real.log (11181412915014739 / 20000000000000000 : ℝ) ≤ (-(5814794347494712517697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11181412915014739 / 20000000000000000 : ℝ) = - (11181412915014739 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11181412915014739 / 10000000000000000 : ℚ)) - (U := (1116677455505287482303 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11181412915014739 / 10000000000000000 : ℝ) ≤ - (1116677455505287482303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5545588924769739 / 10000000000000000 : ℝ)) (q := - (11181412915014739 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11181412915014739 / 20000000000000000 : ℚ)) + (r' := (11181412915014739 / 10000000000000000 : ℚ)) + (U := (-(5814794347494712517697 / 10000000000000000000000 : ℚ))) + (U' := (1116677455505287482303 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (5545588924769739 / 10000000000000000 : ℚ)) + (q := (11181412915014739 / 20000000000000000 : ℚ)) + (U := (-(5814794347494712517697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_9 : Uω (aρ 9) (bρ 9) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1110,25 +969,21 @@ lemma U_570_9 : have hlg : Real.log (5207901117902643 / 10000000000000000 : ℝ) ≤ (-(1631020436464782829367 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5207901117902643 / 10000000000000000 : ℝ) = - (5207901117902643 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5207901117902643 / 5000000000000000 : ℚ)) - (U := (101847514285217170633 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5207901117902643 / 5000000000000000 : ℝ) ≤ - (101847514285217170633 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2560471936960143 / 5000000000000000 : ℝ)) (q := - (5207901117902643 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5207901117902643 / 10000000000000000 : ℚ)) + (r' := (5207901117902643 / 5000000000000000 : ℚ)) + (U := (-(1631020436464782829367 / 2500000000000000000000 : ℚ))) + (U' := (101847514285217170633 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (2560471936960143 / 5000000000000000 : ℚ)) + (q := (5207901117902643 / 10000000000000000 : ℚ)) + (U := (-(1631020436464782829367 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_10 : Uω (aρ 10) (bρ 10) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1136,26 +991,21 @@ lemma U_570_10 : have hlg : Real.log (2373917083235651 / 5000000000000000 : ℝ) ≤ (-(744896543364644492559 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2373917083235651 / 5000000000000000 : ℝ) = - (2373917083235651 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2373917083235651 / 1250000000000000 : ℚ)) - (U := (641397817235355507441 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2373917083235651 / 1250000000000000 : ℝ) ≤ - (641397817235355507441 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1147342251138151 / 2500000000000000 : ℝ)) (q := - (2373917083235651 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2373917083235651 / 5000000000000000 : ℚ)) + (r' := (2373917083235651 / 1250000000000000 : ℚ)) + (U := (-(744896543364644492559 / 1000000000000000000000 : ℚ))) + (U' := (641397817235355507441 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (1147342251138151 / 2500000000000000 : ℚ)) + (q := (2373917083235651 / 5000000000000000 : ℚ)) + (U := (-(744896543364644492559 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_11 : Uω (aρ 11) (bρ 11) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1163,25 +1013,21 @@ lemma U_570_11 : have hlg : Real.log (263288111602721 / 625000000000000 : ℝ) ≤ (-(4322513676307216232947 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (263288111602721 / 625000000000000 : ℝ) = - (263288111602721 / 156250000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (263288111602721 / 156250000000000 : ℚ)) - (U := (2608958126692783767053 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (263288111602721 / 156250000000000 : ℝ) ≤ - (2608958126692783767053 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (492174608637759 / 1250000000000000 : ℝ)) (q := - (263288111602721 / 625000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (263288111602721 / 625000000000000 : ℚ)) + (r' := (263288111602721 / 156250000000000 : ℚ)) + (U := (-(4322513676307216232947 / 5000000000000000000000 : ℚ))) + (U' := (2608958126692783767053 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (492174608637759 / 1250000000000000 : ℚ)) + (q := (263288111602721 / 625000000000000 : ℚ)) + (U := (-(4322513676307216232947 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_12 : Uω (aρ 12) (bρ 12) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1189,26 +1035,21 @@ lemma U_570_12 : have hlg : Real.log (1441298046235793 / 4000000000000000 : ℝ) ≤ (-(10207502320509313781759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1441298046235793 / 4000000000000000 : ℝ) = - (1441298046235793 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1441298046235793 / 1000000000000000 : ℚ)) - (U := (3655441285490686218241 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1441298046235793 / 1000000000000000 : ℝ) ≤ - (3655441285490686218241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (628473525135793 / 2000000000000000 : ℝ)) (q := - (1441298046235793 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1441298046235793 / 4000000000000000 : ℚ)) + (r' := (1441298046235793 / 1000000000000000 : ℚ)) + (U := (-(10207502320509313781759 / 10000000000000000000000 : ℚ))) + (U' := (3655441285490686218241 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (628473525135793 / 2000000000000000 : ℚ)) + (q := (1441298046235793 / 4000000000000000 : ℚ)) + (U := (-(10207502320509313781759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_13 : Uω (aρ 13) (bρ 13) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1216,26 +1057,21 @@ lemma U_570_13 : have hlg : Real.log (5802239205317251 / 20000000000000000 : ℝ) ≤ (-(6187441800526216948877 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5802239205317251 / 20000000000000000 : ℝ) = - (5802239205317251 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5802239205317251 / 5000000000000000 : ℚ)) - (U := (744030002473783051123 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5802239205317251 / 5000000000000000 : ℝ) ≤ - (744030002473783051123 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2137498341412251 / 10000000000000000 : ℝ)) (q := - (5802239205317251 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5802239205317251 / 20000000000000000 : ℚ)) + (r' := (5802239205317251 / 5000000000000000 : ℚ)) + (U := (-(6187441800526216948877 / 5000000000000000000000 : ℚ))) + (U' := (744030002473783051123 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (664241383483 / 1000000000000 : ℚ)) + (s := (2137498341412251 / 10000000000000000 : ℚ)) + (q := (5802239205317251 / 20000000000000000 : ℚ)) + (U := (-(6187441800526216948877 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_570_14 : Uω (aρ 14) (bρ 14) (664241383483 / 1000000000000 : ℝ) ≤ @@ -1343,25 +1179,21 @@ lemma U_571_1 : have hlg : Real.log (26376467391064129 / 40000000000000000 : ℝ) ≤ (-(4164072279252109276981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26376467391064129 / 40000000000000000 : ℝ) = - (26376467391064129 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26376467391064129 / 20000000000000000 : ℚ)) - (U := (2767399523747890723019 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26376467391064129 / 20000000000000000 : ℝ) ≤ - (2767399523747890723019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3297046165389001 / 5000000000000000 : ℝ)) (q := - (26376467391064129 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26376467391064129 / 40000000000000000 : ℚ)) + (r' := (26376467391064129 / 20000000000000000 : ℚ)) + (U := (-(4164072279252109276981 / 10000000000000000000000 : ℚ))) + (U' := (2767399523747890723019 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (3297046165389001 / 5000000000000000 : ℚ)) + (q := (26376467391064129 / 40000000000000000 : ℚ)) + (U := (-(4164072279252109276981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_2 : Uω (aρ 2) (bρ 2) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1369,25 +1201,21 @@ lemma U_571_2 : have hlg : Real.log (26280843507653277 / 40000000000000000 : ℝ) ≤ (-(1050097909525026300293 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26280843507653277 / 40000000000000000 : ℝ) = - (26280843507653277 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26280843507653277 / 20000000000000000 : ℚ)) - (U := (682770041224973699707 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26280843507653277 / 20000000000000000 : ℝ) ≤ - (682770041224973699707 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410628087598911 / 625000000000000 : ℝ)) (q := - (26280843507653277 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26280843507653277 / 40000000000000000 : ℚ)) + (r' := (26280843507653277 / 20000000000000000 : ℚ)) + (U := (-(1050097909525026300293 / 2500000000000000000000 : ℚ))) + (U' := (682770041224973699707 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (410628087598911 / 625000000000000 : ℚ)) + (q := (26280843507653277 / 40000000000000000 : ℚ)) + (U := (-(1050097909525026300293 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_3 : Uω (aρ 3) (bρ 3) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1395,25 +1223,21 @@ lemma U_571_3 : have hlg : Real.log (26089636471977857 / 40000000000000000 : ℝ) ≤ (-(4273412884176880161469 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26089636471977857 / 40000000000000000 : ℝ) = - (26089636471977857 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26089636471977857 / 20000000000000000 : ℚ)) - (U := (2658058918823119838531 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26089636471977857 / 20000000000000000 : ℝ) ≤ - (2658058918823119838531 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3260920995047433 / 5000000000000000 : ℝ)) (q := - (26089636471977857 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26089636471977857 / 40000000000000000 : ℚ)) + (r' := (26089636471977857 / 20000000000000000 : ℚ)) + (U := (-(4273412884176880161469 / 10000000000000000000000 : ℚ))) + (U' := (2658058918823119838531 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (3260920995047433 / 5000000000000000 : ℚ)) + (q := (26089636471977857 / 40000000000000000 : ℚ)) + (U := (-(4273412884176880161469 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_4 : Uω (aρ 4) (bρ 4) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1421,25 +1245,21 @@ lemma U_571_4 : have hlg : Real.log (5154439372292431 / 8000000000000000 : ℝ) ≤ (-(549478980034508885777 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5154439372292431 / 8000000000000000 : ℝ) = - (5154439372292431 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5154439372292431 / 4000000000000000 : ℚ)) - (U := (316954995340491114223 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5154439372292431 / 4000000000000000 : ℝ) ≤ - (316954995340491114223 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1288283273180403 / 2000000000000000 : ℝ)) (q := - (5154439372292431 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5154439372292431 / 8000000000000000 : ℚ)) + (r' := (5154439372292431 / 4000000000000000 : ℚ)) + (U := (-(549478980034508885777 / 1250000000000000000000 : ℚ))) + (U' := (316954995340491114223 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (1288283273180403 / 2000000000000000 : ℚ)) + (q := (5154439372292431 / 8000000000000000 : ℚ)) + (U := (-(549478980034508885777 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_5 : Uω (aρ 5) (bρ 5) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1447,25 +1267,21 @@ lemma U_571_5 : have hlg : Real.log (5057824243530933 / 8000000000000000 : ℝ) ≤ (-(4585051419903753167239 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5057824243530933 / 8000000000000000 : ℝ) = - (5057824243530933 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5057824243530933 / 4000000000000000 : ℚ)) - (U := (2346420383096246832761 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5057824243530933 / 4000000000000000 : ℝ) ≤ - (2346420383096246832761 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (631806846333327 / 1000000000000000 : ℝ)) (q := - (5057824243530933 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5057824243530933 / 8000000000000000 : ℚ)) + (r' := (5057824243530933 / 4000000000000000 : ℚ)) + (U := (-(4585051419903753167239 / 10000000000000000000000 : ℚ))) + (U' := (2346420383096246832761 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (631806846333327 / 1000000000000000 : ℚ)) + (q := (5057824243530933 / 8000000000000000 : ℚ)) + (U := (-(4585051419903753167239 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_6 : Uω (aρ 6) (bρ 6) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1473,25 +1289,21 @@ lemma U_571_6 : have hlg : Real.log (4919418537551503 / 8000000000000000 : ℝ) ≤ (-(303907000827735205621 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4919418537551503 / 8000000000000000 : ℝ) = - (4919418537551503 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4919418537551503 / 4000000000000000 : ℚ)) - (U := (129309986859764794379 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4919418537551503 / 4000000000000000 : ℝ) ≤ - (129309986859764794379 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1227858914704939 / 2000000000000000 : ℝ)) (q := - (4919418537551503 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4919418537551503 / 8000000000000000 : ℚ)) + (r' := (4919418537551503 / 4000000000000000 : ℚ)) + (U := (-(303907000827735205621 / 625000000000000000000 : ℚ))) + (U' := (129309986859764794379 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (1227858914704939 / 2000000000000000 : ℚ)) + (q := (4919418537551503 / 8000000000000000 : ℚ)) + (U := (-(303907000827735205621 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_7 : Uω (aρ 7) (bρ 7) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1499,25 +1311,21 @@ lemma U_571_7 : have hlg : Real.log (23654649224803619 / 40000000000000000 : ℝ) ≤ (-(65664971709746093159 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23654649224803619 / 40000000000000000 : ℝ) = - (23654649224803619 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23654649224803619 / 20000000000000000 : ℚ)) - (U := (20978425827753906841 / 125000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23654649224803619 / 20000000000000000 : ℝ) ≤ - (20978425827753906841 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5891734222807747 / 10000000000000000 : ℝ)) (q := - (23654649224803619 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23654649224803619 / 40000000000000000 : ℚ)) + (r' := (23654649224803619 / 20000000000000000 : ℚ)) + (U := (-(65664971709746093159 / 125000000000000000000 : ℚ))) + (U' := (20978425827753906841 / 125000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (5891734222807747 / 10000000000000000 : ℚ)) + (q := (23654649224803619 / 40000000000000000 : ℚ)) + (U := (-(65664971709746093159 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_8 : Uω (aρ 8) (bρ 8) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1525,25 +1333,21 @@ lemma U_571_8 : have hlg : Real.log (22428251271400941 / 40000000000000000 : ℝ) ≤ (-(1446395180466007862889 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22428251271400941 / 40000000000000000 : ℝ) = - (22428251271400941 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22428251271400941 / 20000000000000000 : ℚ)) - (U := (286472770283992137111 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22428251271400941 / 20000000000000000 : ℝ) ≤ - (286472770283992137111 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (695259612180801 / 1250000000000000 : ℝ)) (q := - (22428251271400941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22428251271400941 / 40000000000000000 : ℚ)) + (r' := (22428251271400941 / 20000000000000000 : ℚ)) + (U := (-(1446395180466007862889 / 2500000000000000000000 : ℚ))) + (U' := (286472770283992137111 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (695259612180801 / 1250000000000000 : ℚ)) + (q := (22428251271400941 / 40000000000000000 : ℚ)) + (U := (-(1446395180466007862889 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_9 : Uω (aρ 9) (bρ 9) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1551,25 +1355,21 @@ lemma U_571_9 : have hlg : Real.log (20897601955097881 / 40000000000000000 : ℝ) ≤ (-(324622520228389607363 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20897601955097881 / 40000000000000000 : ℝ) = - (20897601955097881 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20897601955097881 / 20000000000000000 : ℚ)) - (U := (21951069921610392637 / 500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20897601955097881 / 20000000000000000 : ℝ) ≤ - (21951069921610392637 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2568858933827439 / 5000000000000000 : ℝ)) (q := - (20897601955097881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20897601955097881 / 40000000000000000 : ℚ)) + (r' := (20897601955097881 / 20000000000000000 : ℚ)) + (U := (-(324622520228389607363 / 500000000000000000000 : ℚ))) + (U' := (21951069921610392637 / 500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (2568858933827439 / 5000000000000000 : ℚ)) + (q := (20897601955097881 / 40000000000000000 : ℚ)) + (U := (-(324622520228389607363 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_10 : Uω (aρ 10) (bρ 10) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1577,26 +1377,21 @@ lemma U_571_10 : have hlg : Real.log (19058468373957353 / 40000000000000000 : ℝ) ≤ (-(1482735833462658137863 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19058468373957353 / 40000000000000000 : ℝ) = - (19058468373957353 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19058468373957353 / 10000000000000000 : ℚ)) - (U := (1289852887737341862137 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19058468373957353 / 10000000000000000 : ℝ) ≤ - (1289852887737341862137 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2303355055289807 / 5000000000000000 : ℝ)) (q := - (19058468373957353 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19058468373957353 / 40000000000000000 : ℚ)) + (r' := (19058468373957353 / 10000000000000000 : ℚ)) + (U := (-(1482735833462658137863 / 2000000000000000000000 : ℚ))) + (U' := (1289852887737341862137 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (2303355055289807 / 5000000000000000 : ℚ)) + (q := (19058468373957353 / 40000000000000000 : ℚ)) + (U := (-(1482735833462658137863 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_11 : Uω (aρ 11) (bρ 11) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1604,26 +1399,21 @@ lemma U_571_11 : have hlg : Real.log (16919854485250991 / 40000000000000000 : ℝ) ≤ (-(4301958498077105265997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16919854485250991 / 40000000000000000 : ℝ) = - (16919854485250991 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16919854485250991 / 10000000000000000 : ℚ)) - (U := (2629513304922894734003 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16919854485250991 / 10000000000000000 : ℝ) ≤ - (2629513304922894734003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3955879792431433 / 10000000000000000 : ℝ)) (q := - (16919854485250991 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16919854485250991 / 40000000000000000 : ℚ)) + (r' := (16919854485250991 / 10000000000000000 : ℚ)) + (U := (-(4301958498077105265997 / 5000000000000000000000 : ℚ))) + (U' := (2629513304922894734003 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (3955879792431433 / 10000000000000000 : ℚ)) + (q := (16919854485250991 / 40000000000000000 : ℚ)) + (U := (-(4301958498077105265997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_12 : Uω (aρ 12) (bρ 12) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1631,26 +1421,21 @@ lemma U_571_12 : have hlg : Real.log (14487341928941459 / 40000000000000000 : ℝ) ≤ (-(10156041558459248697277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14487341928941459 / 40000000000000000 : ℝ) = - (14487341928941459 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14487341928941459 / 10000000000000000 : ℚ)) - (U := (3706902047540751302723 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14487341928941459 / 10000000000000000 : ℝ) ≤ - (3706902047540751302723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3163323610961667 / 10000000000000000 : ℝ)) (q := - (14487341928941459 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14487341928941459 / 40000000000000000 : ℚ)) + (r' := (14487341928941459 / 10000000000000000 : ℚ)) + (U := (-(10156041558459248697277 / 10000000000000000000000 : ℚ))) + (U' := (3706902047540751302723 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (3163323610961667 / 10000000000000000 : ℚ)) + (q := (14487341928941459 / 40000000000000000 : ℚ)) + (U := (-(10156041558459248697277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_13 : Uω (aρ 13) (bρ 13) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1658,26 +1443,21 @@ lemma U_571_13 : have hlg : Real.log (11692326769761003 / 40000000000000000 : ℝ) ≤ (-(614973329293170409787 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11692326769761003 / 40000000000000000 : ℝ) = - (11692326769761003 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11692326769761003 / 10000000000000000 : ℚ)) - (U := (78173851006829590213 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11692326769761003 / 10000000000000000 : ℝ) ≤ - (78173851006829590213 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2165197772966439 / 10000000000000000 : ℝ)) (q := - (11692326769761003 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11692326769761003 / 40000000000000000 : ℚ)) + (r' := (11692326769761003 / 10000000000000000 : ℚ)) + (U := (-(614973329293170409787 / 500000000000000000000 : ℚ))) + (U' := (78173851006829590213 / 500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (2165197772966439 / 10000000000000000 : ℚ)) + (q := (11692326769761003 / 40000000000000000 : ℚ)) + (U := (-(614973329293170409787 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_14 : Uω (aρ 14) (bρ 14) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1685,26 +1465,21 @@ lemma U_571_14 : have hlg : Real.log (7331410570258827 / 40000000000000000 : ℝ) ≤ (-(16967115179877088640491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7331410570258827 / 40000000000000000 : ℝ) = - (7331410570258827 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7331410570258827 / 5000000000000000 : ℚ)) - (U := (3827300229122911359509 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7331410570258827 / 5000000000000000 : ℝ) ≤ - (3827300229122911359509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (328666958260351 / 10000000000000000 : ℝ)) (q := - (7331410570258827 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7331410570258827 / 40000000000000000 : ℚ)) + (r' := (7331410570258827 / 5000000000000000 : ℚ)) + (U := (-(16967115179877088640491 / 10000000000000000000000 : ℚ))) + (U' := (3827300229122911359509 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (4261528693017 / 6400000000000 : ℚ)) + (s := (328666958260351 / 10000000000000000 : ℚ)) + (q := (7331410570258827 / 40000000000000000 : ℚ)) + (U := (-(16967115179877088640491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_571_15 : Uω (aρ 15) (bρ 15) (4261528693017 / 6400000000000 : ℝ) ≤ @@ -1805,25 +1580,21 @@ lemma U_572_1 : have hlg : Real.log (330517082797551 / 500000000000000 : ℝ) ≤ (-(2069748762339204639219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (330517082797551 / 500000000000000 : ℝ) = - (330517082797551 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (330517082797551 / 250000000000000 : ℚ)) - (U := (1395987139160795360781 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (330517082797551 / 250000000000000 : ℝ) ≤ - (1395987139160795360781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1322063439827783 / 2000000000000000 : ℝ)) (q := - (330517082797551 / 500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (330517082797551 / 500000000000000 : ℚ)) + (r' := (330517082797551 / 250000000000000 : ℚ)) + (U := (-(2069748762339204639219 / 5000000000000000000000 : ℚ))) + (U' := (1395987139160795360781 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (1322063439827783 / 2000000000000000 : ℚ)) + (q := (330517082797551 / 500000000000000 : ℚ)) + (U := (-(2069748762339204639219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_2 : Uω (aρ 2) (bρ 2) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1831,25 +1602,21 @@ lemma U_572_2 : have hlg : Real.log (13172872045407273 / 20000000000000000 : ℝ) ≤ (-(4175727064915972273783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13172872045407273 / 20000000000000000 : ℝ) = - (13172872045407273 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13172872045407273 / 10000000000000000 : ℚ)) - (U := (2755744738084027726217 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13172872045407273 / 10000000000000000 : ℝ) ≤ - (2755744738084027726217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1646568736288537 / 2500000000000000 : ℝ)) (q := - (13172872045407273 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13172872045407273 / 20000000000000000 : ℚ)) + (r' := (13172872045407273 / 10000000000000000 : ℚ)) + (U := (-(4175727064915972273783 / 10000000000000000000000 : ℚ))) + (U' := (2755744738084027726217 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (1646568736288537 / 2500000000000000 : ℚ)) + (q := (13172872045407273 / 20000000000000000 : ℚ)) + (U := (-(4175727064915972273783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_3 : Uω (aρ 3) (bρ 3) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1857,25 +1624,21 @@ lemma U_572_3 : have hlg : Real.log (13077270546755097 / 20000000000000000 : ℝ) ≤ (-(4248566228358807393553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13077270546755097 / 20000000000000000 : ℝ) = - (13077270546755097 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13077270546755097 / 10000000000000000 : ℚ)) - (U := (2682905574641192606447 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13077270546755097 / 10000000000000000 : ℝ) ≤ - (2682905574641192606447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1634517388212993 / 2500000000000000 : ℝ)) (q := - (13077270546755097 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13077270546755097 / 20000000000000000 : ℚ)) + (r' := (13077270546755097 / 10000000000000000 : ℚ)) + (U := (-(4248566228358807393553 / 10000000000000000000000 : ℚ))) + (U' := (2682905574641192606447 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (1634517388212993 / 2500000000000000 : ℚ)) + (q := (13077270546755097 / 20000000000000000 : ℚ)) + (U := (-(4248566228358807393553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_4 : Uω (aρ 4) (bρ 4) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1883,25 +1646,21 @@ lemma U_572_4 : have hlg : Real.log (12918556131774469 / 20000000000000000 : ℝ) ≤ (-(2185337678456050449133 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12918556131774469 / 20000000000000000 : ℝ) = - (12918556131774469 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12918556131774469 / 10000000000000000 : ℚ)) - (U := (1280398223043949550867 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12918556131774469 / 10000000000000000 : ℝ) ≤ - (1280398223043949550867 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (807206164867043 / 1250000000000000 : ℝ)) (q := - (12918556131774469 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12918556131774469 / 20000000000000000 : ℚ)) + (r' := (12918556131774469 / 10000000000000000 : ℚ)) + (U := (-(2185337678456050449133 / 5000000000000000000000 : ℚ))) + (U' := (1280398223043949550867 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (807206164867043 / 1250000000000000 : ℚ)) + (q := (12918556131774469 / 20000000000000000 : ℚ)) + (U := (-(2185337678456050449133 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_5 : Uω (aρ 5) (bρ 5) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1909,25 +1668,21 @@ lemma U_572_5 : have hlg : Real.log (2535406336269411 / 4000000000000000 : ℝ) ≤ (-(2279702231101783945013 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2535406336269411 / 4000000000000000 : ℝ) = - (2535406336269411 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2535406336269411 / 2000000000000000 : ℚ)) - (U := (1186033670398216054987 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2535406336269411 / 2000000000000000 : ℝ) ≤ - (1186033670398216054987 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (633431478784393 / 1000000000000000 : ℝ)) (q := - (2535406336269411 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2535406336269411 / 4000000000000000 : ℚ)) + (r' := (2535406336269411 / 2000000000000000 : ℚ)) + (U := (-(2279702231101783945013 / 5000000000000000000000 : ℚ))) + (U' := (1186033670398216054987 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (633431478784393 / 1000000000000000 : ℚ)) + (q := (2535406336269411 / 4000000000000000 : ℚ)) + (U := (-(2279702231101783945013 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_6 : Uω (aρ 6) (bρ 6) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1935,25 +1690,21 @@ lemma U_572_6 : have hlg : Real.log (6165524221474687 / 10000000000000000 : ℝ) ≤ (-(4836119278634238343609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6165524221474687 / 10000000000000000 : ℝ) = - (6165524221474687 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6165524221474687 / 5000000000000000 : ℚ)) - (U := (2095352524365761656391 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6165524221474687 / 5000000000000000 : ℝ) ≤ - (2095352524365761656391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6155571924586249 / 10000000000000000 : ℝ)) (q := - (6165524221474687 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6165524221474687 / 10000000000000000 : ℚ)) + (r' := (6165524221474687 / 5000000000000000 : ℚ)) + (U := (-(4836119278634238343609 / 10000000000000000000000 : ℚ))) + (U' := (2095352524365761656391 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (6155571924586249 / 10000000000000000 : ℚ)) + (q := (6165524221474687 / 10000000000000000 : ℚ)) + (U := (-(4836119278634238343609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_7 : Uω (aρ 7) (bρ 7) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1961,25 +1712,21 @@ lemma U_572_7 : have hlg : Real.log (11859894547306783 / 20000000000000000 : ℝ) ≤ (-(2612848856110541349761 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11859894547306783 / 20000000000000000 : ℝ) = - (11859894547306783 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11859894547306783 / 10000000000000000 : ℚ)) - (U := (852887045389458650239 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11859894547306783 / 10000000000000000 : ℝ) ≤ - (852887045389458650239 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2954039704851829 / 5000000000000000 : ℝ)) (q := - (11859894547306783 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11859894547306783 / 20000000000000000 : ℚ)) + (r' := (11859894547306783 / 10000000000000000 : ℚ)) + (U := (-(2612848856110541349761 / 5000000000000000000000 : ℚ))) + (U' := (852887045389458650239 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (2954039704851829 / 5000000000000000 : ℚ)) + (q := (11859894547306783 / 20000000000000000 : ℚ)) + (U := (-(2612848856110541349761 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_8 : Uω (aρ 8) (bρ 8) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -1987,25 +1734,21 @@ lemma U_572_8 : have hlg : Real.log (11246836812835769 / 20000000000000000 : ℝ) ≤ (-(5756453563723046984991 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11246836812835769 / 20000000000000000 : ℝ) = - (11246836812835769 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11246836812835769 / 10000000000000000 : ℚ)) - (U := (1175018239276953015009 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11246836812835769 / 10000000000000000 : ℝ) ≤ - (1175018239276953015009 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1394640831643161 / 2500000000000000 : ℝ)) (q := - (11246836812835769 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11246836812835769 / 20000000000000000 : ℚ)) + (r' := (11246836812835769 / 10000000000000000 : ℚ)) + (U := (-(5756453563723046984991 / 10000000000000000000000 : ℚ))) + (U' := (1175018239276953015009 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (1394640831643161 / 2500000000000000 : ℚ)) + (q := (11246836812835769 / 20000000000000000 : ℚ)) + (U := (-(5756453563723046984991 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_9 : Uω (aρ 9) (bρ 9) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2013,25 +1756,21 @@ lemma U_572_9 : have hlg : Real.log (5240898101526921 / 10000000000000000 : ℝ) ≤ (-(3230461078330779039389 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5240898101526921 / 10000000000000000 : ℝ) = - (5240898101526921 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5240898101526921 / 5000000000000000 : ℚ)) - (U := (235274823169220960611 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5240898101526921 / 5000000000000000 : ℝ) ≤ - (235274823169220960611 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5154488345150717 / 10000000000000000 : ℝ)) (q := - (5240898101526921 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5240898101526921 / 10000000000000000 : ℚ)) + (r' := (5240898101526921 / 5000000000000000 : ℚ)) + (U := (-(3230461078330779039389 / 5000000000000000000000 : ℚ))) + (U' := (235274823169220960611 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (5154488345150717 / 10000000000000000 : ℚ)) + (q := (5240898101526921 / 10000000000000000 : ℚ)) + (U := (-(3230461078330779039389 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_10 : Uω (aρ 10) (bρ 10) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2039,26 +1778,21 @@ lemma U_572_10 : have hlg : Real.log (1912558387479417 / 4000000000000000 : ℝ) ≤ (-(7378525449464564730863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1912558387479417 / 4000000000000000 : ℝ) = - (1912558387479417 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1912558387479417 / 1000000000000000 : ℚ)) - (U := (6484418156535435269137 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1912558387479417 / 1000000000000000 : ℝ) ≤ - (6484418156535435269137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28900269456181 / 62500000000000 : ℝ)) (q := - (1912558387479417 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1912558387479417 / 4000000000000000 : ℚ)) + (r' := (1912558387479417 / 1000000000000000 : ℚ)) + (U := (-(7378525449464564730863 / 10000000000000000000000 : ℚ))) + (U' := (6484418156535435269137 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (28900269456181 / 62500000000000 : ℚ)) + (q := (1912558387479417 / 4000000000000000 : ℚ)) + (U := (-(7378525449464564730863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_11 : Uω (aρ 11) (bρ 11) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2066,26 +1800,21 @@ lemma U_572_11 : have hlg : Real.log (4247307596759467 / 10000000000000000 : ℝ) ≤ (-(4281499084663921275759 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4247307596759467 / 10000000000000000 : ℝ) = - (4247307596759467 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4247307596759467 / 2500000000000000 : ℚ)) - (U := (2649972718336078724241 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4247307596759467 / 2500000000000000 : ℝ) ≤ - (2649972718336078724241 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3974342995315809 / 10000000000000000 : ℝ)) (q := - (4247307596759467 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4247307596759467 / 10000000000000000 : ℚ)) + (r' := (4247307596759467 / 2500000000000000 : ℚ)) + (U := (-(4281499084663921275759 / 5000000000000000000000 : ℚ))) + (U' := (2649972718336078724241 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (3974342995315809 / 10000000000000000 : ℚ)) + (q := (4247307596759467 / 10000000000000000 : ℚ)) + (U := (-(4281499084663921275759 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_12 : Uω (aρ 12) (bρ 12) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2093,25 +1822,21 @@ lemma U_572_12 : have hlg : Real.log (291231858149807 / 800000000000000 : ℝ) ≤ (-(2020984027645203037053 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (291231858149807 / 800000000000000 : ℝ) = - (291231858149807 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (291231858149807 / 200000000000000 : ℚ)) - (U := (751604693554796962947 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (291231858149807 / 200000000000000 : ℝ) ≤ - (751604693554796962947 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (63684487044541 / 200000000000000 : ℝ)) (q := - (291231858149807 / 800000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (291231858149807 / 800000000000000 : ℚ)) + (r' := (291231858149807 / 200000000000000 : ℚ)) + (U := (-(2020984027645203037053 / 2000000000000000000000 : ℚ))) + (U' := (751604693554796962947 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (63684487044541 / 200000000000000 : ℚ)) + (q := (291231858149807 / 800000000000000 : ℚ)) + (U := (-(2020984027645203037053 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_13 : Uω (aρ 13) (bρ 13) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2119,25 +1844,21 @@ lemma U_572_13 : have hlg : Real.log (736232214017377 / 2500000000000000 : ℝ) ≤ (-(12225004331939791329417 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (736232214017377 / 2500000000000000 : ℝ) = - (736232214017377 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (736232214017377 / 625000000000000 : ℚ)) - (U := (1637939274060208670583 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (736232214017377 / 625000000000000 : ℝ) ≤ - (1637939274060208670583 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2192667352215891 / 10000000000000000 : ℝ)) (q := - (736232214017377 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (736232214017377 / 2500000000000000 : ℚ)) + (r' := (736232214017377 / 625000000000000 : ℚ)) + (U := (-(12225004331939791329417 / 10000000000000000000000 : ℚ))) + (U' := (1637939274060208670583 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (2192667352215891 / 10000000000000000 : ℚ)) + (q := (736232214017377 / 2500000000000000 : ℚ)) + (U := (-(12225004331939791329417 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_14 : Uω (aρ 14) (bρ 14) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2145,25 +1866,21 @@ lemma U_572_14 : have hlg : Real.log (477329293762299 / 2500000000000000 : ℝ) ≤ (-(16558394140482642990089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (477329293762299 / 2500000000000000 : ℝ) = - (477329293762299 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (477329293762299 / 312500000000000 : ℚ)) - (U := (4236021268517357009911 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (477329293762299 / 312500000000000 : ℝ) ≤ - (4236021268517357009911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (465371275220267 / 10000000000000000 : ℝ)) (q := - (477329293762299 / 2500000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (477329293762299 / 2500000000000000 : ℚ)) + (r' := (477329293762299 / 312500000000000 : ℚ)) + (U := (-(16558394140482642990089 / 10000000000000000000000 : ℚ))) + (U' := (4236021268517357009911 / 10000000000000000000000 : ℚ)) + 3 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (10679781329357 / 16000000000000 : ℚ)) + (s := (465371275220267 / 10000000000000000 : ℚ)) + (q := (477329293762299 / 2500000000000000 : ℚ)) + (U := (-(16558394140482642990089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_572_15 : Uω (aρ 15) (bρ 15) (10679781329357 / 16000000000000 : ℝ) ≤ @@ -2266,25 +1983,21 @@ lemma U_573_1 : have hlg : Real.log (26506265855365327 / 40000000000000000 : ℝ) ≤ (-(4114983014388123040979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26506265855365327 / 40000000000000000 : ℝ) = - (26506265855365327 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26506265855365327 / 20000000000000000 : ℚ)) - (U := (2816488788611876959021 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26506265855365327 / 20000000000000000 : ℝ) ≤ - (2816488788611876959021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1656635516727619 / 2500000000000000 : ℝ)) (q := - (26506265855365327 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26506265855365327 / 40000000000000000 : ℚ)) + (r' := (26506265855365327 / 20000000000000000 : ℚ)) + (U := (-(4114983014388123040979 / 10000000000000000000000 : ℚ))) + (U' := (2816488788611876959021 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (1656635516727619 / 2500000000000000 : ℚ)) + (q := (26506265855365327 / 40000000000000000 : ℚ)) + (U := (-(4114983014388123040979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_2 : Uω (aρ 2) (bρ 2) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2292,25 +2005,21 @@ lemma U_573_2 : have hlg : Real.log (26410644666155673 / 40000000000000000 : ℝ) ≤ (-(4151123179164884118219 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26410644666155673 / 40000000000000000 : ℝ) = - (26410644666155673 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26410644666155673 / 20000000000000000 : ℚ)) - (U := (2780348623835115881781 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26410644666155673 / 20000000000000000 : ℝ) ≤ - (2780348623835115881781 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6602500484815649 / 10000000000000000 : ℝ)) (q := - (26410644666155673 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26410644666155673 / 40000000000000000 : ℚ)) + (r' := (26410644666155673 / 20000000000000000 : ℚ)) + (U := (-(4151123179164884118219 / 10000000000000000000000 : ℚ))) + (U' := (2780348623835115881781 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (6602500484815649 / 10000000000000000 : ℚ)) + (q := (26410644666155673 / 40000000000000000 : ℚ)) + (U := (-(4151123179164884118219 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_3 : Uω (aρ 3) (bρ 3) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2318,25 +2027,21 @@ lemma U_573_3 : have hlg : Real.log (26219445687169191 / 40000000000000000 : ℝ) ≤ (-(1055945291455342745149 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26219445687169191 / 40000000000000000 : ℝ) = - (26219445687169191 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26219445687169191 / 20000000000000000 : ℚ)) - (U := (676922659294657254851 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26219445687169191 / 20000000000000000 : ℝ) ≤ - (676922659294657254851 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (819287137709051 / 1250000000000000 : ℝ)) (q := - (26219445687169191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26219445687169191 / 40000000000000000 : ℚ)) + (r' := (26219445687169191 / 20000000000000000 : ℚ)) + (U := (-(1055945291455342745149 / 2500000000000000000000 : ℚ))) + (U' := (676922659294657254851 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (819287137709051 / 1250000000000000 : ℚ)) + (q := (26219445687169191 / 40000000000000000 : ℚ)) + (U := (-(1055945291455342745149 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_4 : Uω (aρ 4) (bρ 4) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2344,25 +2049,21 @@ lemma U_573_4 : have hlg : Real.log (25902027583361671 / 40000000000000000 : ℝ) ≤ (-(2172791015703680314347 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25902027583361671 / 40000000000000000 : ℝ) = - (25902027583361671 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25902027583361671 / 20000000000000000 : ℚ)) - (U := (1292944885796319685653 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25902027583361671 / 20000000000000000 : ℝ) ≤ - (1292944885796319685653 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404617639427103 / 625000000000000 : ℝ)) (q := - (25902027583361671 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25902027583361671 / 40000000000000000 : ℚ)) + (r' := (25902027583361671 / 20000000000000000 : ℚ)) + (U := (-(2172791015703680314347 / 5000000000000000000000 : ℚ))) + (U' := (1292944885796319685653 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (404617639427103 / 625000000000000 : ℚ)) + (q := (25902027583361671 / 40000000000000000 : ℚ)) + (U := (-(2172791015703680314347 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_5 : Uω (aρ 5) (bρ 5) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2370,25 +2071,21 @@ lemma U_573_5 : have hlg : Real.log (25419005287087807 / 40000000000000000 : ℝ) ≤ (-(4533823199721012871099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25419005287087807 / 40000000000000000 : ℝ) = - (25419005287087807 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25419005287087807 / 20000000000000000 : ℚ)) - (U := (2397648603278987128901 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25419005287087807 / 20000000000000000 : ℝ) ≤ - (2397648603278987128901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1587640250507929 / 2500000000000000 : ℝ)) (q := - (25419005287087807 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25419005287087807 / 40000000000000000 : ℚ)) + (r' := (25419005287087807 / 20000000000000000 : ℚ)) + (U := (-(4533823199721012871099 / 10000000000000000000000 : ℚ))) + (U' := (2397648603278987128901 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (1587640250507929 / 2500000000000000 : ℚ)) + (q := (25419005287087807 / 40000000000000000 : ℚ)) + (U := (-(4533823199721012871099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_6 : Uω (aρ 6) (bρ 6) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2396,25 +2093,21 @@ lemma U_573_6 : have hlg : Real.log (24727100530005173 / 40000000000000000 : ℝ) ≤ (-(4809796242406969208233 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24727100530005173 / 40000000000000000 : ℝ) = - (24727100530005173 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24727100530005173 / 20000000000000000 : ℚ)) - (U := (2121675560593030791767 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24727100530005173 / 20000000000000000 : ℝ) ≤ - (2121675560593030791767 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6171848998630399 / 10000000000000000 : ℝ)) (q := - (24727100530005173 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24727100530005173 / 40000000000000000 : ℚ)) + (r' := (24727100530005173 / 20000000000000000 : ℚ)) + (U := (-(4809796242406969208233 / 10000000000000000000000 : ℚ))) + (U' := (2121675560593030791767 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (6171848998630399 / 10000000000000000 : ℚ)) + (q := (24727100530005173 / 40000000000000000 : ℚ)) + (U := (-(4809796242406969208233 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_7 : Uω (aρ 7) (bρ 7) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2422,25 +2115,21 @@ lemma U_573_7 : have hlg : Real.log (23784927640181179 / 40000000000000000 : ℝ) ≤ (-(324892103887673495129 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23784927640181179 / 40000000000000000 : ℝ) = - (23784927640181179 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23784927640181179 / 20000000000000000 : ℚ)) - (U := (108324883799826504871 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23784927640181179 / 20000000000000000 : ℝ) ≤ - (108324883799826504871 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2962211967239201 / 5000000000000000 : ℝ)) (q := - (23784927640181179 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23784927640181179 / 40000000000000000 : ℚ)) + (r' := (23784927640181179 / 20000000000000000 : ℚ)) + (U := (-(324892103887673495129 / 625000000000000000000 : ℚ))) + (U' := (108324883799826504871 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (2962211967239201 / 5000000000000000 : ℚ)) + (q := (23784927640181179 / 40000000000000000 : ℚ)) + (U := (-(324892103887673495129 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_8 : Uω (aρ 8) (bρ 8) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2448,25 +2137,21 @@ lemma U_573_8 : have hlg : Real.log (22559092920130721 / 40000000000000000 : ℝ) ≤ (-(5727412354734878097163 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22559092920130721 / 40000000000000000 : ℝ) = - (22559092920130721 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22559092920130721 / 20000000000000000 : ℚ)) - (U := (1204059448265121902837 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22559092920130721 / 20000000000000000 : ℝ) ≤ - (1204059448265121902837 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5595048225793173 / 10000000000000000 : ℝ)) (q := - (22559092920130721 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22559092920130721 / 40000000000000000 : ℚ)) + (r' := (22559092920130721 / 20000000000000000 : ℚ)) + (U := (-(5727412354734878097163 / 10000000000000000000000 : ℚ))) + (U' := (1204059448265121902837 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (5595048225793173 / 10000000000000000 : ℚ)) + (q := (22559092920130721 / 40000000000000000 : ℚ)) + (U := (-(5727412354734878097163 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_9 : Uω (aρ 9) (bρ 9) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2474,25 +2159,21 @@ lemma U_573_9 : have hlg : Real.log (21029575893059351 / 40000000000000000 : ℝ) ≤ (-(803687038877101364811 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21029575893059351 / 40000000000000000 : ℝ) = - (21029575893059351 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21029575893059351 / 20000000000000000 : ℚ)) - (U := (62746936497898635189 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (21029575893059351 / 20000000000000000 : ℝ) ≤ - (62746936497898635189 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (323203458788593 / 625000000000000 : ℝ)) (q := - (21029575893059351 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21029575893059351 / 40000000000000000 : ℚ)) + (r' := (21029575893059351 / 20000000000000000 : ℚ)) + (U := (-(803687038877101364811 / 1250000000000000000000 : ℚ))) + (U' := (62746936497898635189 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (323203458788593 / 625000000000000 : ℚ)) + (q := (21029575893059351 / 40000000000000000 : ℚ)) + (U := (-(803687038877101364811 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_10 : Uω (aρ 10) (bρ 10) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2500,26 +2181,21 @@ lemma U_573_10 : have hlg : Real.log (19192683349971467 / 40000000000000000 : ℝ) ≤ (-(1835875806775894467537 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19192683349971467 / 40000000000000000 : ℝ) = - (19192683349971467 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19192683349971467 / 10000000000000000 : ℚ)) - (U := (1629860094724105532463 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19192683349971467 / 10000000000000000 : ℝ) ≤ - (1629860094724105532463 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2320684051284273 / 5000000000000000 : ℝ)) (q := - (19192683349971467 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19192683349971467 / 40000000000000000 : ℚ)) + (r' := (19192683349971467 / 10000000000000000 : ℚ)) + (U := (-(1835875806775894467537 / 2500000000000000000000 : ℚ))) + (U' := (1629860094724105532463 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (2320684051284273 / 5000000000000000 : ℚ)) + (q := (19192683349971467 / 40000000000000000 : ℚ)) + (U := (-(1835875806775894467537 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_11 : Uω (aρ 11) (bρ 11) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2527,26 +2203,21 @@ lemma U_573_11 : have hlg : Real.log (17058567395075321 / 40000000000000000 : ℝ) ≤ (-(8522268895539115610217 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17058567395075321 / 40000000000000000 : ℝ) = - (17058567395075321 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17058567395075321 / 10000000000000000 : ℚ)) - (U := (5340674710460884389783 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17058567395075321 / 10000000000000000 : ℝ) ≤ - (5340674710460884389783 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3992786751325473 / 10000000000000000 : ℝ)) (q := - (17058567395075321 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17058567395075321 / 40000000000000000 : ℚ)) + (r' := (17058567395075321 / 10000000000000000 : ℚ)) + (U := (-(8522268895539115610217 / 10000000000000000000000 : ℚ))) + (U' := (5340674710460884389783 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (3992786751325473 / 10000000000000000 : ℚ)) + (q := (17058567395075321 / 40000000000000000 : ℚ)) + (U := (-(8522268895539115610217 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_12 : Uω (aρ 12) (bρ 12) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2554,26 +2225,21 @@ lemma U_573_12 : have hlg : Real.log (14635735559531383 / 40000000000000000 : ℝ) ≤ (-(10054132744104097026937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14635735559531383 / 40000000000000000 : ℝ) = - (14635735559531383 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14635735559531383 / 10000000000000000 : ℚ)) - (U := (3808810861895902973063 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14635735559531383 / 10000000000000000 : ℝ) ≤ - (3808810861895902973063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (400633866279813 / 1250000000000000 : ℝ)) (q := - (14635735559531383 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14635735559531383 / 40000000000000000 : ℚ)) + (r' := (14635735559531383 / 10000000000000000 : ℚ)) + (U := (-(10054132744104097026937 / 10000000000000000000000 : ℚ))) + (U' := (3808810861895902973063 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (400633866279813 / 1250000000000000 : ℚ)) + (q := (14635735559531383 / 40000000000000000 : ℚ)) + (U := (-(10054132744104097026937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_13 : Uω (aρ 13) (bρ 13) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2581,26 +2247,21 @@ lemma U_573_13 : have hlg : Real.log (11866661439586277 / 40000000000000000 : ℝ) ≤ (-(1215146544888570115507 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11866661439586277 / 40000000000000000 : ℝ) = - (11866661439586277 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11866661439586277 / 10000000000000000 : ℚ)) - (U := (171147815711429884493 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11866661439586277 / 10000000000000000 : ℝ) ≤ - (171147815711429884493 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2219915611860951 / 10000000000000000 : ℝ)) (q := - (11866661439586277 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11866661439586277 / 40000000000000000 : ℚ)) + (r' := (11866661439586277 / 10000000000000000 : ℚ)) + (U := (-(1215146544888570115507 / 1000000000000000000000 : ℚ))) + (U' := (171147815711429884493 / 1000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (2219915611860951 / 10000000000000000 : ℚ)) + (q := (11866661439586277 / 40000000000000000 : ℚ)) + (U := (-(1215146544888570115507 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_14 : Uω (aρ 14) (bρ 14) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2608,26 +2269,21 @@ lemma U_573_14 : have hlg : Real.log (7880282551114177 / 40000000000000000 : ℝ) ≤ (-(8122578466833861866631 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (7880282551114177 / 40000000000000000 : ℝ) = - (7880282551114177 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7880282551114177 / 5000000000000000 : ℚ)) - (U := (2274629237666138133369 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7880282551114177 / 5000000000000000 : ℝ) ≤ - (2274629237666138133369 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (570653452669901 / 10000000000000000 : ℝ)) (q := - (7880282551114177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7880282551114177 / 40000000000000000 : ℚ)) + (r' := (7880282551114177 / 5000000000000000 : ℚ)) + (U := (-(8122578466833861866631 / 5000000000000000000000 : ℚ))) + (U' := (2274629237666138133369 / 5000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (21411481852343 / 32000000000000 : ℚ)) + (s := (570653452669901 / 10000000000000000 : ℚ)) + (q := (7880282551114177 / 40000000000000000 : ℚ)) + (U := (-(8122578466833861866631 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_573_15 : Uω (aρ 15) (bρ 15) (21411481852343 / 32000000000000 : ℝ) ≤ @@ -2730,25 +2386,21 @@ lemma U_574_1 : have hlg : Real.log (13285582542878253 / 20000000000000000 : ℝ) ≤ (-(2045264226863557451219 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13285582542878253 / 20000000000000000 : ℝ) = - (13285582542878253 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13285582542878253 / 10000000000000000 : ℚ)) - (U := (1420471674636442548781 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13285582542878253 / 10000000000000000 : ℝ) ≤ - (1420471674636442548781 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6642766934097003 / 10000000000000000 : ℝ)) (q := - (13285582542878253 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13285582542878253 / 20000000000000000 : ℚ)) + (r' := (13285582542878253 / 10000000000000000 : ℚ)) + (U := (-(2045264226863557451219 / 5000000000000000000000 : ℚ))) + (U' := (1420471674636442548781 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (6642766934097003 / 10000000000000000 : ℚ)) + (q := (13285582542878253 / 20000000000000000 : ℚ)) + (U := (-(2045264226863557451219 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_2 : Uω (aρ 2) (bρ 2) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2756,25 +2408,21 @@ lemma U_574_2 : have hlg : Real.log (827360788554193 / 1250000000000000 : ℝ) ≤ (-(206328984146057335773 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (827360788554193 / 1250000000000000 : ℝ) = - (827360788554193 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (827360788554193 / 625000000000000 : ℚ)) - (U := (140244606003942664227 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (827360788554193 / 625000000000000 : ℝ) ≤ - (140244606003942664227 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3309363010297919 / 5000000000000000 : ℝ)) (q := - (827360788554193 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (827360788554193 / 1250000000000000 : ℚ)) + (r' := (827360788554193 / 625000000000000 : ℚ)) + (U := (-(206328984146057335773 / 500000000000000000000 : ℚ))) + (U' := (140244606003942664227 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (3309363010297919 / 5000000000000000 : ℚ)) + (q := (827360788554193 / 1250000000000000 : ℚ)) + (U := (-(206328984146057335773 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_3 : Uω (aρ 3) (bρ 3) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2782,25 +2430,21 @@ lemma U_574_3 : have hlg : Real.log (13142175126580683 / 20000000000000000 : ℝ) ≤ (-(2099528695947786887917 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13142175126580683 / 20000000000000000 : ℝ) = - (13142175126580683 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13142175126580683 / 10000000000000000 : ℚ)) - (U := (1366207205552213112083 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13142175126580683 / 10000000000000000 : ℝ) ≤ - (1366207205552213112083 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6570524636659433 / 10000000000000000 : ℝ)) (q := - (13142175126580683 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13142175126580683 / 20000000000000000 : ℚ)) + (r' := (13142175126580683 / 10000000000000000 : ℚ)) + (U := (-(2099528695947786887917 / 5000000000000000000000 : ℚ))) + (U' := (1366207205552213112083 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (6570524636659433 / 10000000000000000 : ℚ)) + (q := (13142175126580683 / 20000000000000000 : ℚ)) + (U := (-(2099528695947786887917 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_4 : Uω (aρ 4) (bρ 4) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2808,25 +2452,21 @@ lemma U_574_4 : have hlg : Real.log (259669428215177 / 400000000000000 : ℝ) ≤ (-(4320551547269413483711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (259669428215177 / 400000000000000 : ℝ) = - (259669428215177 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (259669428215177 / 200000000000000 : ℚ)) - (U := (2610920255730586516289 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (259669428215177 / 200000000000000 : ℝ) ≤ - (2610920255730586516289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (32450575509513 / 50000000000000 : ℝ)) (q := - (259669428215177 / 400000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (259669428215177 / 400000000000000 : ℚ)) + (r' := (259669428215177 / 200000000000000 : ℚ)) + (U := (-(4320551547269413483711 / 10000000000000000000000 : ℚ))) + (U' := (2610920255730586516289 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (32450575509513 / 50000000000000 : ℚ)) + (q := (259669428215177 / 400000000000000 : ℚ)) + (U := (-(4320551547269413483711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_5 : Uω (aρ 5) (bρ 5) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2834,25 +2474,21 @@ lemma U_574_5 : have hlg : Real.log (3185493374065603 / 5000000000000000 : ℝ) ≤ (-(450830729631545839137 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3185493374065603 / 5000000000000000 : ℝ) = - (3185493374065603 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3185493374065603 / 2500000000000000 : ℚ)) - (U := (242316450668454160863 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3185493374065603 / 2500000000000000 : ℝ) ≤ - (242316450668454160863 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3183403553370581 / 5000000000000000 : ℝ)) (q := - (3185493374065603 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3185493374065603 / 5000000000000000 : ℚ)) + (r' := (3185493374065603 / 2500000000000000 : ℚ)) + (U := (-(450830729631545839137 / 1000000000000000000000 : ℚ))) + (U' := (242316450668454160863 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (3183403553370581 / 5000000000000000 : ℚ)) + (q := (3185493374065603 / 5000000000000000 : ℚ)) + (U := (-(450830729631545839137 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_6 : Uω (aρ 6) (bρ 6) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2860,25 +2496,21 @@ lemma U_574_6 : have hlg : Real.log (12396051812224373 / 20000000000000000 : ℝ) ≤ (-(956708507247560145543 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12396051812224373 / 20000000000000000 : ℝ) = - (12396051812224373 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12396051812224373 / 10000000000000000 : ℚ)) - (U := (429585853352439854457 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12396051812224373 / 10000000000000000 : ℝ) ≤ - (429585853352439854457 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6188125797843123 / 10000000000000000 : ℝ)) (q := - (12396051812224373 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12396051812224373 / 20000000000000000 : ℚ)) + (r' := (12396051812224373 / 10000000000000000 : ℚ)) + (U := (-(956708507247560145543 / 2000000000000000000000 : ℚ))) + (U' := (429585853352439854457 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (6188125797843123 / 10000000000000000 : ℚ)) + (q := (12396051812224373 / 20000000000000000 : ℚ)) + (U := (-(956708507247560145543 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_7 : Uω (aρ 7) (bρ 7) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2886,25 +2518,21 @@ lemma U_574_7 : have hlg : Real.log (372657263631819 / 625000000000000 : ℝ) ≤ (-(5170925165050416482019 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (372657263631819 / 625000000000000 : ℝ) = - (372657263631819 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (372657263631819 / 312500000000000 : ℚ)) - (U := (1760546637949583517981 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (372657263631819 / 312500000000000 : ℝ) ≤ - (1760546637949583517981 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2970383901298479 / 5000000000000000 : ℝ)) (q := - (372657263631819 / 625000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (372657263631819 / 625000000000000 : ℚ)) + (r' := (372657263631819 / 312500000000000 : ℚ)) + (U := (-(5170925165050416482019 / 10000000000000000000000 : ℚ))) + (U' := (1760546637949583517981 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (2970383901298479 / 5000000000000000 : ℚ)) + (q := (372657263631819 / 625000000000000 : ℚ)) + (U := (-(5170925165050416482019 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_8 : Uω (aρ 8) (bρ 8) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2912,25 +2540,21 @@ lemma U_574_8 : have hlg : Real.log (11312254590872379 / 20000000000000000 : ℝ) ≤ (-(356153536329907708581 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11312254590872379 / 20000000000000000 : ℝ) = - (11312254590872379 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11312254590872379 / 10000000000000000 : ℚ)) - (U := (77063451357592291419 / 625000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11312254590872379 / 10000000000000000 : ℝ) ≤ - (77063451357592291419 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5611531608591129 / 10000000000000000 : ℝ)) (q := - (11312254590872379 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11312254590872379 / 20000000000000000 : ℚ)) + (r' := (11312254590872379 / 10000000000000000 : ℚ)) + (U := (-(356153536329907708581 / 625000000000000000000 : ℚ))) + (U' := (77063451357592291419 / 625000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (5611531608591129 / 10000000000000000 : ℚ)) + (q := (11312254590872379 / 20000000000000000 : ℚ)) + (U := (-(356153536329907708581 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_9 : Uω (aρ 9) (bρ 9) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2938,25 +2562,21 @@ lemma U_574_9 : have hlg : Real.log (10547776241736821 / 20000000000000000 : ℝ) ≤ (-(6398172183635422242973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10547776241736821 / 20000000000000000 : ℝ) = - (10547776241736821 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10547776241736821 / 10000000000000000 : ℚ)) - (U := (533299619364577757027 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10547776241736821 / 10000000000000000 : ℝ) ≤ - (533299619364577757027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5188018887815571 / 10000000000000000 : ℝ)) (q := - (10547776241736821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10547776241736821 / 20000000000000000 : ℚ)) + (r' := (10547776241736821 / 10000000000000000 : ℚ)) + (U := (-(6398172183635422242973 / 10000000000000000000000 : ℚ))) + (U' := (533299619364577757027 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (5188018887815571 / 10000000000000000 : ℚ)) + (q := (10547776241736821 / 20000000000000000 : ℚ)) + (U := (-(6398172183635422242973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_10 : Uω (aρ 10) (bρ 10) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2964,26 +2584,21 @@ lemma U_574_10 : have hlg : Real.log (4814941744570177 / 10000000000000000 : ℝ) ≤ (-(7308611460365759401711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4814941744570177 / 10000000000000000 : ℝ) = - (4814941744570177 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4814941744570177 / 2500000000000000 : ℚ)) - (U := (6554332145634240598289 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4814941744570177 / 2500000000000000 : ℝ) ≤ - (6554332145634240598289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (582335646089263 / 1250000000000000 : ℝ)) (q := - (4814941744570177 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4814941744570177 / 10000000000000000 : ℚ)) + (r' := (4814941744570177 / 2500000000000000 : ℚ)) + (U := (-(7308611460365759401711 / 10000000000000000000000 : ℚ))) + (U' := (6554332145634240598289 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (582335646089263 / 1250000000000000 : ℚ)) + (q := (4814941744570177 / 10000000000000000 : ℚ)) + (U := (-(7308611460365759401711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_11 : Uω (aρ 11) (bρ 11) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -2991,26 +2606,21 @@ lemma U_574_11 : have hlg : Real.log (2140983255733719 / 5000000000000000 : ℝ) ≤ (-(8481727231061772560251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2140983255733719 / 5000000000000000 : ℝ) = - (2140983255733719 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2140983255733719 / 1250000000000000 : ℚ)) - (U := (5381216374938227439749 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2140983255733719 / 1250000000000000 : ℝ) ≤ - (5381216374938227439749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2005605664356813 / 5000000000000000 : ℝ)) (q := - (2140983255733719 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2140983255733719 / 5000000000000000 : ℚ)) + (r' := (2140983255733719 / 1250000000000000 : ℚ)) + (U := (-(8481727231061772560251 / 10000000000000000000000 : ℚ))) + (U' := (5381216374938227439749 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (2005605664356813 / 5000000000000000 : ℚ)) + (q := (2140983255733719 / 5000000000000000 : ℚ)) + (U := (-(8481727231061772560251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_12 : Uω (aρ 12) (bρ 12) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -3018,26 +2628,21 @@ lemma U_574_12 : have hlg : Real.log (7354885992593791 / 20000000000000000 : ℝ) ≤ (-(625229637354933601691 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7354885992593791 / 20000000000000000 : ℝ) = - (7354885992593791 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7354885992593791 / 5000000000000000 : ℚ)) - (U := (241204338020066398309 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7354885992593791 / 5000000000000000 : ℝ) ≤ - (241204338020066398309 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3225864395057541 / 10000000000000000 : ℝ)) (q := - (7354885992593791 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7354885992593791 / 20000000000000000 : ℚ)) + (r' := (7354885992593791 / 5000000000000000 : ℚ)) + (U := (-(625229637354933601691 / 625000000000000000000 : ℚ))) + (U' := (241204338020066398309 / 625000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (3225864395057541 / 10000000000000000 : ℚ)) + (q := (7354885992593791 / 20000000000000000 : ℚ)) + (U := (-(625229637354933601691 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_13 : Uω (aρ 13) (bρ 13) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -3045,25 +2650,21 @@ lemma U_574_13 : have hlg : Real.log (239063618381401 / 800000000000000 : ℝ) ≤ (-(12078820249414143656001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (239063618381401 / 800000000000000 : ℝ) = - (239063618381401 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (239063618381401 / 200000000000000 : ℚ)) - (U := (1784123356585856343999 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (239063618381401 / 200000000000000 : ℝ) ≤ - (1784123356585856343999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89878024143751 / 400000000000000 : ℝ)) (q := - (239063618381401 / 800000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (239063618381401 / 800000000000000 : ℚ)) + (r' := (239063618381401 / 200000000000000 : ℚ)) + (U := (-(12078820249414143656001 / 10000000000000000000000 : ℚ))) + (U' := (1784123356585856343999 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (89878024143751 / 400000000000000 : ℚ)) + (q := (239063618381401 / 800000000000000 : ℚ)) + (U := (-(12078820249414143656001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_14 : Uω (aρ 14) (bρ 14) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -3071,25 +2672,21 @@ lemma U_574_14 : have hlg : Real.log (809088986232721 / 4000000000000000 : ℝ) ≤ (-(1598140732969455004503 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (809088986232721 / 4000000000000000 : ℝ) = - (809088986232721 / 500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (809088986232721 / 500000000000000 : ℚ)) - (U := (481300807930544995497 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (809088986232721 / 500000000000000 : ℝ) ≤ - (481300807930544995497 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (131946472053471 / 2000000000000000 : ℝ)) (q := - (809088986232721 / 4000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (809088986232721 / 4000000000000000 : ℚ)) + (r' := (809088986232721 / 500000000000000 : ℚ)) + (U := (-(1598140732969455004503 / 1000000000000000000000 : ℚ))) + (U' := (481300807930544995497 / 1000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5365850261493 / 8000000000000 : ℚ)) + (s := (131946472053471 / 2000000000000000 : ℚ)) + (q := (809088986232721 / 4000000000000000 : ℚ)) + (U := (-(1598140732969455004503 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_574_15 : Uω (aρ 15) (bρ 15) (5365850261493 / 8000000000000 : ℝ) ≤ @@ -3190,25 +2787,21 @@ lemma U_575_1 : have hlg : Real.log (26636064314986169 / 40000000000000000 : ℝ) ≤ (-(1016533387549429410351 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26636064314986169 / 40000000000000000 : ℝ) = - (26636064314986169 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26636064314986169 / 20000000000000000 : ℚ)) - (U := (716334563200570589649 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26636064314986169 / 20000000000000000 : ℝ) ≤ - (716334563200570589649 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1664747950175693 / 2500000000000000 : ℝ)) (q := - (26636064314986169 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26636064314986169 / 40000000000000000 : ℚ)) + (r' := (26636064314986169 / 20000000000000000 : ℚ)) + (U := (-(1016533387549429410351 / 2500000000000000000000 : ℚ))) + (U' := (716334563200570589649 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (1664747950175693 / 2500000000000000 : ℚ)) + (q := (26636064314986169 / 40000000000000000 : ℚ)) + (U := (-(1016533387549429410351 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_2 : Uω (aρ 2) (bρ 2) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3216,25 +2809,21 @@ lemma U_575_2 : have hlg : Real.log (26540445793607001 / 40000000000000000 : ℝ) ≤ (-(4102096280447662030521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26540445793607001 / 40000000000000000 : ℝ) = - (26540445793607001 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26540445793607001 / 20000000000000000 : ℚ)) - (U := (2829375522552337969479 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26540445793607001 / 20000000000000000 : ℝ) ≤ - (2829375522552337969479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1658737888130797 / 2500000000000000 : ℝ)) (q := - (26540445793607001 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26540445793607001 / 40000000000000000 : ℚ)) + (r' := (26540445793607001 / 20000000000000000 : ℚ)) + (U := (-(4102096280447662030521 / 10000000000000000000000 : ℚ))) + (U' := (2829375522552337969479 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (1658737888130797 / 2500000000000000 : ℚ)) + (q := (26540445793607001 / 40000000000000000 : ℚ)) + (U := (-(4102096280447662030521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_3 : Uω (aρ 3) (bρ 3) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3242,25 +2831,21 @@ lemma U_575_3 : have hlg : Real.log (26349254791691207 / 40000000000000000 : ℝ) ≤ (-(4174394604167777532657 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26349254791691207 / 40000000000000000 : ℝ) = - (26349254791691207 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26349254791691207 / 20000000000000000 : ℚ)) - (U := (2757077198832222467343 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26349254791691207 / 20000000000000000 : ℝ) ≤ - (2757077198832222467343 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6586752157915291 / 10000000000000000 : ℝ)) (q := - (26349254791691207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26349254791691207 / 40000000000000000 : ℚ)) + (r' := (26349254791691207 / 20000000000000000 : ℚ)) + (U := (-(4174394604167777532657 / 10000000000000000000000 : ℚ))) + (U' := (2757077198832222467343 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (6586752157915291 / 10000000000000000 : ℚ)) + (q := (26349254791691207 / 40000000000000000 : ℚ)) + (U := (-(4174394604167777532657 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_4 : Uω (aρ 4) (bρ 4) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3268,25 +2853,21 @@ lemma U_575_4 : have hlg : Real.log (26031857978628207 / 40000000000000000 : ℝ) ≤ (-(4295583590380036756359 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26031857978628207 / 40000000000000000 : ℝ) = - (26031857978628207 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26031857978628207 / 20000000000000000 : ℚ)) - (U := (2635888212619963243641 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26031857978628207 / 20000000000000000 : ℝ) ≤ - (2635888212619963243641 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6506347932448791 / 10000000000000000 : ℝ)) (q := - (26031857978628207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26031857978628207 / 40000000000000000 : ℚ)) + (r' := (26031857978628207 / 20000000000000000 : ℚ)) + (U := (-(4295583590380036756359 / 10000000000000000000000 : ℚ))) + (U' := (2635888212619963243641 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (6506347932448791 / 10000000000000000 : ℚ)) + (q := (26031857978628207 / 40000000000000000 : ℚ)) + (U := (-(4295583590380036756359 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_5 : Uω (aρ 5) (bρ 5) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3294,25 +2875,21 @@ lemma U_575_5 : have hlg : Real.log (25548888480677023 / 40000000000000000 : ℝ) ≤ (-(448285641842292237797 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25548888480677023 / 40000000000000000 : ℝ) = - (25548888480677023 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25548888480677023 / 20000000000000000 : ℚ)) - (U := (244861538457707762203 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25548888480677023 / 20000000000000000 : ℝ) ≤ - (244861538457707762203 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6383053102808199 / 10000000000000000 : ℝ)) (q := - (25548888480677023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25548888480677023 / 40000000000000000 : ℚ)) + (r' := (25548888480677023 / 20000000000000000 : ℚ)) + (U := (-(448285641842292237797 / 1000000000000000000000 : ℚ))) + (U' := (244861538457707762203 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (6383053102808199 / 10000000000000000 : ℚ)) + (q := (25548888480677023 / 40000000000000000 : ℚ)) + (U := (-(448285641842292237797 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_6 : Uω (aρ 6) (bρ 6) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3320,25 +2897,21 @@ lemma U_575_6 : have hlg : Real.log (4971421234711093 / 8000000000000000 : ℝ) ≤ (-(594669724340460638439 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4971421234711093 / 8000000000000000 : ℝ) = - (4971421234711093 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4971421234711093 / 4000000000000000 : ℚ)) - (U := (271764251034539361561 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4971421234711093 / 4000000000000000 : ℝ) ≤ - (271764251034539361561 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (310220116219371 / 500000000000000 : ℝ)) (q := - (4971421234711093 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4971421234711093 / 8000000000000000 : ℚ)) + (r' := (4971421234711093 / 4000000000000000 : ℚ)) + (U := (-(594669724340460638439 / 1250000000000000000000 : ℚ))) + (U' := (271764251034539361561 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (310220116219371 / 500000000000000 : ℚ)) + (q := (4971421234711093 / 8000000000000000 : ℚ)) + (U := (-(594669724340460638439 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_7 : Uω (aρ 7) (bρ 7) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3346,25 +2919,21 @@ lemma U_575_7 : have hlg : Real.log (23915200802188847 / 40000000000000000 : ℝ) ≤ (-(102873036052304889857 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23915200802188847 / 40000000000000000 : ℝ) = - (23915200802188847 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23915200802188847 / 20000000000000000 : ℚ)) - (U := (35756400007695110143 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23915200802188847 / 20000000000000000 : ℝ) ≤ - (35756400007695110143 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5957111019464111 / 10000000000000000 : ℝ)) (q := - (23915200802188847 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23915200802188847 / 40000000000000000 : ℚ)) + (r' := (23915200802188847 / 20000000000000000 : ℚ)) + (U := (-(102873036052304889857 / 200000000000000000000 : ℚ))) + (U' := (35756400007695110143 / 200000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (5957111019464111 / 10000000000000000 : ℚ)) + (q := (23915200802188847 / 40000000000000000 : ℚ)) + (U := (-(102873036052304889857 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_8 : Uω (aρ 8) (bρ 8) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3372,25 +2941,21 @@ lemma U_575_8 : have hlg : Real.log (22689922437161531 / 40000000000000000 : ℝ) ≤ (-(708698216798880485127 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22689922437161531 / 40000000000000000 : ℝ) = - (22689922437161531 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22689922437161531 / 20000000000000000 : ℚ)) - (U := (157735758576119514873 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22689922437161531 / 20000000000000000 : ℝ) ≤ - (157735758576119514873 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5628013488290453 / 10000000000000000 : ℝ)) (q := - (22689922437161531 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22689922437161531 / 40000000000000000 : ℚ)) + (r' := (22689922437161531 / 20000000000000000 : ℚ)) + (U := (-(708698216798880485127 / 1250000000000000000000 : ℚ))) + (U' := (157735758576119514873 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (5628013488290453 / 10000000000000000 : ℚ)) + (q := (22689922437161531 / 40000000000000000 : ℚ)) + (U := (-(708698216798880485127 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_9 : Uω (aρ 9) (bρ 9) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3398,25 +2963,21 @@ lemma U_575_9 : have hlg : Real.log (21161522243987643 / 40000000000000000 : ℝ) ≤ (-(198967159298271784199 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21161522243987643 / 40000000000000000 : ℝ) = - (21161522243987643 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21161522243987643 / 20000000000000000 : ℚ)) - (U := (17641334545478215801 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21161522243987643 / 20000000000000000 : ℝ) ≤ - (17641334545478215801 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5204779020063509 / 10000000000000000 : ℝ)) (q := - (21161522243987643 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21161522243987643 / 40000000000000000 : ℚ)) + (r' := (21161522243987643 / 20000000000000000 : ℚ)) + (U := (-(198967159298271784199 / 312500000000000000000 : ℚ))) + (U' := (17641334545478215801 / 312500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (5204779020063509 / 10000000000000000 : ℚ)) + (q := (21161522243987643 / 40000000000000000 : ℚ)) + (U := (-(198967159298271784199 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_10 : Uω (aρ 10) (bρ 10) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3424,26 +2985,21 @@ lemma U_575_10 : have hlg : Real.log (19326834935783657 / 40000000000000000 : ℝ) ≤ (-(290953964891705276277 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19326834935783657 / 40000000000000000 : ℝ) = - (19326834935783657 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19326834935783657 / 10000000000000000 : ℚ)) - (U := (263563779348294723723 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19326834935783657 / 10000000000000000 : ℝ) ≤ - (263563779348294723723 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1168998599864129 / 2500000000000000 : ℝ)) (q := - (19326834935783657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19326834935783657 / 40000000000000000 : ℚ)) + (r' := (19326834935783657 / 10000000000000000 : ℚ)) + (U := (-(290953964891705276277 / 400000000000000000000 : ℚ))) + (U' := (263563779348294723723 / 400000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (1168998599864129 / 2500000000000000 : ℚ)) + (q := (19326834935783657 / 40000000000000000 : ℚ)) + (U := (-(290953964891705276277 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_11 : Uω (aρ 11) (bρ 11) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3451,26 +3007,21 @@ lemma U_575_11 : have hlg : Real.log (17197126865562489 / 40000000000000000 : ℝ) ≤ (-(4220685632138396378261 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17197126865562489 / 40000000000000000 : ℝ) = - (17197126865562489 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17197126865562489 / 10000000000000000 : ℚ)) - (U := (2710786170861603621739 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17197126865562489 / 10000000000000000 : ℝ) ≤ - (2710786170861603621739 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1007404247637733 / 2500000000000000 : ℝ)) (q := - (17197126865562489 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17197126865562489 / 40000000000000000 : ℚ)) + (r' := (17197126865562489 / 10000000000000000 : ℚ)) + (U := (-(4220685632138396378261 / 5000000000000000000000 : ℚ))) + (U' := (2710786170861603621739 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (1007404247637733 / 2500000000000000 : ℚ)) + (q := (17197126865562489 / 40000000000000000 : ℚ)) + (U := (-(4220685632138396378261 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_12 : Uω (aρ 12) (bρ 12) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3478,26 +3029,21 @@ lemma U_575_12 : have hlg : Real.log (14783704225496667 / 40000000000000000 : ℝ) ≤ (-(9953539452871187747641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14783704225496667 / 40000000000000000 : ℝ) = - (14783704225496667 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14783704225496667 / 10000000000000000 : ℚ)) - (U := (3909404153128812252359 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14783704225496667 / 10000000000000000 : ℝ) ≤ - (3909404153128812252359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3246605767203021 / 10000000000000000 : ℝ)) (q := - (14783704225496667 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14783704225496667 / 40000000000000000 : ℚ)) + (r' := (14783704225496667 / 10000000000000000 : ℚ)) + (U := (-(9953539452871187747641 / 10000000000000000000000 : ℚ))) + (U' := (3909404153128812252359 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (3246605767203021 / 10000000000000000 : ℚ)) + (q := (14783704225496667 / 40000000000000000 : ℚ)) + (U := (-(9953539452871187747641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_13 : Uω (aρ 13) (bρ 13) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3505,26 +3051,21 @@ lemma U_575_13 : have hlg : Real.log (12039289077146017 / 40000000000000000 : ℝ) ≤ (-(6003520311026841393907 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12039289077146017 / 40000000000000000 : ℝ) = - (12039289077146017 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12039289077146017 / 10000000000000000 : ℚ)) - (U := (927951491973158606093 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12039289077146017 / 10000000000000000 : ℝ) ≤ - (927951491973158606093 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (284222491827837 / 1250000000000000 : ℝ)) (q := - (12039289077146017 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12039289077146017 / 40000000000000000 : ℚ)) + (r' := (12039289077146017 / 10000000000000000 : ℚ)) + (U := (-(6003520311026841393907 / 5000000000000000000000 : ℚ))) + (U' := (927951491973158606093 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (284222491827837 / 1250000000000000 : ℚ)) + (q := (12039289077146017 / 40000000000000000 : ℚ)) + (U := (-(6003520311026841393907 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_14 : Uω (aρ 14) (bρ 14) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3532,26 +3073,21 @@ lemma U_575_14 : have hlg : Real.log (8280864409230463 / 40000000000000000 : ℝ) ≤ (-(15749320931358898036187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8280864409230463 / 40000000000000000 : ℝ) = - (8280864409230463 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8280864409230463 / 5000000000000000 : ℚ)) - (U := (5045094477641101963813 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8280864409230463 / 5000000000000000 : ℝ) ≤ - (5045094477641101963813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (738494885709919 / 10000000000000000 : ℝ)) (q := - (8280864409230463 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8280864409230463 / 40000000000000000 : ℚ)) + (r' := (8280864409230463 / 5000000000000000 : ℚ)) + (U := (-(15749320931358898036187 / 10000000000000000000000 : ℚ))) + (U' := (5045094477641101963813 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (21515320239601 / 32000000000000 : ℚ)) + (s := (738494885709919 / 10000000000000000 : ℚ)) + (q := (8280864409230463 / 40000000000000000 : ℚ)) + (U := (-(15749320931358898036187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_575_15 : Uω (aρ 15) (bρ 15) (21515320239601 / 32000000000000 : ℝ) ≤ @@ -3652,25 +3188,21 @@ lemma U_576_1 : have hlg : Real.log (53337027858336163 / 80000000000000000 : ℝ) ≤ (-(2026979189518170120827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53337027858336163 / 80000000000000000 : ℝ) = - (53337027858336163 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53337027858336163 / 40000000000000000 : ℚ)) - (U := (1438756711981829879173 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53337027858336163 / 40000000000000000 : ℝ) ≤ - (1438756711981829879173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6667104233789197 / 10000000000000000 : ℝ)) (q := - (53337027858336163 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53337027858336163 / 80000000000000000 : ℚ)) + (r' := (53337027858336163 / 40000000000000000 : ℚ)) + (U := (-(2026979189518170120827 / 5000000000000000000000 : ℚ))) + (U' := (1438756711981829879173 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (6667104233789197 / 10000000000000000 : ℚ)) + (q := (53337027858336163 / 80000000000000000 : ℚ)) + (U := (-(2026979189518170120827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_2 : Uω (aρ 2) (bρ 2) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3678,25 +3210,21 @@ lemma U_576_2 : have hlg : Real.log (53145792141342859 / 80000000000000000 : ℝ) ≤ (-(2044938511275047845963 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53145792141342859 / 80000000000000000 : ℝ) = - (53145792141342859 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53145792141342859 / 40000000000000000 : ℚ)) - (U := (1420797390224952154037 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53145792141342859 / 40000000000000000 : ℝ) ≤ - (1420797390224952154037 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6643064317050871 / 10000000000000000 : ℝ)) (q := - (53145792141342859 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53145792141342859 / 80000000000000000 : ℚ)) + (r' := (53145792141342859 / 40000000000000000 : ℚ)) + (U := (-(2044938511275047845963 / 5000000000000000000000 : ℚ))) + (U' := (1420797390224952154037 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (6643064317050871 / 10000000000000000 : ℚ)) + (q := (53145792141342859 / 80000000000000000 : ℚ)) + (U := (-(2044938511275047845963 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_3 : Uω (aρ 3) (bρ 3) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3704,25 +3232,21 @@ lemma U_576_3 : have hlg : Real.log (52763414101442207 / 80000000000000000 : ℝ) ≤ (-(4162085986235097085897 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52763414101442207 / 80000000000000000 : ℝ) = - (52763414101442207 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52763414101442207 / 40000000000000000 : ℚ)) - (U := (2769385816764902914103 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52763414101442207 / 40000000000000000 : ℝ) ≤ - (2769385816764902914103 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1648716478356427 / 2500000000000000 : ℝ)) (q := - (52763414101442207 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52763414101442207 / 80000000000000000 : ℚ)) + (r' := (52763414101442207 / 40000000000000000 : ℚ)) + (U := (-(4162085986235097085897 / 10000000000000000000000 : ℚ))) + (U' := (2769385816764902914103 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (1648716478356427 / 2500000000000000 : ℚ)) + (q := (52763414101442207 / 80000000000000000 : ℚ)) + (U := (-(4162085986235097085897 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_4 : Uω (aρ 4) (bρ 4) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3730,25 +3254,21 @@ lemma U_576_4 : have hlg : Real.log (10425726210792287 / 16000000000000000 : ℝ) ≤ (-(4283122962134978443037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10425726210792287 / 16000000000000000 : ℝ) = - (10425726210792287 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10425726210792287 / 8000000000000000 : ℚ)) - (U := (2648348840865021556963 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10425726210792287 / 8000000000000000 : ℝ) ≤ - (2648348840865021556963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1302892866524103 / 2000000000000000 : ℝ)) (q := - (10425726210792287 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10425726210792287 / 16000000000000000 : ℚ)) + (r' := (10425726210792287 / 8000000000000000 : ℚ)) + (U := (-(4283122962134978443037 / 10000000000000000000000 : ℚ))) + (U' := (2648348840865021556963 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (1302892866524103 / 2000000000000000 : ℚ)) + (q := (10425726210792287 / 16000000000000000 : ℚ)) + (U := (-(4283122962134978443037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_5 : Uω (aρ 5) (bρ 5) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3756,25 +3276,21 @@ lemma U_576_5 : have hlg : Real.log (51162718287578243 / 80000000000000000 : ℝ) ≤ (-(4470155260503364583741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51162718287578243 / 80000000000000000 : ℝ) = - (51162718287578243 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51162718287578243 / 40000000000000000 : ℚ)) - (U := (2461316542496635416259 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51162718287578243 / 40000000000000000 : ℝ) ≤ - (2461316542496635416259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6391176060359717 / 10000000000000000 : ℝ)) (q := - (51162718287578243 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51162718287578243 / 80000000000000000 : ℚ)) + (r' := (51162718287578243 / 40000000000000000 : ℚ)) + (U := (-(4470155260503364583741 / 10000000000000000000000 : ℚ))) + (U' := (2461316542496635416259 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (6391176060359717 / 10000000000000000 : ℚ)) + (q := (51162718287578243 / 80000000000000000 : ℚ)) + (U := (-(4470155260503364583741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_6 : Uω (aρ 6) (bρ 6) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3782,25 +3298,21 @@ lemma U_576_6 : have hlg : Real.log (49779214489893931 / 80000000000000000 : ℝ) ≤ (-(1186072793078736166699 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49779214489893931 / 80000000000000000 : ℝ) = - (49779214489893931 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49779214489893931 / 40000000000000000 : ℚ)) - (U := (546795157671263833301 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49779214489893931 / 40000000000000000 : ℝ) ≤ - (546795157671263833301 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6212540486078639 / 10000000000000000 : ℝ)) (q := - (49779214489893931 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49779214489893931 / 80000000000000000 : ℚ)) + (r' := (49779214489893931 / 40000000000000000 : ℚ)) + (U := (-(1186072793078736166699 / 2500000000000000000000 : ℚ))) + (U' := (546795157671263833301 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (6212540486078639 / 10000000000000000 : ℚ)) + (q := (49779214489893931 / 80000000000000000 : ℚ)) + (U := (-(1186072793078736166699 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_7 : Uω (aρ 7) (bρ 7) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3808,25 +3320,21 @@ lemma U_576_7 : have hlg : Real.log (47895536563943987 / 80000000000000000 : ℝ) ≤ (-(128251079179985541609 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47895536563943987 / 80000000000000000 : ℝ) = - (47895536563943987 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47895536563943987 / 40000000000000000 : ℚ)) - (U := (45035715895014458391 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47895536563943987 / 40000000000000000 : ℝ) ≤ - (45035715895014458391 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5965282385351153 / 10000000000000000 : ℝ)) (q := - (47895536563943987 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47895536563943987 / 80000000000000000 : ℚ)) + (r' := (47895536563943987 / 40000000000000000 : ℚ)) + (U := (-(128251079179985541609 / 250000000000000000000 : ℚ))) + (U' := (45035715895014458391 / 250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (5965282385351153 / 10000000000000000 : ℚ)) + (q := (47895536563943987 / 80000000000000000 : ℚ)) + (U := (-(128251079179985541609 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_8 : Uω (aρ 8) (bρ 8) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3834,25 +3342,21 @@ lemma U_576_8 : have hlg : Real.log (45445255891575023 / 80000000000000000 : ℝ) ≤ (-(2827591000309687841803 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45445255891575023 / 80000000000000000 : ℝ) = - (45445255891575023 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45445255891575023 / 40000000000000000 : ℚ)) - (U := (638144901190312158197 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45445255891575023 / 40000000000000000 : ℝ) ≤ - (638144901190312158197 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44033233348429 / 78125000000000 : ℝ)) (q := - (45445255891575023 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45445255891575023 / 80000000000000000 : ℚ)) + (r' := (45445255891575023 / 40000000000000000 : ℚ)) + (U := (-(2827591000309687841803 / 5000000000000000000000 : ℚ))) + (U' := (638144901190312158197 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (44033233348429 / 78125000000000 : ℚ)) + (q := (45445255891575023 / 80000000000000000 : ℚ)) + (U := (-(2827591000309687841803 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_9 : Uω (aρ 9) (bρ 9) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3860,25 +3364,21 @@ lemma U_576_9 : have hlg : Real.log (42389009167236191 / 80000000000000000 : ℝ) ≤ (-(3175687617663083390177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42389009167236191 / 80000000000000000 : ℝ) = - (42389009167236191 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42389009167236191 / 40000000000000000 : ℚ)) - (U := (290048283836916609823 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42389009167236191 / 40000000000000000 : ℝ) ≤ - (290048283836916609823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1303289453968551 / 2500000000000000 : ℝ)) (q := - (42389009167236191 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42389009167236191 / 80000000000000000 : ℚ)) + (r' := (42389009167236191 / 40000000000000000 : ℚ)) + (U := (-(3175687617663083390177 / 5000000000000000000000 : ℚ))) + (U' := (290048283836916609823 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (1303289453968551 / 2500000000000000 : ℚ)) + (q := (42389009167236191 / 80000000000000000 : ℚ)) + (U := (-(3175687617663083390177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_10 : Uω (aρ 10) (bρ 10) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3886,26 +3386,21 @@ lemma U_576_10 : have hlg : Real.log (38720726184537623 / 80000000000000000 : ℝ) ≤ (-(3628258085777660704223 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38720726184537623 / 80000000000000000 : ℝ) = - (38720726184537623 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38720726184537623 / 20000000000000000 : ℚ)) - (U := (3303213717222339295777 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38720726184537623 / 20000000000000000 : ℝ) ≤ - (3303213717222339295777 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2342323051847281 / 5000000000000000 : ℝ)) (q := - (38720726184537623 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38720726184537623 / 80000000000000000 : ℚ)) + (r' := (38720726184537623 / 20000000000000000 : ℚ)) + (U := (-(3628258085777660704223 / 5000000000000000000000 : ℚ))) + (U' := (3303213717222339295777 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (2342323051847281 / 5000000000000000 : ℚ)) + (q := (38720726184537623 / 80000000000000000 : ℚ)) + (U := (-(3628258085777660704223 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_11 : Uω (aρ 11) (bρ 11) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3913,26 +3408,21 @@ lemma U_576_11 : have hlg : Real.log (34463486500790003 / 80000000000000000 : ℝ) ≤ (-(4210631164367377930677 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34463486500790003 / 80000000000000000 : ℝ) = - (34463486500790003 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34463486500790003 / 20000000000000000 : ℚ)) - (U := (2720840638632622069323 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34463486500790003 / 20000000000000000 : ℝ) ≤ - (2720840638632622069323 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4038812808962657 / 10000000000000000 : ℝ)) (q := - (34463486500790003 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34463486500790003 / 80000000000000000 : ℚ)) + (r' := (34463486500790003 / 20000000000000000 : ℚ)) + (U := (-(4210631164367377930677 / 5000000000000000000000 : ℚ))) + (U' := (2720840638632622069323 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (4038812808962657 / 10000000000000000 : ℚ)) + (q := (34463486500790003 / 80000000000000000 : ℚ)) + (U := (-(4210631164367377930677 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_12 : Uω (aρ 12) (bρ 12) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3940,26 +3430,21 @@ lemma U_576_12 : have hlg : Real.log (29641263796719831 / 80000000000000000 : ℝ) ≤ (-(7756712472024757971 / 7812500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29641263796719831 / 80000000000000000 : ℝ) = - (29641263796719831 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29641263796719831 / 20000000000000000 : ℚ)) - (U := (3073712220162742029 / 7812500000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29641263796719831 / 20000000000000000 : ℝ) ≤ - (3073712220162742029 / 7812500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1628478614815057 / 5000000000000000 : ℝ)) (q := - (29641263796719831 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29641263796719831 / 80000000000000000 : ℚ)) + (r' := (29641263796719831 / 20000000000000000 : ℚ)) + (U := (-(7756712472024757971 / 7812500000000000000 : ℚ))) + (U' := (3073712220162742029 / 7812500000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (1628478614815057 / 5000000000000000 : ℚ)) + (q := (29641263796719831 / 80000000000000000 : ℚ)) + (U := (-(7756712472024757971 / 7812500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_13 : Uω (aρ 13) (bρ 13) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3967,26 +3452,21 @@ lemma U_576_13 : have hlg : Real.log (24164386876963203 / 80000000000000000 : ℝ) ≤ (-(5985733507685321610093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24164386876963203 / 80000000000000000 : ℝ) = - (24164386876963203 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24164386876963203 / 20000000000000000 : ℚ)) - (U := (945738295314678389907 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24164386876963203 / 20000000000000000 : ℝ) ≤ - (945738295314678389907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2287119741285957 / 10000000000000000 : ℝ)) (q := - (24164386876963203 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24164386876963203 / 80000000000000000 : ℚ)) + (r' := (24164386876963203 / 20000000000000000 : ℚ)) + (U := (-(5985733507685321610093 / 5000000000000000000000 : ℚ))) + (U' := (945738295314678389907 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (2287119741285957 / 10000000000000000 : ℚ)) + (q := (24164386876963203 / 80000000000000000 : ℚ)) + (U := (-(5985733507685321610093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_14 : Uω (aρ 14) (bρ 14) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -3994,26 +3474,21 @@ lemma U_576_14 : have hlg : Real.log (16740227371697279 / 80000000000000000 : ℝ) ≤ (-(15642119863862916581919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (16740227371697279 / 80000000000000000 : ℝ) = - (16740227371697279 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16740227371697279 / 10000000000000000 : ℚ)) - (U := (5152295545137083418081 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16740227371697279 / 10000000000000000 : ℝ) ≤ - (5152295545137083418081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (193751787503619 / 2500000000000000 : ℝ)) (q := - (16740227371697279 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16740227371697279 / 80000000000000000 : ℚ)) + (r' := (16740227371697279 / 10000000000000000 : ℚ)) + (U := (-(15642119863862916581919 / 10000000000000000000000 : ℚ))) + (U' := (5152295545137083418081 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43082559672831 / 64000000000000 : ℚ)) + (s := (193751787503619 / 2500000000000000 : ℚ)) + (q := (16740227371697279 / 80000000000000000 : ℚ)) + (U := (-(15642119863862916581919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_576_15 : Uω (aρ 15) (bρ 15) (43082559672831 / 64000000000000 : ℝ) ≤ @@ -4115,24 +3590,21 @@ lemma U_577_1 : have hlg : Real.log (104300638840089 / 156250000000000 : ℝ) ≤ (-(4041798013437740677517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (104300638840089 / 156250000000000 : ℝ) = (104300638840089 / 78125000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (104300638840089 / 78125000000000 : ℚ)) - (U := (2889673789562259322483 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (104300638840089 / 78125000000000 : ℝ) ≤ - (2889673789562259322483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6675216666732017 / 10000000000000000 : ℝ)) (q := - (104300638840089 / 156250000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (104300638840089 / 156250000000000 : ℚ)) + (r' := (104300638840089 / 78125000000000 : ℚ)) + (U := (-(4041798013437740677517 / 10000000000000000000000 : ℚ))) + (U' := (2889673789562259322483 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (6675216666732017 / 10000000000000000 : ℚ)) + (q := (104300638840089 / 156250000000000 : ℚ)) + (U := (-(4041798013437740677517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_2 : Uω (aρ 2) (bρ 2) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4140,25 +3612,21 @@ lemma U_577_2 : have hlg : Real.log (13302673172915271 / 20000000000000000 : ℝ) ≤ (-(254854542385908595437 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13302673172915271 / 20000000000000000 : ℝ) = - (13302673172915271 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13302673172915271 / 10000000000000000 : ℚ)) - (U := (178362445301591404563 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13302673172915271 / 10000000000000000 : ℝ) ≤ - (178362445301591404563 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (831397135078237 / 1250000000000000 : ℝ)) (q := - (13302673172915271 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13302673172915271 / 20000000000000000 : ℚ)) + (r' := (13302673172915271 / 10000000000000000 : ℚ)) + (U := (-(254854542385908595437 / 625000000000000000000 : ℚ))) + (U' := (178362445301591404563 / 625000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (831397135078237 / 1250000000000000 : ℚ)) + (q := (13302673172915271 / 20000000000000000 : ℚ)) + (U := (-(254854542385908595437 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_3 : Uω (aρ 3) (bρ 3) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4166,25 +3634,21 @@ lemma U_577_3 : have hlg : Real.log (6603539825740297 / 10000000000000000 : ℝ) ≤ (-(4149792502457496461927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6603539825740297 / 10000000000000000 : ℝ) = - (6603539825740297 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6603539825740297 / 5000000000000000 : ℚ)) - (U := (2781679300542503538073 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6603539825740297 / 5000000000000000 : ℝ) ≤ - (2781679300542503538073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6602979665541219 / 10000000000000000 : ℝ)) (q := - (6603539825740297 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6603539825740297 / 10000000000000000 : ℚ)) + (r' := (6603539825740297 / 5000000000000000 : ℚ)) + (U := (-(4149792502457496461927 / 10000000000000000000000 : ℚ))) + (U' := (2781679300542503538073 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (6602979665541219 / 10000000000000000 : ℚ)) + (q := (6603539825740297 / 10000000000000000 : ℚ)) + (U := (-(4149792502457496461927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_4 : Uω (aρ 4) (bρ 4) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4192,25 +3656,21 @@ lemma U_577_4 : have hlg : Real.log (1631048315956143 / 2500000000000000 : ℝ) ≤ (-(4270677848971521522911 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1631048315956143 / 2500000000000000 : ℝ) = - (1631048315956143 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1631048315956143 / 1250000000000000 : ℚ)) - (U := (2660793954028478477089 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1631048315956143 / 1250000000000000 : ℝ) ≤ - (2660793954028478477089 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6522580722774769 / 10000000000000000 : ℝ)) (q := - (1631048315956143 / 2500000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1631048315956143 / 2500000000000000 : ℚ)) + (r' := (1631048315956143 / 1250000000000000 : ℚ)) + (U := (-(4270677848971521522911 / 10000000000000000000000 : ℚ))) + (U' := (2660793954028478477089 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (6522580722774769 / 10000000000000000 : ℚ)) + (q := (1631048315956143 / 2500000000000000 : ℚ)) + (U := (-(4270677848971521522911 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_5 : Uω (aρ 5) (bρ 5) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4218,25 +3678,21 @@ lemma U_577_5 : have hlg : Real.log (12806914876599639 / 20000000000000000 : ℝ) ≤ (-(4457470235029769292473 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12806914876599639 / 20000000000000000 : ℝ) = - (12806914876599639 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12806914876599639 / 10000000000000000 : ℚ)) - (U := (2474001567970230707527 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12806914876599639 / 10000000000000000 : ℝ) ≤ - (2474001567970230707527 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (799912373882533 / 1250000000000000 : ℝ)) (q := - (12806914876599639 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12806914876599639 / 20000000000000000 : ℚ)) + (r' := (12806914876599639 / 10000000000000000 : ℚ)) + (U := (-(4457470235029769292473 / 10000000000000000000000 : ℚ))) + (U' := (2474001567970230707527 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (799912373882533 / 1250000000000000 : ℚ)) + (q := (12806914876599639 / 20000000000000000 : ℚ)) + (U := (-(4457470235029769292473 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_6 : Uω (aρ 6) (bρ 6) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4244,25 +3700,21 @@ lemma U_577_6 : have hlg : Real.log (12461054090802993 / 20000000000000000 : ℝ) ≤ (-(2365620827675887082541 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12461054090802993 / 20000000000000000 : ℝ) = - (12461054090802993 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12461054090802993 / 10000000000000000 : ℚ)) - (U := (1100115073824112917459 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12461054090802993 / 10000000000000000 : ℝ) ≤ - (1100115073824112917459 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3110339290201809 / 5000000000000000 : ℝ)) (q := - (12461054090802993 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12461054090802993 / 20000000000000000 : ℚ)) + (r' := (12461054090802993 / 10000000000000000 : ℚ)) + (U := (-(2365620827675887082541 / 5000000000000000000000 : ℚ))) + (U' := (1100115073824112917459 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (3110339290201809 / 5000000000000000 : ℚ)) + (q := (12461054090802993 / 20000000000000000 : ℚ)) + (U := (-(2365620827675887082541 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_7 : Uω (aρ 7) (bρ 7) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4270,25 +3722,21 @@ lemma U_577_7 : have hlg : Real.log (11990167720064659 / 20000000000000000 : ℝ) ≤ (-(1279113290058657057013 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11990167720064659 / 20000000000000000 : ℝ) = - (11990167720064659 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11990167720064659 / 10000000000000000 : ℚ)) - (U := (453754660691342942987 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11990167720064659 / 10000000000000000 : ℝ) ≤ - (453754660691342942987 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1493363397606321 / 2500000000000000 : ℝ)) (q := - (11990167720064659 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11990167720064659 / 20000000000000000 : ℚ)) + (r' := (11990167720064659 / 10000000000000000 : ℚ)) + (U := (-(1279113290058657057013 / 2500000000000000000000 : ℚ))) + (U' := (453754660691342942987 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (1493363397606321 / 2500000000000000 : ℚ)) + (q := (11990167720064659 / 20000000000000000 : ℚ)) + (U := (-(1279113290058657057013 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_8 : Uω (aρ 8) (bρ 8) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4296,25 +3744,21 @@ lemma U_577_8 : have hlg : Real.log (1137766635635763 / 2000000000000000 : ℝ) ≤ (-(1128159861942127147153 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1137766635635763 / 2000000000000000 : ℝ) = - (1137766635635763 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1137766635635763 / 1000000000000000 : ℚ)) - (U := (258134498657872852847 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (1137766635635763 / 1000000000000000 : ℝ) ≤ - (258134498657872852847 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1128898775611651 / 2000000000000000 : ℝ)) (q := - (1137766635635763 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1137766635635763 / 2000000000000000 : ℚ)) + (r' := (1137766635635763 / 1000000000000000 : ℚ)) + (U := (-(1128159861942127147153 / 2000000000000000000000 : ℚ))) + (U' := (258134498657872852847 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (1128898775611651 / 2000000000000000 : ℚ)) + (q := (1137766635635763 / 2000000000000000 : ℚ)) + (U := (-(1128159861942127147153 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_9 : Uω (aρ 9) (bρ 9) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4322,25 +3766,21 @@ lemma U_577_9 : have hlg : Real.log (663358913761543 / 1250000000000000 : ℝ) ≤ (-(6335826382699116403269 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (663358913761543 / 1250000000000000 : ℝ) = - (663358913761543 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (663358913761543 / 625000000000000 : ℚ)) - (U := (595645420300883596731 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (663358913761543 / 625000000000000 : ℝ) ≤ - (595645420300883596731 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5221535770245313 / 10000000000000000 : ℝ)) (q := - (663358913761543 / 1250000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (663358913761543 / 1250000000000000 : ℚ)) + (r' := (663358913761543 / 625000000000000 : ℚ)) + (U := (-(6335826382699116403269 / 10000000000000000000000 : ℚ))) + (U' := (595645420300883596731 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (5221535770245313 / 10000000000000000 : ℚ)) + (q := (663358913761543 / 1250000000000000 : ℚ)) + (U := (-(6335826382699116403269 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_10 : Uω (aρ 10) (bρ 10) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4348,26 +3788,21 @@ lemma U_577_10 : have hlg : Real.log (9696943697932837 / 20000000000000000 : ℝ) ≤ (-(3619607599305394259193 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9696943697932837 / 20000000000000000 : ℝ) = - (9696943697932837 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9696943697932837 / 5000000000000000 : ℚ)) - (U := (3311864203694605740807 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9696943697932837 / 5000000000000000 : ℝ) ≤ - (3311864203694605740807 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2346647940744231 / 5000000000000000 : ℝ)) (q := - (9696943697932837 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9696943697932837 / 20000000000000000 : ℚ)) + (r' := (9696943697932837 / 5000000000000000 : ℚ)) + (U := (-(3619607599305394259193 / 5000000000000000000000 : ℚ))) + (U' := (3311864203694605740807 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (2346647940744231 / 5000000000000000 : ℚ)) + (q := (9696943697932837 / 20000000000000000 : ℚ)) + (U := (-(3619607599305394259193 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_11 : Uω (aρ 11) (bρ 11) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4375,26 +3810,21 @@ lemma U_577_11 : have hlg : Real.log (8633175185095221 / 20000000000000000 : ℝ) ≤ (-(4200599557466197558131 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8633175185095221 / 20000000000000000 : ℝ) = - (8633175185095221 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8633175185095221 / 5000000000000000 : ℚ)) - (U := (2730872245533802441869 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8633175185095221 / 5000000000000000 : ℝ) ≤ - (2730872245533802441869 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2024001997427923 / 5000000000000000 : ℝ)) (q := - (8633175185095221 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8633175185095221 / 20000000000000000 : ℚ)) + (r' := (8633175185095221 / 5000000000000000 : ℚ)) + (U := (-(4200599557466197558131 / 5000000000000000000000 : ℚ))) + (U' := (2730872245533802441869 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (2024001997427923 / 5000000000000000 : ℚ)) + (q := (8633175185095221 / 20000000000000000 : ℚ)) + (U := (-(4200599557466197558131 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_12 : Uω (aρ 12) (bρ 12) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4402,26 +3832,21 @@ lemma U_577_12 : have hlg : Real.log (3714383566154969 / 10000000000000000 : ℝ) ≤ (-(1980744718241945239729 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3714383566154969 / 10000000000000000 : ℝ) = - (3714383566154969 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3714383566154969 / 2500000000000000 : ℚ)) - (U := (791844002958054760271 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3714383566154969 / 2500000000000000 : ℝ) ≤ - (791844002958054760271 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3267296038755563 / 10000000000000000 : ℝ)) (q := - (3714383566154969 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3714383566154969 / 10000000000000000 : ℚ)) + (r' := (3714383566154969 / 2500000000000000 : ℚ)) + (U := (-(1980744718241945239729 / 2000000000000000000000 : ℚ))) + (U' := (791844002958054760271 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (3267296038755563 / 10000000000000000 : ℚ)) + (q := (3714383566154969 / 10000000000000000 : ℚ)) + (U := (-(1980744718241945239729 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_13 : Uω (aρ 13) (bρ 13) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4429,26 +3854,21 @@ lemma U_577_13 : have hlg : Real.log (3031250076342061 / 10000000000000000 : ℝ) ≤ (-(596804995792744646391 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3031250076342061 / 10000000000000000 : ℝ) = - (3031250076342061 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3031250076342061 / 2500000000000000 : ℚ)) - (U := (96342184507255353609 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3031250076342061 / 2500000000000000 : ℝ) ≤ - (96342184507255353609 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2300410800724747 / 10000000000000000 : ℝ)) (q := - (3031250076342061 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3031250076342061 / 10000000000000000 : ℚ)) + (r' := (3031250076342061 / 2500000000000000 : ℚ)) + (U := (-(596804995792744646391 / 500000000000000000000 : ℚ))) + (U' := (96342184507255353609 / 500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (2300410800724747 / 10000000000000000 : ℚ)) + (q := (3031250076342061 / 10000000000000000 : ℚ)) + (U := (-(596804995792744646391 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_14 : Uω (aρ 14) (bρ 14) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4456,26 +3876,21 @@ lemma U_577_14 : have hlg : Real.log (4228118294220143 / 20000000000000000 : ℝ) ≤ (-(3884938065980386746899 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4228118294220143 / 20000000000000000 : ℝ) = - (4228118294220143 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4228118294220143 / 2500000000000000 : ℚ)) - (U := (1313665786269613253101 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4228118294220143 / 2500000000000000 : ℝ) ≤ - (1313665786269613253101 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (101244528413221 / 1250000000000000 : ℝ)) (q := - (4228118294220143 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4228118294220143 / 20000000000000000 : ℚ)) + (r' := (4228118294220143 / 2500000000000000 : ℚ)) + (U := (-(3884938065980386746899 / 2500000000000000000000 : ℚ))) + (U' := (1313665786269613253101 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2156723943323 / 3200000000000 : ℚ)) + (s := (101244528413221 / 1250000000000000 : ℚ)) + (q := (4228118294220143 / 20000000000000000 : ℚ)) + (U := (-(3884938065980386746899 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_577_15 : Uω (aρ 15) (bρ 15) (2156723943323 / 3200000000000 : ℝ) ≤ @@ -4577,25 +3992,21 @@ lemma U_578_1 : have hlg : Real.log (53466826313342649 / 80000000000000000 : ℝ) ≤ (-(4029652417436910217643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53466826313342649 / 80000000000000000 : ℝ) = - (53466826313342649 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53466826313342649 / 40000000000000000 : ℚ)) - (U := (2901819385563089782357 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53466826313342649 / 40000000000000000 : ℝ) ≤ - (2901819385563089782357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1670832274882939 / 2500000000000000 : ℝ)) (q := - (53466826313342649 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53466826313342649 / 80000000000000000 : ℚ)) + (r' := (53466826313342649 / 40000000000000000 : ℚ)) + (U := (-(4029652417436910217643 / 10000000000000000000000 : ℚ))) + (U' := (2901819385563089782357 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (1670832274882939 / 2500000000000000 : ℚ)) + (q := (53466826313342649 / 80000000000000000 : ℚ)) + (U := (-(4029652417436910217643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_2 : Uω (aρ 2) (bρ 2) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4603,25 +4014,21 @@ lemma U_578_2 : have hlg : Real.log (53275593238182609 / 80000000000000000 : ℝ) ≤ (-(4065483210959910322499 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53275593238182609 / 80000000000000000 : ℝ) = - (53275593238182609 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53275593238182609 / 40000000000000000 : ℚ)) - (U := (2865988592040089677501 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53275593238182609 / 40000000000000000 : ℝ) ≤ - (2865988592040089677501 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3329644921625873 / 5000000000000000 : ℝ)) (q := - (53275593238182609 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53275593238182609 / 80000000000000000 : ℚ)) + (r' := (53275593238182609 / 40000000000000000 : ℚ)) + (U := (-(4065483210959910322499 / 10000000000000000000000 : ℚ))) + (U' := (2865988592040089677501 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (3329644921625873 / 5000000000000000 : ℚ)) + (q := (53275593238182609 / 80000000000000000 : ℚ)) + (U := (-(4065483210959910322499 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_3 : Uω (aρ 3) (bρ 3) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4629,25 +4036,21 @@ lemma U_578_3 : have hlg : Real.log (52893223096872921 / 80000000000000000 : ℝ) ≤ (-(4137514115657745432343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52893223096872921 / 80000000000000000 : ℝ) = - (52893223096872921 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52893223096872921 / 40000000000000000 : ℚ)) - (U := (2793957687342254567657 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52893223096872921 / 40000000000000000 : ℝ) ≤ - (2793957687342254567657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1652773353568581 / 2500000000000000 : ℝ)) (q := - (52893223096872921 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52893223096872921 / 80000000000000000 : ℚ)) + (r' := (52893223096872921 / 40000000000000000 : ℚ)) + (U := (-(4137514115657745432343 / 10000000000000000000000 : ℚ))) + (U' := (2793957687342254567657 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (1652773353568581 / 2500000000000000 : ℚ)) + (q := (52893223096872921 / 80000000000000000 : ℚ)) + (U := (-(4137514115657745432343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_4 : Uω (aρ 4) (bρ 4) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4655,25 +4058,21 @@ lemma U_578_4 : have hlg : Real.log (52258461127311233 / 80000000000000000 : ℝ) ≤ (-(2129124106141065259827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52258461127311233 / 80000000000000000 : ℝ) = - (52258461127311233 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52258461127311233 / 40000000000000000 : ℚ)) - (U := (1336611795358934740173 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52258461127311233 / 40000000000000000 : ℝ) ≤ - (1336611795358934740173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3265348551474451 / 5000000000000000 : ℝ)) (q := - (52258461127311233 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52258461127311233 / 80000000000000000 : ℚ)) + (r' := (52258461127311233 / 40000000000000000 : ℚ)) + (U := (-(2129124106141065259827 / 5000000000000000000000 : ℚ))) + (U' := (1336611795358934740173 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (3265348551474451 / 5000000000000000 : ℚ)) + (q := (52258461127311233 / 80000000000000000 : ℚ)) + (U := (-(2129124106141065259827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_5 : Uω (aρ 5) (bρ 5) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4681,25 +4080,21 @@ lemma U_578_5 : have hlg : Real.log (51292600618223461 / 80000000000000000 : ℝ) ≤ (-(1111200325254916125143 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51292600618223461 / 80000000000000000 : ℝ) = - (51292600618223461 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51292600618223461 / 40000000000000000 : ℚ)) - (U := (621667625495083874857 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51292600618223461 / 40000000000000000 : ℝ) ≤ - (621667625495083874857 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6407421895011959 / 10000000000000000 : ℝ)) (q := - (51292600618223461 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51292600618223461 / 80000000000000000 : ℚ)) + (r' := (51292600618223461 / 40000000000000000 : ℚ)) + (U := (-(1111200325254916125143 / 2500000000000000000000 : ℚ))) + (U' := (621667625495083874857 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (6407421895011959 / 10000000000000000 : ℚ)) + (q := (51292600618223461 / 80000000000000000 : ℚ)) + (U := (-(1111200325254916125143 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_6 : Uω (aρ 6) (bρ 6) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4707,25 +4102,21 @@ lemma U_578_6 : have hlg : Real.log (9981843593624249 / 16000000000000000 : ℝ) ≤ (-(1179552299741664472367 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9981843593624249 / 16000000000000000 : ℝ) = - (9981843593624249 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9981843593624249 / 8000000000000000 : ℚ)) - (U := (553315651008335527633 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9981843593624249 / 8000000000000000 : ℝ) ≤ - (553315651008335527633 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1245763321525281 / 2000000000000000 : ℝ)) (q := - (9981843593624249 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9981843593624249 / 16000000000000000 : ℚ)) + (r' := (9981843593624249 / 8000000000000000 : ℚ)) + (U := (-(1179552299741664472367 / 2500000000000000000000 : ℚ))) + (U' := (553315651008335527633 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (1245763321525281 / 2000000000000000 : ℚ)) + (q := (9981843593624249 / 16000000000000000 : ℚ)) + (U := (-(1179552299741664472367 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_7 : Uω (aρ 7) (bρ 7) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4733,25 +4124,21 @@ lemma U_578_7 : have hlg : Real.log (9605160911191557 / 16000000000000000 : ℝ) ≤ (-(5102881730426360024451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9605160911191557 / 16000000000000000 : ℝ) = - (9605160911191557 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9605160911191557 / 8000000000000000 : ℚ)) - (U := (1828590072573639975549 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9605160911191557 / 8000000000000000 : ℝ) ≤ - (1828590072573639975549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (299081231767277 / 500000000000000 : ℝ)) (q := - (9605160911191557 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9605160911191557 / 16000000000000000 : ℚ)) + (r' := (9605160911191557 / 8000000000000000 : ℚ)) + (U := (-(5102881730426360024451 / 10000000000000000000000 : ℚ))) + (U' := (1828590072573639975549 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (299081231767277 / 500000000000000 : ℚ)) + (q := (9605160911191557 / 16000000000000000 : ℚ)) + (U := (-(5102881730426360024451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_8 : Uω (aρ 8) (bρ 8) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4759,25 +4146,21 @@ lemma U_578_8 : have hlg : Real.log (45576073482376601 / 80000000000000000 : ℝ) ≤ (-(1125287519865866481021 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45576073482376601 / 80000000000000000 : ℝ) = - (45576073482376601 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45576073482376601 / 40000000000000000 : ℚ)) - (U := (261006840734133518979 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45576073482376601 / 40000000000000000 : ℝ) ≤ - (261006840734133518979 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1413183379572561 / 2500000000000000 : ℝ)) (q := - (45576073482376601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45576073482376601 / 80000000000000000 : ℚ)) + (r' := (45576073482376601 / 40000000000000000 : ℚ)) + (U := (-(1125287519865866481021 / 2000000000000000000000 : ℚ))) + (U' := (261006840734133518979 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (1413183379572561 / 2500000000000000 : ℚ)) + (q := (45576073482376601 / 80000000000000000 : ℚ)) + (U := (-(1125287519865866481021 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_9 : Uω (aρ 9) (bρ 9) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4785,25 +4168,21 @@ lemma U_578_9 : have hlg : Real.log (42520928444658101 / 80000000000000000 : ℝ) ≤ (-(6320302456974391084841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42520928444658101 / 80000000000000000 : ℝ) = - (42520928444658101 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42520928444658101 / 40000000000000000 : ℚ)) - (U := (611169346025608915159 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42520928444658101 / 40000000000000000 : ℝ) ≤ - (611169346025608915159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5229912887220619 / 10000000000000000 : ℝ)) (q := - (42520928444658101 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42520928444658101 / 80000000000000000 : ℚ)) + (r' := (42520928444658101 / 40000000000000000 : ℚ)) + (U := (-(6320302456974391084841 / 10000000000000000000000 : ℚ))) + (U' := (611169346025608915159 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (5229912887220619 / 10000000000000000 : ℚ)) + (q := (42520928444658101 / 80000000000000000 : ℚ)) + (U := (-(6320302456974391084841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_10 : Uω (aρ 10) (bρ 10) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4811,26 +4190,21 @@ lemma U_578_10 : have hlg : Real.log (38854815735675529 / 80000000000000000 : ℝ) ≤ (-(3610973039310716154581 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38854815735675529 / 80000000000000000 : ℝ) = - (38854815735675529 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38854815735675529 / 20000000000000000 : ℚ)) - (U := (3320498763689283845419 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38854815735675529 / 20000000000000000 : ℝ) ≤ - (3320498763689283845419 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (587742967933747 / 1250000000000000 : ℝ)) (q := - (38854815735675529 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38854815735675529 / 80000000000000000 : ℚ)) + (r' := (38854815735675529 / 20000000000000000 : ℚ)) + (U := (-(3610973039310716154581 / 5000000000000000000000 : ℚ))) + (U' := (3320498763689283845419 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (587742967933747 / 1250000000000000 : ℚ)) + (q := (38854815735675529 / 80000000000000000 : ℚ)) + (U := (-(3610973039310716154581 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_11 : Uω (aρ 11) (bρ 11) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4838,26 +4212,21 @@ lemma U_578_11 : have hlg : Real.log (34601896575832069 / 80000000000000000 : ℝ) ≤ (-(8381181392621563129199 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34601896575832069 / 80000000000000000 : ℝ) = - (34601896575832069 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34601896575832069 / 20000000000000000 : ℚ)) - (U := (5481762213378436870801 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34601896575832069 / 20000000000000000 : ℝ) ≤ - (5481762213378436870801 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4057190579714111 / 10000000000000000 : ℝ)) (q := - (34601896575832069 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34601896575832069 / 80000000000000000 : ℚ)) + (r' := (34601896575832069 / 20000000000000000 : ℚ)) + (U := (-(8381181392621563129199 / 10000000000000000000000 : ℚ))) + (U' := (5481762213378436870801 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (4057190579714111 / 10000000000000000 : ℚ)) + (q := (34601896575832069 / 80000000000000000 : ℚ)) + (U := (-(8381181392621563129199 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_12 : Uω (aρ 12) (bρ 12) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4865,26 +4234,21 @@ lemma U_578_12 : have hlg : Real.log (29788823127510321 / 80000000000000000 : ℝ) ≤ (-(9878933738315134485679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29788823127510321 / 80000000000000000 : ℝ) = - (29788823127510321 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29788823127510321 / 20000000000000000 : ℚ)) - (U := (3984009867684865514321 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29788823127510321 / 20000000000000000 : ℝ) ≤ - (3984009867684865514321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1638811157159337 / 5000000000000000 : ℝ)) (q := - (29788823127510321 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29788823127510321 / 80000000000000000 : ℚ)) + (r' := (29788823127510321 / 20000000000000000 : ℚ)) + (U := (-(9878933738315134485679 / 10000000000000000000000 : ℚ))) + (U' := (3984009867684865514321 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (1638811157159337 / 5000000000000000 : ℚ)) + (q := (29788823127510321 / 80000000000000000 : ℚ)) + (U := (-(9878933738315134485679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_13 : Uω (aρ 13) (bρ 13) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4892,25 +4256,21 @@ lemma U_578_13 : have hlg : Real.log (973416908640921 / 3200000000000000 : ℝ) ≤ (-(2975234050794647865737 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (973416908640921 / 3200000000000000 : ℝ) = - (973416908640921 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (973416908640921 / 800000000000000 : ℚ)) - (U := (490501850705352134263 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (973416908640921 / 800000000000000 : ℝ) ≤ - (490501850705352134263 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46273079060837 / 200000000000000 : ℝ)) (q := - (973416908640921 / 3200000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (973416908640921 / 3200000000000000 : ℚ)) + (r' := (973416908640921 / 800000000000000 : ℚ)) + (U := (-(2975234050794647865737 / 2500000000000000000000 : ℚ))) + (U' := (490501850705352134263 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (46273079060837 / 200000000000000 : ℚ)) + (q := (973416908640921 / 3200000000000000 : ℚ)) + (U := (-(2975234050794647865737 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_14 : Uω (aρ 14) (bρ 14) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -4918,26 +4278,21 @@ lemma U_578_14 : have hlg : Real.log (17079243507897601 / 80000000000000000 : ℝ) ≤ (-(15441627376211997410399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17079243507897601 / 80000000000000000 : ℝ) = - (17079243507897601 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17079243507897601 / 10000000000000000 : ℚ)) - (U := (5352788032788002589601 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17079243507897601 / 10000000000000000 : ℝ) ≤ - (5352788032788002589601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421768218027747 / 5000000000000000 : ℝ)) (q := - (17079243507897601 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17079243507897601 / 80000000000000000 : ℚ)) + (r' := (17079243507897601 / 10000000000000000 : ℚ)) + (U := (-(15441627376211997410399 / 10000000000000000000000 : ℚ))) + (U' := (5352788032788002589601 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43186398060089 / 64000000000000 : ℚ)) + (s := (421768218027747 / 5000000000000000 : ℚ)) + (q := (17079243507897601 / 80000000000000000 : ℚ)) + (U := (-(15441627376211997410399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_578_15 : Uω (aρ 15) (bρ 15) (43186398060089 / 64000000000000 : ℝ) ≤ @@ -5040,25 +4395,21 @@ lemma U_579_1 : have hlg : Real.log (26765862769994741 / 40000000000000000 : ℝ) ≤ (-(2008760777599865418403 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26765862769994741 / 40000000000000000 : ℝ) = - (26765862769994741 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26765862769994741 / 20000000000000000 : ℚ)) - (U := (1456975123900134581597 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26765862769994741 / 20000000000000000 : ℝ) ≤ - (1456975123900134581597 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6691441532188933 / 10000000000000000 : ℝ)) (q := - (26765862769994741 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26765862769994741 / 40000000000000000 : ℚ)) + (r' := (26765862769994741 / 20000000000000000 : ℚ)) + (U := (-(2008760777599865418403 / 5000000000000000000000 : ℚ))) + (U' := (1456975123900134581597 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (6691441532188933 / 10000000000000000 : ℚ)) + (q := (26765862769994741 / 40000000000000000 : ℚ)) + (U := (-(2008760777599865418403 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_2 : Uω (aρ 2) (bρ 2) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5066,25 +4417,21 @@ lemma U_579_2 : have hlg : Real.log (26670246890460647 / 40000000000000000 : ℝ) ≤ (-(506663573084745193583 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26670246890460647 / 40000000000000000 : ℝ) = - (26670246890460647 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26670246890460647 / 20000000000000000 : ℚ)) - (U := (359770402290254806417 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26670246890460647 / 20000000000000000 : ℝ) ≤ - (359770402290254806417 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3333701302465943 / 5000000000000000 : ℝ)) (q := - (26670246890460647 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26670246890460647 / 40000000000000000 : ℚ)) + (r' := (26670246890460647 / 20000000000000000 : ℚ)) + (U := (-(506663573084745193583 / 1250000000000000000000 : ℚ))) + (U' := (359770402290254806417 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (3333701302465943 / 5000000000000000 : ℚ)) + (q := (26670246890460647 / 40000000000000000 : ℚ)) + (U := (-(506663573084745193583 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_3 : Uω (aρ 3) (bρ 3) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5092,25 +4439,21 @@ lemma U_579_3 : have hlg : Real.log (26479063787171797 / 40000000000000000 : ℝ) ≤ (-(4125250788795458835007 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26479063787171797 / 40000000000000000 : ℝ) = - (26479063787171797 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26479063787171797 / 20000000000000000 : ℚ)) - (U := (2806221014204541164993 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26479063787171797 / 20000000000000000 : ℝ) ≤ - (2806221014204541164993 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6619207159637461 / 10000000000000000 : ℝ)) (q := - (26479063787171797 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26479063787171797 / 40000000000000000 : ℚ)) + (r' := (26479063787171797 / 20000000000000000 : ℚ)) + (U := (-(4125250788795458835007 / 10000000000000000000000 : ℚ))) + (U' := (2806221014204541164993 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (6619207159637461 / 10000000000000000 : ℚ)) + (q := (26479063787171797 / 40000000000000000 : ℚ)) + (U := (-(4125250788795458835007 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_4 : Uω (aρ 4) (bρ 4) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5118,25 +4461,21 @@ lemma U_579_4 : have hlg : Real.log (26161688052127029 / 40000000000000000 : ℝ) ≤ (-(2122917006801633900917 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26161688052127029 / 40000000000000000 : ℝ) = - (26161688052127029 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26161688052127029 / 20000000000000000 : ℚ)) - (U := (1342818894698366099083 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26161688052127029 / 20000000000000000 : ℝ) ≤ - (1342818894698366099083 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6538813473180077 / 10000000000000000 : ℝ)) (q := - (26161688052127029 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26161688052127029 / 40000000000000000 : ℚ)) + (r' := (26161688052127029 / 20000000000000000 : ℚ)) + (U := (-(2122917006801633900917 / 5000000000000000000000 : ℚ))) + (U' := (1342818894698366099083 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (6538813473180077 / 10000000000000000 : ℚ)) + (q := (26161688052127029 / 40000000000000000 : ℚ)) + (U := (-(2122917006801633900917 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_5 : Uω (aρ 5) (bρ 5) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5144,25 +4483,21 @@ lemma U_579_5 : have hlg : Real.log (5135754162345937 / 8000000000000000 : ℝ) ≤ (-(1108037104411686499443 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5135754162345937 / 8000000000000000 : ℝ) = - (5135754162345937 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5135754162345937 / 4000000000000000 : ℚ)) - (U := (624830846338313500557 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5135754162345937 / 4000000000000000 : ℝ) ≤ - (624830846338313500557 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1283108954463281 / 2000000000000000 : ℝ)) (q := - (5135754162345937 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5135754162345937 / 8000000000000000 : ℚ)) + (r' := (5135754162345937 / 4000000000000000 : ℚ)) + (U := (-(1108037104411686499443 / 2500000000000000000000 : ℚ))) + (U' := (624830846338313500557 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (1283108954463281 / 2000000000000000 : ℚ)) + (q := (5135754162345937 / 8000000000000000 : ℚ)) + (U := (-(1108037104411686499443 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_6 : Uω (aρ 6) (bρ 6) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5170,25 +4505,21 @@ lemma U_579_6 : have hlg : Real.log (24987109652836207 / 40000000000000000 : ℝ) ≤ (-(4705193758468929470479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24987109652836207 / 40000000000000000 : ℝ) = - (24987109652836207 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24987109652836207 / 20000000000000000 : ℚ)) - (U := (2226278044531070529521 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24987109652836207 / 20000000000000000 : ℝ) ≤ - (2226278044531070529521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3118477284004833 / 5000000000000000 : ℝ)) (q := - (24987109652836207 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24987109652836207 / 40000000000000000 : ℚ)) + (r' := (24987109652836207 / 20000000000000000 : ℚ)) + (U := (-(4705193758468929470479 / 10000000000000000000000 : ℚ))) + (U' := (2226278044531070529521 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (3118477284004833 / 5000000000000000 : ℚ)) + (q := (24987109652836207 / 40000000000000000 : ℚ)) + (U := (-(4705193758468929470479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_7 : Uω (aρ 7) (bρ 7) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5196,25 +4527,21 @@ lemma U_579_7 : have hlg : Real.log (24045468796831573 / 40000000000000000 : ℝ) ≤ (-(508932882669316172813 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24045468796831573 / 40000000000000000 : ℝ) = - (24045468796831573 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24045468796831573 / 20000000000000000 : ℚ)) - (U := (184214297630683827187 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24045468796831573 / 20000000000000000 : ℝ) ≤ - (184214297630683827187 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5989795520767349 / 10000000000000000 : ℝ)) (q := - (24045468796831573 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24045468796831573 / 40000000000000000 : ℚ)) + (r' := (24045468796831573 / 20000000000000000 : ℚ)) + (U := (-(508932882669316172813 / 1000000000000000000000 : ℚ))) + (U' := (184214297630683827187 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (5989795520767349 / 10000000000000000 : ℚ)) + (q := (24045468796831573 / 40000000000000000 : ℚ)) + (U := (-(508932882669316172813 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_8 : Uω (aρ 8) (bρ 8) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5222,25 +4549,21 @@ lemma U_579_8 : have hlg : Real.log (22820740034431137 / 40000000000000000 : ℝ) ≤ (-(5612096807420582264481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22820740034431137 / 40000000000000000 : ℝ) = - (22820740034431137 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22820740034431137 / 20000000000000000 : ℚ)) - (U := (1319374995579417735519 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22820740034431137 / 20000000000000000 : ℝ) ≤ - (1319374995579417735519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5660972790907131 / 10000000000000000 : ℝ)) (q := - (22820740034431137 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22820740034431137 / 40000000000000000 : ℚ)) + (r' := (22820740034431137 / 20000000000000000 : ℚ)) + (U := (-(5612096807420582264481 / 10000000000000000000000 : ℚ))) + (U' := (1319374995579417735519 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (5660972790907131 / 10000000000000000 : ℚ)) + (q := (22820740034431137 / 40000000000000000 : ℚ)) + (U := (-(5612096807420582264481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_9 : Uω (aρ 9) (bρ 9) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5248,25 +4571,21 @@ lemma U_579_9 : have hlg : Real.log (21293441537532141 / 40000000000000000 : ℝ) ≤ (-(6304803375883815152733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21293441537532141 / 40000000000000000 : ℝ) = - (21293441537532141 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21293441537532141 / 20000000000000000 : ℚ)) - (U := (626668427116184847267 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21293441537532141 / 20000000000000000 : ℝ) ≤ - (626668427116184847267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5238289170817633 / 10000000000000000 : ℝ)) (q := - (21293441537532141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21293441537532141 / 40000000000000000 : ℚ)) + (r' := (21293441537532141 / 20000000000000000 : ℚ)) + (U := (-(6304803375883815152733 / 10000000000000000000000 : ℚ))) + (U' := (626668427116184847267 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (5238289170817633 / 10000000000000000 : ℚ)) + (q := (21293441537532141 / 40000000000000000 : ℚ)) + (U := (-(6304803375883815152733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_10 : Uω (aρ 10) (bρ 10) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5274,26 +4593,21 @@ lemma U_579_10 : have hlg : Real.log (19460924529287769 / 40000000000000000 : ℝ) ≤ (-(1440941737503140562409 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19460924529287769 / 40000000000000000 : ℝ) = - (19460924529287769 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19460924529287769 / 10000000000000000 : ℚ)) - (U := (1331646983696859437591 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19460924529287769 / 10000000000000000 : ℝ) ≤ - (1331646983696859437591 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4710589700190447 / 10000000000000000 : ℝ)) (q := - (19460924529287769 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19460924529287769 / 40000000000000000 : ℚ)) + (r' := (19460924529287769 / 10000000000000000 : ℚ)) + (U := (-(1440941737503140562409 / 2000000000000000000000 : ℚ))) + (U' := (1331646983696859437591 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (4710589700190447 / 10000000000000000 : ℚ)) + (q := (19460924529287769 / 40000000000000000 : ℚ)) + (U := (-(1440941737503140562409 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_11 : Uω (aρ 11) (bρ 11) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5301,26 +4615,21 @@ lemma U_579_11 : have hlg : Real.log (3467107413187723 / 8000000000000000 : ℝ) ≤ (-(4180604466712982170821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3467107413187723 / 8000000000000000 : ℝ) = - (3467107413187723 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3467107413187723 / 2000000000000000 : ℚ)) - (U := (2750867336287017829179 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3467107413187723 / 2000000000000000 : ℝ) ≤ - (2750867336287017829179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (406637259472087 / 1000000000000000 : ℝ)) (q := - (3467107413187723 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3467107413187723 / 8000000000000000 : ℚ)) + (r' := (3467107413187723 / 2000000000000000 : ℚ)) + (U := (-(4180604466712982170821 / 5000000000000000000000 : ℚ))) + (U' := (2750867336287017829179 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (406637259472087 / 1000000000000000 : ℚ)) + (q := (3467107413187723 / 8000000000000000 : ℚ)) + (U := (-(4180604466712982170821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_12 : Uω (aρ 12) (bρ 12) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5328,26 +4637,21 @@ lemma U_579_12 : have hlg : Real.log (14931264031947399 / 40000000000000000 : ℝ) ≤ (-(9854221817320635336431 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14931264031947399 / 40000000000000000 : ℝ) = - (14931264031947399 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14931264031947399 / 10000000000000000 : ℚ)) - (U := (4008721788679364663569 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14931264031947399 / 10000000000000000 : ℝ) ≤ - (4008721788679364663569 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1643968087205131 / 5000000000000000 : ℝ)) (q := - (14931264031947399 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14931264031947399 / 40000000000000000 : ℚ)) + (r' := (14931264031947399 / 10000000000000000 : ℚ)) + (U := (-(9854221817320635336431 / 10000000000000000000000 : ℚ))) + (U' := (4008721788679364663569 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (1643968087205131 / 5000000000000000 : ℚ)) + (q := (14931264031947399 / 40000000000000000 : ℚ)) + (U := (-(9854221817320635336431 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_13 : Uω (aρ 13) (bρ 13) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5355,26 +4659,21 @@ lemma U_579_13 : have hlg : Real.log (12210328232377843 / 40000000000000000 : ℝ) ≤ (-(741623302233828881753 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12210328232377843 / 40000000000000000 : ℝ) = - (12210328232377843 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12210328232377843 / 10000000000000000 : ℚ)) - (U := (124810673141171118247 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12210328232377843 / 10000000000000000 : ℝ) ≤ - (124810673141171118247 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (581712504055121 / 2500000000000000 : ℝ)) (q := - (12210328232377843 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12210328232377843 / 40000000000000000 : ℚ)) + (r' := (12210328232377843 / 10000000000000000 : ℚ)) + (U := (-(741623302233828881753 / 625000000000000000000 : ℚ))) + (U' := (124810673141171118247 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (581712504055121 / 2500000000000000 : ℚ)) + (q := (12210328232377843 / 40000000000000000 : ℚ)) + (U := (-(741623302233828881753 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_14 : Uω (aρ 14) (bρ 14) (21619158626859 / 32000000000000 : ℝ) ≤ @@ -5382,26 +4681,21 @@ lemma U_579_14 : have hlg : Real.log (8620584086464821 / 40000000000000000 : ℝ) ≤ (-(15347266115033912343549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8620584086464821 / 40000000000000000 : ℝ) = - (8620584086464821 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8620584086464821 / 5000000000000000 : ℚ)) - (U := (5447149293966087656451 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8620584086464821 / 5000000000000000 : ℝ) ≤ - (5447149293966087656451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (875905228308973 / 10000000000000000 : ℝ)) (q := - (8620584086464821 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8620584086464821 / 40000000000000000 : ℚ)) + (r' := (8620584086464821 / 5000000000000000 : ℚ)) + (U := (-(15347266115033912343549 / 10000000000000000000000 : ℚ))) + (U' := (5447149293966087656451 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (21619158626859 / 32000000000000 : ℚ)) + (s := (875905228308973 / 10000000000000000 : ℚ)) + (q := (8620584086464821 / 40000000000000000 : ℚ)) + (U := (-(15347266115033912343549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_579_15 : Uω (aρ 15) (bρ 15) (21619158626859 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U48.lean b/LeanPool/Zeta5Irrational/Table/U48.lean index e788675a92..548bbf792c 100644 --- a/LeanPool/Zeta5Irrational/Table/U48.lean +++ b/LeanPool/Zeta5Irrational/Table/U48.lean @@ -24,25 +24,21 @@ lemma U_580_1 : have hlg : Real.log (53596624766068143 / 80000000000000000 : ℝ) ≤ (-(4005405391022337117569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53596624766068143 / 80000000000000000 : ℝ) = - (53596624766068143 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53596624766068143 / 40000000000000000 : ℚ)) - (U := (2926066411977662882431 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53596624766068143 / 40000000000000000 : ℝ) ≤ - (2926066411977662882431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6699553964704067 / 10000000000000000 : ℝ)) (q := - (53596624766068143 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53596624766068143 / 80000000000000000 : ℚ)) + (r' := (53596624766068143 / 40000000000000000 : ℚ)) + (U := (-(4005405391022337117569 / 10000000000000000000000 : ℚ))) + (U' := (2926066411977662882431 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (6699553964704067 / 10000000000000000 : ℚ)) + (q := (53596624766068143 / 80000000000000000 : ℚ)) + (U := (-(4005405391022337117569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_2 : Uω (aρ 2) (bρ 2) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_580_2 : have hlg : Real.log (53405394319890923 / 80000000000000000 : ℝ) ≤ (-(2020574381616309005321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53405394319890923 / 80000000000000000 : ℝ) = - (53405394319890923 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53405394319890923 / 40000000000000000 : ℚ)) - (U := (1445161519883690994679 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53405394319890923 / 40000000000000000 : ℝ) ≤ - (1445161519883690994679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3337757682834881 / 5000000000000000 : ℝ)) (q := - (53405394319890923 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53405394319890923 / 80000000000000000 : ℚ)) + (r' := (53405394319890923 / 40000000000000000 : ℚ)) + (U := (-(2020574381616309005321 / 5000000000000000000000 : ℚ))) + (U' := (1445161519883690994679 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (3337757682834881 / 5000000000000000 : ℚ)) + (q := (53405394319890923 / 80000000000000000 : ℚ)) + (U := (-(2020574381616309005321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_3 : Uω (aρ 3) (bρ 3) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_580_3 : have hlg : Real.log (53023032038383907 / 80000000000000000 : ℝ) ≤ (-(4113002484966424445947 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53023032038383907 / 80000000000000000 : ℝ) = - (53023032038383907 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53023032038383907 / 40000000000000000 : ℚ)) - (U := (2818469318033575554053 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53023032038383907 / 40000000000000000 : ℝ) ≤ - (2818469318033575554053 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25887972272043 / 39062500000000 : ℝ)) (q := - (53023032038383907 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53023032038383907 / 80000000000000000 : ℚ)) + (r' := (53023032038383907 / 40000000000000000 : ℚ)) + (U := (-(4113002484966424445947 / 10000000000000000000000 : ℚ))) + (U' := (2818469318033575554053 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (25887972272043 / 39062500000000 : ℚ)) + (q := (53023032038383907 / 80000000000000000 : ℚ)) + (U := (-(4113002484966424445947 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_4 : Uω (aρ 4) (bρ 4) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_580_4 : have hlg : Real.log (52388291041572979 / 80000000000000000 : ℝ) ≤ (-(1058358803653668769017 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52388291041572979 / 80000000000000000 : ℝ) = - (52388291041572979 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52388291041572979 / 40000000000000000 : ℚ)) - (U := (674509147096331230983 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52388291041572979 / 40000000000000000 : ℝ) ≤ - (674509147096331230983 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1636732458376319 / 2500000000000000 : ℝ)) (q := - (52388291041572979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52388291041572979 / 80000000000000000 : ℚ)) + (r' := (52388291041572979 / 40000000000000000 : ℚ)) + (U := (-(1058358803653668769017 / 2500000000000000000000 : ℚ))) + (U' := (674509147096331230983 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (1636732458376319 / 2500000000000000 : ℚ)) + (q := (52388291041572979 / 80000000000000000 : ℚ)) + (U := (-(1058358803653668769017 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_5 : Uω (aρ 5) (bρ 5) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_580_5 : have hlg : Real.log (10284496504502127 / 16000000000000000 : ℝ) ≤ (-(220975577212004283547 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10284496504502127 / 16000000000000000 : ℝ) = - (10284496504502127 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10284496504502127 / 8000000000000000 : ℚ)) - (U := (125598012937995716453 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10284496504502127 / 8000000000000000 : ℝ) ≤ - (125598012937995716453 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (642366762307469 / 1000000000000000 : ℝ)) (q := - (10284496504502127 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10284496504502127 / 16000000000000000 : ℚ)) + (r' := (10284496504502127 / 8000000000000000 : ℚ)) + (U := (-(220975577212004283547 / 500000000000000000000 : ℚ))) + (U' := (125598012937995716453 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (642366762307469 / 1000000000000000 : ℚ)) + (q := (10284496504502127 / 16000000000000000 : ℚ)) + (U := (-(220975577212004283547 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_6 : Uω (aρ 6) (bρ 6) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_580_6 : have hlg : Real.log (50039220376910659 / 80000000000000000 : ℝ) ≤ (-(4692195289343839263543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50039220376910659 / 80000000000000000 : ℝ) = - (50039220376910659 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50039220376910659 / 40000000000000000 : ℚ)) - (U := (2239276513656160736457 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50039220376910659 / 40000000000000000 : ℝ) ≤ - (2239276513656160736457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (780636557726837 / 1250000000000000 : ℝ)) (q := - (50039220376910659 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50039220376910659 / 80000000000000000 : ℚ)) + (r' := (50039220376910659 / 40000000000000000 : ℚ)) + (U := (-(4692195289343839263543 / 10000000000000000000000 : ℚ))) + (U' := (2239276513656160736457 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (780636557726837 / 1250000000000000 : ℚ)) + (q := (50039220376910659 / 80000000000000000 : ℚ)) + (U := (-(4692195289343839263543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_7 : Uω (aρ 7) (bρ 7) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_580_7 : have hlg : Real.log (48156069995982091 / 80000000000000000 : ℝ) ≤ (-(5075794398165442137843 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48156069995982091 / 80000000000000000 : ℝ) = - (48156069995982091 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48156069995982091 / 40000000000000000 : ℚ)) - (U := (1855677404834557862157 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48156069995982091 / 40000000000000000 : ℝ) ≤ - (1855677404834557862157 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2998983123671277 / 5000000000000000 : ℝ)) (q := - (48156069995982091 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48156069995982091 / 80000000000000000 : ℚ)) + (r' := (48156069995982091 / 40000000000000000 : ℚ)) + (U := (-(5075794398165442137843 / 10000000000000000000000 : ℚ))) + (U' := (1855677404834557862157 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (2998983123671277 / 5000000000000000 : ℚ)) + (q := (48156069995982091 / 80000000000000000 : ℚ)) + (U := (-(5075794398165442137843 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_8 : Uω (aρ 8) (bρ 8) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_580_8 : have hlg : Real.log (9141377038259751 / 16000000000000000 : ℝ) ≤ (-(1399444218052103159183 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9141377038259751 / 16000000000000000 : ℝ) = - (9141377038259751 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9141377038259751 / 8000000000000000 : ℚ)) - (U := (333423732697896840817 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (9141377038259751 / 8000000000000000 : ℝ) ≤ - (333423732697896840817 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (141730292437793 / 250000000000000 : ℝ)) (q := - (9141377038259751 / 16000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9141377038259751 / 16000000000000000 : ℚ)) + (r' := (9141377038259751 / 8000000000000000 : ℚ)) + (U := (-(1399444218052103159183 / 2500000000000000000000 : ℚ))) + (U' := (333423732697896840817 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (141730292437793 / 250000000000000 : ℚ)) + (q := (9141377038259751 / 16000000000000000 : ℚ)) + (U := (-(1399444218052103159183 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_9 : Uω (aρ 9) (bρ 9) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_580_9 : have hlg : Real.log (42652834387923127 / 80000000000000000 : ℝ) ≤ (-(6289329057577266237567 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42652834387923127 / 80000000000000000 : ℝ) = - (42652834387923127 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42652834387923127 / 40000000000000000 : ℚ)) - (U := (642142745422733762433 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42652834387923127 / 40000000000000000 : ℝ) ≤ - (642142745422733762433 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5246664625027813 / 10000000000000000 : ℝ)) (q := - (42652834387923127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42652834387923127 / 80000000000000000 : ℚ)) + (r' := (42652834387923127 / 40000000000000000 : ℚ)) + (U := (-(6289329057577266237567 / 10000000000000000000000 : ℚ))) + (U' := (642142745422733762433 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (5246664625027813 / 10000000000000000 : ℚ)) + (q := (42652834387923127 / 80000000000000000 : ℚ)) + (U := (-(6289329057577266237567 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_10 : Uω (aρ 10) (bρ 10) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_580_10 : have hlg : Real.log (38988874802318187 / 80000000000000000 : ℝ) ≤ (-(7187502901981604046617 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (38988874802318187 / 80000000000000000 : ℝ) = - (38988874802318187 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38988874802318187 / 20000000000000000 : ℚ)) - (U := (6675440704018395953383 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (38988874802318187 / 20000000000000000 : ℝ) ≤ - (6675440704018395953383 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2359616881060789 / 5000000000000000 : ℝ)) (q := - (38988874802318187 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38988874802318187 / 80000000000000000 : ℚ)) + (r' := (38988874802318187 / 20000000000000000 : ℚ)) + (U := (-(7187502901981604046617 / 10000000000000000000000 : ℚ))) + (U' := (6675440704018395953383 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (2359616881060789 / 5000000000000000 : ℚ)) + (q := (38988874802318187 / 80000000000000000 : ℚ)) + (U := (-(7187502901981604046617 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_11 : Uω (aρ 11) (bρ 11) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_580_11 : have hlg : Real.log (34740233532064187 / 80000000000000000 : ℝ) ≤ (-(8341281510819861628441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34740233532064187 / 80000000000000000 : ℝ) = - (34740233532064187 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34740233532064187 / 20000000000000000 : ℚ)) - (U := (5521662095180138371559 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34740233532064187 / 20000000000000000 : ℝ) ≤ - (5521662095180138371559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2037775035381539 / 5000000000000000 : ℝ)) (q := - (34740233532064187 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34740233532064187 / 80000000000000000 : ℚ)) + (r' := (34740233532064187 / 20000000000000000 : ℚ)) + (U := (-(8341281510819861628441 / 10000000000000000000000 : ℚ))) + (U' := (5521662095180138371559 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (2037775035381539 / 5000000000000000 : ℚ)) + (q := (34740233532064187 / 80000000000000000 : ℚ)) + (U := (-(8341281510819861628441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_12 : Uω (aρ 12) (bρ 12) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_580_12 : have hlg : Real.log (29936183804283567 / 80000000000000000 : ℝ) ≤ (-(4914793623665919405137 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29936183804283567 / 80000000000000000 : ℝ) = - (29936183804283567 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29936183804283567 / 20000000000000000 : ℚ)) - (U := (2016678179334080594863 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29936183804283567 / 20000000000000000 : ℝ) ≤ - (2016678179334080594863 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3298237735502923 / 10000000000000000 : ℝ)) (q := - (29936183804283567 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29936183804283567 / 80000000000000000 : ℚ)) + (r' := (29936183804283567 / 20000000000000000 : ℚ)) + (U := (-(4914793623665919405137 / 5000000000000000000000 : ℚ))) + (U' := (2016678179334080594863 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (3298237735502923 / 10000000000000000 : ℚ)) + (q := (29936183804283567 / 80000000000000000 : ℚ)) + (U := (-(4914793623665919405137 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_13 : Uω (aρ 13) (bρ 13) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -339,25 +288,21 @@ lemma U_580_13 : have hlg : Real.log (980228201742283 / 3200000000000000 : ℝ) ≤ (-(11831206847900431713959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (980228201742283 / 3200000000000000 : ℝ) = - (980228201742283 / 800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (980228201742283 / 800000000000000 : ℚ)) - (U := (2031736758099568286041 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (980228201742283 / 800000000000000 : ℝ) ≤ - (2031736758099568286041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23399997869163 / 100000000000000 : ℝ)) (q := - (980228201742283 / 3200000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (980228201742283 / 3200000000000000 : ℚ)) + (r' := (980228201742283 / 800000000000000 : ℚ)) + (U := (-(11831206847900431713959 / 10000000000000000000000 : ℚ))) + (U' := (2031736758099568286041 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (23399997869163 / 100000000000000 : ℚ)) + (q := (980228201742283 / 3200000000000000 : ℚ)) + (U := (-(11831206847900431713959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_14 : Uω (aρ 14) (bρ 14) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -365,26 +310,21 @@ lemma U_580_14 : have hlg : Real.log (17398765891887423 / 80000000000000000 : ℝ) ≤ (-(7628136779712544570147 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17398765891887423 / 80000000000000000 : ℝ) = - (17398765891887423 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17398765891887423 / 10000000000000000 : ℚ)) - (U := (2769070924787455429853 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17398765891887423 / 10000000000000000 : ℝ) ≤ - (2769070924787455429853 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (907192284043887 / 10000000000000000 : ℝ)) (q := - (17398765891887423 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17398765891887423 / 80000000000000000 : ℚ)) + (r' := (17398765891887423 / 10000000000000000 : ℚ)) + (U := (-(7628136779712544570147 / 5000000000000000000000 : ℚ))) + (U' := (2769070924787455429853 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43290236447347 / 64000000000000 : ℚ)) + (s := (907192284043887 / 10000000000000000 : ℚ)) + (q := (17398765891887423 / 80000000000000000 : ℚ)) + (U := (-(7628136779712544570147 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_580_15 : Uω (aρ 15) (bρ 15) (43290236447347 / 64000000000000 : ℝ) ≤ @@ -486,25 +426,21 @@ lemma U_581_1 : have hlg : Real.log (3353845249473793 / 5000000000000000 : ℝ) ≤ (-(3993303889330489471621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3353845249473793 / 5000000000000000 : ℝ) = - (3353845249473793 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3353845249473793 / 2500000000000000 : ℚ)) - (U := (2938167913669510528379 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3353845249473793 / 2500000000000000 : ℝ) ≤ - (2938167913669510528379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (838458299634709 / 1250000000000000 : ℝ)) (q := - (3353845249473793 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3353845249473793 / 5000000000000000 : ℚ)) + (r' := (3353845249473793 / 2500000000000000 : ℚ)) + (U := (-(3993303889330489471621 / 10000000000000000000000 : ℚ))) + (U' := (2938167913669510528379 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (838458299634709 / 1250000000000000 : ℚ)) + (q := (3353845249473793 / 5000000000000000 : ℚ)) + (U := (-(3993303889330489471621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_2 : Uω (aρ 2) (bρ 2) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -512,25 +448,21 @@ lemma U_581_2 : have hlg : Real.log (3341893428444077 / 5000000000000000 : ℝ) ≤ (-(4029003710659338433683 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3341893428444077 / 5000000000000000 : ℝ) = - (3341893428444077 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3341893428444077 / 2500000000000000 : ℚ)) - (U := (2902468092340661566317 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3341893428444077 / 2500000000000000 : ℝ) ≤ - (2902468092340661566317 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (835453515683601 / 1250000000000000 : ℝ)) (q := - (3341893428444077 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3341893428444077 / 5000000000000000 : ℚ)) + (r' := (3341893428444077 / 2500000000000000 : ℚ)) + (U := (-(4029003710659338433683 / 10000000000000000000000 : ℚ))) + (U' := (2902468092340661566317 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (835453515683601 / 1250000000000000 : ℚ)) + (q := (3341893428444077 / 5000000000000000 : ℚ)) + (U := (-(4029003710659338433683 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_3 : Uω (aρ 3) (bρ 3) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -538,25 +470,21 @@ lemma U_581_3 : have hlg : Real.log (13271984122260781 / 20000000000000000 : ℝ) ≤ (-(4100769167401937979183 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13271984122260781 / 20000000000000000 : ℝ) = - (13271984122260781 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13271984122260781 / 10000000000000000 : ℚ)) - (U := (2830702635598062020817 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13271984122260781 / 10000000000000000 : ℝ) ≤ - (2830702635598062020817 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6635434640303281 / 10000000000000000 : ℝ)) (q := - (13271984122260781 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13271984122260781 / 20000000000000000 : ℚ)) + (r' := (13271984122260781 / 10000000000000000 : ℚ)) + (U := (-(4100769167401937979183 / 10000000000000000000000 : ℚ))) + (U' := (2830702635598062020817 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (6635434640303281 / 10000000000000000 : ℚ)) + (q := (13271984122260781 / 20000000000000000 : ℚ)) + (U := (-(4100769167401937979183 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_4 : Uω (aρ 4) (bρ 4) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -564,25 +492,21 @@ lemma U_581_4 : have hlg : Real.log (13113301484853793 / 20000000000000000 : ℝ) ≤ (-(4221051777138668487973 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13113301484853793 / 20000000000000000 : ℝ) = - (13113301484853793 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13113301484853793 / 10000000000000000 : ℚ)) - (U := (2710420025861331512027 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13113301484853793 / 10000000000000000 : ℝ) ≤ - (2710420025861331512027 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6555046183961293 / 10000000000000000 : ℝ)) (q := - (13113301484853793 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13113301484853793 / 20000000000000000 : ℚ)) + (r' := (13113301484853793 / 10000000000000000 : ℚ)) + (U := (-(4221051777138668487973 / 10000000000000000000000 : ℚ))) + (U' := (2710420025861331512027 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (6555046183961293 / 10000000000000000 : ℚ)) + (q := (13113301484853793 / 20000000000000000 : ℚ)) + (U := (-(4221051777138668487973 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_5 : Uω (aρ 5) (bρ 5) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -590,25 +514,21 @@ lemma U_581_5 : have hlg : Real.log (3217963957236223 / 5000000000000000 : ℝ) ≤ (-(4406890640283341706941 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3217963957236223 / 5000000000000000 : ℝ) = - (3217963957236223 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3217963957236223 / 2500000000000000 : ℚ)) - (U := (2524581162716658293059 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3217963957236223 / 2500000000000000 : ℝ) ≤ - (2524581162716658293059 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25124181435107 / 39062500000000 : ℝ)) (q := - (3217963957236223 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3217963957236223 / 5000000000000000 : ℚ)) + (r' := (3217963957236223 / 2500000000000000 : ℚ)) + (U := (-(4406890640283341706941 / 10000000000000000000000 : ℚ))) + (U' := (2524581162716658293059 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (25124181435107 / 39062500000000 : ℚ)) + (q := (3217963957236223 / 5000000000000000 : ℚ)) + (U := (-(4406890640283341706941 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_6 : Uω (aρ 6) (bρ 6) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -616,25 +536,21 @@ lemma U_581_6 : have hlg : Real.log (782878455982433 / 1250000000000000 : ℝ) ≤ (-(292450859203226838757 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (782878455982433 / 1250000000000000 : ℝ) = - (782878455982433 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (782878455982433 / 625000000000000 : ℚ)) - (U := (140766128484273161243 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (782878455982433 / 625000000000000 : ℝ) ≤ - (140766128484273161243 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1563307572325357 / 2500000000000000 : ℝ)) (q := - (782878455982433 / 1250000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (782878455982433 / 1250000000000000 : ℚ)) + (r' := (782878455982433 / 625000000000000 : ℚ)) + (U := (-(292450859203226838757 / 625000000000000000000 : ℚ))) + (U' := (140766128484273161243 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (1563307572325357 / 2500000000000000 : ℚ)) + (q := (782878455982433 / 1250000000000000 : ℚ)) + (U := (-(292450859203226838757 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_7 : Uω (aρ 7) (bρ 7) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -642,25 +558,21 @@ lemma U_581_7 : have hlg : Real.log (1506912555172117 / 2500000000000000 : ℝ) ≤ (-(2531139197092148791153 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1506912555172117 / 2500000000000000 : ℝ) = - (1506912555172117 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1506912555172117 / 1250000000000000 : ℚ)) - (U := (934596704407851208847 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1506912555172117 / 1250000000000000 : ℝ) ≤ - (934596704407851208847 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1501534203929859 / 2500000000000000 : ℝ)) (q := - (1506912555172117 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1506912555172117 / 2500000000000000 : ℚ)) + (r' := (1506912555172117 / 1250000000000000 : ℚ)) + (U := (-(2531139197092148791153 / 5000000000000000000000 : ℚ))) + (U' := (934596704407851208847 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (1501534203929859 / 2500000000000000 : ℚ)) + (q := (1506912555172117 / 2500000000000000 : ℚ)) + (U := (-(2531139197092148791153 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_8 : Uω (aρ 8) (bρ 8) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -668,25 +580,21 @@ lemma U_581_8 : have hlg : Real.log (5721536107007471 / 10000000000000000 : ℝ) ≤ (-(5583477732194065256547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5721536107007471 / 10000000000000000 : ℝ) = - (5721536107007471 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5721536107007471 / 5000000000000000 : ℚ)) - (U := (1347994070805934743453 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5721536107007471 / 5000000000000000 : ℝ) ≤ - (1347994070805934743453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2838725119848721 / 5000000000000000 : ℝ)) (q := - (5721536107007471 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5721536107007471 / 10000000000000000 : ℚ)) + (r' := (5721536107007471 / 5000000000000000 : ℚ)) + (U := (-(5583477732194065256547 / 10000000000000000000000 : ℚ))) + (U' := (1347994070805934743453 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (2838725119848721 / 5000000000000000 : ℚ)) + (q := (5721536107007471 / 10000000000000000 : ℚ)) + (U := (-(5583477732194065256547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_9 : Uω (aρ 9) (bρ 9) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -694,25 +602,21 @@ lemma U_581_9 : have hlg : Real.log (2669923899943569 / 5000000000000000 : ℝ) ≤ (-(1568469855154944946347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2669923899943569 / 5000000000000000 : ℝ) = - (2669923899943569 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2669923899943569 / 2500000000000000 : ℚ)) - (U := (164398095595055053653 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2669923899943569 / 2500000000000000 : ℝ) ≤ - (164398095595055053653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (656879906727097 / 1250000000000000 : ℝ)) (q := - (2669923899943569 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2669923899943569 / 5000000000000000 : ℚ)) + (r' := (2669923899943569 / 2500000000000000 : ℚ)) + (U := (-(1568469855154944946347 / 2500000000000000000000 : ℚ))) + (U' := (164398095595055053653 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (656879906727097 / 1250000000000000 : ℚ)) + (q := (2669923899943569 / 5000000000000000 : ℚ)) + (U := (-(1568469855154944946347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_10 : Uω (aρ 10) (bρ 10) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -720,26 +624,21 @@ lemma U_581_10 : have hlg : Real.log (4881986626059351 / 10000000000000000 : ℝ) ≤ (-(7170328599460265511283 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4881986626059351 / 10000000000000000 : ℝ) = - (4881986626059351 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4881986626059351 / 2500000000000000 : ℚ)) - (U := (6692615006539734488717 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4881986626059351 / 2500000000000000 : ℝ) ≤ - (6692615006539734488717 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2363937969828101 / 5000000000000000 : ℝ)) (q := - (4881986626059351 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4881986626059351 / 10000000000000000 : ℚ)) + (r' := (4881986626059351 / 2500000000000000 : ℚ)) + (U := (-(7170328599460265511283 / 10000000000000000000000 : ℚ))) + (U' := (6692615006539734488717 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (2363937969828101 / 5000000000000000 : ℚ)) + (q := (4881986626059351 / 10000000000000000 : ℚ)) + (U := (-(7170328599460265511283 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_11 : Uω (aρ 11) (bρ 11) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -747,26 +646,21 @@ lemma U_581_11 : have hlg : Real.log (1087792965586551 / 2500000000000000 : ℝ) ≤ (-(8321398900107086323937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1087792965586551 / 2500000000000000 : ℝ) = - (1087792965586551 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1087792965586551 / 625000000000000 : ℚ)) - (U := (5541544705892913676063 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1087792965586551 / 625000000000000 : ℝ) ≤ - (5541544705892913676063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1021180759608727 / 2500000000000000 : ℝ)) (q := - (1087792965586551 / 2500000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1087792965586551 / 2500000000000000 : ℚ)) + (r' := (1087792965586551 / 625000000000000 : ℚ)) + (U := (-(8321398900107086323937 / 10000000000000000000000 : ℚ))) + (U' := (5541544705892913676063 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (1021180759608727 / 2500000000000000 : ℚ)) + (q := (1087792965586551 / 2500000000000000 : ℚ)) + (U := (-(8321398900107086323937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_12 : Uω (aρ 12) (bρ 12) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -774,25 +668,21 @@ lemma U_581_12 : have hlg : Real.log (937805962756639 / 2500000000000000 : ℝ) ≤ (-(39220117818480693483 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (937805962756639 / 2500000000000000 : ℝ) = - (937805962756639 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (937805962756639 / 625000000000000 : ℚ)) - (U := (16231656605519306517 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (937805962756639 / 625000000000000 : ℝ) ≤ - (16231656605519306517 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (827131778120153 / 2500000000000000 : ℝ)) (q := - (937805962756639 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (937805962756639 / 2500000000000000 : ℚ)) + (r' := (937805962756639 / 625000000000000 : ℚ)) + (U := (-(39220117818480693483 / 40000000000000000000 : ℚ))) + (U' := (16231656605519306517 / 40000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (827131778120153 / 2500000000000000 : ℚ)) + (q := (937805962756639 / 2500000000000000 : ℚ)) + (U := (-(39220117818480693483 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_13 : Uω (aρ 13) (bρ 13) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -800,26 +690,21 @@ lemma U_581_13 : have hlg : Real.log (1229528577838203 / 4000000000000000 : ℝ) ≤ (-(11796635347326533752359 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1229528577838203 / 4000000000000000 : ℝ) = - (1229528577838203 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1229528577838203 / 1000000000000000 : ℚ)) - (U := (2066308258673466247641 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1229528577838203 / 1000000000000000 : ℝ) ≤ - (2066308258673466247641 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (470620808242703 / 2000000000000000 : ℝ)) (q := - (1229528577838203 / 4000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1229528577838203 / 4000000000000000 : ℚ)) + (r' := (1229528577838203 / 1000000000000000 : ℚ)) + (U := (-(11796635347326533752359 / 10000000000000000000000 : ℚ))) + (U' := (2066308258673466247641 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (470620808242703 / 2000000000000000 : ℚ)) + (q := (1229528577838203 / 4000000000000000 : ℚ)) + (U := (-(11796635347326533752359 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_14 : Uω (aρ 14) (bρ 14) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -827,25 +712,21 @@ lemma U_581_14 : have hlg : Real.log (219405873684427 / 1000000000000000 : ℝ) ≤ (-(1516831959140549096717 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (219405873684427 / 1000000000000000 : ℝ) = - (219405873684427 / 125000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (219405873684427 / 125000000000000 : ℚ)) - (U := (562609581759450903283 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (219405873684427 / 125000000000000 : ℝ) ≤ - (562609581759450903283 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23437647768901 / 250000000000000 : ℝ)) (q := - (219405873684427 / 1000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (219405873684427 / 1000000000000000 : ℚ)) + (r' := (219405873684427 / 125000000000000 : ℚ)) + (U := (-(1516831959140549096717 / 1000000000000000000000 : ℚ))) + (U' := (562609581759450903283 / 1000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2708884727561 / 4000000000000 : ℚ)) + (s := (23437647768901 / 250000000000000 : ℚ)) + (q := (219405873684427 / 1000000000000000 : ℚ)) + (U := (-(1516831959140549096717 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_581_15 : Uω (aρ 15) (bρ 15) (2708884727561 / 4000000000000 : ℝ) ≤ @@ -947,25 +828,21 @@ lemma U_582_1 : have hlg : Real.log (53726423216529177 / 80000000000000000 : ℝ) ≤ (-(497652126834867869363 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53726423216529177 / 80000000000000000 : ℝ) = - (53726423216529177 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53726423216529177 / 40000000000000000 : ℚ)) - (U := (368781848540132130637 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53726423216529177 / 40000000000000000 : ℝ) ≤ - (368781848540132130637 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6715778829310263 / 10000000000000000 : ℝ)) (q := - (53726423216529177 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53726423216529177 / 80000000000000000 : ℚ)) + (r' := (53726423216529177 / 40000000000000000 : ℚ)) + (U := (-(497652126834867869363 / 1250000000000000000000 : ℚ))) + (U' := (368781848540132130637 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (6715778829310263 / 10000000000000000 : ℚ)) + (q := (53726423216529177 / 80000000000000000 : ℚ)) + (U := (-(497652126834867869363 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_2 : Uω (aρ 2) (bρ 2) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -973,25 +850,21 @@ lemma U_582_2 : have hlg : Real.log (53535195386577869 / 80000000000000000 : ℝ) ≤ (-(4016873391124482683507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53535195386577869 / 80000000000000000 : ℝ) = - (53535195386577869 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53535195386577869 / 40000000000000000 : ℚ)) - (U := (2914598411875517316493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53535195386577869 / 40000000000000000 : ℝ) ≤ - (2914598411875517316493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1672935221083109 / 2500000000000000 : ℝ)) (q := - (53535195386577869 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53535195386577869 / 80000000000000000 : ℚ)) + (r' := (53535195386577869 / 40000000000000000 : ℚ)) + (U := (-(4016873391124482683507 / 10000000000000000000000 : ℚ))) + (U' := (2914598411875517316493 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (1672935221083109 / 2500000000000000 : ℚ)) + (q := (53535195386577869 / 80000000000000000 : ℚ)) + (U := (-(4016873391124482683507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_3 : Uω (aρ 3) (bρ 3) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -999,25 +872,21 @@ lemma U_582_3 : have hlg : Real.log (53152840926370277 / 80000000000000000 : ℝ) ≤ (-(4088550799468137633081 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53152840926370277 / 80000000000000000 : ℝ) = - (53152840926370277 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53152840926370277 / 40000000000000000 : ℚ)) - (U := (2842921003531862366919 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53152840926370277 / 40000000000000000 : ℝ) ≤ - (2842921003531862366919 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3321774187815269 / 5000000000000000 : ℝ)) (q := - (53152840926370277 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53152840926370277 / 80000000000000000 : ℚ)) + (r' := (53152840926370277 / 40000000000000000 : ℚ)) + (U := (-(4088550799468137633081 / 10000000000000000000000 : ℚ))) + (U' := (2842921003531862366919 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (3321774187815269 / 5000000000000000 : ℚ)) + (q := (53152840926370277 / 80000000000000000 : ℚ)) + (U := (-(4088550799468137633081 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_4 : Uω (aρ 4) (bρ 4) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1025,25 +894,21 @@ lemma U_582_4 : have hlg : Real.log (52518120797927097 / 80000000000000000 : ℝ) ≤ (-(4208683663139425892631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52518120797927097 / 80000000000000000 : ℝ) = - (52518120797927097 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52518120797927097 / 40000000000000000 : ℚ)) - (U := (2722788139860574107369 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52518120797927097 / 40000000000000000 : ℝ) ≤ - (2722788139860574107369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6563162524584743 / 10000000000000000 : ℝ)) (q := - (52518120797927097 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52518120797927097 / 80000000000000000 : ℚ)) + (r' := (52518120797927097 / 40000000000000000 : ℚ)) + (U := (-(4208683663139425892631 / 10000000000000000000000 : ℚ))) + (U' := (2722788139860574107369 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (6563162524584743 / 10000000000000000 : ℚ)) + (q := (52518120797927097 / 80000000000000000 : ℚ)) + (U := (-(4208683663139425892631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_5 : Uω (aρ 5) (bρ 5) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1051,25 +916,21 @@ lemma U_582_5 : have hlg : Real.log (10310472800733289 / 16000000000000000 : ℝ) ≤ (-(549285708176747111411 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10310472800733289 / 16000000000000000 : ℝ) = - (10310472800733289 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10310472800733289 / 8000000000000000 : ℚ)) - (U := (317148267198252888589 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10310472800733289 / 8000000000000000 : ℝ) ≤ - (317148267198252888589 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (321995662267729 / 500000000000000 : ℝ)) (q := - (10310472800733289 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10310472800733289 / 16000000000000000 : ℚ)) + (r' := (10310472800733289 / 8000000000000000 : ℚ)) + (U := (-(549285708176747111411 / 1250000000000000000000 : ℚ))) + (U' := (317148267198252888589 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (321995662267729 / 500000000000000 : ℚ)) + (q := (10310472800733289 / 16000000000000000 : ℚ)) + (U := (-(549285708176747111411 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_6 : Uω (aρ 6) (bρ 6) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1077,25 +938,21 @@ lemma U_582_6 : have hlg : Real.log (50169221724601889 / 80000000000000000 : ℝ) ≤ (-(466624908802661578893 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50169221724601889 / 80000000000000000 : ℝ) = - (50169221724601889 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50169221724601889 / 40000000000000000 : ℚ)) - (U := (226522271497338421107 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (50169221724601889 / 40000000000000000 : ℝ) ≤ - (226522271497338421107 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6261368050728441 / 10000000000000000 : ℝ)) (q := - (50169221724601889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50169221724601889 / 80000000000000000 : ℚ)) + (r' := (50169221724601889 / 40000000000000000 : ℚ)) + (U := (-(466624908802661578893 / 1000000000000000000000 : ℚ))) + (U' := (226522271497338421107 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (6261368050728441 / 10000000000000000 : ℚ)) + (q := (50169221724601889 / 80000000000000000 : ℚ)) + (U := (-(466624908802661578893 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_7 : Uω (aρ 7) (bρ 7) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1103,25 +960,21 @@ lemma U_582_7 : have hlg : Real.log (48286332904819101 / 80000000000000000 : ℝ) ≤ (-(631097595537542197029 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48286332904819101 / 80000000000000000 : ℝ) = - (48286332904819101 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48286332904819101 / 40000000000000000 : ℚ)) - (U := (235336379837457802971 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48286332904819101 / 40000000000000000 : ℝ) ≤ - (235336379837457802971 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (751788403317843 / 1250000000000000 : ℝ)) (q := - (48286332904819101 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48286332904819101 / 80000000000000000 : ℚ)) + (r' := (48286332904819101 / 40000000000000000 : ℚ)) + (U := (-(631097595537542197029 / 1250000000000000000000 : ℚ))) + (U' := (235336379837457802971 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (751788403317843 / 1250000000000000 : ℚ)) + (q := (48286332904819101 / 80000000000000000 : ℚ)) + (U := (-(631097595537542197029 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_8 : Uω (aρ 8) (bρ 8) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1129,25 +982,21 @@ lemma U_582_8 : have hlg : Real.log (45837691069481813 / 80000000000000000 : ℝ) ≤ (-(1392299831538579844629 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45837691069481813 / 80000000000000000 : ℝ) = - (45837691069481813 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45837691069481813 / 40000000000000000 : ℚ)) - (U := (340568119211420155371 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45837691069481813 / 40000000000000000 : ℝ) ≤ - (340568119211420155371 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2842844209524211 / 5000000000000000 : ℝ)) (q := - (45837691069481813 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45837691069481813 / 80000000000000000 : ℚ)) + (r' := (45837691069481813 / 40000000000000000 : ℚ)) + (U := (-(1392299831538579844629 / 2500000000000000000000 : ℚ))) + (U' := (340568119211420155371 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (2842844209524211 / 5000000000000000 : ℚ)) + (q := (45837691069481813 / 80000000000000000 : ℚ)) + (U := (-(1392299831538579844629 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_9 : Uω (aρ 9) (bρ 9) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1155,25 +1004,21 @@ lemma U_582_9 : have hlg : Real.log (8556945424869233 / 16000000000000000 : ℝ) ≤ (-(6258454383988677137099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8556945424869233 / 16000000000000000 : ℝ) = - (8556945424869233 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8556945424869233 / 8000000000000000 : ℚ)) - (U := (673017419011322862901 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8556945424869233 / 8000000000000000 : ℝ) ≤ - (673017419011322862901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (526341306112451 / 1000000000000000 : ℝ)) (q := - (8556945424869233 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8556945424869233 / 16000000000000000 : ℚ)) + (r' := (8556945424869233 / 8000000000000000 : ℚ)) + (U := (-(6258454383988677137099 / 10000000000000000000000 : ℚ))) + (U' := (673017419011322862901 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (526341306112451 / 1000000000000000 : ℚ)) + (q := (8556945424869233 / 16000000000000000 : ℚ)) + (U := (-(6258454383988677137099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_10 : Uω (aρ 10) (bρ 10) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1181,26 +1026,21 @@ lemma U_582_10 : have hlg : Real.log (7824580743660861 / 16000000000000000 : ℝ) ≤ (-(447074103633723834573 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7824580743660861 / 16000000000000000 : ℝ) = - (7824580743660861 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7824580743660861 / 4000000000000000 : ℚ)) - (U := (419359871741276165427 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7824580743660861 / 4000000000000000 : ℝ) ≤ - (419359871741276165427 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (947303248621809 / 2000000000000000 : ℝ)) (q := - (7824580743660861 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7824580743660861 / 16000000000000000 : ℚ)) + (r' := (7824580743660861 / 4000000000000000 : ℚ)) + (U := (-(447074103633723834573 / 625000000000000000000 : ℚ))) + (U' := (419359871741276165427 / 625000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (947303248621809 / 2000000000000000 : ℚ)) + (q := (7824580743660861 / 16000000000000000 : ℚ)) + (U := (-(447074103633723834573 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_11 : Uω (aρ 11) (bρ 11) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1208,26 +1048,21 @@ lemma U_582_11 : have hlg : Real.log (6975699670642717 / 16000000000000000 : ℝ) ≤ (-(518847554900022932309 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6975699670642717 / 16000000000000000 : ℝ) = - (6975699670642717 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6975699670642717 / 4000000000000000 : ℚ)) - (U := (347586420474977067691 / 625000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6975699670642717 / 4000000000000000 : ℝ) ≤ - (347586420474977067691 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (818778305608273 / 2000000000000000 : ℝ)) (q := - (6975699670642717 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6975699670642717 / 16000000000000000 : ℚ)) + (r' := (6975699670642717 / 4000000000000000 : ℚ)) + (U := (-(518847554900022932309 / 625000000000000000000 : ℚ))) + (U' := (347586420474977067691 / 625000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (818778305608273 / 2000000000000000 : ℚ)) + (q := (6975699670642717 / 16000000000000000 : ℚ)) + (U := (-(518847554900022932309 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_12 : Uω (aρ 12) (bρ 12) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1235,26 +1070,21 @@ lemma U_582_12 : have hlg : Real.log (30083349528978241 / 80000000000000000 : ℝ) ≤ (-(9780547872498677856713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30083349528978241 / 80000000000000000 : ℝ) = - (30083349528978241 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30083349528978241 / 20000000000000000 : ℚ)) - (U := (4082395733501322143287 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30083349528978241 / 20000000000000000 : ℝ) ≤ - (4082395733501322143287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3318804418667529 / 10000000000000000 : ℝ)) (q := - (30083349528978241 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30083349528978241 / 80000000000000000 : ℚ)) + (r' := (30083349528978241 / 20000000000000000 : ℚ)) + (U := (-(9780547872498677856713 / 10000000000000000000000 : ℚ))) + (U' := (4082395733501322143287 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (3318804418667529 / 10000000000000000 : ℚ)) + (q := (30083349528978241 / 80000000000000000 : ℚ)) + (U := (-(9780547872498677856713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_13 : Uω (aρ 13) (bρ 13) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1262,26 +1092,21 @@ lemma U_582_13 : have hlg : Real.log (24675259029316617 / 80000000000000000 : ℝ) ≤ (-(5881127756237673751163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24675259029316617 / 80000000000000000 : ℝ) = - (24675259029316617 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24675259029316617 / 20000000000000000 : ℚ)) - (U := (1050344046762326248837 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24675259029316617 / 20000000000000000 : ℝ) ≤ - (1050344046762326248837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2366163535347123 / 10000000000000000 : ℝ)) (q := - (24675259029316617 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24675259029316617 / 80000000000000000 : ℚ)) + (r' := (24675259029316617 / 20000000000000000 : ℚ)) + (U := (-(5881127756237673751163 / 5000000000000000000000 : ℚ))) + (U' := (1050344046762326248837 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (2366163535347123 / 10000000000000000 : ℚ)) + (q := (24675259029316617 / 80000000000000000 : ℚ)) + (U := (-(5881127756237673751163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_14 : Uω (aρ 14) (bρ 14) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1289,26 +1114,21 @@ lemma U_582_14 : have hlg : Real.log (17702646404448193 / 80000000000000000 : ℝ) ≤ (-(3770781227787045933889 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (17702646404448193 / 80000000000000000 : ℝ) = - (17702646404448193 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17702646404448193 / 10000000000000000 : ℚ)) - (U := (1427822624462954066111 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17702646404448193 / 10000000000000000 : ℝ) ≤ - (1427822624462954066111 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (966937664175017 / 10000000000000000 : ℝ)) (q := - (17702646404448193 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17702646404448193 / 80000000000000000 : ℚ)) + (r' := (17702646404448193 / 10000000000000000 : ℚ)) + (U := (-(3770781227787045933889 / 2500000000000000000000 : ℚ))) + (U' := (1427822624462954066111 / 2500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (8678814966921 / 12800000000000 : ℚ)) + (s := (966937664175017 / 10000000000000000 : ℚ)) + (q := (17702646404448193 / 80000000000000000 : ℚ)) + (U := (-(3770781227787045933889 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_582_15 : Uω (aρ 15) (bρ 15) (8678814966921 / 12800000000000 : ℝ) ≤ @@ -1408,25 +1228,21 @@ lemma U_583_1 : have hlg : Real.log (26895661220457821 / 40000000000000000 : ℝ) ≤ (-(1984572365875415154351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26895661220457821 / 40000000000000000 : ℝ) = - (26895661220457821 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26895661220457821 / 20000000000000000 : ℚ)) - (U := (1481163535624584845649 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26895661220457821 / 20000000000000000 : ℝ) ≤ - (1481163535624584845649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1680972815350587 / 2500000000000000 : ℝ)) (q := - (26895661220457821 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26895661220457821 / 40000000000000000 : ℚ)) + (r' := (26895661220457821 / 20000000000000000 : ℚ)) + (U := (-(1984572365875415154351 / 5000000000000000000000 : ℚ))) + (U' := (1481163535624584845649 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (1680972815350587 / 2500000000000000 : ℚ)) + (q := (26895661220457821 / 40000000000000000 : ℚ)) + (U := (-(1984572365875415154351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_2 : Uω (aρ 2) (bρ 2) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1434,25 +1250,21 @@ lemma U_583_2 : have hlg : Real.log (5360009591432243 / 8000000000000000 : ℝ) ≤ (-(4004757768924670619983 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5360009591432243 / 8000000000000000 : ℝ) = - (5360009591432243 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5360009591432243 / 4000000000000000 : ℚ)) - (U := (2926714034075329380017 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5360009591432243 / 4000000000000000 : ℝ) ≤ - (2926714034075329380017 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1339970728452809 / 2000000000000000 : ℝ)) (q := - (5360009591432243 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5360009591432243 / 8000000000000000 : ℚ)) + (r' := (5360009591432243 / 4000000000000000 : ℚ)) + (U := (-(4004757768924670619983 / 10000000000000000000000 : ℚ))) + (U' := (2926714034075329380017 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (1339970728452809 / 2000000000000000 : ℚ)) + (q := (5360009591432243 / 8000000000000000 : ℚ)) + (U := (-(4004757768924670619983 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_3 : Uω (aρ 3) (bρ 3) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1460,25 +1272,21 @@ lemma U_583_3 : have hlg : Real.log (1064354907008283 / 1600000000000000 : ℝ) ≤ (-(815269468933069742969 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1064354907008283 / 1600000000000000 : ℝ) = - (1064354907008283 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1064354907008283 / 800000000000000 : ℚ)) - (U := (571024891666930257031 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1064354907008283 / 800000000000000 : ℝ) ≤ - (571024891666930257031 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (266066484305479 / 400000000000000 : ℝ)) (q := - (1064354907008283 / 1600000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1064354907008283 / 1600000000000000 : ℚ)) + (r' := (1064354907008283 / 800000000000000 : ℚ)) + (U := (-(815269468933069742969 / 2000000000000000000000 : ℚ))) + (U' := (571024891666930257031 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (266066484305479 / 400000000000000 : ℚ)) + (q := (1064354907008283 / 1600000000000000 : ℚ)) + (U := (-(815269468933069742969 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_4 : Uω (aρ 4) (bρ 4) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1486,25 +1294,21 @@ lemma U_583_4 : have hlg : Real.log (26291517808627243 / 40000000000000000 : ℝ) ≤ (-(2098165417361143833627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26291517808627243 / 40000000000000000 : ℝ) = - (26291517808627243 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26291517808627243 / 20000000000000000 : ℚ)) - (U := (1367570484138856166373 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26291517808627243 / 20000000000000000 : ℝ) ≤ - (1367570484138856166373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6571278855412059 / 10000000000000000 : ℝ)) (q := - (26291517808627243 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26291517808627243 / 40000000000000000 : ℚ)) + (r' := (26291517808627243 / 20000000000000000 : ℚ)) + (U := (-(2098165417361143833627 / 5000000000000000000000 : ℚ))) + (U' := (1367570484138856166373 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (6571278855412059 / 10000000000000000 : ℚ)) + (q := (26291517808627243 / 40000000000000000 : ℚ)) + (U := (-(2098165417361143833627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_5 : Uω (aρ 5) (bρ 5) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1512,25 +1316,21 @@ lemma U_583_5 : have hlg : Real.log (25808652293284761 / 40000000000000000 : ℝ) ≤ (-(4381696579422479512909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25808652293284761 / 40000000000000000 : ℝ) = - (25808652293284761 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25808652293284761 / 20000000000000000 : ℚ)) - (U := (2549775223577520487091 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25808652293284761 / 20000000000000000 : ℝ) ≤ - (2549775223577520487091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3224018008537909 / 5000000000000000 : ℝ)) (q := - (25808652293284761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25808652293284761 / 40000000000000000 : ℚ)) + (r' := (25808652293284761 / 20000000000000000 : ℚ)) + (U := (-(4381696579422479512909 / 10000000000000000000000 : ℚ))) + (U' := (2549775223577520487091 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (3224018008537909 / 5000000000000000 : ℚ)) + (q := (25808652293284761 / 40000000000000000 : ℚ)) + (U := (-(4381696579422479512909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_6 : Uω (aρ 6) (bρ 6) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1538,25 +1338,21 @@ lemma U_583_6 : have hlg : Real.log (25117111001559067 / 40000000000000000 : ℝ) ≤ (-(4653301267676273408001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25117111001559067 / 40000000000000000 : ℝ) = - (25117111001559067 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25117111001559067 / 20000000000000000 : ℚ)) - (U := (2278170535323726591999 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25117111001559067 / 20000000000000000 : ℝ) ≤ - (2278170535323726591999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6269505746352971 / 10000000000000000 : ℝ)) (q := - (25117111001559067 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25117111001559067 / 40000000000000000 : ℚ)) + (r' := (25117111001559067 / 20000000000000000 : ℚ)) + (U := (-(4653301267676273408001 / 10000000000000000000000 : ℚ))) + (U' := (2278170535323726591999 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (6269505746352971 / 10000000000000000 : ℚ)) + (q := (25117111001559067 / 40000000000000000 : ℚ)) + (U := (-(4653301267676273408001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_7 : Uω (aρ 7) (bρ 7) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1564,25 +1360,21 @@ lemma U_583_7 : have hlg : Real.log (4835146341648111 / 8000000000000000 : ℝ) ≤ (-(1258825364568131694757 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4835146341648111 / 8000000000000000 : ℝ) = - (4835146341648111 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4835146341648111 / 4000000000000000 : ℚ)) - (U := (474042586181868305243 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4835146341648111 / 4000000000000000 : ℝ) ≤ - (474042586181868305243 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1204495496090743 / 2000000000000000 : ℝ)) (q := - (4835146341648111 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4835146341648111 / 8000000000000000 : ℚ)) + (r' := (4835146341648111 / 4000000000000000 : ℚ)) + (U := (-(1258825364568131694757 / 2500000000000000000000 : ℚ))) + (U' := (474042586181868305243 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (1204495496090743 / 2000000000000000 : ℚ)) + (q := (4835146341648111 / 8000000000000000 : ℚ)) + (U := (-(1258825364568131694757 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_8 : Uω (aρ 8) (bρ 8) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1590,25 +1382,21 @@ lemma U_583_8 : have hlg : Real.log (22951545918932221 / 40000000000000000 : ℝ) ≤ (-(1388735398284956359487 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22951545918932221 / 40000000000000000 : ℝ) = - (22951545918932221 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22951545918932221 / 20000000000000000 : ℚ)) - (U := (344132552465043640513 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22951545918932221 / 20000000000000000 : ℝ) ≤ - (344132552465043640513 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1423481559284887 / 2500000000000000 : ℝ)) (q := - (22951545918932221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22951545918932221 / 40000000000000000 : ℚ)) + (r' := (22951545918932221 / 20000000000000000 : ℚ)) + (U := (-(1388735398284956359487 / 2500000000000000000000 : ℚ))) + (U' := (344132552465043640513 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (1423481559284887 / 2500000000000000 : ℚ)) + (q := (22951545918932221 / 40000000000000000 : ℚ)) + (U := (-(1388735398284956359487 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_9 : Uω (aρ 9) (bρ 9) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1616,25 +1404,21 @@ lemma U_583_9 : have hlg : Real.log (21425334289664297 / 40000000000000000 : ℝ) ≤ (-(6243053867070716944753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21425334289664297 / 40000000000000000 : ℝ) = - (21425334289664297 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21425334289664297 / 20000000000000000 : ℚ)) - (U := (688417935929283055247 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21425334289664297 / 20000000000000000 : ℝ) ≤ - (688417935929283055247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2635893025432793 / 5000000000000000 : ℝ)) (q := - (21425334289664297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21425334289664297 / 40000000000000000 : ℚ)) + (r' := (21425334289664297 / 20000000000000000 : ℚ)) + (U := (-(6243053867070716944753 / 10000000000000000000000 : ℚ))) + (U' := (688417935929283055247 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (2635893025432793 / 5000000000000000 : ℚ)) + (q := (21425334289664297 / 40000000000000000 : ℚ)) + (U := (-(6243053867070716944753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_10 : Uω (aρ 10) (bρ 10) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1642,26 +1426,21 @@ lemma U_583_10 : have hlg : Real.log (19594953486378081 / 40000000000000000 : ℝ) ≤ (-(7136073956947920528813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19594953486378081 / 40000000000000000 : ℝ) = - (19594953486378081 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19594953486378081 / 10000000000000000 : ℚ)) - (U := (6726869649052079471187 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19594953486378081 / 10000000000000000 : ℝ) ≤ - (6726869649052079471187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2372577341358739 / 5000000000000000 : ℝ)) (q := - (19594953486378081 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19594953486378081 / 40000000000000000 : ℚ)) + (r' := (19594953486378081 / 10000000000000000 : ℚ)) + (U := (-(7136073956947920528813 / 10000000000000000000000 : ℚ))) + (U' := (6726869649052079471187 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (2372577341358739 / 5000000000000000 : ℚ)) + (q := (19594953486378081 / 40000000000000000 : ℚ)) + (U := (-(7136073956947920528813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_11 : Uω (aρ 11) (bρ 11) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1669,26 +1448,21 @@ lemma U_583_11 : have hlg : Real.log (17473802007736831 / 40000000000000000 : ℝ) ≤ (-(8281767224600949070467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17473802007736831 / 40000000000000000 : ℝ) = - (17473802007736831 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17473802007736831 / 10000000000000000 : ℚ)) - (U := (5581176381399050929533 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17473802007736831 / 10000000000000000 : ℝ) ≤ - (5581176381399050929533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4103055569601853 / 10000000000000000 : ℝ)) (q := - (17473802007736831 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17473802007736831 / 40000000000000000 : ℚ)) + (r' := (17473802007736831 / 10000000000000000 : ℚ)) + (U := (-(8281767224600949070467 / 10000000000000000000000 : ℚ))) + (U' := (5581176381399050929533 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (4103055569601853 / 10000000000000000 : ℚ)) + (q := (17473802007736831 / 40000000000000000 : ℚ)) + (U := (-(8281767224600949070467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_12 : Uω (aρ 12) (bρ 12) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1696,26 +1470,21 @@ lemma U_583_12 : have hlg : Real.log (3015686041375169 / 8000000000000000 : ℝ) ≤ (-(9756141941200541419451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3015686041375169 / 8000000000000000 : ℝ) = - (3015686041375169 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3015686041375169 / 2000000000000000 : ℚ)) - (U := (4106801664799458580549 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3015686041375169 / 2000000000000000 : ℝ) ≤ - (4106801664799458580549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83226744146409 / 250000000000000 : ℝ)) (q := - (3015686041375169 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3015686041375169 / 8000000000000000 : ℚ)) + (r' := (3015686041375169 / 2000000000000000 : ℚ)) + (U := (-(9756141941200541419451 / 10000000000000000000000 : ℚ))) + (U' := (4106801664799458580549 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (83226744146409 / 250000000000000 : ℚ)) + (q := (3015686041375169 / 8000000000000000 : ℚ)) + (U := (-(9756141941200541419451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_13 : Uω (aρ 13) (bρ 13) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1723,26 +1492,21 @@ lemma U_583_13 : have hlg : Real.log (2475977040951843 / 8000000000000000 : ℝ) ≤ (-(586403229508580354881 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2475977040951843 / 8000000000000000 : ℝ) = - (2475977040951843 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2475977040951843 / 2000000000000000 : ℚ)) - (U := (106743950791419645119 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2475977040951843 / 2000000000000000 : ℝ) ≤ - (106743950791419645119 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (475835801278609 / 2000000000000000 : ℝ)) (q := - (2475977040951843 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2475977040951843 / 8000000000000000 : ℚ)) + (r' := (2475977040951843 / 2000000000000000 : ℚ)) + (U := (-(586403229508580354881 / 500000000000000000000 : ℚ))) + (U' := (106743950791419645119 / 500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (475835801278609 / 2000000000000000 : ℚ)) + (q := (2475977040951843 / 8000000000000000 : ℚ)) + (U := (-(586403229508580354881 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_14 : Uω (aρ 14) (bρ 14) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1750,26 +1514,21 @@ lemma U_583_14 : have hlg : Real.log (8924804140715513 / 40000000000000000 : ℝ) ≤ (-(3000090141854125438813 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8924804140715513 / 40000000000000000 : ℝ) = - (8924804140715513 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8924804140715513 / 5000000000000000 : ℚ)) - (U := (1158792939945874561187 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8924804140715513 / 5000000000000000 : ℝ) ≤ - (1158792939945874561187 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (497782879708097 / 5000000000000000 : ℝ)) (q := - (8924804140715513 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8924804140715513 / 40000000000000000 : ℚ)) + (r' := (8924804140715513 / 5000000000000000 : ℚ)) + (U := (-(3000090141854125438813 / 2000000000000000000000 : ℚ))) + (U' := (1158792939945874561187 / 2000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (21722997014117 / 32000000000000 : ℚ)) + (s := (497782879708097 / 5000000000000000 : ℚ)) + (q := (8924804140715513 / 40000000000000000 : ℚ)) + (U := (-(3000090141854125438813 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_583_15 : Uω (aρ 15) (bρ 15) (21722997014117 / 32000000000000 : ℝ) ≤ @@ -1871,25 +1630,21 @@ lemma U_584_1 : have hlg : Real.log (53856221664742123 / 80000000000000000 : ℝ) ≤ (-(3957087005357036086949 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53856221664742123 / 80000000000000000 : ℝ) = - (53856221664742123 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53856221664742123 / 40000000000000000 : ℚ)) - (U := (2974384797642963913051 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53856221664742123 / 40000000000000000 : ℝ) ≤ - (2974384797642963913051 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6732003693354437 / 10000000000000000 : ℝ)) (q := - (53856221664742123 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53856221664742123 / 80000000000000000 : ℚ)) + (r' := (53856221664742123 / 40000000000000000 : ℚ)) + (U := (-(3957087005357036086949 / 10000000000000000000000 : ℚ))) + (U' := (2974384797642963913051 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (6732003693354437 / 10000000000000000 : ℚ)) + (q := (53856221664742123 / 80000000000000000 : ℚ)) + (U := (-(3957087005357036086949 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_2 : Uω (aρ 2) (bρ 2) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -1897,25 +1652,21 @@ lemma U_584_2 : have hlg : Real.log (53664996438352443 / 80000000000000000 : ℝ) ≤ (-(1996328404243077264093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53664996438352443 / 80000000000000000 : ℝ) = - (53664996438352443 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53664996438352443 / 40000000000000000 : ℚ)) - (U := (1469407497256922735907 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53664996438352443 / 40000000000000000 : ℝ) ≤ - (1469407497256922735907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6707966399267017 / 10000000000000000 : ℝ)) (q := - (53664996438352443 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53664996438352443 / 80000000000000000 : ℚ)) + (r' := (53664996438352443 / 40000000000000000 : ℚ)) + (U := (-(1996328404243077264093 / 5000000000000000000000 : ℚ))) + (U' := (1469407497256922735907 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (6707966399267017 / 10000000000000000 : ℚ)) + (q := (53664996438352443 / 80000000000000000 : ℚ)) + (U := (-(1996328404243077264093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_3 : Uω (aρ 3) (bρ 3) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -1923,25 +1674,21 @@ lemma U_584_3 : have hlg : Real.log (53282649761223291 / 80000000000000000 : ℝ) ≤ (-(4064158766627427001413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53282649761223291 / 80000000000000000 : ℝ) = - (53282649761223291 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53282649761223291 / 40000000000000000 : ℚ)) - (U := (2867313036372572998587 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53282649761223291 / 40000000000000000 : ℝ) ≤ - (2867313036372572998587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6659775836334729 / 10000000000000000 : ℝ)) (q := - (53282649761223291 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53282649761223291 / 80000000000000000 : ℚ)) + (r' := (53282649761223291 / 40000000000000000 : ℚ)) + (U := (-(4064158766627427001413 / 10000000000000000000000 : ℚ))) + (U' := (2867313036372572998587 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (6659775836334729 / 10000000000000000 : ℚ)) + (q := (53282649761223291 / 80000000000000000 : ℚ)) + (U := (-(4064158766627427001413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_4 : Uω (aρ 4) (bρ 4) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -1949,25 +1696,21 @@ lemma U_584_4 : have hlg : Real.log (10529590079508471 / 16000000000000000 : ℝ) ≤ (-(167359730165322291151 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10529590079508471 / 16000000000000000 : ℝ) = - (10529590079508471 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10529590079508471 / 8000000000000000 : ℚ)) - (U := (109899141954677708849 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10529590079508471 / 8000000000000000 : ℝ) ≤ - (109899141954677708849 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1315879035295899 / 2000000000000000 : ℝ)) (q := - (10529590079508471 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10529590079508471 / 16000000000000000 : ℚ)) + (r' := (10529590079508471 / 8000000000000000 : ℚ)) + (U := (-(167359730165322291151 / 400000000000000000000 : ℚ))) + (U' := (109899141954677708849 / 400000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (1315879035295899 / 2000000000000000 : ℚ)) + (q := (10529590079508471 / 16000000000000000 : ℚ)) + (U := (-(167359730165322291151 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_5 : Uω (aρ 5) (bρ 5) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -1975,25 +1718,21 @@ lemma U_584_5 : have hlg : Real.log (51682245064885059 / 80000000000000000 : ℝ) ≤ (-(4369123342251587632137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51682245064885059 / 80000000000000000 : ℝ) = - (51682245064885059 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51682245064885059 / 40000000000000000 : ℚ)) - (U := (2562348460748412367863 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51682245064885059 / 40000000000000000 : ℝ) ≤ - (2562348460748412367863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6456158762650171 / 10000000000000000 : ℝ)) (q := - (51682245064885059 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51682245064885059 / 80000000000000000 : ℚ)) + (r' := (51682245064885059 / 40000000000000000 : ℚ)) + (U := (-(4369123342251587632137 / 10000000000000000000000 : ℚ))) + (U' := (2562348460748412367863 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (6456158762650171 / 10000000000000000 : ℚ)) + (q := (51682245064885059 / 80000000000000000 : ℚ)) + (U := (-(4369123342251587632137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_6 : Uω (aρ 6) (bρ 6) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2001,25 +1740,21 @@ lemma U_584_6 : have hlg : Real.log (10059844403889607 / 16000000000000000 : ℝ) ≤ (-(1160092560595083378649 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10059844403889607 / 16000000000000000 : ℝ) = - (10059844403889607 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10059844403889607 / 8000000000000000 : ℚ)) - (U := (572775390154916621351 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (10059844403889607 / 8000000000000000 : ℝ) ≤ - (572775390154916621351 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1255528675286183 / 2000000000000000 : ℝ)) (q := - (10059844403889607 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10059844403889607 / 16000000000000000 : ℚ)) + (r' := (10059844403889607 / 8000000000000000 : ℚ)) + (U := (-(1160092560595083378649 / 2500000000000000000000 : ℚ))) + (U' := (572775390154916621351 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (1255528675286183 / 2000000000000000 : ℚ)) + (q := (10059844403889607 / 16000000000000000 : ℚ)) + (U := (-(1160092560595083378649 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_7 : Uω (aρ 7) (bρ 7) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2027,25 +1762,21 @@ lemma U_584_7 : have hlg : Real.log (48416593303044763 / 80000000000000000 : ℝ) ≤ (-(5021840426067032372317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48416593303044763 / 80000000000000000 : ℝ) = - (48416593303044763 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48416593303044763 / 40000000000000000 : ℚ)) - (U := (1909631376932967627683 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48416593303044763 / 40000000000000000 : ℝ) ≤ - (1909631376932967627683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6030647578090097 / 10000000000000000 : ℝ)) (q := - (48416593303044763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48416593303044763 / 80000000000000000 : ℚ)) + (r' := (48416593303044763 / 40000000000000000 : ℚ)) + (U := (-(5021840426067032372317 / 10000000000000000000000 : ℚ))) + (U' := (1909631376932967627683 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (6030647578090097 / 10000000000000000 : ℚ)) + (q := (48416593303044763 / 80000000000000000 : ℚ)) + (U := (-(5021840426067032372317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_8 : Uω (aρ 8) (bρ 8) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2053,25 +1784,21 @@ lemma U_584_8 : have hlg : Real.log (45968491167470523 / 80000000000000000 : ℝ) ≤ (-(2770352236236726762283 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45968491167470523 / 80000000000000000 : ℝ) = - (45968491167470523 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45968491167470523 / 40000000000000000 : ℚ)) - (U := (695383665263273237717 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45968491167470523 / 40000000000000000 : ℝ) ≤ - (695383665263273237717 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5702163695536537 / 10000000000000000 : ℝ)) (q := - (45968491167470523 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45968491167470523 / 80000000000000000 : ℚ)) + (r' := (45968491167470523 / 40000000000000000 : ℚ)) + (U := (-(2770352236236726762283 / 5000000000000000000000 : ℚ))) + (U' := (695383665263273237717 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (5702163695536537 / 10000000000000000 : ℚ)) + (q := (45968491167470523 / 80000000000000000 : ℚ)) + (U := (-(2770352236236726762283 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_9 : Uω (aρ 9) (bρ 9) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2079,25 +1806,21 @@ lemma U_584_9 : have hlg : Real.log (42916606779601831 / 80000000000000000 : ℝ) ≤ (-(6227677789659275289543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42916606779601831 / 80000000000000000 : ℝ) = - (42916606779601831 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42916606779601831 / 40000000000000000 : ℚ)) - (U := (703794013340724710457 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42916606779601831 / 40000000000000000 : ℝ) ≤ - (703794013340724710457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1320039556732341 / 2500000000000000 : ℝ)) (q := - (42916606779601831 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42916606779601831 / 80000000000000000 : ℚ)) + (r' := (42916606779601831 / 40000000000000000 : ℚ)) + (U := (-(6227677789659275289543 / 10000000000000000000000 : ℚ))) + (U' := (703794013340724710457 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (1320039556732341 / 2500000000000000 : ℚ)) + (q := (42916606779601831 / 80000000000000000 : ℚ)) + (U := (-(6227677789659275289543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_10 : Uω (aρ 10) (bρ 10) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2105,26 +1828,21 @@ lemma U_584_10 : have hlg : Real.log (39256902812473411 / 80000000000000000 : ℝ) ≤ (-(7118993375547906127047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39256902812473411 / 80000000000000000 : ℝ) = - (39256902812473411 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39256902812473411 / 20000000000000000 : ℚ)) - (U := (6743950230452093872953 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39256902812473411 / 20000000000000000 : ℝ) ≤ - (6743950230452093872953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4753791268642259 / 10000000000000000 : ℝ)) (q := - (39256902812473411 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39256902812473411 / 80000000000000000 : ℚ)) + (r' := (39256902812473411 / 20000000000000000 : ℚ)) + (U := (-(7118993375547906127047 / 10000000000000000000000 : ℚ))) + (U' := (6743950230452093872953 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (4753791268642259 / 10000000000000000 : ℚ)) + (q := (39256902812473411 / 80000000000000000 : ℚ)) + (U := (-(7118993375547906127047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_11 : Uω (aρ 11) (bρ 11) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2132,26 +1850,21 @@ lemma U_584_11 : have hlg : Real.log (35016692004499127 / 80000000000000000 : ℝ) ≤ (-(1652403543875702179933 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35016692004499127 / 80000000000000000 : ℝ) = - (35016692004499127 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35016692004499127 / 20000000000000000 : ℚ)) - (U := (1120185177324297820067 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35016692004499127 / 20000000000000000 : ℝ) ≤ - (1120185177324297820067 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (514026899106711 / 1250000000000000 : ℝ)) (q := - (35016692004499127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35016692004499127 / 80000000000000000 : ℚ)) + (r' := (35016692004499127 / 20000000000000000 : ℚ)) + (U := (-(1652403543875702179933 / 2000000000000000000000 : ℚ))) + (U' := (1120185177324297820067 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (514026899106711 / 1250000000000000 : ℚ)) + (q := (35016692004499127 / 80000000000000000 : ℚ)) + (U := (-(1652403543875702179933 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_12 : Uω (aρ 12) (bρ 12) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2159,26 +1872,21 @@ lemma U_584_12 : have hlg : Real.log (30230323903687811 / 80000000000000000 : ℝ) ≤ (-(9731811107760359174813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30230323903687811 / 80000000000000000 : ℝ) = - (30230323903687811 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30230323903687811 / 20000000000000000 : ℚ)) - (U := (4131132498239640825187 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30230323903687811 / 20000000000000000 : ℝ) ≤ - (4131132498239640825187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3339323264335859 / 10000000000000000 : ℝ)) (q := - (30230323903687811 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30230323903687811 / 80000000000000000 : ℚ)) + (r' := (30230323903687811 / 20000000000000000 : ℚ)) + (U := (-(9731811107760359174813 / 10000000000000000000000 : ℚ))) + (U' := (4131132498239640825187 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (3339323264335859 / 10000000000000000 : ℚ)) + (q := (30230323903687811 / 80000000000000000 : ℚ)) + (U := (-(9731811107760359174813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_13 : Uω (aρ 13) (bρ 13) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2186,26 +1894,21 @@ lemma U_584_13 : have hlg : Real.log (4968821714335203 / 16000000000000000 : ℝ) ≤ (-(11694059893297898993841 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4968821714335203 / 16000000000000000 : ℝ) = - (4968821714335203 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4968821714335203 / 4000000000000000 : ℚ)) - (U := (2168883712702101006159 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4968821714335203 / 4000000000000000 : ℝ) ≤ - (2168883712702101006159 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (239215117292791 / 1000000000000000 : ℝ)) (q := - (4968821714335203 / 16000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4968821714335203 / 16000000000000000 : ℚ)) + (r' := (4968821714335203 / 4000000000000000 : ℚ)) + (U := (-(11694059893297898993841 / 10000000000000000000000 : ℚ))) + (U' := (2168883712702101006159 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (239215117292791 / 1000000000000000 : ℚ)) + (q := (4968821714335203 / 16000000000000000 : ℚ)) + (U := (-(11694059893297898993841 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_14 : Uω (aρ 14) (bρ 14) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2213,26 +1916,21 @@ lemma U_584_14 : have hlg : Real.log (3598725058625411 / 16000000000000000 : ℝ) ≤ (-(14920090891057678189429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (3598725058625411 / 16000000000000000 : ℝ) = - (3598725058625411 / 2000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3598725058625411 / 2000000000000000 : ℚ)) - (U := (5874324517942321810571 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3598725058625411 / 2000000000000000 : ℝ) ≤ - (5874324517942321810571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (102345763833567 / 1000000000000000 : ℝ)) (q := - (3598725058625411 / 16000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3598725058625411 / 16000000000000000 : ℚ)) + (r' := (3598725058625411 / 2000000000000000 : ℚ)) + (U := (-(14920090891057678189429 / 10000000000000000000000 : ℚ))) + (U' := (5874324517942321810571 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43497913221863 / 64000000000000 : ℚ)) + (s := (102345763833567 / 1000000000000000 : ℚ)) + (q := (3598725058625411 / 16000000000000000 : ℚ)) + (U := (-(14920090891057678189429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_584_15 : Uω (aρ 15) (bρ 15) (43497913221863 / 64000000000000 : ℝ) ≤ @@ -2334,25 +2032,21 @@ lemma U_585_1 : have hlg : Real.log (674014011100133 / 1000000000000000 : ℝ) ≤ (-(986260950108896607393 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (674014011100133 / 1000000000000000 : ℝ) = - (674014011100133 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (674014011100133 / 500000000000000 : ℚ)) - (U := (746607000641103392607 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (674014011100133 / 500000000000000 : ℝ) ≤ - (746607000641103392607 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1348023225033407 / 2000000000000000 : ℝ)) (q := - (674014011100133 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (674014011100133 / 1000000000000000 : ℚ)) + (r' := (674014011100133 / 500000000000000 : ℚ)) + (U := (-(986260950108896607393 / 2500000000000000000000 : ℚ))) + (U' := (746607000641103392607 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1348023225033407 / 2000000000000000 : ℚ)) + (q := (674014011100133 / 1000000000000000 : ℚ)) + (U := (-(986260950108896607393 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_2 : Uω (aρ 2) (bρ 2) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2360,25 +2054,21 @@ lemma U_585_2 : have hlg : Real.log (13432474239670343 / 20000000000000000 : ℝ) ≤ (-(995142618591047904077 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13432474239670343 / 20000000000000000 : ℝ) = - (13432474239670343 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13432474239670343 / 10000000000000000 : ℚ)) - (U := (737725332158952095923 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13432474239670343 / 10000000000000000 : ℝ) ≤ - (737725332158952095923 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3358039577672359 / 5000000000000000 : ℝ)) (q := - (13432474239670343 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13432474239670343 / 20000000000000000 : ℚ)) + (r' := (13432474239670343 / 10000000000000000 : ℚ)) + (U := (-(995142618591047904077 / 2500000000000000000000 : ℚ))) + (U' := (737725332158952095923 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (3358039577672359 / 5000000000000000 : ℚ)) + (q := (13432474239670343 / 20000000000000000 : ℚ)) + (U := (-(995142618591047904077 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_3 : Uω (aρ 3) (bρ 3) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2386,25 +2076,21 @@ lemma U_585_3 : have hlg : Real.log (2667377707942301 / 4000000000000000 : ℝ) ≤ (-(4051985029121106850783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2667377707942301 / 4000000000000000 : ℝ) = - (2667377707942301 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2667377707942301 / 2000000000000000 : ℚ)) - (U := (2879486773878893149217 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2667377707942301 / 2000000000000000 : ℝ) ≤ - (2879486773878893149217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (166697239043397 / 250000000000000 : ℝ)) (q := - (2667377707942301 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2667377707942301 / 4000000000000000 : ℚ)) + (r' := (2667377707942301 / 2000000000000000 : ℚ)) + (U := (-(4051985029121106850783 / 10000000000000000000000 : ℚ))) + (U' := (2879486773878893149217 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (166697239043397 / 250000000000000 : ℚ)) + (q := (2667377707942301 / 4000000000000000 : ℚ)) + (U := (-(4051985029121106850783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_4 : Uω (aρ 4) (bρ 4) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2412,25 +2098,21 @@ lemma U_585_4 : have hlg : Real.log (13178216284733751 / 20000000000000000 : ℝ) ≤ (-(1042917720939327110799 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13178216284733751 / 20000000000000000 : ℝ) = - (13178216284733751 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13178216284733751 / 10000000000000000 : ℚ)) - (U := (689950229810672889201 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13178216284733751 / 10000000000000000 : ℝ) ≤ - (689950229810672889201 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3293755743911563 / 5000000000000000 : ℝ)) (q := - (13178216284733751 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13178216284733751 / 20000000000000000 : ℚ)) + (r' := (13178216284733751 / 10000000000000000 : ℚ)) + (U := (-(1042917720939327110799 / 2500000000000000000000 : ℚ))) + (U' := (689950229810672889201 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (3293755743911563 / 5000000000000000 : ℚ)) + (q := (13178216284733751 / 20000000000000000 : ℚ)) + (U := (-(1042917720939327110799 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_5 : Uω (aρ 5) (bρ 5) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2438,25 +2120,21 @@ lemma U_585_5 : have hlg : Real.log (3234199089937957 / 5000000000000000 : ℝ) ≤ (-(4356565913995524418331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3234199089937957 / 5000000000000000 : ℝ) = - (3234199089937957 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3234199089937957 / 2500000000000000 : ℚ)) - (U := (2574905889004475581669 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3234199089937957 / 2500000000000000 : ℝ) ≤ - (2574905889004475581669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6464281482176203 / 10000000000000000 : ℝ)) (q := - (3234199089937957 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3234199089937957 / 5000000000000000 : ℚ)) + (r' := (3234199089937957 / 2500000000000000 : ℚ)) + (U := (-(4356565913995524418331 / 10000000000000000000000 : ℚ))) + (U' := (2574905889004475581669 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (6464281482176203 / 10000000000000000 : ℚ)) + (q := (3234199089937957 / 5000000000000000 : ℚ)) + (U := (-(4356565913995524418331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_6 : Uω (aρ 6) (bρ 6) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2464,25 +2142,21 @@ lemma U_585_6 : have hlg : Real.log (1259105544365247 / 2000000000000000 : ℝ) ≤ (-(4627455968489878491293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1259105544365247 / 2000000000000000 : ℝ) = - (1259105544365247 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1259105544365247 / 1000000000000000 : ℚ)) - (U := (2304015834510121508707 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1259105544365247 / 1000000000000000 : ℝ) ≤ - (2304015834510121508707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1257156188243369 / 2000000000000000 : ℝ)) (q := - (1259105544365247 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1259105544365247 / 2000000000000000 : ℚ)) + (r' := (1259105544365247 / 1000000000000000 : ℚ)) + (U := (-(4627455968489878491293 / 10000000000000000000000 : ℚ))) + (U' := (2304015834510121508707 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1257156188243369 / 2000000000000000 : ℚ)) + (q := (1259105544365247 / 2000000000000000 : ℚ)) + (U := (-(4627455968489878491293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_7 : Uω (aρ 7) (bρ 7) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2490,25 +2164,21 @@ lemma U_585_7 : have hlg : Real.log (12120430641761801 / 20000000000000000 : ℝ) ≤ (-(500839761785607599 / 1000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12120430641761801 / 20000000000000000 : ℝ) = - (12120430641761801 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12120430641761801 / 10000000000000000 : ℚ)) - (U := (192307418514392401 / 1000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12120430641761801 / 10000000000000000 : ℝ) ≤ - (192307418514392401 / 1000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (188713047502693 / 312500000000000 : ℝ)) (q := - (12120430641761801 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12120430641761801 / 20000000000000000 : ℚ)) + (r' := (12120430641761801 / 10000000000000000 : ℚ)) + (U := (-(500839761785607599 / 1000000000000000000 : ℚ))) + (U' := (192307418514392401 / 1000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (188713047502693 / 312500000000000 : ℚ)) + (q := (12120430641761801 / 20000000000000000 : ℚ)) + (U := (-(500839761785607599 / 1000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_8 : Uω (aρ 8) (bρ 8) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2516,25 +2186,21 @@ lemma U_585_8 : have hlg : Real.log (11508472266131629 / 20000000000000000 : ℝ) ≤ (-(2763243951874325661233 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11508472266131629 / 20000000000000000 : ℝ) = - (11508472266131629 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11508472266131629 / 10000000000000000 : ℚ)) - (U := (702491949625674338767 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11508472266131629 / 10000000000000000 : ℝ) ≤ - (702491949625674338767 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1427600198949001 / 2500000000000000 : ℝ)) (q := - (11508472266131629 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11508472266131629 / 20000000000000000 : ℚ)) + (r' := (11508472266131629 / 10000000000000000 : ℚ)) + (U := (-(2763243951874325661233 / 5000000000000000000000 : ℚ))) + (U' := (702491949625674338767 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1427600198949001 / 2500000000000000 : ℚ)) + (q := (11508472266131629 / 20000000000000000 : ℚ)) + (U := (-(2763243951874325661233 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_9 : Uω (aρ 9) (bρ 9) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2542,25 +2208,21 @@ lemma U_585_9 : have hlg : Real.log (10745635435155821 / 20000000000000000 : ℝ) ≤ (-(6212326071951551424699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10745635435155821 / 20000000000000000 : ℝ) = - (10745635435155821 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10745635435155821 / 10000000000000000 : ℚ)) - (U := (719145731048448575301 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10745635435155821 / 10000000000000000 : ℝ) ≤ - (719145731048448575301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1322132398295049 / 2500000000000000 : ℝ)) (q := - (10745635435155821 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10745635435155821 / 20000000000000000 : ℚ)) + (r' := (10745635435155821 / 10000000000000000 : ℚ)) + (U := (-(6212326071951551424699 / 10000000000000000000000 : ℚ))) + (U' := (719145731048448575301 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1322132398295049 / 2500000000000000 : ℚ)) + (q := (10745635435155821 / 20000000000000000 : ℚ)) + (U := (-(6212326071951551424699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_10 : Uω (aρ 10) (bρ 10) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2568,26 +2230,21 @@ lemma U_585_10 : have hlg : Real.log (9830972819448893 / 20000000000000000 : ℝ) ≤ (-(443871487145641250981 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9830972819448893 / 20000000000000000 : ℝ) = - (9830972819448893 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9830972819448893 / 5000000000000000 : ℚ)) - (U := (422562488229358749019 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9830972819448893 / 5000000000000000 : ℝ) ≤ - (422562488229358749019 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1190606502742067 / 2500000000000000 : ℝ)) (q := - (9830972819448893 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9830972819448893 / 20000000000000000 : ℚ)) + (r' := (9830972819448893 / 5000000000000000 : ℚ)) + (U := (-(443871487145641250981 / 625000000000000000000 : ℚ))) + (U' := (422562488229358749019 / 625000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1190606502742067 / 2500000000000000 : ℚ)) + (q := (9830972819448893 / 20000000000000000 : ℚ)) + (U := (-(443871487145641250981 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_11 : Uω (aρ 11) (bρ 11) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2595,26 +2252,21 @@ lemma U_585_11 : have hlg : Real.log (4385720304765587 / 10000000000000000 : ℝ) ≤ (-(257572254535980578843 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4385720304765587 / 10000000000000000 : ℝ) = - (4385720304765587 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4385720304765587 / 2500000000000000 : ℚ)) - (U := (175644733151519421157 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4385720304765587 / 2500000000000000 : ℝ) ≤ - (175644733151519421157 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4121370427255549 / 10000000000000000 : ℝ)) (q := - (4385720304765587 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4385720304765587 / 10000000000000000 : ℚ)) + (r' := (4385720304765587 / 2500000000000000 : ℚ)) + (U := (-(257572254535980578843 / 312500000000000000000 : ℚ))) + (U' := (175644733151519421157 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (4121370427255549 / 10000000000000000 : ℚ)) + (q := (4385720304765587 / 10000000000000000 : ℚ)) + (U := (-(257572254535980578843 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_12 : Uω (aρ 12) (bρ 12) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2622,26 +2274,21 @@ lemma U_585_12 : have hlg : Real.log (1515187021701689 / 4000000000000000 : ℝ) ≤ (-(9707554825897988957459 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1515187021701689 / 4000000000000000 : ℝ) = - (1515187021701689 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1515187021701689 / 1000000000000000 : ℚ)) - (U := (4155388780102011042541 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1515187021701689 / 1000000000000000 : ℝ) ≤ - (4155388780102011042541 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (167478251145891 / 500000000000000 : ℝ)) (q := - (1515187021701689 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1515187021701689 / 4000000000000000 : ℚ)) + (r' := (1515187021701689 / 1000000000000000 : ℚ)) + (U := (-(9707554825897988957459 / 10000000000000000000000 : ℚ))) + (U' := (4155388780102011042541 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (167478251145891 / 500000000000000 : ℚ)) + (q := (1515187021701689 / 4000000000000000 : ℚ)) + (U := (-(9707554825897988957459 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_13 : Uω (aρ 13) (bρ 13) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2649,26 +2296,21 @@ lemma U_585_13 : have hlg : Real.log (6232069079655727 / 20000000000000000 : ℝ) ≤ (-(11660238798583253649693 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6232069079655727 / 20000000000000000 : ℝ) = - (6232069079655727 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6232069079655727 / 5000000000000000 : ℚ)) - (U := (2202704807416746350307 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6232069079655727 / 5000000000000000 : ℝ) ≤ - (2202704807416746350307 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1202540367830051 / 5000000000000000 : ℝ)) (q := - (6232069079655727 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6232069079655727 / 20000000000000000 : ℚ)) + (r' := (6232069079655727 / 5000000000000000 : ℚ)) + (U := (-(11660238798583253649693 / 10000000000000000000000 : ℚ))) + (U' := (2202704807416746350307 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (1202540367830051 / 5000000000000000 : ℚ)) + (q := (6232069079655727 / 20000000000000000 : ℚ)) + (U := (-(11660238798583253649693 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_14 : Uω (aρ 14) (bρ 14) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2676,26 +2318,21 @@ lemma U_585_14 : have hlg : Real.log (4533732993874791 / 20000000000000000 : ℝ) ≤ (-(14841866121726024649593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4533732993874791 / 20000000000000000 : ℝ) = - (4533732993874791 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4533732993874791 / 2500000000000000 : ℚ)) - (U := (5952549287273975350407 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4533732993874791 / 2500000000000000 : ℝ) ≤ - (5952549287273975350407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (525335967462083 / 5000000000000000 : ℝ)) (q := - (4533732993874791 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4533732993874791 / 20000000000000000 : ℚ)) + (r' := (4533732993874791 / 2500000000000000 : ℚ)) + (U := (-(14841866121726024649593 / 10000000000000000000000 : ℚ))) + (U' := (5952549287273975350407 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (10887458103873 / 16000000000000 : ℚ)) + (s := (525335967462083 / 5000000000000000 : ℚ)) + (q := (4533732993874791 / 20000000000000000 : ℚ)) + (U := (-(14841866121726024649593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_585_15 : Uω (aρ 15) (bρ 15) (10887458103873 / 16000000000000 : ℝ) ≤ @@ -2795,25 +2432,21 @@ lemma U_586_1 : have hlg : Real.log (53986020110723201 / 80000000000000000 : ℝ) ≤ (-(1966507541025517927749 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53986020110723201 / 80000000000000000 : ℝ) = - (53986020110723201 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53986020110723201 / 40000000000000000 : ℚ)) - (U := (1499228360474482072251 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (53986020110723201 / 40000000000000000 : ℝ) ≤ - (1499228360474482072251 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1687057139210161 / 2500000000000000 : ℝ)) (q := - (53986020110723201 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53986020110723201 / 80000000000000000 : ℚ)) + (r' := (53986020110723201 / 40000000000000000 : ℚ)) + (U := (-(1966507541025517927749 / 5000000000000000000000 : ℚ))) + (U' := (1499228360474482072251 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (1687057139210161 / 2500000000000000 : ℚ)) + (q := (53986020110723201 / 80000000000000000 : ℚ)) + (U := (-(1966507541025517927749 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_2 : Uω (aρ 2) (bρ 2) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2821,25 +2454,21 @@ lemma U_586_2 : have hlg : Real.log (10758959495064521 / 16000000000000000 : ℝ) ≤ (-(158739949249696931061 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10758959495064521 / 16000000000000000 : ℝ) = - (10758959495064521 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10758959495064521 / 8000000000000000 : ℚ)) - (U := (118518922870303068939 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10758959495064521 / 8000000000000000 : ℝ) ≤ - (118518922870303068939 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1344838382100099 / 2000000000000000 : ℝ)) (q := - (10758959495064521 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10758959495064521 / 16000000000000000 : ℚ)) + (r' := (10758959495064521 / 8000000000000000 : ℚ)) + (U := (-(158739949249696931061 / 400000000000000000000 : ℚ))) + (U' := (118518922870303068939 / 400000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (1344838382100099 / 2000000000000000 : ℚ)) + (q := (10758959495064521 / 16000000000000000 : ℚ)) + (U := (-(158739949249696931061 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_3 : Uω (aρ 3) (bρ 3) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2847,25 +2476,21 @@ lemma U_586_3 : have hlg : Real.log (53412458543330409 / 80000000000000000 : ℝ) ≤ (-(4039826096045358521497 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53412458543330409 / 80000000000000000 : ℝ) = - (53412458543330409 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53412458543330409 / 40000000000000000 : ℚ)) - (U := (2891645706954641478503 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53412458543330409 / 40000000000000000 : ℝ) ≤ - (2891645706954641478503 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3338001641926223 / 5000000000000000 : ℝ)) (q := - (53412458543330409 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53412458543330409 / 80000000000000000 : ℚ)) + (r' := (53412458543330409 / 40000000000000000 : ℚ)) + (U := (-(4039826096045358521497 / 10000000000000000000000 : ℚ))) + (U' := (2891645706954641478503 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (3338001641926223 / 5000000000000000 : ℚ)) + (q := (53412458543330409 / 80000000000000000 : ℚ)) + (U := (-(4039826096045358521497 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_4 : Uω (aρ 4) (bρ 4) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2873,25 +2498,21 @@ lemma U_586_4 : have hlg : Real.log (52777779841576017 / 80000000000000000 : ℝ) ≤ (-(1039840921529924137879 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52777779841576017 / 80000000000000000 : ℝ) = - (52777779841576017 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52777779841576017 / 40000000000000000 : ℚ)) - (U := (693027029220075862121 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52777779841576017 / 40000000000000000 : ℝ) ≤ - (693027029220075862121 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103056684210607 / 156250000000000 : ℝ)) (q := - (52777779841576017 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52777779841576017 / 80000000000000000 : ℚ)) + (r' := (52777779841576017 / 40000000000000000 : ℚ)) + (U := (-(1039840921529924137879 / 2500000000000000000000 : ℚ))) + (U' := (693027029220075862121 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (103056684210607 / 156250000000000 : ℚ)) + (q := (52777779841576017 / 80000000000000000 : ℚ)) + (U := (-(1039840921529924137879 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_5 : Uω (aρ 5) (bρ 5) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2899,25 +2520,21 @@ lemma U_586_5 : have hlg : Real.log (10362425141865713 / 16000000000000000 : ℝ) ≤ (-(4344024254899230569613 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10362425141865713 / 16000000000000000 : ℝ) = - (10362425141865713 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10362425141865713 / 8000000000000000 : ℚ)) - (U := (2587447548100769430387 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10362425141865713 / 8000000000000000 : ℝ) ≤ - (2587447548100769430387 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1294480835150397 / 2000000000000000 : ℝ)) (q := - (10362425141865713 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10362425141865713 / 16000000000000000 : ℚ)) + (r' := (10362425141865713 / 8000000000000000 : ℚ)) + (U := (-(4344024254899230569613 / 10000000000000000000000 : ℚ))) + (U' := (2587447548100769430387 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (1294480835150397 / 2000000000000000 : ℚ)) + (q := (10362425141865713 / 16000000000000000 : ℚ)) + (U := (-(4344024254899230569613 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_6 : Uω (aρ 6) (bρ 6) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2925,25 +2542,21 @@ lemma U_586_6 : have hlg : Real.log (50429221269616689 / 80000000000000000 : ℝ) ≤ (-(4614558402526447368687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50429221269616689 / 80000000000000000 : ℝ) = - (50429221269616689 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50429221269616689 / 40000000000000000 : ℚ)) - (U := (2316913400473552631313 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50429221269616689 / 40000000000000000 : ℝ) ≤ - (2316913400473552631313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (393369902560251 / 625000000000000 : ℝ)) (q := - (50429221269616689 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50429221269616689 / 80000000000000000 : ℚ)) + (r' := (50429221269616689 / 40000000000000000 : ℚ)) + (U := (-(4614558402526447368687 / 10000000000000000000000 : ℚ))) + (U' := (2316913400473552631313 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (393369902560251 / 625000000000000 : ℚ)) + (q := (50429221269616689 / 80000000000000000 : ℚ)) + (U := (-(4614558402526447368687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_7 : Uω (aρ 7) (bρ 7) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2951,25 +2564,21 @@ lemma U_586_7 : have hlg : Real.log (48546851211011821 / 80000000000000000 : ℝ) ≤ (-(998994596803359351861 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48546851211011821 / 80000000000000000 : ℝ) = - (48546851211011821 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48546851211011821 / 40000000000000000 : ℚ)) - (U := (387299763796640648139 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48546851211011821 / 40000000000000000 : ℝ) ≤ - (387299763796640648139 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6046987307072799 / 10000000000000000 : ℝ)) (q := - (48546851211011821 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48546851211011821 / 80000000000000000 : ℚ)) + (r' := (48546851211011821 / 40000000000000000 : ℚ)) + (U := (-(998994596803359351861 / 2000000000000000000000 : ℚ))) + (U' := (387299763796640648139 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (6046987307072799 / 10000000000000000 : ℚ)) + (q := (48546851211011821 / 80000000000000000 : ℚ)) + (U := (-(998994596803359351861 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_8 : Uω (aρ 8) (bρ 8) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -2977,25 +2586,21 @@ lemma U_586_8 : have hlg : Real.log (46099285535222737 / 80000000000000000 : ℝ) ≤ (-(2756145913413908321303 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46099285535222737 / 80000000000000000 : ℝ) = - (46099285535222737 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46099285535222737 / 40000000000000000 : ℚ)) - (U := (709589988086091678697 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46099285535222737 / 40000000000000000 : ℝ) ≤ - (709589988086091678697 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (714829692433191 / 1250000000000000 : ℝ)) (q := - (46099285535222737 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46099285535222737 / 80000000000000000 : ℚ)) + (r' := (46099285535222737 / 40000000000000000 : ℚ)) + (U := (-(2756145913413908321303 / 5000000000000000000000 : ℚ))) + (U' := (709589988086091678697 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (714829692433191 / 1250000000000000 : ℚ)) + (q := (46099285535222737 / 80000000000000000 : ℚ)) + (U := (-(2756145913413908321303 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_9 : Uω (aρ 9) (bρ 9) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3003,25 +2608,21 @@ lemma U_586_9 : have hlg : Real.log (8609694695550233 / 16000000000000000 : ℝ) ≤ (-(774624829318223816123 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8609694695550233 / 16000000000000000 : ℝ) = - (8609694695550233 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8609694695550233 / 8000000000000000 : ℚ)) - (U := (91809146056776183877 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8609694695550233 / 8000000000000000 : ℝ) ≤ - (91809146056776183877 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1059380030691527 / 2000000000000000 : ℝ)) (q := - (8609694695550233 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8609694695550233 / 16000000000000000 : ℚ)) + (r' := (8609694695550233 / 8000000000000000 : ℚ)) + (U := (-(774624829318223816123 / 1250000000000000000000 : ℚ))) + (U' := (91809146056776183877 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (1059380030691527 / 2000000000000000 : ℚ)) + (q := (8609694695550233 / 16000000000000000 : ℚ)) + (U := (-(774624829318223816123 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_10 : Uω (aρ 10) (bρ 10) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3029,26 +2630,21 @@ lemma U_586_10 : have hlg : Real.log (39390872408761549 / 80000000000000000 : ℝ) ≤ (-(3542462547203858067021 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39390872408761549 / 80000000000000000 : ℝ) = - (39390872408761549 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39390872408761549 / 20000000000000000 : ℚ)) - (U := (3389009255796141932979 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39390872408761549 / 20000000000000000 : ℝ) ≤ - (3389009255796141932979 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4771058919705231 / 10000000000000000 : ℝ)) (q := - (39390872408761549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39390872408761549 / 80000000000000000 : ℚ)) + (r' := (39390872408761549 / 20000000000000000 : ℚ)) + (U := (-(3542462547203858067021 / 5000000000000000000000 : ℚ))) + (U' := (3389009255796141932979 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (4771058919705231 / 10000000000000000 : ℚ)) + (q := (39390872408761549 / 80000000000000000 : ℚ)) + (U := (-(3542462547203858067021 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_11 : Uω (aρ 11) (bρ 11) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3056,26 +2652,21 @@ lemma U_586_11 : have hlg : Real.log (35154815433084153 / 80000000000000000 : ℝ) ≤ (-(8222650286067020655741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35154815433084153 / 80000000000000000 : ℝ) = - (35154815433084153 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35154815433084153 / 20000000000000000 : ℚ)) - (U := (5640293319932979344259 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35154815433084153 / 20000000000000000 : ℝ) ≤ - (5640293319932979344259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2065260650995441 / 5000000000000000 : ℝ)) (q := - (35154815433084153 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35154815433084153 / 80000000000000000 : ℚ)) + (r' := (35154815433084153 / 20000000000000000 : ℚ)) + (U := (-(8222650286067020655741 / 10000000000000000000000 : ℚ))) + (U' := (5640293319932979344259 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (2065260650995441 / 5000000000000000 : ℚ)) + (q := (35154815433084153 / 80000000000000000 : ℚ)) + (U := (-(8222650286067020655741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_12 : Uω (aρ 12) (bρ 12) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3083,26 +2674,21 @@ lemma U_586_12 : have hlg : Real.log (30377110434234341 / 80000000000000000 : ℝ) ≤ (-(591026156976621987 / 610351562500000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30377110434234341 / 80000000000000000 : ℝ) = - (30377110434234341 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30377110434234341 / 20000000000000000 : ℚ)) - (U := (510201544201052901 / 1220703125000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30377110434234341 / 20000000000000000 : ℝ) ≤ - (510201544201052901 / 1220703125000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3359795148963429 / 10000000000000000 : ℝ)) (q := - (30377110434234341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30377110434234341 / 80000000000000000 : ℚ)) + (r' := (30377110434234341 / 20000000000000000 : ℚ)) + (U := (-(591026156976621987 / 610351562500000000 : ℚ))) + (U' := (510201544201052901 / 1220703125000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (3359795148963429 / 10000000000000000 : ℚ)) + (q := (30377110434234341 / 80000000000000000 : ℚ)) + (U := (-(591026156976621987 / 610351562500000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_13 : Uω (aρ 13) (bρ 13) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3110,26 +2696,21 @@ lemma U_586_13 : have hlg : Real.log (25012276384134889 / 80000000000000000 : ℝ) ≤ (-(11626598744486248832609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25012276384134889 / 80000000000000000 : ℝ) = - (25012276384134889 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25012276384134889 / 20000000000000000 : ℚ)) - (U := (2236344861513751167391 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25012276384134889 / 20000000000000000 : ℝ) ≤ - (2236344861513751167391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1208984189016783 / 5000000000000000 : ℝ)) (q := - (25012276384134889 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25012276384134889 / 80000000000000000 : ℚ)) + (r' := (25012276384134889 / 20000000000000000 : ℚ)) + (U := (-(11626598744486248832609 / 10000000000000000000000 : ℚ))) + (U' := (2236344861513751167391 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (1208984189016783 / 5000000000000000 : ℚ)) + (q := (25012276384134889 / 80000000000000000 : ℚ)) + (U := (-(11626598744486248832609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_14 : Uω (aρ 14) (bρ 14) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3137,26 +2718,21 @@ lemma U_586_14 : have hlg : Real.log (18273733742646113 / 80000000000000000 : ℝ) ≤ (-(7382809598534463882491 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18273733742646113 / 80000000000000000 : ℝ) = - (18273733742646113 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18273733742646113 / 10000000000000000 : ℚ)) - (U := (3014398105965536117509 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18273733742646113 / 10000000000000000 : ℝ) ≤ - (3014398105965536117509 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (269315000676593 / 2500000000000000 : ℝ)) (q := - (18273733742646113 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18273733742646113 / 80000000000000000 : ℚ)) + (r' := (18273733742646113 / 10000000000000000 : ℚ)) + (U := (-(7382809598534463882491 / 5000000000000000000000 : ℚ))) + (U' := (3014398105965536117509 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43601751609121 / 64000000000000 : ℚ)) + (s := (269315000676593 / 2500000000000000 : ℚ)) + (q := (18273733742646113 / 80000000000000000 : ℚ)) + (U := (-(7382809598534463882491 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_586_15 : Uω (aρ 15) (bρ 15) (43601751609121 / 64000000000000 : ℝ) ≤ @@ -3258,25 +2834,21 @@ lemma U_587_1 : have hlg : Real.log (27025459666440907 / 40000000000000000 : ℝ) ≤ (-(1960500407696928441209 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27025459666440907 / 40000000000000000 : ℝ) = - (27025459666440907 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27025459666440907 / 20000000000000000 : ℚ)) - (U := (1505235493803071558791 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27025459666440907 / 20000000000000000 : ℝ) ≤ - (1505235493803071558791 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3378170494187883 / 5000000000000000 : ℝ)) (q := - (27025459666440907 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27025459666440907 / 40000000000000000 : ℚ)) + (r' := (27025459666440907 / 20000000000000000 : ℚ)) + (U := (-(1960500407696928441209 / 5000000000000000000000 : ℚ))) + (U' := (1505235493803071558791 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (174614683211 / 256000000000 : ℚ)) + (s := (3378170494187883 / 5000000000000000 : ℚ)) + (q := (27025459666440907 / 40000000000000000 : ℚ)) + (U := (-(1960500407696928441209 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_2 : Uω (aρ 2) (bρ 2) (174614683211 / 256000000000 : ℝ) ≤ @@ -3284,25 +2856,21 @@ lemma U_587_2 : have hlg : Real.log (26929848994144739 / 40000000000000000 : ℝ) ≤ (-(3956441543932251401597 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26929848994144739 / 40000000000000000 : ℝ) = - (26929848994144739 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26929848994144739 / 20000000000000000 : ℚ)) - (U := (2975030259067748598403 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26929848994144739 / 20000000000000000 : ℝ) ≤ - (2975030259067748598403 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3366152332368841 / 5000000000000000 : ℝ)) (q := - (26929848994144739 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26929848994144739 / 40000000000000000 : ℚ)) + (r' := (26929848994144739 / 20000000000000000 : ℚ)) + (U := (-(3956441543932251401597 / 10000000000000000000000 : ℚ))) + (U' := (2975030259067748598403 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (174614683211 / 256000000000 : ℚ)) + (s := (3366152332368841 / 5000000000000000 : ℚ)) + (q := (26929848994144739 / 40000000000000000 : ℚ)) + (U := (-(3956441543932251401597 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_3 : Uω (aρ 3) (bρ 3) (174614683211 / 256000000000 : ℝ) ≤ @@ -3310,25 +2878,21 @@ lemma U_587_3 : have hlg : Real.log (26738681457362153 / 40000000000000000 : ℝ) ≤ (-(2013840965715370581603 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26738681457362153 / 40000000000000000 : ℝ) = - (26738681457362153 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26738681457362153 / 20000000000000000 : ℚ)) - (U := (1451894935784629418397 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26738681457362153 / 20000000000000000 : ℝ) ≤ - (1451894935784629418397 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6684117002696389 / 10000000000000000 : ℝ)) (q := - (26738681457362153 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26738681457362153 / 40000000000000000 : ℚ)) + (r' := (26738681457362153 / 20000000000000000 : ℚ)) + (U := (-(2013840965715370581603 / 5000000000000000000000 : ℚ))) + (U' := (1451894935784629418397 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (174614683211 / 256000000000 : ℚ)) + (s := (6684117002696389 / 10000000000000000 : ℚ)) + (q := (26738681457362153 / 40000000000000000 : ℚ)) + (U := (-(2013840965715370581603 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_4 : Uω (aρ 4) (bρ 4) (174614683211 / 256000000000 : ℝ) ≤ @@ -3336,25 +2900,21 @@ lemma U_587_4 : have hlg : Real.log (26421347252804141 / 40000000000000000 : ℝ) ≤ (-(4147071623883270545931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26421347252804141 / 40000000000000000 : ℝ) = - (26421347252804141 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26421347252804141 / 20000000000000000 : ℚ)) - (U := (2784400179116729454069 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26421347252804141 / 20000000000000000 : ℝ) ≤ - (2784400179116729454069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6603744081482383 / 10000000000000000 : ℝ)) (q := - (26421347252804141 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26421347252804141 / 40000000000000000 : ℚ)) + (r' := (26421347252804141 / 20000000000000000 : ℚ)) + (U := (-(4147071623883270545931 / 10000000000000000000000 : ℚ))) + (U' := (2784400179116729454069 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (174614683211 / 256000000000 : ℚ)) + (s := (6603744081482383 / 10000000000000000 : ℚ)) + (q := (26421347252804141 / 40000000000000000 : ℚ)) + (U := (-(4147071623883270545931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_5 : Uω (aρ 5) (bρ 5) (174614683211 / 256000000000 : ℝ) ≤ @@ -3362,25 +2922,21 @@ lemma U_587_5 : have hlg : Real.log (25938532938119563 / 40000000000000000 : ℝ) ≤ (-(866299665071521699251 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25938532938119563 / 40000000000000000 : ℝ) = - (25938532938119563 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25938532938119563 / 20000000000000000 : ℚ)) - (U := (519994695528478300749 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25938532938119563 / 20000000000000000 : ℝ) ≤ - (519994695528478300749 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3240263421737547 / 5000000000000000 : ℝ)) (q := - (25938532938119563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25938532938119563 / 40000000000000000 : ℚ)) + (r' := (25938532938119563 / 20000000000000000 : ℚ)) + (U := (-(866299665071521699251 / 2000000000000000000000 : ℚ))) + (U' := (519994695528478300749 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (174614683211 / 256000000000 : ℚ)) + (s := (3240263421737547 / 5000000000000000 : ℚ)) + (q := (25938532938119563 / 40000000000000000 : ℚ)) + (U := (-(866299665071521699251 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_6 : Uω (aρ 6) (bρ 6) (174614683211 / 256000000000 : ℝ) ≤ @@ -3388,25 +2944,21 @@ lemma U_587_6 : have hlg : Real.log (25247110252738111 / 40000000000000000 : ℝ) ≤ (-(4601677501181152033433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25247110252738111 / 40000000000000000 : ℝ) = - (25247110252738111 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25247110252738111 / 20000000000000000 : ℚ)) - (U := (2329794301818847966567 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25247110252738111 / 20000000000000000 : ℝ) ≤ - (2329794301818847966567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (393878492245273 / 625000000000000 : ℝ)) (q := - (25247110252738111 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25247110252738111 / 40000000000000000 : ℚ)) + (r' := (25247110252738111 / 20000000000000000 : ℚ)) + (U := (-(4601677501181152033433 / 10000000000000000000000 : ℚ))) + (U' := (2329794301818847966567 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (174614683211 / 256000000000 : ℚ)) + (s := (393878492245273 / 625000000000000 : ℚ)) + (q := (25247110252738111 / 40000000000000000 : ℚ)) + (U := (-(4601677501181152033433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_7 : Uω (aρ 7) (bρ 7) (174614683211 / 256000000000 : ℝ) ≤ @@ -3414,25 +2966,21 @@ lemma U_587_7 : have hlg : Real.log (24305989618724163 / 40000000000000000 : ℝ) ≤ (-(1245391618782531133827 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24305989618724163 / 40000000000000000 : ℝ) = - (24305989618724163 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24305989618724163 / 20000000000000000 : ℚ)) - (U := (487476331967468866173 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24305989618724163 / 20000000000000000 : ℝ) ≤ - (487476331967468866173 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3027578469838697 / 5000000000000000 : ℝ)) (q := - (24305989618724163 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24305989618724163 / 40000000000000000 : ℚ)) + (r' := (24305989618724163 / 20000000000000000 : ℚ)) + (U := (-(1245391618782531133827 / 2500000000000000000000 : ℚ))) + (U' := (487476331967468866173 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (174614683211 / 256000000000 : ℚ)) + (s := (3027578469838697 / 5000000000000000 : ℚ)) + (q := (24305989618724163 / 40000000000000000 : ℚ)) + (U := (-(1245391618782531133827 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_8 : Uω (aρ 8) (bρ 8) (174614683211 / 256000000000 : ℝ) ≤ @@ -3440,25 +2988,21 @@ lemma U_587_8 : have hlg : Real.log (4616468058571363 / 8000000000000000 : ℝ) ≤ (-(2749058090920340042383 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4616468058571363 / 8000000000000000 : ℝ) = - (4616468058571363 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4616468058571363 / 4000000000000000 : ℚ)) - (U := (716677810579659957617 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4616468058571363 / 4000000000000000 : ℝ) ≤ - (716677810579659957617 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (143171848202093 / 250000000000000 : ℝ)) (q := - (4616468058571363 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4616468058571363 / 8000000000000000 : ℚ)) + (r' := (4616468058571363 / 4000000000000000 : ℚ)) + (U := (-(2749058090920340042383 / 5000000000000000000000 : ℚ))) + (U' := (716677810579659957617 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (174614683211 / 256000000000 : ℚ)) + (s := (143171848202093 / 250000000000000 : ℚ)) + (q := (4616468058571363 / 8000000000000000 : ℚ)) + (U := (-(2749058090920340042383 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_9 : Uω (aρ 9) (bρ 9) (174614683211 / 256000000000 : ℝ) ≤ @@ -3466,25 +3010,21 @@ lemma U_587_9 : have hlg : Real.log (21557201003122639 / 40000000000000000 : ℝ) ≤ (-(6181695398438540011231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21557201003122639 / 40000000000000000 : ℝ) = - (21557201003122639 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21557201003122639 / 20000000000000000 : ℚ)) - (U := (749776404561459988769 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21557201003122639 / 20000000000000000 : ℝ) ≤ - (749776404561459988769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (663158738947079 / 1250000000000000 : ℝ)) (q := - (21557201003122639 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21557201003122639 / 40000000000000000 : ℚ)) + (r' := (21557201003122639 / 20000000000000000 : ℚ)) + (U := (-(6181695398438540011231 / 10000000000000000000000 : ℚ))) + (U' := (749776404561459988769 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (174614683211 / 256000000000 : ℚ)) + (s := (663158738947079 / 1250000000000000 : ℚ)) + (q := (21557201003122639 / 40000000000000000 : ℚ)) + (U := (-(6181695398438540011231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_10 : Uω (aρ 10) (bρ 10) (174614683211 / 256000000000 : ℝ) ≤ @@ -3492,26 +3032,21 @@ lemma U_587_10 : have hlg : Real.log (19728923122556263 / 40000000000000000 : ℝ) ≤ (-(7067937157608990501517 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19728923122556263 / 40000000000000000 : ℝ) = - (19728923122556263 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19728923122556263 / 10000000000000000 : ℚ)) - (U := (6795006448391009498483 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19728923122556263 / 10000000000000000 : ℝ) ≤ - (6795006448391009498483 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1194922501197111 / 2500000000000000 : ℝ)) (q := - (19728923122556263 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19728923122556263 / 40000000000000000 : ℚ)) + (r' := (19728923122556263 / 10000000000000000 : ℚ)) + (U := (-(7067937157608990501517 / 10000000000000000000000 : ℚ))) + (U' := (6795006448391009498483 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (174614683211 / 256000000000 : ℚ)) + (s := (1194922501197111 / 2500000000000000 : ℚ)) + (q := (19728923122556263 / 40000000000000000 : ℚ)) + (U := (-(7067937157608990501517 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_11 : Uω (aρ 11) (bρ 11) (174614683211 / 256000000000 : ℝ) ≤ @@ -3519,26 +3054,21 @@ lemma U_587_11 : have hlg : Real.log (17611925552511887 / 40000000000000000 : ℝ) ≤ (-(1640606385596563904279 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17611925552511887 / 40000000000000000 : ℝ) = - (17611925552511887 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17611925552511887 / 10000000000000000 : ℚ)) - (U := (1131982335603436095721 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17611925552511887 / 10000000000000000 : ℝ) ≤ - (1131982335603436095721 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (517458480746407 / 1250000000000000 : ℝ)) (q := - (17611925552511887 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17611925552511887 / 40000000000000000 : ℚ)) + (r' := (17611925552511887 / 10000000000000000 : ℚ)) + (U := (-(1640606385596563904279 / 2000000000000000000000 : ℚ))) + (U' := (1131982335603436095721 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (174614683211 / 256000000000 : ℚ)) + (s := (517458480746407 / 1250000000000000 : ℚ)) + (q := (17611925552511887 / 40000000000000000 : ℚ)) + (U := (-(1640606385596563904279 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_12 : Uω (aρ 12) (bρ 12) (174614683211 / 256000000000 : ℝ) ≤ @@ -3546,26 +3076,21 @@ lemma U_587_12 : have hlg : Real.log (15225217164017443 / 40000000000000000 : ℝ) ≤ (-(965926376453343920951 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15225217164017443 / 40000000000000000 : ℝ) = - (15225217164017443 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15225217164017443 / 10000000000000000 : ℚ)) - (U := (420367984146656079049 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15225217164017443 / 10000000000000000 : ℝ) ≤ - (420367984146656079049 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1685006874204517 / 5000000000000000 : ℝ)) (q := - (15225217164017443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15225217164017443 / 40000000000000000 : ℚ)) + (r' := (15225217164017443 / 10000000000000000 : ℚ)) + (U := (-(965926376453343920951 / 1000000000000000000000 : ℚ))) + (U' := (420367984146656079049 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (174614683211 / 256000000000 : ℚ)) + (s := (1685006874204517 / 5000000000000000 : ℚ)) + (q := (15225217164017443 / 40000000000000000 : ℚ)) + (U := (-(965926376453343920951 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_13 : Uω (aρ 13) (bρ 13) (174614683211 / 256000000000 : ℝ) ≤ @@ -3573,26 +3098,21 @@ lemma U_587_13 : have hlg : Real.log (12548055717620997 / 40000000000000000 : ℝ) ≤ (-(724571076822981242243 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12548055717620997 / 40000000000000000 : ℝ) = - (12548055717620997 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12548055717620997 / 10000000000000000 : ℚ)) - (U := (141862898552018757757 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12548055717620997 / 10000000000000000 : ℝ) ≤ - (141862898552018757757 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2430814766805811 / 10000000000000000 : ℝ)) (q := - (12548055717620997 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12548055717620997 / 40000000000000000 : ℚ)) + (r' := (12548055717620997 / 10000000000000000 : ℚ)) + (U := (-(724571076822981242243 / 625000000000000000000 : ℚ))) + (U' := (141862898552018757757 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (174614683211 / 256000000000 : ℚ)) + (s := (2430814766805811 / 10000000000000000 : ℚ)) + (q := (12548055717620997 / 40000000000000000 : ℚ)) + (U := (-(724571076822981242243 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_14 : Uω (aρ 14) (bρ 14) (174614683211 / 256000000000 : ℝ) ≤ @@ -3600,26 +3120,21 @@ lemma U_587_14 : have hlg : Real.log (9205105849546417 / 40000000000000000 : ℝ) ≤ (-(7345605697896120243709 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9205105849546417 / 40000000000000000 : ℝ) = - (9205105849546417 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9205105849546417 / 5000000000000000 : ℚ)) - (U := (3051602006603879756291 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9205105849546417 / 5000000000000000 : ℝ) ≤ - (3051602006603879756291 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1103267117813521 / 10000000000000000 : ℝ)) (q := - (9205105849546417 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9205105849546417 / 40000000000000000 : ℚ)) + (r' := (9205105849546417 / 5000000000000000 : ℚ)) + (U := (-(7345605697896120243709 / 5000000000000000000000 : ℚ))) + (U' := (3051602006603879756291 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (174614683211 / 256000000000 : ℚ)) + (s := (1103267117813521 / 10000000000000000 : ℚ)) + (q := (9205105849546417 / 40000000000000000 : ℚ)) + (U := (-(7345605697896120243709 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_587_15 : Uω (aρ 15) (bρ 15) (174614683211 / 256000000000 : ℝ) ≤ @@ -3720,25 +3235,21 @@ lemma U_588_1 : have hlg : Real.log (54115818554488467 / 80000000000000000 : ℝ) ≤ (-(39090009657798394581 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54115818554488467 / 80000000000000000 : ℝ) = - (54115818554488467 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54115818554488467 / 40000000000000000 : ℚ)) - (U := (30224708372201605419 / 100000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54115818554488467 / 40000000000000000 : ℝ) ≤ - (30224708372201605419 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3382226709886449 / 5000000000000000 : ℝ)) (q := - (54115818554488467 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54115818554488467 / 80000000000000000 : ℚ)) + (r' := (54115818554488467 / 40000000000000000 : ℚ)) + (U := (-(39090009657798394581 / 100000000000000000000 : ℚ))) + (U' := (30224708372201605419 / 100000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (3382226709886449 / 5000000000000000 : ℚ)) + (q := (54115818554488467 / 80000000000000000 : ℚ)) + (U := (-(39090009657798394581 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_2 : Uω (aρ 2) (bρ 2) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3746,25 +3257,21 @@ lemma U_588_2 : have hlg : Real.log (53924598497595259 / 80000000000000000 : ℝ) ≤ (-(394439887737222588027 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53924598497595259 / 80000000000000000 : ℝ) = - (53924598497595259 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53924598497595259 / 40000000000000000 : ℚ)) - (U := (298707292562777411973 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53924598497595259 / 40000000000000000 : ℝ) ≤ - (298707292562777411973 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1685104354514899 / 2500000000000000 : ℝ)) (q := - (53924598497595259 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53924598497595259 / 80000000000000000 : ℚ)) + (r' := (53924598497595259 / 40000000000000000 : ℚ)) + (U := (-(394439887737222588027 / 1000000000000000000000 : ℚ))) + (U' := (298707292562777411973 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (1685104354514899 / 2500000000000000 : ℚ)) + (q := (53924598497595259 / 80000000000000000 : ℚ)) + (U := (-(394439887737222588027 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_3 : Uω (aρ 3) (bρ 3) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3772,25 +3279,21 @@ lemma U_588_3 : have hlg : Real.log (53542267273075323 / 80000000000000000 : ℝ) ≤ (-(4015552499438766461231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53542267273075323 / 80000000000000000 : ℝ) = - (53542267273075323 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53542267273075323 / 40000000000000000 : ℚ)) - (U := (2915919303561233538769 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53542267273075323 / 40000000000000000 : ℝ) ≤ - (2915919303561233538769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1673057679569903 / 2500000000000000 : ℝ)) (q := - (53542267273075323 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53542267273075323 / 80000000000000000 : ℚ)) + (r' := (53542267273075323 / 40000000000000000 : ℚ)) + (U := (-(4015552499438766461231 / 10000000000000000000000 : ℚ))) + (U' := (2915919303561233538769 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (1673057679569903 / 2500000000000000 : ℚ)) + (q := (53542267273075323 / 80000000000000000 : ℚ)) + (U := (-(4015552499438766461231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_4 : Uω (aρ 4) (bρ 4) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3798,25 +3301,21 @@ lemma U_588_4 : have hlg : Real.log (2116304365246959 / 3200000000000000 : ℝ) ≤ (-(413479465984879583207 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2116304365246959 / 3200000000000000 : ℝ) = - (2116304365246959 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2116304365246959 / 1600000000000000 : ℚ)) - (U := (279667714315120416793 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2116304365246959 / 1600000000000000 : ℝ) ≤ - (279667714315120416793 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (264474414554771 / 400000000000000 : ℝ)) (q := - (2116304365246959 / 3200000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2116304365246959 / 3200000000000000 : ℚ)) + (r' := (2116304365246959 / 1600000000000000 : ℚ)) + (U := (-(413479465984879583207 / 1000000000000000000000 : ℚ))) + (U' := (279667714315120416793 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (264474414554771 / 400000000000000 : ℚ)) + (q := (2116304365246959 / 3200000000000000 : ℚ)) + (U := (-(413479465984879583207 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_5 : Uω (aρ 5) (bρ 5) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3824,25 +3323,21 @@ lemma U_588_5 : have hlg : Real.log (51942005940127359 / 80000000000000000 : ℝ) ≤ (-(539873510739345538629 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51942005940127359 / 80000000000000000 : ℝ) = - (51942005940127359 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51942005940127359 / 40000000000000000 : ℚ)) - (U := (326560464635654461371 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51942005940127359 / 40000000000000000 : ℝ) ≤ - (326560464635654461371 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6488649485442621 / 10000000000000000 : ℝ)) (q := - (51942005940127359 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51942005940127359 / 80000000000000000 : ℚ)) + (r' := (51942005940127359 / 40000000000000000 : ℚ)) + (U := (-(539873510739345538629 / 1250000000000000000000 : ℚ))) + (U' := (326560464635654461371 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (6488649485442621 / 10000000000000000 : ℚ)) + (q := (51942005940127359 / 80000000000000000 : ℚ)) + (U := (-(539873510739345538629 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_6 : Uω (aρ 6) (bρ 6) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3850,25 +3345,21 @@ lemma U_588_6 : have hlg : Real.log (10111843896638211 / 16000000000000000 : ℝ) ≤ (-(573601652664223193247 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10111843896638211 / 16000000000000000 : ℝ) = - (10111843896638211 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10111843896638211 / 8000000000000000 : ℚ)) - (U := (292832322710776806753 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10111843896638211 / 8000000000000000 : ℝ) ≤ - (292832322710776806753 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1262038649269709 / 2000000000000000 : ℝ)) (q := - (10111843896638211 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10111843896638211 / 16000000000000000 : ℚ)) + (r' := (10111843896638211 / 8000000000000000 : ℚ)) + (U := (-(573601652664223193247 / 1250000000000000000000 : ℚ))) + (U' := (292832322710776806753 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (1262038649269709 / 2000000000000000 : ℚ)) + (q := (10111843896638211 / 16000000000000000 : ℚ)) + (U := (-(573601652664223193247 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_7 : Uω (aρ 7) (bρ 7) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3876,25 +3367,21 @@ lemma U_588_7 : have hlg : Real.log (48677106648852863 / 80000000000000000 : ℝ) ≤ (-(4968178041979655025511 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48677106648852863 / 80000000000000000 : ℝ) = - (48677106648852863 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48677106648852863 / 40000000000000000 : ℚ)) - (U := (1963293761020344974489 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48677106648852863 / 40000000000000000 : ℝ) ≤ - (1963293761020344974489 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6063326418523997 / 10000000000000000 : ℝ)) (q := - (48677106648852863 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48677106648852863 / 80000000000000000 : ℚ)) + (r' := (48677106648852863 / 40000000000000000 : ℚ)) + (U := (-(4968178041979655025511 / 10000000000000000000000 : ℚ))) + (U' := (1963293761020344974489 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (6063326418523997 / 10000000000000000 : ℚ)) + (q := (48677106648852863 / 80000000000000000 : ℚ)) + (U := (-(4968178041979655025511 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_8 : Uω (aρ 8) (bρ 8) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3902,25 +3389,21 @@ lemma U_588_8 : have hlg : Real.log (46230074222117999 / 80000000000000000 : ℝ) ≤ (-(2741980454591354062683 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46230074222117999 / 80000000000000000 : ℝ) = - (46230074222117999 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46230074222117999 / 40000000000000000 : ℚ)) - (U := (723755446908645937317 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46230074222117999 / 40000000000000000 : ℝ) ≤ - (723755446908645937317 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5735109963180281 / 10000000000000000 : ℝ)) (q := - (46230074222117999 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46230074222117999 / 80000000000000000 : ℚ)) + (r' := (46230074222117999 / 40000000000000000 : ℚ)) + (U := (-(2741980454591354062683 / 5000000000000000000000 : ℚ))) + (U' := (723755446908645937317 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (5735109963180281 / 10000000000000000 : ℚ)) + (q := (46230074222117999 / 80000000000000000 : ℚ)) + (U := (-(2741980454591354062683 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_9 : Uω (aρ 9) (bρ 9) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3928,25 +3411,21 @@ lemma U_588_9 : have hlg : Real.log (43180327341267823 / 80000000000000000 : ℝ) ≤ (-(6166416285021924208357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43180327341267823 / 80000000000000000 : ℝ) = - (43180327341267823 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43180327341267823 / 40000000000000000 : ℚ)) - (U := (765055517978075791643 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43180327341267823 / 40000000000000000 : ℝ) ≤ - (765055517978075791643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5313638871327737 / 10000000000000000 : ℝ)) (q := - (43180327341267823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43180327341267823 / 80000000000000000 : ℚ)) + (r' := (43180327341267823 / 40000000000000000 : ℚ)) + (U := (-(6166416285021924208357 / 10000000000000000000000 : ℚ))) + (U' := (765055517978075791643 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (5313638871327737 / 10000000000000000 : ℚ)) + (q := (43180327341267823 / 80000000000000000 : ℚ)) + (U := (-(6166416285021924208357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_10 : Uω (aρ 10) (bρ 10) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3954,26 +3433,21 @@ lemma U_588_10 : have hlg : Real.log (39524812826294763 / 80000000000000000 : ℝ) ≤ (-(7050979866472832607387 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39524812826294763 / 80000000000000000 : ℝ) = - (39524812826294763 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39524812826294763 / 20000000000000000 : ℚ)) - (U := (6811963739527167392613 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39524812826294763 / 20000000000000000 : ℝ) ≤ - (6811963739527167392613 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (299269954754967 / 625000000000000 : ℝ)) (q := - (39524812826294763 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39524812826294763 / 80000000000000000 : ℚ)) + (r' := (39524812826294763 / 20000000000000000 : ℚ)) + (U := (-(7050979866472832607387 / 10000000000000000000000 : ℚ))) + (U' := (6811963739527167392613 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (299269954754967 / 625000000000000 : ℚ)) + (q := (39524812826294763 / 80000000000000000 : ℚ)) + (U := (-(7050979866472832607387 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_11 : Uω (aρ 11) (bρ 11) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -3981,26 +3455,21 @@ lemma U_588_11 : have hlg : Real.log (35292869568515511 / 80000000000000000 : ℝ) ≤ (-(8183456858447127867951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35292869568515511 / 80000000000000000 : ℝ) = - (35292869568515511 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35292869568515511 / 20000000000000000 : ℚ)) - (U := (5679486747552872132049 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (35292869568515511 / 20000000000000000 : ℝ) ≤ - (5679486747552872132049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4148810087839659 / 10000000000000000 : ℝ)) (q := - (35292869568515511 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35292869568515511 / 80000000000000000 : ℚ)) + (r' := (35292869568515511 / 20000000000000000 : ℚ)) + (U := (-(8183456858447127867951 / 10000000000000000000000 : ℚ))) + (U' := (5679486747552872132049 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (4148810087839659 / 10000000000000000 : ℚ)) + (q := (35292869568515511 / 80000000000000000 : ℚ)) + (U := (-(8183456858447127867951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_12 : Uω (aρ 12) (bρ 12) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -4008,26 +3477,21 @@ lemma U_588_12 : have hlg : Real.log (30523712533582199 / 80000000000000000 : ℝ) ≤ (-(1204403490610925670401 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30523712533582199 / 80000000000000000 : ℝ) = - (30523712533582199 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30523712533582199 / 20000000000000000 : ℚ)) - (U := (528464460139074329599 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30523712533582199 / 20000000000000000 : ℝ) ≤ - (528464460139074329599 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3380220925791331 / 10000000000000000 : ℝ)) (q := - (30523712533582199 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30523712533582199 / 80000000000000000 : ℚ)) + (r' := (30523712533582199 / 20000000000000000 : ℚ)) + (U := (-(1204403490610925670401 / 1250000000000000000000 : ℚ))) + (U' := (528464460139074329599 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (3380220925791331 / 10000000000000000 : ℚ)) + (q := (30523712533582199 / 80000000000000000 : ℚ)) + (U := (-(1204403490610925670401 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_13 : Uω (aρ 13) (bρ 13) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -4035,26 +3499,21 @@ lemma U_588_13 : have hlg : Real.log (25179784074442571 / 80000000000000000 : ℝ) ≤ (-(11559851808548369618159 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25179784074442571 / 80000000000000000 : ℝ) = - (25179784074442571 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25179784074442571 / 20000000000000000 : ℚ)) - (U := (2303091797451630381841 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25179784074442571 / 20000000000000000 : ℝ) ≤ - (2303091797451630381841 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (152726284537589 / 625000000000000 : ℝ)) (q := - (25179784074442571 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25179784074442571 / 80000000000000000 : ℚ)) + (r' := (25179784074442571 / 20000000000000000 : ℚ)) + (U := (-(11559851808548369618159 / 10000000000000000000000 : ℚ))) + (U' := (2303091797451630381841 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (152726284537589 / 625000000000000 : ℚ)) + (q := (25179784074442571 / 80000000000000000 : ℚ)) + (U := (-(11559851808548369618159 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_14 : Uω (aρ 14) (bρ 14) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -4062,26 +3521,21 @@ lemma U_588_14 : have hlg : Real.log (18544526476265923 / 80000000000000000 : ℝ) ≤ (-(1461851957046835182271 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18544526476265923 / 80000000000000000 : ℝ) = - (18544526476265923 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18544526476265923 / 10000000000000000 : ℚ)) - (U := (617589583853164817729 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18544526476265923 / 10000000000000000 : ℝ) ≤ - (617589583853164817729 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (564366719051131 / 5000000000000000 : ℝ)) (q := - (18544526476265923 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18544526476265923 / 80000000000000000 : ℚ)) + (r' := (18544526476265923 / 10000000000000000 : ℚ)) + (U := (-(1461851957046835182271 / 1000000000000000000000 : ℚ))) + (U' := (617589583853164817729 / 1000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43705589996379 / 64000000000000 : ℚ)) + (s := (564366719051131 / 5000000000000000 : ℚ)) + (q := (18544526476265923 / 80000000000000000 : ℚ)) + (U := (-(1461851957046835182271 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_588_15 : Uω (aρ 15) (bρ 15) (43705589996379 / 64000000000000 : ℝ) ≤ @@ -4183,25 +3637,21 @@ lemma U_589_1 : have hlg : Real.log (13545179443886287 / 20000000000000000 : ℝ) ≤ (-(1948507749324743187031 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13545179443886287 / 20000000000000000 : ℝ) = - (13545179443886287 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13545179443886287 / 10000000000000000 : ℚ)) - (U := (1517228152175256812969 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13545179443886287 / 10000000000000000 : ℝ) ≤ - (1517228152175256812969 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6772565851032537 / 10000000000000000 : ℝ)) (q := - (13545179443886287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13545179443886287 / 20000000000000000 : ℚ)) + (r' := (13545179443886287 / 10000000000000000 : ℚ)) + (U := (-(1948507749324743187031 / 5000000000000000000000 : ℚ))) + (U' := (1517228152175256812969 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (6772565851032537 / 10000000000000000 : ℚ)) + (q := (13545179443886287 / 20000000000000000 : ℚ)) + (U := (-(1948507749324743187031 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_2 : Uω (aρ 2) (bρ 2) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4209,25 +3659,21 @@ lemma U_589_2 : have hlg : Real.log (13497374750813287 / 20000000000000000 : ℝ) ≤ (-(245773168539214552107 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13497374750813287 / 20000000000000000 : ℝ) = - (13497374750813287 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13497374750813287 / 10000000000000000 : ℚ)) - (U := (187443819148285447893 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13497374750813287 / 10000000000000000 : ℝ) ≤ - (187443819148285447893 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6748530170469537 / 10000000000000000 : ℝ)) (q := - (13497374750813287 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13497374750813287 / 20000000000000000 : ℚ)) + (r' := (13497374750813287 / 10000000000000000 : ℚ)) + (U := (-(245773168539214552107 / 625000000000000000000 : ℚ))) + (U' := (187443819148285447893 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (6748530170469537 / 10000000000000000 : ℚ)) + (q := (13497374750813287 / 20000000000000000 : ℚ)) + (U := (-(245773168539214552107 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_3 : Uω (aρ 3) (bρ 3) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4235,25 +3681,21 @@ lemma U_589_3 : have hlg : Real.log (418806028268991 / 625000000000000 : ℝ) ≤ (-(2001718882180630828503 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (418806028268991 / 625000000000000 : ℝ) = - (418806028268991 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (418806028268991 / 312500000000000 : ℚ)) - (U := (1464017019319369171497 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (418806028268991 / 312500000000000 : ℝ) ≤ - (1464017019319369171497 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3350172215306981 / 5000000000000000 : ℝ)) (q := - (418806028268991 / 625000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (418806028268991 / 625000000000000 : ℚ)) + (r' := (418806028268991 / 312500000000000 : ℚ)) + (U := (-(2001718882180630828503 / 5000000000000000000000 : ℚ))) + (U' := (1464017019319369171497 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (3350172215306981 / 5000000000000000 : ℚ)) + (q := (418806028268991 / 625000000000000 : ℚ)) + (U := (-(2001718882180630828503 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_4 : Uω (aρ 4) (bρ 4) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4261,25 +3703,21 @@ lemma U_589_4 : have hlg : Real.log (6621565464801823 / 10000000000000000 : ℝ) ≤ (-(824506551390814758131 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6621565464801823 / 10000000000000000 : ℝ) = - (6621565464801823 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6621565464801823 / 5000000000000000 : ℚ)) - (U := (561787809209185241869 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6621565464801823 / 5000000000000000 : ℝ) ≤ - (561787809209185241869 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (413748539792181 / 625000000000000 : ℝ)) (q := - (6621565464801823 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6621565464801823 / 10000000000000000 : ℚ)) + (r' := (6621565464801823 / 5000000000000000 : ℚ)) + (U := (-(824506551390814758131 / 2000000000000000000000 : ℚ))) + (U' := (561787809209185241869 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (413748539792181 / 625000000000000 : ℚ)) + (q := (6621565464801823 / 10000000000000000 : ℚ)) + (U := (-(824506551390814758131 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_5 : Uω (aρ 5) (bρ 5) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4287,25 +3725,21 @@ lemma U_589_5 : have hlg : Real.log (6500868237672459 / 10000000000000000 : ℝ) ≤ (-(4306493497263263020103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6500868237672459 / 10000000000000000 : ℝ) = - (6500868237672459 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6500868237672459 / 5000000000000000 : ℚ)) - (U := (2624978305736736979897 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6500868237672459 / 5000000000000000 : ℝ) ≤ - (2624978305736736979897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (50756032044931 / 78125000000000 : ℝ)) (q := - (6500868237672459 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6500868237672459 / 10000000000000000 : ℚ)) + (r' := (6500868237672459 / 5000000000000000 : ℚ)) + (U := (-(4306493497263263020103 / 10000000000000000000000 : ℚ))) + (U' := (2624978305736736979897 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (50756032044931 / 78125000000000 : ℚ)) + (q := (6500868237672459 / 10000000000000000 : ℚ)) + (U := (-(4306493497263263020103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_6 : Uω (aρ 6) (bρ 6) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4313,25 +3747,21 @@ lemma U_589_6 : have hlg : Real.log (3164013637734911 / 5000000000000000 : ℝ) ≤ (-(4575965519951952109527 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3164013637734911 / 5000000000000000 : ℝ) = - (3164013637734911 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3164013637734911 / 2500000000000000 : ℚ)) - (U := (2355506283048047890473 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3164013637734911 / 2500000000000000 : ℝ) ≤ - (2355506283048047890473 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3159165276242947 / 5000000000000000 : ℝ)) (q := - (3164013637734911 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3164013637734911 / 5000000000000000 : ℚ)) + (r' := (3164013637734911 / 2500000000000000 : ℚ)) + (U := (-(4575965519951952109527 / 10000000000000000000000 : ℚ))) + (U' := (2355506283048047890473 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (3159165276242947 / 5000000000000000 : ℚ)) + (q := (3164013637734911 / 5000000000000000 : ℚ)) + (U := (-(4575965519951952109527 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_7 : Uω (aρ 7) (bρ 7) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4339,25 +3769,21 @@ lemma U_589_7 : have hlg : Real.log (487422334477081 / 800000000000000 : ℝ) ≤ (-(1238701908887633955801 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (487422334477081 / 800000000000000 : ℝ) = - (487422334477081 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (487422334477081 / 400000000000000 : ℚ)) - (U := (494166041862366044199 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (487422334477081 / 400000000000000 : ℝ) ≤ - (494166041862366044199 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242859829769331 / 400000000000000 : ℝ)) (q := - (487422334477081 / 800000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (487422334477081 / 800000000000000 : ℚ)) + (r' := (487422334477081 / 400000000000000 : ℚ)) + (U := (-(1238701908887633955801 / 2500000000000000000000 : ℚ))) + (U' := (494166041862366044199 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (242859829769331 / 400000000000000 : ℚ)) + (q := (487422334477081 / 800000000000000 : ℚ)) + (U := (-(1238701908887633955801 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_8 : Uω (aρ 8) (bρ 8) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4365,25 +3791,21 @@ lemma U_589_8 : have hlg : Real.log (2893466653157457 / 5000000000000000 : ℝ) ≤ (-(5469825949513502250433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2893466653157457 / 5000000000000000 : ℝ) = - (2893466653157457 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2893466653157457 / 2500000000000000 : ℚ)) - (U := (1461645853486497749567 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2893466653157457 / 2500000000000000 : ℝ) ≤ - (1461645853486497749567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2871672823138039 / 5000000000000000 : ℝ)) (q := - (2893466653157457 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2893466653157457 / 5000000000000000 : ℚ)) + (r' := (2893466653157457 / 2500000000000000 : ℚ)) + (U := (-(5469825949513502250433 / 10000000000000000000000 : ℚ))) + (U' := (1461645853486497749567 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (2871672823138039 / 5000000000000000 : ℚ)) + (q := (2893466653157457 / 5000000000000000 : ℚ)) + (U := (-(5469825949513502250433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_9 : Uω (aρ 9) (bρ 9) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4391,25 +3813,21 @@ lemma U_589_9 : have hlg : Real.log (1351445296808881 / 2500000000000000 : ℝ) ≤ (-(6151161216080942852501 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1351445296808881 / 2500000000000000 : ℝ) = - (1351445296808881 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1351445296808881 / 1250000000000000 : ℚ)) - (U := (780310586919057147499 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1351445296808881 / 1250000000000000 : ℝ) ≤ - (780310586919057147499 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2661003518238649 / 5000000000000000 : ℝ)) (q := - (1351445296808881 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1351445296808881 / 2500000000000000 : ℚ)) + (r' := (1351445296808881 / 1250000000000000 : ℚ)) + (U := (-(6151161216080942852501 / 10000000000000000000000 : ℚ))) + (U' := (780310586919057147499 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (2661003518238649 / 5000000000000000 : ℚ)) + (q := (1351445296808881 / 2500000000000000 : ℚ)) + (U := (-(6151161216080942852501 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_10 : Uω (aρ 10) (bρ 10) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4417,26 +3835,21 @@ lemma U_589_10 : have hlg : Real.log (1237242880983201 / 2500000000000000 : ℝ) ≤ (-(7034053104242121893583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1237242880983201 / 2500000000000000 : ℝ) = - (1237242880983201 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1237242880983201 / 625000000000000 : ℚ)) - (U := (6828890501757878106417 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1237242880983201 / 625000000000000 : ℝ) ≤ - (6828890501757878106417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2398473371683429 / 5000000000000000 : ℝ)) (q := - (1237242880983201 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1237242880983201 / 2500000000000000 : ℚ)) + (r' := (1237242880983201 / 625000000000000 : ℚ)) + (U := (-(7034053104242121893583 / 10000000000000000000000 : ℚ))) + (U' := (6828890501757878106417 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (2398473371683429 / 5000000000000000 : ℚ)) + (q := (1237242880983201 / 2500000000000000 : ℚ)) + (U := (-(7034053104242121893583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_11 : Uω (aρ 11) (bρ 11) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4444,26 +3857,21 @@ lemma U_589_11 : have hlg : Real.log (1768093546853501 / 4000000000000000 : ℝ) ≤ (-(4081962433340292229409 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1768093546853501 / 4000000000000000 : ℝ) = - (1768093546853501 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1768093546853501 / 1000000000000000 : ℚ)) - (U := (2849509369659707770591 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1768093546853501 / 1000000000000000 : ℝ) ≤ - (2849509369659707770591 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (831589611194751 / 2000000000000000 : ℝ)) (q := - (1768093546853501 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1768093546853501 / 4000000000000000 : ℚ)) + (r' := (1768093546853501 / 1000000000000000 : ℚ)) + (U := (-(4081962433340292229409 / 5000000000000000000000 : ℚ))) + (U' := (2849509369659707770591 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (831589611194751 / 2000000000000000 : ℚ)) + (q := (1768093546853501 / 4000000000000000 : ℚ)) + (U := (-(4081962433340292229409 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_12 : Uω (aρ 12) (bρ 12) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4471,26 +3879,21 @@ lemma U_589_12 : have hlg : Real.log (1912309091470187 / 5000000000000000 : ℝ) ≤ (-(1201408064539557201607 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1912309091470187 / 5000000000000000 : ℝ) = - (1912309091470187 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1912309091470187 / 1250000000000000 : ℚ)) - (U := (531459886210442798393 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1912309091470187 / 1250000000000000 : ℝ) ≤ - (531459886210442798393 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1695208392135999 / 5000000000000000 : ℝ)) (q := - (1912309091470187 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1912309091470187 / 5000000000000000 : ℚ)) + (r' := (1912309091470187 / 1250000000000000 : ℚ)) + (U := (-(1201408064539557201607 / 1250000000000000000000 : ℚ))) + (U' := (531459886210442798393 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (1695208392135999 / 5000000000000000 : ℚ)) + (q := (1912309091470187 / 5000000000000000 : ℚ)) + (U := (-(1201408064539557201607 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_13 : Uω (aρ 13) (bρ 13) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4498,25 +3901,21 @@ lemma U_589_13 : have hlg : Real.log (789478026307013 / 2500000000000000 : ℝ) ≤ (-(11526740094447365904059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (789478026307013 / 2500000000000000 : ℝ) = - (789478026307013 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (789478026307013 / 625000000000000 : ℚ)) - (U := (2336203511552634095941 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (789478026307013 / 625000000000000 : ℝ) ≤ - (2336203511552634095941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1228193185221177 / 5000000000000000 : ℝ)) (q := - (789478026307013 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (789478026307013 / 2500000000000000 : ℚ)) + (r' := (789478026307013 / 625000000000000 : ℚ)) + (U := (-(11526740094447365904059 / 10000000000000000000000 : ℚ))) + (U' := (2336203511552634095941 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (1228193185221177 / 5000000000000000 : ℚ)) + (q := (789478026307013 / 2500000000000000 : ℚ)) + (U := (-(11526740094447365904059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_14 : Uω (aρ 14) (bρ 14) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4524,25 +3923,21 @@ lemma U_589_14 : have hlg : Real.log (583650666392007 / 2500000000000000 : ℝ) ≤ (-(1818429225264942628537 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (583650666392007 / 2500000000000000 : ℝ) = - (583650666392007 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (583650666392007 / 312500000000000 : ℚ)) - (U := (780872700860057371463 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (583650666392007 / 312500000000000 : ℝ) ≤ - (780872700860057371463 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (576847388083653 / 5000000000000000 : ℝ)) (q := - (583650666392007 / 2500000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (583650666392007 / 2500000000000000 : ℚ)) + (r' := (583650666392007 / 312500000000000 : ℚ)) + (U := (-(1818429225264942628537 / 1250000000000000000000 : ℚ))) + (U' := (780872700860057371463 / 1250000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5469688648751 / 8000000000000 : ℚ)) + (s := (576847388083653 / 5000000000000000 : ℚ)) + (q := (583650666392007 / 2500000000000000 : ℚ)) + (U := (-(1818429225264942628537 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_589_15 : Uω (aρ 15) (bρ 15) (5469688648751 / 8000000000000 : ℝ) ≤ @@ -4645,25 +4040,21 @@ lemma U_590_1 : have hlg : Real.log (2169824679842153 / 3200000000000000 : ℝ) ≤ (-(1942522189783709894671 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2169824679842153 / 3200000000000000 : ℝ) = - (2169824679842153 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2169824679842153 / 1600000000000000 : ℚ)) - (U := (1523213711716290105329 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2169824679842153 / 1600000000000000 : ℝ) ≤ - (1523213711716290105329 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (271227131286207 / 400000000000000 : ℝ)) (q := - (2169824679842153 / 3200000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2169824679842153 / 3200000000000000 : ℚ)) + (r' := (2169824679842153 / 1600000000000000 : ℚ)) + (U := (-(1942522189783709894671 / 5000000000000000000000 : ℚ))) + (U' := (1523213711716290105329 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (271227131286207 / 400000000000000 : ℚ)) + (q := (2169824679842153 / 3200000000000000 : ℚ)) + (U := (-(1942522189783709894671 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_2 : Uω (aρ 2) (bρ 2) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4671,25 +4062,21 @@ lemma U_590_2 : have hlg : Real.log (54054399505276293 / 80000000000000000 : ℝ) ≤ (-(980089241722220861977 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54054399505276293 / 80000000000000000 : ℝ) = - (54054399505276293 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54054399505276293 / 40000000000000000 : ℚ)) - (U := (752778709027779138023 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54054399505276293 / 40000000000000000 : ℝ) ≤ - (752778709027779138023 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (844580365246349 / 1250000000000000 : ℝ)) (q := - (54054399505276293 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54054399505276293 / 80000000000000000 : ℚ)) + (r' := (54054399505276293 / 40000000000000000 : ℚ)) + (U := (-(980089241722220861977 / 2500000000000000000000 : ℚ))) + (U' := (752778709027779138023 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (844580365246349 / 1250000000000000 : ℚ)) + (q := (54054399505276293 / 80000000000000000 : ℚ)) + (U := (-(980089241722220861977 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_3 : Uω (aρ 3) (bρ 3) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4697,25 +4084,21 @@ lemma U_590_3 : have hlg : Real.log (2146883038033521 / 3200000000000000 : ℝ) ≤ (-(1995668845309871194029 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2146883038033521 / 3200000000000000 : ℝ) = - (2146883038033521 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2146883038033521 / 1600000000000000 : ℚ)) - (U := (1470067056190128805971 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2146883038033521 / 1600000000000000 : ℝ) ≤ - (1470067056190128805971 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (268338325588449 / 400000000000000 : ℝ)) (q := - (2146883038033521 / 3200000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2146883038033521 / 3200000000000000 : ℚ)) + (r' := (2146883038033521 / 1600000000000000 : ℚ)) + (U := (-(1995668845309871194029 / 5000000000000000000000 : ℚ))) + (U' := (1470067056190128805971 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (268338325588449 / 400000000000000 : ℚ)) + (q := (2146883038033521 / 3200000000000000 : ℚ)) + (U := (-(1995668845309871194029 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_4 : Uω (aρ 4) (bρ 4) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4723,25 +4106,21 @@ lemma U_590_4 : have hlg : Real.log (53037438267470893 / 80000000000000000 : ℝ) ≤ (-(4110285878273273006483 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53037438267470893 / 80000000000000000 : ℝ) = - (53037438267470893 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53037438267470893 / 40000000000000000 : ℚ)) - (U := (2821185924726726993517 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53037438267470893 / 40000000000000000 : ℝ) ≤ - (2821185924726726993517 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3314046449967221 / 5000000000000000 : ℝ)) (q := - (53037438267470893 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53037438267470893 / 80000000000000000 : ℚ)) + (r' := (53037438267470893 / 40000000000000000 : ℚ)) + (U := (-(4110285878273273006483 / 10000000000000000000000 : ℚ))) + (U' := (2821185924726726993517 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (3314046449967221 / 5000000000000000 : ℚ)) + (q := (53037438267470893 / 80000000000000000 : ℚ)) + (U := (-(4110285878273273006483 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_5 : Uω (aρ 5) (bρ 5) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4749,25 +4128,21 @@ lemma U_590_5 : have hlg : Real.log (52071885760380549 / 80000000000000000 : ℝ) ≤ (-(4294014520243379947173 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52071885760380549 / 80000000000000000 : ℝ) = - (52071885760380549 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52071885760380549 / 40000000000000000 : ℚ)) - (U := (2637457282756620052827 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52071885760380549 / 40000000000000000 : ℝ) ≤ - (2637457282756620052827 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (813111836562107 / 1250000000000000 : ℝ)) (q := - (52071885760380549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52071885760380549 / 80000000000000000 : ℚ)) + (r' := (52071885760380549 / 40000000000000000 : ℚ)) + (U := (-(4294014520243379947173 / 10000000000000000000000 : ℚ))) + (U' := (2637457282756620052827 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (813111836562107 / 1250000000000000 : ℚ)) + (q := (52071885760380549 / 80000000000000000 : ℚ)) + (U := (-(4294014520243379947173 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_6 : Uω (aρ 6) (bρ 6) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4775,25 +4150,21 @@ lemma U_590_6 : have hlg : Real.log (50689216668171037 / 80000000000000000 : ℝ) ≤ (-(912626870858038316583 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50689216668171037 / 80000000000000000 : ℝ) = - (50689216668171037 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50689216668171037 / 40000000000000000 : ℚ)) - (U := (473667489741961683417 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50689216668171037 / 40000000000000000 : ℝ) ≤ - (473667489741961683417 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3163233897292239 / 5000000000000000 : ℝ)) (q := - (50689216668171037 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50689216668171037 / 80000000000000000 : ℚ)) + (r' := (50689216668171037 / 40000000000000000 : ℚ)) + (U := (-(912626870858038316583 / 2000000000000000000000 : ℚ))) + (U' := (473667489741961683417 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (3163233897292239 / 5000000000000000 : ℚ)) + (q := (50689216668171037 / 80000000000000000 : ℚ)) + (U := (-(912626870858038316583 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_7 : Uω (aρ 7) (bρ 7) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4801,25 +4172,21 @@ lemma U_590_7 : have hlg : Real.log (48807359636483301 / 80000000000000000 : ℝ) ≤ (-(4941455207028364076573 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48807359636483301 / 80000000000000000 : ℝ) = - (48807359636483301 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48807359636483301 / 40000000000000000 : ℚ)) - (U := (1990016595971635923427 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48807359636483301 / 40000000000000000 : ℝ) ≤ - (1990016595971635923427 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (379979057338909 / 625000000000000 : ℝ)) (q := - (48807359636483301 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48807359636483301 / 80000000000000000 : ℚ)) + (r' := (48807359636483301 / 40000000000000000 : ℚ)) + (U := (-(4941455207028364076573 / 10000000000000000000000 : ℚ))) + (U' := (1990016595971635923427 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (379979057338909 / 625000000000000 : ℚ)) + (q := (48807359636483301 / 80000000000000000 : ℚ)) + (U := (-(4941455207028364076573 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_8 : Uω (aρ 8) (bρ 8) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4827,25 +4194,21 @@ lemma U_590_8 : have hlg : Real.log (46360857276965921 / 80000000000000000 : ℝ) ≤ (-(545571124375522783539 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46360857276965921 / 80000000000000000 : ℝ) = - (46360857276965921 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46360857276965921 / 40000000000000000 : ℚ)) - (U := (147576055924477216461 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46360857276965921 / 40000000000000000 : ℝ) ≤ - (147576055924477216461 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5751580978883199 / 10000000000000000 : ℝ)) (q := - (46360857276965921 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46360857276965921 / 80000000000000000 : ℚ)) + (r' := (46360857276965921 / 40000000000000000 : ℚ)) + (U := (-(545571124375522783539 / 1000000000000000000000 : ℚ))) + (U' := (147576055924477216461 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (5751580978883199 / 10000000000000000 : ℚ)) + (q := (46360857276965921 / 80000000000000000 : ℚ)) + (U := (-(545571124375522783539 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_9 : Uω (aρ 9) (bρ 9) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4853,25 +4216,21 @@ lemma U_590_9 : have hlg : Real.log (43312168491063741 / 80000000000000000 : ℝ) ≤ (-(766991264223849596283 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43312168491063741 / 80000000000000000 : ℝ) = - (43312168491063741 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43312168491063741 / 40000000000000000 : ℚ)) - (U := (99442711151150403717 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43312168491063741 / 40000000000000000 : ℝ) ≤ - (99442711151150403717 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2665187205383827 / 5000000000000000 : ℝ)) (q := - (43312168491063741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43312168491063741 / 80000000000000000 : ℚ)) + (r' := (43312168491063741 / 40000000000000000 : ℚ)) + (U := (-(766991264223849596283 / 1250000000000000000000 : ℚ))) + (U' := (99442711151150403717 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (2665187205383827 / 5000000000000000 : ℚ)) + (q := (43312168491063741 / 80000000000000000 : ℚ)) + (U := (-(766991264223849596283 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_10 : Uω (aρ 10) (bρ 10) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4879,26 +4238,21 @@ lemma U_590_10 : have hlg : Real.log (7931744875896073 / 16000000000000000 : ℝ) ≤ (-(3508578377429020554659 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7931744875896073 / 16000000000000000 : ℝ) = - (7931744875896073 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7931744875896073 / 4000000000000000 : ℚ)) - (U := (3422893425570979445341 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7931744875896073 / 4000000000000000 : ℝ) ≤ - (3422893425570979445341 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (480557241636681 / 1000000000000000 : ℝ)) (q := - (7931744875896073 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7931744875896073 / 16000000000000000 : ℚ)) + (r' := (7931744875896073 / 4000000000000000 : ℚ)) + (U := (-(3508578377429020554659 / 5000000000000000000000 : ℚ))) + (U' := (3422893425570979445341 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (480557241636681 / 1000000000000000 : ℚ)) + (q := (7931744875896073 / 16000000000000000 : ℚ)) + (U := (-(3508578377429020554659 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_11 : Uω (aρ 11) (bρ 11) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4906,26 +4260,21 @@ lemma U_590_11 : have hlg : Real.log (35430855323149441 / 80000000000000000 : ℝ) ≤ (-(8144435743557710104167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35430855323149441 / 80000000000000000 : ℝ) = - (35430855323149441 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35430855323149441 / 20000000000000000 : ℚ)) - (U := (5718507862442289895833 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35430855323149441 / 20000000000000000 : ℝ) ≤ - (5718507862442289895833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4167081778489079 / 10000000000000000 : ℝ)) (q := - (35430855323149441 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35430855323149441 / 80000000000000000 : ℚ)) + (r' := (35430855323149441 / 20000000000000000 : ℚ)) + (U := (-(8144435743557710104167 / 10000000000000000000000 : ℚ))) + (U' := (5718507862442289895833 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (4167081778489079 / 10000000000000000 : ℚ)) + (q := (35430855323149441 / 80000000000000000 : ℚ)) + (U := (-(8144435743557710104167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_12 : Uω (aρ 12) (bρ 12) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4933,26 +4282,21 @@ lemma U_590_12 : have hlg : Real.log (6134026705020049 / 16000000000000000 : ℝ) ≤ (-(2396843256077924959477 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6134026705020049 / 16000000000000000 : ℝ) = - (6134026705020049 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6134026705020049 / 4000000000000000 : ℚ)) - (U := (1068892645422075040523 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (6134026705020049 / 4000000000000000 : ℝ) ≤ - (1068892645422075040523 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (170030071283089 / 500000000000000 : ℝ)) (q := - (6134026705020049 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6134026705020049 / 16000000000000000 : ℚ)) + (r' := (6134026705020049 / 4000000000000000 : ℚ)) + (U := (-(2396843256077924959477 / 2500000000000000000000 : ℚ))) + (U' := (1068892645422075040523 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (170030071283089 / 500000000000000 : ℚ)) + (q := (6134026705020049 / 16000000000000000 : ℚ)) + (U := (-(2396843256077924959477 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_13 : Uω (aρ 13) (bρ 13) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4960,26 +4304,21 @@ lemma U_590_13 : have hlg : Real.log (25346652217097741 / 80000000000000000 : ℝ) ≤ (-(5746899876398573163821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25346652217097741 / 80000000000000000 : ℝ) = - (25346652217097741 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25346652217097741 / 20000000000000000 : ℚ)) - (U := (1184571926601426836179 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25346652217097741 / 20000000000000000 : ℝ) ≤ - (1184571926601426836179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1234556420128077 / 5000000000000000 : ℝ)) (q := - (25346652217097741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25346652217097741 / 80000000000000000 : ℚ)) + (r' := (25346652217097741 / 20000000000000000 : ℚ)) + (U := (-(5746899876398573163821 / 5000000000000000000000 : ℚ))) + (U' := (1184571926601426836179 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (1234556420128077 / 5000000000000000 : ℚ)) + (q := (25346652217097741 / 80000000000000000 : ℚ)) + (U := (-(5746899876398573163821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_14 : Uω (aρ 14) (bρ 14) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -4987,26 +4326,21 @@ lemma U_590_14 : have hlg : Real.log (18807224630108041 / 80000000000000000 : ℝ) ≤ (-(14477855490426510840571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (18807224630108041 / 80000000000000000 : ℝ) = - (18807224630108041 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18807224630108041 / 10000000000000000 : ℚ)) - (U := (6316559918573489159429 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18807224630108041 / 10000000000000000 : ℝ) ≤ - (6316559918573489159429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1178183228553729 / 10000000000000000 : ℝ)) (q := - (18807224630108041 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18807224630108041 / 80000000000000000 : ℚ)) + (r' := (18807224630108041 / 10000000000000000 : ℚ)) + (U := (-(14477855490426510840571 / 10000000000000000000000 : ℚ))) + (U' := (6316559918573489159429 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (43809428383637 / 64000000000000 : ℚ)) + (s := (1178183228553729 / 10000000000000000 : ℚ)) + (q := (18807224630108041 / 80000000000000000 : ℚ)) + (U := (-(14477855490426510840571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_590_15 : Uω (aρ 15) (bρ 15) (43809428383637 / 64000000000000 : ℝ) ≤ @@ -5109,25 +4443,21 @@ lemma U_591_1 : have hlg : Real.log (5431051621601647 / 8000000000000000 : ℝ) ≤ (-(3873087574221783174133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5431051621601647 / 8000000000000000 : ℝ) = - (5431051621601647 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5431051621601647 / 4000000000000000 : ℚ)) - (U := (3058384228778216825867 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5431051621601647 / 4000000000000000 : ℝ) ≤ - (3058384228778216825867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1357758142628261 / 2000000000000000 : ℝ)) (q := - (5431051621601647 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5431051621601647 / 8000000000000000 : ℚ)) + (r' := (5431051621601647 / 4000000000000000 : ℚ)) + (U := (-(3873087574221783174133 / 10000000000000000000000 : ℚ))) + (U' := (3058384228778216825867 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (1357758142628261 / 2000000000000000 : ℚ)) + (q := (5431051621601647 / 8000000000000000 : ℚ)) + (U := (-(3873087574221783174133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_2 : Uω (aρ 2) (bρ 2) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5135,25 +4465,21 @@ lemma U_591_2 : have hlg : Real.log (27059650001838881 / 40000000000000000 : ℝ) ≤ (-(3908357653472914841141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27059650001838881 / 40000000000000000 : ℝ) = - (27059650001838881 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27059650001838881 / 20000000000000000 : ℚ)) - (U := (3023114149527085158859 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27059650001838881 / 20000000000000000 : ℝ) ≤ - (3023114149527085158859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1691188918141657 / 2500000000000000 : ℝ)) (q := - (27059650001838881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27059650001838881 / 40000000000000000 : ℚ)) + (r' := (27059650001838881 / 20000000000000000 : ℚ)) + (U := (-(3908357653472914841141 / 10000000000000000000000 : ℚ))) + (U' := (3023114149527085158859 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (1691188918141657 / 2500000000000000 : ℚ)) + (q := (27059650001838881 / 40000000000000000 : ℚ)) + (U := (-(3908357653472914841141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_3 : Uω (aρ 3) (bρ 3) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5161,25 +4487,21 @@ lemma U_591_3 : have hlg : Real.log (26868490135171893 / 40000000000000000 : ℝ) ≤ (-(497406530345597454679 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26868490135171893 / 40000000000000000 : ℝ) = - (26868490135171893 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26868490135171893 / 20000000000000000 : ℚ)) - (U := (369027445029402545321 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26868490135171893 / 20000000000000000 : ℝ) ≤ - (369027445029402545321 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3358285922791567 / 5000000000000000 : ℝ)) (q := - (26868490135171893 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26868490135171893 / 40000000000000000 : ℚ)) + (r' := (26868490135171893 / 20000000000000000 : ℚ)) + (U := (-(497406530345597454679 / 1250000000000000000000 : ℚ))) + (U' := (369027445029402545321 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (3358285922791567 / 5000000000000000 : ℚ)) + (q := (26868490135171893 / 40000000000000000 : ℚ)) + (U := (-(497406530345597454679 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_4 : Uω (aρ 4) (bρ 4) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5187,25 +4509,21 @@ lemma U_591_4 : have hlg : Real.log (5310235277848301 / 8000000000000000 : ℝ) ≤ (-(512256748377032037619 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5310235277848301 / 8000000000000000 : ℝ) = - (5310235277848301 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5310235277848301 / 4000000000000000 : ℚ)) - (U := (354177226997967962381 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5310235277848301 / 4000000000000000 : ℝ) ≤ - (354177226997967962381 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (331810457684147 / 500000000000000 : ℝ)) (q := - (5310235277848301 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5310235277848301 / 8000000000000000 : ℚ)) + (r' := (5310235277848301 / 4000000000000000 : ℚ)) + (U := (-(512256748377032037619 / 1250000000000000000000 : ℚ))) + (U' := (354177226997967962381 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (331810457684147 / 500000000000000 : ℚ)) + (q := (5310235277848301 / 8000000000000000 : ℚ)) + (U := (-(512256748377032037619 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_5 : Uω (aρ 5) (bρ 5) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5213,25 +4531,21 @@ lemma U_591_5 : have hlg : Real.log (1042736510350251 / 1600000000000000 : ℝ) ≤ (-(2140775557921181468381 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1042736510350251 / 1600000000000000 : ℝ) = - (1042736510350251 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1042736510350251 / 800000000000000 : ℚ)) - (U := (1324960343578818531619 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1042736510350251 / 800000000000000 : ℝ) ≤ - (1324960343578818531619 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260520690311013 / 400000000000000 : ℝ)) (q := - (1042736510350251 / 1600000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1042736510350251 / 1600000000000000 : ℚ)) + (r' := (1042736510350251 / 800000000000000 : ℚ)) + (U := (-(2140775557921181468381 / 5000000000000000000000 : ℚ))) + (U' := (1324960343578818531619 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (260520690311013 / 400000000000000 : ℚ)) + (q := (1042736510350251 / 1600000000000000 : ℚ)) + (U := (-(2140775557921181468381 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_6 : Uω (aρ 6) (bρ 6) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5239,25 +4553,21 @@ lemma U_591_6 : have hlg : Real.log (5075421487741559 / 8000000000000000 : ℝ) ≤ (-(4550319681689112793929 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5075421487741559 / 8000000000000000 : ℝ) = - (5075421487741559 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5075421487741559 / 4000000000000000 : ℚ)) - (U := (2381152121310887206071 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5075421487741559 / 4000000000000000 : ℝ) ≤ - (2381152121310887206071 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1266920994578217 / 2000000000000000 : ℝ)) (q := - (5075421487741559 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5075421487741559 / 8000000000000000 : ℚ)) + (r' := (5075421487741559 / 4000000000000000 : ℚ)) + (U := (-(4550319681689112793929 / 10000000000000000000000 : ℚ))) + (U' := (2381152121310887206071 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (1266920994578217 / 2000000000000000 : ℚ)) + (q := (5075421487741559 / 8000000000000000 : ℚ)) + (U := (-(4550319681689112793929 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_7 : Uω (aρ 7) (bρ 7) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5265,25 +4575,21 @@ lemma U_591_7 : have hlg : Real.log (24436242608817219 / 40000000000000000 : ℝ) ≤ (-(4928120707798083417323 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24436242608817219 / 40000000000000000 : ℝ) = - (24436242608817219 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24436242608817219 / 20000000000000000 : ℚ)) - (U := (2003351095201916582677 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24436242608817219 / 20000000000000000 : ℝ) ≤ - (2003351095201916582677 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6087833938705797 / 10000000000000000 : ℝ)) (q := - (24436242608817219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24436242608817219 / 40000000000000000 : ℚ)) + (r' := (24436242608817219 / 20000000000000000 : ℚ)) + (U := (-(4928120707798083417323 / 10000000000000000000000 : ℚ))) + (U' := (2003351095201916582677 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (6087833938705797 / 10000000000000000 : ℚ)) + (q := (24436242608817219 / 40000000000000000 : ℚ)) + (U := (-(4928120707798083417323 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_8 : Uω (aρ 8) (bρ 8) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5291,25 +4597,21 @@ lemma U_591_8 : have hlg : Real.log (4642624670747133 / 8000000000000000 : ℝ) ≤ (-(272080836654552202981 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4642624670747133 / 8000000000000000 : ℝ) = - (4642624670747133 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4642624670747133 / 4000000000000000 : ℚ)) - (U := (74492753495447797019 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4642624670747133 / 4000000000000000 : ℝ) ≤ - (74492753495447797019 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (287990798125251 / 500000000000000 : ℝ)) (q := - (4642624670747133 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4642624670747133 / 8000000000000000 : ℚ)) + (r' := (4642624670747133 / 4000000000000000 : ℚ)) + (U := (-(272080836654552202981 / 500000000000000000000 : ℚ))) + (U' := (74492753495447797019 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (287990798125251 / 500000000000000 : ℚ)) + (q := (4642624670747133 / 8000000000000000 : ℚ)) + (U := (-(272080836654552202981 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_9 : Uω (aρ 9) (bρ 9) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5317,25 +4619,21 @@ lemma U_591_9 : have hlg : Real.log (21689042167840287 / 40000000000000000 : ℝ) ≤ (-(6120722900714232247101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21689042167840287 / 40000000000000000 : ℝ) = - (21689042167840287 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21689042167840287 / 20000000000000000 : ℚ)) - (U := (810748902285767752899 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21689042167840287 / 20000000000000000 : ℝ) ≤ - (810748902285767752899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5338740997917331 / 10000000000000000 : ℝ)) (q := - (21689042167840287 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21689042167840287 / 40000000000000000 : ℚ)) + (r' := (21689042167840287 / 20000000000000000 : ℚ)) + (U := (-(6120722900714232247101 / 10000000000000000000000 : ℚ))) + (U' := (810748902285767752899 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (5338740997917331 / 10000000000000000 : ℚ)) + (q := (21689042167840287 / 40000000000000000 : ℚ)) + (U := (-(6120722900714232247101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_10 : Uω (aρ 10) (bρ 10) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5343,26 +4641,21 @@ lemma U_591_10 : have hlg : Real.log (3972566942892681 / 8000000000000000 : ℝ) ≤ (-(7000290702954301500691 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3972566942892681 / 8000000000000000 : ℝ) = - (3972566942892681 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3972566942892681 / 2000000000000000 : ℚ)) - (U := (6862652903045698499309 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3972566942892681 / 2000000000000000 : ℝ) ≤ - (6862652903045698499309 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (481419630472389 / 1000000000000000 : ℝ)) (q := - (3972566942892681 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3972566942892681 / 8000000000000000 : ℚ)) + (r' := (3972566942892681 / 2000000000000000 : ℚ)) + (U := (-(7000290702954301500691 / 10000000000000000000000 : ℚ))) + (U' := (6862652903045698499309 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (481419630472389 / 1000000000000000 : ℚ)) + (q := (3972566942892681 / 8000000000000000 : ℚ)) + (U := (-(7000290702954301500691 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_11 : Uω (aρ 11) (bρ 11) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5370,26 +4663,21 @@ lemma U_591_11 : have hlg : Real.log (17749911419090027 / 40000000000000000 : ℝ) ≤ (-(2031247320397186581489 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17749911419090027 / 40000000000000000 : ℝ) = - (17749911419090027 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17749911419090027 / 10000000000000000 : ℚ)) - (U := (1434488581102813418511 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17749911419090027 / 10000000000000000 : ℝ) ≤ - (1434488581102813418511 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4176211283242201 / 10000000000000000 : ℝ)) (q := - (17749911419090027 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17749911419090027 / 40000000000000000 : ℚ)) + (r' := (17749911419090027 / 10000000000000000 : ℚ)) + (U := (-(2031247320397186581489 / 2500000000000000000000 : ℚ))) + (U' := (1434488581102813418511 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (4176211283242201 / 10000000000000000 : ℚ)) + (q := (17749911419090027 / 40000000000000000 : ℚ)) + (U := (-(2031247320397186581489 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_12 : Uω (aρ 12) (bρ 12) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5397,26 +4685,21 @@ lemma U_591_12 : have hlg : Real.log (15371638560123711 / 40000000000000000 : ℝ) ≤ (-(9563552940403943445557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15371638560123711 / 40000000000000000 : ℝ) = - (15371638560123711 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15371638560123711 / 10000000000000000 : ℚ)) - (U := (4299390665596056554443 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15371638560123711 / 10000000000000000 : ℝ) ≤ - (4299390665596056554443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3410774950444043 / 10000000000000000 : ℝ)) (q := - (15371638560123711 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15371638560123711 / 40000000000000000 : ℚ)) + (r' := (15371638560123711 / 10000000000000000 : ℚ)) + (U := (-(9563552940403943445557 / 10000000000000000000000 : ℚ))) + (U' := (4299390665596056554443 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (3410774950444043 / 10000000000000000 : ℚ)) + (q := (15371638560123711 / 40000000000000000 : ℚ)) + (U := (-(9563552940403943445557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_13 : Uω (aρ 13) (bρ 13) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5424,26 +4707,21 @@ lemma U_591_13 : have hlg : Real.log (12714926310772163 / 40000000000000000 : ℝ) ≤ (-(2865257125482834296423 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12714926310772163 / 40000000000000000 : ℝ) = - (12714926310772163 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12714926310772163 / 10000000000000000 : ℚ)) - (U := (600478776017165703577 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12714926310772163 / 10000000000000000 : ℝ) ≤ - (600478776017165703577 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2481800567363269 / 10000000000000000 : ℝ)) (q := - (12714926310772163 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12714926310772163 / 40000000000000000 : ℚ)) + (r' := (12714926310772163 / 10000000000000000 : ℚ)) + (U := (-(2865257125482834296423 / 2500000000000000000000 : ℚ))) + (U' := (600478776017165703577 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (2481800567363269 / 10000000000000000 : ℚ)) + (q := (12714926310772163 / 40000000000000000 : ℚ)) + (U := (-(2865257125482834296423 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_14 : Uω (aρ 14) (bρ 14) (21930673788633 / 32000000000000 : ℝ) ≤ @@ -5451,26 +4729,21 @@ lemma U_591_14 : have hlg : Real.log (9467925991076191 / 40000000000000000 : ℝ) ≤ (-(225151496633754432083 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9467925991076191 / 40000000000000000 : ℝ) = - (9467925991076191 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9467925991076191 / 5000000000000000 : ℚ)) - (U := (99761244131870567917 / 156250000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9467925991076191 / 5000000000000000 : ℝ) ≤ - (99761244131870567917 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1202227692560283 / 10000000000000000 : ℝ)) (q := - (9467925991076191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9467925991076191 / 40000000000000000 : ℚ)) + (r' := (9467925991076191 / 5000000000000000 : ℚ)) + (U := (-(225151496633754432083 / 156250000000000000000 : ℚ))) + (U' := (99761244131870567917 / 156250000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (21930673788633 / 32000000000000 : ℚ)) + (s := (1202227692560283 / 10000000000000000 : ℚ)) + (q := (9467925991076191 / 40000000000000000 : ℚ)) + (U := (-(225151496633754432083 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_591_15 : Uω (aρ 15) (bρ 15) (21930673788633 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U49.lean b/LeanPool/Zeta5Irrational/Table/U49.lean index 185c0c5d4c..f33c904a86 100644 --- a/LeanPool/Zeta5Irrational/Table/U49.lean +++ b/LeanPool/Zeta5Irrational/Table/U49.lean @@ -24,25 +24,21 @@ lemma U_592_1 : have hlg : Real.log (10875083087087007 / 16000000000000000 : ℝ) ≤ (-(3861145048423655657401 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10875083087087007 / 16000000000000000 : ℝ) = - (10875083087087007 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10875083087087007 / 8000000000000000 : ℚ)) - (U := (3070326754576344342599 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (10875083087087007 / 8000000000000000 : ℝ) ≤ - (3070326754576344342599 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1359380628798283 / 2000000000000000 : ℝ)) (q := - (10875083087087007 / 16000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10875083087087007 / 16000000000000000 : ℚ)) + (r' := (10875083087087007 / 8000000000000000 : ℚ)) + (U := (-(3861145048423655657401 / 10000000000000000000000 : ℚ))) + (U' := (3070326754576344342599 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (1359380628798283 / 2000000000000000 : ℚ)) + (q := (10875083087087007 / 16000000000000000 : ℚ)) + (U := (-(3861145048423655657401 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_2 : Uω (aρ 2) (bρ 2) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_592_2 : have hlg : Real.log (2167368019938823 / 3200000000000000 : ℝ) ≤ (-(243523295113786450747 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2167368019938823 / 3200000000000000 : ℝ) = - (2167368019938823 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2167368019938823 / 1600000000000000 : ℚ)) - (U := (189693692573713549253 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2167368019938823 / 1600000000000000 : ℝ) ≤ - (189693692573713549253 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (67728684222603 / 100000000000000 : ℝ)) (q := - (2167368019938823 / 3200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2167368019938823 / 3200000000000000 : ℚ)) + (r' := (2167368019938823 / 1600000000000000 : ℚ)) + (U := (-(243523295113786450747 / 625000000000000000000 : ℚ))) + (U' := (189693692573713549253 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (67728684222603 / 100000000000000 : ℚ)) + (q := (2167368019938823 / 3200000000000000 : ℚ)) + (U := (-(243523295113786450747 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_3 : Uω (aρ 3) (bρ 3) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_592_3 : have hlg : Real.log (53801884576994823 / 80000000000000000 : ℝ) ≤ (-(991795346368845415999 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53801884576994823 / 80000000000000000 : ℝ) = - (53801884576994823 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53801884576994823 / 40000000000000000 : ℚ)) - (U := (741072604381154584001 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53801884576994823 / 40000000000000000 : ℝ) ≤ - (741072604381154584001 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3362342774120681 / 5000000000000000 : ℝ)) (q := - (53801884576994823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53801884576994823 / 80000000000000000 : ℚ)) + (r' := (53801884576994823 / 40000000000000000 : ℚ)) + (U := (-(991795346368845415999 / 2500000000000000000000 : ℚ))) + (U' := (741072604381154584001 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (3362342774120681 / 5000000000000000 : ℚ)) + (q := (53801884576994823 / 80000000000000000 : ℚ)) + (U := (-(991795346368845415999 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_4 : Uω (aρ 4) (bρ 4) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_592_4 : have hlg : Real.log (53167267251590347 / 80000000000000000 : ℝ) ≤ (-(51072963081599011411 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53167267251590347 / 80000000000000000 : ℝ) = - (53167267251590347 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53167267251590347 / 40000000000000000 : ℚ)) - (U := (35570434455900988589 / 125000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53167267251590347 / 40000000000000000 : ℝ) ≤ - (35570434455900988589 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6644325397955243 / 10000000000000000 : ℝ)) (q := - (53167267251590347 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53167267251590347 / 80000000000000000 : ℚ)) + (r' := (53167267251590347 / 40000000000000000 : ℚ)) + (U := (-(51072963081599011411 / 125000000000000000000 : ℚ))) + (U' := (35570434455900988589 / 125000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (6644325397955243 / 10000000000000000 : ℚ)) + (q := (53167267251590347 / 80000000000000000 : ℚ)) + (U := (-(51072963081599011411 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_5 : Uω (aρ 5) (bρ 5) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_592_5 : have hlg : Real.log (52201765173156339 / 80000000000000000 : ℝ) ≤ (-(4269103245193693824213 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52201765173156339 / 80000000000000000 : ℝ) = - (52201765173156339 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52201765173156339 / 40000000000000000 : ℚ)) - (U := (2662368557806306175787 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52201765173156339 / 40000000000000000 : ℝ) ≤ - (2662368557806306175787 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6521139797681741 / 10000000000000000 : ℝ)) (q := - (52201765173156339 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52201765173156339 / 80000000000000000 : ℚ)) + (r' := (52201765173156339 / 40000000000000000 : ℚ)) + (U := (-(4269103245193693824213 / 10000000000000000000000 : ℚ))) + (U' := (2662368557806306175787 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (6521139797681741 / 10000000000000000 : ℚ)) + (q := (52201765173156339 / 80000000000000000 : ℚ)) + (U := (-(4269103245193693824213 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_6 : Uω (aρ 6) (bρ 6) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_592_6 : have hlg : Real.log (50819212832474303 / 80000000000000000 : ℝ) ≤ (-(4537521459674536368377 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50819212832474303 / 80000000000000000 : ℝ) = - (50819212832474303 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50819212832474303 / 40000000000000000 : ℚ)) - (U := (2393950343325463631623 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50819212832474303 / 40000000000000000 : ℝ) ≤ - (2393950343325463631623 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (198210690239101 / 312500000000000 : ℝ)) (q := - (50819212832474303 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50819212832474303 / 80000000000000000 : ℚ)) + (r' := (50819212832474303 / 40000000000000000 : ℚ)) + (U := (-(4537521459674536368377 / 10000000000000000000000 : ℚ))) + (U' := (2393950343325463631623 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (198210690239101 / 312500000000000 : ℚ)) + (q := (50819212832474303 / 80000000000000000 : ℚ)) + (U := (-(4537521459674536368377 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_7 : Uω (aρ 7) (bρ 7) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_592_7 : have hlg : Real.log (48937610193604279 / 80000000000000000 : ℝ) ≤ (-(614350511180361655339 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48937610193604279 / 80000000000000000 : ℝ) = - (48937610193604279 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48937610193604279 / 40000000000000000 : ℚ)) - (U := (252083464194638344661 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48937610193604279 / 40000000000000000 : ℝ) ≤ - (252083464194638344661 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3048001404346863 / 5000000000000000 : ℝ)) (q := - (48937610193604279 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48937610193604279 / 80000000000000000 : ℚ)) + (r' := (48937610193604279 / 40000000000000000 : ℚ)) + (U := (-(614350511180361655339 / 1250000000000000000000 : ℚ))) + (U' := (252083464194638344661 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (3048001404346863 / 5000000000000000 : ℚ)) + (q := (48937610193604279 / 80000000000000000 : ℚ)) + (U := (-(614350511180361655339 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_8 : Uω (aρ 8) (bρ 8) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_592_8 : have hlg : Real.log (46491634748014451 / 80000000000000000 : ℝ) ≤ (-(1356885589740886941109 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46491634748014451 / 80000000000000000 : ℝ) = - (46491634748014451 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46491634748014451 / 40000000000000000 : ℚ)) - (U := (375982361009113058891 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46491634748014451 / 40000000000000000 : ℝ) ≤ - (375982361009113058891 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5768050598636269 / 10000000000000000 : ℝ)) (q := - (46491634748014451 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46491634748014451 / 80000000000000000 : ℚ)) + (r' := (46491634748014451 / 40000000000000000 : ℚ)) + (U := (-(1356885589740886941109 / 2500000000000000000000 : ℚ))) + (U' := (375982361009113058891 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (5768050598636269 / 10000000000000000 : ℚ)) + (q := (46491634748014451 / 80000000000000000 : ℚ)) + (U := (-(1356885589740886941109 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_9 : Uω (aρ 9) (bρ 9) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_592_9 : have hlg : Real.log (43443997046514299 / 80000000000000000 : ℝ) ≤ (-(6105539499798913087489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43443997046514299 / 80000000000000000 : ℝ) = - (43443997046514299 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43443997046514299 / 40000000000000000 : ℚ)) - (U := (825932303201086912511 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43443997046514299 / 40000000000000000 : ℝ) ≤ - (825932303201086912511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5347106801621231 / 10000000000000000 : ℝ)) (q := - (43443997046514299 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43443997046514299 / 80000000000000000 : ℚ)) + (r' := (43443997046514299 / 40000000000000000 : ℚ)) + (U := (-(6105539499798913087489 / 10000000000000000000000 : ℚ))) + (U' := (825932303201086912511 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (5347106801621231 / 10000000000000000 : ℚ)) + (q := (43443997046514299 / 80000000000000000 : ℚ)) + (U := (-(6105539499798913087489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_10 : Uω (aρ 10) (bρ 10) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_592_10 : have hlg : Real.log (39792607378096127 / 80000000000000000 : ℝ) ≤ (-(43646592711571477181 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39792607378096127 / 80000000000000000 : ℝ) = - (39792607378096127 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39792607378096127 / 20000000000000000 : ℚ)) - (U := (42996804825928522819 / 62500000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (39792607378096127 / 20000000000000000 : ℝ) ≤ - (42996804825928522819 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (602852302251461 / 1250000000000000 : ℝ)) (q := - (39792607378096127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39792607378096127 / 80000000000000000 : ℚ)) + (r' := (39792607378096127 / 20000000000000000 : ℚ)) + (U := (-(43646592711571477181 / 62500000000000000000 : ℚ))) + (U' := (42996804825928522819 / 62500000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (602852302251461 / 1250000000000000 : ℚ)) + (q := (39792607378096127 / 80000000000000000 : ℚ)) + (U := (-(43646592711571477181 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_11 : Uω (aρ 11) (bρ 11) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_592_11 : have hlg : Real.log (35568773592564671 / 80000000000000000 : ℝ) ≤ (-(253299539840680361623 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35568773592564671 / 80000000000000000 : ℝ) = - (35568773592564671 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35568773592564671 / 20000000000000000 : ℚ)) - (U := (179917447846819638377 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35568773592564671 / 20000000000000000 : ℝ) ≤ - (179917447846819638377 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (130791768682307 / 312500000000000 : ℝ)) (q := - (35568773592564671 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35568773592564671 / 80000000000000000 : ℚ)) + (r' := (35568773592564671 / 20000000000000000 : ℚ)) + (U := (-(253299539840680361623 / 312500000000000000000 : ℚ))) + (U' := (179917447846819638377 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (130791768682307 / 312500000000000 : ℚ)) + (q := (35568773592564671 / 80000000000000000 : ℚ)) + (U := (-(253299539840680361623 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_12 : Uω (aρ 12) (bρ 12) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_592_12 : have hlg : Real.log (30816376645680631 / 80000000000000000 : ℝ) ≤ (-(9539803762064064091603 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30816376645680631 / 80000000000000000 : ℝ) = - (30816376645680631 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30816376645680631 / 20000000000000000 : ℚ)) - (U := (4323139843935935908397 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30816376645680631 / 20000000000000000 : ℝ) ≤ - (4323139843935935908397 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1710468728898907 / 5000000000000000 : ℝ)) (q := - (30816376645680631 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30816376645680631 / 80000000000000000 : ℚ)) + (r' := (30816376645680631 / 20000000000000000 : ℚ)) + (U := (-(9539803762064064091603 / 10000000000000000000000 : ℚ))) + (U' := (4323139843935935908397 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (1710468728898907 / 5000000000000000 : ℚ)) + (q := (30816376645680631 / 80000000000000000 : ℚ)) + (U := (-(9539803762064064091603 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_13 : Uω (aρ 13) (bρ 13) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -339,26 +288,21 @@ lemma U_592_13 : have hlg : Real.log (25512900419887071 / 80000000000000000 : ℝ) ≤ (-(11428424110941748224189 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25512900419887071 / 80000000000000000 : ℝ) = - (25512900419887071 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25512900419887071 / 20000000000000000 : ℚ)) - (U := (2434519495058251775811 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25512900419887071 / 20000000000000000 : ℝ) ≤ - (2434519495058251775811 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (311806267868053 / 1250000000000000 : ℝ)) (q := - (25512900419887071 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25512900419887071 / 80000000000000000 : ℚ)) + (r' := (25512900419887071 / 20000000000000000 : ℚ)) + (U := (-(11428424110941748224189 / 10000000000000000000000 : ℚ))) + (U' := (2434519495058251775811 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (311806267868053 / 1250000000000000 : ℚ)) + (q := (25512900419887071 / 80000000000000000 : ℚ)) + (U := (-(11428424110941748224189 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_14 : Uω (aρ 14) (bρ 14) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -366,26 +310,21 @@ lemma U_592_14 : have hlg : Real.log (19062807884872551 / 80000000000000000 : ℝ) ≤ (-(7171437141596351498281 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19062807884872551 / 80000000000000000 : ℝ) = - (19062807884872551 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19062807884872551 / 10000000000000000 : ℚ)) - (U := (3225770562903648501719 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19062807884872551 / 10000000000000000 : ℝ) ≤ - (3225770562903648501719 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (612927147117897 / 5000000000000000 : ℝ)) (q := - (19062807884872551 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19062807884872551 / 80000000000000000 : ℚ)) + (r' := (19062807884872551 / 10000000000000000 : ℚ)) + (U := (-(7171437141596351498281 / 5000000000000000000000 : ℚ))) + (U' := (3225770562903648501719 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (8782653354179 / 12800000000000 : ℚ)) + (s := (612927147117897 / 5000000000000000 : ℚ)) + (q := (19062807884872551 / 80000000000000000 : ℚ)) + (U := (-(7171437141596351498281 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_592_15 : Uω (aρ 15) (bρ 15) (8782653354179 / 12800000000000 : ℝ) ≤ @@ -485,25 +424,21 @@ lemma U_593_1 : have hlg : Real.log (6805039331788933 / 10000000000000000 : ℝ) ≤ (-(76984335362129264989 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6805039331788933 / 10000000000000000 : ℝ) = - (6805039331788933 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6805039331788933 / 5000000000000000 : ℚ)) - (U := (61645100697870735011 / 200000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6805039331788933 / 5000000000000000 : ℝ) ≤ - (61645100697870735011 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6805015574705991 / 10000000000000000 : ℝ)) (q := - (6805039331788933 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6805039331788933 / 10000000000000000 : ℚ)) + (r' := (6805039331788933 / 5000000000000000 : ℚ)) + (U := (-(76984335362129264989 / 200000000000000000000 : ℚ))) + (U' := (61645100697870735011 / 200000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (6805015574705991 / 10000000000000000 : ℚ)) + (q := (6805039331788933 / 10000000000000000 : ℚ)) + (U := (-(76984335362129264989 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_2 : Uω (aρ 2) (bρ 2) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -511,25 +446,21 @@ lemma U_593_2 : have hlg : Real.log (339056881185423 / 500000000000000 : ℝ) ≤ (-(9711005343742677657 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (339056881185423 / 500000000000000 : ℝ) = - (339056881185423 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (339056881185423 / 250000000000000 : ℚ)) - (U := (7617674163757322343 / 25000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (339056881185423 / 250000000000000 : ℝ) ≤ - (7617674163757322343 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1356196234211009 / 2000000000000000 : ℝ)) (q := - (339056881185423 / 500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (339056881185423 / 500000000000000 : ℚ)) + (r' := (339056881185423 / 250000000000000 : ℚ)) + (U := (-(9711005343742677657 / 25000000000000000000 : ℚ))) + (U' := (7617674163757322343 / 25000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (1356196234211009 / 2000000000000000 : ℚ)) + (q := (339056881185423 / 500000000000000 : ℚ)) + (U := (-(9711005343742677657 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_3 : Uω (aρ 3) (bρ 3) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -537,25 +468,21 @@ lemma U_593_3 : have hlg : Real.log (2693339443541881 / 4000000000000000 : ℝ) ≤ (-(31641000668466948117 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2693339443541881 / 4000000000000000 : ℝ) = - (2693339443541881 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2693339443541881 / 2000000000000000 : ℚ)) - (U := (23810773755533051883 / 80000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2693339443541881 / 2000000000000000 : ℝ) ≤ - (23810773755533051883 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (673279924769753 / 1000000000000000 : ℝ)) (q := - (2693339443541881 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2693339443541881 / 4000000000000000 : ℚ)) + (r' := (2693339443541881 / 2000000000000000 : ℚ)) + (U := (-(31641000668466948117 / 80000000000000000000 : ℚ))) + (U' := (23810773755533051883 / 80000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (673279924769753 / 1000000000000000 : ℚ)) + (q := (2693339443541881 / 4000000000000000 : ℚ)) + (U := (-(31641000668466948117 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_4 : Uω (aρ 4) (bρ 4) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -563,25 +490,21 @@ lemma U_593_4 : have hlg : Real.log (1330804542173291 / 2000000000000000 : ℝ) ≤ (-(4073635020287535188957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1330804542173291 / 2000000000000000 : ℝ) = - (1330804542173291 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1330804542173291 / 1000000000000000 : ℚ)) - (U := (2857836782712464811043 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1330804542173291 / 1000000000000000 : ℝ) ≤ - (2857836782712464811043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1330488326557207 / 2000000000000000 : ℝ)) (q := - (1330804542173291 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1330804542173291 / 2000000000000000 : ℚ)) + (r' := (1330804542173291 / 1000000000000000 : ℚ)) + (U := (-(4073635020287535188957 / 10000000000000000000000 : ℚ))) + (U' := (2857836782712464811043 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (1330488326557207 / 2000000000000000 : ℚ)) + (q := (1330804542173291 / 2000000000000000 : ℚ)) + (U := (-(4073635020287535188957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_5 : Uω (aρ 5) (bρ 5) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -589,25 +512,21 @@ lemma U_593_5 : have hlg : Real.log (13066676181922667 / 20000000000000000 : ℝ) ≤ (-(4256670869576362918179 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13066676181922667 / 20000000000000000 : ℝ) = - (13066676181922667 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13066676181922667 / 10000000000000000 : ℚ)) - (U := (2674800933423637081821 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13066676181922667 / 10000000000000000 : ℝ) ≤ - (2674800933423637081821 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (816157789038849 / 1250000000000000 : ℝ)) (q := - (13066676181922667 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13066676181922667 / 20000000000000000 : ℚ)) + (r' := (13066676181922667 / 10000000000000000 : ℚ)) + (U := (-(4256670869576362918179 / 10000000000000000000000 : ℚ))) + (U' := (2674800933423637081821 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (816157789038849 / 1250000000000000 : ℚ)) + (q := (13066676181922667 / 20000000000000000 : ℚ)) + (U := (-(4256670869576362918179 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_6 : Uω (aρ 6) (bρ 6) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -615,25 +534,21 @@ lemma U_593_6 : have hlg : Real.log (12721052633581053 / 20000000000000000 : ℝ) ≤ (-(452473964593663599121 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12721052633581053 / 20000000000000000 : ℝ) = - (12721052633581053 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12721052633581053 / 10000000000000000 : ℚ)) - (U := (240673215706336400879 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12721052633581053 / 10000000000000000 : ℝ) ≤ - (240673215706336400879 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3175439569554589 / 5000000000000000 : ℝ)) (q := - (12721052633581053 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12721052633581053 / 20000000000000000 : ℚ)) + (r' := (12721052633581053 / 10000000000000000 : ℚ)) + (U := (-(452473964593663599121 / 1000000000000000000000 : ℚ))) + (U' := (240673215706336400879 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (3175439569554589 / 5000000000000000 : ℚ)) + (q := (12721052633581053 / 20000000000000000 : ℚ)) + (U := (-(452473964593663599121 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_7 : Uω (aρ 7) (bρ 7) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -641,25 +556,21 @@ lemma U_593_7 : have hlg : Real.log (2450136728341123 / 4000000000000000 : ℝ) ≤ (-(4901505303743168612503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2450136728341123 / 4000000000000000 : ℝ) = - (2450136728341123 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2450136728341123 / 2000000000000000 : ℚ)) - (U := (2029966499256831387497 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2450136728341123 / 2000000000000000 : ℝ) ≤ - (2029966499256831387497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (305208576399687 / 500000000000000 : ℝ)) (q := - (2450136728341123 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2450136728341123 / 4000000000000000 : ℚ)) + (r' := (2450136728341123 / 2000000000000000 : ℚ)) + (U := (-(4901505303743168612503 / 10000000000000000000000 : ℚ))) + (U' := (2029966499256831387497 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (305208576399687 / 500000000000000 : ℚ)) + (q := (2450136728341123 / 4000000000000000 : ℚ)) + (U := (-(4901505303743168612503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_8 : Uω (aρ 8) (bρ 8) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -667,25 +578,21 @@ lemma U_593_8 : have hlg : Real.log (11639255351134963 / 20000000000000000 : ℝ) ≤ (-(2706744031536615135693 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11639255351134963 / 20000000000000000 : ℝ) = - (11639255351134963 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11639255351134963 / 10000000000000000 : ℚ)) - (U := (758991869963384864307 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11639255351134963 / 10000000000000000 : ℝ) ≤ - (758991869963384864307 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (361017805547693 / 625000000000000 : ℝ)) (q := - (11639255351134963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11639255351134963 / 20000000000000000 : ℚ)) + (r' := (11639255351134963 / 10000000000000000 : ℚ)) + (U := (-(2706744031536615135693 / 5000000000000000000000 : ℚ))) + (U' := (758991869963384864307 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (361017805547693 / 625000000000000 : ℚ)) + (q := (11639255351134963 / 20000000000000000 : ℚ)) + (U := (-(2706744031536615135693 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_9 : Uω (aρ 9) (bρ 9) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -693,25 +600,21 @@ lemma U_593_9 : have hlg : Real.log (10877476659562703 / 20000000000000000 : ℝ) ≤ (-(1522594958593701806993 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10877476659562703 / 20000000000000000 : ℝ) = - (10877476659562703 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10877476659562703 / 10000000000000000 : ℚ)) - (U := (210272992156298193007 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10877476659562703 / 10000000000000000 : ℝ) ≤ - (210272992156298193007 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1338867956387707 / 2500000000000000 : ℝ)) (q := - (10877476659562703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10877476659562703 / 20000000000000000 : ℚ)) + (r' := (10877476659562703 / 10000000000000000 : ℚ)) + (U := (-(1522594958593701806993 / 2500000000000000000000 : ℚ))) + (U' := (210272992156298193007 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (1338867956387707 / 2500000000000000 : ℚ)) + (q := (10877476659562703 / 20000000000000000 : ℚ)) + (U := (-(1522594958593701806993 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_10 : Uω (aρ 10) (bρ 10) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -719,26 +622,21 @@ lemma U_593_10 : have hlg : Real.log (2491221141562591 / 5000000000000000 : ℝ) ≤ (-(6966649033551154060933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2491221141562591 / 5000000000000000 : ℝ) = - (2491221141562591 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2491221141562591 / 1250000000000000 : ℚ)) - (U := (6896294572448845939067 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2491221141562591 / 1250000000000000 : ℝ) ≤ - (6896294572448845939067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4831438765733489 / 10000000000000000 : ℝ)) (q := - (2491221141562591 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2491221141562591 / 5000000000000000 : ℚ)) + (r' := (2491221141562591 / 1250000000000000 : ℚ)) + (U := (-(6966649033551154060933 / 10000000000000000000000 : ℚ))) + (U' := (6896294572448845939067 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (4831438765733489 / 10000000000000000 : ℚ)) + (q := (2491221141562591 / 5000000000000000 : ℚ)) + (U := (-(6966649033551154060933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_11 : Uω (aρ 11) (bρ 11) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -746,25 +644,21 @@ lemma U_593_11 : have hlg : Real.log (556839182745233 / 1250000000000000 : ℝ) ≤ (-(8086223519225050504341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (556839182745233 / 1250000000000000 : ℝ) = - (556839182745233 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (556839182745233 / 312500000000000 : ℚ)) - (U := (5776720086774949495659 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (556839182745233 / 312500000000000 : ℝ) ≤ - (5776720086774949495659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4194457749611853 / 10000000000000000 : ℝ)) (q := - (556839182745233 / 1250000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (556839182745233 / 1250000000000000 : ℚ)) + (r' := (556839182745233 / 312500000000000 : ℚ)) + (U := (-(8086223519225050504341 / 10000000000000000000000 : ℚ))) + (U' := (5776720086774949495659 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (4194457749611853 / 10000000000000000 : ℚ)) + (q := (556839182745233 / 1250000000000000 : ℚ)) + (U := (-(8086223519225050504341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_12 : Uω (aρ 12) (bρ 12) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -772,26 +666,21 @@ lemma U_593_12 : have hlg : Real.log (1544471624649439 / 4000000000000000 : ℝ) ≤ (-(1903224998521094270931 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1544471624649439 / 4000000000000000 : ℝ) = - (1544471624649439 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1544471624649439 / 1000000000000000 : ℚ)) - (U := (869363722678905729069 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1544471624649439 / 1000000000000000 : ℝ) ≤ - (869363722678905729069 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (21444306535127 / 62500000000000 : ℝ)) (q := - (1544471624649439 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1544471624649439 / 4000000000000000 : ℚ)) + (r' := (1544471624649439 / 1000000000000000 : ℚ)) + (U := (-(1903224998521094270931 / 2000000000000000000000 : ℚ))) + (U' := (869363722678905729069 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (21444306535127 / 62500000000000 : ℚ)) + (q := (1544471624649439 / 4000000000000000 : ℚ)) + (U := (-(1903224998521094270931 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_13 : Uω (aρ 13) (bρ 13) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -799,26 +688,21 @@ lemma U_593_13 : have hlg : Real.log (6398949480520967 / 20000000000000000 : ℝ) ≤ (-(1424498049762649303159 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6398949480520967 / 20000000000000000 : ℝ) = - (6398949480520967 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6398949480520967 / 5000000000000000 : ℚ)) - (U := (308369900987350696841 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6398949480520967 / 5000000000000000 : ℝ) ≤ - (308369900987350696841 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (626765536122273 / 2500000000000000 : ℝ)) (q := - (6398949480520967 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6398949480520967 / 20000000000000000 : ℚ)) + (r' := (6398949480520967 / 5000000000000000 : ℚ)) + (U := (-(1424498049762649303159 / 1250000000000000000000 : ℚ))) + (U' := (308369900987350696841 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (626765536122273 / 2500000000000000 : ℚ)) + (q := (6398949480520967 / 20000000000000000 : ℚ)) + (U := (-(1424498049762649303159 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_14 : Uω (aρ 14) (bρ 14) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -826,26 +710,21 @@ lemma U_593_14 : have hlg : Real.log (1199261699129129 / 5000000000000000 : ℝ) ≤ (-(713865897465215119503 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1199261699129129 / 5000000000000000 : ℝ) = - (1199261699129129 / 625000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1199261699129129 / 625000000000000 : ℚ)) - (U := (325854872984784880497 / 500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1199261699129129 / 625000000000000 : ℝ) ≤ - (325854872984784880497 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1249086745529641 / 10000000000000000 : ℝ)) (q := - (1199261699129129 / 5000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1199261699129129 / 5000000000000000 : ℚ)) + (r' := (1199261699129129 / 625000000000000 : ℚ)) + (U := (-(713865897465215119503 / 500000000000000000000 : ℚ))) + (U' := (325854872984784880497 / 500000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (10991296491131 / 16000000000000 : ℚ)) + (s := (1249086745529641 / 10000000000000000 : ℚ)) + (q := (1199261699129129 / 5000000000000000 : ℚ)) + (U := (-(713865897465215119503 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_593_15 : Uω (aρ 15) (bρ 15) (10991296491131 / 16000000000000 : ℝ) ≤ @@ -945,25 +824,21 @@ lemma U_594_1 : have hlg : Real.log (54505213872647697 / 80000000000000000 : ℝ) ≤ (-(3837302699325395042261 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54505213872647697 / 80000000000000000 : ℝ) = - (54505213872647697 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54505213872647697 / 40000000000000000 : ℚ)) - (U := (3094169103674604957739 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54505213872647697 / 40000000000000000 : ℝ) ≤ - (3094169103674604957739 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3406564002642759 / 5000000000000000 : ℝ)) (q := - (54505213872647697 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54505213872647697 / 80000000000000000 : ℚ)) + (r' := (54505213872647697 / 40000000000000000 : ℚ)) + (U := (-(3837302699325395042261 / 10000000000000000000000 : ℚ))) + (U' := (3094169103674604957739 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (3406564002642759 / 5000000000000000 : ℚ)) + (q := (54505213872647697 / 80000000000000000 : ℚ)) + (U := (-(3837302699325395042261 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_2 : Uω (aρ 2) (bρ 2) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -971,25 +846,21 @@ lemma U_594_2 : have hlg : Real.log (54314001477281973 / 80000000000000000 : ℝ) ≤ (-(3872445866191089838999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54314001477281973 / 80000000000000000 : ℝ) = - (54314001477281973 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54314001477281973 / 40000000000000000 : ℚ)) - (U := (3059025936808910161001 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54314001477281973 / 40000000000000000 : ℝ) ≤ - (3059025936808910161001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6789093918954087 / 10000000000000000 : ℝ)) (q := - (54314001477281973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54314001477281973 / 80000000000000000 : ℚ)) + (r' := (54314001477281973 / 40000000000000000 : ℚ)) + (U := (-(3872445866191089838999 / 10000000000000000000000 : ℚ))) + (U' := (3059025936808910161001 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (6789093918954087 / 10000000000000000 : ℚ)) + (q := (54314001477281973 / 80000000000000000 : ℚ)) + (U := (-(3872445866191089838999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_3 : Uω (aρ 3) (bρ 3) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -997,25 +868,21 @@ lemma U_594_3 : have hlg : Real.log (53931693151918417 / 80000000000000000 : ℝ) ≤ (-(1971541650973881459497 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53931693151918417 / 80000000000000000 : ℝ) = - (53931693151918417 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53931693151918417 / 40000000000000000 : ℚ)) - (U := (1494194250526118540503 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53931693151918417 / 40000000000000000 : ℝ) ≤ - (1494194250526118540503 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3370456471981599 / 5000000000000000 : ℝ)) (q := - (53931693151918417 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53931693151918417 / 80000000000000000 : ℚ)) + (r' := (53931693151918417 / 40000000000000000 : ℚ)) + (U := (-(1971541650973881459497 / 5000000000000000000000 : ℚ))) + (U' := (1494194250526118540503 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (3370456471981599 / 5000000000000000 : ℚ)) + (q := (53931693151918417 / 80000000000000000 : ℚ)) + (U := (-(1971541650973881459497 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_4 : Uω (aρ 4) (bρ 4) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1023,25 +890,21 @@ lemma U_594_4 : have hlg : Real.log (53297096084644953 / 80000000000000000 : ℝ) ≤ (-(2030723935954041162807 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53297096084644953 / 80000000000000000 : ℝ) = - (53297096084644953 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53297096084644953 / 40000000000000000 : ℚ)) - (U := (1435011965545958837193 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53297096084644953 / 40000000000000000 : ℝ) ≤ - (1435011965545958837193 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (832569732276229 / 1250000000000000 : ℝ)) (q := - (53297096084644953 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53297096084644953 / 80000000000000000 : ℚ)) + (r' := (53297096084644953 / 40000000000000000 : ℚ)) + (U := (-(2030723935954041162807 / 5000000000000000000000 : ℚ))) + (U' := (1435011965545958837193 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (832569732276229 / 1250000000000000 : ℚ)) + (q := (53297096084644953 / 80000000000000000 : ℚ)) + (U := (-(2030723935954041162807 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_5 : Uω (aρ 5) (bρ 5) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1049,25 +912,21 @@ lemma U_594_5 : have hlg : Real.log (52331644181492417 / 80000000000000000 : ℝ) ≤ (-(4244253950414137293169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52331644181492417 / 80000000000000000 : ℝ) = - (52331644181492417 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52331644181492417 / 40000000000000000 : ℚ)) - (U := (2687217852585862706831 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52331644181492417 / 40000000000000000 : ℝ) ≤ - (2687217852585862706831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3268692400878349 / 5000000000000000 : ℝ)) (q := - (52331644181492417 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52331644181492417 / 80000000000000000 : ℚ)) + (r' := (52331644181492417 / 40000000000000000 : ℚ)) + (U := (-(4244253950414137293169 / 10000000000000000000000 : ℚ))) + (U' := (2687217852585862706831 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (3268692400878349 / 5000000000000000 : ℚ)) + (q := (52331644181492417 / 80000000000000000 : ℚ)) + (U := (-(4244253950414137293169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_6 : Uω (aρ 6) (bρ 6) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1075,25 +934,21 @@ lemma U_594_6 : have hlg : Real.log (50949207983937341 / 80000000000000000 : ℝ) ≤ (-(4511974198329091467151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50949207983937341 / 80000000000000000 : ℝ) = - (50949207983937341 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50949207983937341 / 40000000000000000 : ℚ)) - (U := (2419497604670908532849 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50949207983937341 / 40000000000000000 : ℝ) ≤ - (2419497604670908532849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6359016127507929 / 10000000000000000 : ℝ)) (q := - (50949207983937341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50949207983937341 / 80000000000000000 : ℚ)) + (r' := (50949207983937341 / 40000000000000000 : ℚ)) + (U := (-(4511974198329091467151 / 10000000000000000000000 : ℚ))) + (U' := (2419497604670908532849 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (6359016127507929 / 10000000000000000 : ℚ)) + (q := (50949207983937341 / 80000000000000000 : ℚ)) + (U := (-(4511974198329091467151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_7 : Uω (aρ 7) (bρ 7) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1101,25 +956,21 @@ lemma U_594_7 : have hlg : Real.log (49067858339705593 / 80000000000000000 : ℝ) ≤ (-(2444112151337690036797 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49067858339705593 / 80000000000000000 : ℝ) = - (49067858339705593 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49067858339705593 / 40000000000000000 : ℚ)) - (U := (1021623750162309963203 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49067858339705593 / 40000000000000000 : ℝ) ≤ - (1021623750162309963203 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (764042512151249 / 1250000000000000 : ℝ)) (q := - (49067858339705593 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49067858339705593 / 80000000000000000 : ℚ)) + (r' := (49067858339705593 / 40000000000000000 : ℚ)) + (U := (-(2444112151337690036797 / 5000000000000000000000 : ℚ))) + (U' := (1021623750162309963203 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (764042512151249 / 1250000000000000 : ℚ)) + (q := (49067858339705593 / 80000000000000000 : ℚ)) + (U := (-(2444112151337690036797 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_8 : Uω (aρ 8) (bρ 8) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1127,25 +978,21 @@ lemma U_594_8 : have hlg : Real.log (46622406682957993 / 80000000000000000 : ℝ) ≤ (-(43195630299015583237 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46622406682957993 / 80000000000000000 : ℝ) = - (46622406682957993 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46622406682957993 / 40000000000000000 : ℚ)) - (U := (12256144124984416763 / 80000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46622406682957993 / 40000000000000000 : ℝ) ≤ - (12256144124984416763 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1446129708590773 / 2500000000000000 : ℝ)) (q := - (46622406682957993 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46622406682957993 / 80000000000000000 : ℚ)) + (r' := (46622406682957993 / 40000000000000000 : ℚ)) + (U := (-(43195630299015583237 / 80000000000000000000 : ℚ))) + (U' := (12256144124984416763 / 80000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (1446129708590773 / 2500000000000000 : ℚ)) + (q := (46622406682957993 / 80000000000000000 : ℚ)) + (U := (-(43195630299015583237 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_9 : Uω (aρ 9) (bρ 9) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1153,25 +1000,21 @@ lemma U_594_9 : have hlg : Real.log (43575813125483009 / 80000000000000000 : ℝ) ≤ (-(1215048765630322143733 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43575813125483009 / 80000000000000000 : ℝ) = - (43575813125483009 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43575813125483009 / 40000000000000000 : ℚ)) - (U := (171245594969677856267 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43575813125483009 / 40000000000000000 : ℝ) ≤ - (171245594969677856267 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2681918036677173 / 5000000000000000 : ℝ)) (q := - (43575813125483009 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43575813125483009 / 80000000000000000 : ℚ)) + (r' := (43575813125483009 / 40000000000000000 : ℚ)) + (U := (-(1215048765630322143733 / 2000000000000000000000 : ℚ))) + (U' := (171245594969677856267 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (2681918036677173 / 5000000000000000 : ℚ)) + (q := (43575813125483009 / 80000000000000000 : ℚ)) + (U := (-(1215048765630322143733 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_10 : Uω (aρ 10) (bρ 10) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1179,26 +1022,21 @@ lemma U_594_10 : have hlg : Real.log (39926462127377373 / 80000000000000000 : ℝ) ≤ (-(1389974637746149243031 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (39926462127377373 / 80000000000000000 : ℝ) = - (39926462127377373 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39926462127377373 / 20000000000000000 : ℚ)) - (U := (1382614083453850756969 / 2000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (39926462127377373 / 20000000000000000 : ℝ) ≤ - (1382614083453850756969 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4840057357322937 / 10000000000000000 : ℝ)) (q := - (39926462127377373 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39926462127377373 / 80000000000000000 : ℚ)) + (r' := (39926462127377373 / 20000000000000000 : ℚ)) + (U := (-(1389974637746149243031 / 2000000000000000000000 : ℚ))) + (U' := (1382614083453850756969 / 2000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (4840057357322937 / 10000000000000000 : ℚ)) + (q := (39926462127377373 / 80000000000000000 : ℚ)) + (U := (-(1389974637746149243031 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_11 : Uω (aρ 11) (bρ 11) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1206,26 +1044,21 @@ lemma U_594_11 : have hlg : Real.log (35706625255963241 / 80000000000000000 : ℝ) ≤ (-(8066903811869647594891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35706625255963241 / 80000000000000000 : ℝ) = - (35706625255963241 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35706625255963241 / 20000000000000000 : ℚ)) - (U := (5796039794130352405109 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35706625255963241 / 20000000000000000 : ℝ) ≤ - (5796039794130352405109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1050893691418601 / 2500000000000000 : ℝ)) (q := - (35706625255963241 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35706625255963241 / 80000000000000000 : ℚ)) + (r' := (35706625255963241 / 20000000000000000 : ℚ)) + (U := (-(8066903811869647594891 / 10000000000000000000000 : ℚ))) + (U' := (5796039794130352405109 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (1050893691418601 / 2500000000000000 : ℚ)) + (q := (35706625255963241 / 80000000000000000 : ℚ)) + (U := (-(8066903811869647594891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_12 : Uω (aρ 12) (bρ 12) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1233,26 +1066,21 @@ lemma U_594_12 : have hlg : Real.log (30962445048721753 / 80000000000000000 : ℝ) ≤ (-(4746258070544322986259 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (30962445048721753 / 80000000000000000 : ℝ) = - (30962445048721753 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30962445048721753 / 20000000000000000 : ℚ)) - (U := (2185213732455677013741 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30962445048721753 / 20000000000000000 : ℝ) ≤ - (2185213732455677013741 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (430153726318629 / 1250000000000000 : ℝ)) (q := - (30962445048721753 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30962445048721753 / 80000000000000000 : ℚ)) + (r' := (30962445048721753 / 20000000000000000 : ℚ)) + (U := (-(4746258070544322986259 / 5000000000000000000000 : ℚ))) + (U' := (2185213732455677013741 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (430153726318629 / 1250000000000000 : ℚ)) + (q := (30962445048721753 / 80000000000000000 : ℚ)) + (U := (-(4746258070544322986259 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_13 : Uω (aρ 13) (bρ 13) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1260,26 +1088,21 @@ lemma U_594_13 : have hlg : Real.log (25678547385049509 / 80000000000000000 : ℝ) ≤ (-(2272741445869784425119 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25678547385049509 / 80000000000000000 : ℝ) = - (25678547385049509 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25678547385049509 / 20000000000000000 : ℚ)) - (U := (499847275330215574881 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25678547385049509 / 20000000000000000 : ℝ) ≤ - (499847275330215574881 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2519637136225971 / 10000000000000000 : ℝ)) (q := - (25678547385049509 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25678547385049509 / 80000000000000000 : ℚ)) + (r' := (25678547385049509 / 20000000000000000 : ℚ)) + (U := (-(2272741445869784425119 / 2000000000000000000000 : ℚ))) + (U' := (499847275330215574881 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (2519637136225971 / 10000000000000000 : ℚ)) + (q := (25678547385049509 / 80000000000000000 : ℚ)) + (U := (-(2272741445869784425119 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_14 : Uω (aρ 14) (bρ 14) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1287,26 +1110,21 @@ lemma U_594_14 : have hlg : Real.log (19312076277633053 / 80000000000000000 : ℝ) ≤ (-(14212960197935088470847 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19312076277633053 / 80000000000000000 : ℝ) = - (19312076277633053 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19312076277633053 / 10000000000000000 : ℚ)) - (U := (6581455211064911529153 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19312076277633053 / 10000000000000000 : ℝ) ≤ - (6581455211064911529153 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1271946644416857 / 10000000000000000 : ℝ)) (q := - (19312076277633053 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19312076277633053 / 80000000000000000 : ℚ)) + (r' := (19312076277633053 / 10000000000000000 : ℚ)) + (U := (-(14212960197935088470847 / 10000000000000000000000 : ℚ))) + (U' := (6581455211064911529153 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (44017105158153 / 64000000000000 : ℚ)) + (s := (1271946644416857 / 10000000000000000 : ℚ)) + (q := (19312076277633053 / 80000000000000000 : ℚ)) + (U := (-(14212960197935088470847 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_594_15 : Uω (aρ 15) (bρ 15) (44017105158153 / 64000000000000 : ℝ) ≤ @@ -1408,25 +1226,21 @@ lemma U_595_1 : have hlg : Real.log (27285056545222829 / 40000000000000000 : ℝ) ≤ (-(3825402808256825816339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27285056545222829 / 40000000000000000 : ℝ) = - (27285056545222829 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27285056545222829 / 20000000000000000 : ℚ)) - (U := (3106068994743174183661 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27285056545222829 / 20000000000000000 : ℝ) ≤ - (3106068994743174183661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6821240435730477 / 10000000000000000 : ℝ)) (q := - (27285056545222829 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27285056545222829 / 40000000000000000 : ℚ)) + (r' := (27285056545222829 / 20000000000000000 : ℚ)) + (U := (-(3825402808256825816339 / 10000000000000000000000 : ℚ))) + (U' := (3106068994743174183661 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (6821240435730477 / 10000000000000000 : ℚ)) + (q := (27285056545222829 / 40000000000000000 : ℚ)) + (U := (-(3825402808256825816339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_2 : Uω (aρ 2) (bρ 2) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1434,25 +1248,21 @@ lemma U_595_2 : have hlg : Real.log (27189450980663139 / 40000000000000000 : ℝ) ≤ (-(965125968428573373733 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27189450980663139 / 40000000000000000 : ℝ) = - (27189450980663139 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27189450980663139 / 20000000000000000 : ℚ)) - (U := (767741982321426626267 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27189450980663139 / 20000000000000000 : ℝ) ≤ - (767741982321426626267 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (849650833245079 / 1250000000000000 : ℝ)) (q := - (27189450980663139 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27189450980663139 / 40000000000000000 : ℚ)) + (r' := (27189450980663139 / 20000000000000000 : ℚ)) + (U := (-(965125968428573373733 / 2500000000000000000000 : ℚ))) + (U' := (767741982321426626267 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (849650833245079 / 1250000000000000 : ℚ)) + (q := (27189450980663139 / 40000000000000000 : ℚ)) + (U := (-(965125968428573373733 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_3 : Uω (aρ 3) (bρ 3) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1460,25 +1270,21 @@ lemma U_595_3 : have hlg : Real.log (215986389681133 / 320000000000000 : ℝ) ≤ (-(786211201140834157933 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (215986389681133 / 320000000000000 : ℝ) = - (215986389681133 / 160000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (215986389681133 / 160000000000000 : ℚ)) - (U := (600083159459165842067 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (215986389681133 / 160000000000000 : ℝ) ≤ - (600083159459165842067 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53992213096399 / 80000000000000 : ℝ)) (q := - (215986389681133 / 320000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (215986389681133 / 320000000000000 : ℚ)) + (r' := (215986389681133 / 160000000000000 : ℚ)) + (U := (-(786211201140834157933 / 2000000000000000000000 : ℚ))) + (U' := (600083159459165842067 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (53992213096399 / 80000000000000 : ℚ)) + (q := (215986389681133 / 320000000000000 : ℚ)) + (U := (-(786211201140834157933 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_4 : Uω (aρ 4) (bρ 4) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1486,25 +1292,21 @@ lemma U_595_4 : have hlg : Real.log (5336201044486767 / 8000000000000000 : ℝ) ≤ (-(2024637782567805178767 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5336201044486767 / 8000000000000000 : ℝ) = - (5336201044486767 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5336201044486767 / 4000000000000000 : ℚ)) - (U := (1441098118932194821233 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5336201044486767 / 4000000000000000 : ℝ) ≤ - (1441098118932194821233 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (333433703713049 / 500000000000000 : ℝ)) (q := - (5336201044486767 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5336201044486767 / 8000000000000000 : ℚ)) + (r' := (5336201044486767 / 4000000000000000 : ℚ)) + (U := (-(2024637782567805178767 / 5000000000000000000000 : ℚ))) + (U' := (1441098118932194821233 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (333433703713049 / 500000000000000 : ℚ)) + (q := (5336201044486767 / 8000000000000000 : ℚ)) + (U := (-(2024637782567805178767 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_5 : Uω (aρ 5) (bρ 5) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1512,25 +1314,21 @@ lemma U_595_5 : have hlg : Real.log (5239658353493659 / 8000000000000000 : ℝ) ≤ (-(528981556159355254323 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5239658353493659 / 8000000000000000 : ℝ) = - (5239658353493659 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5239658353493659 / 4000000000000000 : ℚ)) - (U := (337452419215644745677 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5239658353493659 / 4000000000000000 : ℝ) ≤ - (337452419215644745677 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (654550726611321 / 1000000000000000 : ℝ)) (q := - (5239658353493659 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5239658353493659 / 8000000000000000 : ℚ)) + (r' := (5239658353493659 / 4000000000000000 : ℚ)) + (U := (-(528981556159355254323 / 1250000000000000000000 : ℚ))) + (U' := (337452419215644745677 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (654550726611321 / 1000000000000000 : ℚ)) + (q := (5239658353493659 / 8000000000000000 : ℚ)) + (U := (-(528981556159355254323 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_6 : Uω (aρ 6) (bρ 6) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1538,25 +1336,21 @@ lemma U_595_6 : have hlg : Real.log (25507102591140369 / 40000000000000000 : ℝ) ≤ (-(4499225074868244073119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25507102591140369 / 40000000000000000 : ℝ) = - (25507102591140369 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25507102591140369 / 20000000000000000 : ℚ)) - (U := (2432246728131755926881 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25507102591140369 / 20000000000000000 : ℝ) ≤ - (2432246728131755926881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6367153053089247 / 10000000000000000 : ℝ)) (q := - (25507102591140369 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25507102591140369 / 40000000000000000 : ℚ)) + (r' := (25507102591140369 / 20000000000000000 : ℚ)) + (U := (-(4499225074868244073119 / 10000000000000000000000 : ℚ))) + (U' := (2432246728131755926881 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (6367153053089247 / 10000000000000000 : ℚ)) + (q := (25507102591140369 / 40000000000000000 : ℚ)) + (U := (-(4499225074868244073119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_7 : Uω (aρ 7) (bρ 7) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1564,25 +1358,21 @@ lemma U_595_7 : have hlg : Real.log (24566490757328667 / 40000000000000000 : ℝ) ≤ (-(97499220768220577801 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24566490757328667 / 40000000000000000 : ℝ) = - (24566490757328667 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24566490757328667 / 20000000000000000 : ℚ)) - (U := (41130215291779422199 / 200000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24566490757328667 / 20000000000000000 : ℝ) ≤ - (41130215291779422199 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1530127129235849 / 2500000000000000 : ℝ)) (q := - (24566490757328667 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24566490757328667 / 40000000000000000 : ℚ)) + (r' := (24566490757328667 / 20000000000000000 : ℚ)) + (U := (-(97499220768220577801 / 200000000000000000000 : ℚ))) + (U' := (41130215291779422199 / 200000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (1530127129235849 / 2500000000000000 : ℚ)) + (q := (24566490757328667 / 40000000000000000 : ℚ)) + (U := (-(97499220768220577801 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_8 : Uω (aρ 8) (bρ 8) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1590,25 +1380,21 @@ lemma U_595_8 : have hlg : Real.log (23343895294572749 / 40000000000000000 : ℝ) ≤ (-(5385439474086395814851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23343895294572749 / 40000000000000000 : ℝ) = - (23343895294572749 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23343895294572749 / 20000000000000000 : ℚ)) - (U := (1546032328913604185149 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23343895294572749 / 20000000000000000 : ℝ) ≤ - (1546032328913604185149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5792752436905437 / 10000000000000000 : ℝ)) (q := - (23343895294572749 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23343895294572749 / 40000000000000000 : ℚ)) + (r' := (23343895294572749 / 20000000000000000 : ℚ)) + (U := (-(5385439474086395814851 / 10000000000000000000000 : ℚ))) + (U' := (1546032328913604185149 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (5792752436905437 / 10000000000000000 : ℚ)) + (q := (23343895294572749 / 40000000000000000 : ℚ)) + (U := (-(5385439474086395814851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_9 : Uω (aρ 9) (bρ 9) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1616,25 +1402,21 @@ lemma U_595_9 : have hlg : Real.log (21820858261355787 / 40000000000000000 : ℝ) ≤ (-(94689553206502731041 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21820858261355787 / 40000000000000000 : ℝ) = - (21820858261355787 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21820858261355787 / 20000000000000000 : ℚ)) - (U := (13614693715372268959 / 156250000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21820858261355787 / 20000000000000000 : ℝ) ≤ - (13614693715372268959 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1343049887164239 / 2500000000000000 : ℝ)) (q := - (21820858261355787 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21820858261355787 / 40000000000000000 : ℚ)) + (r' := (21820858261355787 / 20000000000000000 : ℚ)) + (U := (-(94689553206502731041 / 156250000000000000000 : ℚ))) + (U' := (13614693715372268959 / 156250000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (1343049887164239 / 2500000000000000 : ℚ)) + (q := (21820858261355787 / 40000000000000000 : ℚ)) + (U := (-(94689553206502731041 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_10 : Uω (aρ 10) (bρ 10) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1642,26 +1424,21 @@ lemma U_595_10 : have hlg : Real.log (19996689501341251 / 40000000000000000 : ℝ) ≤ (-(3466563593368778755967 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19996689501341251 / 40000000000000000 : ℝ) = - (19996689501341251 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19996689501341251 / 10000000000000000 : ℚ)) - (U := (3464908209631221244033 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (19996689501341251 / 10000000000000000 : ℝ) ≤ - (3464908209631221244033 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (303042137634043 / 625000000000000 : ℝ)) (q := - (19996689501341251 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19996689501341251 / 40000000000000000 : ℚ)) + (r' := (19996689501341251 / 10000000000000000 : ℚ)) + (U := (-(3466563593368778755967 / 5000000000000000000000 : ℚ))) + (U' := (3464908209631221244033 / 5000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (303042137634043 / 625000000000000 : ℚ)) + (q := (19996689501341251 / 40000000000000000 : ℚ)) + (U := (-(3466563593368778755967 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_11 : Uω (aρ 11) (bρ 11) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1669,26 +1446,21 @@ lemma U_595_11 : have hlg : Real.log (17887763190387439 / 40000000000000000 : ℝ) ≤ (-(502976621982016817177 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17887763190387439 / 40000000000000000 : ℝ) = - (17887763190387439 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17887763190387439 / 10000000000000000 : ℚ)) - (U := (363457353392983182823 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17887763190387439 / 10000000000000000 : ℝ) ≤ - (363457353392983182823 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2106343836436391 / 5000000000000000 : ℝ)) (q := - (17887763190387439 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17887763190387439 / 40000000000000000 : ℚ)) + (r' := (17887763190387439 / 10000000000000000 : ℚ)) + (U := (-(502976621982016817177 / 625000000000000000000 : ℚ))) + (U' := (363457353392983182823 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (2106343836436391 / 5000000000000000 : ℚ)) + (q := (17887763190387439 / 40000000000000000 : ℚ)) + (U := (-(502976621982016817177 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_12 : Uω (aρ 12) (bρ 12) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1696,26 +1468,21 @@ lemma U_595_12 : have hlg : Real.log (15517707347238349 / 40000000000000000 : ℝ) ≤ (-(9468976722227678351319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15517707347238349 / 40000000000000000 : ℝ) = - (15517707347238349 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15517707347238349 / 10000000000000000 : ℚ)) - (U := (4393966883772321648681 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15517707347238349 / 10000000000000000 : ℝ) ≤ - (4393966883772321648681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3451359847983237 / 10000000000000000 : ℝ)) (q := - (15517707347238349 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15517707347238349 / 40000000000000000 : ℚ)) + (r' := (15517707347238349 / 10000000000000000 : ℚ)) + (U := (-(9468976722227678351319 / 10000000000000000000000 : ℚ))) + (U' := (4393966883772321648681 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (3451359847983237 / 10000000000000000 : ℚ)) + (q := (15517707347238349 / 40000000000000000 : ℚ)) + (U := (-(9468976722227678351319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_13 : Uω (aρ 13) (bρ 13) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1723,26 +1490,21 @@ lemma U_595_13 : have hlg : Real.log (2576115101430907 / 8000000000000000 : ℝ) ≤ (-(708224407302227743551 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2576115101430907 / 8000000000000000 : ℝ) = - (2576115101430907 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2576115101430907 / 2000000000000000 : ℚ)) - (U := (158209568072772256449 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2576115101430907 / 2000000000000000 : ℝ) ≤ - (158209568072772256449 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (253217566953633 / 1000000000000000 : ℝ)) (q := - (2576115101430907 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2576115101430907 / 8000000000000000 : ℚ)) + (r' := (2576115101430907 / 2000000000000000 : ℚ)) + (U := (-(708224407302227743551 / 625000000000000000000 : ℚ))) + (U' := (158209568072772256449 / 625000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (253217566953633 / 1000000000000000 : ℚ)) + (q := (2576115101430907 / 8000000000000000 : ℚ)) + (U := (-(708224407302227743551 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_14 : Uω (aρ 14) (bρ 14) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1750,26 +1512,21 @@ lemma U_595_14 : have hlg : Real.log (9717277055474861 / 40000000000000000 : ℝ) ≤ (-(1768717515541818394809 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9717277055474861 / 40000000000000000 : ℝ) = - (9717277055474861 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9717277055474861 / 5000000000000000 : ℚ)) - (U := (830584410583181605191 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9717277055474861 / 5000000000000000 : ℝ) ≤ - (830584410583181605191 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1294453728741493 / 10000000000000000 : ℝ)) (q := - (9717277055474861 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9717277055474861 / 40000000000000000 : ℚ)) + (r' := (9717277055474861 / 5000000000000000 : ℚ)) + (U := (-(1768717515541818394809 / 1250000000000000000000 : ℚ))) + (U' := (830584410583181605191 / 1250000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22034512175891 / 32000000000000 : ℚ)) + (s := (1294453728741493 / 10000000000000000 : ℚ)) + (q := (9717277055474861 / 40000000000000000 : ℚ)) + (U := (-(1768717515541818394809 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_595_15 : Uω (aρ 15) (bρ 15) (22034512175891 / 32000000000000 : ℝ) ≤ @@ -1868,25 +1625,21 @@ lemma U_596_1 : have hlg : Real.log (54635012307707267 / 80000000000000000 : ℝ) ≤ (-(3813517061197737683561 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54635012307707267 / 80000000000000000 : ℝ) = - (54635012307707267 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54635012307707267 / 40000000000000000 : ℚ)) - (U := (3117954741802262316439 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54635012307707267 / 40000000000000000 : ℝ) ≤ - (3117954741802262316439 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1707338216510337 / 2500000000000000 : ℝ)) (q := - (54635012307707267 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54635012307707267 / 80000000000000000 : ℚ)) + (r' := (54635012307707267 / 40000000000000000 : ℚ)) + (U := (-(3813517061197737683561 / 10000000000000000000000 : ℚ))) + (U' := (3117954741802262316439 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (1707338216510337 / 2500000000000000 : ℚ)) + (q := (54635012307707267 / 80000000000000000 : ℚ)) + (U := (-(3813517061197737683561 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_2 : Uω (aρ 2) (bρ 2) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -1894,25 +1647,21 @@ lemma U_596_2 : have hlg : Real.log (54443802441813363 / 80000000000000000 : ℝ) ≤ (-(962144031500172235307 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54443802441813363 / 80000000000000000 : ℝ) = - (54443802441813363 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54443802441813363 / 40000000000000000 : ℚ)) - (U := (770723919249827764693 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54443802441813363 / 40000000000000000 : ℝ) ≤ - (770723919249827764693 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (425332463254867 / 625000000000000 : ℝ)) (q := - (54443802441813363 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54443802441813363 / 80000000000000000 : ℚ)) + (r' := (54443802441813363 / 40000000000000000 : ℚ)) + (U := (-(962144031500172235307 / 2500000000000000000000 : ℚ))) + (U' := (770723919249827764693 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (425332463254867 / 625000000000000 : ℚ)) + (q := (54443802441813363 / 80000000000000000 : ℚ)) + (U := (-(962144031500172235307 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_3 : Uω (aρ 3) (bρ 3) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -1920,25 +1669,21 @@ lemma U_596_3 : have hlg : Real.log (54061501675977919 / 80000000000000000 : ℝ) ≤ (-(1959521580007089325513 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54061501675977919 / 80000000000000000 : ℝ) = - (54061501675977919 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54061501675977919 / 40000000000000000 : ℚ)) - (U := (1506214321492910674487 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54061501675977919 / 40000000000000000 : ℝ) ≤ - (1506214321492910674487 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6757140326969011 / 10000000000000000 : ℝ)) (q := - (54061501675977919 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54061501675977919 / 80000000000000000 : ℚ)) + (r' := (54061501675977919 / 40000000000000000 : ℚ)) + (U := (-(1959521580007089325513 / 5000000000000000000000 : ℚ))) + (U' := (1506214321492910674487 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (6757140326969011 / 10000000000000000 : ℚ)) + (q := (54061501675977919 / 80000000000000000 : ℚ)) + (U := (-(1959521580007089325513 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_4 : Uω (aρ 4) (bρ 4) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -1946,25 +1691,21 @@ lemma U_596_4 : have hlg : Real.log (53426924767736511 / 80000000000000000 : ℝ) ≤ (-(2018559031924290803153 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53426924767736511 / 80000000000000000 : ℝ) = - (53426924767736511 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53426924767736511 / 40000000000000000 : ℚ)) - (U := (1447176869575709196847 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53426924767736511 / 40000000000000000 : ℝ) ≤ - (1447176869575709196847 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6676790280973659 / 10000000000000000 : ℝ)) (q := - (53426924767736511 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53426924767736511 / 80000000000000000 : ℚ)) + (r' := (53426924767736511 / 40000000000000000 : ℚ)) + (U := (-(2018559031924290803153 / 5000000000000000000000 : ℚ))) + (U' := (1447176869575709196847 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (6676790280973659 / 10000000000000000 : ℚ)) + (q := (53426924767736511 / 80000000000000000 : ℚ)) + (U := (-(2018559031924290803153 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_5 : Uω (aρ 5) (bρ 5) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -1972,25 +1713,21 @@ lemma U_596_5 : have hlg : Real.log (10492304557679267 / 16000000000000000 : ℝ) ≤ (-(105486658196741034191 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10492304557679267 / 16000000000000000 : ℝ) = - (10492304557679267 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10492304557679267 / 8000000000000000 : ℚ)) - (U := (67800136878258965809 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10492304557679267 / 8000000000000000 : ℝ) ≤ - (67800136878258965809 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1310725941094723 / 2000000000000000 : ℝ)) (q := - (10492304557679267 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10492304557679267 / 16000000000000000 : ℚ)) + (r' := (10492304557679267 / 8000000000000000 : ℚ)) + (U := (-(105486658196741034191 / 250000000000000000000 : ℚ))) + (U' := (67800136878258965809 / 250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (1310725941094723 / 2000000000000000 : ℚ)) + (q := (10492304557679267 / 16000000000000000 : ℚ)) + (U := (-(105486658196741034191 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_6 : Uω (aρ 6) (bρ 6) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -1998,25 +1735,21 @@ lemma U_596_6 : have hlg : Real.log (51079202130316507 / 80000000000000000 : ℝ) ≤ (-(4486492233732258104221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51079202130316507 / 80000000000000000 : ℝ) = - (51079202130316507 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51079202130316507 / 40000000000000000 : ℚ)) - (U := (2444979569267741895779 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51079202130316507 / 40000000000000000 : ℝ) ≤ - (2444979569267741895779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3187644958046829 / 5000000000000000 : ℝ)) (q := - (51079202130316507 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51079202130316507 / 80000000000000000 : ℚ)) + (r' := (51079202130316507 / 40000000000000000 : ℚ)) + (U := (-(4486492233732258104221 / 10000000000000000000000 : ℚ))) + (U' := (2444979569267741895779 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (3187644958046829 / 5000000000000000 : ℚ)) + (q := (51079202130316507 / 80000000000000000 : ℚ)) + (U := (-(4486492233732258104221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_7 : Uω (aρ 7) (bρ 7) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2024,25 +1757,21 @@ lemma U_596_7 : have hlg : Real.log (49198104094068487 / 80000000000000000 : ℝ) ≤ (-(4861715463315582096821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49198104094068487 / 80000000000000000 : ℝ) = - (49198104094068487 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49198104094068487 / 40000000000000000 : ℚ)) - (U := (2069756339684417903179 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49198104094068487 / 40000000000000000 : ℝ) ≤ - (2069756339684417903179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6128676787791653 / 10000000000000000 : ℝ)) (q := - (49198104094068487 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49198104094068487 / 80000000000000000 : ℚ)) + (r' := (49198104094068487 / 40000000000000000 : ℚ)) + (U := (-(4861715463315582096821 / 10000000000000000000000 : ℚ))) + (U' := (2069756339684417903179 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (6128676787791653 / 10000000000000000 : ℚ)) + (q := (49198104094068487 / 80000000000000000 : ℚ)) + (U := (-(4861715463315582096821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_8 : Uω (aρ 8) (bρ 8) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2050,25 +1779,21 @@ lemma U_596_8 : have hlg : Real.log (46753173128945367 / 80000000000000000 : ℝ) ≤ (-(42971560525332844949 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46753173128945367 / 80000000000000000 : ℝ) = - (46753173128945367 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46753173128945367 / 40000000000000000 : ℚ)) - (U := (12480213898667155051 / 80000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46753173128945367 / 40000000000000000 : ℝ) ≤ - (12480213898667155051 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5800985697850873 / 10000000000000000 : ℝ)) (q := - (46753173128945367 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46753173128945367 / 80000000000000000 : ℚ)) + (r' := (46753173128945367 / 40000000000000000 : ℚ)) + (U := (-(42971560525332844949 / 80000000000000000000 : ℚ))) + (U' := (12480213898667155051 / 80000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (5800985697850873 / 10000000000000000 : ℚ)) + (q := (46753173128945367 / 80000000000000000 : ℚ)) + (U := (-(42971560525332844949 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_9 : Uω (aρ 9) (bρ 9) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2076,25 +1801,21 @@ lemma U_596_9 : have hlg : Real.log (43707616844345691 / 80000000000000000 : ℝ) ≤ (-(1209008498005994149171 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43707616844345691 / 80000000000000000 : ℝ) = - (43707616844345691 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43707616844345691 / 40000000000000000 : ℚ)) - (U := (177285862594005850829 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43707616844345691 / 40000000000000000 : ℝ) ≤ - (177285862594005850829 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2690281127530477 / 5000000000000000 : ℝ)) (q := - (43707616844345691 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43707616844345691 / 80000000000000000 : ℚ)) + (r' := (43707616844345691 / 40000000000000000 : ℚ)) + (U := (-(1209008498005994149171 / 2000000000000000000000 : ℚ))) + (U' := (177285862594005850829 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (2690281127530477 / 5000000000000000 : ℚ)) + (q := (43707616844345691 / 80000000000000000 : ℚ)) + (U := (-(1209008498005994149171 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_10 : Uω (aρ 10) (bρ 10) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2102,26 +1823,21 @@ lemma U_596_10 : have hlg : Real.log (40060288928102091 / 80000000000000000 : ℝ) ≤ (-(3458205459091484569321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40060288928102091 / 80000000000000000 : ℝ) = - (40060288928102091 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40060288928102091 / 40000000000000000 : ℚ)) - (U := (7530442408515430679 / 5000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (40060288928102091 / 40000000000000000 : ℝ) ≤ - (7530442408515430679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2428644654747527 / 5000000000000000 : ℝ)) (q := - (40060288928102091 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40060288928102091 / 80000000000000000 : ℚ)) + (r' := (40060288928102091 / 40000000000000000 : ℚ)) + (U := (-(3458205459091484569321 / 5000000000000000000000 : ℚ))) + (U' := (7530442408515430679 / 5000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (2428644654747527 / 5000000000000000 : ℚ)) + (q := (40060288928102091 / 80000000000000000 : ℚ)) + (U := (-(3458205459091484569321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_11 : Uω (aρ 11) (bρ 11) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2129,26 +1845,21 @@ lemma U_596_11 : have hlg : Real.log (35844411176559483 / 80000000000000000 : ℝ) ≤ (-(8028389739178359166687 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35844411176559483 / 80000000000000000 : ℝ) = - (35844411176559483 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35844411176559483 / 20000000000000000 : ℚ)) - (U := (5834553866821640833313 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35844411176559483 / 20000000000000000 : ℝ) ≤ - (5834553866821640833313 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2110898248907201 / 5000000000000000 : ℝ)) (q := - (35844411176559483 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35844411176559483 / 80000000000000000 : ℚ)) + (r' := (35844411176559483 / 20000000000000000 : ℚ)) + (U := (-(8028389739178359166687 / 10000000000000000000000 : ℚ))) + (U' := (5834553866821640833313 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (2110898248907201 / 5000000000000000 : ℚ)) + (q := (35844411176559483 / 80000000000000000 : ℚ)) + (U := (-(8028389739178359166687 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_12 : Uω (aρ 12) (bρ 12) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2156,26 +1867,21 @@ lemma U_596_12 : have hlg : Real.log (31108341806982459 / 80000000000000000 : ℝ) ≤ (-(295172070509336324951 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31108341806982459 / 80000000000000000 : ℝ) = - (31108341806982459 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31108341806982459 / 20000000000000000 : ℚ)) - (U := (138044917178163675049 / 312500000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31108341806982459 / 20000000000000000 : ℝ) ≤ - (138044917178163675049 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1730739626052573 / 5000000000000000 : ℝ)) (q := - (31108341806982459 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31108341806982459 / 80000000000000000 : ℚ)) + (r' := (31108341806982459 / 20000000000000000 : ℚ)) + (U := (-(295172070509336324951 / 312500000000000000000 : ℚ))) + (U' := (138044917178163675049 / 312500000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (1730739626052573 / 5000000000000000 : ℚ)) + (q := (31108341806982459 / 80000000000000000 : ℚ)) + (U := (-(295172070509336324951 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_13 : Uω (aρ 13) (bρ 13) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2183,26 +1889,21 @@ lemma U_596_13 : have hlg : Real.log (25843610965586107 / 80000000000000000 : ℝ) ≤ (-(2259926443505063997727 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25843610965586107 / 80000000000000000 : ℝ) = - (25843610965586107 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25843610965586107 / 20000000000000000 : ℚ)) - (U := (512662277694936002273 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25843610965586107 / 20000000000000000 : ℝ) ≤ - (512662277694936002273 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1272339141675529 / 5000000000000000 : ℝ)) (q := - (25843610965586107 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25843610965586107 / 80000000000000000 : ℚ)) + (r' := (25843610965586107 / 20000000000000000 : ℚ)) + (U := (-(2259926443505063997727 / 2000000000000000000000 : ℚ))) + (U' := (512662277694936002273 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (1272339141675529 / 5000000000000000 : ℚ)) + (q := (25843610965586107 / 80000000000000000 : ℚ)) + (U := (-(2259926443505063997727 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_14 : Uω (aρ 14) (bρ 14) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2210,26 +1911,21 @@ lemma U_596_14 : have hlg : Real.log (19555693060838851 / 80000000000000000 : ℝ) ≤ (-(7043800923483328933247 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19555693060838851 / 80000000000000000 : ℝ) = - (19555693060838851 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19555693060838851 / 10000000000000000 : ℚ)) - (U := (3353406781016671066753 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19555693060838851 / 10000000000000000 : ℝ) ≤ - (3353406781016671066753 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (329156523052311 / 2500000000000000 : ℝ)) (q := - (19555693060838851 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19555693060838851 / 80000000000000000 : ℚ)) + (r' := (19555693060838851 / 10000000000000000 : ℚ)) + (U := (-(7043800923483328933247 / 5000000000000000000000 : ℚ))) + (U' := (3353406781016671066753 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (44120943545411 / 64000000000000 : ℚ)) + (s := (329156523052311 / 2500000000000000 : ℚ)) + (q := (19555693060838851 / 80000000000000000 : ℚ)) + (U := (-(7043800923483328933247 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_596_15 : Uω (aρ 15) (bρ 15) (44120943545411 / 64000000000000 : ℝ) ≤ @@ -2329,24 +2025,21 @@ lemma U_597_1 : have hlg : Real.log (106835764696161 / 156250000000000 : ℝ) ≤ (-(475205678070643602751 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (106835764696161 / 156250000000000 : ℝ) = (106835764696161 / 78125000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (106835764696161 / 78125000000000 : ℚ)) - (U := (391228297304356397249 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (106835764696161 / 78125000000000 : ℝ) ≤ - (391228297304356397249 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (427341581013663 / 625000000000000 : ℝ)) (q := - (106835764696161 / 156250000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (106835764696161 / 156250000000000 : ℚ)) + (r' := (106835764696161 / 78125000000000 : ℚ)) + (U := (-(475205678070643602751 / 1250000000000000000000 : ℚ))) + (U' := (391228297304356397249 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (276080392119 / 400000000000 : ℚ)) + (s := (427341581013663 / 625000000000000 : ℚ)) + (q := (106835764696161 / 156250000000000 : ℚ)) + (U := (-(475205678070643602751 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_2 : Uω (aρ 2) (bρ 2) (276080392119 / 400000000000 : ℝ) ≤ @@ -2354,25 +2047,21 @@ lemma U_597_2 : have hlg : Real.log (1703396966211123 / 2500000000000000 : ℝ) ≤ (-(959165647276513419161 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1703396966211123 / 2500000000000000 : ℝ) = - (1703396966211123 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1703396966211123 / 1250000000000000 : ℚ)) - (U := (773702303473486580839 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1703396966211123 / 1250000000000000 : ℝ) ≤ - (773702303473486580839 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (851679019663623 / 1250000000000000 : ℝ)) (q := - (1703396966211123 / 2500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1703396966211123 / 2500000000000000 : ℚ)) + (r' := (1703396966211123 / 1250000000000000 : ℚ)) + (U := (-(959165647276513419161 / 2500000000000000000000 : ℚ))) + (U' := (773702303473486580839 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (276080392119 / 400000000000 : ℚ)) + (s := (851679019663623 / 1250000000000000 : ℚ)) + (q := (1703396966211123 / 2500000000000000 : ℚ)) + (U := (-(959165647276513419161 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_3 : Uω (aρ 3) (bρ 3) (276080392119 / 400000000000 : ℝ) ≤ @@ -2380,25 +2069,21 @@ lemma U_597_3 : have hlg : Real.log (13531601479762003 / 20000000000000000 : ℝ) ≤ (-(195352236509487228353 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13531601479762003 / 20000000000000000 : ℝ) = - (13531601479762003 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13531601479762003 / 10000000000000000 : ℚ)) - (U := (151221353640512771647 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13531601479762003 / 10000000000000000 : ℝ) ≤ - (151221353640512771647 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6765254013732003 / 10000000000000000 : ℝ)) (q := - (13531601479762003 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13531601479762003 / 20000000000000000 : ℚ)) + (r' := (13531601479762003 / 10000000000000000 : ℚ)) + (U := (-(195352236509487228353 / 500000000000000000000 : ℚ))) + (U' := (151221353640512771647 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (276080392119 / 400000000000 : ℚ)) + (s := (6765254013732003 / 10000000000000000 : ℚ)) + (q := (13531601479762003 / 20000000000000000 : ℚ)) + (U := (-(195352236509487228353 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_4 : Uω (aρ 4) (bρ 4) (276080392119 / 400000000000 : ℝ) ≤ @@ -2406,25 +2091,21 @@ lemma U_597_4 : have hlg : Real.log (6686479881673441 / 10000000000000000 : ℝ) ≤ (-(4024975332057229824131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6686479881673441 / 10000000000000000 : ℝ) = - (6686479881673441 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6686479881673441 / 5000000000000000 : ℚ)) - (U := (2906496470942770175869 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6686479881673441 / 5000000000000000 : ℝ) ≤ - (2906496470942770175869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3342453239190941 / 5000000000000000 : ℝ)) (q := - (6686479881673441 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6686479881673441 / 10000000000000000 : ℚ)) + (r' := (6686479881673441 / 5000000000000000 : ℚ)) + (U := (-(4024975332057229824131 / 10000000000000000000000 : ℚ))) + (U' := (2906496470942770175869 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (276080392119 / 400000000000 : ℚ)) + (s := (3342453239190941 / 5000000000000000 : ℚ)) + (q := (6686479881673441 / 10000000000000000 : ℚ)) + (U := (-(4024975332057229824131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_5 : Uω (aρ 5) (bρ 5) (276080392119 / 400000000000 : ℝ) ≤ @@ -2432,25 +2113,21 @@ lemma U_597_5 : have hlg : Real.log (410362983923773 / 625000000000000 : ℝ) ≤ (-(4207095548052328053339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (410362983923773 / 625000000000000 : ℝ) = - (410362983923773 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (410362983923773 / 312500000000000 : ℚ)) - (U := (2724376254947671946661 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (410362983923773 / 312500000000000 : ℝ) ≤ - (2724376254947671946661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (410109507495671 / 625000000000000 : ℝ)) (q := - (410362983923773 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (410362983923773 / 625000000000000 : ℚ)) + (r' := (410362983923773 / 312500000000000 : ℚ)) + (U := (-(4207095548052328053339 / 10000000000000000000000 : ℚ))) + (U' := (2724376254947671946661 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (276080392119 / 400000000000 : ℚ)) + (s := (410109507495671 / 625000000000000 : ℚ)) + (q := (410362983923773 / 625000000000000 : ℚ)) + (U := (-(4207095548052328053339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_6 : Uω (aρ 6) (bρ 6) (276080392119 / 400000000000 : ℝ) ≤ @@ -2458,25 +2135,21 @@ lemma U_597_6 : have hlg : Real.log (639302485362523 / 1000000000000000 : ℝ) ≤ (-(4473775633260287782671 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (639302485362523 / 1000000000000000 : ℝ) = - (639302485362523 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (639302485362523 / 500000000000000 : ℚ)) - (U := (2457696169739712217329 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (639302485362523 / 500000000000000 : ℝ) ≤ - (2457696169739712217329 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (319171335838023 / 500000000000000 : ℝ)) (q := - (639302485362523 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (639302485362523 / 1000000000000000 : ℚ)) + (r' := (639302485362523 / 500000000000000 : ℚ)) + (U := (-(4473775633260287782671 / 10000000000000000000000 : ℚ))) + (U' := (2457696169739712217329 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (276080392119 / 400000000000 : ℚ)) + (s := (319171335838023 / 500000000000000 : ℚ)) + (q := (639302485362523 / 1000000000000000 : ℚ)) + (U := (-(4473775633260287782671 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_7 : Uω (aρ 7) (bρ 7) (276080392119 / 400000000000 : ℝ) ≤ @@ -2484,25 +2157,21 @@ lemma U_597_7 : have hlg : Real.log (1539475815009909 / 2500000000000000 : ℝ) ≤ (-(4848487529947418754959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1539475815009909 / 2500000000000000 : ℝ) = - (1539475815009909 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1539475815009909 / 1250000000000000 : ℚ)) - (U := (2082984273052581245041 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1539475815009909 / 1250000000000000 : ℝ) ≤ - (2082984273052581245041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (767105613793659 / 1250000000000000 : ℝ)) (q := - (1539475815009909 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1539475815009909 / 2500000000000000 : ℚ)) + (r' := (1539475815009909 / 1250000000000000 : ℚ)) + (U := (-(4848487529947418754959 / 10000000000000000000000 : ℚ))) + (U' := (2082984273052581245041 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (276080392119 / 400000000000 : ℚ)) + (s := (767105613793659 / 1250000000000000 : ℚ)) + (q := (1539475815009909 / 2500000000000000 : ℚ)) + (U := (-(4848487529947418754959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_8 : Uω (aρ 8) (bρ 8) (276080392119 / 400000000000 : ℝ) ≤ @@ -2510,25 +2179,21 @@ lemma U_597_8 : have hlg : Real.log (2926159644260453 / 5000000000000000 : ℝ) ≤ (-(214298820193377640081 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2926159644260453 / 5000000000000000 : ℝ) = - (2926159644260453 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2926159644260453 / 2500000000000000 : ℚ)) - (U := (62960051926622359919 / 400000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2926159644260453 / 2500000000000000 : ℝ) ≤ - (62960051926622359919 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1452304654662953 / 2500000000000000 : ℝ)) (q := - (2926159644260453 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2926159644260453 / 5000000000000000 : ℚ)) + (r' := (2926159644260453 / 2500000000000000 : ℚ)) + (U := (-(214298820193377640081 / 400000000000000000000 : ℚ))) + (U' := (62960051926622359919 / 400000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (276080392119 / 400000000000 : ℚ)) + (s := (1452304654662953 / 2500000000000000 : ℚ)) + (q := (2926159644260453 / 5000000000000000 : ℚ)) + (U := (-(214298820193377640081 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_9 : Uω (aρ 9) (bρ 9) (276080392119 / 400000000000 : ℝ) ≤ @@ -2536,25 +2201,21 @@ lemma U_597_9 : have hlg : Real.log (2188675705235189 / 4000000000000000 : ℝ) ≤ (-(6029977007426569530737 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2188675705235189 / 4000000000000000 : ℝ) = - (2188675705235189 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2188675705235189 / 2000000000000000 : ℚ)) - (U := (901494795573430469263 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2188675705235189 / 2000000000000000 : ℝ) ≤ - (901494795573430469263 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1077784839229189 / 2000000000000000 : ℝ)) (q := - (2188675705235189 / 4000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2188675705235189 / 4000000000000000 : ℚ)) + (r' := (2188675705235189 / 2000000000000000 : ℚ)) + (U := (-(6029977007426569530737 / 10000000000000000000000 : ℚ))) + (U' := (901494795573430469263 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (276080392119 / 400000000000 : ℚ)) + (s := (1077784839229189 / 2000000000000000 : ℚ)) + (q := (2188675705235189 / 4000000000000000 : ℚ)) + (U := (-(6029977007426569530737 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_10 : Uω (aρ 10) (bρ 10) (276080392119 / 400000000000 : ℝ) ≤ @@ -2562,26 +2223,21 @@ lemma U_597_10 : have hlg : Real.log (10031797985137643 / 20000000000000000 : ℝ) ≤ (-(107808191664674528683 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10031797985137643 / 20000000000000000 : ℝ) = - (10031797985137643 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10031797985137643 / 10000000000000000 : ℚ)) - (U := (496055257200471317 / 156250000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10031797985137643 / 10000000000000000 : ℝ) ≤ - (496055257200471317 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4865902688602643 / 10000000000000000 : ℝ)) (q := - (10031797985137643 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10031797985137643 / 20000000000000000 : ℚ)) + (r' := (10031797985137643 / 10000000000000000 : ℚ)) + (U := (-(107808191664674528683 / 156250000000000000000 : ℚ))) + (U' := (496055257200471317 / 156250000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (276080392119 / 400000000000 : ℚ)) + (s := (4865902688602643 / 10000000000000000 : ℚ)) + (q := (10031797985137643 / 20000000000000000 : ℚ)) + (U := (-(107808191664674528683 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_11 : Uω (aρ 11) (bρ 11) (276080392119 / 400000000000 : ℝ) ≤ @@ -2589,26 +2245,21 @@ lemma U_597_11 : have hlg : Real.log (8978319937195677 / 20000000000000000 : ℝ) ≤ (-(2002298744056355109751 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8978319937195677 / 20000000000000000 : ℝ) = - (8978319937195677 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8978319937195677 / 5000000000000000 : ℚ)) - (U := (1463437157443644890249 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8978319937195677 / 5000000000000000 : ℝ) ≤ - (1463437157443644890249 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4230901266865677 / 10000000000000000 : ℝ)) (q := - (8978319937195677 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8978319937195677 / 20000000000000000 : ℚ)) + (r' := (8978319937195677 / 5000000000000000 : ℚ)) + (U := (-(2002298744056355109751 / 2500000000000000000000 : ℚ))) + (U' := (1463437157443644890249 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (276080392119 / 400000000000 : ℚ)) + (s := (4230901266865677 / 10000000000000000 : ℚ)) + (q := (8978319937195677 / 20000000000000000 : ℚ)) + (U := (-(2002298744056355109751 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_12 : Uω (aρ 12) (bρ 12) (276080392119 / 400000000000 : ℝ) ≤ @@ -2616,26 +2267,21 @@ lemma U_597_12 : have hlg : Real.log (3897653344772773 / 10000000000000000 : ℝ) ≤ (-(4711052134525300289301 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3897653344772773 / 10000000000000000 : ℝ) = - (3897653344772773 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3897653344772773 / 2500000000000000 : ℚ)) - (U := (2220419668474699710699 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3897653344772773 / 2500000000000000 : ℝ) ≤ - (2220419668474699710699 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1735794057950273 / 5000000000000000 : ℝ)) (q := - (3897653344772773 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3897653344772773 / 10000000000000000 : ℚ)) + (r' := (3897653344772773 / 2500000000000000 : ℚ)) + (U := (-(4711052134525300289301 / 5000000000000000000000 : ℚ))) + (U' := (2220419668474699710699 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (276080392119 / 400000000000 : ℚ)) + (s := (1735794057950273 / 5000000000000000 : ℚ)) + (q := (3897653344772773 / 10000000000000000 : ℚ)) + (U := (-(4711052134525300289301 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_13 : Uω (aρ 13) (bρ 13) (276080392119 / 400000000000 : ℝ) ≤ @@ -2643,26 +2289,21 @@ lemma U_597_13 : have hlg : Real.log (6481482336582191 / 20000000000000000 : ℝ) ≤ (-(1408478791481375428463 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6481482336582191 / 20000000000000000 : ℝ) = - (6481482336582191 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6481482336582191 / 5000000000000000 : ℚ)) - (U := (324389159268624571537 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6481482336582191 / 5000000000000000 : ℝ) ≤ - (324389159268624571537 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2557145504532191 / 10000000000000000 : ℝ)) (q := - (6481482336582191 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6481482336582191 / 20000000000000000 : ℚ)) + (r' := (6481482336582191 / 5000000000000000 : ℚ)) + (U := (-(1408478791481375428463 / 1250000000000000000000 : ℚ))) + (U' := (324389159268624571537 / 1250000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (276080392119 / 400000000000 : ℚ)) + (s := (2557145504532191 / 10000000000000000 : ℚ)) + (q := (6481482336582191 / 20000000000000000 : ℚ)) + (U := (-(1408478791481375428463 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_14 : Uω (aρ 14) (bρ 14) (276080392119 / 400000000000 : ℝ) ≤ @@ -2670,25 +2311,21 @@ lemma U_597_14 : have hlg : Real.log (491888991620867 / 2000000000000000 : ℝ) ≤ (-(7013246972571734108403 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (491888991620867 / 2000000000000000 : ℝ) = - (491888991620867 / 250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (491888991620867 / 250000000000000 : ℚ)) - (U := (3383960731928265891597 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (491888991620867 / 250000000000000 : ℝ) ≤ - (3383960731928265891597 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (133848036920367 / 1000000000000000 : ℝ)) (q := - (491888991620867 / 2000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (491888991620867 / 2000000000000000 : ℚ)) + (r' := (491888991620867 / 250000000000000 : ℚ)) + (U := (-(7013246972571734108403 / 5000000000000000000000 : ℚ))) + (U' := (3383960731928265891597 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (276080392119 / 400000000000 : ℚ)) + (s := (133848036920367 / 1000000000000000 : ℚ)) + (q := (491888991620867 / 2000000000000000 : ℚ)) + (U := (-(7013246972571734108403 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_597_15 : Uω (aρ 15) (bρ 15) (276080392119 / 400000000000 : ℝ) ≤ @@ -2790,25 +2427,21 @@ lemma U_598_1 : have hlg : Real.log (54764810740629053 / 80000000000000000 : ℝ) ≤ (-(3789787864895543404819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54764810740629053 / 80000000000000000 : ℝ) = - (54764810740629053 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54764810740629053 / 40000000000000000 : ℚ)) - (U := (3141683938104456595181 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54764810740629053 / 40000000000000000 : ℝ) ≤ - (3141683938104456595181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1711394431565683 / 2500000000000000 : ℝ)) (q := - (54764810740629053 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54764810740629053 / 80000000000000000 : ℚ)) + (r' := (54764810740629053 / 40000000000000000 : ℚ)) + (U := (-(3789787864895543404819 / 10000000000000000000000 : ℚ))) + (U' := (3141683938104456595181 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (1711394431565683 / 2500000000000000 : ℚ)) + (q := (54764810740629053 / 80000000000000000 : ℚ)) + (U := (-(3789787864895543404819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_2 : Uω (aρ 2) (bρ 2) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2816,25 +2449,21 @@ lemma U_598_2 : have hlg : Real.log (10914720678433329 / 16000000000000000 : ℝ) ≤ (-(3824763229207356151267 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10914720678433329 / 16000000000000000 : ℝ) = - (10914720678433329 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10914720678433329 / 8000000000000000 : ℚ)) - (U := (3106708573792643848733 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (10914720678433329 / 8000000000000000 : ℝ) ≤ - (3106708573792643848733 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (682154490165713 / 1000000000000000 : ℝ)) (q := - (10914720678433329 / 16000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10914720678433329 / 16000000000000000 : ℚ)) + (r' := (10914720678433329 / 8000000000000000 : ℚ)) + (U := (-(3824763229207356151267 / 10000000000000000000000 : ℚ))) + (U' := (3106708573792643848733 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (682154490165713 / 1000000000000000 : ℚ)) + (q := (10914720678433329 / 16000000000000000 : ℚ)) + (U := (-(3824763229207356151267 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_3 : Uω (aρ 3) (bρ 3) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2842,25 +2471,21 @@ lemma U_598_3 : have hlg : Real.log (54191310149538897 / 80000000000000000 : ℝ) ≤ (-(3895060681667598397467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54191310149538897 / 80000000000000000 : ℝ) = - (54191310149538897 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54191310149538897 / 40000000000000000 : ℚ)) - (U := (3036411121332401602533 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54191310149538897 / 40000000000000000 : ℝ) ≤ - (3036411121332401602533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6773367697350193 / 10000000000000000 : ℝ)) (q := - (54191310149538897 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54191310149538897 / 80000000000000000 : ℚ)) + (r' := (54191310149538897 / 40000000000000000 : ℚ)) + (U := (-(3895060681667598397467 / 10000000000000000000000 : ℚ))) + (U' := (3036411121332401602533 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (6773367697350193 / 10000000000000000 : ℚ)) + (q := (54191310149538897 / 80000000000000000 : ℚ)) + (U := (-(3895060681667598397467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_4 : Uω (aρ 4) (bρ 4) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2868,25 +2493,21 @@ lemma U_598_4 : have hlg : Real.log (53556753301956121 / 80000000000000000 : ℝ) ≤ (-(250802958368932343957 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53556753301956121 / 80000000000000000 : ℝ) = - (53556753301956121 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53556753301956121 / 40000000000000000 : ℚ)) - (U := (182414029318567656043 / 625000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53556753301956121 / 40000000000000000 : ℝ) ≤ - (182414029318567656043 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6693022666519499 / 10000000000000000 : ℝ)) (q := - (53556753301956121 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53556753301956121 / 80000000000000000 : ℚ)) + (r' := (53556753301956121 / 40000000000000000 : ℚ)) + (U := (-(250802958368932343957 / 625000000000000000000 : ℚ))) + (U' := (182414029318567656043 / 625000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (6693022666519499 / 10000000000000000 : ℚ)) + (q := (53556753301956121 / 80000000000000000 : ℚ)) + (U := (-(250802958368932343957 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_5 : Uω (aρ 5) (bρ 5) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2894,25 +2515,21 @@ lemma U_598_5 : have hlg : Real.log (52591400996845877 / 80000000000000000 : ℝ) ≤ (-(2097370035909306309519 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52591400996845877 / 80000000000000000 : ℝ) = - (52591400996845877 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52591400996845877 / 40000000000000000 : ℚ)) - (U := (1368365865590693690481 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52591400996845877 / 40000000000000000 : ℝ) ≤ - (1368365865590693690481 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3284937254788469 / 5000000000000000 : ℝ)) (q := - (52591400996845877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52591400996845877 / 80000000000000000 : ℚ)) + (r' := (52591400996845877 / 40000000000000000 : ℚ)) + (U := (-(2097370035909306309519 / 5000000000000000000000 : ℚ))) + (U' := (1368365865590693690481 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (3284937254788469 / 5000000000000000 : ℚ)) + (q := (52591400996845877 / 80000000000000000 : ℚ)) + (U := (-(2097370035909306309519 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_6 : Uω (aρ 6) (bρ 6) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2920,25 +2537,21 @@ lemma U_598_6 : have hlg : Real.log (51209195279289041 / 80000000000000000 : ℝ) ≤ (-(4461075231951651050771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51209195279289041 / 80000000000000000 : ℝ) = - (51209195279289041 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51209195279289041 / 40000000000000000 : ℚ)) - (U := (2470396571048348949229 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51209195279289041 / 40000000000000000 : ℝ) ≤ - (2470396571048348949229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6391563455327729 / 10000000000000000 : ℝ)) (q := - (51209195279289041 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51209195279289041 / 80000000000000000 : ℚ)) + (r' := (51209195279289041 / 40000000000000000 : ℚ)) + (U := (-(4461075231951651050771 / 10000000000000000000000 : ℚ))) + (U' := (2470396571048348949229 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (6391563455327729 / 10000000000000000 : ℚ)) + (q := (51209195279289041 / 80000000000000000 : ℚ)) + (U := (-(4461075231951651050771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_7 : Uω (aρ 7) (bρ 7) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2946,25 +2559,21 @@ lemma U_598_7 : have hlg : Real.log (49328347475768481 / 80000000000000000 : ℝ) ≤ (-(967055438211356976147 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49328347475768481 / 80000000000000000 : ℝ) = - (49328347475768481 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49328347475768481 / 40000000000000000 : ℚ)) - (U := (419238922388643023853 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49328347475768481 / 40000000000000000 : ℝ) ≤ - (419238922388643023853 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6145012885207589 / 10000000000000000 : ℝ)) (q := - (49328347475768481 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49328347475768481 / 80000000000000000 : ℚ)) + (r' := (49328347475768481 / 40000000000000000 : ℚ)) + (U := (-(967055438211356976147 / 2000000000000000000000 : ℚ))) + (U' := (419238922388643023853 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (6145012885207589 / 10000000000000000 : ℚ)) + (q := (49328347475768481 / 80000000000000000 : ℚ)) + (U := (-(967055438211356976147 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_8 : Uω (aρ 8) (bρ 8) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2972,25 +2581,21 @@ lemma U_598_8 : have hlg : Real.log (46883934132587653 / 80000000000000000 : ℝ) ≤ (-(534351573455711606301 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46883934132587653 / 80000000000000000 : ℝ) = - (46883934132587653 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46883934132587653 / 40000000000000000 : ℚ)) - (U := (158795606844288393699 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46883934132587653 / 40000000000000000 : ℝ) ≤ - (158795606844288393699 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2908725600376191 / 5000000000000000 : ℝ)) (q := - (46883934132587653 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46883934132587653 / 80000000000000000 : ℚ)) + (r' := (46883934132587653 / 40000000000000000 : ℚ)) + (U := (-(534351573455711606301 / 1000000000000000000000 : ℚ))) + (U' := (158795606844288393699 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (2908725600376191 / 5000000000000000 : ℚ)) + (q := (46883934132587653 / 80000000000000000 : ℚ)) + (U := (-(534351573455711606301 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_9 : Uω (aρ 9) (bρ 9) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -2998,25 +2603,21 @@ lemma U_598_9 : have hlg : Real.log (43839408318014213 / 80000000000000000 : ℝ) ≤ (-(187966715081535804873 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43839408318014213 / 80000000000000000 : ℝ) = - (43839408318014213 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43839408318014213 / 40000000000000000 : ℚ)) - (U := (28641778762214195127 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43839408318014213 / 40000000000000000 : ℝ) ≤ - (28641778762214195127 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2698642687734511 / 5000000000000000 : ℝ)) (q := - (43839408318014213 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43839408318014213 / 80000000000000000 : ℚ)) + (r' := (43839408318014213 / 40000000000000000 : ℚ)) + (U := (-(187966715081535804873 / 312500000000000000000 : ℚ))) + (U' := (28641778762214195127 / 312500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (2698642687734511 / 5000000000000000 : ℚ)) + (q := (43839408318014213 / 80000000000000000 : ℚ)) + (U := (-(187966715081535804873 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_10 : Uω (aρ 10) (bρ 10) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3024,26 +2625,21 @@ lemma U_598_10 : have hlg : Real.log (8038817615334817 / 16000000000000000 : ℝ) ≤ (-(1720766780932629166881 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8038817615334817 / 16000000000000000 : ℝ) = - (8038817615334817 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8038817615334817 / 8000000000000000 : ℚ)) - (U := (12101169817370833119 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (8038817615334817 / 8000000000000000 : ℝ) ≤ - (12101169817370833119 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (487451434862899 / 1000000000000000 : ℝ)) (q := - (8038817615334817 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8038817615334817 / 16000000000000000 : ℚ)) + (r' := (8038817615334817 / 8000000000000000 : ℚ)) + (U := (-(1720766780932629166881 / 2500000000000000000000 : ℚ))) + (U' := (12101169817370833119 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (487451434862899 / 1000000000000000 : ℚ)) + (q := (8038817615334817 / 16000000000000000 : ℚ)) + (U := (-(1720766780932629166881 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_11 : Uω (aρ 11) (bρ 11) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3051,26 +2647,21 @@ lemma U_598_11 : have hlg : Real.log (35982132201957549 / 80000000000000000 : ℝ) ≤ (-(7990041466326574167593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (35982132201957549 / 80000000000000000 : ℝ) = - (35982132201957549 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35982132201957549 / 20000000000000000 : ℚ)) - (U := (5872902139673425832407 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35982132201957549 / 20000000000000000 : ℝ) ≤ - (5872902139673425832407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (530000250769357 / 1250000000000000 : ℝ)) (q := - (35982132201957549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35982132201957549 / 80000000000000000 : ℚ)) + (r' := (35982132201957549 / 20000000000000000 : ℚ)) + (U := (-(7990041466326574167593 / 10000000000000000000000 : ℚ))) + (U' := (5872902139673425832407 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (530000250769357 / 1250000000000000 : ℚ)) + (q := (35982132201957549 / 80000000000000000 : ℚ)) + (U := (-(7990041466326574167593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_12 : Uω (aρ 12) (bρ 12) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3078,26 +2669,21 @@ lemma U_598_12 : have hlg : Real.log (31254069915314197 / 80000000000000000 : ℝ) ≤ (-(469938514580832882803 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31254069915314197 / 80000000000000000 : ℝ) = - (31254069915314197 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31254069915314197 / 20000000000000000 : ℚ)) - (U := (223208665719167117197 / 500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31254069915314197 / 20000000000000000 : ℝ) ≤ - (223208665719167117197 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1740843265589509 / 5000000000000000 : ℝ)) (q := - (31254069915314197 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31254069915314197 / 80000000000000000 : ℚ)) + (r' := (31254069915314197 / 20000000000000000 : ℚ)) + (U := (-(469938514580832882803 / 500000000000000000000 : ℚ))) + (U' := (223208665719167117197 / 500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (1740843265589509 / 5000000000000000 : ℚ)) + (q := (31254069915314197 / 80000000000000000 : ℚ)) + (U := (-(469938514580832882803 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_13 : Uω (aρ 13) (bρ 13) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3105,26 +2691,21 @@ lemma U_598_13 : have hlg : Real.log (26008108217176697 / 80000000000000000 : ℝ) ≤ (-(11236182902422223580447 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26008108217176697 / 80000000000000000 : ℝ) = - (26008108217176697 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26008108217176697 / 20000000000000000 : ℚ)) - (U := (2626760703577776419553 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26008108217176697 / 20000000000000000 : ℝ) ≤ - (2626760703577776419553 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2569577848239643 / 10000000000000000 : ℝ)) (q := - (26008108217176697 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26008108217176697 / 80000000000000000 : ℚ)) + (r' := (26008108217176697 / 20000000000000000 : ℚ)) + (U := (-(11236182902422223580447 / 10000000000000000000000 : ℚ))) + (U' := (2626760703577776419553 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (2569577848239643 / 10000000000000000 : ℚ)) + (q := (26008108217176697 / 80000000000000000 : ℚ)) + (U := (-(11236182902422223580447 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_14 : Uω (aρ 14) (bρ 14) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3132,26 +2713,21 @@ lemma U_598_14 : have hlg : Real.log (19794215259049549 / 80000000000000000 : ℝ) ≤ (-(2793273795028130683401 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (19794215259049549 / 80000000000000000 : ℝ) = - (19794215259049549 / 10000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19794215259049549 / 10000000000000000 : ℚ)) - (U := (1365609286771869316599 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19794215259049549 / 10000000000000000 : ℝ) ≤ - (1365609286771869316599 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (170003986719107 / 1250000000000000 : ℝ)) (q := - (19794215259049549 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19794215259049549 / 80000000000000000 : ℚ)) + (r' := (19794215259049549 / 10000000000000000 : ℚ)) + (U := (-(2793273795028130683401 / 2000000000000000000000 : ℚ))) + (U' := (1365609286771869316599 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (44224781932669 / 64000000000000 : ℚ)) + (s := (170003986719107 / 1250000000000000 : ℚ)) + (q := (19794215259049549 / 80000000000000000 : ℚ)) + (U := (-(2793273795028130683401 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_598_15 : Uω (aρ 15) (bρ 15) (44224781932669 / 64000000000000 : ℝ) ≤ @@ -3252,25 +2828,21 @@ lemma U_599_1 : have hlg : Real.log (27414854978146513 / 40000000000000000 : ℝ) ≤ (-(944486087211076226443 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27414854978146513 / 40000000000000000 : ℝ) = - (27414854978146513 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27414854978146513 / 20000000000000000 : ℚ)) - (U := (788381863538923773557 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27414854978146513 / 20000000000000000 : ℝ) ≤ - (788381863538923773557 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3426845078087097 / 5000000000000000 : ℝ)) (q := - (27414854978146513 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27414854978146513 / 40000000000000000 : ℚ)) + (r' := (27414854978146513 / 20000000000000000 : ℚ)) + (U := (-(944486087211076226443 / 2500000000000000000000 : ℚ))) + (U' := (788381863538923773557 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (3426845078087097 / 5000000000000000 : ℚ)) + (q := (27414854978146513 / 40000000000000000 : ℚ)) + (U := (-(944486087211076226443 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_2 : Uω (aρ 2) (bρ 2) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3278,25 +2850,21 @@ lemma U_599_2 : have hlg : Real.log (27319251931029037 / 40000000000000000 : ℝ) ≤ (-(381287801260218030659 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27319251931029037 / 40000000000000000 : ℝ) = - (27319251931029037 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27319251931029037 / 20000000000000000 : ℚ)) - (U := (311859379039781969341 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27319251931029037 / 20000000000000000 : ℝ) ≤ - (311859379039781969341 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (426853602820341 / 625000000000000 : ℝ)) (q := - (27319251931029037 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27319251931029037 / 40000000000000000 : ℚ)) + (r' := (27319251931029037 / 20000000000000000 : ℚ)) + (U := (-(381287801260218030659 / 1000000000000000000000 : ℚ))) + (U' := (311859379039781969341 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (426853602820341 / 625000000000000 : ℚ)) + (q := (27319251931029037 / 40000000000000000 : ℚ)) + (U := (-(381287801260218030659 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_3 : Uω (aρ 3) (bρ 3) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3304,25 +2872,21 @@ lemma U_599_3 : have hlg : Real.log (5425621436749573 / 8000000000000000 : ℝ) ≤ (-(1941545490004321403837 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5425621436749573 / 8000000000000000 : ℝ) = - (5425621436749573 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5425621436749573 / 4000000000000000 : ℚ)) - (U := (1524190411495678596163 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5425621436749573 / 4000000000000000 : ℝ) ≤ - (1524190411495678596163 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (678148137783487 / 1000000000000000 : ℝ)) (q := - (5425621436749573 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5425621436749573 / 8000000000000000 : ℚ)) + (r' := (5425621436749573 / 4000000000000000 : ℚ)) + (U := (-(1941545490004321403837 / 5000000000000000000000 : ℚ))) + (U' := (1524190411495678596163 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (678148137783487 / 1000000000000000 : ℚ)) + (q := (5425621436749573 / 8000000000000000 : ℚ)) + (U := (-(1941545490004321403837 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_4 : Uω (aρ 4) (bρ 4) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3330,25 +2894,21 @@ lemma U_599_4 : have hlg : Real.log (5362166751357703 / 8000000000000000 : ℝ) ≤ (-(4000734033657501560457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5362166751357703 / 8000000000000000 : ℝ) = - (5362166751357703 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5362166751357703 / 4000000000000000 : ℚ)) - (U := (2930737769342498439543 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5362166751357703 / 4000000000000000 : ℝ) ≤ - (2930737769342498439543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1340227769084039 / 2000000000000000 : ℝ)) (q := - (5362166751357703 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5362166751357703 / 8000000000000000 : ℚ)) + (r' := (5362166751357703 / 4000000000000000 : ℚ)) + (U := (-(4000734033657501560457 / 10000000000000000000000 : ℚ))) + (U' := (2930737769342498439543 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (1340227769084039 / 2000000000000000 : ℚ)) + (q := (5362166751357703 / 8000000000000000 : ℚ)) + (U := (-(4000734033657501560457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_5 : Uω (aρ 5) (bρ 5) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3356,25 +2916,21 @@ lemma U_599_5 : have hlg : Real.log (5265633995257277 / 8000000000000000 : ℝ) ≤ (-(418239986130542002681 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5265633995257277 / 8000000000000000 : ℝ) = - (5265633995257277 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5265633995257277 / 4000000000000000 : ℚ)) - (U := (274907194169457997319 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5265633995257277 / 4000000000000000 : ℝ) ≤ - (274907194169457997319 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (657799687450413 / 1000000000000000 : ℝ)) (q := - (5265633995257277 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5265633995257277 / 8000000000000000 : ℚ)) + (r' := (5265633995257277 / 4000000000000000 : ℚ)) + (U := (-(418239986130542002681 / 1000000000000000000000 : ℚ))) + (U' := (274907194169457997319 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (657799687450413 / 1000000000000000 : ℚ)) + (q := (5265633995257277 / 8000000000000000 : ℚ)) + (U := (-(418239986130542002681 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_6 : Uω (aρ 6) (bρ 6) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3382,25 +2938,21 @@ lemma U_599_6 : have hlg : Real.log (25637095741062787 / 40000000000000000 : ℝ) ≤ (-(4448390988465003952377 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25637095741062787 / 40000000000000000 : ℝ) = - (25637095741062787 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25637095741062787 / 20000000000000000 : ℚ)) - (U := (2483080814534996047623 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25637095741062787 / 20000000000000000 : ℝ) ≤ - (2483080814534996047623 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6399700132032331 / 10000000000000000 : ℝ)) (q := - (25637095741062787 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25637095741062787 / 40000000000000000 : ℚ)) + (r' := (25637095741062787 / 20000000000000000 : ℚ)) + (U := (-(4448390988465003952377 / 10000000000000000000000 : ℚ))) + (U' := (2483080814534996047623 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (6399700132032331 / 10000000000000000 : ℚ)) + (q := (25637095741062787 / 40000000000000000 : ℚ)) + (U := (-(4448390988465003952377 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_7 : Uω (aρ 7) (bρ 7) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3408,25 +2960,21 @@ lemma U_599_7 : have hlg : Real.log (24696734141387703 / 40000000000000000 : ℝ) ≤ (-(602760549948094116003 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24696734141387703 / 40000000000000000 : ℝ) = - (24696734141387703 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24696734141387703 / 20000000000000000 : ℚ)) - (U := (263673425426905883997 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24696734141387703 / 20000000000000000 : ℝ) ≤ - (263673425426905883997 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6153180712954789 / 10000000000000000 : ℝ)) (q := - (24696734141387703 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24696734141387703 / 40000000000000000 : ℚ)) + (r' := (24696734141387703 / 20000000000000000 : ℚ)) + (U := (-(602760549948094116003 / 1250000000000000000000 : ℚ))) + (U' := (263673425426905883997 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (6153180712954789 / 10000000000000000 : ℚ)) + (q := (24696734141387703 / 40000000000000000 : ℚ)) + (U := (-(602760549948094116003 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_8 : Uω (aρ 8) (bρ 8) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3434,25 +2982,21 @@ lemma U_599_8 : have hlg : Real.log (4694931260795021 / 8000000000000000 : ℝ) ≤ (-(1065916139610143317519 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4694931260795021 / 8000000000000000 : ℝ) = - (4694931260795021 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4694931260795021 / 4000000000000000 : ℚ)) - (U := (320378220989856682481 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4694931260795021 / 4000000000000000 : ℝ) ≤ - (320378220989856682481 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (582568344558849 / 1000000000000000 : ℝ)) (q := - (4694931260795021 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4694931260795021 / 8000000000000000 : ℚ)) + (r' := (4694931260795021 / 4000000000000000 : ℚ)) + (U := (-(1065916139610143317519 / 2000000000000000000000 : ℚ))) + (U' := (320378220989856682481 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (582568344558849 / 1000000000000000 : ℚ)) + (q := (4694931260795021 / 8000000000000000 : ℚ)) + (U := (-(1065916139610143317519 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_9 : Uω (aρ 9) (bρ 9) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3460,25 +3004,21 @@ lemma U_599_9 : have hlg : Real.log (21952649749208029 / 40000000000000000 : ℝ) ≤ (-(5999916041147995132601 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21952649749208029 / 40000000000000000 : ℝ) = - (21952649749208029 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21952649749208029 / 20000000000000000 : ℚ)) - (U := (931555761852004867399 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21952649749208029 / 20000000000000000 : ℝ) ≤ - (931555761852004867399 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (675705724570619 / 1250000000000000 : ℝ)) (q := - (21952649749208029 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21952649749208029 / 40000000000000000 : ℚ)) + (r' := (21952649749208029 / 20000000000000000 : ℚ)) + (U := (-(5999916041147995132601 / 10000000000000000000000 : ℚ))) + (U' := (931555761852004867399 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (675705724570619 / 1250000000000000 : ℚ)) + (q := (21952649749208029 / 40000000000000000 : ℚ)) + (U := (-(5999916041147995132601 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_10 : Uω (aρ 10) (bρ 10) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3486,26 +3026,21 @@ lemma U_599_10 : have hlg : Real.log (20130488686426481 / 40000000000000000 : ℝ) ≤ (-(6866439379730423357791 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20130488686426481 / 40000000000000000 : ℝ) = - (20130488686426481 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20130488686426481 / 20000000000000000 : ℚ)) - (U := (65032423269576642209 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20130488686426481 / 20000000000000000 : ℝ) ≤ - (65032423269576642209 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2441562149334589 / 5000000000000000 : ℝ)) (q := - (20130488686426481 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20130488686426481 / 40000000000000000 : ℚ)) + (r' := (20130488686426481 / 20000000000000000 : ℚ)) + (U := (-(6866439379730423357791 / 10000000000000000000000 : ℚ))) + (U' := (65032423269576642209 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (2441562149334589 / 5000000000000000 : ℚ)) + (q := (20130488686426481 / 40000000000000000 : ℚ)) + (U := (-(6866439379730423357791 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_11 : Uω (aρ 11) (bρ 11) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3513,26 +3048,21 @@ lemma U_599_11 : have hlg : Real.log (18025484319827781 / 40000000000000000 : ℝ) ≤ (-(7970929014454339731257 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18025484319827781 / 40000000000000000 : ℝ) = - (18025484319827781 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18025484319827781 / 10000000000000000 : ℚ)) - (U := (5892014591545660268743 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18025484319827781 / 10000000000000000 : ℝ) ≤ - (5892014591545660268743 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1062274685393707 / 2500000000000000 : ℝ)) (q := - (18025484319827781 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18025484319827781 / 40000000000000000 : ℚ)) + (r' := (18025484319827781 / 10000000000000000 : ℚ)) + (U := (-(7970929014454339731257 / 10000000000000000000000 : ℚ))) + (U' := (5892014591545660268743 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (1062274685393707 / 2500000000000000 : ℚ)) + (q := (18025484319827781 / 40000000000000000 : ℚ)) + (U := (-(7970929014454339731257 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_12 : Uω (aρ 12) (bρ 12) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3540,26 +3070,21 @@ lemma U_599_12 : have hlg : Real.log (15663435820495567 / 40000000000000000 : ℝ) ≤ (-(1875100772085846270361 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15663435820495567 / 40000000000000000 : ℝ) = - (15663435820495567 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15663435820495567 / 10000000000000000 : ℚ)) - (U := (897487949114153729639 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15663435820495567 / 10000000000000000 : ℝ) ≤ - (897487949114153729639 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3491774588593721 / 10000000000000000 : ℝ)) (q := - (15663435820495567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15663435820495567 / 40000000000000000 : ℚ)) + (r' := (15663435820495567 / 10000000000000000 : ℚ)) + (U := (-(1875100772085846270361 / 2000000000000000000000 : ℚ))) + (U' := (897487949114153729639 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (3491774588593721 / 10000000000000000 : ℚ)) + (q := (15663435820495567 / 40000000000000000 : ℚ)) + (U := (-(1875100772085846270361 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_13 : Uω (aρ 13) (bρ 13) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3567,26 +3092,21 @@ lemma U_599_13 : have hlg : Real.log (13045074796685817 / 40000000000000000 : ℝ) ≤ (-(2240937602556298459121 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13045074796685817 / 40000000000000000 : ℝ) = - (13045074796685817 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13045074796685817 / 10000000000000000 : ℚ)) - (U := (531651118643701540879 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13045074796685817 / 10000000000000000 : ℝ) ≤ - (531651118643701540879 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1290987909141923 / 5000000000000000 : ℝ)) (q := - (13045074796685817 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13045074796685817 / 40000000000000000 : ℚ)) + (r' := (13045074796685817 / 10000000000000000 : ℚ)) + (U := (-(2240937602556298459121 / 2000000000000000000000 : ℚ))) + (U' := (531651118643701540879 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (1290987909141923 / 5000000000000000 : ℚ)) + (q := (13045074796685817 / 40000000000000000 : ℚ)) + (U := (-(2240937602556298459121 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_14 : Uω (aρ 14) (bρ 14) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3594,26 +3114,21 @@ lemma U_599_14 : have hlg : Real.log (1991171652777751 / 8000000000000000 : ℝ) ≤ (-(13907183051807184338793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1991171652777751 / 8000000000000000 : ℝ) = - (1991171652777751 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1991171652777751 / 1000000000000000 : ℚ)) - (U := (6887232357192815661207 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1991171652777751 / 1000000000000000 : ℝ) ≤ - (6887232357192815661207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (276258967386063 / 2000000000000000 : ℝ)) (q := - (1991171652777751 / 8000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1991171652777751 / 8000000000000000 : ℚ)) + (r' := (1991171652777751 / 1000000000000000 : ℚ)) + (U := (-(13907183051807184338793 / 10000000000000000000000 : ℚ))) + (U' := (6887232357192815661207 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22138350563149 / 32000000000000 : ℚ)) + (s := (276258967386063 / 2000000000000000 : ℚ)) + (q := (1991171652777751 / 8000000000000000 : ℚ)) + (U := (-(13907183051807184338793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_599_15 : Uω (aρ 15) (bρ 15) (22138350563149 / 32000000000000 : ℝ) ≤ @@ -3715,25 +3230,21 @@ lemma U_600_1 : have hlg : Real.log (54894609171428223 / 80000000000000000 : ℝ) ≤ (-(3766114843185157129627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54894609171428223 / 80000000000000000 : ℝ) = - (54894609171428223 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54894609171428223 / 40000000000000000 : ℚ)) - (U := (3165356959814842870373 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54894609171428223 / 40000000000000000 : ℝ) ≤ - (3165356959814842870373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3430901292976731 / 5000000000000000 : ℝ)) (q := - (54894609171428223 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54894609171428223 / 80000000000000000 : ℚ)) + (r' := (54894609171428223 / 40000000000000000 : ℚ)) + (U := (-(3766114843185157129627 / 10000000000000000000000 : ℚ))) + (U' := (3165356959814842870373 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (3430901292976731 / 5000000000000000 : ℚ)) + (q := (54894609171428223 / 80000000000000000 : ℚ)) + (U := (-(3766114843185157129627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_2 : Uω (aρ 2) (bρ 2) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3741,25 +3252,21 @@ lemma U_600_2 : have hlg : Real.log (54703404328442747 / 80000000000000000 : ℝ) ≤ (-(19005034528540760341 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54703404328442747 / 80000000000000000 : ℝ) = - (54703404328442747 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54703404328442747 / 40000000000000000 : ℚ)) - (U := (15652324486459239659 / 50000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54703404328442747 / 40000000000000000 : ℝ) ≤ - (15652324486459239659 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6837770387717093 / 10000000000000000 : ℝ)) (q := - (54703404328442747 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54703404328442747 / 80000000000000000 : ℚ)) + (r' := (54703404328442747 / 40000000000000000 : ℚ)) + (U := (-(19005034528540760341 / 50000000000000000000 : ℚ))) + (U' := (15652324486459239659 / 50000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (6837770387717093 / 10000000000000000 : ℚ)) + (q := (54703404328442747 / 80000000000000000 : ℚ)) + (U := (-(19005034528540760341 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_3 : Uω (aρ 3) (bρ 3) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3767,25 +3274,21 @@ lemma U_600_3 : have hlg : Real.log (54321118572963439 / 80000000000000000 : ℝ) ≤ (-(38711355908973622577 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54321118572963439 / 80000000000000000 : ℝ) = - (54321118572963439 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54321118572963439 / 40000000000000000 : ℚ)) - (U := (30603362121026377423 / 100000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54321118572963439 / 40000000000000000 : ℝ) ≤ - (30603362121026377423 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3394797527598633 / 5000000000000000 : ℝ)) (q := - (54321118572963439 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54321118572963439 / 80000000000000000 : ℚ)) + (r' := (54321118572963439 / 40000000000000000 : ℚ)) + (U := (-(38711355908973622577 / 100000000000000000000 : ℚ))) + (U' := (30603362121026377423 / 100000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (3394797527598633 / 5000000000000000 : ℚ)) + (q := (54321118572963439 / 80000000000000000 : ℚ)) + (U := (-(38711355908973622577 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_4 : Uω (aρ 4) (bρ 4) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3793,25 +3296,21 @@ lemma U_600_4 : have hlg : Real.log (10737316337676867 / 16000000000000000 : ℝ) ≤ (-(3988635395722701368637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10737316337676867 / 16000000000000000 : ℝ) = - (10737316337676867 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10737316337676867 / 8000000000000000 : ℚ)) - (U := (2942836407277298631363 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10737316337676867 / 8000000000000000 : ℝ) ≤ - (2942836407277298631363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (670925501511749 / 1000000000000000 : ℝ)) (q := - (10737316337676867 / 16000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10737316337676867 / 16000000000000000 : ℚ)) + (r' := (10737316337676867 / 8000000000000000 : ℚ)) + (U := (-(3988635395722701368637 / 10000000000000000000000 : ℚ))) + (U' := (2942836407277298631363 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (670925501511749 / 1000000000000000 : ℚ)) + (q := (10737316337676867 / 16000000000000000 : ℚ)) + (U := (-(3988635395722701368637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_5 : Uω (aρ 5) (bρ 5) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3819,25 +3318,21 @@ lemma U_600_5 : have hlg : Real.log (10544255761957887 / 16000000000000000 : ℝ) ≤ (-(834014975758038440671 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10544255761957887 / 16000000000000000 : ℝ) = - (10544255761957887 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10544255761957887 / 8000000000000000 : ℚ)) - (U := (552279384841961559329 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10544255761957887 / 8000000000000000 : ℝ) ≤ - (552279384841961559329 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1317223842960753 / 2000000000000000 : ℝ)) (q := - (10544255761957887 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10544255761957887 / 16000000000000000 : ℚ)) + (r' := (10544255761957887 / 8000000000000000 : ℚ)) + (U := (-(834014975758038440671 / 2000000000000000000000 : ℚ))) + (U' := (552279384841961559329 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (1317223842960753 / 2000000000000000 : ℚ)) + (q := (10544255761957887 / 16000000000000000 : ℚ)) + (U := (-(834014975758038440671 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_6 : Uω (aρ 6) (bρ 6) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3845,25 +3340,21 @@ lemma U_600_6 : have hlg : Real.log (51339187438454079 / 80000000000000000 : ℝ) ≤ (-(887144572323505302381 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51339187438454079 / 80000000000000000 : ℝ) = - (51339187438454079 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51339187438454079 / 40000000000000000 : ℚ)) - (U := (499149788276494697619 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51339187438454079 / 40000000000000000 : ℝ) ≤ - (499149788276494697619 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3203918373554963 / 5000000000000000 : ℝ)) (q := - (51339187438454079 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51339187438454079 / 80000000000000000 : ℚ)) + (r' := (51339187438454079 / 40000000000000000 : ℚ)) + (U := (-(887144572323505302381 / 2000000000000000000000 : ℚ))) + (U' := (499149788276494697619 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (3203918373554963 / 5000000000000000 : ℚ)) + (q := (51339187438454079 / 80000000000000000 : ℚ)) + (U := (-(887144572323505302381 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_7 : Uω (aρ 7) (bρ 7) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3871,25 +3362,21 @@ lemma U_600_7 : have hlg : Real.log (49458588503678087 / 80000000000000000 : ℝ) ≤ (-(4808909108662188216689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49458588503678087 / 80000000000000000 : ℝ) = - (49458588503678087 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49458588503678087 / 40000000000000000 : ℚ)) - (U := (2122562694337811783311 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49458588503678087 / 40000000000000000 : ℝ) ≤ - (2122562694337811783311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (770168549271991 / 1250000000000000 : ℝ)) (q := - (49458588503678087 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49458588503678087 / 80000000000000000 : ℚ)) + (r' := (49458588503678087 / 40000000000000000 : ℚ)) + (U := (-(4808909108662188216689 / 10000000000000000000000 : ℚ))) + (U' := (2122562694337811783311 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (770168549271991 / 1250000000000000 : ℚ)) + (q := (49458588503678087 / 80000000000000000 : ℚ)) + (U := (-(4808909108662188216689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_8 : Uω (aρ 8) (bρ 8) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3897,25 +3384,21 @@ lemma U_600_8 : have hlg : Real.log (47014689739965883 / 80000000000000000 : ℝ) ≤ (-(5315665338778738707151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47014689739965883 / 80000000000000000 : ℝ) = - (47014689739965883 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47014689739965883 / 40000000000000000 : ℚ)) - (U := (1615806464221261292849 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (47014689739965883 / 40000000000000000 : ℝ) ≤ - (1615806464221261292849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5833915354587877 / 10000000000000000 : ℝ)) (q := - (47014689739965883 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47014689739965883 / 80000000000000000 : ℚ)) + (r' := (47014689739965883 / 40000000000000000 : ℚ)) + (U := (-(5315665338778738707151 / 10000000000000000000000 : ℚ))) + (U' := (1615806464221261292849 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (5833915354587877 / 10000000000000000 : ℚ)) + (q := (47014689739965883 / 80000000000000000 : ℚ)) + (U := (-(5315665338778738707151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_9 : Uω (aρ 9) (bρ 9) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3923,25 +3406,21 @@ lemma U_600_9 : have hlg : Real.log (8794237531991951 / 16000000000000000 : ℝ) ≤ (-(598492040897808695309 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8794237531991951 / 16000000000000000 : ℝ) = - (8794237531991951 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8794237531991951 / 8000000000000000 : ℚ)) - (U := (94655139402191304691 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (8794237531991951 / 8000000000000000 : ℝ) ≤ - (94655139402191304691 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1082801092589269 / 2000000000000000 : ℝ)) (q := - (8794237531991951 / 16000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8794237531991951 / 16000000000000000 : ℚ)) + (r' := (8794237531991951 / 8000000000000000 : ℚ)) + (U := (-(598492040897808695309 / 1000000000000000000000 : ℚ))) + (U' := (94655139402191304691 / 1000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (1082801092589269 / 2000000000000000 : ℚ)) + (q := (8794237531991951 / 16000000000000000 : ℚ)) + (U := (-(598492040897808695309 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_10 : Uω (aρ 10) (bρ 10) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3949,26 +3428,21 @@ lemma U_600_10 : have hlg : Real.log (40327859865204219 / 80000000000000000 : ℝ) ≤ (-(6849840925155560255049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40327859865204219 / 80000000000000000 : ℝ) = - (40327859865204219 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40327859865204219 / 40000000000000000 : ℚ)) - (U := (81630877844439744951 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40327859865204219 / 40000000000000000 : ℝ) ≤ - (81630877844439744951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4891732547752461 / 10000000000000000 : ℝ)) (q := - (40327859865204219 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40327859865204219 / 80000000000000000 : ℚ)) + (r' := (40327859865204219 / 40000000000000000 : ℚ)) + (U := (-(6849840925155560255049 / 10000000000000000000000 : ℚ))) + (U' := (81630877844439744951 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (4891732547752461 / 10000000000000000 : ℚ)) + (q := (40327859865204219 / 80000000000000000 : ℚ)) + (U := (-(6849840925155560255049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_11 : Uω (aρ 11) (bρ 11) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -3976,26 +3450,21 @@ lemma U_600_11 : have hlg : Real.log (36119789164517907 / 80000000000000000 : ℝ) ≤ (-(3975928713532320038747 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36119789164517907 / 80000000000000000 : ℝ) = - (36119789164517907 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36119789164517907 / 20000000000000000 : ℚ)) - (U := (2955543089467679961253 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36119789164517907 / 20000000000000000 : ℝ) ≤ - (2955543089467679961253 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4258191498785883 / 10000000000000000 : ℝ)) (q := - (36119789164517907 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36119789164517907 / 80000000000000000 : ℚ)) + (r' := (36119789164517907 / 20000000000000000 : ℚ)) + (U := (-(3975928713532320038747 / 5000000000000000000000 : ℚ))) + (U' := (2955543089467679961253 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (4258191498785883 / 10000000000000000 : ℚ)) + (q := (36119789164517907 / 80000000000000000 : ℚ)) + (U := (-(3975928713532320038747 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_12 : Uω (aρ 12) (bρ 12) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -4003,26 +3472,21 @@ lemma U_600_12 : have hlg : Real.log (31399632293277399 / 80000000000000000 : ℝ) ≤ (-(9352304517135290160901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31399632293277399 / 80000000000000000 : ℝ) = - (31399632293277399 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31399632293277399 / 20000000000000000 : ℚ)) - (U := (4510639088864709839099 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31399632293277399 / 20000000000000000 : ℝ) ≤ - (4510639088864709839099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (875463094415189 / 2500000000000000 : ℝ)) (q := - (31399632293277399 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31399632293277399 / 80000000000000000 : ℚ)) + (r' := (31399632293277399 / 20000000000000000 : ℚ)) + (U := (-(9352304517135290160901 / 10000000000000000000000 : ℚ))) + (U' := (4510639088864709839099 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (875463094415189 / 2500000000000000 : ℚ)) + (q := (31399632293277399 / 80000000000000000 : ℚ)) + (U := (-(9352304517135290160901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_13 : Uω (aρ 13) (bρ 13) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -4030,26 +3494,21 @@ lemma U_600_13 : have hlg : Real.log (26172055446114123 / 80000000000000000 : ℝ) ≤ (-(5586671893103846167657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (26172055446114123 / 80000000000000000 : ℝ) = - (26172055446114123 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26172055446114123 / 20000000000000000 : ℚ)) - (U := (1344799909896153832343 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26172055446114123 / 20000000000000000 : ℝ) ≤ - (1344799909896153832343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2594339907464937 / 10000000000000000 : ℝ)) (q := - (26172055446114123 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26172055446114123 / 80000000000000000 : ℚ)) + (r' := (26172055446114123 / 20000000000000000 : ℚ)) + (U := (-(5586671893103846167657 / 5000000000000000000000 : ℚ))) + (U' := (1344799909896153832343 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (2594339907464937 / 10000000000000000 : ℚ)) + (q := (26172055446114123 / 80000000000000000 : ℚ)) + (U := (-(5586671893103846167657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_14 : Uω (aρ 14) (bρ 14) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -4057,26 +3516,21 @@ lemma U_600_14 : have hlg : Real.log (4005623196142587 / 16000000000000000 : ℝ) ≤ (-(2769779097549425911313 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4005623196142587 / 16000000000000000 : ℝ) = - (4005623196142587 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4005623196142587 / 4000000000000000 : ℚ)) - (U := (2809623650574088687 / 2000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (4005623196142587 / 4000000000000000 : ℝ) ≤ - (2809623650574088687 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35057058153991 / 250000000000000 : ℝ)) (q := - (4005623196142587 / 16000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4005623196142587 / 16000000000000000 : ℚ)) + (r' := (4005623196142587 / 4000000000000000 : ℚ)) + (U := (-(2769779097549425911313 / 2000000000000000000000 : ℚ))) + (U' := (2809623650574088687 / 2000000000000000000000 : ℚ)) + 2 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (44328620319927 / 64000000000000 : ℚ)) + (s := (35057058153991 / 250000000000000 : ℚ)) + (q := (4005623196142587 / 16000000000000000 : ℚ)) + (U := (-(2769779097549425911313 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_600_15 : Uω (aρ 15) (bρ 15) (44328620319927 / 64000000000000 : ℝ) ≤ @@ -4176,25 +3630,21 @@ lemma U_601_1 : have hlg : Real.log (3434969274127283 / 5000000000000000 : ℝ) ≤ (-(938574828702399587789 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3434969274127283 / 5000000000000000 : ℝ) = - (3434969274127283 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3434969274127283 / 2500000000000000 : ℚ)) - (U := (794293122047600412211 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3434969274127283 / 2500000000000000 : ℝ) ≤ - (794293122047600412211 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6869915015601007 / 10000000000000000 : ℝ)) (q := - (3434969274127283 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3434969274127283 / 5000000000000000 : ℚ)) + (r' := (3434969274127283 / 2500000000000000 : ℚ)) + (U := (-(938574828702399587789 / 2500000000000000000000 : ℚ))) + (U' := (794293122047600412211 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (6869915015601007 / 10000000000000000 : ℚ)) + (q := (3434969274127283 / 5000000000000000 : ℚ)) + (U := (-(938574828702399587789 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_2 : Uω (aρ 2) (bρ 2) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4202,25 +3652,21 @@ lemma U_601_2 : have hlg : Real.log (3423019049458321 / 5000000000000000 : ℝ) ≤ (-(757829975012473701853 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3423019049458321 / 5000000000000000 : ℝ) = - (3423019049458321 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3423019049458321 / 2500000000000000 : ℚ)) - (U := (628464385587526298147 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3423019049458321 / 2500000000000000 : ℝ) ≤ - (628464385587526298147 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6845883129435159 / 10000000000000000 : ℝ)) (q := - (3423019049458321 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3423019049458321 / 5000000000000000 : ℚ)) + (r' := (3423019049458321 / 2500000000000000 : ℚ)) + (U := (-(757829975012473701853 / 2000000000000000000000 : ℚ))) + (U' := (628464385587526298147 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (6845883129435159 / 10000000000000000 : ℚ)) + (q := (3423019049458321 / 5000000000000000 : ℚ)) + (U := (-(757829975012473701853 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_3 : Uω (aρ 3) (bρ 3) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4228,25 +3674,21 @@ lemma U_601_3 : have hlg : Real.log (13596505691496687 / 20000000000000000 : ℝ) ≤ (-(964798620035307040553 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13596505691496687 / 20000000000000000 : ℝ) = - (13596505691496687 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13596505691496687 / 10000000000000000 : ℚ)) - (U := (768069330714692959447 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13596505691496687 / 10000000000000000 : ℝ) ≤ - (768069330714692959447 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3398854364724281 / 5000000000000000 : ℝ)) (q := - (13596505691496687 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13596505691496687 / 20000000000000000 : ℚ)) + (r' := (13596505691496687 / 10000000000000000 : ℚ)) + (U := (-(964798620035307040553 / 2500000000000000000000 : ℚ))) + (U' := (768069330714692959447 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (3398854364724281 / 5000000000000000 : ℚ)) + (q := (13596505691496687 / 20000000000000000 : ℚ)) + (U := (-(964798620035307040553 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_4 : Uω (aρ 4) (bρ 4) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4254,25 +3696,21 @@ lemma U_601_4 : have hlg : Real.log (13437873956627869 / 20000000000000000 : ℝ) ≤ (-(994137846157366722441 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13437873956627869 / 20000000000000000 : ℝ) = - (13437873956627869 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13437873956627869 / 10000000000000000 : ℚ)) - (U := (738730104592633277559 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13437873956627869 / 10000000000000000 : ℝ) ≤ - (738730104592633277559 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (839671396955593 / 1250000000000000 : ℝ)) (q := - (13437873956627869 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13437873956627869 / 20000000000000000 : ℚ)) + (r' := (13437873956627869 / 10000000000000000 : ℚ)) + (U := (-(994137846157366722441 / 2500000000000000000000 : ℚ))) + (U' := (738730104592633277559 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (839671396955593 / 1250000000000000 : ℚ)) + (q := (13437873956627869 / 20000000000000000 : ℚ)) + (U := (-(994137846157366722441 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_5 : Uω (aρ 5) (bρ 5) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4280,25 +3718,21 @@ lemma U_601_5 : have hlg : Real.log (13196554392214973 / 20000000000000000 : ℝ) ≤ (-(4157765086690188808493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13196554392214973 / 20000000000000000 : ℝ) = - (13196554392214973 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13196554392214973 / 10000000000000000 : ℚ)) - (U := (2773706716309811191507 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13196554392214973 / 10000000000000000 : ℝ) ≤ - (2773706716309811191507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (103035023915107 / 156250000000000 : ℝ)) (q := - (13196554392214973 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13196554392214973 / 20000000000000000 : ℚ)) + (r' := (13196554392214973 / 10000000000000000 : ℚ)) + (U := (-(4157765086690188808493 / 10000000000000000000000 : ℚ))) + (U' := (2773706716309811191507 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (103035023915107 / 156250000000000 : ℚ)) + (q := (13196554392214973 / 20000000000000000 : ℚ)) + (U := (-(4157765086690188808493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_6 : Uω (aρ 6) (bρ 6) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4306,25 +3740,21 @@ lemma U_601_6 : have hlg : Real.log (12851045787303101 / 20000000000000000 : ℝ) ≤ (-(2211535405192055338863 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12851045787303101 / 20000000000000000 : ℝ) = - (12851045787303101 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12851045787303101 / 10000000000000000 : ℚ)) - (U := (1254200496307944661137 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12851045787303101 / 10000000000000000 : ℝ) ≤ - (1254200496307944661137 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (200499165649843 / 312500000000000 : ℝ)) (q := - (12851045787303101 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12851045787303101 / 20000000000000000 : ℚ)) + (r' := (12851045787303101 / 10000000000000000 : ℚ)) + (U := (-(2211535405192055338863 / 5000000000000000000000 : ℚ))) + (U' := (1254200496307944661137 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (200499165649843 / 312500000000000 : ℚ)) + (q := (12851045787303101 / 20000000000000000 : ℚ)) + (U := (-(2211535405192055338863 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_7 : Uω (aρ 7) (bρ 7) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4332,25 +3762,21 @@ lemma U_601_7 : have hlg : Real.log (309523175880027 / 500000000000000 : ℝ) ≤ (-(959150254321744450281 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (309523175880027 / 500000000000000 : ℝ) = - (309523175880027 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (309523175880027 / 250000000000000 : ℚ)) - (U := (427144106278255549719 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (309523175880027 / 250000000000000 : ℝ) ≤ - (427144106278255549719 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1233903185890591 / 2000000000000000 : ℝ)) (q := - (309523175880027 / 500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (309523175880027 / 500000000000000 : ℚ)) + (r' := (309523175880027 / 250000000000000 : ℚ)) + (U := (-(959150254321744450281 / 2000000000000000000000 : ℚ))) + (U' := (427144106278255549719 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (1233903185890591 / 2000000000000000 : ℚ)) + (q := (309523175880027 / 500000000000000 : ℚ)) + (U := (-(959150254321744450281 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_8 : Uω (aρ 8) (bρ 8) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4358,25 +3784,21 @@ lemma U_601_8 : have hlg : Real.log (2942504095894577 / 5000000000000000 : ℝ) ≤ (-(265088480022531474809 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2942504095894577 / 5000000000000000 : ℝ) = - (2942504095894577 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2942504095894577 / 2500000000000000 : ℚ)) - (U := (81485110127468525191 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2942504095894577 / 2500000000000000 : ℝ) ≤ - (81485110127468525191 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5842146929170183 / 10000000000000000 : ℝ)) (q := - (2942504095894577 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2942504095894577 / 5000000000000000 : ℚ)) + (r' := (2942504095894577 / 2500000000000000 : ℚ)) + (U := (-(265088480022531474809 / 500000000000000000000 : ℚ))) + (U' := (81485110127468525191 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (5842146929170183 / 10000000000000000 : ℚ)) + (q := (2942504095894577 / 5000000000000000 : ℚ)) + (U := (-(265088480022531474809 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_9 : Uω (aρ 9) (bρ 9) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4384,25 +3806,21 @@ lemma U_601_9 : have hlg : Real.log (11009268204151959 / 20000000000000000 : ℝ) ≤ (-(5969947912396625863489 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11009268204151959 / 20000000000000000 : ℝ) = - (11009268204151959 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11009268204151959 / 10000000000000000 : ℚ)) - (U := (961523890603374136511 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11009268204151959 / 10000000000000000 : ℝ) ≤ - (961523890603374136511 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2711182189051917 / 5000000000000000 : ℝ)) (q := - (11009268204151959 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11009268204151959 / 20000000000000000 : ℚ)) + (r' := (11009268204151959 / 10000000000000000 : ℚ)) + (U := (-(5969947912396625863489 / 10000000000000000000000 : ℚ))) + (U' := (961523890603374136511 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (2711182189051917 / 5000000000000000 : ℚ)) + (q := (11009268204151959 / 20000000000000000 : ℚ)) + (U := (-(5969947912396625863489 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_10 : Uω (aρ 10) (bρ 10) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4410,26 +3828,21 @@ lemma U_601_10 : have hlg : Real.log (1262335487174499 / 2500000000000000 : ℝ) ≤ (-(3416635825630334296627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1262335487174499 / 2500000000000000 : ℝ) = - (1262335487174499 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1262335487174499 / 1250000000000000 : ℚ)) - (U := (49100075869665703373 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1262335487174499 / 1250000000000000 : ℝ) ≤ - (49100075869665703373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4900339104842867 / 10000000000000000 : ℝ)) (q := - (1262335487174499 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1262335487174499 / 2500000000000000 : ℚ)) + (r' := (1262335487174499 / 1250000000000000 : ℚ)) + (U := (-(3416635825630334296627 / 5000000000000000000000 : ℚ))) + (U' := (49100075869665703373 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (4900339104842867 / 10000000000000000 : ℚ)) + (q := (1262335487174499 / 2500000000000000 : ℚ)) + (U := (-(3416635825630334296627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_11 : Uω (aρ 11) (bρ 11) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4437,26 +3850,21 @@ lemma U_601_11 : have hlg : Real.log (9047148469566547 / 20000000000000000 : ℝ) ≤ (-(7932826512081039083167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9047148469566547 / 20000000000000000 : ℝ) = - (9047148469566547 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9047148469566547 / 5000000000000000 : ℚ)) - (U := (5930117093918960916833 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9047148469566547 / 5000000000000000 : ℝ) ≤ - (5930117093918960916833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2133640151609211 / 5000000000000000 : ℝ)) (q := - (9047148469566547 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9047148469566547 / 20000000000000000 : ℚ)) + (r' := (9047148469566547 / 5000000000000000 : ℚ)) + (U := (-(7932826512081039083167 / 10000000000000000000000 : ℚ))) + (U' := (5930117093918960916833 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (2133640151609211 / 5000000000000000 : ℚ)) + (q := (9047148469566547 / 20000000000000000 : ℚ)) + (U := (-(7932826512081039083167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_12 : Uω (aρ 12) (bρ 12) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4464,25 +3872,21 @@ lemma U_601_12 : have hlg : Real.log (983511007055157 / 2500000000000000 : ℝ) ≤ (-(9329171808514020960711 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (983511007055157 / 2500000000000000 : ℝ) = - (983511007055157 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (983511007055157 / 625000000000000 : ℚ)) - (U := (4533771797485979039289 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (983511007055157 / 625000000000000 : ℝ) ≤ - (4533771797485979039289 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3511919986778131 / 10000000000000000 : ℝ)) (q := - (983511007055157 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (983511007055157 / 2500000000000000 : ℚ)) + (r' := (983511007055157 / 625000000000000 : ℚ)) + (U := (-(9329171808514020960711 / 10000000000000000000000 : ℚ))) + (U' := (4533771797485979039289 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (3511919986778131 / 10000000000000000 : ℚ)) + (q := (983511007055157 / 2500000000000000 : ℚ)) + (U := (-(9329171808514020960711 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_13 : Uω (aρ 13) (bρ 13) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4490,26 +3894,21 @@ lemma U_601_13 : have hlg : Real.log (6563456925967253 / 20000000000000000 : ℝ) ≤ (-(11142148384564178563437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6563456925967253 / 20000000000000000 : ℝ) = - (6563456925967253 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6563456925967253 / 5000000000000000 : ℚ)) - (U := (2720795221435821436563 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6563456925967253 / 5000000000000000 : ℝ) ≤ - (2720795221435821436563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325833824737391 / 1250000000000000 : ℝ)) (q := - (6563456925967253 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6563456925967253 / 20000000000000000 : ℚ)) + (r' := (6563456925967253 / 5000000000000000 : ℚ)) + (U := (-(11142148384564178563437 / 10000000000000000000000 : ℚ))) + (U' := (2720795221435821436563 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (325833824737391 / 1250000000000000 : ℚ)) + (q := (6563456925967253 / 20000000000000000 : ℚ)) + (U := (-(11142148384564178563437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_14 : Uω (aρ 14) (bρ 14) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4517,26 +3916,21 @@ lemma U_601_14 : have hlg : Real.log (5035865592274749 / 20000000000000000 : ℝ) ≤ (-(551658738635868358737 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5035865592274749 / 20000000000000000 : ℝ) = - (5035865592274749 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5035865592274749 / 5000000000000000 : ℚ)) - (U := (2859005604131641263 / 400000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5035865592274749 / 5000000000000000 : ℝ) ≤ - (2859005604131641263 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (177875818656453 / 1250000000000000 : ℝ)) (q := - (5035865592274749 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5035865592274749 / 20000000000000000 : ℚ)) + (r' := (5035865592274749 / 5000000000000000 : ℚ)) + (U := (-(551658738635868358737 / 400000000000000000000 : ℚ))) + (U' := (2859005604131641263 / 400000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11095134878389 / 16000000000000 : ℚ)) + (s := (177875818656453 / 1250000000000000 : ℚ)) + (q := (5035865592274749 / 20000000000000000 : ℚ)) + (U := (-(551658738635868358737 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_601_15 : Uω (aρ 15) (bρ 15) (11095134878389 / 16000000000000 : ℝ) ≤ @@ -4638,25 +4032,21 @@ lemma U_602_1 : have hlg : Real.log (55024407600119797 / 80000000000000000 : ℝ) ≤ (-(233906108170397038313 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (55024407600119797 / 80000000000000000 : ℝ) = - (55024407600119797 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55024407600119797 / 40000000000000000 : ℚ)) - (U := (199310879517102961687 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55024407600119797 / 40000000000000000 : ℝ) ≤ - (199310879517102961687 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6878027445117293 / 10000000000000000 : ℝ)) (q := - (55024407600119797 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55024407600119797 / 80000000000000000 : ℚ)) + (r' := (55024407600119797 / 40000000000000000 : ℚ)) + (U := (-(233906108170397038313 / 625000000000000000000 : ℚ))) + (U' := (199310879517102961687 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (6878027445117293 / 10000000000000000 : ℚ)) + (q := (55024407600119797 / 80000000000000000 : ℚ)) + (U := (-(233906108170397038313 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_2 : Uω (aρ 2) (bρ 2) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4664,25 +4054,21 @@ lemma U_602_2 : have hlg : Real.log (54833205250741649 / 80000000000000000 : ℝ) ≤ (-(944326721830208510903 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (54833205250741649 / 80000000000000000 : ℝ) = - (54833205250741649 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54833205250741649 / 40000000000000000 : ℚ)) - (U := (788541228919791489097 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54833205250741649 / 40000000000000000 : ℝ) ≤ - (788541228919791489097 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1713498967570689 / 2500000000000000 : ℝ)) (q := - (54833205250741649 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54833205250741649 / 80000000000000000 : ℚ)) + (r' := (54833205250741649 / 40000000000000000 : ℚ)) + (U := (-(944326721830208510903 / 2500000000000000000000 : ℚ))) + (U' := (788541228919791489097 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (1713498967570689 / 2500000000000000 : ℚ)) + (q := (54833205250741649 / 80000000000000000 : ℚ)) + (U := (-(944326721830208510903 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_3 : Uω (aρ 3) (bρ 3) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4690,25 +4076,21 @@ lemma U_602_3 : have hlg : Real.log (10890185389322033 / 16000000000000000 : ℝ) ≤ (-(384726761367011421543 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10890185389322033 / 16000000000000000 : ℝ) = - (10890185389322033 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10890185389322033 / 8000000000000000 : ℚ)) - (U := (308420418932988578457 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (10890185389322033 / 8000000000000000 : ℝ) ≤ - (308420418932988578457 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1361164480119977 / 2000000000000000 : ℝ)) (q := - (10890185389322033 / 16000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10890185389322033 / 16000000000000000 : ℚ)) + (r' := (10890185389322033 / 8000000000000000 : ℚ)) + (U := (-(384726761367011421543 / 1000000000000000000000 : ℚ))) + (U' := (308420418932988578457 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (1361164480119977 / 2000000000000000 : ℚ)) + (q := (10890185389322033 / 16000000000000000 : ℚ)) + (U := (-(384726761367011421543 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_4 : Uω (aρ 4) (bρ 4) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4716,25 +4098,21 @@ lemma U_602_4 : have hlg : Real.log (53816409928091253 / 80000000000000000 : ℝ) ≤ (-(792896393007470868719 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53816409928091253 / 80000000000000000 : ℝ) = - (53816409928091253 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53816409928091253 / 40000000000000000 : ℚ)) - (U := (593397967592529131281 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53816409928091253 / 40000000000000000 : ℝ) ≤ - (593397967592529131281 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6725487327035157 / 10000000000000000 : ℝ)) (q := - (53816409928091253 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53816409928091253 / 80000000000000000 : ℚ)) + (r' := (53816409928091253 / 40000000000000000 : ℚ)) + (U := (-(792896393007470868719 / 2000000000000000000000 : ℚ))) + (U' := (593397967592529131281 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (6725487327035157 / 10000000000000000 : ℚ)) + (q := (53816409928091253 / 80000000000000000 : ℚ)) + (U := (-(792896393007470868719 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_5 : Uω (aρ 5) (bρ 5) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4742,25 +4120,21 @@ lemma U_602_5 : have hlg : Real.log (52851156230146361 / 80000000000000000 : ℝ) ≤ (-(165818817902471995431 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52851156230146361 / 80000000000000000 : ℝ) = - (52851156230146361 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52851156230146361 / 40000000000000000 : ℚ)) - (U := (111440054217528004569 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52851156230146361 / 40000000000000000 : ℝ) ≤ - (111440054217528004569 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3301181910941967 / 5000000000000000 : ℝ)) (q := - (52851156230146361 / 80000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52851156230146361 / 80000000000000000 : ℚ)) + (r' := (52851156230146361 / 40000000000000000 : ℚ)) + (U := (-(165818817902471995431 / 400000000000000000000 : ℚ))) + (U' := (111440054217528004569 / 400000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (3301181910941967 / 5000000000000000 : ℚ)) + (q := (52851156230146361 / 80000000000000000 : ℚ)) + (U := (-(165818817902471995431 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_6 : Uω (aρ 6) (bρ 6) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4768,25 +4142,21 @@ lemma U_602_6 : have hlg : Real.log (51469178615333637 / 80000000000000000 : ℝ) ≤ (-(88208695877931068533 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (51469178615333637 / 80000000000000000 : ℝ) = - (51469178615333637 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51469178615333637 / 40000000000000000 : ℚ)) - (U := (50420740182068931467 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (51469178615333637 / 40000000000000000 : ℝ) ≤ - (50420740182068931467 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6424109793320753 / 10000000000000000 : ℝ)) (q := - (51469178615333637 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51469178615333637 / 80000000000000000 : ℚ)) + (r' := (51469178615333637 / 40000000000000000 : ℚ)) + (U := (-(88208695877931068533 / 200000000000000000000 : ℚ))) + (U' := (50420740182068931467 / 200000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (6424109793320753 / 10000000000000000 : ℚ)) + (q := (51469178615333637 / 80000000000000000 : ℚ)) + (U := (-(88208695877931068533 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_7 : Uω (aρ 7) (bρ 7) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4794,25 +4164,21 @@ lemma U_602_7 : have hlg : Real.log (49588827196469537 / 80000000000000000 : ℝ) ≤ (-(478261084193173771567 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49588827196469537 / 80000000000000000 : ℝ) = - (49588827196469537 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49588827196469537 / 40000000000000000 : ℚ)) - (U := (214886096106826228433 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49588827196469537 / 40000000000000000 : ℝ) ≤ - (214886096106826228433 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (772210414920591 / 1250000000000000 : ℝ)) (q := - (49588827196469537 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49588827196469537 / 80000000000000000 : ℚ)) + (r' := (49588827196469537 / 40000000000000000 : ℚ)) + (U := (-(478261084193173771567 / 1000000000000000000000 : ℚ))) + (U' := (214886096106826228433 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (772210414920591 / 1250000000000000 : ℚ)) + (q := (49588827196469537 / 80000000000000000 : ℚ)) + (U := (-(478261084193173771567 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_8 : Uω (aρ 8) (bρ 8) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4820,25 +4186,21 @@ lemma U_602_8 : have hlg : Real.log (47145439996638613 / 80000000000000000 : ℝ) ≤ (-(5287893427020350660491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47145439996638613 / 80000000000000000 : ℝ) = - (47145439996638613 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47145439996638613 / 40000000000000000 : ℚ)) - (U := (1643578375979649339509 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (47145439996638613 / 40000000000000000 : ℝ) ≤ - (1643578375979649339509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5850378170746997 / 10000000000000000 : ℝ)) (q := - (47145439996638613 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47145439996638613 / 80000000000000000 : ℚ)) + (r' := (47145439996638613 / 40000000000000000 : ℚ)) + (U := (-(5287893427020350660491 / 10000000000000000000000 : ℚ))) + (U' := (1643578375979649339509 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (5850378170746997 / 10000000000000000 : ℚ)) + (q := (47145439996638613 / 80000000000000000 : ℚ)) + (U := (-(5287893427020350660491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_9 : Uω (aρ 9) (bρ 9) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4846,25 +4208,21 @@ lemma U_602_9 : have hlg : Real.log (44102954982235617 / 80000000000000000 : ℝ) ≤ (-(5954998478060639171699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44102954982235617 / 80000000000000000 : ℝ) = - (44102954982235617 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44102954982235617 / 40000000000000000 : ℚ)) - (U := (976473324939360828301 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (44102954982235617 / 40000000000000000 : ℝ) ≤ - (976473324939360828301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (678840318188281 / 1250000000000000 : ℝ)) (q := - (44102954982235617 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44102954982235617 / 80000000000000000 : ℚ)) + (r' := (44102954982235617 / 40000000000000000 : ℚ)) + (U := (-(5954998478060639171699 / 10000000000000000000000 : ℚ))) + (U' := (976473324939360828301 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (678840318188281 / 1250000000000000 : ℚ)) + (q := (44102954982235617 / 80000000000000000 : ℚ)) + (U := (-(5954998478060639171699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_10 : Uω (aρ 10) (bρ 10) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4872,26 +4230,21 @@ lemma U_602_10 : have hlg : Real.log (8092320916317969 / 16000000000000000 : ℝ) ≤ (-(6816731449933417676493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8092320916317969 / 16000000000000000 : ℝ) = - (8092320916317969 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8092320916317969 / 8000000000000000 : ℚ)) - (U := (114740353066582323507 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (8092320916317969 / 8000000000000000 : ℝ) ≤ - (114740353066582323507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (981788795767961 / 2000000000000000 : ℝ)) (q := - (8092320916317969 / 16000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8092320916317969 / 16000000000000000 : ℚ)) + (r' := (8092320916317969 / 8000000000000000 : ℚ)) + (U := (-(6816731449933417676493 / 10000000000000000000000 : ℚ))) + (U' := (114740353066582323507 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (981788795767961 / 2000000000000000 : ℚ)) + (q := (8092320916317969 / 16000000000000000 : ℚ)) + (U := (-(6816731449933417676493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_11 : Uω (aρ 11) (bρ 11) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4899,26 +4252,21 @@ lemma U_602_11 : have hlg : Real.log (36257382881713221 / 80000000000000000 : ℝ) ≤ (-(3956918039439585658247 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36257382881713221 / 80000000000000000 : ℝ) = - (36257382881713221 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36257382881713221 / 20000000000000000 : ℚ)) - (U := (2974553763560414341753 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36257382881713221 / 20000000000000000 : ℝ) ≤ - (2974553763560414341753 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4276365180075649 / 10000000000000000 : ℝ)) (q := - (36257382881713221 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36257382881713221 / 80000000000000000 : ℚ)) + (r' := (36257382881713221 / 20000000000000000 : ℚ)) + (U := (-(3956918039439585658247 / 5000000000000000000000 : ℚ))) + (U' := (2974553763560414341753 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (4276365180075649 / 10000000000000000 : ℚ)) + (q := (36257382881713221 / 80000000000000000 : ℚ)) + (U := (-(3956918039439585658247 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_12 : Uω (aρ 12) (bρ 12) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4926,26 +4274,21 @@ lemma U_602_12 : have hlg : Real.log (31545031787647909 / 80000000000000000 : ℝ) ≤ (-(9306105286396064384171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (31545031787647909 / 80000000000000000 : ℝ) = - (31545031787647909 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31545031787647909 / 20000000000000000 : ℚ)) - (U := (4556838319603935615829 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31545031787647909 / 20000000000000000 : ℝ) ≤ - (4556838319603935615829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3521977503244321 / 10000000000000000 : ℝ)) (q := - (31545031787647909 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31545031787647909 / 80000000000000000 : ℚ)) + (r' := (31545031787647909 / 20000000000000000 : ℚ)) + (U := (-(9306105286396064384171 / 10000000000000000000000 : ℚ))) + (U' := (4556838319603935615829 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (3521977503244321 / 10000000000000000 : ℚ)) + (q := (31545031787647909 / 80000000000000000 : ℚ)) + (U := (-(9306105286396064384171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_13 : Uω (aρ 13) (bρ 13) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4953,26 +4296,21 @@ lemma U_602_13 : have hlg : Real.log (5267093650724393 / 16000000000000000 : ℝ) ≤ (-(5555550003594789216321 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5267093650724393 / 16000000000000000 : ℝ) = - (5267093650724393 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5267093650724393 / 4000000000000000 : ℚ)) - (U := (1375921799405210783679 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5267093650724393 / 4000000000000000 : ℝ) ≤ - (1375921799405210783679 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (523793672266567 / 2000000000000000 : ℝ)) (q := - (5267093650724393 / 16000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5267093650724393 / 16000000000000000 : ℚ)) + (r' := (5267093650724393 / 4000000000000000 : ℚ)) + (U := (-(5555550003594789216321 / 5000000000000000000000 : ℚ))) + (U' := (1375921799405210783679 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (523793672266567 / 2000000000000000 : ℚ)) + (q := (5267093650724393 / 16000000000000000 : ℚ)) + (U := (-(5555550003594789216321 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_14 : Uω (aρ 14) (bρ 14) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -4980,26 +4318,21 @@ lemma U_602_14 : have hlg : Real.log (20257801050088877 / 80000000000000000 : ℝ) ≤ (-(6867433388723770022023 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20257801050088877 / 80000000000000000 : ℝ) = - (20257801050088877 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20257801050088877 / 20000000000000000 : ℚ)) - (U := (64038414276229977977 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20257801050088877 / 20000000000000000 : ℝ) ≤ - (64038414276229977977 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1443478845494563 / 10000000000000000 : ℝ)) (q := - (20257801050088877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20257801050088877 / 80000000000000000 : ℚ)) + (r' := (20257801050088877 / 20000000000000000 : ℚ)) + (U := (-(6867433388723770022023 / 5000000000000000000000 : ℚ))) + (U' := (64038414276229977977 / 5000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (8886491741437 / 12800000000000 : ℚ)) + (s := (1443478845494563 / 10000000000000000 : ℚ)) + (q := (20257801050088877 / 80000000000000000 : ℚ)) + (U := (-(6867433388723770022023 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_602_15 : Uω (aρ 15) (bρ 15) (8886491741437 / 12800000000000 : ℝ) ≤ @@ -5100,25 +4433,21 @@ lemma U_603_1 : have hlg : Real.log (27544653406839947 / 40000000000000000 : ℝ) ≤ (-(3730710058060810453223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27544653406839947 / 40000000000000000 : ℝ) = - (27544653406839947 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27544653406839947 / 20000000000000000 : ℚ)) - (U := (3200761744939189546777 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27544653406839947 / 20000000000000000 : ℝ) ≤ - (3200761744939189546777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3443069937251393 / 5000000000000000 : ℝ)) (q := - (27544653406839947 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27544653406839947 / 40000000000000000 : ℚ)) + (r' := (27544653406839947 / 20000000000000000 : ℚ)) + (U := (-(3730710058060810453223 / 10000000000000000000000 : ℚ))) + (U' := (3200761744939189546777 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (3443069937251393 / 5000000000000000 : ℚ)) + (q := (27544653406839947 / 40000000000000000 : ℚ)) + (U := (-(3730710058060810453223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_2 : Uω (aρ 2) (bρ 2) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5126,25 +4455,21 @@ lemma U_603_2 : have hlg : Real.log (5489810570668063 / 8000000000000000 : ℝ) ≤ (-(3765477909257897765203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5489810570668063 / 8000000000000000 : ℝ) = - (5489810570668063 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5489810570668063 / 4000000000000000 : ℚ)) - (U := (3165993893742102234797 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5489810570668063 / 4000000000000000 : ℝ) ≤ - (3165993893742102234797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (686210861026297 / 1000000000000000 : ℝ)) (q := - (5489810570668063 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5489810570668063 / 8000000000000000 : ℚ)) + (r' := (5489810570668063 / 4000000000000000 : ℚ)) + (U := (-(3765477909257897765203 / 10000000000000000000000 : ℚ))) + (U' := (3165993893742102234797 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (686210861026297 / 1000000000000000 : ℚ)) + (q := (5489810570668063 / 8000000000000000 : ℚ)) + (U := (-(3765477909257897765203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_3 : Uω (aρ 3) (bρ 3) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5152,25 +4477,21 @@ lemma U_603_3 : have hlg : Real.log (27257915557438993 / 40000000000000000 : ℝ) ≤ (-(1917677478767856130919 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27257915557438993 / 40000000000000000 : ℝ) = - (27257915557438993 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27257915557438993 / 20000000000000000 : ℚ)) - (U := (1548058422732143869081 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27257915557438993 / 20000000000000000 : ℝ) ≤ - (1548058422732143869081 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6813936068662309 / 10000000000000000 : ℝ)) (q := - (27257915557438993 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27257915557438993 / 40000000000000000 : ℚ)) + (r' := (27257915557438993 / 20000000000000000 : ℚ)) + (U := (-(1917677478767856130919 / 5000000000000000000000 : ℚ))) + (U' := (1548058422732143869081 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (6813936068662309 / 10000000000000000 : ℚ)) + (q := (27257915557438993 / 40000000000000000 : ℚ)) + (U := (-(1917677478767856130919 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_4 : Uω (aρ 4) (bρ 4) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5178,25 +4499,21 @@ lemma U_603_4 : have hlg : Real.log (26940661996627907 / 40000000000000000 : ℝ) ≤ (-(4940533877167384837 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26940661996627907 / 40000000000000000 : ℝ) = - (26940661996627907 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26940661996627907 / 20000000000000000 : ℚ)) - (U := (3723805876582615163 / 12500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26940661996627907 / 20000000000000000 : ℝ) ≤ - (3723805876582615163 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3366801734660883 / 5000000000000000 : ℝ)) (q := - (26940661996627907 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26940661996627907 / 40000000000000000 : ℚ)) + (r' := (26940661996627907 / 20000000000000000 : ℚ)) + (U := (-(4940533877167384837 / 12500000000000000000 : ℚ))) + (U' := (3723805876582615163 / 12500000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (3366801734660883 / 5000000000000000 : ℚ)) + (q := (26940661996627907 / 40000000000000000 : ℚ)) + (U := (-(4940533877167384837 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_5 : Uω (aρ 5) (bρ 5) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5204,25 +4521,21 @@ lemma U_603_5 : have hlg : Real.log (26458047397004643 / 40000000000000000 : ℝ) ≤ (-(413319092409985669183 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26458047397004643 / 40000000000000000 : ℝ) = - (26458047397004643 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26458047397004643 / 20000000000000000 : ℚ)) - (U := (279828087890014330817 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26458047397004643 / 20000000000000000 : ℝ) ≤ - (279828087890014330817 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3305243044422567 / 5000000000000000 : ℝ)) (q := - (26458047397004643 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26458047397004643 / 40000000000000000 : ℚ)) + (r' := (26458047397004643 / 20000000000000000 : ℚ)) + (U := (-(413319092409985669183 / 1000000000000000000000 : ℚ))) + (U' := (279828087890014330817 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (3305243044422567 / 5000000000000000 : ℚ)) + (q := (26458047397004643 / 40000000000000000 : ℚ)) + (U := (-(413319092409985669183 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_6 : Uω (aρ 6) (bρ 6) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5230,25 +4543,21 @@ lemma U_603_6 : have hlg : Real.log (1030683476754923 / 1600000000000000 : ℝ) ≤ (-(87956295428855053233 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1030683476754923 / 1600000000000000 : ℝ) = - (1030683476754923 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1030683476754923 / 800000000000000 : ℚ)) - (U := (50673140631144946767 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1030683476754923 / 800000000000000 : ℝ) ≤ - (50673140631144946767 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128644924498387 / 200000000000000 : ℝ)) (q := - (1030683476754923 / 1600000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1030683476754923 / 1600000000000000 : ℚ)) + (r' := (1030683476754923 / 800000000000000 : ℚ)) + (U := (-(87956295428855053233 / 200000000000000000000 : ℚ))) + (U' := (50673140631144946767 / 200000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (128644924498387 / 200000000000000 : ℚ)) + (q := (1030683476754923 / 1600000000000000 : ℚ)) + (U := (-(87956295428855053233 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_7 : Uω (aρ 7) (bρ 7) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5256,25 +4565,21 @@ lemma U_603_7 : have hlg : Real.log (4965394567297691 / 8000000000000000 : ℝ) ≤ (-(4769487773325352152819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4965394567297691 / 8000000000000000 : ℝ) = - (4965394567297691 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4965394567297691 / 4000000000000000 : ℚ)) - (U := (2161984029674647847181 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4965394567297691 / 4000000000000000 : ℝ) ≤ - (2161984029674647847181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9665391507011 / 15625000000000 : ℝ)) (q := - (4965394567297691 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4965394567297691 / 8000000000000000 : ℚ)) + (r' := (4965394567297691 / 4000000000000000 : ℚ)) + (U := (-(4769487773325352152819 / 10000000000000000000000 : ℚ))) + (U' := (2161984029674647847181 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (9665391507011 / 15625000000000 : ℚ)) + (q := (4965394567297691 / 8000000000000000 : ℚ)) + (U := (-(4769487773325352152819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_8 : Uω (aρ 8) (bρ 8) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5282,25 +4587,21 @@ lemma U_603_8 : have hlg : Real.log (4721081313255643 / 8000000000000000 : ℝ) ≤ (-(5274036762684941512903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4721081313255643 / 8000000000000000 : ℝ) = - (4721081313255643 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4721081313255643 / 4000000000000000 : ℚ)) - (U := (1657435040315058487097 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4721081313255643 / 4000000000000000 : ℝ) ≤ - (1657435040315058487097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2288519172157 / 3906250000000 : ℝ)) (q := - (4721081313255643 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4721081313255643 / 8000000000000000 : ℚ)) + (r' := (4721081313255643 / 4000000000000000 : ℚ)) + (U := (-(5274036762684941512903 / 10000000000000000000000 : ℚ))) + (U' := (1657435040315058487097 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (2288519172157 / 3906250000000 : ℚ)) + (q := (4721081313255643 / 8000000000000000 : ℚ)) + (U := (-(5274036762684941512903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_9 : Uω (aρ 9) (bρ 9) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5308,25 +4609,21 @@ lemma U_603_9 : have hlg : Real.log (22084417085315947 / 40000000000000000 : ℝ) ≤ (-(5940072032984582198809 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22084417085315947 / 40000000000000000 : ℝ) = - (22084417085315947 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22084417085315947 / 20000000000000000 : ℚ)) - (U := (991399770015417801191 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22084417085315947 / 20000000000000000 : ℝ) ≤ - (991399770015417801191 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2719539984300393 / 5000000000000000 : ℝ)) (q := - (22084417085315947 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22084417085315947 / 40000000000000000 : ℚ)) + (r' := (22084417085315947 / 20000000000000000 : ℚ)) + (U := (-(5940072032984582198809 / 10000000000000000000000 : ℚ))) + (U' := (991399770015417801191 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (2719539984300393 / 5000000000000000 : ℚ)) + (q := (22084417085315947 / 40000000000000000 : ℚ)) + (U := (-(5940072032984582198809 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_10 : Uω (aρ 10) (bρ 10) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5334,26 +4631,21 @@ lemma U_603_10 : have hlg : Real.log (4052846687656339 / 8000000000000000 : ℝ) ≤ (-(6800220213689320315221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4052846687656339 / 8000000000000000 : ℝ) = - (4052846687656339 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4052846687656339 / 4000000000000000 : ℚ)) - (U := (131251589310679684779 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (4052846687656339 / 4000000000000000 : ℝ) ≤ - (131251589310679684779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (245877358928933 / 500000000000000 : ℝ)) (q := - (4052846687656339 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4052846687656339 / 8000000000000000 : ℚ)) + (r' := (4052846687656339 / 4000000000000000 : ℚ)) + (U := (-(6800220213689320315221 / 10000000000000000000000 : ℚ))) + (U' := (131251589310679684779 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (245877358928933 / 500000000000000 : ℚ)) + (q := (4052846687656339 / 8000000000000000 : ℚ)) + (U := (-(6800220213689320315221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_11 : Uω (aρ 11) (bρ 11) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5361,26 +4653,21 @@ lemma U_603_11 : have hlg : Real.log (18163078137386779 / 40000000000000000 : ℝ) ≤ (-(3947442969135704496559 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18163078137386779 / 40000000000000000 : ℝ) = - (18163078137386779 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18163078137386779 / 10000000000000000 : ℚ)) - (U := (2984028833864295503441 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18163078137386779 / 10000000000000000 : ℝ) ≤ - (2984028833864295503441 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2142723077168101 / 5000000000000000 : ℝ)) (q := - (18163078137386779 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18163078137386779 / 40000000000000000 : ℚ)) + (r' := (18163078137386779 / 10000000000000000 : ℚ)) + (U := (-(3947442969135704496559 / 5000000000000000000000 : ℚ))) + (U' := (2984028833864295503441 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (2142723077168101 / 5000000000000000 : ℚ)) + (q := (18163078137386779 / 40000000000000000 : ℚ)) + (U := (-(3947442969135704496559 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_12 : Uω (aρ 12) (bρ 12) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5388,26 +4675,21 @@ lemma U_603_12 : have hlg : Real.log (15808835661897267 / 40000000000000000 : ℝ) ≤ (-(9283104507584379732129 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15808835661897267 / 40000000000000000 : ℝ) = - (15808835661897267 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15808835661897267 / 10000000000000000 : ℚ)) - (U := (4579839098415620267871 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15808835661897267 / 10000000000000000 : ℝ) ≤ - (4579839098415620267871 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1766012506638223 / 5000000000000000 : ℝ)) (q := - (15808835661897267 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15808835661897267 / 40000000000000000 : ℚ)) + (r' := (15808835661897267 / 10000000000000000 : ℚ)) + (U := (-(9283104507584379732129 / 10000000000000000000000 : ℚ))) + (U' := (4579839098415620267871 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (1766012506638223 / 5000000000000000 : ℚ)) + (q := (15808835661897267 / 40000000000000000 : ℚ)) + (U := (-(9283104507584379732129 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_13 : Uω (aρ 13) (bρ 13) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5415,26 +4697,21 @@ lemma U_603_13 : have hlg : Real.log (13208489471044621 / 40000000000000000 : ℝ) ≤ (-(11080196889829367210413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13208489471044621 / 40000000000000000 : ℝ) = - (13208489471044621 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13208489471044621 / 10000000000000000 : ℚ)) - (U := (2782746716170632789587 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13208489471044621 / 10000000000000000 : ℝ) ≤ - (2782746716170632789587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2631233659445123 / 10000000000000000 : ℝ)) (q := - (13208489471044621 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13208489471044621 / 40000000000000000 : ℚ)) + (r' := (13208489471044621 / 10000000000000000 : ℚ)) + (U := (-(11080196889829367210413 / 10000000000000000000000 : ℚ))) + (U' := (2782746716170632789587 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (2631233659445123 / 10000000000000000 : ℚ)) + (q := (13208489471044621 / 40000000000000000 : ℚ)) + (U := (-(11080196889829367210413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_14 : Uω (aρ 14) (bρ 14) (22242188950407 / 32000000000000 : ℝ) ≤ @@ -5442,26 +4719,21 @@ lemma U_603_14 : have hlg : Real.log (10185587153490103 / 40000000000000000 : ℝ) ≤ (-(341976439182884107769 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10185587153490103 / 40000000000000000 : ℝ) = - (10185587153490103 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10185587153490103 / 10000000000000000 : ℚ)) - (U := (4597150967115892231 / 250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10185587153490103 / 10000000000000000 : ℝ) ≤ - (4597150967115892231 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45740930803527 / 312500000000000 : ℝ)) (q := - (10185587153490103 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10185587153490103 / 40000000000000000 : ℚ)) + (r' := (10185587153490103 / 10000000000000000 : ℚ)) + (U := (-(341976439182884107769 / 250000000000000000000 : ℚ))) + (U' := (4597150967115892231 / 250000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22242188950407 / 32000000000000 : ℚ)) + (s := (45740930803527 / 312500000000000 : ℚ)) + (q := (10185587153490103 / 40000000000000000 : ℚ)) + (U := (-(341976439182884107769 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_603_15 : Uω (aρ 15) (bρ 15) (22242188950407 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U50.lean b/LeanPool/Zeta5Irrational/Table/U50.lean index cfa11a4ba7..c88b9c3244 100644 --- a/LeanPool/Zeta5Irrational/Table/U50.lean +++ b/LeanPool/Zeta5Irrational/Table/U50.lean @@ -24,25 +24,21 @@ lemma U_604_1 : have hlg : Real.log (6902388154904741 / 10000000000000000 : ℝ) ≤ (-(185358815803223170541 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6902388154904741 / 10000000000000000 : ℝ) = - (6902388154904741 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6902388154904741 / 5000000000000000 : ℚ)) - (U := (161214774346776829459 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6902388154904741 / 5000000000000000 : ℝ) ≤ - (161214774346776829459 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (215698897902601 / 312500000000000 : ℝ)) (q := - (6902388154904741 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6902388154904741 / 10000000000000000 : ℚ)) + (r' := (6902388154904741 / 5000000000000000 : ℚ)) + (U := (-(185358815803223170541 / 500000000000000000000 : ℚ))) + (U' := (161214774346776829459 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (215698897902601 / 312500000000000 : ℚ)) + (q := (6902388154904741 / 10000000000000000 : ℚ)) + (U := (-(185358815803223170541 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_2 : Uω (aρ 2) (bρ 2) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_604_2 : have hlg : Real.log (6878488326024889 / 10000000000000000 : ℝ) ≤ (-(3741861849853575925477 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6878488326024889 / 10000000000000000 : ℝ) = - (6878488326024889 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6878488326024889 / 5000000000000000 : ℚ)) - (U := (3189609953146424074523 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6878488326024889 / 5000000000000000 : ℝ) ≤ - (3189609953146424074523 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (859791760954191 / 1250000000000000 : ℝ)) (q := - (6878488326024889 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6878488326024889 / 10000000000000000 : ℚ)) + (r' := (6878488326024889 / 5000000000000000 : ℚ)) + (U := (-(3741861849853575925477 / 10000000000000000000000 : ℚ))) + (U' := (3189609953146424074523 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (859791760954191 / 1250000000000000 : ℚ)) + (q := (6878488326024889 / 10000000000000000 : ℚ)) + (U := (-(3741861849853575925477 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_3 : Uω (aρ 3) (bρ 3) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_604_3 : have hlg : Real.log (13661409853630741 / 20000000000000000 : ℝ) ≤ (-(762314428217885278549 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13661409853630741 / 20000000000000000 : ℝ) = - (13661409853630741 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13661409853630741 / 10000000000000000 : ℚ)) - (U := (623979932382114721451 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13661409853630741 / 10000000000000000 : ℝ) ≤ - (623979932382114721451 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6830163395564491 / 10000000000000000 : ℝ)) (q := - (13661409853630741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13661409853630741 / 20000000000000000 : ℚ)) + (r' := (13661409853630741 / 10000000000000000 : ℚ)) + (U := (-(762314428217885278549 / 2000000000000000000000 : ℚ))) + (U' := (623979932382114721451 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (6830163395564491 / 10000000000000000 : ℚ)) + (q := (13661409853630741 / 20000000000000000 : ℚ)) + (U := (-(762314428217885278549 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_4 : Uω (aρ 4) (bρ 4) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_604_4 : have hlg : Real.log (6751394001858091 / 10000000000000000 : ℝ) ≤ (-(392836090377941199433 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6751394001858091 / 10000000000000000 : ℝ) = - (6751394001858091 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6751394001858091 / 5000000000000000 : ℚ)) - (U := (300311089922058800567 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6751394001858091 / 5000000000000000 : ℝ) ≤ - (300311089922058800567 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1687458931678733 / 2500000000000000 : ℝ)) (q := - (6751394001858091 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6751394001858091 / 10000000000000000 : ℚ)) + (r' := (6751394001858091 / 5000000000000000 : ℚ)) + (U := (-(392836090377941199433 / 1000000000000000000000 : ℚ))) + (U' := (300311089922058800567 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (1687458931678733 / 2500000000000000 : ℚ)) + (q := (6751394001858091 / 10000000000000000 : ℚ)) + (U := (-(392836090377941199433 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_5 : Uω (aρ 5) (bρ 5) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_604_5 : have hlg : Real.log (13261492907724353 / 20000000000000000 : ℝ) ≤ (-(2054338537821379043431 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13261492907724353 / 20000000000000000 : ℝ) = - (13261492907724353 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13261492907724353 / 10000000000000000 : ℚ)) - (U := (1411397363678620956569 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13261492907724353 / 10000000000000000 : ℝ) ≤ - (1411397363678620956569 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6626730550058103 / 10000000000000000 : ℝ)) (q := - (13261492907724353 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13261492907724353 / 20000000000000000 : ℚ)) + (r' := (13261492907724353 / 10000000000000000 : ℚ)) + (U := (-(2054338537821379043431 / 5000000000000000000000 : ℚ))) + (U' := (1411397363678620956569 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (6626730550058103 / 10000000000000000 : ℚ)) + (q := (13261492907724353 / 20000000000000000 : ℚ)) + (U := (-(2054338537821379043431 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_6 : Uω (aρ 6) (bρ 6) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_604_6 : have hlg : Real.log (12916040888783747 / 20000000000000000 : ℝ) ≤ (-(1093155636640941648659 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12916040888783747 / 20000000000000000 : ℝ) = - (12916040888783747 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12916040888783747 / 10000000000000000 : ℚ)) - (U := (639712314109058351341 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12916040888783747 / 10000000000000000 : ℝ) ≤ - (639712314109058351341 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6448518906257497 / 10000000000000000 : ℝ)) (q := - (12916040888783747 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12916040888783747 / 20000000000000000 : ℚ)) + (r' := (12916040888783747 / 10000000000000000 : ℚ)) + (U := (-(1093155636640941648659 / 2500000000000000000000 : ℚ))) + (U' := (639712314109058351341 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (6448518906257497 / 10000000000000000 : ℚ)) + (q := (12916040888783747 / 20000000000000000 : ℚ)) + (U := (-(1093155636640941648659 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_7 : Uω (aρ 7) (bρ 7) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_604_7 : have hlg : Real.log (12446045224417483 / 20000000000000000 : ℝ) ≤ (-(948658707005702538837 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12446045224417483 / 20000000000000000 : ℝ) = - (12446045224417483 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12446045224417483 / 10000000000000000 : ℚ)) - (U := (437635653594297461163 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12446045224417483 / 10000000000000000 : ℝ) ≤ - (437635653594297461163 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6202184622651233 / 10000000000000000 : ℝ)) (q := - (12446045224417483 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12446045224417483 / 20000000000000000 : ℚ)) + (r' := (12446045224417483 / 10000000000000000 : ℚ)) + (U := (-(948658707005702538837 / 2000000000000000000000 : ℚ))) + (U' := (437635653594297461163 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (6202184622651233 / 10000000000000000 : ℚ)) + (q := (12446045224417483 / 20000000000000000 : ℚ)) + (U := (-(948658707005702538837 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_8 : Uω (aρ 8) (bρ 8) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_604_8 : have hlg : Real.log (5917694430933567 / 10000000000000000 : ℝ) ≤ (-(5246381739293769484407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5917694430933567 / 10000000000000000 : ℝ) = - (5917694430933567 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5917694430933567 / 5000000000000000 : ℚ)) - (U := (1685090063706230515593 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5917694430933567 / 5000000000000000 : ℝ) ≤ - (1685090063706230515593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1468767477860221 / 2500000000000000 : ℝ)) (q := - (5917694430933567 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5917694430933567 / 10000000000000000 : ℚ)) + (r' := (5917694430933567 / 5000000000000000 : ℚ)) + (U := (-(5246381739293769484407 / 10000000000000000000000 : ℚ))) + (U' := (1685090063706230515593 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (1468767477860221 / 2500000000000000 : ℚ)) + (q := (5917694430933567 / 10000000000000000 : ℚ)) + (U := (-(5246381739293769484407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_9 : Uω (aρ 9) (bρ 9) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_604_9 : have hlg : Real.log (11075145917614141 / 20000000000000000 : ℝ) ≤ (-(591028782044301194203 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11075145917614141 / 20000000000000000 : ℝ) = - (11075145917614141 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11075145917614141 / 10000000000000000 : ℚ)) - (U := (102118398255698805797 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11075145917614141 / 10000000000000000 : ℝ) ≤ - (102118398255698805797 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5455792595547891 / 10000000000000000 : ℝ)) (q := - (11075145917614141 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11075145917614141 / 20000000000000000 : ℚ)) + (r' := (11075145917614141 / 10000000000000000 : ℚ)) + (U := (-(591028782044301194203 / 1000000000000000000000 : ℚ))) + (U' := (102118398255698805797 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (5455792595547891 / 10000000000000000 : ℚ)) + (q := (11075145917614141 / 20000000000000000 : ℚ)) + (U := (-(591028782044301194203 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_10 : Uω (aρ 10) (bρ 10) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_604_10 : have hlg : Real.log (10165542878878319 / 20000000000000000 : ℝ) ≤ (-(6767284209621708981663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10165542878878319 / 20000000000000000 : ℝ) = - (10165542878878319 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10165542878878319 / 10000000000000000 : ℚ)) - (U := (164187593378291018337 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10165542878878319 / 10000000000000000 : ℝ) ≤ - (164187593378291018337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4934748590307069 / 10000000000000000 : ℝ)) (q := - (10165542878878319 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10165542878878319 / 20000000000000000 : ℚ)) + (r' := (10165542878878319 / 10000000000000000 : ℚ)) + (U := (-(6767284209621708981663 / 10000000000000000000000 : ℚ))) + (U' := (164187593378291018337 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (4934748590307069 / 10000000000000000 : ℚ)) + (q := (10165542878878319 / 20000000000000000 : ℚ)) + (U := (-(6767284209621708981663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_11 : Uω (aρ 11) (bρ 11) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_604_11 : have hlg : Real.log (4557957078120433 / 10000000000000000 : ℝ) ≤ (-(1964276446295185408741 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4557957078120433 / 10000000000000000 : ℝ) = - (4557957078120433 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4557957078120433 / 2500000000000000 : ℚ)) - (U := (1501459455204814591259 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4557957078120433 / 2500000000000000 : ℝ) ≤ - (1501459455204814591259 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (537949561734327 / 1250000000000000 : ℝ)) (q := - (4557957078120433 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4557957078120433 / 10000000000000000 : ℚ)) + (r' := (4557957078120433 / 2500000000000000 : ℚ)) + (U := (-(1964276446295185408741 / 2500000000000000000000 : ℚ))) + (U' := (1501459455204814591259 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (537949561734327 / 1250000000000000 : ℚ)) + (q := (4557957078120433 / 10000000000000000 : ℚ)) + (U := (-(1964276446295185408741 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_12 : Uω (aρ 12) (bρ 12) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_604_12 : have hlg : Real.log (1588141583857573 / 4000000000000000 : ℝ) ≤ (-(9237298431489610316859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1588141583857573 / 4000000000000000 : ℝ) = - (1588141583857573 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1588141583857573 / 1000000000000000 : ℚ)) - (U := (4625645174510389683141 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1588141583857573 / 1000000000000000 : ℝ) ≤ - (4625645174510389683141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (710418070721323 / 2000000000000000 : ℝ)) (q := - (1588141583857573 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1588141583857573 / 4000000000000000 : ℚ)) + (r' := (1588141583857573 / 1000000000000000 : ℚ)) + (U := (-(9237298431489610316859 / 10000000000000000000000 : ℚ))) + (U' := (4625645174510389683141 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (710418070721323 / 2000000000000000 : ℚ)) + (q := (1588141583857573 / 4000000000000000 : ℚ)) + (U := (-(9237298431489610316859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_13 : Uω (aρ 13) (bρ 13) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -339,26 +288,21 @@ lemma U_604_13 : have hlg : Real.log (6644904481908243 / 20000000000000000 : ℝ) ≤ (-(440752782161147218229 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6644904481908243 / 20000000000000000 : ℝ) = - (6644904481908243 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6644904481908243 / 5000000000000000 : ℚ)) - (U := (113764962078852781771 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6644904481908243 / 5000000000000000 : ℝ) ≤ - (113764962078852781771 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2655668657821993 / 10000000000000000 : ℝ)) (q := - (6644904481908243 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6644904481908243 / 20000000000000000 : ℚ)) + (r' := (6644904481908243 / 5000000000000000 : ℚ)) + (U := (-(440752782161147218229 / 400000000000000000000 : ℚ))) + (U' := (113764962078852781771 / 400000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (2655668657821993 / 10000000000000000 : ℚ)) + (q := (6644904481908243 / 20000000000000000 : ℚ)) + (U := (-(440752782161147218229 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_14 : Uω (aρ 14) (bρ 14) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -366,26 +310,21 @@ lemma U_604_14 : have hlg : Real.log (1029758998734929 / 4000000000000000 : ℝ) ≤ (-(13569695675472187431089 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1029758998734929 / 4000000000000000 : ℝ) = - (1029758998734929 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1029758998734929 / 1000000000000000 : ℚ)) - (U := (293247930527812568911 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1029758998734929 / 1000000000000000 : ℝ) ≤ - (293247930527812568911 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (300697290926679 / 2000000000000000 : ℝ)) (q := - (1029758998734929 / 4000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1029758998734929 / 4000000000000000 : ℚ)) + (r' := (1029758998734929 / 1000000000000000 : ℚ)) + (U := (-(13569695675472187431089 / 10000000000000000000000 : ℚ))) + (U' := (293247930527812568911 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5573527036009 / 8000000000000 : ℚ)) + (s := (300697290926679 / 2000000000000000 : ℚ)) + (q := (1029758998734929 / 4000000000000000 : ℚ)) + (U := (-(13569695675472187431089 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_604_15 : Uω (aρ 15) (bρ 15) (5573527036009 / 8000000000000 : ℝ) ≤ @@ -487,25 +426,21 @@ lemma U_605_1 : have hlg : Real.log (27674451831362653 / 40000000000000000 : ℝ) ≤ (-(3683697828136284471879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27674451831362653 / 40000000000000000 : ℝ) = - (27674451831362653 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27674451831362653 / 20000000000000000 : ℚ)) - (U := (3247773974863715528121 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27674451831362653 / 20000000000000000 : ℝ) ≤ - (3247773974863715528121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3459294795373007 / 5000000000000000 : ℝ)) (q := - (27674451831362653 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27674451831362653 / 40000000000000000 : ℚ)) + (r' := (27674451831362653 / 20000000000000000 : ℚ)) + (U := (-(3683697828136284471879 / 10000000000000000000000 : ℚ))) + (U' := (3247773974863715528121 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (3459294795373007 / 5000000000000000 : ℚ)) + (q := (27674451831362653 / 40000000000000000 : ℚ)) + (U := (-(3683697828136284471879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_2 : Uω (aρ 2) (bρ 2) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -513,25 +448,21 @@ lemma U_605_2 : have hlg : Real.log (27578853747993111 / 40000000000000000 : ℝ) ≤ (-(743660286677977302009 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27578853747993111 / 40000000000000000 : ℝ) = - (27578853747993111 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27578853747993111 / 20000000000000000 : ℚ)) - (U := (642634073922022697991 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27578853747993111 / 20000000000000000 : ℝ) ≤ - (642634073922022697991 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6894559561571243 / 10000000000000000 : ℝ)) (q := - (27578853747993111 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27578853747993111 / 40000000000000000 : ℚ)) + (r' := (27578853747993111 / 20000000000000000 : ℚ)) + (U := (-(743660286677977302009 / 2000000000000000000000 : ℚ))) + (U' := (642634073922022697991 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (6894559561571243 / 10000000000000000 : ℚ)) + (q := (27578853747993111 / 40000000000000000 : ℚ)) + (U := (-(743660286677977302009 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_3 : Uω (aρ 3) (bρ 3) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -539,25 +470,21 @@ lemma U_605_3 : have hlg : Real.log (27387723832635927 / 40000000000000000 : ℝ) ≤ (-(236740360101894332047 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27387723832635927 / 40000000000000000 : ℝ) = - (27387723832635927 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27387723832635927 / 20000000000000000 : ℚ)) - (U := (196476627585605667953 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27387723832635927 / 20000000000000000 : ℝ) ≤ - (196476627585605667953 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6846390710242651 / 10000000000000000 : ℝ)) (q := - (27387723832635927 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27387723832635927 / 40000000000000000 : ℚ)) + (r' := (27387723832635927 / 20000000000000000 : ℚ)) + (U := (-(236740360101894332047 / 625000000000000000000 : ℚ))) + (U' := (196476627585605667953 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (6846390710242651 / 10000000000000000 : ℚ)) + (q := (27387723832635927 / 40000000000000000 : ℚ)) + (U := (-(236740360101894332047 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_4 : Uω (aρ 4) (bρ 4) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -565,25 +492,21 @@ lemma U_605_4 : have hlg : Real.log (27070489946191399 / 40000000000000000 : ℝ) ≤ (-(488044063950332874121 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27070489946191399 / 40000000000000000 : ℝ) = - (27070489946191399 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27070489946191399 / 20000000000000000 : ℚ)) - (U := (378389911424667125879 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27070489946191399 / 20000000000000000 : ℝ) ≤ - (378389911424667125879 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6766067948085387 / 10000000000000000 : ℝ)) (q := - (27070489946191399 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27070489946191399 / 40000000000000000 : ℚ)) + (r' := (27070489946191399 / 20000000000000000 : ℚ)) + (U := (-(488044063950332874121 / 1250000000000000000000 : ℚ))) + (U' := (378389911424667125879 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (6766067948085387 / 10000000000000000 : ℚ)) + (q := (27070489946191399 / 40000000000000000 : ℚ)) + (U := (-(488044063950332874121 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_5 : Uω (aρ 5) (bρ 5) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -591,25 +514,21 @@ lemma U_605_5 : have hlg : Real.log (26587924041186297 / 40000000000000000 : ℝ) ≤ (-(1021055811405140322069 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26587924041186297 / 40000000000000000 : ℝ) = - (26587924041186297 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26587924041186297 / 20000000000000000 : ℚ)) - (U := (711812139344859677931 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26587924041186297 / 20000000000000000 : ℝ) ≤ - (711812139344859677931 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1660743728729459 / 2500000000000000 : ℝ)) (q := - (26587924041186297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26587924041186297 / 40000000000000000 : ℚ)) + (r' := (26587924041186297 / 20000000000000000 : ℚ)) + (U := (-(1021055811405140322069 / 2500000000000000000000 : ℚ))) + (U' := (711812139344859677931 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (1660743728729459 / 2500000000000000 : ℚ)) + (q := (26587924041186297 / 40000000000000000 : ℚ)) + (U := (-(1021055811405140322069 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_6 : Uω (aρ 6) (bρ 6) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -617,25 +536,21 @@ lemma U_605_6 : have hlg : Real.log (25897076154356201 / 40000000000000000 : ℝ) ≤ (-(4347493813142281048483 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25897076154356201 / 40000000000000000 : ℝ) = - (25897076154356201 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25897076154356201 / 20000000000000000 : ℚ)) - (U := (2583977989857718951517 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25897076154356201 / 20000000000000000 : ℝ) ≤ - (2583977989857718951517 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1616197836660697 / 2500000000000000 : ℝ)) (q := - (25897076154356201 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25897076154356201 / 40000000000000000 : ℚ)) + (r' := (25897076154356201 / 20000000000000000 : ℚ)) + (U := (-(4347493813142281048483 / 10000000000000000000000 : ℚ))) + (U' := (2583977989857718951517 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (1616197836660697 / 2500000000000000 : ℚ)) + (q := (25897076154356201 / 40000000000000000 : ℚ)) + (U := (-(4347493813142281048483 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_7 : Uω (aρ 7) (bρ 7) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -643,25 +558,21 @@ lemma U_605_7 : have hlg : Real.log (24957206916533209 / 40000000000000000 : ℝ) ≤ (-(235858409498393209151 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24957206916533209 / 40000000000000000 : ℝ) = - (24957206916533209 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24957206916533209 / 20000000000000000 : ℚ)) - (U := (110715180651606790849 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24957206916533209 / 20000000000000000 : ℝ) ≤ - (110715180651606790849 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1554629527122823 / 2500000000000000 : ℝ)) (q := - (24957206916533209 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24957206916533209 / 40000000000000000 : ℚ)) + (r' := (24957206916533209 / 20000000000000000 : ℚ)) + (U := (-(235858409498393209151 / 500000000000000000000 : ℚ))) + (U' := (110715180651606790849 / 500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (1554629527122823 / 2500000000000000 : ℚ)) + (q := (24957206916533209 / 40000000000000000 : ℚ)) + (U := (-(235858409498393209151 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_8 : Uω (aρ 8) (bρ 8) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -669,25 +580,21 @@ lemma U_605_8 : have hlg : Real.log (23736146261667077 / 40000000000000000 : ℝ) ≤ (-(5218804088661256319739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23736146261667077 / 40000000000000000 : ℝ) = - (23736146261667077 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23736146261667077 / 20000000000000000 : ℚ)) - (U := (1712667714338743680261 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23736146261667077 / 20000000000000000 : ℝ) ≤ - (1712667714338743680261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2945764716199113 / 5000000000000000 : ℝ)) (q := - (23736146261667077 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23736146261667077 / 40000000000000000 : ℚ)) + (r' := (23736146261667077 / 20000000000000000 : ℚ)) + (U := (-(5218804088661256319739 / 10000000000000000000000 : ℚ))) + (U' := (1712667714338743680261 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (2945764716199113 / 5000000000000000 : ℚ)) + (q := (23736146261667077 / 40000000000000000 : ℚ)) + (U := (-(5218804088661256319739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_9 : Uω (aρ 9) (bρ 9) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -695,25 +602,21 @@ lemma U_605_9 : have hlg : Real.log (22216160712343729 / 40000000000000000 : ℝ) ≤ (-(1470148674486619797487 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22216160712343729 / 40000000000000000 : ℝ) = - (22216160712343729 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22216160712343729 / 20000000000000000 : ℚ)) - (U := (262719276263380202513 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22216160712343729 / 20000000000000000 : ℝ) ≤ - (262719276263380202513 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (684062785762069 / 1250000000000000 : ℝ)) (q := - (22216160712343729 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22216160712343729 / 40000000000000000 : ℚ)) + (r' := (22216160712343729 / 20000000000000000 : ℚ)) + (U := (-(1470148674486619797487 / 2500000000000000000000 : ℚ))) + (U' := (262719276263380202513 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (684062785762069 / 1250000000000000 : ℚ)) + (q := (22216160712343729 / 40000000000000000 : ℚ)) + (U := (-(1470148674486619797487 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_10 : Uω (aρ 10) (bρ 10) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -721,26 +624,21 @@ lemma U_605_10 : have hlg : Real.log (20397924892066461 / 40000000000000000 : ℝ) ≤ (-(3367231395774420070013 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20397924892066461 / 40000000000000000 : ℝ) = - (20397924892066461 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20397924892066461 / 20000000000000000 : ℚ)) - (U := (98504505725579929987 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20397924892066461 / 20000000000000000 : ℝ) ≤ - (98504505725579929987 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2475971704726459 / 5000000000000000 : ℝ)) (q := - (20397924892066461 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20397924892066461 / 40000000000000000 : ℚ)) + (r' := (20397924892066461 / 20000000000000000 : ℚ)) + (U := (-(3367231395774420070013 / 5000000000000000000000 : ℚ))) + (U' := (98504505725579929987 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (2475971704726459 / 5000000000000000 : ℚ)) + (q := (20397924892066461 / 40000000000000000 : ℚ)) + (U := (-(3367231395774420070013 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_11 : Uω (aρ 11) (bρ 11) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -748,26 +646,21 @@ lemma U_605_11 : have hlg : Real.log (18300547855289677 / 40000000000000000 : ℝ) ≤ (-(977435570934079413611 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18300547855289677 / 40000000000000000 : ℝ) = - (18300547855289677 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18300547855289677 / 10000000000000000 : ℚ)) - (U := (755432379815920586389 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18300547855289677 / 10000000000000000 : ℝ) ≤ - (755432379815920586389 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2160865758634763 / 5000000000000000 : ℝ)) (q := - (18300547855289677 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18300547855289677 / 40000000000000000 : ℚ)) + (r' := (18300547855289677 / 10000000000000000 : ℚ)) + (U := (-(977435570934079413611 / 1250000000000000000000 : ℚ))) + (U' := (755432379815920586389 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (2160865758634763 / 5000000000000000 : ℚ)) + (q := (18300547855289677 / 40000000000000000 : ℚ)) + (U := (-(977435570934079413611 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_12 : Uω (aρ 12) (bρ 12) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -775,26 +668,21 @@ lemma U_605_12 : have hlg : Real.log (15953917980471991 / 40000000000000000 : ℝ) ≤ (-(4595875065596004995123 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15953917980471991 / 40000000000000000 : ℝ) = - (15953917980471991 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15953917980471991 / 10000000000000000 : ℚ)) - (U := (2335596737403995004877 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15953917980471991 / 10000000000000000 : ℝ) ≤ - (2335596737403995004877 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3572116676545683 / 10000000000000000 : ℝ)) (q := - (15953917980471991 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15953917980471991 / 40000000000000000 : ℚ)) + (r' := (15953917980471991 / 10000000000000000 : ℚ)) + (U := (-(4595875065596004995123 / 5000000000000000000000 : ℚ))) + (U' := (2335596737403995004877 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (3572116676545683 / 10000000000000000 : ℚ)) + (q := (15953917980471991 / 40000000000000000 : ℚ)) + (U := (-(4595875065596004995123 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_13 : Uω (aρ 13) (bρ 13) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -802,26 +690,21 @@ lemma U_605_13 : have hlg : Real.log (2674175867206639 / 8000000000000000 : ℝ) ≤ (-(10958002953060884909373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2674175867206639 / 8000000000000000 : ℝ) = - (2674175867206639 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2674175867206639 / 2000000000000000 : ℚ)) - (U := (2904940652939115090627 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2674175867206639 / 2000000000000000 : ℝ) ≤ - (2904940652939115090627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (535995819184257 / 2000000000000000 : ℝ)) (q := - (2674175867206639 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2674175867206639 / 8000000000000000 : ℚ)) + (r' := (2674175867206639 / 2000000000000000 : ℚ)) + (U := (-(10958002953060884909373 / 10000000000000000000000 : ℚ))) + (U' := (2904940652939115090627 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (535995819184257 / 2000000000000000 : ℚ)) + (q := (2674175867206639 / 8000000000000000 : ℚ)) + (U := (-(10958002953060884909373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_14 : Uω (aρ 14) (bρ 14) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -829,26 +712,21 @@ lemma U_605_14 : have hlg : Real.log (10407883059168421 / 40000000000000000 : ℝ) ≤ (-(6731579740574347026997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10407883059168421 / 40000000000000000 : ℝ) = - (10407883059168421 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10407883059168421 / 10000000000000000 : ℚ)) - (U := (199892062425652973003 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10407883059168421 / 10000000000000000 : ℝ) ≤ - (199892062425652973003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (771204121266949 / 5000000000000000 : ℝ)) (q := - (10407883059168421 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10407883059168421 / 40000000000000000 : ℚ)) + (r' := (10407883059168421 / 10000000000000000 : ℚ)) + (U := (-(6731579740574347026997 / 5000000000000000000000 : ℚ))) + (U' := (199892062425652973003 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (4469205467533 / 6400000000000 : ℚ)) + (s := (771204121266949 / 5000000000000000 : ℚ)) + (q := (10407883059168421 / 40000000000000000 : ℚ)) + (U := (-(6731579740574347026997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_605_15 : Uω (aρ 15) (bρ 15) (4469205467533 / 6400000000000 : ℝ) ≤ @@ -951,25 +829,21 @@ lemma U_606_1 : have hlg : Real.log (693483776051957 / 1000000000000000 : ℝ) ≤ (-(36602743354238826769 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (693483776051957 / 1000000000000000 : ℝ) = - (693483776051957 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (693483776051957 / 500000000000000 : ℚ)) - (U := (32711974675761173231 / 100000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (693483776051957 / 500000000000000 : ℝ) ≤ - (32711974675761173231 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1386962889618953 / 2000000000000000 : ℝ)) (q := - (693483776051957 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (693483776051957 / 1000000000000000 : ℚ)) + (r' := (693483776051957 / 500000000000000 : ℚ)) + (U := (-(36602743354238826769 / 100000000000000000000 : ℚ))) + (U' := (32711974675761173231 / 100000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (1386962889618953 / 2000000000000000 : ℚ)) + (q := (693483776051957 / 1000000000000000 : ℚ)) + (U := (-(36602743354238826769 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_2 : Uω (aρ 2) (bρ 2) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -977,25 +851,21 @@ lemma U_606_2 : have hlg : Real.log (3455469273133667 / 5000000000000000 : ℝ) ≤ (-(1847398199132677266083 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3455469273133667 / 5000000000000000 : ℝ) = - (3455469273133667 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3455469273133667 / 2500000000000000 : ℚ)) - (U := (1618337702367322733917 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3455469273133667 / 2500000000000000 : ℝ) ≤ - (1618337702367322733917 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6910785032100293 / 10000000000000000 : ℝ)) (q := - (3455469273133667 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3455469273133667 / 5000000000000000 : ℚ)) + (r' := (3455469273133667 / 2500000000000000 : ℚ)) + (U := (-(1847398199132677266083 / 5000000000000000000000 : ℚ))) + (U' := (1618337702367322733917 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (6910785032100293 / 10000000000000000 : ℚ)) + (q := (3455469273133667 / 5000000000000000 : ℚ)) + (U := (-(1847398199132677266083 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_3 : Uω (aρ 3) (bρ 3) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1003,25 +873,21 @@ lemma U_606_3 : have hlg : Real.log (6863156983433939 / 10000000000000000 : ℝ) ≤ (-(47052194398732723493 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6863156983433939 / 10000000000000000 : ℝ) = - (6863156983433939 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6863156983433939 / 5000000000000000 : ℚ)) - (U := (39591203138767276507 / 125000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6863156983433939 / 5000000000000000 : ℝ) ≤ - (39591203138767276507 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6862618012783503 / 10000000000000000 : ℝ)) (q := - (6863156983433939 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6863156983433939 / 10000000000000000 : ℚ)) + (r' := (6863156983433939 / 5000000000000000 : ℚ)) + (U := (-(47052194398732723493 / 125000000000000000000 : ℚ))) + (U' := (39591203138767276507 / 125000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (6862618012783503 / 10000000000000000 : ℚ)) + (q := (6863156983433939 / 10000000000000000 : ℚ)) + (U := (-(47052194398732723493 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_4 : Uω (aρ 4) (bρ 4) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1029,25 +895,21 @@ lemma U_606_4 : have hlg : Real.log (6783850953355573 / 10000000000000000 : ℝ) ≤ (-(1940200824024491061991 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6783850953355573 / 10000000000000000 : ℝ) = - (6783850953355573 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6783850953355573 / 5000000000000000 : ℚ)) - (U := (1525535077475508938009 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6783850953355573 / 5000000000000000 : ℝ) ≤ - (1525535077475508938009 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6782300133691771 / 10000000000000000 : ℝ)) (q := - (6783850953355573 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6783850953355573 / 10000000000000000 : ℚ)) + (r' := (6783850953355573 / 5000000000000000 : ℚ)) + (U := (-(1940200824024491061991 / 5000000000000000000000 : ℚ))) + (U' := (1525535077475508938009 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (6782300133691771 / 10000000000000000 : ℚ)) + (q := (6783850953355573 / 10000000000000000 : ℚ)) + (U := (-(1940200824024491061991 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_5 : Uω (aρ 5) (bρ 5) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1055,25 +917,21 @@ lemma U_606_5 : have hlg : Real.log (13326431037813833 / 20000000000000000 : ℝ) ≤ (-(4059829140506769287007 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13326431037813833 / 20000000000000000 : ℝ) = - (13326431037813833 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13326431037813833 / 10000000000000000 : ℚ)) - (U := (2871642662493230712993 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13326431037813833 / 10000000000000000 : ℝ) ≤ - (2871642662493230712993 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3329609592064729 / 5000000000000000 : ℝ)) (q := - (13326431037813833 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13326431037813833 / 20000000000000000 : ℚ)) + (r' := (13326431037813833 / 10000000000000000 : ℚ)) + (U := (-(4059829140506769287007 / 10000000000000000000000 : ℚ))) + (U' := (2871642662493230712993 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (3329609592064729 / 5000000000000000 : ℚ)) + (q := (13326431037813833 / 20000000000000000 : ℚ)) + (U := (-(4059829140506769287007 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_6 : Uω (aρ 6) (bρ 6) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1081,25 +939,21 @@ lemma U_606_6 : have hlg : Real.log (519241401057381 / 800000000000000 : ℝ) ≤ (-(2161214125510321744941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (519241401057381 / 800000000000000 : ℝ) = - (519241401057381 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (519241401057381 / 400000000000000 : ℚ)) - (U := (1304521775989678255059 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (519241401057381 / 400000000000000 : ℝ) ≤ - (1304521775989678255059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (129621270957803 / 200000000000000 : ℝ)) (q := - (519241401057381 / 800000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (519241401057381 / 800000000000000 : ℚ)) + (r' := (519241401057381 / 400000000000000 : ℚ)) + (U := (-(2161214125510321744941 / 5000000000000000000000 : ℚ))) + (U' := (1304521775989678255059 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (129621270957803 / 200000000000000 : ℚ)) + (q := (519241401057381 / 800000000000000 : ℚ)) + (U := (-(2161214125510321744941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_7 : Uω (aρ 7) (bρ 7) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1107,25 +961,21 @@ lemma U_606_7 : have hlg : Real.log (12511161124289557 / 20000000000000000 : ℝ) ≤ (-(4691111374317235430867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12511161124289557 / 20000000000000000 : ℝ) = - (12511161124289557 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12511161124289557 / 10000000000000000 : ℚ)) - (U := (2240360428682764569133 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12511161124289557 / 10000000000000000 : ℝ) ≤ - (2240360428682764569133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3117425513252591 / 5000000000000000 : ℝ)) (q := - (12511161124289557 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12511161124289557 / 20000000000000000 : ℚ)) + (r' := (12511161124289557 / 10000000000000000 : ℚ)) + (U := (-(4691111374317235430867 / 10000000000000000000000 : ℚ))) + (U' := (2240360428682764569133 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (3117425513252591 / 5000000000000000 : ℚ)) + (q := (12511161124289557 / 20000000000000000 : ℚ)) + (U := (-(4691111374317235430867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_8 : Uω (aρ 8) (bρ 8) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1133,25 +983,21 @@ lemma U_606_8 : have hlg : Real.log (11900756100985221 / 20000000000000000 : ℝ) ≤ (-(2595651686485454946769 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11900756100985221 / 20000000000000000 : ℝ) = - (11900756100985221 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11900756100985221 / 10000000000000000 : ℚ)) - (U := (870084215014545053231 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11900756100985221 / 10000000000000000 : ℝ) ≤ - (870084215014545053231 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2953993827270423 / 5000000000000000 : ℝ)) (q := - (11900756100985221 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11900756100985221 / 20000000000000000 : ℚ)) + (r' := (11900756100985221 / 10000000000000000 : ℚ)) + (U := (-(2595651686485454946769 / 5000000000000000000000 : ℚ))) + (U' := (870084215014545053231 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (2953993827270423 / 5000000000000000 : ℚ)) + (q := (11900756100985221 / 20000000000000000 : ℚ)) + (U := (-(2595651686485454946769 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_9 : Uω (aρ 9) (bρ 9) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1159,25 +1005,21 @@ lemma U_606_9 : have hlg : Real.log (2785252971286799 / 5000000000000000 : ℝ) ≤ (-(5850992094238623056519 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2785252971286799 / 5000000000000000 : ℝ) = - (2785252971286799 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2785252971286799 / 2500000000000000 : ℚ)) - (U := (1080479708761376943481 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2785252971286799 / 2500000000000000 : ℝ) ≤ - (1080479708761376943481 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5489209067062821 / 10000000000000000 : ℝ)) (q := - (2785252971286799 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2785252971286799 / 5000000000000000 : ℚ)) + (r' := (2785252971286799 / 2500000000000000 : ℚ)) + (U := (-(5850992094238623056519 / 10000000000000000000000 : ℚ))) + (U' := (1080479708761376943481 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (5489209067062821 / 10000000000000000 : ℚ)) + (q := (2785252971286799 / 5000000000000000 : ℚ)) + (U := (-(5850992094238623056519 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_10 : Uω (aρ 10) (bρ 10) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1185,25 +1027,21 @@ lemma U_606_10 : have hlg : Real.log (204647509780861 / 400000000000000 : ℝ) ≤ (-(837719390211303050617 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (204647509780861 / 400000000000000 : ℝ) = - (204647509780861 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (204647509780861 / 200000000000000 : ℚ)) - (U := (28714585163696949383 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (204647509780861 / 200000000000000 : ℝ) ≤ - (28714585163696949383 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (198765268178147 / 400000000000000 : ℝ)) (q := - (204647509780861 / 400000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (204647509780861 / 400000000000000 : ℚ)) + (r' := (204647509780861 / 200000000000000 : ℚ)) + (U := (-(837719390211303050617 / 1250000000000000000000 : ℚ))) + (U' := (28714585163696949383 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (198765268178147 / 400000000000000 : ℚ)) + (q := (204647509780861 / 400000000000000 : ℚ)) + (U := (-(837719390211303050617 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_11 : Uω (aρ 11) (bρ 11) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1211,26 +1049,21 @@ lemma U_606_11 : have hlg : Real.log (9184618574910929 / 20000000000000000 : ℝ) ≤ (-(7782020821850845249701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9184618574910929 / 20000000000000000 : ℝ) = - (9184618574910929 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9184618574910929 / 5000000000000000 : ℚ)) - (U := (6080922784149154750299 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9184618574910929 / 5000000000000000 : ℝ) ≤ - (6080922784149154750299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2169925708263277 / 5000000000000000 : ℝ)) (q := - (9184618574910929 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9184618574910929 / 20000000000000000 : ℚ)) + (r' := (9184618574910929 / 5000000000000000 : ℚ)) + (U := (-(7782020821850845249701 / 10000000000000000000000 : ℚ))) + (U' := (6080922784149154750299 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (2169925708263277 / 5000000000000000 : ℚ)) + (q := (9184618574910929 / 20000000000000000 : ℚ)) + (U := (-(7782020821850845249701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_12 : Uω (aρ 12) (bρ 12) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1238,26 +1071,21 @@ lemma U_606_12 : have hlg : Real.log (1602634339274003 / 4000000000000000 : ℝ) ≤ (-(2286614058101796570093 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1602634339274003 / 4000000000000000 : ℝ) = - (1602634339274003 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1602634339274003 / 1000000000000000 : ℚ)) - (U := (1179121843398203429907 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1602634339274003 / 1000000000000000 : ℝ) ≤ - (1179121843398203429907 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44901307933383 / 125000000000000 : ℝ)) (q := - (1602634339274003 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1602634339274003 / 4000000000000000 : ℚ)) + (r' := (1602634339274003 / 1000000000000000 : ℚ)) + (U := (-(2286614058101796570093 / 2500000000000000000000 : ℚ))) + (U' := (1179121843398203429907 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (44901307933383 / 125000000000000 : ℚ)) + (q := (1602634339274003 / 4000000000000000 : ℚ)) + (U := (-(2286614058101796570093 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_13 : Uω (aρ 13) (bρ 13) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1265,26 +1093,21 @@ lemma U_606_13 : have hlg : Real.log (6725853653235283 / 20000000000000000 : ℝ) ≤ (-(5448867091589979705297 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6725853653235283 / 20000000000000000 : ℝ) = - (6725853653235283 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6725853653235283 / 5000000000000000 : ℚ)) - (U := (1482604711410020294703 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6725853653235283 / 5000000000000000 : ℝ) ≤ - (1482604711410020294703 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (676042083282727 / 2500000000000000 : ℝ)) (q := - (6725853653235283 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6725853653235283 / 20000000000000000 : ℚ)) + (r' := (6725853653235283 / 5000000000000000 : ℚ)) + (U := (-(5448867091589979705297 / 5000000000000000000000 : ℚ))) + (U' := (1482604711410020294703 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (676042083282727 / 2500000000000000 : ℚ)) + (q := (6725853653235283 / 20000000000000000 : ℚ)) + (U := (-(5448867091589979705297 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_14 : Uω (aρ 14) (bρ 14) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1292,25 +1115,21 @@ lemma U_606_14 : have hlg : Real.log (657287042718211 / 2500000000000000 : ℝ) ≤ (-(13359251881499432432203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (657287042718211 / 2500000000000000 : ℝ) = - (657287042718211 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (657287042718211 / 625000000000000 : ℚ)) - (U := (503691724500567567797 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (657287042718211 / 625000000000000 : ℝ) ≤ - (503691724500567567797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1580538306686313 / 10000000000000000 : ℝ)) (q := - (657287042718211 / 2500000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (657287042718211 / 2500000000000000 : ℚ)) + (r' := (657287042718211 / 625000000000000 : ℚ)) + (U := (-(13359251881499432432203 / 10000000000000000000000 : ℚ))) + (U' := (503691724500567567797 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11198973265647 / 16000000000000 : ℚ)) + (s := (1580538306686313 / 10000000000000000 : ℚ)) + (q := (657287042718211 / 2500000000000000 : ℚ)) + (U := (-(13359251881499432432203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_606_15 : Uω (aρ 15) (bρ 15) (11198973265647 / 16000000000000 : ℝ) ≤ @@ -1412,25 +1231,21 @@ lemma U_607_1 : have hlg : Real.log (27804250251773043 / 40000000000000000 : ℝ) ≤ (-(727381116177924738757 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27804250251773043 / 40000000000000000 : ℝ) = - (27804250251773043 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27804250251773043 / 20000000000000000 : ℚ)) - (U := (658913244422075261243 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27804250251773043 / 20000000000000000 : ℝ) ≤ - (658913244422075261243 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1737759826233271 / 2500000000000000 : ℝ)) (q := - (27804250251773043 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27804250251773043 / 40000000000000000 : ℚ)) + (r' := (27804250251773043 / 20000000000000000 : ℚ)) + (U := (-(727381116177924738757 / 2000000000000000000000 : ℚ))) + (U' := (658913244422075261243 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (1737759826233271 / 2500000000000000 : ℚ)) + (q := (27804250251773043 / 40000000000000000 : ℚ)) + (U := (-(727381116177924738757 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_2 : Uω (aρ 2) (bρ 2) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1438,25 +1253,21 @@ lemma U_607_2 : have hlg : Real.log (27708654615376139 / 40000000000000000 : ℝ) ≤ (-(1835673242359555576149 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27708654615376139 / 40000000000000000 : ℝ) = - (27708654615376139 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27708654615376139 / 20000000000000000 : ℚ)) - (U := (1630062659140444423851 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27708654615376139 / 20000000000000000 : ℝ) ≤ - (1630062659140444423851 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (865876312405579 / 1250000000000000 : ℝ)) (q := - (27708654615376139 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27708654615376139 / 40000000000000000 : ℚ)) + (r' := (27708654615376139 / 20000000000000000 : ℚ)) + (U := (-(1835673242359555576149 / 5000000000000000000000 : ℚ))) + (U' := (1630062659140444423851 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (865876312405579 / 1250000000000000 : ℚ)) + (q := (27708654615376139 / 40000000000000000 : ℚ)) + (U := (-(1835673242359555576149 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_3 : Uω (aρ 3) (bρ 3) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1464,25 +1275,21 @@ lemma U_607_3 : have hlg : Real.log (27517532010732761 / 40000000000000000 : ℝ) ≤ (-(748112249305770301769 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27517532010732761 / 40000000000000000 : ℝ) = - (27517532010732761 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27517532010732761 / 20000000000000000 : ℚ)) - (U := (638182111294229698231 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27517532010732761 / 20000000000000000 : ℝ) ≤ - (638182111294229698231 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6878845303272943 / 10000000000000000 : ℝ)) (q := - (27517532010732761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27517532010732761 / 40000000000000000 : ℚ)) + (r' := (27517532010732761 / 20000000000000000 : ℚ)) + (U := (-(748112249305770301769 / 2000000000000000000000 : ℚ))) + (U' := (638182111294229698231 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (6878845303272943 / 10000000000000000 : ℚ)) + (q := (27517532010732761 / 40000000000000000 : ℚ)) + (U := (-(748112249305770301769 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_4 : Uω (aρ 4) (bρ 4) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1490,25 +1297,21 @@ lemma U_607_4 : have hlg : Real.log (5440063521927477 / 8000000000000000 : ℝ) ≤ (-(3856508037953090883837 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5440063521927477 / 8000000000000000 : ℝ) = - (5440063521927477 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5440063521927477 / 4000000000000000 : ℚ)) - (U := (3074963765046909116163 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5440063521927477 / 4000000000000000 : ℝ) ≤ - (3074963765046909116163 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1359706456758051 / 2000000000000000 : ℝ)) (q := - (5440063521927477 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5440063521927477 / 8000000000000000 : ℚ)) + (r' := (5440063521927477 / 4000000000000000 : ℚ)) + (U := (-(3856508037953090883837 / 10000000000000000000000 : ℚ))) + (U' := (3074963765046909116163 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (1359706456758051 / 2000000000000000 : ℚ)) + (q := (5440063521927477 / 8000000000000000 : ℚ)) + (U := (-(3856508037953090883837 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_5 : Uω (aρ 5) (bρ 5) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1516,25 +1319,21 @@ lemma U_607_5 : have hlg : Real.log (26717799920169329 / 40000000000000000 : ℝ) ≤ (-(4035494468925474550957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26717799920169329 / 40000000000000000 : ℝ) = - (26717799920169329 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26717799920169329 / 20000000000000000 : ℚ)) - (U := (2895977334074525449043 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26717799920169329 / 20000000000000000 : ℝ) ≤ - (2895977334074525449043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6675463358391227 / 10000000000000000 : ℝ)) (q := - (26717799920169329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26717799920169329 / 40000000000000000 : ℚ)) + (r' := (26717799920169329 / 20000000000000000 : ℚ)) + (U := (-(4035494468925474550957 / 10000000000000000000000 : ℚ))) + (U' := (2895977334074525449043 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (6675463358391227 / 10000000000000000 : ℚ)) + (q := (26717799920169329 / 40000000000000000 : ℚ)) + (U := (-(4035494468925474550957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_6 : Uω (aρ 6) (bρ 6) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1542,25 +1341,21 @@ lemma U_607_6 : have hlg : Real.log (26027063476699487 / 40000000000000000 : ℝ) ≤ (-(4297425542463654092731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26027063476699487 / 40000000000000000 : ℝ) = - (26027063476699487 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26027063476699487 / 20000000000000000 : ℚ)) - (U := (2634046260536345907269 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26027063476699487 / 20000000000000000 : ℝ) ≤ - (2634046260536345907269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3248667755898153 / 5000000000000000 : ℝ)) (q := - (26027063476699487 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26027063476699487 / 40000000000000000 : ℚ)) + (r' := (26027063476699487 / 20000000000000000 : ℚ)) + (U := (-(4297425542463654092731 / 10000000000000000000000 : ℚ))) + (U' := (2634046260536345907269 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (3248667755898153 / 5000000000000000 : ℚ)) + (q := (26027063476699487 / 40000000000000000 : ℚ)) + (U := (-(4297425542463654092731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_7 : Uω (aρ 7) (bρ 7) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1568,25 +1363,21 @@ lemma U_607_7 : have hlg : Real.log (25087436453874287 / 40000000000000000 : ℝ) ≤ (-(466512272714342381551 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25087436453874287 / 40000000000000000 : ℝ) = - (25087436453874287 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25087436453874287 / 20000000000000000 : ℚ)) - (U := (226634907585657618449 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25087436453874287 / 20000000000000000 : ℝ) ≤ - (226634907585657618449 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3125591690571853 / 5000000000000000 : ℝ)) (q := - (25087436453874287 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25087436453874287 / 40000000000000000 : ℚ)) + (r' := (25087436453874287 / 20000000000000000 : ℚ)) + (U := (-(466512272714342381551 / 1000000000000000000000 : ℚ))) + (U' := (226634907585657618449 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (3125591690571853 / 5000000000000000 : ℚ)) + (q := (25087436453874287 / 40000000000000000 : ℚ)) + (U := (-(466512272714342381551 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_8 : Uω (aρ 8) (bρ 8) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1594,25 +1385,21 @@ lemma U_607_8 : have hlg : Real.log (23866875566293157 / 40000000000000000 : ℝ) ≤ (-(1032775831632319691089 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23866875566293157 / 40000000000000000 : ℝ) = - (23866875566293157 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23866875566293157 / 20000000000000000 : ℚ)) - (U := (353518528967680308911 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23866875566293157 / 20000000000000000 : ℝ) ≤ - (353518528967680308911 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5924444588693141 / 10000000000000000 : ℝ)) (q := - (23866875566293157 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23866875566293157 / 40000000000000000 : ℚ)) + (r' := (23866875566293157 / 20000000000000000 : ℚ)) + (U := (-(1032775831632319691089 / 2000000000000000000000 : ℚ))) + (U' := (353518528967680308911 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (5924444588693141 / 10000000000000000 : ℚ)) + (q := (23866875566293157 / 40000000000000000 : ℚ)) + (U := (-(1032775831632319691089 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_9 : Uω (aρ 9) (bρ 9) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1620,25 +1407,21 @@ lemma U_607_9 : have hlg : Real.log (22347881062052147 / 40000000000000000 : ℝ) ≤ (-(29107397217795261913 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22347881062052147 / 40000000000000000 : ℝ) = - (22347881062052147 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22347881062052147 / 20000000000000000 : ℚ)) - (U := (5549961797204738087 / 50000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22347881062052147 / 20000000000000000 : ℝ) ≤ - (5549961797204738087 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1376478241233159 / 2500000000000000 : ℝ)) (q := - (22347881062052147 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22347881062052147 / 40000000000000000 : ℚ)) + (r' := (22347881062052147 / 20000000000000000 : ℚ)) + (U := (-(29107397217795261913 / 50000000000000000000 : ℚ))) + (U' := (5549961797204738087 / 50000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (1376478241233159 / 2500000000000000 : ℚ)) + (q := (22347881062052147 / 40000000000000000 : ℚ)) + (U := (-(29107397217795261913 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_10 : Uω (aρ 10) (bρ 10) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1646,26 +1429,21 @@ lemma U_607_10 : have hlg : Real.log (20531564150751633 / 40000000000000000 : ℝ) ≤ (-(666916037184109468323 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20531564150751633 / 40000000000000000 : ℝ) = - (20531564150751633 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20531564150751633 / 20000000000000000 : ℚ)) - (U := (26231143115890531677 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20531564150751633 / 20000000000000000 : ℝ) ≤ - (26231143115890531677 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4986313542777379 / 10000000000000000 : ℝ)) (q := - (20531564150751633 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20531564150751633 / 40000000000000000 : ℚ)) + (r' := (20531564150751633 / 20000000000000000 : ℚ)) + (U := (-(666916037184109468323 / 1000000000000000000000 : ℚ))) + (U' := (26231143115890531677 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (4986313542777379 / 10000000000000000 : ℚ)) + (q := (20531564150751633 / 40000000000000000 : ℚ)) + (U := (-(666916037184109468323 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_11 : Uω (aρ 11) (bρ 11) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1673,26 +1451,21 @@ lemma U_607_11 : have hlg : Real.log (18437896573385211 / 40000000000000000 : ℝ) ≤ (-(193617827665090779411 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18437896573385211 / 40000000000000000 : ℝ) = - (18437896573385211 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18437896573385211 / 10000000000000000 : ℚ)) - (U := (152955762484909220589 / 250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18437896573385211 / 10000000000000000 : ℝ) ≤ - (152955762484909220589 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (136186136884349 / 312500000000000 : ℝ)) (q := - (18437896573385211 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18437896573385211 / 40000000000000000 : ℚ)) + (r' := (18437896573385211 / 10000000000000000 : ℚ)) + (U := (-(193617827665090779411 / 250000000000000000000 : ℚ))) + (U' := (152955762484909220589 / 250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (136186136884349 / 312500000000000 : ℚ)) + (q := (18437896573385211 / 40000000000000000 : ℚ)) + (U := (-(193617827665090779411 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_12 : Uω (aρ 12) (bρ 12) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1700,26 +1473,21 @@ lemma U_607_12 : have hlg : Real.log (16098693349171741 / 40000000000000000 : ℝ) ≤ (-(9101413433336903069591 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16098693349171741 / 40000000000000000 : ℝ) = - (16098693349171741 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16098693349171741 / 10000000000000000 : ℚ)) - (U := (4761530172663096930409 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16098693349171741 / 10000000000000000 : ℝ) ≤ - (4761530172663096930409 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3612054864877433 / 10000000000000000 : ℝ)) (q := - (16098693349171741 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16098693349171741 / 40000000000000000 : ℚ)) + (r' := (16098693349171741 / 10000000000000000 : ℚ)) + (U := (-(9101413433336903069591 / 10000000000000000000000 : ℚ))) + (U' := (4761530172663096930409 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (3612054864877433 / 10000000000000000 : ℚ)) + (q := (16098693349171741 / 40000000000000000 : ℚ)) + (U := (-(9101413433336903069591 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_13 : Uω (aρ 13) (bρ 13) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1727,26 +1495,21 @@ lemma U_607_13 : have hlg : Real.log (13532299322712177 / 40000000000000000 : ℝ) ≤ (-(2709500208247898408319 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13532299322712177 / 40000000000000000 : ℝ) = - (13532299322712177 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13532299322712177 / 10000000000000000 : ℚ)) - (U := (756235693252101591681 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13532299322712177 / 10000000000000000 : ℝ) ≤ - (756235693252101591681 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2728239593242651 / 10000000000000000 : ℝ)) (q := - (13532299322712177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13532299322712177 / 40000000000000000 : ℚ)) + (r' := (13532299322712177 / 10000000000000000 : ℚ)) + (U := (-(2709500208247898408319 / 2500000000000000000000 : ℚ))) + (U' := (756235693252101591681 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (2728239593242651 / 10000000000000000 : ℚ)) + (q := (13532299322712177 / 40000000000000000 : ℚ)) + (U := (-(2709500208247898408319 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_14 : Uω (aρ 14) (bρ 14) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1754,26 +1517,21 @@ lemma U_607_14 : have hlg : Real.log (10623830814298537 / 40000000000000000 : ℝ) ≤ (-(1325779785845717507177 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10623830814298537 / 40000000000000000 : ℝ) = - (10623830814298537 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10623830814298537 / 10000000000000000 : ℚ)) - (U := (60514574754282492823 / 1000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10623830814298537 / 10000000000000000 : ℝ) ≤ - (60514574754282492823 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1617932624080831 / 10000000000000000 : ℝ)) (q := - (10623830814298537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10623830814298537 / 40000000000000000 : ℚ)) + (r' := (10623830814298537 / 10000000000000000 : ℚ)) + (U := (-(1325779785845717507177 / 1000000000000000000000 : ℚ))) + (U' := (60514574754282492823 / 1000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22449865724923 / 32000000000000 : ℚ)) + (s := (1617932624080831 / 10000000000000000 : ℚ)) + (q := (10623830814298537 / 40000000000000000 : ℚ)) + (U := (-(1325779785845717507177 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_607_15 : Uω (aρ 15) (bρ 15) (22449865724923 / 32000000000000 : ℝ) ≤ @@ -1875,25 +1633,21 @@ lemma U_608_1 : have hlg : Real.log (6967287365113519 / 10000000000000000 : ℝ) ≤ (-(3613591309293704288903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6967287365113519 / 10000000000000000 : ℝ) = - (6967287365113519 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6967287365113519 / 5000000000000000 : ℚ)) - (U := (3317880493706295711097 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6967287365113519 / 5000000000000000 : ℝ) ≤ - (3317880493706295711097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3483632080632269 / 5000000000000000 : ℝ)) (q := - (6967287365113519 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6967287365113519 / 10000000000000000 : ℚ)) + (r' := (6967287365113519 / 5000000000000000 : ℚ)) + (U := (-(3613591309293704288903 / 10000000000000000000000 : ℚ))) + (U' := (3317880493706295711097 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (3483632080632269 / 5000000000000000 : ℚ)) + (q := (6967287365113519 / 10000000000000000 : ℚ)) + (U := (-(3613591309293704288903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_2 : Uω (aρ 2) (bρ 2) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -1901,25 +1655,21 @@ lemma U_608_2 : have hlg : Real.log (13886777519480489 / 20000000000000000 : ℝ) ≤ (-(1823975717406834395501 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13886777519480489 / 20000000000000000 : ℝ) = - (13886777519480489 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13886777519480489 / 10000000000000000 : ℚ)) - (U := (1641760184093165604499 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13886777519480489 / 10000000000000000 : ℝ) ≤ - (1641760184093165604499 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6943235963027989 / 10000000000000000 : ℝ)) (q := - (13886777519480489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13886777519480489 / 20000000000000000 : ℚ)) + (r' := (13886777519480489 / 10000000000000000 : ℚ)) + (U := (-(1823975717406834395501 / 5000000000000000000000 : ℚ))) + (U' := (1641760184093165604499 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (6943235963027989 / 10000000000000000 : ℚ)) + (q := (13886777519480489 / 20000000000000000 : ℚ)) + (U := (-(1823975717406834395501 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_3 : Uω (aρ 3) (bρ 3) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -1927,24 +1677,21 @@ lemma U_608_3 : have hlg : Real.log (43097556349683 / 62500000000000 : ℝ) ≤ (-(29039082672124137669 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43097556349683 / 62500000000000 : ℝ) = (43097556349683 / 31250000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43097556349683 / 31250000000000 : ℚ)) - (U := (25113040788813362331 / 78125000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (43097556349683 / 31250000000000 : ℝ) ≤ - (25113040788813362331 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (344753629089803 / 500000000000000 : ℝ)) (q := - (43097556349683 / 62500000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43097556349683 / 62500000000000 : ℚ)) + (r' := (43097556349683 / 31250000000000 : ℚ)) + (U := (-(29039082672124137669 / 78125000000000000000 : ℚ))) + (U' := (25113040788813362331 / 78125000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (344753629089803 / 500000000000000 : ℚ)) + (q := (43097556349683 / 62500000000000 : ℚ)) + (U := (-(29039082672124137669 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_4 : Uω (aρ 4) (bρ 4) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -1952,25 +1699,21 @@ lemma U_608_4 : have hlg : Real.log (13632615667672069 / 20000000000000000 : ℝ) ≤ (-(479083926015013648739 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13632615667672069 / 20000000000000000 : ℝ) = - (13632615667672069 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13632615667672069 / 10000000000000000 : ℚ)) - (U := (387350049359986351261 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13632615667672069 / 10000000000000000 : ℝ) ≤ - (387350049359986351261 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6814764398634569 / 10000000000000000 : ℝ)) (q := - (13632615667672069 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13632615667672069 / 20000000000000000 : ℚ)) + (r' := (13632615667672069 / 10000000000000000 : ℚ)) + (U := (-(479083926015013648739 / 1250000000000000000000 : ℚ))) + (U' := (387350049359986351261 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (6814764398634569 / 10000000000000000 : ℚ)) + (q := (13632615667672069 / 20000000000000000 : ℚ)) + (U := (-(479083926015013648739 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_5 : Uω (aρ 5) (bρ 5) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -1978,24 +1721,21 @@ lemma U_608_5 : have hlg : Real.log (83696054925607 / 125000000000000 : ℝ) ≤ (-(2005609470815187270507 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83696054925607 / 125000000000000 : ℝ) = (83696054925607 / 62500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83696054925607 / 62500000000000 : ℚ)) - (U := (1460126430684812729493 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (83696054925607 / 62500000000000 : ℝ) ≤ - (1460126430684812729493 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (334585371919731 / 500000000000000 : ℝ)) (q := - (83696054925607 / 125000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83696054925607 / 125000000000000 : ℚ)) + (r' := (83696054925607 / 62500000000000 : ℚ)) + (U := (-(2005609470815187270507 / 5000000000000000000000 : ℚ))) + (U' := (1460126430684812729493 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (334585371919731 / 500000000000000 : ℚ)) + (q := (83696054925607 / 125000000000000 : ℚ)) + (U := (-(2005609470815187270507 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_6 : Uω (aρ 6) (bρ 6) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2003,25 +1743,21 @@ lemma U_608_6 : have hlg : Real.log (13046028214702497 / 20000000000000000 : ℝ) ≤ (-(4272485372134123980927 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13046028214702497 / 20000000000000000 : ℝ) = - (13046028214702497 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13046028214702497 / 10000000000000000 : ℚ)) - (U := (2658986430865876019073 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13046028214702497 / 10000000000000000 : ℝ) ≤ - (2658986430865876019073 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6513607240139997 / 10000000000000000 : ℝ)) (q := - (13046028214702497 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13046028214702497 / 20000000000000000 : ℚ)) + (r' := (13046028214702497 / 10000000000000000 : ℚ)) + (U := (-(4272485372134123980927 / 10000000000000000000000 : ℚ))) + (U' := (2658986430865876019073 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (6513607240139997 / 10000000000000000 : ℚ)) + (q := (13046028214702497 / 20000000000000000 : ℚ)) + (U := (-(4272485372134123980927 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_7 : Uω (aρ 7) (bρ 7) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2029,25 +1765,21 @@ lemma U_608_7 : have hlg : Real.log (6288137385306809 / 10000000000000000 : ℝ) ≤ (-(4639201890375419235181 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6288137385306809 / 10000000000000000 : ℝ) = - (6288137385306809 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6288137385306809 / 5000000000000000 : ℚ)) - (U := (2292269912624580764819 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6288137385306809 / 5000000000000000 : ℝ) ≤ - (2292269912624580764819 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3133757588405559 / 5000000000000000 : ℝ)) (q := - (6288137385306809 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6288137385306809 / 10000000000000000 : ℚ)) + (r' := (6288137385306809 / 5000000000000000 : ℚ)) + (U := (-(4639201890375419235181 / 10000000000000000000000 : ℚ))) + (U' := (2292269912624580764819 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (3133757588405559 / 5000000000000000 : ℚ)) + (q := (6288137385306809 / 10000000000000000 : ℚ)) + (U := (-(4639201890375419235181 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_8 : Uω (aρ 8) (bρ 8) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2055,25 +1787,21 @@ lemma U_608_8 : have hlg : Real.log (11966118188021229 / 20000000000000000 : ℝ) ≤ (-(1027306202776836780947 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11966118188021229 / 20000000000000000 : ℝ) = - (11966118188021229 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11966118188021229 / 10000000000000000 : ℚ)) - (U := (358988157823163219053 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11966118188021229 / 10000000000000000 : ℝ) ≤ - (358988157823163219053 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5940900245558729 / 10000000000000000 : ℝ)) (q := - (11966118188021229 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11966118188021229 / 20000000000000000 : ℚ)) + (r' := (11966118188021229 / 10000000000000000 : ℚ)) + (U := (-(1027306202776836780947 / 2000000000000000000000 : ℚ))) + (U' := (358988157823163219053 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (5940900245558729 / 10000000000000000 : ℚ)) + (q := (11966118188021229 / 20000000000000000 : ℚ)) + (U := (-(1027306202776836780947 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_9 : Uω (aρ 9) (bρ 9) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2081,25 +1809,21 @@ lemma U_608_9 : have hlg : Real.log (2801716579992363 / 5000000000000000 : ℝ) ≤ (-(579205618557146584257 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2801716579992363 / 5000000000000000 : ℝ) = - (2801716579992363 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2801716579992363 / 2500000000000000 : ℚ)) - (U := (113941561742853415743 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2801716579992363 / 2500000000000000 : ℝ) ≤ - (113941561742853415743 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (690326750733369 / 1250000000000000 : ℝ)) (q := - (2801716579992363 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2801716579992363 / 5000000000000000 : ℚ)) + (r' := (2801716579992363 / 2500000000000000 : ℚ)) + (U := (-(579205618557146584257 / 1000000000000000000000 : ℚ))) + (U' := (113941561742853415743 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (690326750733369 / 1250000000000000 : ℚ)) + (q := (2801716579992363 / 5000000000000000 : ℚ)) + (U := (-(579205618557146584257 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_10 : Uω (aρ 10) (bρ 10) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2107,25 +1831,21 @@ lemma U_608_10 : have hlg : Real.log (643698891971729 / 1250000000000000 : ℝ) ≤ (-(3318338861609870053377 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (643698891971729 / 1250000000000000 : ℝ) = - (643698891971729 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (643698891971729 / 625000000000000 : ℚ)) - (U := (147397039890129946623 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (643698891971729 / 625000000000000 : ℝ) ≤ - (147397039890129946623 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1250872247735041 / 2500000000000000 : ℝ)) (q := - (643698891971729 / 1250000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (643698891971729 / 1250000000000000 : ℚ)) + (r' := (643698891971729 / 625000000000000 : ℚ)) + (U := (-(3318338861609870053377 / 5000000000000000000000 : ℚ))) + (U' := (147397039890129946623 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (1250872247735041 / 2500000000000000 : ℚ)) + (q := (643698891971729 / 1250000000000000 : ℚ)) + (U := (-(3318338861609870053377 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_11 : Uω (aρ 11) (bρ 11) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2133,26 +1853,21 @@ lemma U_608_11 : have hlg : Real.log (9253263248367061 / 20000000000000000 : ℝ) ≤ (-(481722500072513733311 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9253263248367061 / 20000000000000000 : ℝ) = - (9253263248367061 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9253263248367061 / 5000000000000000 : ℚ)) - (U := (384711475302486266689 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9253263248367061 / 5000000000000000 : ℝ) ≤ - (384711475302486266689 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4376046593964561 / 10000000000000000 : ℝ)) (q := - (9253263248367061 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9253263248367061 / 20000000000000000 : ℚ)) + (r' := (9253263248367061 / 5000000000000000 : ℚ)) + (U := (-(481722500072513733311 / 625000000000000000000 : ℚ))) + (U' := (384711475302486266689 / 625000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (4376046593964561 / 10000000000000000 : ℚ)) + (q := (9253263248367061 / 20000000000000000 : ℚ)) + (U := (-(481722500072513733311 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_12 : Uω (aρ 12) (bρ 12) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2160,26 +1875,21 @@ lemma U_608_12 : have hlg : Real.log (8085484546596681 / 20000000000000000 : ℝ) ≤ (-(4528309251245035771429 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8085484546596681 / 20000000000000000 : ℝ) = - (8085484546596681 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8085484546596681 / 5000000000000000 : ℚ)) - (U := (2403162551754964228571 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8085484546596681 / 5000000000000000 : ℝ) ≤ - (2403162551754964228571 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3631967988879181 / 10000000000000000 : ℝ)) (q := - (8085484546596681 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8085484546596681 / 20000000000000000 : ℚ)) + (r' := (8085484546596681 / 5000000000000000 : ℚ)) + (U := (-(4528309251245035771429 / 5000000000000000000000 : ℚ))) + (U' := (2403162551754964228571 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (3631967988879181 / 10000000000000000 : ℚ)) + (q := (8085484546596681 / 20000000000000000 : ℚ)) + (U := (-(4528309251245035771429 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_13 : Uω (aρ 13) (bρ 13) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2187,26 +1897,21 @@ lemma U_608_13 : have hlg : Real.log (3403165393967557 / 10000000000000000 : ℝ) ≤ (-(538939547868169931167 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3403165393967557 / 10000000000000000 : ℝ) = - (3403165393967557 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3403165393967557 / 2500000000000000 : ℚ)) - (U := (154207632431830068833 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3403165393967557 / 2500000000000000 : ℝ) ≤ - (154207632431830068833 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1376097985906307 / 5000000000000000 : ℝ)) (q := - (3403165393967557 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3403165393967557 / 10000000000000000 : ℚ)) + (r' := (3403165393967557 / 2500000000000000 : ℚ)) + (U := (-(538939547868169931167 / 500000000000000000000 : ℚ))) + (U' := (154207632431830068833 / 500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (1376097985906307 / 5000000000000000 : ℚ)) + (q := (3403165393967557 / 10000000000000000 : ℚ)) + (U := (-(538939547868169931167 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_14 : Uω (aρ 14) (bρ 14) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2214,25 +1919,21 @@ lemma U_608_14 : have hlg : Real.log (536484860941541 / 2000000000000000 : ℝ) ≤ (-(13158641155386919367299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (536484860941541 / 2000000000000000 : ℝ) = - (536484860941541 / 500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (536484860941541 / 500000000000000 : ℚ)) - (U := (704302450613080632701 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (536484860941541 / 500000000000000 : ℝ) ≤ - (704302450613080632701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (165464107833791 / 1000000000000000 : ℝ)) (q := - (536484860941541 / 2000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (536484860941541 / 2000000000000000 : ℚ)) + (r' := (536484860941541 / 500000000000000 : ℚ)) + (U := (-(13158641155386919367299 / 10000000000000000000000 : ℚ))) + (U' := (704302450613080632701 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2812723114819 / 4000000000000 : ℚ)) + (s := (165464107833791 / 1000000000000000 : ℚ)) + (q := (536484860941541 / 2000000000000000 : ℚ)) + (U := (-(13158641155386919367299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_608_15 : Uω (aρ 15) (bρ 15) (2812723114819 / 4000000000000 : ℝ) ≤ @@ -2332,25 +2033,21 @@ lemma U_609_1 : have hlg : Real.log (27934048668128443 / 40000000000000000 : ℝ) ≤ (-(718066253435485445603 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27934048668128443 / 40000000000000000 : ℝ) = - (27934048668128443 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27934048668128443 / 20000000000000000 : ℚ)) - (U := (668228107164514554397 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27934048668128443 / 20000000000000000 : ℝ) ≤ - (668228107164514554397 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6983489017092659 / 10000000000000000 : ℝ)) (q := - (27934048668128443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27934048668128443 / 40000000000000000 : ℚ)) + (r' := (27934048668128443 / 20000000000000000 : ℚ)) + (U := (-(718066253435485445603 / 2000000000000000000000 : ℚ))) + (U' := (668228107164514554397 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (6983489017092659 / 10000000000000000 : ℚ)) + (q := (27934048668128443 / 40000000000000000 : ℚ)) + (U := (-(718066253435485445603 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_2 : Uω (aρ 2) (bρ 2) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2358,25 +2055,21 @@ lemma U_609_2 : have hlg : Real.log (5567691091174173 / 8000000000000000 : ℝ) ≤ (-(1812305496208947558473 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5567691091174173 / 8000000000000000 : ℝ) = - (5567691091174173 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5567691091174173 / 4000000000000000 : ℚ)) - (U := (1653430405291052441527 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5567691091174173 / 4000000000000000 : ℝ) ≤ - (1653430405291052441527 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (695946142347387 / 1000000000000000 : ℝ)) (q := - (5567691091174173 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5567691091174173 / 8000000000000000 : ℚ)) + (r' := (5567691091174173 / 4000000000000000 : ℚ)) + (U := (-(1812305496208947558473 / 5000000000000000000000 : ℚ))) + (U' := (1653430405291052441527 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (695946142347387 / 1000000000000000 : ℚ)) + (q := (5567691091174173 / 8000000000000000 : ℚ)) + (U := (-(1812305496208947558473 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_3 : Uω (aρ 3) (bρ 3) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2384,25 +2077,21 @@ lemma U_609_3 : have hlg : Real.log (27647340093097407 / 40000000000000000 : ℝ) ≤ (-(1846749648388671706299 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27647340093097407 / 40000000000000000 : ℝ) = - (27647340093097407 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27647340093097407 / 20000000000000000 : ℚ)) - (U := (1618986253111328293701 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27647340093097407 / 20000000000000000 : ℝ) ≤ - (1618986253111328293701 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6911299848437141 / 10000000000000000 : ℝ)) (q := - (27647340093097407 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27647340093097407 / 40000000000000000 : ℚ)) + (r' := (27647340093097407 / 20000000000000000 : ℚ)) + (U := (-(1846749648388671706299 / 5000000000000000000000 : ℚ))) + (U' := (1618986253111328293701 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (6911299848437141 / 10000000000000000 : ℚ)) + (q := (27647340093097407 / 40000000000000000 : ℚ)) + (U := (-(1846749648388671706299 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_4 : Uω (aρ 4) (bρ 4) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2410,25 +2099,21 @@ lemma U_609_4 : have hlg : Real.log (27330144991045187 / 40000000000000000 : ℝ) ≤ (-(119027858978336842039 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27330144991045187 / 40000000000000000 : ℝ) = - (27330144991045187 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27330144991045187 / 20000000000000000 : ℚ)) - (U := (97580634865413157961 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27330144991045187 / 20000000000000000 : ℝ) ≤ - (97580634865413157961 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6830996478476031 / 10000000000000000 : ℝ)) (q := - (27330144991045187 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27330144991045187 / 40000000000000000 : ℚ)) + (r' := (27330144991045187 / 20000000000000000 : ℚ)) + (U := (-(119027858978336842039 / 312500000000000000000 : ℚ))) + (U' := (97580634865413157961 / 312500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (6830996478476031 / 10000000000000000 : ℚ)) + (q := (27330144991045187 / 40000000000000000 : ℚ)) + (U := (-(119027858978336842039 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_5 : Uω (aρ 5) (bρ 5) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2436,25 +2121,21 @@ lemma U_609_5 : have hlg : Real.log (26847675045071939 / 40000000000000000 : ℝ) ≤ (-(797400454296810172779 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26847675045071939 / 40000000000000000 : ℝ) = - (26847675045071939 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26847675045071939 / 20000000000000000 : ℚ)) - (U := (588893906303189827221 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26847675045071939 / 20000000000000000 : ℝ) ≤ - (588893906303189827221 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6707951424824407 / 10000000000000000 : ℝ)) (q := - (26847675045071939 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26847675045071939 / 40000000000000000 : ℚ)) + (r' := (26847675045071939 / 20000000000000000 : ℚ)) + (U := (-(797400454296810172779 / 2000000000000000000000 : ℚ))) + (U' := (588893906303189827221 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (6707951424824407 / 10000000000000000 : ℚ)) + (q := (26847675045071939 / 40000000000000000 : ℚ)) + (U := (-(797400454296810172779 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_6 : Uω (aρ 6) (bρ 6) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2462,25 +2143,21 @@ lemma U_609_6 : have hlg : Real.log (5231409782901509 / 8000000000000000 : ℝ) ≤ (-(212380371353436732361 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5231409782901509 / 8000000000000000 : ℝ) = - (5231409782901509 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5231409782901509 / 4000000000000000 : ℚ)) - (U := (134193218796563267639 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5231409782901509 / 4000000000000000 : ℝ) ≤ - (134193218796563267639 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (652987873468221 / 1000000000000000 : ℝ)) (q := - (5231409782901509 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5231409782901509 / 8000000000000000 : ℚ)) + (r' := (5231409782901509 / 4000000000000000 : ℚ)) + (U := (-(212380371353436732361 / 500000000000000000000 : ℚ))) + (U' := (134193218796563267639 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (652987873468221 / 1000000000000000 : ℚ)) + (q := (5231409782901509 / 8000000000000000 : ℚ)) + (U := (-(212380371353436732361 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_7 : Uω (aρ 7) (bρ 7) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2488,25 +2165,21 @@ lemma U_609_7 : have hlg : Real.log (25217661519354599 / 40000000000000000 : ℝ) ≤ (-(2306674254387015104923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25217661519354599 / 40000000000000000 : ℝ) = - (25217661519354599 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25217661519354599 / 20000000000000000 : ℚ)) - (U := (1159061647112984895077 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25217661519354599 / 20000000000000000 : ℝ) ≤ - (1159061647112984895077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6283846417865737 / 10000000000000000 : ℝ)) (q := - (25217661519354599 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25217661519354599 / 40000000000000000 : ℚ)) + (r' := (25217661519354599 / 20000000000000000 : ℚ)) + (U := (-(2306674254387015104923 / 5000000000000000000000 : ℚ))) + (U' := (1159061647112984895077 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (6283846417865737 / 10000000000000000 : ℚ)) + (q := (25217661519354599 / 40000000000000000 : ℚ)) + (U := (-(2306674254387015104923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_8 : Uω (aρ 8) (bρ 8) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2514,25 +2187,21 @@ lemma U_609_8 : have hlg : Real.log (23997594652387391 / 40000000000000000 : ℝ) ≤ (-(5109258513458795500777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23997594652387391 / 40000000000000000 : ℝ) = - (23997594652387391 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23997594652387391 / 20000000000000000 : ℚ)) - (U := (1822213289541204499223 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23997594652387391 / 20000000000000000 : ℝ) ≤ - (1822213289541204499223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5957354635722133 / 10000000000000000 : ℝ)) (q := - (23997594652387391 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23997594652387391 / 40000000000000000 : ℚ)) + (r' := (23997594652387391 / 20000000000000000 : ℚ)) + (U := (-(5109258513458795500777 / 10000000000000000000000 : ℚ))) + (U' := (1822213289541204499223 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (5957354635722133 / 10000000000000000 : ℚ)) + (q := (23997594652387391 / 40000000000000000 : ℚ)) + (U := (-(5109258513458795500777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_9 : Uω (aρ 9) (bρ 9) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2540,25 +2209,21 @@ lemma U_609_9 : have hlg : Real.log (22479578555636669 / 40000000000000000 : ℝ) ≤ (-(720340220661621150801 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22479578555636669 / 40000000000000000 : ℝ) = - (22479578555636669 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22479578555636669 / 20000000000000000 : ℚ)) - (U := (146093754713378849199 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22479578555636669 / 20000000000000000 : ℝ) ≤ - (146093754713378849199 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1384828053926693 / 2500000000000000 : ℝ)) (q := - (22479578555636669 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22479578555636669 / 40000000000000000 : ℚ)) + (r' := (22479578555636669 / 20000000000000000 : ℚ)) + (U := (-(720340220661621150801 / 1250000000000000000000 : ℚ))) + (U' := (146093754713378849199 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (1384828053926693 / 2500000000000000 : ℚ)) + (q := (22479578555636669 / 40000000000000000 : ℚ)) + (U := (-(720340220661621150801 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_10 : Uω (aρ 10) (bρ 10) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2566,25 +2231,21 @@ lemma U_609_10 : have hlg : Real.log (826606091451197 / 1600000000000000 : ℝ) ≤ (-(1651076591580467623333 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (826606091451197 / 1600000000000000 : ℝ) = - (826606091451197 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (826606091451197 / 800000000000000 : ℚ)) - (U := (81791359169532376667 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (826606091451197 / 800000000000000 : ℝ) ≤ - (81791359169532376667 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (25103290572617 / 50000000000000 : ℝ)) (q := - (826606091451197 / 1600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (826606091451197 / 1600000000000000 : ℚ)) + (r' := (826606091451197 / 800000000000000 : ℚ)) + (U := (-(1651076591580467623333 / 2500000000000000000000 : ℚ))) + (U' := (81791359169532376667 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (25103290572617 / 50000000000000 : ℚ)) + (q := (826606091451197 / 1600000000000000 : ℚ)) + (U := (-(1651076591580467623333 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_11 : Uω (aρ 11) (bρ 11) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2592,26 +2253,21 @@ lemma U_609_11 : have hlg : Real.log (18575127284217941 / 40000000000000000 : ℝ) ≤ (-(3835280052829488580907 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18575127284217941 / 40000000000000000 : ℝ) = - (18575127284217941 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18575127284217941 / 10000000000000000 : ℚ)) - (U := (3096191750170511419093 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18575127284217941 / 10000000000000000 : ℝ) ≤ - (3096191750170511419093 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8582269999409 / 19531250000000 : ℝ)) (q := - (18575127284217941 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18575127284217941 / 40000000000000000 : ℚ)) + (r' := (18575127284217941 / 10000000000000000 : ℚ)) + (U := (-(3835280052829488580907 / 5000000000000000000000 : ℚ))) + (U' := (3096191750170511419093 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (8582269999409 / 19531250000000 : ℚ)) + (q := (18575127284217941 / 40000000000000000 : ℚ)) + (U := (-(3835280052829488580907 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_12 : Uω (aρ 12) (bρ 12) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2619,26 +2275,21 @@ lemma U_609_12 : have hlg : Real.log (16243171838822357 / 40000000000000000 : ℝ) ≤ (-(2253017069146923309059 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16243171838822357 / 40000000000000000 : ℝ) = - (16243171838822357 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16243171838822357 / 10000000000000000 : ℚ)) - (U := (1212718832353076690941 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16243171838822357 / 10000000000000000 : ℝ) ≤ - (1212718832353076690941 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (456480576710577 / 1250000000000000 : ℝ)) (q := - (16243171838822357 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16243171838822357 / 40000000000000000 : ℚ)) + (r' := (16243171838822357 / 10000000000000000 : ℚ)) + (U := (-(2253017069146923309059 / 2500000000000000000000 : ℚ))) + (U' := (1212718832353076690941 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (456480576710577 / 1250000000000000 : ℚ)) + (q := (16243171838822357 / 40000000000000000 : ℚ)) + (U := (-(2253017069146923309059 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_13 : Uω (aρ 13) (bρ 13) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2646,26 +2297,21 @@ lemma U_609_13 : have hlg : Real.log (13692800014302969 / 40000000000000000 : ℝ) ≤ (-(2144018610618247468463 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13692800014302969 / 40000000000000000 : ℝ) = - (13692800014302969 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13692800014302969 / 10000000000000000 : ℚ)) - (U := (628570110581752531537 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13692800014302969 / 10000000000000000 : ℝ) ≤ - (628570110581752531537 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1388020221509961 / 5000000000000000 : ℝ)) (q := - (13692800014302969 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13692800014302969 / 40000000000000000 : ℚ)) + (r' := (13692800014302969 / 10000000000000000 : ℚ)) + (U := (-(2144018610618247468463 / 2000000000000000000000 : ℚ))) + (U' := (628570110581752531537 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (1388020221509961 / 5000000000000000 : ℚ)) + (q := (13692800014302969 / 40000000000000000 : ℚ)) + (U := (-(2144018610618247468463 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_14 : Uω (aρ 14) (bρ 14) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2673,26 +2319,21 @@ lemma U_609_14 : have hlg : Real.log (10834281246531611 / 40000000000000000 : ℝ) ≤ (-(6530820785372481273627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10834281246531611 / 40000000000000000 : ℝ) = - (10834281246531611 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10834281246531611 / 10000000000000000 : ℚ)) - (U := (400651017627518726373 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10834281246531611 / 10000000000000000 : ℝ) ≤ - (400651017627518726373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1690708344179243 / 10000000000000000 : ℝ)) (q := - (10834281246531611 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10834281246531611 / 40000000000000000 : ℚ)) + (r' := (10834281246531611 / 10000000000000000 : ℚ)) + (U := (-(6530820785372481273627 / 5000000000000000000000 : ℚ))) + (U' := (400651017627518726373 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22553704112181 / 32000000000000 : ℚ)) + (s := (1690708344179243 / 10000000000000000 : ℚ)) + (q := (10834281246531611 / 40000000000000000 : ℚ)) + (U := (-(6530820785372481273627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_609_15 : Uω (aρ 15) (bρ 15) (22553704112181 / 32000000000000 : ℝ) ≤ @@ -2793,25 +2434,21 @@ lemma U_610_1 : have hlg : Real.log (3499868484350393 / 5000000000000000 : ℝ) ≤ (-(3567125202846665950607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3499868484350393 / 5000000000000000 : ℝ) = - (3499868484350393 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3499868484350393 / 2500000000000000 : ℚ)) - (U := (3364346600153334049393 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3499868484350393 / 2500000000000000 : ℝ) ≤ - (3364346600153334049393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6999713872420947 / 10000000000000000 : ℝ)) (q := - (3499868484350393 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3499868484350393 / 5000000000000000 : ℚ)) + (r' := (3499868484350393 / 2500000000000000 : ℚ)) + (U := (-(3567125202846665950607 / 10000000000000000000000 : ℚ))) + (U' := (3364346600153334049393 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (6999713872420947 / 10000000000000000 : ℚ)) + (q := (3499868484350393 / 5000000000000000 : ℚ)) + (U := (-(3567125202846665950607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_2 : Uω (aρ 2) (bρ 2) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2819,25 +2456,21 @@ lemma U_610_2 : have hlg : Real.log (13951677933076191 / 20000000000000000 : ℝ) ≤ (-(720264980638036197189 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13951677933076191 / 20000000000000000 : ℝ) = - (13951677933076191 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13951677933076191 / 10000000000000000 : ℚ)) - (U := (666029379961963802811 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13951677933076191 / 10000000000000000 : ℝ) ≤ - (666029379961963802811 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3487843440302783 / 5000000000000000 : ℝ)) (q := - (13951677933076191 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13951677933076191 / 20000000000000000 : ℚ)) + (r' := (13951677933076191 / 10000000000000000 : ℚ)) + (U := (-(720264980638036197189 / 2000000000000000000000 : ℚ))) + (U' := (666029379961963802811 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (3487843440302783 / 5000000000000000 : ℚ)) + (q := (13951677933076191 / 20000000000000000 : ℚ)) + (U := (-(720264980638036197189 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_3 : Uω (aρ 3) (bρ 3) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2845,25 +2478,21 @@ lemma U_610_3 : have hlg : Real.log (13856122049400311 / 20000000000000000 : ℝ) ≤ (-(146802045239044294797 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13856122049400311 / 20000000000000000 : ℝ) = - (13856122049400311 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13856122049400311 / 10000000000000000 : ℚ)) - (U := (130456826880955705203 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13856122049400311 / 10000000000000000 : ℝ) ≤ - (130456826880955705203 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3463763551639843 / 5000000000000000 : ℝ)) (q := - (13856122049400311 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13856122049400311 / 20000000000000000 : ℚ)) + (r' := (13856122049400311 / 10000000000000000 : ℚ)) + (U := (-(146802045239044294797 / 400000000000000000000 : ℚ))) + (U' := (130456826880955705203 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (3463763551639843 / 5000000000000000 : ℚ)) + (q := (13856122049400311 / 20000000000000000 : ℚ)) + (U := (-(146802045239044294797 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_4 : Uω (aρ 4) (bρ 4) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2871,23 +2500,21 @@ lemma U_610_4 : have hlg : Real.log (8560955805387 / 12500000000000 : ℝ) ≤ (-(1892584003101455628531 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show (8560955805387 / 12500000000000 : ℝ) = (8560955805387 / 6250000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8560955805387 / 6250000000000 : ℚ)) - (U := (1573151898398544371469 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (8560955805387 / 6250000000000 : ℝ) ≤ - (1573151898398544371469 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (273889140942543 / 400000000000000 : ℝ)) (q := - (8560955805387 / 12500000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8560955805387 / 12500000000000 : ℚ)) + (r' := (8560955805387 / 6250000000000 : ℚ)) + (U := (-(1892584003101455628531 / 5000000000000000000000 : ℚ))) + (U' := (1573151898398544371469 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (273889140942543 / 400000000000000 : ℚ)) + (q := (8560955805387 / 12500000000000 : ℚ)) + (U := (-(1892584003101455628531 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_5 : Uω (aρ 5) (bρ 5) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2895,25 +2522,21 @@ lemma U_610_5 : have hlg : Real.log (13456306164079367 / 20000000000000000 : ℝ) ≤ (-(3962844173437486658913 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13456306164079367 / 20000000000000000 : ℝ) = - (13456306164079367 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13456306164079367 / 10000000000000000 : ℚ)) - (U := (2968627629562513341087 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13456306164079367 / 10000000000000000 : ℝ) ≤ - (2968627629562513341087 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3362097659179371 / 5000000000000000 : ℝ)) (q := - (13456306164079367 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13456306164079367 / 20000000000000000 : ℚ)) + (r' := (13456306164079367 / 10000000000000000 : ℚ)) + (U := (-(3962844173437486658913 / 10000000000000000000000 : ℚ))) + (U' := (2968627629562513341087 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (3362097659179371 / 5000000000000000 : ℚ)) + (q := (13456306164079367 / 20000000000000000 : ℚ)) + (U := (-(3962844173437486658913 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_6 : Uω (aρ 6) (bρ 6) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2921,25 +2544,21 @@ lemma U_610_6 : have hlg : Real.log (655551023387351 / 1000000000000000 : ℝ) ≤ (-(2111395698327103507627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (655551023387351 / 1000000000000000 : ℝ) = - (655551023387351 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (655551023387351 / 500000000000000 : ℚ)) - (U := (1354340203172896492373 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (655551023387351 / 500000000000000 : ℝ) ≤ - (1354340203172896492373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1309229999433279 / 2000000000000000 : ℝ)) (q := - (655551023387351 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (655551023387351 / 1000000000000000 : ℚ)) + (r' := (655551023387351 / 500000000000000 : ℚ)) + (U := (-(2111395698327103507627 / 5000000000000000000000 : ℚ))) + (U' := (1354340203172896492373 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (1309229999433279 / 2000000000000000 : ℚ)) + (q := (655551023387351 / 1000000000000000 : ℚ)) + (U := (-(2111395698327103507627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_7 : Uω (aρ 7) (bρ 7) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2947,25 +2566,21 @@ lemma U_610_7 : have hlg : Real.log (1264138619844117 / 2000000000000000 : ℝ) ≤ (-(4587562229901919172883 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1264138619844117 / 2000000000000000 : ℝ) = - (1264138619844117 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1264138619844117 / 1000000000000000 : ℚ)) - (U := (2343909573098080827117 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1264138619844117 / 1000000000000000 : ℝ) ≤ - (2343909573098080827117 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1260035421724109 / 2000000000000000 : ℝ)) (q := - (1264138619844117 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1264138619844117 / 2000000000000000 : ℚ)) + (r' := (1264138619844117 / 1000000000000000 : ℚ)) + (U := (-(4587562229901919172883 / 10000000000000000000000 : ℚ))) + (U' := (2343909573098080827117 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (1260035421724109 / 2000000000000000 : ℚ)) + (q := (1264138619844117 / 2000000000000000 : ℚ)) + (U := (-(4587562229901919172883 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_8 : Uω (aρ 8) (bρ 8) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2973,25 +2588,21 @@ lemma U_610_8 : have hlg : Real.log (12031475208131079 / 20000000000000000 : ℝ) ≤ (-(2541030616916354549827 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12031475208131079 / 20000000000000000 : ℝ) = - (12031475208131079 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12031475208131079 / 10000000000000000 : ℚ)) - (U := (924705284583645450173 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12031475208131079 / 10000000000000000 : ℝ) ≤ - (924705284583645450173 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2986903884825227 / 5000000000000000 : ℝ)) (q := - (12031475208131079 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12031475208131079 / 20000000000000000 : ℚ)) + (r' := (12031475208131079 / 10000000000000000 : ℚ)) + (U := (-(2541030616916354549827 / 5000000000000000000000 : ℚ))) + (U' := (924705284583645450173 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (2986903884825227 / 5000000000000000 : ℚ)) + (q := (12031475208131079 / 20000000000000000 : ℚ)) + (U := (-(2541030616916354549827 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_9 : Uω (aρ 9) (bρ 9) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -2999,25 +2610,21 @@ lemma U_610_9 : have hlg : Real.log (5636354715049359 / 10000000000000000 : ℝ) ≤ (-(179171113532017318017 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5636354715049359 / 10000000000000000 : ℝ) = - (5636354715049359 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5636354715049359 / 5000000000000000 : ℚ)) - (U := (37437380311732681983 / 312500000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5636354715049359 / 5000000000000000 : ℝ) ≤ - (37437380311732681983 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5556007619978093 / 10000000000000000 : ℝ)) (q := - (5636354715049359 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5636354715049359 / 10000000000000000 : ℚ)) + (r' := (5636354715049359 / 5000000000000000 : ℚ)) + (U := (-(179171113532017318017 / 312500000000000000000 : ℚ))) + (U' := (37437380311732681983 / 312500000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (5556007619978093 / 10000000000000000 : ℚ)) + (q := (5636354715049359 / 10000000000000000 : ℚ)) + (U := (-(179171113532017318017 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_10 : Uω (aρ 10) (bρ 10) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3025,26 +2632,21 @@ lemma U_610_10 : have hlg : Real.log (10365963754816079 / 20000000000000000 : ℝ) ≤ (-(821505687596867965743 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10365963754816079 / 20000000000000000 : ℝ) = - (10365963754816079 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10365963754816079 / 10000000000000000 : ℚ)) - (U := (44928287778132034257 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10365963754816079 / 10000000000000000 : ℝ) ≤ - (44928287778132034257 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2518910489095227 / 5000000000000000 : ℝ)) (q := - (10365963754816079 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10365963754816079 / 20000000000000000 : ℚ)) + (r' := (10365963754816079 / 10000000000000000 : ℚ)) + (U := (-(821505687596867965743 / 1250000000000000000000 : ℚ))) + (U' := (44928287778132034257 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (2518910489095227 / 5000000000000000 : ℚ)) + (q := (10365963754816079 / 20000000000000000 : ℚ)) + (U := (-(821505687596867965743 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_11 : Uω (aρ 11) (bρ 11) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3052,26 +2654,21 @@ lemma U_610_11 : have hlg : Real.log (2330462411740549 / 5000000000000000 : ℝ) ≤ (-(7633712040526915893759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2330462411740549 / 5000000000000000 : ℝ) = - (2330462411740549 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2330462411740549 / 1250000000000000 : ℚ)) - (U := (6229231565473084106241 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2330462411740549 / 1250000000000000 : ℝ) ≤ - (6229231565473084106241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4412183496541571 / 10000000000000000 : ℝ)) (q := - (2330462411740549 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2330462411740549 / 5000000000000000 : ℚ)) + (r' := (2330462411740549 / 1250000000000000 : ℚ)) + (U := (-(7633712040526915893759 / 10000000000000000000000 : ℚ))) + (U' := (6229231565473084106241 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (4412183496541571 / 10000000000000000 : ℚ)) + (q := (2330462411740549 / 5000000000000000 : ℚ)) + (U := (-(7633712040526915893759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_12 : Uω (aρ 12) (bρ 12) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3079,26 +2676,21 @@ lemma U_610_12 : have hlg : Real.log (4078825692896653 / 10000000000000000 : ℝ) ≤ (-(8967759658547838351263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4078825692896653 / 10000000000000000 : ℝ) = - (4078825692896653 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4078825692896653 / 2500000000000000 : ℚ)) - (U := (4895183947452161648737 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4078825692896653 / 2500000000000000 : ℝ) ≤ - (4895183947452161648737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3671685332057681 / 10000000000000000 : ℝ)) (q := - (4078825692896653 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4078825692896653 / 10000000000000000 : ℚ)) + (r' := (4078825692896653 / 2500000000000000 : ℚ)) + (U := (-(8967759658547838351263 / 10000000000000000000000 : ℚ))) + (U' := (4895183947452161648737 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (3671685332057681 / 10000000000000000 : ℚ)) + (q := (4078825692896653 / 10000000000000000 : ℚ)) + (U := (-(8967759658547838351263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_13 : Uω (aρ 13) (bρ 13) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3106,26 +2698,21 @@ lemma U_610_13 : have hlg : Real.log (1721590044551353 / 5000000000000000 : ℝ) ≤ (-(10661896036179101416151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1721590044551353 / 5000000000000000 : ℝ) = - (1721590044551353 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1721590044551353 / 1250000000000000 : ℚ)) - (U := (3201047569820898583849 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1721590044551353 / 1250000000000000 : ℝ) ≤ - (3201047569820898583849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2799775866064787 / 10000000000000000 : ℝ)) (q := - (1721590044551353 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1721590044551353 / 5000000000000000 : ℚ)) + (r' := (1721590044551353 / 1250000000000000 : ℚ)) + (U := (-(10661896036179101416151 / 10000000000000000000000 : ℚ))) + (U' := (3201047569820898583849 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (2799775866064787 / 10000000000000000 : ℚ)) + (q := (1721590044551353 / 5000000000000000 : ℚ)) + (U := (-(10661896036179101416151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_14 : Uω (aρ 14) (bρ 14) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3133,26 +2720,21 @@ lemma U_610_14 : have hlg : Real.log (5468831640779683 / 20000000000000000 : ℝ) ≤ (-(6483336367110149200723 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5468831640779683 / 20000000000000000 : ℝ) = - (5468831640779683 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5468831640779683 / 5000000000000000 : ℚ)) - (U := (448135435889850799277 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5468831640779683 / 5000000000000000 : ℝ) ≤ - (448135435889850799277 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (863087306842029 / 5000000000000000 : ℝ)) (q := - (5468831640779683 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5468831640779683 / 20000000000000000 : ℚ)) + (r' := (5468831640779683 / 5000000000000000 : ℚ)) + (U := (-(6483336367110149200723 / 5000000000000000000000 : ℚ))) + (U' := (448135435889850799277 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2260562330581 / 3200000000000 : ℚ)) + (s := (863087306842029 / 5000000000000000 : ℚ)) + (q := (5468831640779683 / 20000000000000000 : ℚ)) + (U := (-(6483336367110149200723 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_610_15 : Uω (aρ 15) (bρ 15) (2260562330581 / 3200000000000 : ℝ) ≤ @@ -3255,25 +2837,21 @@ lemma U_611_1 : have hlg : Real.log (28063847080485117 / 40000000000000000 : ℝ) ≤ (-(1771986433177761046279 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28063847080485117 / 40000000000000000 : ℝ) = - (28063847080485117 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28063847080485117 / 20000000000000000 : ℚ)) - (U := (1693749468322238953721 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28063847080485117 / 20000000000000000 : ℝ) ≤ - (1693749468322238953721 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7015938727252871 / 10000000000000000 : ℝ)) (q := - (28063847080485117 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28063847080485117 / 40000000000000000 : ℚ)) + (r' := (28063847080485117 / 20000000000000000 : ℚ)) + (U := (-(1771986433177761046279 / 5000000000000000000000 : ℚ))) + (U' := (1693749468322238953721 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (7015938727252871 / 10000000000000000 : ℚ)) + (q := (28063847080485117 / 40000000000000000 : ℚ)) + (U := (-(1771986433177761046279 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_2 : Uω (aρ 2) (bρ 2) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3281,25 +2859,21 @@ lemma U_611_2 : have hlg : Real.log (27968256269851673 / 40000000000000000 : ℝ) ≤ (-(715618582912362501781 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27968256269851673 / 40000000000000000 : ℝ) = - (27968256269851673 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27968256269851673 / 20000000000000000 : ℚ)) - (U := (670675777687637498219 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27968256269851673 / 20000000000000000 : ℝ) ≤ - (670675777687637498219 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6991912334446149 / 10000000000000000 : ℝ)) (q := - (27968256269851673 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27968256269851673 / 40000000000000000 : ℚ)) + (r' := (27968256269851673 / 20000000000000000 : ℚ)) + (U := (-(715618582912362501781 / 2000000000000000000000 : ℚ))) + (U' := (670675777687637498219 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (6991912334446149 / 10000000000000000 : ℚ)) + (q := (27968256269851673 / 40000000000000000 : ℚ)) + (U := (-(715618582912362501781 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_3 : Uω (aρ 3) (bρ 3) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3307,25 +2881,21 @@ lemma U_611_3 : have hlg : Real.log (27777148081072199 / 40000000000000000 : ℝ) ≤ (-(91166445666578071919 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27777148081072199 / 40000000000000000 : ℝ) = - (27777148081072199 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27777148081072199 / 20000000000000000 : ℚ)) - (U := (82120349408421928081 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27777148081072199 / 20000000000000000 : ℝ) ≤ - (82120349408421928081 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1735938586601603 / 2500000000000000 : ℝ)) (q := - (27777148081072199 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27777148081072199 / 40000000000000000 : ℚ)) + (r' := (27777148081072199 / 20000000000000000 : ℚ)) + (U := (-(91166445666578071919 / 250000000000000000000 : ℚ))) + (U' := (82120349408421928081 / 250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (1735938586601603 / 2500000000000000 : ℚ)) + (q := (27777148081072199 / 40000000000000000 : ℚ)) + (U := (-(91166445666578071919 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_4 : Uω (aρ 4) (bρ 4) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3333,25 +2903,21 @@ lemma U_611_4 : have hlg : Real.log (27459972094416933 / 40000000000000000 : ℝ) ≤ (-(3761500697413053400093 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27459972094416933 / 40000000000000000 : ℝ) = - (27459972094416933 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27459972094416933 / 20000000000000000 : ℚ)) - (U := (3169971105586946599907 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27459972094416933 / 20000000000000000 : ℝ) ≤ - (3169971105586946599907 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6863460534143779 / 10000000000000000 : ℝ)) (q := - (27459972094416933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27459972094416933 / 40000000000000000 : ℚ)) + (r' := (27459972094416933 / 20000000000000000 : ℚ)) + (U := (-(3761500697413053400093 / 10000000000000000000000 : ℚ))) + (U' := (3169971105586946599907 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (6863460534143779 / 10000000000000000 : ℚ)) + (q := (27459972094416933 / 40000000000000000 : ℚ)) + (U := (-(3761500697413053400093 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_5 : Uω (aρ 5) (bρ 5) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3359,25 +2925,21 @@ lemma U_611_5 : have hlg : Real.log (5395509885359569 / 8000000000000000 : ℝ) ≤ (-(1969372182254922753893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5395509885359569 / 8000000000000000 : ℝ) = - (5395509885359569 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5395509885359569 / 4000000000000000 : ℚ)) - (U := (1496363719245077246107 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5395509885359569 / 4000000000000000 : ℝ) ≤ - (1496363719245077246107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1348087823933847 / 2000000000000000 : ℝ)) (q := - (5395509885359569 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5395509885359569 / 8000000000000000 : ℚ)) + (r' := (5395509885359569 / 4000000000000000 : ℚ)) + (U := (-(1969372182254922753893 / 5000000000000000000000 : ℚ))) + (U' := (1496363719245077246107 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (1348087823933847 / 2000000000000000 : ℚ)) + (q := (5395509885359569 / 8000000000000000 : ℚ)) + (U := (-(1969372182254922753893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_6 : Uω (aρ 6) (bρ 6) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3385,25 +2947,21 @@ lemma U_611_6 : have hlg : Real.log (26287032495816753 / 40000000000000000 : ℝ) ≤ (-(4198036972603761804577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26287032495816753 / 40000000000000000 : ℝ) = - (26287032495816753 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26287032495816753 / 20000000000000000 : ℚ)) - (U := (2733434830396238195423 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26287032495816753 / 20000000000000000 : ℝ) ≤ - (2733434830396238195423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6562421029318689 / 10000000000000000 : ℝ)) (q := - (26287032495816753 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26287032495816753 / 40000000000000000 : ℚ)) + (r' := (26287032495816753 / 20000000000000000 : ℚ)) + (U := (-(4198036972603761804577 / 10000000000000000000000 : ℚ))) + (U' := (2733434830396238195423 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (6562421029318689 / 10000000000000000 : ℚ)) + (q := (26287032495816753 / 40000000000000000 : ℚ)) + (U := (-(4198036972603761804577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_7 : Uω (aρ 7) (bρ 7) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3411,25 +2969,21 @@ lemma U_611_7 : have hlg : Real.log (1013915287293877 / 1600000000000000 : ℝ) ≤ (-(912368540818807209291 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1013915287293877 / 1600000000000000 : ℝ) = - (1013915287293877 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1013915287293877 / 800000000000000 : ℚ)) - (U := (473925819781192790709 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1013915287293877 / 800000000000000 : ℝ) ≤ - (473925819781192790709 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252660290133751 / 400000000000000 : ℝ)) (q := - (1013915287293877 / 1600000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1013915287293877 / 1600000000000000 : ℚ)) + (r' := (1013915287293877 / 800000000000000 : ℚ)) + (U := (-(912368540818807209291 / 2000000000000000000000 : ℚ))) + (U' := (473925819781192790709 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (252660290133751 / 400000000000000 : ℚ)) + (q := (1013915287293877 / 1600000000000000 : ℚ)) + (U := (-(912368540818807209291 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_8 : Uω (aρ 8) (bρ 8) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3437,25 +2991,21 @@ lemma U_611_8 : have hlg : Real.log (24128303688369371 / 40000000000000000 : ℝ) ≤ (-(5054938755538850791503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24128303688369371 / 40000000000000000 : ℝ) = - (24128303688369371 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24128303688369371 / 20000000000000000 : ℚ)) - (U := (1876533047461149208497 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24128303688369371 / 20000000000000000 : ℝ) ≤ - (1876533047461149208497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2995129828847499 / 5000000000000000 : ℝ)) (q := - (24128303688369371 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24128303688369371 / 40000000000000000 : ℚ)) + (r' := (24128303688369371 / 20000000000000000 : ℚ)) + (U := (-(5054938755538850791503 / 10000000000000000000000 : ℚ))) + (U' := (1876533047461149208497 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (2995129828847499 / 5000000000000000 : ℚ)) + (q := (24128303688369371 / 40000000000000000 : ℚ)) + (U := (-(5054938755538850791503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_9 : Uω (aρ 9) (bρ 9) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3463,25 +3013,21 @@ lemma U_611_9 : have hlg : Real.log (22611253604052877 / 40000000000000000 : ℝ) ≤ (-(713039655535341428553 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22611253604052877 / 40000000000000000 : ℝ) = - (22611253604052877 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22611253604052877 / 20000000000000000 : ℚ)) - (U := (153394319839658571447 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22611253604052877 / 20000000000000000 : ℝ) ≤ - (153394319839658571447 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5572700243896751 / 10000000000000000 : ℝ)) (q := - (22611253604052877 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22611253604052877 / 40000000000000000 : ℚ)) + (r' := (22611253604052877 / 20000000000000000 : ℚ)) + (U := (-(713039655535341428553 / 1250000000000000000000 : ℚ))) + (U' := (153394319839658571447 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (5572700243896751 / 10000000000000000 : ℚ)) + (q := (22611253604052877 / 40000000000000000 : ℚ)) + (U := (-(713039655535341428553 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_10 : Uω (aρ 10) (bρ 10) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3489,26 +3035,21 @@ lemma U_611_10 : have hlg : Real.log (20798690340675543 / 40000000000000000 : ℝ) ≤ (-(6539894335196580513757 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20798690340675543 / 40000000000000000 : ℝ) = - (20798690340675543 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20798690340675543 / 20000000000000000 : ℚ)) - (U := (391577467803419486243 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20798690340675543 / 20000000000000000 : ℝ) ≤ - (391577467803419486243 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1263744411425771 / 2500000000000000 : ℝ)) (q := - (20798690340675543 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20798690340675543 / 40000000000000000 : ℚ)) + (r' := (20798690340675543 / 20000000000000000 : ℚ)) + (U := (-(6539894335196580513757 / 10000000000000000000000 : ℚ))) + (U' := (391577467803419486243 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (1263744411425771 / 2500000000000000 : ℚ)) + (q := (20798690340675543 / 40000000000000000 : ℚ)) + (U := (-(6539894335196580513757 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_11 : Uω (aρ 11) (bρ 11) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3516,26 +3057,21 @@ lemma U_611_11 : have hlg : Real.log (18712242877819023 / 40000000000000000 : ℝ) ≤ (-(1899253611517541986453 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (18712242877819023 / 40000000000000000 : ℝ) = - (18712242877819023 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18712242877819023 / 10000000000000000 : ℚ)) - (U := (1566482289982458013547 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18712242877819023 / 10000000000000000 : ℝ) ≤ - (1566482289982458013547 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (276889408779989 / 625000000000000 : ℝ)) (q := - (18712242877819023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18712242877819023 / 40000000000000000 : ℚ)) + (r' := (18712242877819023 / 10000000000000000 : ℚ)) + (U := (-(1899253611517541986453 / 2500000000000000000000 : ℚ))) + (U' := (1566482289982458013547 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (276889408779989 / 625000000000000 : ℚ)) + (q := (18712242877819023 / 40000000000000000 : ℚ)) + (U := (-(1899253611517541986453 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_12 : Uω (aρ 12) (bρ 12) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3543,26 +3079,21 @@ lemma U_611_12 : have hlg : Real.log (16387363049407717 / 40000000000000000 : ℝ) ≤ (-(8923689615546948989069 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16387363049407717 / 40000000000000000 : ℝ) = - (16387363049407717 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16387363049407717 / 10000000000000000 : ℚ)) - (U := (4939253990453051010931 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16387363049407717 / 10000000000000000 : ℝ) ≤ - (4939253990453051010931 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3691490722959171 / 10000000000000000 : ℝ)) (q := - (16387363049407717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16387363049407717 / 40000000000000000 : ℚ)) + (r' := (16387363049407717 / 10000000000000000 : ℚ)) + (U := (-(8923689615546948989069 / 10000000000000000000000 : ℚ))) + (U' := (4939253990453051010931 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (3691490722959171 / 10000000000000000 : ℚ)) + (q := (16387363049407717 / 40000000000000000 : ℚ)) + (U := (-(8923689615546948989069 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_13 : Uω (aρ 13) (bρ 13) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3570,26 +3101,21 @@ lemma U_611_13 : have hlg : Real.log (13852428102585417 / 40000000000000000 : ℝ) ≤ (-(1325523652575441464269 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13852428102585417 / 40000000000000000 : ℝ) = - (13852428102585417 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13852428102585417 / 10000000000000000 : ℚ)) - (U := (407344298174558535731 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13852428102585417 / 10000000000000000 : ℝ) ≤ - (407344298174558535731 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2823404991143021 / 10000000000000000 : ℝ)) (q := - (13852428102585417 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13852428102585417 / 40000000000000000 : ℚ)) + (r' := (13852428102585417 / 10000000000000000 : ℚ)) + (U := (-(1325523652575441464269 / 1250000000000000000000 : ℚ))) + (U' := (407344298174558535731 / 1250000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (2823404991143021 / 10000000000000000 : ℚ)) + (q := (13852428102585417 / 40000000000000000 : ℚ)) + (U := (-(1325523652575441464269 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_14 : Uω (aρ 14) (bρ 14) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3597,26 +3123,21 @@ lemma U_611_14 : have hlg : Real.log (11039915945363911 / 40000000000000000 : ℝ) ≤ (-(3218405066046634124583 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11039915945363911 / 40000000000000000 : ℝ) = - (11039915945363911 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11039915945363911 / 10000000000000000 : ℚ)) - (U := (247330835453365875417 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (11039915945363911 / 10000000000000000 : ℝ) ≤ - (247330835453365875417 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (440269049394317 / 2500000000000000 : ℝ)) (q := - (11039915945363911 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11039915945363911 / 40000000000000000 : ℚ)) + (r' := (11039915945363911 / 10000000000000000 : ℚ)) + (U := (-(3218405066046634124583 / 2500000000000000000000 : ℚ))) + (U' := (247330835453365875417 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22657542499439 / 32000000000000 : ℚ)) + (s := (440269049394317 / 2500000000000000 : ℚ)) + (q := (11039915945363911 / 40000000000000000 : ℚ)) + (U := (-(3218405066046634124583 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_611_15 : Uω (aρ 15) (bρ 15) (22657542499439 / 32000000000000 : ℝ) ≤ @@ -3718,25 +3239,21 @@ lemma U_612_1 : have hlg : Real.log (2812874628518123 / 4000000000000000 : ℝ) ≤ (-(704174801898035062819 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2812874628518123 / 4000000000000000 : ℝ) = - (2812874628518123 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2812874628518123 / 2000000000000000 : ℚ)) - (U := (682119558701964937181 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2812874628518123 / 2000000000000000 : ℝ) ≤ - (682119558701964937181 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1406432716318373 / 2000000000000000 : ℝ)) (q := - (2812874628518123 / 4000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2812874628518123 / 4000000000000000 : ℚ)) + (r' := (2812874628518123 / 2000000000000000 : ℚ)) + (U := (-(704174801898035062819 / 2000000000000000000000 : ℚ))) + (U' := (682119558701964937181 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (1406432716318373 / 2000000000000000 : ℚ)) + (q := (2812874628518123 / 4000000000000000 : ℚ)) + (U := (-(704174801898035062819 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_2 : Uω (aρ 2) (bρ 2) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3744,25 +3261,21 @@ lemma U_612_2 : have hlg : Real.log (14016578333507227 / 20000000000000000 : ℝ) ≤ (-(888728693930132351883 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14016578333507227 / 20000000000000000 : ℝ) = - (14016578333507227 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14016578333507227 / 10000000000000000 : ℚ)) - (U := (844139256819867648117 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14016578333507227 / 10000000000000000 : ℝ) ≤ - (844139256819867648117 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7008137785018477 / 10000000000000000 : ℝ)) (q := - (14016578333507227 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14016578333507227 / 20000000000000000 : ℚ)) + (r' := (14016578333507227 / 10000000000000000 : ℚ)) + (U := (-(888728693930132351883 / 2500000000000000000000 : ℚ))) + (U' := (844139256819867648117 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (7008137785018477 / 10000000000000000 : ℚ)) + (q := (14016578333507227 / 20000000000000000 : ℚ)) + (U := (-(888728693930132351883 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_3 : Uω (aρ 3) (bρ 3) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3770,24 +3283,21 @@ lemma U_612_3 : have hlg : Real.log (108758015781547 / 156250000000000 : ℝ) ≤ (-(3623319127680336539177 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (108758015781547 / 156250000000000 : ℝ) = (108758015781547 / 78125000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (108758015781547 / 78125000000000 : ℚ)) - (U := (3308152675319663460823 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (108758015781547 / 78125000000000 : ℝ) ≤ - (3308152675319663460823 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3479990788949633 / 5000000000000000 : ℝ)) (q := - (108758015781547 / 156250000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (108758015781547 / 156250000000000 : ℚ)) + (r' := (108758015781547 / 78125000000000 : ℚ)) + (U := (-(3623319127680336539177 / 10000000000000000000000 : ℚ))) + (U' := (3308152675319663460823 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (3479990788949633 / 5000000000000000 : ℚ)) + (q := (108758015781547 / 156250000000000 : ℚ)) + (U := (-(3623319127680336539177 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_4 : Uω (aρ 4) (bρ 4) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3795,25 +3305,21 @@ lemma U_612_4 : have hlg : Real.log (13762442771534643 / 20000000000000000 : ℝ) ≤ (-(116809040482449137779 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13762442771534643 / 20000000000000000 : ℝ) = - (13762442771534643 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13762442771534643 / 10000000000000000 : ℚ)) - (U := (99799453361300862221 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13762442771534643 / 10000000000000000 : ℝ) ≤ - (99799453361300862221 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6879692510460893 / 10000000000000000 : ℝ)) (q := - (13762442771534643 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13762442771534643 / 20000000000000000 : ℚ)) + (r' := (13762442771534643 / 10000000000000000 : ℚ)) + (U := (-(116809040482449137779 / 312500000000000000000 : ℚ))) + (U' := (99799453361300862221 / 312500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (6879692510460893 / 10000000000000000 : ℚ)) + (q := (13762442771534643 / 20000000000000000 : ℚ)) + (U := (-(116809040482449137779 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_5 : Uω (aρ 5) (bρ 5) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3821,25 +3327,21 @@ lemma U_612_5 : have hlg : Real.log (1690155396394973 / 2500000000000000 : ℝ) ≤ (-(1957351281884243234707 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1690155396394973 / 2500000000000000 : ℝ) = - (1690155396394973 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1690155396394973 / 1250000000000000 : ℚ)) - (U := (1508384619615756765293 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1690155396394973 / 1250000000000000 : ℝ) ≤ - (1508384619615756765293 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3378341414710517 / 5000000000000000 : ℝ)) (q := - (1690155396394973 / 2500000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1690155396394973 / 2500000000000000 : ℚ)) + (r' := (1690155396394973 / 1250000000000000 : ℚ)) + (U := (-(1957351281884243234707 / 5000000000000000000000 : ℚ))) + (U' := (1508384619615756765293 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (3378341414710517 / 5000000000000000 : ℚ)) + (q := (1690155396394973 / 2500000000000000 : ℚ)) + (U := (-(1957351281884243234707 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_6 : Uω (aρ 6) (bρ 6) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3847,25 +3349,21 @@ lemma U_612_6 : have hlg : Real.log (13176011799446877 / 20000000000000000 : ℝ) ≤ (-(4173343848933882049953 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13176011799446877 / 20000000000000000 : ℝ) = - (13176011799446877 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13176011799446877 / 10000000000000000 : ℚ)) - (U := (2758127954066117950047 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13176011799446877 / 10000000000000000 : ℝ) ≤ - (2758127954066117950047 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6578691832848127 / 10000000000000000 : ℝ)) (q := - (13176011799446877 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13176011799446877 / 20000000000000000 : ℚ)) + (r' := (13176011799446877 / 10000000000000000 : ℚ)) + (U := (-(4173343848933882049953 / 10000000000000000000000 : ℚ))) + (U' := (2758127954066117950047 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (6578691832848127 / 10000000000000000 : ℚ)) + (q := (13176011799446877 / 20000000000000000 : ℚ)) + (U := (-(4173343848933882049953 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_7 : Uω (aρ 7) (bρ 7) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3873,25 +3371,21 @@ lemma U_612_7 : have hlg : Real.log (3176623860524561 / 5000000000000000 : ℝ) ≤ (-(2268094792214219806731 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3176623860524561 / 5000000000000000 : ℝ) = - (3176623860524561 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3176623860524561 / 2500000000000000 : ℚ)) - (U := (1197641109285780193269 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3176623860524561 / 2500000000000000 : ℝ) ≤ - (1197641109285780193269 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3166418428129747 / 5000000000000000 : ℝ)) (q := - (3176623860524561 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3176623860524561 / 5000000000000000 : ℚ)) + (r' := (3176623860524561 / 2500000000000000 : ℚ)) + (U := (-(2268094792214219806731 / 5000000000000000000000 : ℚ))) + (U' := (1197641109285780193269 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (3166418428129747 / 5000000000000000 : ℚ)) + (q := (3176623860524561 / 5000000000000000 : ℚ)) + (U := (-(2268094792214219806731 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_8 : Uω (aρ 8) (bρ 8) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3899,25 +3393,21 @@ lemma U_612_8 : have hlg : Real.log (3024206811147909 / 5000000000000000 : ℝ) ≤ (-(2513945331327445238627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3024206811147909 / 5000000000000000 : ℝ) = - (3024206811147909 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3024206811147909 / 2500000000000000 : ℚ)) - (U := (951790570172554761373 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3024206811147909 / 2500000000000000 : ℝ) ≤ - (951790570172554761373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3003355155046443 / 5000000000000000 : ℝ)) (q := - (3024206811147909 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3024206811147909 / 5000000000000000 : ℚ)) + (r' := (3024206811147909 / 2500000000000000 : ℚ)) + (U := (-(2513945331327445238627 / 5000000000000000000000 : ℚ))) + (U' := (951790570172554761373 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (3003355155046443 / 5000000000000000 : ℚ)) + (q := (3024206811147909 / 5000000000000000 : ℚ)) + (U := (-(2513945331327445238627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_9 : Uω (aρ 9) (bρ 9) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3925,25 +3415,21 @@ lemma U_612_9 : have hlg : Real.log (2834635354627983 / 5000000000000000 : ℝ) ≤ (-(5675246059732281515241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2834635354627983 / 5000000000000000 : ℝ) = - (2834635354627983 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2834635354627983 / 2500000000000000 : ℚ)) - (U := (1256225743267718484759 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2834635354627983 / 2500000000000000 : ℝ) ≤ - (1256225743267718484759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2794695056186591 / 5000000000000000 : ℝ)) (q := - (2834635354627983 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2834635354627983 / 5000000000000000 : ℚ)) + (r' := (2834635354627983 / 2500000000000000 : ℚ)) + (U := (-(5675246059732281515241 / 10000000000000000000000 : ℚ))) + (U' := (1256225743267718484759 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (2794695056186591 / 5000000000000000 : ℚ)) + (q := (2834635354627983 / 5000000000000000 : ℚ)) + (U := (-(5675246059732281515241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_10 : Uω (aρ 10) (bρ 10) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3951,26 +3437,21 @@ lemma U_612_10 : have hlg : Real.log (10432720452581229 / 20000000000000000 : ℝ) ≤ (-(650785208705559288509 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10432720452581229 / 20000000000000000 : ℝ) = - (10432720452581229 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10432720452581229 / 10000000000000000 : ℚ)) - (U := (42361971594440711491 / 1000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10432720452581229 / 10000000000000000 : ℝ) ≤ - (42361971594440711491 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5072128179937479 / 10000000000000000 : ℝ)) (q := - (10432720452581229 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10432720452581229 / 20000000000000000 : ℚ)) + (r' := (10432720452581229 / 10000000000000000 : ℚ)) + (U := (-(650785208705559288509 / 1000000000000000000000 : ℚ))) + (U' := (42361971594440711491 / 1000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (5072128179937479 / 10000000000000000 : ℚ)) + (q := (10432720452581229 / 20000000000000000 : ℚ)) + (U := (-(650785208705559288509 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_11 : Uω (aρ 11) (bρ 11) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -3978,26 +3459,21 @@ lemma U_612_11 : have hlg : Real.log (1878075838188081 / 4000000000000000 : ℝ) ≤ (-(7560465982075085006291 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1878075838188081 / 4000000000000000 : ℝ) = - (1878075838188081 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1878075838188081 / 1000000000000000 : ℚ)) - (U := (6302477623924914993709 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1878075838188081 / 1000000000000000 : ℝ) ≤ - (6302477623924914993709 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (889652708900331 / 2000000000000000 : ℝ)) (q := - (1878075838188081 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1878075838188081 / 4000000000000000 : ℚ)) + (r' := (1878075838188081 / 1000000000000000 : ℚ)) + (U := (-(7560465982075085006291 / 10000000000000000000000 : ℚ))) + (U' := (6302477623924914993709 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (889652708900331 / 2000000000000000 : ℚ)) + (q := (1878075838188081 / 4000000000000000 : ℚ)) + (U := (-(7560465982075085006291 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_12 : Uω (aρ 12) (bρ 12) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -4005,26 +3481,21 @@ lemma U_612_12 : have hlg : Real.log (4114838450862511 / 10000000000000000 : ℝ) ≤ (-(8879855177153937258143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4114838450862511 / 10000000000000000 : ℝ) = - (4114838450862511 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4114838450862511 / 2500000000000000 : ℚ)) - (U := (4983088428846062741857 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (4114838450862511 / 2500000000000000 : ℝ) ≤ - (4983088428846062741857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (463907668996409 / 1250000000000000 : ℝ)) (q := - (4114838450862511 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4114838450862511 / 10000000000000000 : ℚ)) + (r' := (4114838450862511 / 2500000000000000 : ℚ)) + (U := (-(8879855177153937258143 / 10000000000000000000000 : ℚ))) + (U' := (4983088428846062741857 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (463907668996409 / 1250000000000000 : ℚ)) + (q := (4114838450862511 / 10000000000000000 : ℚ)) + (U := (-(8879855177153937258143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_13 : Uω (aρ 13) (bρ 13) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -4032,26 +3503,21 @@ lemma U_612_13 : have hlg : Real.log (3482982136594709 / 10000000000000000 : ℝ) ≤ (-(2636740574611385909277 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3482982136594709 / 10000000000000000 : ℝ) = - (3482982136594709 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3482982136594709 / 2500000000000000 : ℚ)) - (U := (828995326888614090723 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3482982136594709 / 2500000000000000 : ℝ) ≤ - (828995326888614090723 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (711732616257667 / 2500000000000000 : ℝ)) (q := - (3482982136594709 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3482982136594709 / 10000000000000000 : ℚ)) + (r' := (3482982136594709 / 2500000000000000 : ℚ)) + (U := (-(2636740574611385909277 / 2500000000000000000000 : ℚ))) + (U' := (828995326888614090723 / 2500000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (711732616257667 / 2500000000000000 : ℚ)) + (q := (3482982136594709 / 10000000000000000 : ℚ)) + (U := (-(2636740574611385909277 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_14 : Uω (aρ 14) (bρ 14) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -4059,26 +3525,21 @@ lemma U_612_14 : have hlg : Real.log (5570552549959177 / 20000000000000000 : ℝ) ≤ (-(12782380229451382714503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5570552549959177 / 20000000000000000 : ℝ) = - (5570552549959177 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5570552549959177 / 5000000000000000 : ℚ)) - (U := (1080563376548617285497 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5570552549959177 / 5000000000000000 : ℝ) ≤ - (1080563376548617285497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1795446026845427 / 10000000000000000 : ℝ)) (q := - (5570552549959177 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5570552549959177 / 20000000000000000 : ℚ)) + (r' := (5570552549959177 / 5000000000000000 : ℚ)) + (U := (-(12782380229451382714503 / 10000000000000000000000 : ℚ))) + (U' := (1080563376548617285497 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5677365423267 / 8000000000000 : ℚ)) + (s := (1795446026845427 / 10000000000000000 : ℚ)) + (q := (5570552549959177 / 20000000000000000 : ℚ)) + (U := (-(12782380229451382714503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_612_15 : Uω (aρ 15) (bρ 15) (5677365423267 / 8000000000000 : ℝ) ≤ @@ -4180,25 +3641,21 @@ lemma U_613_1 : have hlg : Real.log (28193645488898291 / 40000000000000000 : ℝ) ≤ (-(874457096438228208609 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28193645488898291 / 40000000000000000 : ℝ) = - (28193645488898291 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28193645488898291 / 20000000000000000 : ℚ)) - (U := (858410854311771791391 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28193645488898291 / 20000000000000000 : ℝ) ≤ - (858410854311771791391 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7048388435441333 / 10000000000000000 : ℝ)) (q := - (28193645488898291 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28193645488898291 / 40000000000000000 : ℚ)) + (r' := (28193645488898291 / 20000000000000000 : ℚ)) + (U := (-(874457096438228208609 / 2500000000000000000000 : ℚ))) + (U' := (858410854311771791391 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (7048388435441333 / 10000000000000000 : ℚ)) + (q := (28193645488898291 / 40000000000000000 : ℚ)) + (U := (-(874457096438228208609 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_2 : Uω (aρ 2) (bρ 2) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4206,25 +3663,21 @@ lemma U_613_2 : have hlg : Real.log (28098057057686023 / 40000000000000000 : ℝ) ≤ (-(3531790237594273493879 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28098057057686023 / 40000000000000000 : ℝ) = - (28098057057686023 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28098057057686023 / 20000000000000000 : ℚ)) - (U := (3399681565405726506121 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28098057057686023 / 20000000000000000 : ℝ) ≤ - (3399681565405726506121 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7024363232345199 / 10000000000000000 : ℝ)) (q := - (28098057057686023 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28098057057686023 / 40000000000000000 : ℚ)) + (r' := (28098057057686023 / 20000000000000000 : ℚ)) + (U := (-(3531790237594273493879 / 10000000000000000000000 : ℚ))) + (U' := (3399681565405726506121 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (7024363232345199 / 10000000000000000 : ℚ)) + (q := (28098057057686023 / 40000000000000000 : ℚ)) + (U := (-(3531790237594273493879 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_3 : Uω (aρ 3) (bρ 3) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4232,25 +3685,21 @@ lemma U_613_3 : have hlg : Real.log (27906955975974487 / 40000000000000000 : ℝ) ≤ (-(3600034779659862000939 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27906955975974487 / 40000000000000000 : ℝ) = - (27906955975974487 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27906955975974487 / 20000000000000000 : ℚ)) - (U := (3331437023340137999061 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27906955975974487 / 20000000000000000 : ℝ) ≤ - (3331437023340137999061 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6976208797839431 / 10000000000000000 : ℝ)) (q := - (27906955975974487 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27906955975974487 / 40000000000000000 : ℚ)) + (r' := (27906955975974487 / 20000000000000000 : ℚ)) + (U := (-(3600034779659862000939 / 10000000000000000000000 : ℚ))) + (U' := (3331437023340137999061 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (6976208797839431 / 10000000000000000 : ℚ)) + (q := (27906955975974487 / 40000000000000000 : ℚ)) + (U := (-(3600034779659862000939 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_4 : Uω (aρ 4) (bρ 4) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4258,25 +3707,21 @@ lemma U_613_4 : have hlg : Real.log (27589798923679363 / 40000000000000000 : ℝ) ≤ (-(371433353665875078499 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27589798923679363 / 40000000000000000 : ℝ) = - (27589798923679363 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27589798923679363 / 20000000000000000 : ℚ)) - (U := (321713826634124921501 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27589798923679363 / 20000000000000000 : ℝ) ≤ - (321713826634124921501 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6895924452756869 / 10000000000000000 : ℝ)) (q := - (27589798923679363 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27589798923679363 / 40000000000000000 : ℚ)) + (r' := (27589798923679363 / 20000000000000000 : ℚ)) + (U := (-(371433353665875078499 / 1000000000000000000000 : ℚ))) + (U' := (321713826634124921501 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (6895924452756869 / 10000000000000000 : ℚ)) + (q := (27589798923679363 / 40000000000000000 : ℚ)) + (U := (-(371433353665875078499 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_5 : Uω (aρ 5) (bρ 5) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4284,25 +3729,21 @@ lemma U_613_5 : have hlg : Real.log (27107423076041433 / 40000000000000000 : ℝ) ≤ (-(486339811538652721501 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27107423076041433 / 40000000000000000 : ℝ) = - (27107423076041433 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27107423076041433 / 20000000000000000 : ℚ)) - (U := (380094163836347278499 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27107423076041433 / 20000000000000000 : ℝ) ≤ - (380094163836347278499 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (846615806034113 / 1250000000000000 : ℝ)) (q := - (27107423076041433 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27107423076041433 / 40000000000000000 : ℚ)) + (r' := (27107423076041433 / 20000000000000000 : ℚ)) + (U := (-(486339811538652721501 / 1250000000000000000000 : ℚ))) + (U' := (380094163836347278499 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (846615806034113 / 1250000000000000 : ℚ)) + (q := (27107423076041433 / 40000000000000000 : ℚ)) + (U := (-(486339811538652721501 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_6 : Uω (aρ 6) (bρ 6) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4310,25 +3751,21 @@ lemma U_613_6 : have hlg : Real.log (26417014248109331 / 40000000000000000 : ℝ) ≤ (-(1037177930485340854641 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26417014248109331 / 40000000000000000 : ℝ) = - (26417014248109331 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26417014248109331 / 20000000000000000 : ℚ)) - (U := (695690020264659145359 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26417014248109331 / 20000000000000000 : ℝ) ≤ - (695690020264659145359 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6594962409446853 / 10000000000000000 : ℝ)) (q := - (26417014248109331 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26417014248109331 / 40000000000000000 : ℚ)) + (r' := (26417014248109331 / 20000000000000000 : ℚ)) + (U := (-(1037177930485340854641 / 2500000000000000000000 : ℚ))) + (U' := (695690020264659145359 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (6594962409446853 / 10000000000000000 : ℚ)) + (q := (26417014248109331 / 40000000000000000 : ℚ)) + (U := (-(1037177930485340854641 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_7 : Uω (aρ 7) (bρ 7) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4336,25 +3773,21 @@ lemma U_613_7 : have hlg : Real.log (25478098510791969 / 40000000000000000 : ℝ) ≤ (-(902120505339501589781 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25478098510791969 / 40000000000000000 : ℝ) = - (25478098510791969 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25478098510791969 / 20000000000000000 : ℚ)) - (U := (484173855260498410219 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25478098510791969 / 20000000000000000 : ℝ) ≤ - (484173855260498410219 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1587291480387043 / 2500000000000000 : ℝ)) (q := - (25478098510791969 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25478098510791969 / 40000000000000000 : ℚ)) + (r' := (25478098510791969 / 20000000000000000 : ℚ)) + (U := (-(902120505339501589781 / 2000000000000000000000 : ℚ))) + (U' := (484173855260498410219 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (1587291480387043 / 2500000000000000 : ℚ)) + (q := (25478098510791969 / 40000000000000000 : ℚ)) + (U := (-(902120505339501589781 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_8 : Uω (aρ 8) (bρ 8) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4362,25 +3795,21 @@ lemma U_613_8 : have hlg : Real.log (24259002838952893 / 40000000000000000 : ℝ) ≤ (-(1250229135690731567857 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24259002838952893 / 40000000000000000 : ℝ) = - (24259002838952893 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24259002838952893 / 20000000000000000 : ℚ)) - (U := (482638815059268432143 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24259002838952893 / 20000000000000000 : ℝ) ≤ - (482638815059268432143 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3011579868484317 / 5000000000000000 : ℝ)) (q := - (24259002838952893 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24259002838952893 / 40000000000000000 : ℚ)) + (r' := (24259002838952893 / 20000000000000000 : ℚ)) + (U := (-(1250229135690731567857 / 2500000000000000000000 : ℚ))) + (U' := (482638815059268432143 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (3011579868484317 / 5000000000000000 : ℚ)) + (q := (24259002838952893 / 40000000000000000 : ℚ)) + (U := (-(1250229135690731567857 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_9 : Uω (aρ 9) (bρ 9) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4388,25 +3817,21 @@ lemma U_613_9 : have hlg : Real.log (22742906608329809 / 40000000000000000 : ℝ) ≤ (-(141156538628002730241 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22742906608329809 / 40000000000000000 : ℝ) = - (22742906608329809 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22742906608329809 / 20000000000000000 : ℚ)) - (U := (32130256446997269759 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22742906608329809 / 20000000000000000 : ℝ) ≤ - (32130256446997269759 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1401519312504273 / 2500000000000000 : ℝ)) (q := - (22742906608329809 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22742906608329809 / 40000000000000000 : ℚ)) + (r' := (22742906608329809 / 20000000000000000 : ℚ)) + (U := (-(141156538628002730241 / 250000000000000000000 : ℚ))) + (U' := (32130256446997269759 / 250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (1401519312504273 / 2500000000000000 : ℚ)) + (q := (22742906608329809 / 40000000000000000 : ℚ)) + (U := (-(141156538628002730241 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_10 : Uω (aρ 10) (bρ 10) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4414,26 +3839,21 @@ lemma U_613_10 : have hlg : Real.log (20932179327105513 / 40000000000000000 : ℝ) ≤ (-(6475917982535767971497 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20932179327105513 / 40000000000000000 : ℝ) = - (20932179327105513 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20932179327105513 / 20000000000000000 : ℚ)) - (U := (455553820464232028503 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20932179327105513 / 20000000000000000 : ℝ) ≤ - (455553820464232028503 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (636159080362493 / 1250000000000000 : ℝ)) (q := - (20932179327105513 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20932179327105513 / 40000000000000000 : ℚ)) + (r' := (20932179327105513 / 20000000000000000 : ℚ)) + (U := (-(6475917982535767971497 / 10000000000000000000000 : ℚ))) + (U' := (455553820464232028503 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (636159080362493 / 1250000000000000 : ℚ)) + (q := (20932179327105513 / 40000000000000000 : ℚ)) + (U := (-(6475917982535767971497 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_11 : Uω (aρ 11) (bρ 11) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4441,26 +3861,21 @@ lemma U_613_11 : have hlg : Real.log (3769849229246809 / 8000000000000000 : ℝ) ≤ (-(7524065327419626836843 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3769849229246809 / 8000000000000000 : ℝ) = - (3769849229246809 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3769849229246809 / 2000000000000000 : ℚ)) - (U := (6338878278580373163157 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3769849229246809 / 2000000000000000 : ℝ) ≤ - (6338878278580373163157 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (446628267866921 / 1000000000000000 : ℝ)) (q := - (3769849229246809 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3769849229246809 / 8000000000000000 : ℚ)) + (r' := (3769849229246809 / 2000000000000000 : ℚ)) + (U := (-(7524065327419626836843 / 10000000000000000000000 : ℚ))) + (U' := (6338878278580373163157 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (446628267866921 / 1000000000000000 : ℚ)) + (q := (3769849229246809 / 8000000000000000 : ℚ)) + (U := (-(7524065327419626836843 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_12 : Uω (aρ 12) (bρ 12) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4468,26 +3883,21 @@ lemma U_613_12 : have hlg : Real.log (16531276138937201 / 40000000000000000 : ℝ) ≤ (-(8836253433533761614819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16531276138937201 / 40000000000000000 : ℝ) = - (16531276138937201 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16531276138937201 / 10000000000000000 : ℚ)) - (U := (5026690172466238385181 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16531276138937201 / 10000000000000000 : ℝ) ≤ - (5026690172466238385181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (932749442926447 / 2500000000000000 : ℝ)) (q := - (16531276138937201 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16531276138937201 / 40000000000000000 : ℚ)) + (r' := (16531276138937201 / 10000000000000000 : ℚ)) + (U := (-(8836253433533761614819 / 10000000000000000000000 : ℚ))) + (U' := (5026690172466238385181 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (932749442926447 / 2500000000000000 : ℚ)) + (q := (16531276138937201 / 40000000000000000 : ℚ)) + (U := (-(8836253433533761614819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_13 : Uω (aρ 13) (bρ 13) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4495,26 +3905,21 @@ lemma U_613_13 : have hlg : Real.log (14011226784954181 / 40000000000000000 : ℝ) ≤ (-(2098041064256764806811 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14011226784954181 / 40000000000000000 : ℝ) = - (14011226784954181 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14011226784954181 / 10000000000000000 : ℚ)) - (U := (674547656943235193189 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14011226784954181 / 10000000000000000 : ℝ) ≤ - (674547656943235193189 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1435177418154639 / 5000000000000000 : ℝ)) (q := - (14011226784954181 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14011226784954181 / 40000000000000000 : ℚ)) + (r' := (14011226784954181 / 10000000000000000 : ℚ)) + (U := (-(2098041064256764806811 / 2000000000000000000000 : ℚ))) + (U' := (674547656943235193189 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (1435177418154639 / 5000000000000000 : ℚ)) + (q := (14011226784954181 / 40000000000000000 : ℚ)) + (U := (-(2098041064256764806811 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_14 : Uω (aρ 14) (bρ 14) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4522,26 +3927,21 @@ lemma U_613_14 : have hlg : Real.log (11241290690528949 / 40000000000000000 : ℝ) ≤ (-(1586607232003425158267 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11241290690528949 / 40000000000000000 : ℝ) = - (11241290690528949 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11241290690528949 / 10000000000000000 : ℚ)) - (U := (146260718746574841733 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11241290690528949 / 10000000000000000 : ℝ) ≤ - (146260718746574841733 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (914657037070831 / 5000000000000000 : ℝ)) (q := - (11241290690528949 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11241290690528949 / 40000000000000000 : ℚ)) + (r' := (11241290690528949 / 10000000000000000 : ℚ)) + (U := (-(1586607232003425158267 / 1250000000000000000000 : ℚ))) + (U' := (146260718746574841733 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (22761380886697 / 32000000000000 : ℚ)) + (s := (914657037070831 / 5000000000000000 : ℚ)) + (q := (11241290690528949 / 40000000000000000 : ℚ)) + (U := (-(1586607232003425158267 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_613_15 : Uω (aρ 15) (bρ 15) (22761380886697 / 32000000000000 : ℝ) ≤ @@ -4643,25 +4043,21 @@ lemma U_614_1 : have hlg : Real.log (565170893832861 / 800000000000000 : ℝ) ≤ (-(347483575034634540937 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (565170893832861 / 800000000000000 : ℝ) = - (565170893832861 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (565170893832861 / 400000000000000 : ℚ)) - (U := (345663605265365459063 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (565170893832861 / 400000000000000 : ℝ) ≤ - (345663605265365459063 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (141292265776093 / 200000000000000 : ℝ)) (q := - (565170893832861 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (565170893832861 / 800000000000000 : ℚ)) + (r' := (565170893832861 / 400000000000000 : ℚ)) + (U := (-(347483575034634540937 / 1000000000000000000000 : ℚ))) + (U' := (345663605265365459063 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (141292265776093 / 200000000000000 : ℚ)) + (q := (565170893832861 / 800000000000000 : ℚ)) + (U := (-(347483575034634540937 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_2 : Uω (aρ 2) (bρ 2) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4669,25 +4065,21 @@ lemma U_614_2 : have hlg : Real.log (14081478720955629 / 20000000000000000 : ℝ) ≤ (-(350871905283512890253 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14081478720955629 / 20000000000000000 : ℝ) = - (14081478720955629 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14081478720955629 / 10000000000000000 : ℚ)) - (U := (342275275016487109747 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14081478720955629 / 10000000000000000 : ℝ) ≤ - (342275275016487109747 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3520294338224377 / 5000000000000000 : ℝ)) (q := - (14081478720955629 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14081478720955629 / 20000000000000000 : ℚ)) + (r' := (14081478720955629 / 10000000000000000 : ℚ)) + (U := (-(350871905283512890253 / 1000000000000000000000 : ℚ))) + (U' := (342275275016487109747 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (3520294338224377 / 5000000000000000 : ℚ)) + (q := (14081478720955629 / 20000000000000000 : ℚ)) + (U := (-(350871905283512890253 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_3 : Uω (aρ 3) (bρ 3) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4695,25 +4087,21 @@ lemma U_614_3 : have hlg : Real.log (6992964972232107 / 10000000000000000 : ℝ) ≤ (-(894201132501833096559 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6992964972232107 / 10000000000000000 : ℝ) = - (6992964972232107 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6992964972232107 / 5000000000000000 : ℚ)) - (U := (838666818248166903441 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6992964972232107 / 5000000000000000 : ℝ) ≤ - (838666818248166903441 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6992436006307339 / 10000000000000000 : ℝ)) (q := - (6992964972232107 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6992964972232107 / 10000000000000000 : ℚ)) + (r' := (6992964972232107 / 5000000000000000 : ℚ)) + (U := (-(894201132501833096559 / 2500000000000000000000 : ℚ))) + (U' := (838666818248166903441 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (6992436006307339 / 10000000000000000 : ℚ)) + (q := (6992964972232107 / 10000000000000000 : ℚ)) + (U := (-(894201132501833096559 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_4 : Uω (aρ 4) (bρ 4) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4721,25 +4109,21 @@ lemma U_614_4 : have hlg : Real.log (13827356118363259 / 20000000000000000 : ℝ) ≤ (-(3690833159315097836869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13827356118363259 / 20000000000000000 : ℝ) = - (13827356118363259 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13827356118363259 / 10000000000000000 : ℚ)) - (U := (3240638643684902163131 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13827356118363259 / 10000000000000000 : ℝ) ≤ - (3240638643684902163131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (864019545158923 / 1250000000000000 : ℝ)) (q := - (13827356118363259 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13827356118363259 / 20000000000000000 : ℚ)) + (r' := (13827356118363259 / 10000000000000000 : ℚ)) + (U := (-(3690833159315097836869 / 10000000000000000000000 : ℚ))) + (U' := (3240638643684902163131 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (864019545158923 / 1250000000000000 : ℚ)) + (q := (13827356118363259 / 20000000000000000 : ℚ)) + (U := (-(3690833159315097836869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_5 : Uω (aρ 5) (bρ 5) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4747,25 +4131,21 @@ lemma U_614_5 : have hlg : Real.log (6793089907317087 / 10000000000000000 : ℝ) ≤ (-(3866791873236816182813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6793089907317087 / 10000000000000000 : ℝ) = - (6793089907317087 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6793089907317087 / 5000000000000000 : ℚ)) - (U := (3064679929763183817187 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6793089907317087 / 5000000000000000 : ℝ) ≤ - (3064679929763183817187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6789169976877299 / 10000000000000000 : ℝ)) (q := - (6793089907317087 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6793089907317087 / 10000000000000000 : ℚ)) + (r' := (6793089907317087 / 5000000000000000 : ℚ)) + (U := (-(3866791873236816182813 / 10000000000000000000000 : ℚ))) + (U' := (3064679929763183817187 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (6789169976877299 / 10000000000000000 : ℚ)) + (q := (6793089907317087 / 10000000000000000 : ℚ)) + (U := (-(3866791873236816182813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_6 : Uω (aρ 6) (bρ 6) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4773,25 +4153,21 @@ lemma U_614_6 : have hlg : Real.log (13241002223407207 / 20000000000000000 : ℝ) ≤ (-(412414029018064730309 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13241002223407207 / 20000000000000000 : ℝ) = - (13241002223407207 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13241002223407207 / 10000000000000000 : ℚ)) - (U := (280733151281935269691 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13241002223407207 / 10000000000000000 : ℝ) ≤ - (280733151281935269691 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1652808190197583 / 2500000000000000 : ℝ)) (q := - (13241002223407207 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13241002223407207 / 20000000000000000 : ℚ)) + (r' := (13241002223407207 / 10000000000000000 : ℚ)) + (U := (-(412414029018064730309 / 1000000000000000000000 : ℚ))) + (U' := (280733151281935269691 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (1652808190197583 / 2500000000000000 : ℚ)) + (q := (13241002223407207 / 20000000000000000 : ℚ)) + (U := (-(412414029018064730309 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_7 : Uω (aρ 7) (bρ 7) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4799,25 +4175,21 @@ lemma U_614_7 : have hlg : Real.log (12771602535204123 / 20000000000000000 : ℝ) ≤ (-(897016237875904629603 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12771602535204123 / 20000000000000000 : ℝ) = - (12771602535204123 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12771602535204123 / 10000000000000000 : ℚ)) - (U := (489278122724095370397 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12771602535204123 / 10000000000000000 : ℝ) ≤ - (489278122724095370397 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397843403334203 / 625000000000000 : ℝ)) (q := - (12771602535204123 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12771602535204123 / 20000000000000000 : ℚ)) + (r' := (12771602535204123 / 10000000000000000 : ℚ)) + (U := (-(897016237875904629603 / 2000000000000000000000 : ℚ))) + (U' := (489278122724095370397 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (397843403334203 / 625000000000000 : ℚ)) + (q := (12771602535204123 / 20000000000000000 : ℚ)) + (U := (-(897016237875904629603 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_8 : Uω (aρ 8) (bρ 8) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4825,25 +4197,21 @@ lemma U_614_8 : have hlg : Real.log (1520271797356573 / 2500000000000000 : ℝ) ≤ (-(4974015986909744955749 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1520271797356573 / 2500000000000000 : ℝ) = - (1520271797356573 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1520271797356573 / 1250000000000000 : ℚ)) - (U := (1957455816090255044251 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1520271797356573 / 1250000000000000 : ℝ) ≤ - (1957455816090255044251 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6039607948335709 / 10000000000000000 : ℝ)) (q := - (1520271797356573 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1520271797356573 / 2500000000000000 : ℚ)) + (r' := (1520271797356573 / 1250000000000000 : ℚ)) + (U := (-(4974015986909744955749 / 10000000000000000000000 : ℚ))) + (U' := (1957455816090255044251 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (6039607948335709 / 10000000000000000 : ℚ)) + (q := (1520271797356573 / 2500000000000000 : ℚ)) + (U := (-(4974015986909744955749 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_9 : Uω (aρ 9) (bρ 9) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4851,25 +4219,21 @@ lemma U_614_9 : have hlg : Real.log (11404362483298911 / 20000000000000000 : ℝ) ≤ (-(1404340792802545254119 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11404362483298911 / 20000000000000000 : ℝ) = - (11404362483298911 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11404362483298911 / 10000000000000000 : ℚ)) - (U := (328527157947454745881 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11404362483298911 / 10000000000000000 : ℝ) ≤ - (328527157947454745881 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1405690420285509 / 2500000000000000 : ℝ)) (q := - (11404362483298911 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11404362483298911 / 20000000000000000 : ℚ)) + (r' := (11404362483298911 / 10000000000000000 : ℚ)) + (U := (-(1404340792802545254119 / 2500000000000000000000 : ℚ))) + (U' := (328527157947454745881 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (1405690420285509 / 2500000000000000 : ℚ)) + (q := (11404362483298911 / 20000000000000000 : ℚ)) + (U := (-(1404340792802545254119 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_10 : Uω (aρ 10) (bρ 10) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4877,25 +4241,21 @@ lemma U_614_10 : have hlg : Real.log (328107902012629 / 625000000000000 : ℝ) ≤ (-(6444091256402327224063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (328107902012629 / 625000000000000 : ℝ) = - (328107902012629 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (328107902012629 / 312500000000000 : ℚ)) - (U := (487380546597672775937 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (328107902012629 / 312500000000000 : ℝ) ≤ - (487380546597672775937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5106411095742253 / 10000000000000000 : ℝ)) (q := - (328107902012629 / 625000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (328107902012629 / 625000000000000 : ℚ)) + (r' := (328107902012629 / 312500000000000 : ℚ)) + (U := (-(6444091256402327224063 / 10000000000000000000000 : ℚ))) + (U' := (487380546597672775937 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (5106411095742253 / 10000000000000000 : ℚ)) + (q := (328107902012629 / 625000000000000 : ℚ)) + (U := (-(6444091256402327224063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_11 : Uω (aρ 11) (bρ 11) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4903,26 +4263,21 @@ lemma U_614_11 : have hlg : Real.log (2364713313159581 / 5000000000000000 : ℝ) ≤ (-(7487811179694703890357 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2364713313159581 / 5000000000000000 : ℝ) = - (2364713313159581 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2364713313159581 / 1250000000000000 : ℚ)) - (U := (6375132426305296109643 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2364713313159581 / 1250000000000000 : ℝ) ≤ - (6375132426305296109643 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4484288110181449 / 10000000000000000 : ℝ)) (q := - (2364713313159581 / 5000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2364713313159581 / 5000000000000000 : ℚ)) + (r' := (2364713313159581 / 1250000000000000 : ℚ)) + (U := (-(7487811179694703890357 / 10000000000000000000000 : ℚ))) + (U' := (6375132426305296109643 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (4484288110181449 / 10000000000000000 : ℚ)) + (q := (2364713313159581 / 5000000000000000 : ℚ)) + (U := (-(7487811179694703890357 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_12 : Uω (aρ 12) (bρ 12) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4930,26 +4285,21 @@ lemma U_614_12 : have hlg : Real.log (4150782783984341 / 10000000000000000 : ℝ) ≤ (-(8792881533717337725777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4150782783984341 / 10000000000000000 : ℝ) = - (4150782783984341 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4150782783984341 / 2500000000000000 : ℚ)) - (U := (5070062072282662274223 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4150782783984341 / 2500000000000000 : ℝ) ≤ - (5070062072282662274223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3750700522196807 / 10000000000000000 : ℝ)) (q := - (4150782783984341 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4150782783984341 / 10000000000000000 : ℚ)) + (r' := (4150782783984341 / 2500000000000000 : ℚ)) + (U := (-(8792881533717337725777 / 10000000000000000000000 : ℚ))) + (U' := (5070062072282662274223 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (3750700522196807 / 10000000000000000 : ℚ)) + (q := (4150782783984341 / 10000000000000000 : ℚ)) + (U := (-(8792881533717337725777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_13 : Uω (aρ 13) (bρ 13) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4957,26 +4307,21 @@ lemma U_614_13 : have hlg : Real.log (3522581932218237 / 10000000000000000 : ℝ) ≤ (-(5216954341376271766899 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3522581932218237 / 10000000000000000 : ℝ) = - (3522581932218237 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3522581932218237 / 2500000000000000 : ℚ)) - (U := (1714517461623728233101 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3522581932218237 / 2500000000000000 : ℝ) ≤ - (1714517461623728233101 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2893680560259599 / 10000000000000000 : ℝ)) (q := - (3522581932218237 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3522581932218237 / 10000000000000000 : ℚ)) + (r' := (3522581932218237 / 2500000000000000 : ℚ)) + (U := (-(5216954341376271766899 / 5000000000000000000000 : ℚ))) + (U' := (1714517461623728233101 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (2893680560259599 / 10000000000000000 : ℚ)) + (q := (3522581932218237 / 10000000000000000 : ℚ)) + (U := (-(5216954341376271766899 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_14 : Uω (aρ 14) (bρ 14) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -4984,26 +4329,21 @@ lemma U_614_14 : have hlg : Real.log (5670263729237359 / 20000000000000000 : ℝ) ≤ (-(6302483216415656992739 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5670263729237359 / 20000000000000000 : ℝ) = - (5670263729237359 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5670263729237359 / 5000000000000000 : ℚ)) - (U := (628988586584343007261 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5670263729237359 / 5000000000000000 : ℝ) ≤ - (628988586584343007261 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (465676927526371 / 2500000000000000 : ℝ)) (q := - (5670263729237359 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5670263729237359 / 20000000000000000 : ℚ)) + (r' := (5670263729237359 / 5000000000000000 : ℚ)) + (U := (-(6302483216415656992739 / 5000000000000000000000 : ℚ))) + (U' := (628988586584343007261 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11406650040163 / 16000000000000 : ℚ)) + (s := (465676927526371 / 2500000000000000 : ℚ)) + (q := (5670263729237359 / 20000000000000000 : ℚ)) + (U := (-(6302483216415656992739 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_614_15 : Uω (aρ 15) (bρ 15) (11406650040163 / 16000000000000 : ℝ) ≤ @@ -5106,25 +4446,21 @@ lemma U_615_1 : have hlg : Real.log (7097085773560581 / 10000000000000000 : ℝ) ≤ (-(3429008473743938263037 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7097085773560581 / 10000000000000000 : ℝ) = - (7097085773560581 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7097085773560581 / 5000000000000000 : ℚ)) - (U := (3502463329256061736963 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7097085773560581 / 5000000000000000 : ℝ) ≤ - (3502463329256061736963 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3548531497043081 / 5000000000000000 : ℝ)) (q := - (7097085773560581 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7097085773560581 / 10000000000000000 : ℚ)) + (r' := (7097085773560581 / 5000000000000000 : ℚ)) + (U := (-(3429008473743938263037 / 10000000000000000000000 : ℚ))) + (U' := (3502463329256061736963 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (89520072139 / 125000000000 : ℚ)) + (s := (3548531497043081 / 5000000000000000 : ℚ)) + (q := (7097085773560581 / 10000000000000000 : ℚ)) + (U := (-(3429008473743938263037 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_2 : Uω (aρ 2) (bρ 2) (89520072139 / 125000000000 : ℝ) ≤ @@ -5132,25 +4468,21 @@ lemma U_615_2 : have hlg : Real.log (14146379095600089 / 20000000000000000 : ℝ) ≤ (-(432841970319017025881 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14146379095600089 / 20000000000000000 : ℝ) = - (14146379095600089 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14146379095600089 / 10000000000000000 : ℚ)) - (U := (433592005055982974119 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14146379095600089 / 10000000000000000 : ℝ) ≤ - (433592005055982974119 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7073039555075089 / 10000000000000000 : ℝ)) (q := - (14146379095600089 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14146379095600089 / 20000000000000000 : ℚ)) + (r' := (14146379095600089 / 10000000000000000 : ℚ)) + (U := (-(432841970319017025881 / 1250000000000000000000 : ℚ))) + (U' := (433592005055982974119 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (89520072139 / 125000000000 : ℚ)) + (s := (7073039555075089 / 10000000000000000 : ℚ)) + (q := (14146379095600089 / 20000000000000000 : ℚ)) + (U := (-(432841970319017025881 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_3 : Uω (aρ 3) (bρ 3) (89520072139 / 125000000000 : ℝ) ≤ @@ -5158,25 +4490,21 @@ lemma U_615_3 : have hlg : Real.log (7025416911659693 / 10000000000000000 : ℝ) ≤ (-(882626331049433886807 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7025416911659693 / 10000000000000000 : ℝ) = - (7025416911659693 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7025416911659693 / 5000000000000000 : ℚ)) - (U := (850241619700566113193 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7025416911659693 / 5000000000000000 : ℝ) ≤ - (850241619700566113193 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3512445194572193 / 5000000000000000 : ℝ)) (q := - (7025416911659693 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7025416911659693 / 10000000000000000 : ℚ)) + (r' := (7025416911659693 / 5000000000000000 : ℚ)) + (U := (-(882626331049433886807 / 2500000000000000000000 : ℚ))) + (U' := (850241619700566113193 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (89520072139 / 125000000000 : ℚ)) + (s := (3512445194572193 / 5000000000000000 : ℚ)) + (q := (7025416911659693 / 10000000000000000 : ℚ)) + (U := (-(882626331049433886807 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_4 : Uω (aρ 4) (bρ 4) (89520072139 / 125000000000 : ℝ) ≤ @@ -5184,25 +4512,21 @@ lemma U_615_4 : have hlg : Real.log (13892269331013533 / 20000000000000000 : ℝ) ≤ (-(728799502219952959019 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13892269331013533 / 20000000000000000 : ℝ) = - (13892269331013533 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13892269331013533 / 10000000000000000 : ℚ)) - (U := (657494858380047040981 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13892269331013533 / 10000000000000000 : ℝ) ≤ - (657494858380047040981 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6944620077903533 / 10000000000000000 : ℝ)) (q := - (13892269331013533 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13892269331013533 / 20000000000000000 : ℚ)) + (r' := (13892269331013533 / 10000000000000000 : ℚ)) + (U := (-(728799502219952959019 / 2000000000000000000000 : ℚ))) + (U' := (657494858380047040981 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (89520072139 / 125000000000 : ℚ)) + (s := (6944620077903533 / 10000000000000000 : ℚ)) + (q := (13892269331013533 / 20000000000000000 : ℚ)) + (U := (-(728799502219952959019 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_5 : Uω (aρ 5) (bρ 5) (89520072139 / 125000000000 : ℝ) ≤ @@ -5210,25 +4534,21 @@ lemma U_615_5 : have hlg : Real.log (6825558049848699 / 10000000000000000 : ℝ) ≤ (-(954777473650250097291 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6825558049848699 / 10000000000000000 : ℝ) = - (6825558049848699 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6825558049848699 / 5000000000000000 : ℚ)) - (U := (778090477099749902709 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6825558049848699 / 5000000000000000 : ℝ) ≤ - (778090477099749902709 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3410828382961199 / 5000000000000000 : ℝ)) (q := - (6825558049848699 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6825558049848699 / 10000000000000000 : ℚ)) + (r' := (6825558049848699 / 5000000000000000 : ℚ)) + (U := (-(954777473650250097291 / 2500000000000000000000 : ℚ))) + (U' := (778090477099749902709 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (89520072139 / 125000000000 : ℚ)) + (s := (3410828382961199 / 5000000000000000 : ℚ)) + (q := (6825558049848699 / 10000000000000000 : ℚ)) + (U := (-(954777473650250097291 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_6 : Uω (aρ 6) (bρ 6) (89520072139 / 125000000000 : ℝ) ≤ @@ -5236,25 +4556,21 @@ lemma U_615_6 : have hlg : Real.log (532239670118649 / 800000000000000 : ℝ) ≤ (-(1018794579431653135779 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (532239670118649 / 800000000000000 : ℝ) = - (532239670118649 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (532239670118649 / 400000000000000 : ℚ)) - (U := (714073371318346864221 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (532239670118649 / 400000000000000 : ℝ) ≤ - (714073371318346864221 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (265750911773249 / 400000000000000 : ℝ)) (q := - (532239670118649 / 800000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (532239670118649 / 800000000000000 : ℚ)) + (r' := (532239670118649 / 400000000000000 : ℚ)) + (U := (-(1018794579431653135779 / 2500000000000000000000 : ℚ))) + (U' := (714073371318346864221 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (89520072139 / 125000000000 : ℚ)) + (s := (265750911773249 / 400000000000000 : ℚ)) + (q := (532239670118649 / 800000000000000 : ℚ)) + (U := (-(1018794579431653135779 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_7 : Uω (aρ 7) (bρ 7) (89520072139 / 125000000000 : ℝ) ≤ @@ -5262,25 +4578,21 @@ lemma U_615_7 : have hlg : Real.log (12836707510689501 / 20000000000000000 : ℝ) ≤ (-(4434234323157178674073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12836707510689501 / 20000000000000000 : ℝ) = - (12836707510689501 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12836707510689501 / 10000000000000000 : ℚ)) - (U := (2497237479842821325927 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12836707510689501 / 10000000000000000 : ℝ) ≤ - (2497237479842821325927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6398149932814501 / 10000000000000000 : ℝ)) (q := - (12836707510689501 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12836707510689501 / 20000000000000000 : ℚ)) + (r' := (12836707510689501 / 10000000000000000 : ℚ)) + (U := (-(4434234323157178674073 / 10000000000000000000000 : ℚ))) + (U' := (2497237479842821325927 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (89520072139 / 125000000000 : ℚ)) + (s := (6398149932814501 / 10000000000000000 : ℚ)) + (q := (12836707510689501 / 20000000000000000 : ℚ)) + (U := (-(4434234323157178674073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_8 : Uω (aρ 8) (bρ 8) (89520072139 / 125000000000 : ℝ) ≤ @@ -5288,25 +4600,21 @@ lemma U_615_8 : have hlg : Real.log (12227516690586597 / 20000000000000000 : ℝ) ≤ (-(307527121787241753561 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12227516690586597 / 20000000000000000 : ℝ) = - (12227516690586597 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12227516690586597 / 10000000000000000 : ℚ)) - (U := (125689865900258246439 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12227516690586597 / 10000000000000000 : ℝ) ≤ - (125689865900258246439 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6072500764051597 / 10000000000000000 : ℝ)) (q := - (12227516690586597 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12227516690586597 / 20000000000000000 : ℚ)) + (r' := (12227516690586597 / 10000000000000000 : ℚ)) + (U := (-(307527121787241753561 / 625000000000000000000 : ℚ))) + (U' := (125689865900258246439 / 625000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (89520072139 / 125000000000 : ℚ)) + (s := (6072500764051597 / 10000000000000000 : ℚ)) + (q := (12227516690586597 / 20000000000000000 : ℚ)) + (U := (-(307527121787241753561 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_9 : Uω (aρ 9) (bρ 9) (89520072139 / 125000000000 : ℝ) ≤ @@ -5314,25 +4622,21 @@ lemma U_615_9 : have hlg : Real.log (5735086408905213 / 10000000000000000 : ℝ) ≤ (-(5559822753255195245599 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5735086408905213 / 10000000000000000 : ℝ) = - (5735086408905213 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5735086408905213 / 5000000000000000 : ℚ)) - (U := (1371649049744804754401 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5735086408905213 / 5000000000000000 : ℝ) ≤ - (1371649049744804754401 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2828061259817713 / 5000000000000000 : ℝ)) (q := - (5735086408905213 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5735086408905213 / 10000000000000000 : ℚ)) + (r' := (5735086408905213 / 5000000000000000 : ℚ)) + (U := (-(5559822753255195245599 / 10000000000000000000000 : ℚ))) + (U' := (1371649049744804754401 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (89520072139 / 125000000000 : ℚ)) + (s := (2828061259817713 / 5000000000000000 : ℚ)) + (q := (5735086408905213 / 10000000000000000 : ℚ)) + (U := (-(5559822753255195245599 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_10 : Uω (aρ 10) (bρ 10) (89520072139 / 125000000000 : ℝ) ≤ @@ -5340,26 +4644,21 @@ lemma U_615_10 : have hlg : Real.log (10566161476170617 / 20000000000000000 : ℝ) ≤ (-(6380756920479711852741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10566161476170617 / 20000000000000000 : ℝ) = - (10566161476170617 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10566161476170617 / 10000000000000000 : ℚ)) - (U := (550714882520288147259 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10566161476170617 / 10000000000000000 : ℝ) ≤ - (550714882520288147259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5140670211490617 / 10000000000000000 : ℝ)) (q := - (10566161476170617 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10566161476170617 / 20000000000000000 : ℚ)) + (r' := (10566161476170617 / 10000000000000000 : ℚ)) + (U := (-(6380756920479711852741 / 10000000000000000000000 : ℚ))) + (U' := (550714882520288147259 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (89520072139 / 125000000000 : ℚ)) + (s := (5140670211490617 / 10000000000000000 : ℚ)) + (q := (10566161476170617 / 20000000000000000 : ℚ)) + (U := (-(6380756920479711852741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_11 : Uω (aρ 11) (bρ 11) (89520072139 / 125000000000 : ℝ) ≤ @@ -5367,26 +4666,21 @@ lemma U_615_11 : have hlg : Real.log (9527273158567701 / 20000000000000000 : ℝ) ≤ (-(1853934321690048881789 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9527273158567701 / 20000000000000000 : ℝ) = - (9527273158567701 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9527273158567701 / 5000000000000000 : ℚ)) - (U := (1611801579809951118211 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9527273158567701 / 5000000000000000 : ℝ) ≤ - (1611801579809951118211 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4520258520092701 / 10000000000000000 : ℝ)) (q := - (9527273158567701 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9527273158567701 / 20000000000000000 : ℚ)) + (r' := (9527273158567701 / 5000000000000000 : ℚ)) + (U := (-(1853934321690048881789 / 2500000000000000000000 : ℚ))) + (U' := (1611801579809951118211 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (89520072139 / 125000000000 : ℚ)) + (s := (4520258520092701 / 10000000000000000 : ℚ)) + (q := (9527273158567701 / 20000000000000000 : ℚ)) + (U := (-(1853934321690048881789 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_12 : Uω (aρ 12) (bρ 12) (89520072139 / 125000000000 : ℝ) ≤ @@ -5394,25 +4688,21 @@ lemma U_615_12 : have hlg : Real.log (209333041418471 / 500000000000000 : ℝ) ≤ (-(272088004562792016049 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (209333041418471 / 500000000000000 : ℝ) = - (209333041418471 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (209333041418471 / 125000000000000 : ℚ)) - (U := (161128983124707983951 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (209333041418471 / 125000000000000 : ℝ) ≤ - (161128983124707983951 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (94750177873721 / 250000000000000 : ℝ)) (q := - (209333041418471 / 500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (209333041418471 / 500000000000000 : ℚ)) + (r' := (209333041418471 / 125000000000000 : ℚ)) + (U := (-(272088004562792016049 / 312500000000000000000 : ℚ))) + (U' := (161128983124707983951 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (89520072139 / 125000000000 : ℚ)) + (s := (94750177873721 / 250000000000000 : ℚ)) + (q := (209333041418471 / 500000000000000 : ℚ)) + (U := (-(272088004562792016049 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_13 : Uω (aρ 13) (bρ 13) (89520072139 / 125000000000 : ℝ) ≤ @@ -5420,26 +4710,21 @@ lemma U_615_13 : have hlg : Real.log (3561989124115103 / 10000000000000000 : ℝ) ≤ (-(5161329804599260628999 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3561989124115103 / 10000000000000000 : ℝ) = - (3561989124115103 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3561989124115103 / 2500000000000000 : ℚ)) - (U := (1770141998400739371001 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3561989124115103 / 2500000000000000 : ℝ) ≤ - (1770141998400739371001 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1470022724017603 / 5000000000000000 : ℝ)) (q := - (3561989124115103 / 10000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3561989124115103 / 10000000000000000 : ℚ)) + (r' := (3561989124115103 / 2500000000000000 : ℚ)) + (U := (-(5161329804599260628999 / 5000000000000000000000 : ℚ))) + (U' := (1770141998400739371001 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (89520072139 / 125000000000 : ℚ)) + (s := (1470022724017603 / 5000000000000000 : ℚ)) + (q := (3561989124115103 / 10000000000000000 : ℚ)) + (U := (-(5161329804599260628999 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_14 : Uω (aρ 14) (bρ 14) (89520072139 / 125000000000 : ℝ) ≤ @@ -5447,26 +4732,21 @@ lemma U_615_14 : have hlg : Real.log (2884087755233591 / 10000000000000000 : ℝ) ≤ (-(6216882226043502495963 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2884087755233591 / 10000000000000000 : ℝ) = - (2884087755233591 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2884087755233591 / 2500000000000000 : ℚ)) - (U := (714589576956497504037 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2884087755233591 / 2500000000000000 : ℝ) ≤ - (714589576956497504037 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (964084997658591 / 5000000000000000 : ℝ)) (q := - (2884087755233591 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2884087755233591 / 10000000000000000 : ℚ)) + (r' := (2884087755233591 / 2500000000000000 : ℚ)) + (U := (-(6216882226043502495963 / 5000000000000000000000 : ℚ))) + (U' := (714589576956497504037 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (89520072139 / 125000000000 : ℚ)) + (s := (964084997658591 / 5000000000000000 : ℚ)) + (q := (2884087755233591 / 10000000000000000 : ℚ)) + (U := (-(6216882226043502495963 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_615_15 : Uω (aρ 15) (bρ 15) (89520072139 / 125000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U51.lean b/LeanPool/Zeta5Irrational/Table/U51.lean index 82b5a02e4a..981476ebf4 100644 --- a/LeanPool/Zeta5Irrational/Table/U51.lean +++ b/LeanPool/Zeta5Irrational/Table/U51.lean @@ -24,25 +24,21 @@ lemma U_616_1 : have hlg : Real.log (7116133783633341 / 10000000000000000 : ℝ) ≤ (-(106318913346585029177 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7116133783633341 / 10000000000000000 : ℝ) = - (7116133783633341 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7116133783633341 / 5000000000000000 : ℚ)) - (U := (110289580497164970823 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7116133783633341 / 5000000000000000 : ℝ) ≤ - (110289580497164970823 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7116111065133557 / 10000000000000000 : ℝ)) (q := - (7116133783633341 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7116133783633341 / 10000000000000000 : ℚ)) + (r' := (7116133783633341 / 5000000000000000 : ℚ)) + (U := (-(106318913346585029177 / 312500000000000000000 : ℚ))) + (U' := (110289580497164970823 / 312500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (7116111065133557 / 10000000000000000 : ℚ)) + (q := (7116133783633341 / 10000000000000000 : ℚ)) + (U := (-(106318913346585029177 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_2 : Uω (aρ 2) (bρ 2) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_616_2 : have hlg : Real.log (14184475799498081 / 20000000000000000 : ℝ) ≤ (-(3435841602808840498403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14184475799498081 / 20000000000000000 : ℝ) = - (14184475799498081 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14184475799498081 / 10000000000000000 : ℚ)) - (U := (3495630200191159501597 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14184475799498081 / 10000000000000000 : ℝ) ≤ - (3495630200191159501597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1773022077468739 / 2500000000000000 : ℝ)) (q := - (14184475799498081 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14184475799498081 / 20000000000000000 : ℚ)) + (r' := (14184475799498081 / 10000000000000000 : ℚ)) + (U := (-(3435841602808840498403 / 10000000000000000000000 : ℚ))) + (U' := (3495630200191159501597 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (1773022077468739 / 2500000000000000 : ℚ)) + (q := (14184475799498081 / 20000000000000000 : ℚ)) + (U := (-(3435841602808840498403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_3 : Uω (aρ 3) (bρ 3) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_616_3 : have hlg : Real.log (1761116571139903 / 2500000000000000 : ℝ) ≤ (-(3503427083001394159311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1761116571139903 / 2500000000000000 : ℝ) = - (1761116571139903 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1761116571139903 / 1250000000000000 : ℚ)) - (U := (3428044719998605840689 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1761116571139903 / 1250000000000000 : ℝ) ≤ - (3428044719998605840689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7043941185846099 / 10000000000000000 : ℝ)) (q := - (1761116571139903 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1761116571139903 / 2500000000000000 : ℚ)) + (r' := (1761116571139903 / 1250000000000000 : ℚ)) + (U := (-(3503427083001394159311 / 10000000000000000000000 : ℚ))) + (U' := (3428044719998605840689 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (7043941185846099 / 10000000000000000 : ℚ)) + (q := (1761116571139903 / 2500000000000000 : ℚ)) + (U := (-(3503427083001394159311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_4 : Uω (aρ 4) (bρ 4) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_616_4 : have hlg : Real.log (13930373515006951 / 20000000000000000 : ℝ) ≤ (-(904151680374748223911 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13930373515006951 / 20000000000000000 : ℝ) = - (13930373515006951 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13930373515006951 / 10000000000000000 : ℚ)) - (U := (828716270375251776089 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13930373515006951 / 10000000000000000 : ℝ) ≤ - (828716270375251776089 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3481838156399413 / 5000000000000000 : ℝ)) (q := - (13930373515006951 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13930373515006951 / 20000000000000000 : ℚ)) + (r' := (13930373515006951 / 10000000000000000 : ℚ)) + (U := (-(904151680374748223911 / 2500000000000000000000 : ℚ))) + (U' := (828716270375251776089 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (3481838156399413 / 5000000000000000 : ℚ)) + (q := (13930373515006951 / 20000000000000000 : ℚ)) + (U := (-(904151680374748223911 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_5 : Uω (aρ 5) (bρ 5) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_616_5 : have hlg : Real.log (1368923372411711 / 2000000000000000 : ℝ) ≤ (-(3791226089629521932043 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1368923372411711 / 2000000000000000 : ℝ) = - (1368923372411711 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1368923372411711 / 1000000000000000 : ℚ)) - (U := (3140245713370478067957 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1368923372411711 / 1000000000000000 : ℝ) ≤ - (3140245713370478067957 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1368145288248797 / 2000000000000000 : ℝ)) (q := - (1368923372411711 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1368923372411711 / 2000000000000000 : ℚ)) + (r' := (1368923372411711 / 1000000000000000 : ℚ)) + (U := (-(3791226089629521932043 / 10000000000000000000000 : ℚ))) + (U' := (3140245713370478067957 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (1368145288248797 / 2000000000000000 : ℚ)) + (q := (1368923372411711 / 2000000000000000 : ℚ)) + (U := (-(3791226089629521932043 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_6 : Uω (aρ 6) (bρ 6) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_616_6 : have hlg : Real.log (3336035096403903 / 5000000000000000 : ℝ) ≤ (-(202327453614113887511 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3336035096403903 / 5000000000000000 : ℝ) = - (3336035096403903 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3336035096403903 / 2500000000000000 : ℚ)) - (U := (144246136535886112489 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3336035096403903 / 2500000000000000 : ℝ) ≤ - (144246136535886112489 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6662873477882487 / 10000000000000000 : ℝ)) (q := - (3336035096403903 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3336035096403903 / 5000000000000000 : ℚ)) + (r' := (3336035096403903 / 2500000000000000 : ℚ)) + (U := (-(202327453614113887511 / 500000000000000000000 : ℚ))) + (U' := (144246136535886112489 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (6662873477882487 / 10000000000000000 : ℚ)) + (q := (3336035096403903 / 5000000000000000 : ℚ)) + (U := (-(202327453614113887511 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_7 : Uω (aρ 7) (bρ 7) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_616_7 : have hlg : Real.log (1609365418549547 / 2500000000000000 : ℝ) ≤ (-(2202253901422898501509 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1609365418549547 / 2500000000000000 : ℝ) = - (1609365418549547 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1609365418549547 / 1250000000000000 : ℚ)) - (U := (1263482000077101498491 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1609365418549547 / 1250000000000000 : ℝ) ≤ - (1263482000077101498491 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6417317821423251 / 10000000000000000 : ℝ)) (q := - (1609365418549547 / 2500000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1609365418549547 / 2500000000000000 : ℚ)) + (r' := (1609365418549547 / 1250000000000000 : ℚ)) + (U := (-(2202253901422898501509 / 5000000000000000000000 : ℚ))) + (U' := (1263482000077101498491 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (6417317821423251 / 10000000000000000 : ℚ)) + (q := (1609365418549547 / 2500000000000000 : ℚ)) + (U := (-(2202253901422898501509 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_8 : Uω (aρ 8) (bρ 8) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_616_8 : have hlg : Real.log (3066467650961623 / 5000000000000000 : ℝ) ≤ (-(4889116153186919824119 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3066467650961623 / 5000000000000000 : ℝ) = - (3066467650961623 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3066467650961623 / 2500000000000000 : ℚ)) - (U := (2042355649813080175881 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3066467650961623 / 2500000000000000 : ℝ) ≤ - (2042355649813080175881 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6091806728213367 / 10000000000000000 : ℝ)) (q := - (3066467650961623 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3066467650961623 / 5000000000000000 : ℚ)) + (r' := (3066467650961623 / 2500000000000000 : ℚ)) + (U := (-(4889116153186919824119 / 10000000000000000000000 : ℚ))) + (U' := (2042355649813080175881 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (6091806728213367 / 10000000000000000 : ℚ)) + (q := (3066467650961623 / 5000000000000000 : ℚ)) + (U := (-(4889116153186919824119 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_9 : Uω (aρ 9) (bρ 9) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_616_9 : have hlg : Real.log (2877199688669567 / 5000000000000000 : ℝ) ≤ (-(1105240842738283865227 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2877199688669567 / 5000000000000000 : ℝ) = - (2877199688669567 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2877199688669567 / 2500000000000000 : ℚ)) - (U := (281053517861716134773 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2877199688669567 / 2500000000000000 : ℝ) ≤ - (281053517861716134773 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5675700507405143 / 10000000000000000 : ℝ)) (q := - (2877199688669567 / 5000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2877199688669567 / 5000000000000000 : ℚ)) + (r' := (2877199688669567 / 2500000000000000 : ℚ)) + (U := (-(1105240842738283865227 / 2000000000000000000000 : ℚ))) + (U' := (281053517861716134773 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (5675700507405143 / 10000000000000000 : ℚ)) + (q := (2877199688669567 / 5000000000000000 : ℚ)) + (U := (-(1105240842738283865227 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_10 : Uω (aρ 10) (bρ 10) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_616_10 : have hlg : Real.log (10605308731064837 / 20000000000000000 : ℝ) ≤ (-(6343775738609869476143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10605308731064837 / 20000000000000000 : ℝ) = - (10605308731064837 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10605308731064837 / 10000000000000000 : ℚ)) - (U := (587696064390130523857 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10605308731064837 / 10000000000000000 : ℝ) ≤ - (587696064390130523857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (645096189660839 / 1250000000000000 : ℝ)) (q := - (10605308731064837 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10605308731064837 / 20000000000000000 : ℚ)) + (r' := (10605308731064837 / 10000000000000000 : ℚ)) + (U := (-(6343775738609869476143 / 10000000000000000000000 : ℚ))) + (U' := (587696064390130523857 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (645096189660839 / 1250000000000000 : ℚ)) + (q := (10605308731064837 / 20000000000000000 : ℚ)) + (U := (-(6343775738609869476143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_11 : Uω (aρ 11) (bρ 11) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_616_11 : have hlg : Real.log (9567411135391271 / 20000000000000000 : ℝ) ≤ (-(3686848114669659335923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9567411135391271 / 20000000000000000 : ℝ) = - (9567411135391271 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9567411135391271 / 5000000000000000 : ℚ)) - (U := (3244623688330340664077 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9567411135391271 / 5000000000000000 : ℝ) ≤ - (3244623688330340664077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2270674273909073 / 5000000000000000 : ℝ)) (q := - (9567411135391271 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9567411135391271 / 20000000000000000 : ℚ)) + (r' := (9567411135391271 / 5000000000000000 : ℚ)) + (U := (-(3686848114669659335923 / 5000000000000000000000 : ℚ))) + (U' := (3244623688330340664077 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (2270674273909073 / 5000000000000000 : ℚ)) + (q := (9567411135391271 / 20000000000000000 : ℚ)) + (U := (-(3686848114669659335923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_12 : Uω (aρ 12) (bρ 12) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_616_12 : have hlg : Real.log (2103845646309407 / 5000000000000000 : ℝ) ≤ (-(4328354908750573873291 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2103845646309407 / 5000000000000000 : ℝ) = - (2103845646309407 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2103845646309407 / 1250000000000000 : ℚ)) - (U := (2603116894249426126709 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2103845646309407 / 1250000000000000 : ℝ) ≤ - (2603116894249426126709 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3813020094349503 / 10000000000000000 : ℝ)) (q := - (2103845646309407 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2103845646309407 / 5000000000000000 : ℚ)) + (r' := (2103845646309407 / 1250000000000000 : ℚ)) + (U := (-(4328354908750573873291 / 5000000000000000000000 : ℚ))) + (U' := (2603116894249426126709 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (3813020094349503 / 10000000000000000 : ℚ)) + (q := (2103845646309407 / 5000000000000000 : ℚ)) + (U := (-(4328354908750573873291 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_13 : Uω (aρ 13) (bρ 13) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -339,25 +288,21 @@ lemma U_616_13 : have hlg : Real.log (286802814271449 / 800000000000000 : ℝ) ≤ (-(10258168058087591677167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (286802814271449 / 800000000000000 : ℝ) = - (286802814271449 / 200000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (286802814271449 / 200000000000000 : ℚ)) - (U := (3604775547912408322833 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (286802814271449 / 200000000000000 : ℝ) ≤ - (3604775547912408322833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (29670896074931 / 100000000000000 : ℝ)) (q := - (286802814271449 / 800000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (286802814271449 / 800000000000000 : ℚ)) + (r' := (286802814271449 / 200000000000000 : ℚ)) + (U := (-(10258168058087591677167 / 10000000000000000000000 : ℚ))) + (U' := (3604775547912408322833 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (29670896074931 / 100000000000000 : ℚ)) + (q := (286802814271449 / 800000000000000 : ℚ)) + (U := (-(10258168058087591677167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_14 : Uω (aρ 14) (bρ 14) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -365,26 +310,21 @@ lemma U_616_14 : have hlg : Real.log (2912442142317699 / 10000000000000000 : ℝ) ≤ (-(6167965695391489451341 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2912442142317699 / 10000000000000000 : ℝ) = - (2912442142317699 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2912442142317699 / 2500000000000000 : ℚ)) - (U := (763506107608510548659 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2912442142317699 / 2500000000000000 : ℝ) ≤ - (763506107608510548659 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1965830820387273 / 10000000000000000 : ℝ)) (q := - (2912442142317699 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2912442142317699 / 10000000000000000 : ℚ)) + (r' := (2912442142317699 / 2500000000000000 : ℚ)) + (U := (-(6167965695391489451341 / 5000000000000000000000 : ℚ))) + (U' := (763506107608510548659 / 5000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (1965830820387273 / 10000000000000000 : ℚ)) + (q := (2912442142317699 / 10000000000000000 : ℚ)) + (U := (-(6167965695391489451341 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_15 : Uω (aρ 15) (bρ 15) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -392,26 +332,21 @@ lemma U_616_15 : have hlg : Real.log (1984647236594003 / 10000000000000000 : ℝ) ≤ (-(16171439084303750819383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1984647236594003 / 10000000000000000 : ℝ) = - (1984647236594003 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1984647236594003 / 1250000000000000 : ℚ)) - (U := (4622976324696249180617 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1984647236594003 / 1250000000000000 : ℝ) ≤ - (4622976324696249180617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (369814286354881 / 10000000000000000 : ℝ)) (q := - (1984647236594003 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1984647236594003 / 10000000000000000 : ℚ)) + (r' := (1984647236594003 / 1250000000000000 : ℚ)) + (U := (-(16171439084303750819383 / 10000000000000000000000 : ℚ))) + (U' := (4622976324696249180617 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11489045952349 / 16000000000000 : ℚ)) + (s := (369814286354881 / 10000000000000000 : ℚ)) + (q := (1984647236594003 / 10000000000000000 : ℚ)) + (U := (-(16171439084303750819383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_616_16 : Uω (aρ 16) (bρ 16) (11489045952349 / 16000000000000 : ℝ) ≤ @@ -509,25 +444,21 @@ lemma U_617_1 : have hlg : Real.log (28502631154189897 / 40000000000000000 : ℝ) ≤ (-(847207624102700801571 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28502631154189897 / 40000000000000000 : ℝ) = - (28502631154189897 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28502631154189897 / 20000000000000000 : ℚ)) - (U := (885660326647299198429 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28502631154189897 / 20000000000000000 : ℝ) ≤ - (885660326647299198429 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7125635100412761 / 10000000000000000 : ℝ)) (q := - (28502631154189897 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28502631154189897 / 40000000000000000 : ℚ)) + (r' := (28502631154189897 / 20000000000000000 : ℚ)) + (U := (-(847207624102700801571 / 2500000000000000000000 : ℚ))) + (U' := (885660326647299198429 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (7125635100412761 / 10000000000000000 : ℚ)) + (q := (28502631154189897 / 40000000000000000 : ℚ)) + (U := (-(847207624102700801571 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_2 : Uω (aρ 2) (bρ 2) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -535,25 +466,21 @@ lemma U_617_2 : have hlg : Real.log (5681409659930501 / 8000000000000000 : ℝ) ≤ (-(3422421599130554510801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5681409659930501 / 8000000000000000 : ℝ) = - (5681409659930501 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5681409659930501 / 4000000000000000 : ℚ)) - (U := (3509050203869445489199 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5681409659930501 / 4000000000000000 : ℝ) ≤ - (3509050203869445489199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1420322537130813 / 2000000000000000 : ℝ)) (q := - (5681409659930501 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5681409659930501 / 8000000000000000 : ℚ)) + (r' := (5681409659930501 / 4000000000000000 : ℚ)) + (U := (-(3422421599130554510801 / 10000000000000000000000 : ℚ))) + (U' := (3509050203869445489199 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (1420322537130813 / 2000000000000000 : ℚ)) + (q := (5681409659930501 / 8000000000000000 : ℚ)) + (U := (-(3422421599130554510801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_3 : Uω (aρ 3) (bρ 3) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -561,25 +488,21 @@ lemma U_617_3 : have hlg : Real.log (28215963872502457 / 40000000000000000 : ℝ) ≤ (-(109059856659853529079 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28215963872502457 / 40000000000000000 : ℝ) = - (28215963872502457 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28215963872502457 / 20000000000000000 : ℚ)) - (U := (107548637183896470921 / 312500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28215963872502457 / 20000000000000000 : ℝ) ≤ - (107548637183896470921 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7053466578429041 / 10000000000000000 : ℝ)) (q := - (28215963872502457 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28215963872502457 / 40000000000000000 : ℚ)) + (r' := (28215963872502457 / 20000000000000000 : ℚ)) + (U := (-(109059856659853529079 / 312500000000000000000 : ℚ))) + (U' := (107548637183896470921 / 312500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (7053466578429041 / 10000000000000000 : ℚ)) + (q := (28215963872502457 / 40000000000000000 : ℚ)) + (U := (-(109059856659853529079 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_4 : Uω (aρ 4) (bρ 4) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -587,25 +510,21 @@ lemma U_617_4 : have hlg : Real.log (27898851180049809 / 40000000000000000 : ℝ) ≤ (-(3602939422167406557651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27898851180049809 / 40000000000000000 : ℝ) = - (27898851180049809 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27898851180049809 / 20000000000000000 : ℚ)) - (U := (3328532380832593442349 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27898851180049809 / 20000000000000000 : ℝ) ≤ - (3328532380832593442349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6973204413267717 / 10000000000000000 : ℝ)) (q := - (27898851180049809 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27898851180049809 / 40000000000000000 : ℚ)) + (r' := (27898851180049809 / 20000000000000000 : ℚ)) + (U := (-(3602939422167406557651 / 10000000000000000000000 : ℚ))) + (U' := (3328532380832593442349 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (6973204413267717 / 10000000000000000 : ℚ)) + (q := (27898851180049809 / 40000000000000000 : ℚ)) + (U := (-(3602939422167406557651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_5 : Uω (aρ 5) (bρ 5) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -613,25 +532,21 @@ lemma U_617_5 : have hlg : Real.log (27416584981983811 / 40000000000000000 : ℝ) ≤ (-(1888656661307937322841 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27416584981983811 / 40000000000000000 : ℝ) = - (27416584981983811 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27416584981983811 / 20000000000000000 : ℚ)) - (U := (1577079240192062677159 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27416584981983811 / 20000000000000000 : ℝ) ≤ - (1577079240192062677159 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3425130616784859 / 5000000000000000 : ℝ)) (q := - (27416584981983811 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27416584981983811 / 40000000000000000 : ℚ)) + (r' := (27416584981983811 / 20000000000000000 : ℚ)) + (U := (-(1888656661307937322841 / 5000000000000000000000 : ℚ))) + (U' := (1577079240192062677159 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (3425130616784859 / 5000000000000000 : ℚ)) + (q := (27416584981983811 / 40000000000000000 : ℚ)) + (U := (-(1888656661307937322841 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_6 : Uω (aρ 6) (bρ 6) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -639,25 +554,21 @@ lemma U_617_6 : have hlg : Real.log (26726429177754317 / 40000000000000000 : ℝ) ≤ (-(1008066302970724523623 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26726429177754317 / 40000000000000000 : ℝ) = - (26726429177754317 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26726429177754317 / 20000000000000000 : ℚ)) - (U := (724801647779275476377 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26726429177754317 / 20000000000000000 : ℝ) ≤ - (724801647779275476377 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6672423706594971 / 10000000000000000 : ℝ)) (q := - (26726429177754317 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26726429177754317 / 40000000000000000 : ℚ)) + (r' := (26726429177754317 / 20000000000000000 : ℚ)) + (U := (-(1008066302970724523623 / 2500000000000000000000 : ℚ))) + (U' := (724801647779275476377 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (6672423706594971 / 10000000000000000 : ℚ)) + (q := (26726429177754317 / 40000000000000000 : ℚ)) + (U := (-(1008066302970724523623 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_7 : Uω (aρ 7) (bρ 7) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -665,25 +576,21 @@ lemma U_617_7 : have hlg : Real.log (25788061999608657 / 40000000000000000 : ℝ) ≤ (-(1097419455511665411643 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25788061999608657 / 40000000000000000 : ℝ) = - (25788061999608657 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25788061999608657 / 20000000000000000 : ℚ)) - (U := (635448495238334588357 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25788061999608657 / 20000000000000000 : ℝ) ≤ - (635448495238334588357 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6426901498282141 / 10000000000000000 : ℝ)) (q := - (25788061999608657 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25788061999608657 / 40000000000000000 : ℚ)) + (r' := (25788061999608657 / 20000000000000000 : ℚ)) + (U := (-(1097419455511665411643 / 2500000000000000000000 : ℚ))) + (U' := (635448495238334588357 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (6426901498282141 / 10000000000000000 : ℚ)) + (q := (25788061999608657 / 40000000000000000 : ℚ)) + (U := (-(1097419455511665411643 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_8 : Uω (aρ 8) (bρ 8) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -691,25 +598,21 @@ lemma U_617_8 : have hlg : Real.log (24570093904536439 / 40000000000000000 : ℝ) ≤ (-(2436747227048758859281 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24570093904536439 / 40000000000000000 : ℝ) = - (24570093904536439 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24570093904536439 / 20000000000000000 : ℚ)) - (U := (1028988674451241140719 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24570093904536439 / 20000000000000000 : ℝ) ≤ - (1028988674451241140719 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (381341193880377 / 625000000000000 : ℝ)) (q := - (24570093904536439 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24570093904536439 / 40000000000000000 : ℚ)) + (r' := (24570093904536439 / 20000000000000000 : ℚ)) + (U := (-(2436747227048758859281 / 5000000000000000000000 : ℚ))) + (U' := (1028988674451241140719 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (381341193880377 / 625000000000000 : ℚ)) + (q := (24570093904536439 / 40000000000000000 : ℚ)) + (U := (-(2436747227048758859281 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_9 : Uω (aρ 9) (bρ 9) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -717,25 +620,21 @@ lemma U_617_9 : have hlg : Real.log (23056220745501421 / 40000000000000000 : ℝ) ≤ (-(1377359600808868290677 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23056220745501421 / 40000000000000000 : ℝ) = - (23056220745501421 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23056220745501421 / 20000000000000000 : ℚ)) - (U := (355508349941131709323 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23056220745501421 / 20000000000000000 : ℝ) ≤ - (355508349941131709323 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5685488150928523 / 10000000000000000 : ℝ)) (q := - (23056220745501421 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23056220745501421 / 40000000000000000 : ℚ)) + (r' := (23056220745501421 / 20000000000000000 : ℚ)) + (U := (-(1377359600808868290677 / 2500000000000000000000 : ℚ))) + (U' := (355508349941131709323 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (5685488150928523 / 10000000000000000 : ℚ)) + (q := (23056220745501421 / 40000000000000000 : ℚ)) + (U := (-(1377359600808868290677 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_10 : Uω (aρ 10) (bρ 10) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -743,26 +642,21 @@ lemma U_617_10 : have hlg : Real.log (21249758747311093 / 40000000000000000 : ℝ) ≤ (-(158133477903931247259 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21249758747311093 / 40000000000000000 : ℝ) = - (21249758747311093 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21249758747311093 / 20000000000000000 : ℚ)) - (U := (15153317171068752741 / 250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21249758747311093 / 20000000000000000 : ℝ) ≤ - (15153317171068752741 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5170816185328359 / 10000000000000000 : ℝ)) (q := - (21249758747311093 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21249758747311093 / 40000000000000000 : ℚ)) + (r' := (21249758747311093 / 20000000000000000 : ℚ)) + (U := (-(158133477903931247259 / 250000000000000000000 : ℚ))) + (U' := (15153317171068752741 / 250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (5170816185328359 / 10000000000000000 : ℚ)) + (q := (21249758747311093 / 40000000000000000 : ℚ)) + (U := (-(158133477903931247259 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_11 : Uω (aρ 11) (bρ 11) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -770,26 +664,21 @@ lemma U_617_11 : have hlg : Real.log (19174946742517903 / 40000000000000000 : ℝ) ≤ (-(3676374418941192739521 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19174946742517903 / 40000000000000000 : ℝ) = - (19174946742517903 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19174946742517903 / 10000000000000000 : ℚ)) - (U := (3255097384058807260479 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19174946742517903 / 10000000000000000 : ℝ) ≤ - (3255097384058807260479 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1137971702284191 / 2500000000000000 : ℝ)) (q := - (19174946742517903 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19174946742517903 / 40000000000000000 : ℚ)) + (r' := (19174946742517903 / 10000000000000000 : ℚ)) + (U := (-(3676374418941192739521 / 5000000000000000000000 : ℚ))) + (U' := (3255097384058807260479 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (1137971702284191 / 2500000000000000 : ℚ)) + (q := (19174946742517903 / 40000000000000000 : ℚ)) + (U := (-(3676374418941192739521 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_12 : Uω (aρ 12) (bρ 12) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -797,26 +686,21 @@ lemma U_617_12 : have hlg : Real.log (16872793394296307 / 40000000000000000 : ℝ) ≤ (-(431588493602501169943 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16872793394296307 / 40000000000000000 : ℝ) = - (16872793394296307 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16872793394296307 / 10000000000000000 : ℚ)) - (U := (261558686697498830057 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16872793394296307 / 10000000000000000 : ℝ) ≤ - (261558686697498830057 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1912255115855483 / 5000000000000000 : ℝ)) (q := - (16872793394296307 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16872793394296307 / 40000000000000000 : ℚ)) + (r' := (16872793394296307 / 10000000000000000 : ℚ)) + (U := (-(431588493602501169943 / 500000000000000000000 : ℚ))) + (U' := (261558686697498830057 / 500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (1912255115855483 / 5000000000000000 : ℚ)) + (q := (16872793394296307 / 40000000000000000 : ℚ)) + (U := (-(431588493602501169943 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_13 : Uω (aρ 13) (bρ 13) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -824,26 +708,21 @@ lemma U_617_13 : have hlg : Real.log (14386140081501321 / 40000000000000000 : ℝ) ≤ (-(10226142048473857112987 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14386140081501321 / 40000000000000000 : ℝ) = - (14386140081501321 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14386140081501321 / 10000000000000000 : ℚ)) - (U := (3636801557526142887013 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14386140081501321 / 10000000000000000 : ℝ) ≤ - (3636801557526142887013 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2980565316908473 / 10000000000000000 : ℝ)) (q := - (14386140081501321 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14386140081501321 / 40000000000000000 : ℚ)) + (r' := (14386140081501321 / 10000000000000000 : ℚ)) + (U := (-(10226142048473857112987 / 10000000000000000000000 : ℚ))) + (U' := (3636801557526142887013 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (2980565316908473 / 10000000000000000 : ℚ)) + (q := (14386140081501321 / 40000000000000000 : ℚ)) + (U := (-(10226142048473857112987 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_14 : Uω (aρ 14) (bρ 14) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -851,26 +730,21 @@ lemma U_617_14 : have hlg : Real.log (11706078446739869 / 40000000000000000 : ℝ) ≤ (-(12287712213345314582721 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11706078446739869 / 40000000000000000 : ℝ) = - (11706078446739869 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11706078446739869 / 10000000000000000 : ℚ)) - (U := (1575231392654685417279 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11706078446739869 / 10000000000000000 : ℝ) ≤ - (1575231392654685417279 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1984461784572747 / 10000000000000000 : ℝ)) (q := - (11706078446739869 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11706078446739869 / 40000000000000000 : ℚ)) + (r' := (11706078446739869 / 10000000000000000 : ℚ)) + (U := (-(12287712213345314582721 / 10000000000000000000000 : ℚ))) + (U' := (1575231392654685417279 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (1984461784572747 / 10000000000000000 : ℚ)) + (q := (11706078446739869 / 40000000000000000 : ℚ)) + (U := (-(12287712213345314582721 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_15 : Uω (aρ 15) (bρ 15) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -878,26 +752,21 @@ lemma U_617_15 : have hlg : Real.log (8124465222703667 / 40000000000000000 : ℝ) ≤ (-(15939995460286118426859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8124465222703667 / 40000000000000000 : ℝ) = - (8124465222703667 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8124465222703667 / 5000000000000000 : ℚ)) - (U := (4854419948713881573141 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8124465222703667 / 5000000000000000 : ℝ) ≤ - (4854419948713881573141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (226614224984823 / 5000000000000000 : ℝ)) (q := - (8124465222703667 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8124465222703667 / 40000000000000000 : ℚ)) + (r' := (8124465222703667 / 5000000000000000 : ℚ)) + (U := (-(15939995460286118426859 / 10000000000000000000000 : ℚ))) + (U' := (4854419948713881573141 / 10000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (4601713724651 / 6400000000000 : ℚ)) + (s := (226614224984823 / 5000000000000000 : ℚ)) + (q := (8124465222703667 / 40000000000000000 : ℚ)) + (U := (-(15939995460286118426859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_617_16 : Uω (aρ 16) (bρ 16) (4601713724651 / 6400000000000 : ℝ) ≤ @@ -993,25 +862,21 @@ lemma U_618_1 : have hlg : Real.log (1427036358676109 / 2000000000000000 : ℝ) ≤ (-(337547363029600780631 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1427036358676109 / 2000000000000000 : ℝ) = - (1427036358676109 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1427036358676109 / 1000000000000000 : ℚ)) - (U := (355599817270399219369 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1427036358676109 / 1000000000000000 : ℝ) ≤ - (355599817270399219369 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (89189489194123 / 125000000000000 : ℝ)) (q := - (1427036358676109 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1427036358676109 / 2000000000000000 : ℚ)) + (r' := (1427036358676109 / 1000000000000000 : ℚ)) + (U := (-(337547363029600780631 / 1000000000000000000000 : ℚ))) + (U' := (355599817270399219369 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (89189489194123 / 125000000000000 : ℚ)) + (q := (1427036358676109 / 2000000000000000 : ℚ)) + (U := (-(337547363029600780631 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_2 : Uω (aρ 2) (bρ 2) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1019,25 +884,21 @@ lemma U_618_2 : have hlg : Real.log (14222572499079663 / 20000000000000000 : ℝ) ≤ (-(3409019581723940330361 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14222572499079663 / 20000000000000000 : ℝ) = - (14222572499079663 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14222572499079663 / 10000000000000000 : ℚ)) - (U := (3522452221276059669639 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14222572499079663 / 10000000000000000 : ℝ) ≤ - (3522452221276059669639 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7111137060358413 / 10000000000000000 : ℝ)) (q := - (14222572499079663 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14222572499079663 / 20000000000000000 : ℚ)) + (r' := (14222572499079663 / 10000000000000000 : ℚ)) + (U := (-(3409019581723940330361 / 10000000000000000000000 : ℚ))) + (U' := (3522452221276059669639 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (7111137060358413 / 10000000000000000 : ℚ)) + (q := (14222572499079663 / 20000000000000000 : ℚ)) + (U := (-(3409019581723940330361 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_3 : Uω (aρ 3) (bρ 3) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1045,25 +906,21 @@ lemma U_618_3 : have hlg : Real.log (14127031299558699 / 20000000000000000 : ℝ) ≤ (-(173821098891361459987 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14127031299558699 / 20000000000000000 : ℝ) = - (14127031299558699 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14127031299558699 / 10000000000000000 : ℚ)) - (U := (172752491258638540013 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14127031299558699 / 10000000000000000 : ℝ) ≤ - (172752491258638540013 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7062991967187449 / 10000000000000000 : ℝ)) (q := - (14127031299558699 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14127031299558699 / 20000000000000000 : ℚ)) + (r' := (14127031299558699 / 10000000000000000 : ℚ)) + (U := (-(173821098891361459987 / 500000000000000000000 : ℚ))) + (U' := (172752491258638540013 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (7062991967187449 / 10000000000000000 : ℚ)) + (q := (14127031299558699 / 20000000000000000 : ℚ)) + (U := (-(173821098891361459987 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_4 : Uω (aρ 4) (bρ 4) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1071,25 +928,21 @@ lemma U_618_4 : have hlg : Real.log (1396847765378547 / 2000000000000000 : ℝ) ≤ (-(179464539245497928923 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1396847765378547 / 2000000000000000 : ℝ) = - (1396847765378547 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1396847765378547 / 1000000000000000 : ℚ)) - (U := (167109050904502071077 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1396847765378547 / 1000000000000000 : ℝ) ≤ - (167109050904502071077 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (349136625123961 / 500000000000000 : ℝ)) (q := - (1396847765378547 / 2000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1396847765378547 / 2000000000000000 : ℚ)) + (r' := (1396847765378547 / 1000000000000000 : ℚ)) + (U := (-(179464539245497928923 / 500000000000000000000 : ℚ))) + (U' := (167109050904502071077 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (349136625123961 / 500000000000000 : ℚ)) + (q := (1396847765378547 / 2000000000000000 : ℚ)) + (U := (-(179464539245497928923 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_5 : Uω (aρ 5) (bρ 5) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1097,25 +950,21 @@ lemma U_618_5 : have hlg : Real.log (13727351227811363 / 20000000000000000 : ℝ) ≤ (-(940854976778895516571 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13727351227811363 / 20000000000000000 : ℝ) = - (13727351227811363 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13727351227811363 / 10000000000000000 : ℚ)) - (U := (792012973971104483429 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13727351227811363 / 10000000000000000 : ℝ) ≤ - (792012973971104483429 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6859795995840113 / 10000000000000000 : ℝ)) (q := - (13727351227811363 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13727351227811363 / 20000000000000000 : ℚ)) + (r' := (13727351227811363 / 10000000000000000 : ℚ)) + (U := (-(940854976778895516571 / 2500000000000000000000 : ℚ))) + (U' := (792012973971104483429 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (6859795995840113 / 10000000000000000 : ℚ)) + (q := (13727351227811363 / 20000000000000000 : ℚ)) + (U := (-(940854976778895516571 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_6 : Uω (aρ 6) (bρ 6) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1123,25 +972,21 @@ lemma U_618_6 : have hlg : Real.log (3345572179298549 / 5000000000000000 : ℝ) ≤ (-(803600356250984112259 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3345572179298549 / 5000000000000000 : ℝ) = - (3345572179298549 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3345572179298549 / 2500000000000000 : ℚ)) - (U := (582694004349015887741 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3345572179298549 / 2500000000000000 : ℝ) ≤ - (582694004349015887741 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3340986930181473 / 5000000000000000 : ℝ)) (q := - (3345572179298549 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3345572179298549 / 5000000000000000 : ℚ)) + (r' := (3345572179298549 / 2500000000000000 : ℚ)) + (U := (-(803600356250984112259 / 2000000000000000000000 : ℚ))) + (U' := (582694004349015887741 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (3340986930181473 / 5000000000000000 : ℚ)) + (q := (3345572179298549 / 5000000000000000 : ℚ)) + (U := (-(803600356250984112259 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_7 : Uω (aρ 7) (bρ 7) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1149,25 +994,21 @@ lemma U_618_7 : have hlg : Real.log (2582627694795441 / 4000000000000000 : ℝ) ≤ (-(2187434969384649431987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2582627694795441 / 4000000000000000 : ℝ) = - (2582627694795441 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2582627694795441 / 2000000000000000 : ℚ)) - (U := (1278300932115350568013 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2582627694795441 / 2000000000000000 : ℝ) ≤ - (1278300932115350568013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1287296999581191 / 2000000000000000 : ℝ)) (q := - (2582627694795441 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2582627694795441 / 4000000000000000 : ℚ)) + (r' := (2582627694795441 / 2000000000000000 : ℚ)) + (U := (-(2187434969384649431987 / 5000000000000000000000 : ℚ))) + (U' := (1278300932115350568013 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (1287296999581191 / 2000000000000000 : ℚ)) + (q := (2582627694795441 / 4000000000000000 : ℚ)) + (U := (-(2187434969384649431987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_8 : Uω (aρ 8) (bρ 8) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1175,25 +1016,21 @@ lemma U_618_8 : have hlg : Real.log (12304222897779567 / 20000000000000000 : ℝ) ≤ (-(1214474362038736148431 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12304222897779567 / 20000000000000000 : ℝ) = - (12304222897779567 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12304222897779567 / 10000000000000000 : ℚ)) - (U := (518393588711263851569 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12304222897779567 / 10000000000000000 : ℝ) ≤ - (518393588711263851569 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6111111073048317 / 10000000000000000 : ℝ)) (q := - (12304222897779567 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12304222897779567 / 20000000000000000 : ℚ)) + (r' := (12304222897779567 / 10000000000000000 : ℚ)) + (U := (-(1214474362038736148431 / 2500000000000000000000 : ℚ))) + (U' := (518393588711263851569 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (6111111073048317 / 10000000000000000 : ℚ)) + (q := (12304222897779567 / 20000000000000000 : ℚ)) + (U := (-(1214474362038736148431 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_9 : Uω (aρ 9) (bρ 9) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1201,25 +1038,21 @@ lemma U_618_9 : have hlg : Real.log (11547421096770763 / 20000000000000000 : ℝ) ≤ (-(1373175357305435607103 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11547421096770763 / 20000000000000000 : ℝ) = - (11547421096770763 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11547421096770763 / 10000000000000000 : ℚ)) - (U := (359692593444564392897 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11547421096770763 / 10000000000000000 : ℝ) ≤ - (359692593444564392897 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5695274900399513 / 10000000000000000 : ℝ)) (q := - (11547421096770763 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11547421096770763 / 20000000000000000 : ℚ)) + (r' := (11547421096770763 / 10000000000000000 : ℚ)) + (U := (-(1373175357305435607103 / 2500000000000000000000 : ℚ))) + (U' := (359692593444564392897 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (5695274900399513 / 10000000000000000 : ℚ)) + (q := (11547421096770763 / 20000000000000000 : ℚ)) + (U := (-(1373175357305435607103 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_10 : Uω (aρ 10) (bρ 10) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1227,26 +1060,21 @@ lemma U_618_10 : have hlg : Real.log (2128889608355591 / 4000000000000000 : ℝ) ≤ (-(3153469138497098411407 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2128889608355591 / 4000000000000000 : ℝ) = - (2128889608355591 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2128889608355591 / 2000000000000000 : ℚ)) - (U := (312266763002901588593 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2128889608355591 / 2000000000000000 : ℝ) ≤ - (312266763002901588593 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1036172175780341 / 2000000000000000 : ℝ)) (q := - (2128889608355591 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2128889608355591 / 4000000000000000 : ℚ)) + (r' := (2128889608355591 / 2000000000000000 : ℚ)) + (U := (-(3153469138497098411407 / 5000000000000000000000 : ℚ))) + (U' := (312266763002901588593 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (1036172175780341 / 2000000000000000 : ℚ)) + (q := (2128889608355591 / 4000000000000000 : ℚ)) + (U := (-(3153469138497098411407 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_11 : Uω (aρ 11) (bρ 11) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1254,26 +1082,21 @@ lemma U_618_11 : have hlg : Real.log (4803765573513503 / 10000000000000000 : ℝ) ≤ (-(7331849876332865554959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4803765573513503 / 10000000000000000 : ℝ) = - (4803765573513503 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4803765573513503 / 2500000000000000 : ℚ)) - (U := (6531093729667134445041 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4803765573513503 / 2500000000000000 : ℝ) ≤ - (6531093729667134445041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1140605152588939 / 2500000000000000 : ℝ)) (q := - (4803765573513503 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4803765573513503 / 10000000000000000 : ℚ)) + (r' := (4803765573513503 / 2500000000000000 : ℚ)) + (U := (-(7331849876332865554959 / 10000000000000000000000 : ℚ))) + (U' := (6531093729667134445041 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (1140605152588939 / 2500000000000000 : ℚ)) + (q := (4803765573513503 / 10000000000000000 : ℚ)) + (U := (-(7331849876332865554959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_12 : Uω (aρ 12) (bρ 12) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1281,26 +1104,21 @@ lemma U_618_12 : have hlg : Real.log (1057175004768303 / 2500000000000000 : ℝ) ≤ (-(8606904707458635042521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1057175004768303 / 2500000000000000 : ℝ) = - (1057175004768303 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1057175004768303 / 625000000000000 : ℚ)) - (U := (5256038898541364957479 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1057175004768303 / 625000000000000 : ℝ) ≤ - (5256038898541364957479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1917994799080087 / 5000000000000000 : ℝ)) (q := - (1057175004768303 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1057175004768303 / 2500000000000000 : ℚ)) + (r' := (1057175004768303 / 625000000000000 : ℚ)) + (U := (-(8606904707458635042521 / 10000000000000000000000 : ℚ))) + (U' := (5256038898541364957479 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (1917994799080087 / 5000000000000000 : ℚ)) + (q := (1057175004768303 / 2500000000000000 : ℚ)) + (U := (-(8606904707458635042521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_13 : Uω (aρ 13) (bρ 13) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1308,26 +1126,21 @@ lemma U_618_13 : have hlg : Real.log (7216039368045631 / 20000000000000000 : ℝ) ≤ (-(2038852069256468634701 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7216039368045631 / 20000000000000000 : ℝ) = - (7216039368045631 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7216039368045631 / 5000000000000000 : ℚ)) - (U := (733736651943531365299 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7216039368045631 / 5000000000000000 : ℝ) ≤ - (733736651943531365299 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2994010669654381 / 10000000000000000 : ℝ)) (q := - (7216039368045631 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7216039368045631 / 20000000000000000 : ℚ)) + (r' := (7216039368045631 / 5000000000000000 : ℚ)) + (U := (-(2038852069256468634701 / 2000000000000000000000 : ℚ))) + (U' := (733736651943531365299 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (2994010669654381 / 10000000000000000 : ℚ)) + (q := (7216039368045631 / 20000000000000000 : ℚ)) + (U := (-(2038852069256468634701 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_14 : Uω (aρ 14) (bρ 14) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1335,26 +1148,21 @@ lemma U_618_14 : have hlg : Real.log (5881066152590859 / 20000000000000000 : ℝ) ≤ (-(3059985522729845712219 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5881066152590859 / 20000000000000000 : ℝ) = - (5881066152590859 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5881066152590859 / 5000000000000000 : ℚ)) - (U := (405750378770154287781 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5881066152590859 / 5000000000000000 : ℝ) ≤ - (405750378770154287781 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2002964739244609 / 10000000000000000 : ℝ)) (q := - (5881066152590859 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5881066152590859 / 20000000000000000 : ℚ)) + (r' := (5881066152590859 / 5000000000000000 : ℚ)) + (U := (-(3059985522729845712219 / 2500000000000000000000 : ℚ))) + (U' := (405750378770154287781 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (2002964739244609 / 10000000000000000 : ℚ)) + (q := (5881066152590859 / 20000000000000000 : ℚ)) + (U := (-(3059985522729845712219 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_15 : Uω (aρ 15) (bρ 15) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1362,25 +1170,21 @@ lemma U_618_15 : have hlg : Real.log (517777224673183 / 2500000000000000 : ℝ) ≤ (-(15745009285213127229491 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (517777224673183 / 2500000000000000 : ℝ) = - (517777224673183 / 312500000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (517777224673183 / 312500000000000 : ℚ)) - (U := (5049406123786872770509 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (517777224673183 / 312500000000000 : ℝ) ≤ - (5049406123786872770509 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (261844830727107 / 5000000000000000 : ℝ)) (q := - (517777224673183 / 2500000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [bρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (517777224673183 / 2500000000000000 : ℚ)) + (r' := (517777224673183 / 312500000000000 : ℚ)) + (U := (-(15745009285213127229491 / 10000000000000000000000 : ℚ))) + (U' := (5049406123786872770509 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (5759761335453 / 8000000000000 : ℚ)) + (s := (261844830727107 / 5000000000000000 : ℚ)) + (q := (517777224673183 / 2500000000000000 : ℚ)) + (U := (-(15745009285213127229491 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_618_16 : Uω (aρ 16) (bρ 16) (5759761335453 / 8000000000000 : ℝ) ≤ @@ -1476,25 +1280,21 @@ lemma U_619_1 : have hlg : Real.log (28578823192531509 / 40000000000000000 : ℝ) ≤ (-(840533645271613096197 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28578823192531509 / 40000000000000000 : ℝ) = - (28578823192531509 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28578823192531509 / 20000000000000000 : ℚ)) - (U := (892334305478386903803 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28578823192531509 / 20000000000000000 : ℝ) ≤ - (892334305478386903803 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3572341585242721 / 5000000000000000 : ℝ)) (q := - (28578823192531509 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28578823192531509 / 40000000000000000 : ℚ)) + (r' := (28578823192531509 / 20000000000000000 : ℚ)) + (U := (-(840533645271613096197 / 2500000000000000000000 : ℚ))) + (U' := (892334305478386903803 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (3572341585242721 / 5000000000000000 : ℚ)) + (q := (28578823192531509 / 40000000000000000 : ℚ)) + (U := (-(840533645271613096197 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_2 : Uω (aρ 2) (bρ 2) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1502,25 +1302,21 @@ lemma U_619_2 : have hlg : Real.log (28483241694525251 / 40000000000000000 : ℝ) ≤ (-(1697817751219501552147 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28483241694525251 / 40000000000000000 : ℝ) = - (28483241694525251 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28483241694525251 / 20000000000000000 : ℚ)) - (U := (1767918150280498447853 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28483241694525251 / 20000000000000000 : ℝ) ≤ - (1767918150280498447853 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7120661433992313 / 10000000000000000 : ℝ)) (q := - (28483241694525251 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28483241694525251 / 40000000000000000 : ℚ)) + (r' := (28483241694525251 / 20000000000000000 : ℚ)) + (U := (-(1697817751219501552147 / 5000000000000000000000 : ℚ))) + (U' := (1767918150280498447853 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (7120661433992313 / 10000000000000000 : ℚ)) + (q := (28483241694525251 / 40000000000000000 : ℚ)) + (U := (-(1697817751219501552147 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_3 : Uω (aρ 3) (bρ 3) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1528,25 +1324,21 @@ lemma U_619_3 : have hlg : Real.log (28292161318114177 / 40000000000000000 : ℝ) ≤ (-(3462946727979391038407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28292161318114177 / 40000000000000000 : ℝ) = - (28292161318114177 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28292161318114177 / 20000000000000000 : ℚ)) - (U := (3468525075020608961593 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28292161318114177 / 20000000000000000 : ℝ) ≤ - (3468525075020608961593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (884064669017097 / 1250000000000000 : ℝ)) (q := - (28292161318114177 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28292161318114177 / 40000000000000000 : ℚ)) + (r' := (28292161318114177 / 20000000000000000 : ℚ)) + (U := (-(3462946727979391038407 / 10000000000000000000000 : ℚ))) + (U' := (3468525075020608961593 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (884064669017097 / 1250000000000000 : ℚ)) + (q := (28292161318114177 / 40000000000000000 : ℚ)) + (U := (-(3462946727979391038407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_4 : Uω (aρ 4) (bρ 4) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1554,25 +1346,21 @@ lemma U_619_4 : have hlg : Real.log (5595011882533867 / 8000000000000000 : ℝ) ≤ (-(3575660758809798843429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5595011882533867 / 8000000000000000 : ℝ) = - (5595011882533867 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5595011882533867 / 4000000000000000 : ℚ)) - (U := (3355811044190201156571 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5595011882533867 / 4000000000000000 : ℝ) ≤ - (3355811044190201156571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1398452116095871 / 2000000000000000 : ℝ)) (q := - (5595011882533867 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5595011882533867 / 8000000000000000 : ℚ)) + (r' := (5595011882533867 / 4000000000000000 : ℚ)) + (U := (-(3575660758809798843429 / 10000000000000000000000 : ℚ))) + (U' := (3355811044190201156571 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (1398452116095871 / 2000000000000000 : ℚ)) + (q := (5595011882533867 / 8000000000000000 : ℚ)) + (U := (-(3575660758809798843429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_5 : Uω (aρ 5) (bρ 5) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1580,25 +1368,21 @@ lemma U_619_5 : have hlg : Real.log (27492819869401271 / 40000000000000000 : ℝ) ≤ (-(3749545789310065404481 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27492819869401271 / 40000000000000000 : ℝ) = - (27492819869401271 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27492819869401271 / 20000000000000000 : ℚ)) - (U := (3181926013689934595519 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27492819869401271 / 20000000000000000 : ℝ) ≤ - (3181926013689934595519 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6869330728180323 / 10000000000000000 : ℝ)) (q := - (27492819869401271 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27492819869401271 / 40000000000000000 : ℚ)) + (r' := (27492819869401271 / 20000000000000000 : ℚ)) + (U := (-(3749545789310065404481 / 10000000000000000000000 : ℚ))) + (U' := (3181926013689934595519 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (6869330728180323 / 10000000000000000 : ℚ)) + (q := (27492819869401271 / 40000000000000000 : ℚ)) + (U := (-(3749545789310065404481 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_6 : Uω (aρ 6) (bρ 6) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1606,25 +1390,21 @@ lemma U_619_6 : have hlg : Real.log (5360545108355043 / 8000000000000000 : ℝ) ≤ (-(4003758721882345394807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5360545108355043 / 8000000000000000 : ℝ) = - (5360545108355043 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5360545108355043 / 4000000000000000 : ℚ)) - (U := (2927713081117654605193 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5360545108355043 / 4000000000000000 : ℝ) ≤ - (2927713081117654605193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1338304787901459 / 2000000000000000 : ℝ)) (q := - (5360545108355043 / 8000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5360545108355043 / 8000000000000000 : ℚ)) + (r' := (5360545108355043 / 4000000000000000 : ℚ)) + (U := (-(4003758721882345394807 / 10000000000000000000000 : ℚ))) + (U' := (2927713081117654605193 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (1338304787901459 / 2000000000000000 : ℚ)) + (q := (5360545108355043 / 8000000000000000 : ℚ)) + (U := (-(4003758721882345394807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_7 : Uω (aρ 7) (bρ 7) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1632,25 +1412,21 @@ lemma U_619_7 : have hlg : Real.log (25864491543411003 / 40000000000000000 : ℝ) ≤ (-(872016817370518790959 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25864491543411003 / 40000000000000000 : ℝ) = - (25864491543411003 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25864491543411003 / 20000000000000000 : ℚ)) - (U := (514277543229481209041 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25864491543411003 / 20000000000000000 : ℝ) ≤ - (514277543229481209041 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6446068321085189 / 10000000000000000 : ℝ)) (q := - (25864491543411003 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25864491543411003 / 40000000000000000 : ℚ)) + (r' := (25864491543411003 / 20000000000000000 : ℚ)) + (U := (-(872016817370518790959 / 2000000000000000000000 : ℚ))) + (U' := (514277543229481209041 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (6446068321085189 / 10000000000000000 : ℚ)) + (q := (25864491543411003 / 40000000000000000 : ℚ)) + (U := (-(872016817370518790959 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_8 : Uω (aρ 8) (bρ 8) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1658,25 +1434,21 @@ lemma U_619_8 : have hlg : Real.log (24646796884573221 / 40000000000000000 : ℝ) ≤ (-(4842325056394238771433 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24646796884573221 / 40000000000000000 : ℝ) = - (24646796884573221 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24646796884573221 / 20000000000000000 : ℚ)) - (U := (2089146746605761228567 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24646796884573221 / 20000000000000000 : ℝ) ≤ - (2089146746605761228567 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3060381321503149 / 5000000000000000 : ℝ)) (q := - (24646796884573221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24646796884573221 / 40000000000000000 : ℚ)) + (r' := (24646796884573221 / 20000000000000000 : ℚ)) + (U := (-(4842325056394238771433 / 10000000000000000000000 : ℚ))) + (U' := (2089146746605761228567 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (3060381321503149 / 5000000000000000 : ℚ)) + (q := (24646796884573221 / 40000000000000000 : ℚ)) + (U := (-(4842325056394238771433 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_9 : Uω (aρ 9) (bρ 9) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1684,25 +1456,21 @@ lemma U_619_9 : have hlg : Real.log (23133461862679071 / 40000000000000000 : ℝ) ≤ (-(5475993190011855433897 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23133461862679071 / 40000000000000000 : ℝ) = - (23133461862679071 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23133461862679071 / 20000000000000000 : ℚ)) - (U := (1455478612988144566103 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23133461862679071 / 20000000000000000 : ℝ) ≤ - (1455478612988144566103 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5705060760419223 / 10000000000000000 : ℝ)) (q := - (23133461862679071 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23133461862679071 / 40000000000000000 : ℚ)) + (r' := (23133461862679071 / 20000000000000000 : ℚ)) + (U := (-(5475993190011855433897 / 10000000000000000000000 : ℚ))) + (U' := (1455478612988144566103 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (5705060760419223 / 10000000000000000 : ℚ)) + (q := (23133461862679071 / 40000000000000000 : ℚ)) + (U := (-(5475993190011855433897 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_10 : Uω (aρ 10) (bρ 10) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1710,25 +1478,21 @@ lemma U_619_10 : have hlg : Real.log (170624235950307 / 320000000000000 : ℝ) ≤ (-(6288573075515474583353 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (170624235950307 / 320000000000000 : ℝ) = - (170624235950307 / 160000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (170624235950307 / 160000000000000 : ℚ)) - (U := (642898727484525416647 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (170624235950307 / 160000000000000 : ℝ) ≤ - (642898727484525416647 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (41527228875751 / 80000000000000 : ℝ)) (q := - (170624235950307 / 320000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (170624235950307 / 320000000000000 : ℚ)) + (r' := (170624235950307 / 160000000000000 : ℚ)) + (U := (-(6288573075515474583353 / 10000000000000000000000 : ℚ))) + (U' := (642898727484525416647 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (41527228875751 / 80000000000000 : ℚ)) + (q := (170624235950307 / 320000000000000 : ℚ)) + (U := (-(6288573075515474583353 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_11 : Uω (aρ 11) (bρ 11) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1736,26 +1500,21 @@ lemma U_619_11 : have hlg : Real.log (19255168987033969 / 40000000000000000 : ℝ) ≤ (-(1827749775245038889841 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19255168987033969 / 40000000000000000 : ℝ) = - (19255168987033969 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19255168987033969 / 10000000000000000 : ℚ)) - (U := (1637986126254961110159 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19255168987033969 / 10000000000000000 : ℝ) ≤ - (1637986126254961110159 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (142904686946771 / 312500000000000 : ℝ)) (q := - (19255168987033969 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19255168987033969 / 40000000000000000 : ℚ)) + (r' := (19255168987033969 / 10000000000000000 : ℚ)) + (U := (-(1827749775245038889841 / 2500000000000000000000 : ℚ))) + (U' := (1637986126254961110159 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (142904686946771 / 312500000000000 : ℚ)) + (q := (19255168987033969 / 40000000000000000 : ℚ)) + (U := (-(1827749775245038889841 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_12 : Uω (aρ 12) (bρ 12) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1763,26 +1522,21 @@ lemma U_619_12 : have hlg : Real.log (16956785409282959 / 40000000000000000 : ℝ) ≤ (-(343284552296869609383 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16956785409282959 / 40000000000000000 : ℝ) = - (16956785409282959 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16956785409282959 / 10000000000000000 : ℚ)) - (U := (211233191943130390617 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16956785409282959 / 10000000000000000 : ℝ) ≤ - (211233191943130390617 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3847458290106167 / 10000000000000000 : ℝ)) (q := - (16956785409282959 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16956785409282959 / 40000000000000000 : ℚ)) + (r' := (16956785409282959 / 10000000000000000 : ℚ)) + (U := (-(343284552296869609383 / 400000000000000000000 : ℚ))) + (U' := (211233191943130390617 / 400000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (3847458290106167 / 10000000000000000 : ℚ)) + (q := (16956785409282959 / 40000000000000000 : ℚ)) + (U := (-(343284552296869609383 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_13 : Uω (aρ 13) (bρ 13) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1790,26 +1544,21 @@ lemma U_619_13 : have hlg : Real.log (14477957491638911 / 40000000000000000 : ℝ) ≤ (-(1016252133793236407923 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14477957491638911 / 40000000000000000 : ℝ) = - (14477957491638911 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14477957491638911 / 10000000000000000 : ℚ)) - (U := (370042226806763592077 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14477957491638911 / 10000000000000000 : ℝ) ≤ - (370042226806763592077 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3007426072879143 / 10000000000000000 : ℝ)) (q := - (14477957491638911 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14477957491638911 / 40000000000000000 : ℚ)) + (r' := (14477957491638911 / 10000000000000000 : ℚ)) + (U := (-(1016252133793236407923 / 1000000000000000000000 : ℚ))) + (U' := (370042226806763592077 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (3007426072879143 / 10000000000000000 : ℚ)) + (q := (14477957491638911 / 40000000000000000 : ℚ)) + (U := (-(1016252133793236407923 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_14 : Uω (aρ 14) (bρ 14) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1817,25 +1566,21 @@ lemma U_619_14 : have hlg : Real.log (472717487009481 / 1600000000000000 : ℝ) ≤ (-(12192609767079604075557 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (472717487009481 / 1600000000000000 : ℝ) = - (472717487009481 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (472717487009481 / 400000000000000 : ℚ)) - (U := (1670333838920395924443 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (472717487009481 / 400000000000000 : ℝ) ≤ - (1670333838920395924443 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1263339499827 / 6250000000000 : ℝ)) (q := - (472717487009481 / 1600000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (472717487009481 / 1600000000000000 : ℚ)) + (r' := (472717487009481 / 400000000000000 : ℚ)) + (U := (-(12192609767079604075557 / 10000000000000000000000 : ℚ))) + (U' := (1670333838920395924443 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (1263339499827 / 6250000000000 : ℚ)) + (q := (472717487009481 / 1600000000000000 : ℚ)) + (U := (-(12192609767079604075557 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_15 : Uω (aρ 15) (bρ 15) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1843,26 +1588,21 @@ lemma U_619_15 : have hlg : Real.log (8427884246986999 / 40000000000000000 : ℝ) ≤ (-(3893334229564846221071 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8427884246986999 / 40000000000000000 : ℝ) = - (8427884246986999 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8427884246986999 / 5000000000000000 : ℚ)) - (U := (1305269622685153778929 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8427884246986999 / 5000000000000000 : ℝ) ≤ - (1305269622685153778929 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (585890013013187 / 10000000000000000 : ℝ)) (q := - (8427884246986999 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8427884246986999 / 40000000000000000 : ℚ)) + (r' := (8427884246986999 / 5000000000000000 : ℚ)) + (U := (-(3893334229564846221071 / 2500000000000000000000 : ℚ))) + (U' := (1305269622685153778929 / 2500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23069522060369 / 32000000000000 : ℚ)) + (s := (585890013013187 / 10000000000000000 : ℚ)) + (q := (8427884246986999 / 40000000000000000 : ℚ)) + (U := (-(3893334229564846221071 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_619_16 : Uω (aρ 16) (bρ 16) (23069522060369 / 32000000000000 : ℝ) ≤ @@ -1959,25 +1699,21 @@ lemma U_620_1 : have hlg : Real.log (3577114901402397 / 5000000000000000 : ℝ) ≤ (-(133952532052508978969 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3577114901402397 / 5000000000000000 : ℝ) = - (3577114901402397 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3577114901402397 / 2500000000000000 : ℚ)) - (U := (143306340067491021031 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3577114901402397 / 2500000000000000 : ℝ) ≤ - (143306340067491021031 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7154207205280213 / 10000000000000000 : ℝ)) (q := - (3577114901402397 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3577114901402397 / 5000000000000000 : ℚ)) + (r' := (3577114901402397 / 2500000000000000 : ℚ)) + (U := (-(133952532052508978969 / 400000000000000000000 : ℚ))) + (U' := (143306340067491021031 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (7154207205280213 / 10000000000000000 : ℚ)) + (q := (3577114901402397 / 5000000000000000 : ℚ)) + (U := (-(133952532052508978969 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_2 : Uω (aρ 2) (bρ 2) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -1985,25 +1721,21 @@ lemma U_620_2 : have hlg : Real.log (1426066919437943 / 2000000000000000 : ℝ) ≤ (-(3382269313318846887479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1426066919437943 / 2000000000000000 : ℝ) = - (1426066919437943 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1426066919437943 / 1000000000000000 : ℚ)) - (U := (3549202489681153112521 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1426066919437943 / 1000000000000000 : ℝ) ≤ - (3549202489681153112521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1426037161312011 / 2000000000000000 : ℝ)) (q := - (1426066919437943 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1426066919437943 / 2000000000000000 : ℚ)) + (r' := (1426066919437943 / 1000000000000000 : ℚ)) + (U := (-(3382269313318846887479 / 10000000000000000000000 : ℚ))) + (U' := (3549202489681153112521 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (1426037161312011 / 2000000000000000 : ℚ)) + (q := (1426066919437943 / 2000000000000000 : ℚ)) + (U := (-(3382269313318846887479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_3 : Uω (aρ 3) (bρ 3) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2011,25 +1743,21 @@ lemma U_620_3 : have hlg : Real.log (1770641251845221 / 2500000000000000 : ℝ) ≤ (-(1724744807306295194459 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1770641251845221 / 2500000000000000 : ℝ) = - (1770641251845221 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1770641251845221 / 1250000000000000 : ℚ)) - (U := (1740991094193704805541 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1770641251845221 / 1250000000000000 : ℝ) ≤ - (1740991094193704805541 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7082042733292393 / 10000000000000000 : ℝ)) (q := - (1770641251845221 / 2500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1770641251845221 / 2500000000000000 : ℚ)) + (r' := (1770641251845221 / 1250000000000000 : ℚ)) + (U := (-(1724744807306295194459 / 5000000000000000000000 : ℚ))) + (U' := (1740991094193704805541 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (7082042733292393 / 10000000000000000 : ℚ)) + (q := (1770641251845221 / 2500000000000000 : ℚ)) + (U := (-(1724744807306295194459 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_4 : Uω (aρ 4) (bρ 4) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2037,25 +1765,21 @@ lemma U_620_4 : have hlg : Real.log (2801316349543653 / 4000000000000000 : ℝ) ≤ (-(1781024646579131442769 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2801316349543653 / 4000000000000000 : ℝ) = - (2801316349543653 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2801316349543653 / 2000000000000000 : ℚ)) - (U := (1684711254920868557231 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2801316349543653 / 2000000000000000 : ℝ) ≤ - (1684711254920868557231 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (700178864731389 / 1000000000000000 : ℝ)) (q := - (2801316349543653 / 4000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2801316349543653 / 4000000000000000 : ℚ)) + (r' := (2801316349543653 / 2000000000000000 : ℚ)) + (U := (-(1781024646579131442769 / 5000000000000000000000 : ℚ))) + (U' := (1684711254920868557231 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (700178864731389 / 1000000000000000 : ℚ)) + (q := (2801316349543653 / 4000000000000000 : ℚ)) + (U := (-(1781024646579131442769 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_5 : Uω (aρ 5) (bρ 5) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2063,25 +1787,21 @@ lemma U_620_5 : have hlg : Real.log (13765468611784181 / 20000000000000000 : ℝ) ≤ (-(233480682225324909683 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13765468611784181 / 20000000000000000 : ℝ) = - (13765468611784181 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13765468611784181 / 10000000000000000 : ℚ)) - (U := (199736305462175090317 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13765468611784181 / 10000000000000000 : ℝ) ≤ - (199736305462175090317 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3439432715357403 / 5000000000000000 : ℝ)) (q := - (13765468611784181 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13765468611784181 / 20000000000000000 : ℚ)) + (r' := (13765468611784181 / 10000000000000000 : ℚ)) + (U := (-(233480682225324909683 / 625000000000000000000 : ℚ))) + (U' := (199736305462175090317 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (3439432715357403 / 5000000000000000 : ℚ)) + (q := (13765468611784181 / 20000000000000000 : ℚ)) + (U := (-(233480682225324909683 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_6 : Uω (aρ 6) (bρ 6) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2089,25 +1809,21 @@ lemma U_620_6 : have hlg : Real.log (2684087350055289 / 4000000000000000 : ℝ) ≤ (-(124672999234403041657 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2684087350055289 / 4000000000000000 : ℝ) = - (2684087350055289 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2684087350055289 / 2000000000000000 : ℚ)) - (U := (91935494609346958343 / 312500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2684087350055289 / 2000000000000000 : ℝ) ≤ - (91935494609346958343 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (670107394434707 / 1000000000000000 : ℝ)) (q := - (2684087350055289 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2684087350055289 / 4000000000000000 : ℚ)) + (r' := (2684087350055289 / 2000000000000000 : ℚ)) + (U := (-(124672999234403041657 / 312500000000000000000 : ℚ))) + (U' := (91935494609346958343 / 312500000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (670107394434707 / 1000000000000000 : ℚ)) + (q := (2684087350055289 / 4000000000000000 : ℚ)) + (U := (-(124672999234403041657 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_7 : Uω (aρ 7) (bρ 7) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2115,25 +1831,21 @@ lemma U_620_7 : have hlg : Real.log (404729777930469 / 625000000000000 : ℝ) ≤ (-(543165025054239187137 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (404729777930469 / 625000000000000 : ℝ) = - (404729777930469 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (404729777930469 / 312500000000000 : ℚ)) - (U := (323268950320760812863 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (404729777930469 / 312500000000000 : ℝ) ≤ - (323268950320760812863 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6455651468605633 / 10000000000000000 : ℝ)) (q := - (404729777930469 / 625000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (404729777930469 / 625000000000000 : ℚ)) + (r' := (404729777930469 / 312500000000000 : ℚ)) + (U := (-(543165025054239187137 / 1250000000000000000000 : ℚ))) + (U' := (323268950320760812863 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (6455651468605633 / 10000000000000000 : ℚ)) + (q := (404729777930469 / 625000000000000 : ℚ)) + (U := (-(543165025054239187137 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_8 : Uω (aρ 8) (bρ 8) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2141,25 +1853,21 @@ lemma U_620_8 : have hlg : Real.log (12342573587683343 / 20000000000000000 : ℝ) ≤ (-(2413388600116685197157 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12342573587683343 / 20000000000000000 : ℝ) = - (12342573587683343 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12342573587683343 / 10000000000000000 : ℚ)) - (U := (1052347301383314802843 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12342573587683343 / 10000000000000000 : ℝ) ≤ - (1052347301383314802843 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (383150863365873 / 625000000000000 : ℝ)) (q := - (12342573587683343 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12342573587683343 / 20000000000000000 : ℚ)) + (r' := (12342573587683343 / 10000000000000000 : ℚ)) + (U := (-(2413388600116685197157 / 5000000000000000000000 : ℚ))) + (U' := (1052347301383314802843 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (383150863365873 / 625000000000000 : ℚ)) + (q := (12342573587683343 / 20000000000000000 : ℚ)) + (U := (-(2413388600116685197157 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_9 : Uω (aρ 9) (bρ 9) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2167,25 +1875,21 @@ lemma U_620_9 : have hlg : Real.log (11586039881026203 / 20000000000000000 : ℝ) ≤ (-(1364828396129223884731 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11586039881026203 / 20000000000000000 : ℝ) = - (11586039881026203 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11586039881026203 / 10000000000000000 : ℚ)) - (U := (368039554620776115269 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11586039881026203 / 10000000000000000 : ℝ) ≤ - (368039554620776115269 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1428711433889207 / 2500000000000000 : ℝ)) (q := - (11586039881026203 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11586039881026203 / 20000000000000000 : ℚ)) + (r' := (11586039881026203 / 10000000000000000 : ℚ)) + (U := (-(1364828396129223884731 / 2500000000000000000000 : ℚ))) + (U' := (368039554620776115269 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (1428711433889207 / 2500000000000000 : ℚ)) + (q := (11586039881026203 / 20000000000000000 : ℚ)) + (U := (-(1364828396129223884731 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_10 : Uω (aρ 10) (bρ 10) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2193,26 +1897,21 @@ lemma U_620_10 : have hlg : Real.log (10683579500375607 / 20000000000000000 : ℝ) ≤ (-(3135121683520498290713 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10683579500375607 / 20000000000000000 : ℝ) = - (10683579500375607 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10683579500375607 / 10000000000000000 : ℚ)) - (U := (330614217979501709287 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10683579500375607 / 10000000000000000 : ℝ) ≤ - (330614217979501709287 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (325059024275077 / 625000000000000 : ℝ)) (q := - (10683579500375607 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10683579500375607 / 20000000000000000 : ℚ)) + (r' := (10683579500375607 / 10000000000000000 : ℚ)) + (U := (-(3135121683520498290713 / 5000000000000000000000 : ℚ))) + (U' := (330614217979501709287 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (325059024275077 / 625000000000000 : ℚ)) + (q := (10683579500375607 / 20000000000000000 : ℚ)) + (U := (-(3135121683520498290713 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_11 : Uω (aρ 11) (bρ 11) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2220,26 +1919,21 @@ lemma U_620_11 : have hlg : Real.log (9647633441254317 / 20000000000000000 : ℝ) ≤ (-(3645098135037624419509 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9647633441254317 / 20000000000000000 : ℝ) = - (9647633441254317 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9647633441254317 / 5000000000000000 : ℚ)) - (U := (3286373667962375580491 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9647633441254317 / 5000000000000000 : ℝ) ≤ - (3286373667962375580491 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2291737477742471 / 5000000000000000 : ℝ)) (q := - (9647633441254317 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9647633441254317 / 20000000000000000 : ℚ)) + (r' := (9647633441254317 / 5000000000000000 : ℚ)) + (U := (-(3645098135037624419509 / 5000000000000000000000 : ℚ))) + (U' := (3286373667962375580491 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (2291737477742471 / 5000000000000000 : ℚ)) + (q := (9647633441254317 / 20000000000000000 : ℚ)) + (U := (-(3645098135037624419509 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_12 : Uω (aρ 12) (bρ 12) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2247,26 +1941,21 @@ lemma U_620_12 : have hlg : Real.log (8499374791807127 / 20000000000000000 : ℝ) ≤ (-(8557396661480946125929 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8499374791807127 / 20000000000000000 : ℝ) = - (8499374791807127 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8499374791807127 / 5000000000000000 : ℚ)) - (U := (5305546944519053874071 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8499374791807127 / 5000000000000000 : ℝ) ≤ - (5305546944519053874071 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (60295568792543 / 156250000000000 : ℝ)) (q := - (8499374791807127 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8499374791807127 / 20000000000000000 : ℚ)) + (r' := (8499374791807127 / 5000000000000000 : ℚ)) + (U := (-(8557396661480946125929 / 10000000000000000000000 : ℚ))) + (U' := (5305546944519053874071 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (60295568792543 / 156250000000000 : ℚ)) + (q := (8499374791807127 / 20000000000000000 : ℚ)) + (U := (-(8557396661480946125929 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_13 : Uω (aρ 13) (bρ 13) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2274,26 +1963,21 @@ lemma U_620_13 : have hlg : Real.log (7261888573088961 / 20000000000000000 : ℝ) ≤ (-(506546171996047407941 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7261888573088961 / 20000000000000000 : ℝ) = - (7261888573088961 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7261888573088961 / 5000000000000000 : ℚ)) - (U := (186601008303952592059 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7261888573088961 / 5000000000000000 : ℝ) ≤ - (186601008303952592059 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1510405962799793 / 5000000000000000 : ℝ)) (q := - (7261888573088961 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7261888573088961 / 20000000000000000 : ℚ)) + (r' := (7261888573088961 / 5000000000000000 : ℚ)) + (U := (-(506546171996047407941 / 500000000000000000000 : ℚ))) + (U' := (186601008303952592059 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (1510405962799793 / 5000000000000000 : ℚ)) + (q := (7261888573088961 / 20000000000000000 : ℚ)) + (U := (-(506546171996047407941 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_14 : Uω (aρ 14) (bρ 14) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2301,26 +1985,21 @@ lemma U_620_14 : have hlg : Real.log (5936749893837629 / 20000000000000000 : ℝ) ≤ (-(12145704453235629212067 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5936749893837629 / 20000000000000000 : ℝ) = - (5936749893837629 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5936749893837629 / 5000000000000000 : ℚ)) - (U := (1717239152764370787933 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5936749893837629 / 5000000000000000 : ℝ) ≤ - (1717239152764370787933 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1019800265696627 / 5000000000000000 : ℝ)) (q := - (5936749893837629 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5936749893837629 / 20000000000000000 : ℚ)) + (r' := (5936749893837629 / 5000000000000000 : ℚ)) + (U := (-(12145704453235629212067 / 10000000000000000000000 : ℚ))) + (U' := (1717239152764370787933 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (1019800265696627 / 5000000000000000 : ℚ)) + (q := (5936749893837629 / 20000000000000000 : ℚ)) + (U := (-(12145704453235629212067 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_15 : Uω (aρ 15) (bρ 15) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2328,26 +2007,21 @@ lemma U_620_15 : have hlg : Real.log (4279810283251159 / 20000000000000000 : ℝ) ≤ (-(15418235905060781715109 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4279810283251159 / 20000000000000000 : ℝ) = - (4279810283251159 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4279810283251159 / 2500000000000000 : ℚ)) - (U := (5376179503939218284891 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (4279810283251159 / 2500000000000000 : ℝ) ≤ - (5376179503939218284891 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (80279274777723 / 1250000000000000 : ℝ)) (q := - (4279810283251159 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4279810283251159 / 20000000000000000 : ℚ)) + (r' := (4279810283251159 / 2500000000000000 : ℚ)) + (U := (-(15418235905060781715109 / 10000000000000000000000 : ℚ))) + (U' := (5376179503939218284891 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11549999389463 / 16000000000000 : ℚ)) + (s := (80279274777723 / 1250000000000000 : ℚ)) + (q := (4279810283251159 / 20000000000000000 : ℚ)) + (U := (-(15418235905060781715109 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_620_16 : Uω (aρ 16) (bρ 16) (11549999389463 / 16000000000000 : ℝ) ≤ @@ -2443,25 +2117,21 @@ lemma U_621_1 : have hlg : Real.log (28655015229586461 / 40000000000000000 : ℝ) ≤ (-(667101948738974140143 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28655015229586461 / 40000000000000000 : ℝ) = - (28655015229586461 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28655015229586461 / 20000000000000000 : ℚ)) - (U := (719192411861025859857 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28655015229586461 / 20000000000000000 : ℝ) ≤ - (719192411861025859857 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7163731239914793 / 10000000000000000 : ℝ)) (q := - (28655015229586461 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28655015229586461 / 40000000000000000 : ℚ)) + (r' := (28655015229586461 / 20000000000000000 : ℚ)) + (U := (-(667101948738974140143 / 2000000000000000000000 : ℚ))) + (U' := (719192411861025859857 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (7163731239914793 / 10000000000000000 : ℚ)) + (q := (28655015229586461 / 40000000000000000 : ℚ)) + (U := (-(667101948738974140143 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_2 : Uω (aρ 2) (bρ 2) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2469,25 +2139,21 @@ lemma U_621_2 : have hlg : Real.log (28559435080868687 / 40000000000000000 : ℝ) ≤ (-(3368920966598643556611 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28559435080868687 / 40000000000000000 : ℝ) = - (28559435080868687 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28559435080868687 / 20000000000000000 : ℚ)) - (U := (3562550836401356443389 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28559435080868687 / 20000000000000000 : ℝ) ≤ - (3562550836401356443389 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3569855089032953 / 5000000000000000 : ℝ)) (q := - (28559435080868687 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28559435080868687 / 40000000000000000 : ℚ)) + (r' := (28559435080868687 / 20000000000000000 : ℚ)) + (U := (-(3368920966598643556611 / 10000000000000000000000 : ℚ))) + (U' := (3562550836401356443389 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (3569855089032953 / 5000000000000000 : ℚ)) + (q := (28559435080868687 / 40000000000000000 : ℚ)) + (U := (-(3368920966598643556611 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_3 : Uω (aρ 3) (bρ 3) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2495,25 +2161,21 @@ lemma U_621_3 : have hlg : Real.log (28368358733376049 / 40000000000000000 : ℝ) ≤ (-(214753161810318558973 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28368358733376049 / 40000000000000000 : ℝ) = - (28368358733376049 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28368358733376049 / 20000000000000000 : ℚ)) - (U := (218463825877181441027 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28368358733376049 / 20000000000000000 : ℝ) ≤ - (218463825877181441027 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7091568110669587 / 10000000000000000 : ℝ)) (q := - (28368358733376049 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28368358733376049 / 40000000000000000 : ℚ)) + (r' := (28368358733376049 / 20000000000000000 : ℚ)) + (U := (-(214753161810318558973 / 625000000000000000000 : ℚ))) + (U' := (218463825877181441027 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (7091568110669587 / 10000000000000000 : ℚ)) + (q := (28368358733376049 / 40000000000000000 : ℚ)) + (U := (-(214753161810318558973 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_4 : Uω (aρ 4) (bρ 4) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2521,25 +2183,21 @@ lemma U_621_4 : have hlg : Real.log (28051267555963567 / 40000000000000000 : ℝ) ≤ (-(709691267490747128891 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28051267555963567 / 40000000000000000 : ℝ) = - (28051267555963567 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28051267555963567 / 20000000000000000 : ℚ)) - (U := (676603093109252871109 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28051267555963567 / 20000000000000000 : ℝ) ≤ - (676603093109252871109 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3505658351514173 / 5000000000000000 : ℝ)) (q := - (28051267555963567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28051267555963567 / 40000000000000000 : ℚ)) + (r' := (28051267555963567 / 20000000000000000 : ℚ)) + (U := (-(709691267490747128891 / 2000000000000000000000 : ℚ))) + (U' := (676603093109252871109 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (3505658351514173 / 5000000000000000 : ℚ)) + (q := (28051267555963567 / 40000000000000000 : ℚ)) + (U := (-(709691267490747128891 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_5 : Uω (aρ 5) (bρ 5) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2547,25 +2205,21 @@ lemma U_621_5 : have hlg : Real.log (5513810903674307 / 8000000000000000 : ℝ) ≤ (-(3721855232630060188191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5513810903674307 / 8000000000000000 : ℝ) = - (5513810903674307 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5513810903674307 / 4000000000000000 : ℚ)) - (U := (3209616570369939811809 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5513810903674307 / 4000000000000000 : ℝ) ≤ - (3209616570369939811809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (688840010356733 / 1000000000000000 : ℝ)) (q := - (5513810903674307 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5513810903674307 / 8000000000000000 : ℚ)) + (r' := (5513810903674307 / 4000000000000000 : ℚ)) + (U := (-(3721855232630060188191 / 10000000000000000000000 : ℚ))) + (U' := (3209616570369939811809 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (688840010356733 / 1000000000000000 : ℚ)) + (q := (5513810903674307 / 8000000000000000 : ℚ)) + (U := (-(3721855232630060188191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_6 : Uω (aρ 6) (bρ 6) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2573,25 +2227,21 @@ lemma U_621_6 : have hlg : Real.log (26879021311355879 / 40000000000000000 : ℝ) ≤ (-(1987666742048291147841 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26879021311355879 / 40000000000000000 : ℝ) = - (26879021311355879 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26879021311355879 / 20000000000000000 : ℚ)) - (U := (1478069159451708852159 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26879021311355879 / 20000000000000000 : ℝ) ≤ - (1478069159451708852159 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3355311937599751 / 5000000000000000 : ℝ)) (q := - (26879021311355879 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26879021311355879 / 40000000000000000 : ℚ)) + (r' := (26879021311355879 / 20000000000000000 : ℚ)) + (U := (-(1987666742048291147841 / 5000000000000000000000 : ℚ))) + (U' := (1478069159451708852159 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (3355311937599751 / 5000000000000000 : ℚ)) + (q := (26879021311355879 / 40000000000000000 : ℚ)) + (U := (-(1987666742048291147841 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_7 : Uω (aρ 7) (bρ 7) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2599,25 +2249,21 @@ lemma U_621_7 : have hlg : Real.log (25940919681933677 / 40000000000000000 : ℝ) ≤ (-(4330578213947306030187 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25940919681933677 / 40000000000000000 : ℝ) = - (25940919681933677 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25940919681933677 / 20000000000000000 : ℚ)) - (U := (2600893589052693969813 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25940919681933677 / 20000000000000000 : ℝ) ≤ - (2600893589052693969813 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6465234441248401 / 10000000000000000 : ℝ)) (q := - (25940919681933677 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25940919681933677 / 40000000000000000 : ℚ)) + (r' := (25940919681933677 / 20000000000000000 : ℚ)) + (U := (-(4330578213947306030187 / 10000000000000000000000 : ℚ))) + (U' := (2600893589052693969813 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (6465234441248401 / 10000000000000000 : ℚ)) + (q := (25940919681933677 / 40000000000000000 : ℚ)) + (U := (-(4330578213947306030187 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_8 : Uω (aρ 8) (bρ 8) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2625,25 +2271,21 @@ lemma U_621_8 : have hlg : Real.log (24723496671703543 / 40000000000000000 : ℝ) ≤ (-(4811253801470739519341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24723496671703543 / 40000000000000000 : ℝ) = - (24723496671703543 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24723496671703543 / 20000000000000000 : ℚ)) - (U := (2120218001529260480659 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24723496671703543 / 20000000000000000 : ℝ) ≤ - (2120218001529260480659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3070032293736667 / 5000000000000000 : ℝ)) (q := - (24723496671703543 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24723496671703543 / 40000000000000000 : ℚ)) + (r' := (24723496671703543 / 20000000000000000 : ℚ)) + (U := (-(4811253801470739519341 / 10000000000000000000000 : ℚ))) + (U' := (2120218001529260480659 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (3070032293736667 / 5000000000000000 : ℚ)) + (q := (24723496671703543 / 40000000000000000 : ℚ)) + (U := (-(4811253801470739519341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_9 : Uω (aρ 9) (bρ 9) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2651,25 +2293,21 @@ lemma U_621_9 : have hlg : Real.log (23210695900736581 / 40000000000000000 : ℝ) ≤ (-(1360665628048339499749 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23210695900736581 / 40000000000000000 : ℝ) = - (23210695900736581 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23210695900736581 / 20000000000000000 : ℚ)) - (U := (372202322701660500251 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23210695900736581 / 20000000000000000 : ℝ) ≤ - (372202322701660500251 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5724629830349853 / 10000000000000000 : ℝ)) (q := - (23210695900736581 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23210695900736581 / 40000000000000000 : ℚ)) + (r' := (23210695900736581 / 20000000000000000 : ℚ)) + (U := (-(1360665628048339499749 / 2500000000000000000000 : ℚ))) + (U' := (372202322701660500251 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (5724629830349853 / 10000000000000000 : ℚ)) + (q := (23210695900736581 / 40000000000000000 : ℚ)) + (U := (-(1360665628048339499749 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_10 : Uω (aρ 10) (bρ 10) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2677,26 +2315,21 @@ lemma U_621_10 : have hlg : Real.log (21406284627007463 / 40000000000000000 : ℝ) ≤ (-(1562987251951932787287 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21406284627007463 / 40000000000000000 : ℝ) = - (21406284627007463 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21406284627007463 / 20000000000000000 : ℚ)) - (U := (169880698798067212713 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21406284627007463 / 20000000000000000 : ℝ) ≤ - (169880698798067212713 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2605491613490147 / 5000000000000000 : ℝ)) (q := - (21406284627007463 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21406284627007463 / 40000000000000000 : ℚ)) + (r' := (21406284627007463 / 20000000000000000 : ℚ)) + (U := (-(1562987251951932787287 / 2500000000000000000000 : ℚ))) + (U' := (169880698798067212713 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (2605491613490147 / 5000000000000000 : ℚ)) + (q := (21406284627007463 / 40000000000000000 : ℚ)) + (U := (-(1562987251951932787287 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_11 : Uω (aρ 11) (bρ 11) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2704,26 +2337,21 @@ lemma U_621_11 : have hlg : Real.log (19335356040944007 / 40000000000000000 : ℝ) ≤ (-(726944114380871616587 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19335356040944007 / 40000000000000000 : ℝ) = - (19335356040944007 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19335356040944007 / 10000000000000000 : ℚ)) - (U := (659350246219128383413 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19335356040944007 / 10000000000000000 : ℝ) ≤ - (659350246219128383413 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2296997780076783 / 5000000000000000 : ℝ)) (q := - (19335356040944007 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19335356040944007 / 40000000000000000 : ℚ)) + (r' := (19335356040944007 / 10000000000000000 : ℚ)) + (U := (-(726944114380871616587 / 1000000000000000000000 : ℚ))) + (U' := (659350246219128383413 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (2296997780076783 / 5000000000000000 : ℚ)) + (q := (19335356040944007 / 40000000000000000 : ℚ)) + (U := (-(726944114380871616587 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_12 : Uω (aρ 12) (bρ 12) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2731,26 +2359,21 @@ lemma U_621_12 : have hlg : Real.log (17040692787205723 / 40000000000000000 : ℝ) ≤ (-(8532752764931727160707 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17040692787205723 / 40000000000000000 : ℝ) = - (17040692787205723 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17040692787205723 / 10000000000000000 : ℚ)) - (U := (5330190841068272839293 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17040692787205723 / 10000000000000000 : ℝ) ≤ - (5330190841068272839293 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (241897751873089 / 625000000000000 : ℝ)) (q := - (17040692787205723 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17040692787205723 / 40000000000000000 : ℚ)) + (r' := (17040692787205723 / 10000000000000000 : ℚ)) + (U := (-(8532752764931727160707 / 10000000000000000000000 : ℚ))) + (U' := (5330190841068272839293 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (241897751873089 / 625000000000000 : ℚ)) + (q := (17040692787205723 / 40000000000000000 : ℚ)) + (U := (-(8532752764931727160707 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_13 : Uω (aρ 13) (bρ 13) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2758,26 +2381,21 @@ lemma U_621_13 : have hlg : Real.log (14569538481916747 / 40000000000000000 : ℝ) ≤ (-(5049732549018707484119 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14569538481916747 / 40000000000000000 : ℝ) = - (14569538481916747 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14569538481916747 / 10000000000000000 : ℚ)) - (U := (1881739253981292515881 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14569538481916747 / 10000000000000000 : ℝ) ≤ - (1881739253981292515881 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1481527645957 / 4882812500000 : ℝ)) (q := - (14569538481916747 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14569538481916747 / 40000000000000000 : ℚ)) + (r' := (14569538481916747 / 10000000000000000 : ℚ)) + (U := (-(5049732549018707484119 / 5000000000000000000000 : ℚ))) + (U' := (1881739253981292515881 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (1481527645957 / 4882812500000 : ℚ)) + (q := (14569538481916747 / 40000000000000000 : ℚ)) + (U := (-(5049732549018707484119 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_14 : Uω (aρ 14) (bρ 14) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2785,26 +2403,21 @@ lemma U_621_14 : have hlg : Real.log (11928826590805561 / 40000000000000000 : ℝ) ≤ (-(12099215801753549008383 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11928826590805561 / 40000000000000000 : ℝ) = - (11928826590805561 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11928826590805561 / 10000000000000000 : ℚ)) - (U := (1763727804246450991617 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11928826590805561 / 10000000000000000 : ℝ) ≤ - (1763727804246450991617 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2057739958409343 / 10000000000000000 : ℝ)) (q := - (11928826590805561 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11928826590805561 / 40000000000000000 : ℚ)) + (r' := (11928826590805561 / 10000000000000000 : ℚ)) + (U := (-(12099215801753549008383 / 10000000000000000000000 : ℚ))) + (U' := (1763727804246450991617 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (2057739958409343 / 10000000000000000 : ℚ)) + (q := (11928826590805561 / 40000000000000000 : ℚ)) + (U := (-(12099215801753549008383 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_15 : Uω (aρ 15) (bρ 15) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2812,26 +2425,21 @@ lemma U_621_15 : have hlg : Real.log (1736499912346799 / 8000000000000000 : ℝ) ≤ (-(1909462497718683193977 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (1736499912346799 / 8000000000000000 : ℝ) = - (1736499912346799 / 1000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1736499912346799 / 1000000000000000 : ℚ)) - (U := (689839428406316806023 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1736499912346799 / 1000000000000000 : ℝ) ≤ - (689839428406316806023 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8676871516107 / 125000000000000 : ℝ)) (q := - (1736499912346799 / 8000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1736499912346799 / 8000000000000000 : ℚ)) + (r' := (1736499912346799 / 1000000000000000 : ℚ)) + (U := (-(1909462497718683193977 / 1250000000000000000000 : ℚ))) + (U' := (689839428406316806023 / 1250000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23130475497483 / 32000000000000 : ℚ)) + (s := (8676871516107 / 125000000000000 : ℚ)) + (q := (1736499912346799 / 8000000000000000 : ℚ)) + (U := (-(1909462497718683193977 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_621_16 : Uω (aρ 16) (bρ 16) (23130475497483 / 32000000000000 : ℝ) ≤ @@ -2929,25 +2537,21 @@ lemma U_622_1 : have hlg : Real.log (14346555623817321 / 20000000000000000 : ℝ) ≤ (-(664444772228277286747 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14346555623817321 / 20000000000000000 : ℝ) = - (14346555623817321 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14346555623817321 / 10000000000000000 : ℚ)) - (U := (721849588371722713253 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14346555623817321 / 10000000000000000 : ℝ) ≤ - (721849588371722713253 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7173255274389821 / 10000000000000000 : ℝ)) (q := - (14346555623817321 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14346555623817321 / 20000000000000000 : ℚ)) + (r' := (14346555623817321 / 10000000000000000 : ℚ)) + (U := (-(664444772228277286747 / 2000000000000000000000 : ℚ))) + (U' := (721849588371722713253 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (579023805401 / 800000000000 : ℚ)) + (s := (7173255274389821 / 10000000000000000 : ℚ)) + (q := (14346555623817321 / 20000000000000000 : ℚ)) + (U := (-(664444772228277286747 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_2 : Uω (aρ 2) (bρ 2) (579023805401 / 800000000000 : ℝ) ≤ @@ -2955,25 +2559,21 @@ lemma U_622_2 : have hlg : Real.log (14298765885431609 / 20000000000000000 : ℝ) ≤ (-(1677795207352304648309 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14298765885431609 / 20000000000000000 : ℝ) = - (14298765885431609 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14298765885431609 / 10000000000000000 : ℚ)) - (U := (1787940694147695351691 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14298765885431609 / 10000000000000000 : ℝ) ≤ - (1787940694147695351691 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7149234548514109 / 10000000000000000 : ℝ)) (q := - (14298765885431609 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14298765885431609 / 20000000000000000 : ℚ)) + (r' := (14298765885431609 / 10000000000000000 : ℚ)) + (U := (-(1677795207352304648309 / 5000000000000000000000 : ℚ))) + (U' := (1787940694147695351691 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (579023805401 / 800000000000 : ℚ)) + (s := (7149234548514109 / 10000000000000000 : ℚ)) + (q := (14298765885431609 / 20000000000000000 : ℚ)) + (U := (-(1677795207352304648309 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_3 : Uω (aρ 3) (bρ 3) (579023805401 / 800000000000 : ℝ) ≤ @@ -2981,25 +2581,21 @@ lemma U_622_3 : have hlg : Real.log (14203228714851061 / 20000000000000000 : ℝ) ≤ (-(3422629602471597769299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14203228714851061 / 20000000000000000 : ℝ) = - (14203228714851061 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14203228714851061 / 10000000000000000 : ℚ)) - (U := (3508842200528402230701 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14203228714851061 / 10000000000000000 : ℝ) ≤ - (3508842200528402230701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7101093484283561 / 10000000000000000 : ℝ)) (q := - (14203228714851061 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14203228714851061 / 20000000000000000 : ℚ)) + (r' := (14203228714851061 / 10000000000000000 : ℚ)) + (U := (-(3422629602471597769299 / 10000000000000000000000 : ℚ))) + (U' := (3508842200528402230701 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (579023805401 / 800000000000 : ℚ)) + (s := (7101093484283561 / 10000000000000000 : ℚ)) + (q := (14203228714851061 / 20000000000000000 : ℚ)) + (U := (-(3422629602471597769299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_4 : Uω (aρ 4) (bρ 4) (579023805401 / 800000000000 : ℝ) ≤ @@ -3007,25 +2603,21 @@ lemma U_622_4 : have hlg : Real.log (7022342898585249 / 10000000000000000 : ℝ) ≤ (-(17674409207002628977 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7022342898585249 / 10000000000000000 : ℝ) = - (7022342898585249 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7022342898585249 / 5000000000000000 : ℚ)) - (U := (16982949807997371023 / 50000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7022342898585249 / 5000000000000000 : ℝ) ≤ - (16982949807997371023 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3510422373833999 / 5000000000000000 : ℝ)) (q := - (7022342898585249 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7022342898585249 / 10000000000000000 : ℚ)) + (r' := (7022342898585249 / 5000000000000000 : ℚ)) + (U := (-(17674409207002628977 / 50000000000000000000 : ℚ))) + (U' := (16982949807997371023 / 50000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (579023805401 / 800000000000 : ℚ)) + (s := (3510422373833999 / 5000000000000000 : ℚ)) + (q := (7022342898585249 / 10000000000000000 : ℚ)) + (U := (-(17674409207002628977 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_5 : Uω (aρ 5) (bρ 5) (579023805401 / 800000000000 : ℝ) ≤ @@ -3033,25 +2625,21 @@ lemma U_622_5 : have hlg : Real.log (6901792938514239 / 10000000000000000 : ℝ) ≤ (-(23175241795223090519 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6901792938514239 / 10000000000000000 : ℝ) = - (6901792938514239 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6901792938514239 / 5000000000000000 : ℚ)) - (U := (20146456973526909481 / 62500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6901792938514239 / 5000000000000000 : ℝ) ≤ - (20146456973526909481 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3448967373430489 / 5000000000000000 : ℝ)) (q := - (6901792938514239 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6901792938514239 / 10000000000000000 : ℚ)) + (r' := (6901792938514239 / 5000000000000000 : ℚ)) + (U := (-(23175241795223090519 / 62500000000000000000 : ℚ))) + (U' := (20146456973526909481 / 62500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (579023805401 / 800000000000 : ℚ)) + (s := (3448967373430489 / 5000000000000000 : ℚ)) + (q := (6901792938514239 / 10000000000000000 : ℚ)) + (U := (-(23175241795223090519 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_6 : Uω (aρ 6) (bρ 6) (579023805401 / 800000000000 : ℝ) ≤ @@ -3059,25 +2647,21 @@ lemma U_622_6 : have hlg : Real.log (13458584487407519 / 20000000000000000 : ℝ) ≤ (-(1980575594952124207391 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13458584487407519 / 20000000000000000 : ℝ) = - (13458584487407519 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13458584487407519 / 10000000000000000 : ℚ)) - (U := (1485160306547875792609 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13458584487407519 / 10000000000000000 : ℝ) ≤ - (1485160306547875792609 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6720173732380019 / 10000000000000000 : ℝ)) (q := - (13458584487407519 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13458584487407519 / 20000000000000000 : ℚ)) + (r' := (13458584487407519 / 10000000000000000 : ℚ)) + (U := (-(1980575594952124207391 / 5000000000000000000000 : ℚ))) + (U' := (1485160306547875792609 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (579023805401 / 800000000000 : ℚ)) + (s := (6720173732380019 / 10000000000000000 : ℚ)) + (q := (13458584487407519 / 20000000000000000 : ℚ)) + (U := (-(1980575594952124207391 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_7 : Uω (aρ 7) (bρ 7) (579023805401 / 800000000000 : ℝ) ≤ @@ -3085,25 +2669,21 @@ lemma U_622_7 : have hlg : Real.log (12989566614057469 / 20000000000000000 : ℝ) ≤ (-(4315858062121709975551 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12989566614057469 / 20000000000000000 : ℝ) = - (12989566614057469 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12989566614057469 / 10000000000000000 : ℚ)) - (U := (2615613740878290024449 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12989566614057469 / 10000000000000000 : ℝ) ≤ - (2615613740878290024449 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6474817239789969 / 10000000000000000 : ℝ)) (q := - (12989566614057469 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12989566614057469 / 20000000000000000 : ℚ)) + (r' := (12989566614057469 / 10000000000000000 : ℚ)) + (U := (-(4315858062121709975551 / 10000000000000000000000 : ℚ))) + (U' := (2615613740878290024449 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (579023805401 / 800000000000 : ℚ)) + (s := (6474817239789969 / 10000000000000000 : ℚ)) + (q := (12989566614057469 / 20000000000000000 : ℚ)) + (U := (-(4315858062121709975551 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_8 : Uω (aρ 8) (bρ 8) (579023805401 / 800000000000 : ℝ) ≤ @@ -3111,25 +2691,21 @@ lemma U_622_8 : have hlg : Real.log (12380922688662013 / 20000000000000000 : ℝ) ≤ (-(119893869557067372297 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12380922688662013 / 20000000000000000 : ℝ) = - (12380922688662013 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12380922688662013 / 10000000000000000 : ℚ)) - (U := (53392925517932627703 / 250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12380922688662013 / 10000000000000000 : ℝ) ≤ - (53392925517932627703 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6149714965734513 / 10000000000000000 : ℝ)) (q := - (12380922688662013 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12380922688662013 / 20000000000000000 : ℚ)) + (r' := (12380922688662013 / 10000000000000000 : ℚ)) + (U := (-(119893869557067372297 / 250000000000000000000 : ℚ))) + (U' := (53392925517932627703 / 250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (579023805401 / 800000000000 : ℚ)) + (s := (6149714965734513 / 10000000000000000 : ℚ)) + (q := (12380922688662013 / 20000000000000000 : ℚ)) + (U := (-(119893869557067372297 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_9 : Uω (aρ 9) (bρ 9) (579023805401 / 800000000000 : ℝ) ≤ @@ -3137,25 +2713,21 @@ lemma U_622_9 : have hlg : Real.log (11624655143871947 / 20000000000000000 : ℝ) ≤ (-(5426039873039151492967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11624655143871947 / 20000000000000000 : ℝ) = - (11624655143871947 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11624655143871947 / 10000000000000000 : ℚ)) - (U := (1505431929960848507033 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11624655143871947 / 10000000000000000 : ℝ) ≤ - (1505431929960848507033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5734413049304447 / 10000000000000000 : ℝ)) (q := - (11624655143871947 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11624655143871947 / 20000000000000000 : ℚ)) + (r' := (11624655143871947 / 10000000000000000 : ℚ)) + (U := (-(5426039873039151492967 / 10000000000000000000000 : ℚ))) + (U' := (1505431929960848507033 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (579023805401 / 800000000000 : ℚ)) + (s := (5734413049304447 / 10000000000000000 : ℚ)) + (q := (11624655143871947 / 20000000000000000 : ℚ)) + (U := (-(5426039873039151492967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_10 : Uω (aρ 10) (bρ 10) (579023805401 / 800000000000 : ℝ) ≤ @@ -3163,25 +2735,21 @@ lemma U_622_10 : have hlg : Real.log (536135159873557 / 1000000000000000 : ℝ) ≤ (-(6233689854961697792241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (536135159873557 / 1000000000000000 : ℝ) = - (536135159873557 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (536135159873557 / 500000000000000 : ℚ)) - (U := (697781948038302207759 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (536135159873557 / 500000000000000 : ℝ) ≤ - (697781948038302207759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (65262751704983 / 125000000000000 : ℝ)) (q := - (536135159873557 / 1000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (536135159873557 / 1000000000000000 : ℚ)) + (r' := (536135159873557 / 500000000000000 : ℚ)) + (U := (-(6233689854961697792241 / 10000000000000000000000 : ℚ))) + (U' := (697781948038302207759 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (579023805401 / 800000000000 : ℚ)) + (s := (65262751704983 / 125000000000000 : ℚ)) + (q := (536135159873557 / 1000000000000000 : ℚ)) + (U := (-(6233689854961697792241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_11 : Uω (aρ 11) (bρ 11) (579023805401 / 800000000000 : ℝ) ≤ @@ -3189,26 +2757,21 @@ lemma U_622_11 : have hlg : Real.log (9687718261114239 / 20000000000000000 : ℝ) ≤ (-(906091685536126654847 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9687718261114239 / 20000000000000000 : ℝ) = - (9687718261114239 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9687718261114239 / 5000000000000000 : ℚ)) - (U := (826776265213873345153 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9687718261114239 / 5000000000000000 : ℝ) ≤ - (826776265213873345153 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4604511826246739 / 10000000000000000 : ℝ)) (q := - (9687718261114239 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9687718261114239 / 20000000000000000 : ℚ)) + (r' := (9687718261114239 / 5000000000000000 : ℚ)) + (U := (-(906091685536126654847 / 1250000000000000000000 : ℚ))) + (U' := (826776265213873345153 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (579023805401 / 800000000000 : ℚ)) + (s := (4604511826246739 / 10000000000000000 : ℚ)) + (q := (9687718261114239 / 20000000000000000 : ℚ)) + (U := (-(906091685536126654847 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_12 : Uω (aρ 12) (bρ 12) (579023805401 / 800000000000 : ℝ) ≤ @@ -3216,26 +2779,21 @@ lemma U_622_12 : have hlg : Real.log (1708261520558867 / 4000000000000000 : ℝ) ≤ (-(1063522702341544572123 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1708261520558867 / 4000000000000000 : ℝ) = - (1708261520558867 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1708261520558867 / 1000000000000000 : ℚ)) - (U := (669345248408455427877 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1708261520558867 / 1000000000000000 : ℝ) ≤ - (669345248408455427877 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (776360252922367 / 2000000000000000 : ℝ)) (q := - (1708261520558867 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1708261520558867 / 4000000000000000 : ℚ)) + (r' := (1708261520558867 / 1000000000000000 : ℚ)) + (U := (-(1063522702341544572123 / 1250000000000000000000 : ℚ))) + (U' := (669345248408455427877 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (579023805401 / 800000000000 : ℚ)) + (s := (776360252922367 / 2000000000000000 : ℚ)) + (q := (1708261520558867 / 4000000000000000 : ℚ)) + (U := (-(1063522702341544572123 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_13 : Uω (aρ 13) (bρ 13) (579023805401 / 800000000000 : ℝ) ≤ @@ -3243,26 +2801,21 @@ lemma U_622_13 : have hlg : Real.log (7307621132830777 / 20000000000000000 : ℝ) ≤ (-(10068144786604213098637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7307621132830777 / 20000000000000000 : ℝ) = - (7307621132830777 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7307621132830777 / 5000000000000000 : ℚ)) - (U := (3794798819395786901363 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7307621132830777 / 5000000000000000 : ℝ) ≤ - (3794798819395786901363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3047496536243277 / 10000000000000000 : ℝ)) (q := - (7307621132830777 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7307621132830777 / 20000000000000000 : ℚ)) + (r' := (7307621132830777 / 5000000000000000 : ℚ)) + (U := (-(10068144786604213098637 / 10000000000000000000000 : ℚ))) + (U' := (3794798819395786901363 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (579023805401 / 800000000000 : ℚ)) + (s := (3047496536243277 / 10000000000000000 : ℚ)) + (q := (7307621132830777 / 20000000000000000 : ℚ)) + (U := (-(10068144786604213098637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_14 : Uω (aρ 14) (bρ 14) (579023805401 / 800000000000 : ℝ) ≤ @@ -3270,26 +2823,21 @@ lemma U_622_14 : have hlg : Real.log (5991961883306781 / 20000000000000000 : ℝ) ≤ (-(753320867564564560021 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5991961883306781 / 20000000000000000 : ℝ) = - (5991961883306781 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5991961883306781 / 5000000000000000 : ℚ)) - (U := (113113107810435439979 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5991961883306781 / 5000000000000000 : ℝ) ≤ - (113113107810435439979 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2075764571764281 / 10000000000000000 : ℝ)) (q := - (5991961883306781 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5991961883306781 / 20000000000000000 : ℚ)) + (r' := (5991961883306781 / 5000000000000000 : ℚ)) + (U := (-(753320867564564560021 / 625000000000000000000 : ℚ))) + (U' := (113113107810435439979 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (579023805401 / 800000000000 : ℚ)) + (s := (2075764571764281 / 10000000000000000 : ℚ)) + (q := (5991961883306781 / 20000000000000000 : ℚ)) + (U := (-(753320867564564560021 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_15 : Uω (aρ 15) (bρ 15) (579023805401 / 800000000000 : ℝ) ≤ @@ -3297,26 +2845,21 @@ lemma U_622_15 : have hlg : Real.log (2199595035106191 / 10000000000000000 : ℝ) ≤ (-(15143118237455441992627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2199595035106191 / 10000000000000000 : ℝ) = - (2199595035106191 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2199595035106191 / 1250000000000000 : ℚ)) - (U := (5651297171544558007373 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2199595035106191 / 1250000000000000 : ℝ) ≤ - (5651297171544558007373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (371283018042441 / 5000000000000000 : ℝ)) (q := - (2199595035106191 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2199595035106191 / 10000000000000000 : ℚ)) + (r' := (2199595035106191 / 1250000000000000 : ℚ)) + (U := (-(15143118237455441992627 / 10000000000000000000000 : ℚ))) + (U' := (5651297171544558007373 / 10000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (579023805401 / 800000000000 : ℚ)) + (s := (371283018042441 / 5000000000000000 : ℚ)) + (q := (2199595035106191 / 10000000000000000 : ℚ)) + (U := (-(15143118237455441992627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_622_16 : Uω (aρ 16) (bρ 16) (579023805401 / 800000000000 : ℝ) ≤ @@ -3411,25 +2954,21 @@ lemma U_623_1 : have hlg : Real.log (28731207265364987 / 40000000000000000 : ℝ) ≤ (-(3308955606748218408403 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28731207265364987 / 40000000000000000 : ℝ) = - (28731207265364987 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28731207265364987 / 20000000000000000 : ℚ)) - (U := (3622516196251781591597 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28731207265364987 / 20000000000000000 : ℝ) ≤ - (3622516196251781591597 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7182779308705931 / 10000000000000000 : ℝ)) (q := - (28731207265364987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28731207265364987 / 40000000000000000 : ℚ)) + (r' := (28731207265364987 / 20000000000000000 : ℚ)) + (U := (-(3308955606748218408403 / 10000000000000000000000 : ℚ))) + (U' := (3622516196251781591597 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (7182779308705931 / 10000000000000000 : ℚ)) + (q := (28731207265364987 / 40000000000000000 : ℚ)) + (U := (-(3308955606748218408403 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_2 : Uω (aρ 2) (bρ 2) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3437,25 +2976,21 @@ lemma U_623_2 : have hlg : Real.log (5727125691750179 / 8000000000000000 : ℝ) ≤ (-(835569402563246451051 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5727125691750179 / 8000000000000000 : ℝ) = - (5727125691750179 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5727125691750179 / 4000000000000000 : ℚ)) - (U := (897298548186753548949 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5727125691750179 / 4000000000000000 : ℝ) ≤ - (897298548186753548949 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1431751783581777 / 2000000000000000 : ℝ)) (q := - (5727125691750179 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5727125691750179 / 8000000000000000 : ℚ)) + (r' := (5727125691750179 / 4000000000000000 : ℚ)) + (U := (-(835569402563246451051 / 2500000000000000000000 : ℚ))) + (U' := (897298548186753548949 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (1431751783581777 / 2000000000000000 : ℚ)) + (q := (5727125691750179 / 8000000000000000 : ℚ)) + (U := (-(835569402563246451051 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_3 : Uω (aρ 3) (bρ 3) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3463,25 +2998,21 @@ lemma U_623_3 : have hlg : Real.log (28444556118532007 / 40000000000000000 : ℝ) ≤ (-(3409226606762139118281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28444556118532007 / 40000000000000000 : ℝ) = - (28444556118532007 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28444556118532007 / 20000000000000000 : ℚ)) - (U := (3522245196237860881719 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28444556118532007 / 20000000000000000 : ℝ) ≤ - (3522245196237860881719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7110618854149441 / 10000000000000000 : ℝ)) (q := - (28444556118532007 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28444556118532007 / 40000000000000000 : ℚ)) + (r' := (28444556118532007 / 20000000000000000 : ℚ)) + (U := (-(3409226606762139118281 / 10000000000000000000000 : ℚ))) + (U' := (3522245196237860881719 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (7110618854149441 / 10000000000000000 : ℚ)) + (q := (28444556118532007 / 40000000000000000 : ℚ)) + (U := (-(3409226606762139118281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_4 : Uω (aρ 4) (bρ 4) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3489,25 +3020,21 @@ lemma U_623_4 : have hlg : Real.log (28127475610658871 / 40000000000000000 : ℝ) ≤ (-(3521325754907749846863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28127475610658871 / 40000000000000000 : ℝ) = - (28127475610658871 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28127475610658871 / 20000000000000000 : ℚ)) - (U := (3410146048092250153137 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28127475610658871 / 20000000000000000 : ℝ) ≤ - (3410146048092250153137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7030372781277873 / 10000000000000000 : ℝ)) (q := - (28127475610658871 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28127475610658871 / 40000000000000000 : ℚ)) + (r' := (28127475610658871 / 20000000000000000 : ℚ)) + (U := (-(3521325754907749846863 / 10000000000000000000000 : ℚ))) + (U' := (3410146048092250153137 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (7030372781277873 / 10000000000000000 : ℚ)) + (q := (28127475610658871 / 40000000000000000 : ℚ)) + (U := (-(3521325754907749846863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_5 : Uω (aρ 5) (bρ 5) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3515,25 +3042,21 @@ lemma U_623_5 : have hlg : Real.log (5529057786173887 / 8000000000000000 : ℝ) ≤ (-(461780153311734872569 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5529057786173887 / 8000000000000000 : ℝ) = - (5529057786173887 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5529057786173887 / 4000000000000000 : ℚ)) - (U := (404653822063265127431 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5529057786173887 / 4000000000000000 : ℝ) ≤ - (404653822063265127431 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1381493872143631 / 2000000000000000 : ℝ)) (q := - (5529057786173887 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5529057786173887 / 8000000000000000 : ℚ)) + (r' := (5529057786173887 / 4000000000000000 : ℚ)) + (U := (-(461780153311734872569 / 1250000000000000000000 : ℚ))) + (U' := (404653822063265127431 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (1381493872143631 / 2000000000000000 : ℚ)) + (q := (5529057786173887 / 8000000000000000 : ℚ)) + (U := (-(461780153311734872569 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_6 : Uω (aρ 6) (bρ 6) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3541,25 +3064,21 @@ lemma U_623_6 : have hlg : Real.log (26955316491557633 / 40000000000000000 : ℝ) ≤ (-(3946989035406164734171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26955316491557633 / 40000000000000000 : ℝ) = - (26955316491557633 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26955316491557633 / 20000000000000000 : ℚ)) - (U := (2984482767593835265829 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26955316491557633 / 20000000000000000 : ℝ) ≤ - (2984482767593835265829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3364861758101127 / 5000000000000000 : ℝ)) (q := - (26955316491557633 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26955316491557633 / 40000000000000000 : ℚ)) + (r' := (26955316491557633 / 20000000000000000 : ℚ)) + (U := (-(3946989035406164734171 / 10000000000000000000000 : ℚ))) + (U' := (2984482767593835265829 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (3364861758101127 / 5000000000000000 : ℚ)) + (q := (26955316491557633 / 40000000000000000 : ℚ)) + (U := (-(3946989035406164734171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_7 : Uω (aρ 7) (bρ 7) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3567,25 +3086,21 @@ lemma U_623_7 : have hlg : Real.log (26017346427637547 / 40000000000000000 : ℝ) ≤ (-(4301159679979176426909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26017346427637547 / 40000000000000000 : ℝ) = - (26017346427637547 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26017346427637547 / 20000000000000000 : ℚ)) - (U := (2630312123020823573091 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26017346427637547 / 20000000000000000 : ℝ) ≤ - (2630312123020823573091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6484399865002211 / 10000000000000000 : ℝ)) (q := - (26017346427637547 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26017346427637547 / 40000000000000000 : ℚ)) + (r' := (26017346427637547 / 20000000000000000 : ℚ)) + (U := (-(4301159679979176426909 / 10000000000000000000000 : ℚ))) + (U' := (2630312123020823573091 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (6484399865002211 / 10000000000000000 : ℚ)) + (q := (26017346427637547 / 40000000000000000 : ℚ)) + (U := (-(4301159679979176426909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_8 : Uω (aρ 8) (bρ 8) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3593,25 +3108,21 @@ lemma U_623_8 : have hlg : Real.log (24800193295944771 / 40000000000000000 : ℝ) ≤ (-(4780280065221076428117 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24800193295944771 / 40000000000000000 : ℝ) = - (24800193295944771 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24800193295944771 / 20000000000000000 : ℚ)) - (U := (2151191737778923571883 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24800193295944771 / 20000000000000000 : ℝ) ≤ - (2151191737778923571883 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6159364950495823 / 10000000000000000 : ℝ)) (q := - (24800193295944771 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24800193295944771 / 40000000000000000 : ℚ)) + (r' := (24800193295944771 / 20000000000000000 : ℚ)) + (U := (-(4780280065221076428117 / 10000000000000000000000 : ℚ))) + (U' := (2151191737778923571883 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (6159364950495823 / 10000000000000000 : ℚ)) + (q := (24800193295944771 / 40000000000000000 : ℚ)) + (U := (-(4780280065221076428117 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_9 : Uω (aρ 9) (bρ 9) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3619,25 +3130,21 @@ lemma U_623_9 : have hlg : Real.log (23287922932024447 / 40000000000000000 : ℝ) ≤ (-(5409445567589630971793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23287922932024447 / 40000000000000000 : ℝ) = - (23287922932024447 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23287922932024447 / 20000000000000000 : ℚ)) - (U := (1522026235410369028207 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23287922932024447 / 20000000000000000 : ℝ) ≤ - (1522026235410369028207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5744195396895661 / 10000000000000000 : ℝ)) (q := - (23287922932024447 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23287922932024447 / 40000000000000000 : ℚ)) + (r' := (23287922932024447 / 20000000000000000 : ℚ)) + (U := (-(5409445567589630971793 / 10000000000000000000000 : ℚ))) + (U' := (1522026235410369028207 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (5744195396895661 / 10000000000000000 : ℚ)) + (q := (23287922932024447 / 40000000000000000 : ℚ)) + (U := (-(5409445567589630971793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_10 : Uω (aρ 10) (bρ 10) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3645,26 +3152,21 @@ lemma U_623_10 : have hlg : Real.log (4296904865352947 / 8000000000000000 : ℝ) ≤ (-(6215465766550052784111 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4296904865352947 / 8000000000000000 : ℝ) = - (4296904865352947 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4296904865352947 / 4000000000000000 : ℚ)) - (U := (716006036449947215889 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4296904865352947 / 4000000000000000 : ℝ) ≤ - (716006036449947215889 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1046211025552161 / 2000000000000000 : ℝ)) (q := - (4296904865352947 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4296904865352947 / 8000000000000000 : ℚ)) + (r' := (4296904865352947 / 4000000000000000 : ℚ)) + (U := (-(6215465766550052784111 / 10000000000000000000000 : ℚ))) + (U' := (716006036449947215889 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (1046211025552161 / 2000000000000000 : ℚ)) + (q := (4296904865352947 / 8000000000000000 : ℚ)) + (U := (-(6215465766550052784111 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_11 : Uω (aρ 11) (bρ 11) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3672,26 +3174,21 @@ lemma U_623_11 : have hlg : Real.log (3883101677135997 / 8000000000000000 : ℝ) ≤ (-(903509131940136337699 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3883101677135997 / 8000000000000000 : ℝ) = - (3883101677135997 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3883101677135997 / 2000000000000000 : ℚ)) - (U := (829358818809863662301 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3883101677135997 / 2000000000000000 : ℝ) ≤ - (829358818809863662301 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (461502378342343 / 1000000000000000 : ℝ)) (q := - (3883101677135997 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3883101677135997 / 8000000000000000 : ℚ)) + (r' := (3883101677135997 / 2000000000000000 : ℚ)) + (U := (-(903509131940136337699 / 1250000000000000000000 : ℚ))) + (U' := (829358818809863662301 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (461502378342343 / 1000000000000000 : ℚ)) + (q := (3883101677135997 / 8000000000000000 : ℚ)) + (U := (-(903509131940136337699 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_12 : Uω (aρ 12) (bρ 12) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3699,26 +3196,21 @@ lemma U_623_12 : have hlg : Real.log (17124517021946789 / 40000000000000000 : ℝ) ≤ (-(848368272941469264369 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17124517021946789 / 40000000000000000 : ℝ) = - (17124517021946789 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17124517021946789 / 10000000000000000 : ℚ)) - (U := (537926087658530735631 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17124517021946789 / 10000000000000000 : ℝ) ≤ - (537926087658530735631 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (486653524780229 / 1250000000000000 : ℝ)) (q := - (17124517021946789 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17124517021946789 / 40000000000000000 : ℚ)) + (r' := (17124517021946789 / 10000000000000000 : ℚ)) + (U := (-(848368272941469264369 / 1000000000000000000000 : ℚ))) + (U' := (537926087658530735631 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (486653524780229 / 1250000000000000 : ℚ)) + (q := (17124517021946789 / 40000000000000000 : ℚ)) + (U := (-(848368272941469264369 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_13 : Uω (aρ 13) (bρ 13) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3726,26 +3218,21 @@ lemma U_623_13 : have hlg : Real.log (14660889249224863 / 40000000000000000 : ℝ) ≤ (-(5018480503871485516127 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14660889249224863 / 40000000000000000 : ℝ) = - (14660889249224863 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14660889249224863 / 10000000000000000 : ℚ)) - (U := (1912991299128514483873 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14660889249224863 / 10000000000000000 : ℝ) ≤ - (1912991299128514483873 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3060796053475869 / 10000000000000000 : ℝ)) (q := - (14660889249224863 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14660889249224863 / 40000000000000000 : ℚ)) + (r' := (14660889249224863 / 10000000000000000 : ℚ)) + (U := (-(5018480503871485516127 / 5000000000000000000000 : ℚ))) + (U' := (1912991299128514483873 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (3060796053475869 / 10000000000000000 : ℚ)) + (q := (14660889249224863 / 40000000000000000 : ℚ)) + (U := (-(5018480503871485516127 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_14 : Uω (aρ 14) (bρ 14) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3753,26 +3240,21 @@ lemma U_623_14 : have hlg : Real.log (12038797245736077 / 40000000000000000 : ℝ) ≤ (-(12007449152369101586589 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12038797245736077 / 40000000000000000 : ℝ) = - (12038797245736077 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12038797245736077 / 10000000000000000 : ℚ)) - (U := (1855494453630898413411 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12038797245736077 / 10000000000000000 : ℝ) ≤ - (1855494453630898413411 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (523419334194119 / 2500000000000000 : ℝ)) (q := - (12038797245736077 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12038797245736077 / 40000000000000000 : ℚ)) + (r' := (12038797245736077 / 10000000000000000 : ℚ)) + (U := (-(12007449152369101586589 / 10000000000000000000000 : ℚ))) + (U' := (1855494453630898413411 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (523419334194119 / 2500000000000000 : ℚ)) + (q := (12038797245736077 / 40000000000000000 : ℚ)) + (U := (-(12007449152369101586589 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_15 : Uω (aρ 15) (bρ 15) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3780,26 +3262,21 @@ lemma U_623_15 : have hlg : Real.log (8908552611326413 / 40000000000000000 : ℝ) ≤ (-(15018676704649794032253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (8908552611326413 / 40000000000000000 : ℝ) = - (8908552611326413 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8908552611326413 / 5000000000000000 : ℚ)) - (U := (5775738704350205967747 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (8908552611326413 / 5000000000000000 : ℝ) ≤ - (5775738704350205967747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (197032074246661 / 2500000000000000 : ℝ)) (q := - (8908552611326413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8908552611326413 / 40000000000000000 : ℚ)) + (r' := (8908552611326413 / 5000000000000000 : ℚ)) + (U := (-(15018676704649794032253 / 10000000000000000000000 : ℚ))) + (U' := (5775738704350205967747 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23191428934597 / 32000000000000 : ℚ)) + (s := (197032074246661 / 2500000000000000 : ℚ)) + (q := (8908552611326413 / 40000000000000000 : ℚ)) + (U := (-(15018676704649794032253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_623_16 : Uω (aρ 16) (bρ 16) (23191428934597 / 32000000000000 : ℝ) ≤ @@ -3896,25 +3373,21 @@ lemma U_624_1 : have hlg : Real.log (719232582069469 / 1000000000000000 : ℝ) ≤ (-(3295704933797769085771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (719232582069469 / 1000000000000000 : ℝ) = - (719232582069469 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (719232582069469 / 500000000000000 : ℚ)) - (U := (3635766869202230914229 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (719232582069469 / 500000000000000 : ℝ) ≤ - (3635766869202230914229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1438460668572751 / 2000000000000000 : ℝ)) (q := - (719232582069469 / 1000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (719232582069469 / 1000000000000000 : ℚ)) + (r' := (719232582069469 / 500000000000000 : ℚ)) + (U := (-(3295704933797769085771 / 10000000000000000000000 : ℚ))) + (U' := (3635766869202230914229 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (1438460668572751 / 2000000000000000 : ℚ)) + (q := (719232582069469 / 1000000000000000 : ℚ)) + (U := (-(3295704933797769085771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_2 : Uω (aρ 2) (bρ 2) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -3922,25 +3395,21 @@ lemma U_624_2 : have hlg : Real.log (716843128613503 / 1000000000000000 : ℝ) ≤ (-(665796501209805653239 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (716843128613503 / 1000000000000000 : ℝ) = - (716843128613503 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (716843128613503 / 500000000000000 : ℚ)) - (U := (720497859390194346761 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (716843128613503 / 500000000000000 : ℝ) ≤ - (720497859390194346761 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1433656657250887 / 2000000000000000 : ℝ)) (q := - (716843128613503 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (716843128613503 / 1000000000000000 : ℚ)) + (r' := (716843128613503 / 500000000000000 : ℚ)) + (U := (-(665796501209805653239 / 2000000000000000000000 : ℚ))) + (U' := (720497859390194346761 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (1433656657250887 / 2000000000000000 : ℚ)) + (q := (716843128613503 / 1000000000000000 : ℚ)) + (U := (-(665796501209805653239 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_3 : Uω (aρ 3) (bρ 3) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -3948,25 +3417,21 @@ lemma U_624_3 : have hlg : Real.log (7120663699973947 / 10000000000000000 : ℝ) ≤ (-(3395841553661085159127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7120663699973947 / 10000000000000000 : ℝ) = - (7120663699973947 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7120663699973947 / 5000000000000000 : ℚ)) - (U := (3535630249338914840873 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7120663699973947 / 5000000000000000 : ℝ) ≤ - (3535630249338914840873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7120144220282269 / 10000000000000000 : ℝ)) (q := - (7120663699973947 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7120663699973947 / 10000000000000000 : ℚ)) + (r' := (7120663699973947 / 5000000000000000 : ℚ)) + (U := (-(3395841553661085159127 / 10000000000000000000000 : ℚ))) + (U' := (3535630249338914840873 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (7120144220282269 / 10000000000000000 : ℚ)) + (q := (7120663699973947 / 10000000000000000 : ℚ)) + (U := (-(3395841553661085159127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_4 : Uω (aρ 4) (bρ 4) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -3974,25 +3439,21 @@ lemma U_624_4 : have hlg : Real.log (14082789802503379 / 20000000000000000 : ℝ) ≤ (-(3507788028088219534127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14082789802503379 / 20000000000000000 : ℝ) = - (14082789802503379 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14082789802503379 / 10000000000000000 : ℚ)) - (U := (3423683774911780465873 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14082789802503379 / 10000000000000000 : ℝ) ≤ - (3423683774911780465873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3519950401951377 / 5000000000000000 : ℝ)) (q := - (14082789802503379 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14082789802503379 / 20000000000000000 : ℚ)) + (r' := (14082789802503379 / 10000000000000000 : ℚ)) + (U := (-(3507788028088219534127 / 10000000000000000000000 : ℚ))) + (U' := (3423683774911780465873 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (3519950401951377 / 5000000000000000 : ℚ)) + (q := (14082789802503379 / 20000000000000000 : ℚ)) + (U := (-(3507788028088219534127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_5 : Uω (aρ 5) (bρ 5) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4000,25 +3461,21 @@ lemma U_624_5 : have hlg : Real.log (6920851512263107 / 10000000000000000 : ℝ) ≤ (-(3680462797695905282609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6920851512263107 / 10000000000000000 : ℝ) = - (6920851512263107 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6920851512263107 / 5000000000000000 : ℚ)) - (U := (3251009005304094717391 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6920851512263107 / 5000000000000000 : ℝ) ≤ - (3251009005304094717391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6917003945260589 / 10000000000000000 : ℝ)) (q := - (6920851512263107 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6920851512263107 / 10000000000000000 : ℚ)) + (r' := (6920851512263107 / 5000000000000000 : ℚ)) + (U := (-(3680462797695905282609 / 10000000000000000000000 : ℚ))) + (U' := (3251009005304094717391 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (6917003945260589 / 10000000000000000 : ℚ)) + (q := (6920851512263107 / 10000000000000000 : ℚ)) + (U := (-(3680462797695905282609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_6 : Uω (aρ 6) (bρ 6) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4026,25 +3483,21 @@ lemma U_624_6 : have hlg : Real.log (6748365965551843 / 10000000000000000 : ℝ) ≤ (-(1966423481665302052459 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6748365965551843 / 10000000000000000 : ℝ) = - (6748365965551843 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6748365965551843 / 5000000000000000 : ℚ)) - (U := (1499312419834697947541 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6748365965551843 / 5000000000000000 : ℝ) ≤ - (1499312419834697947541 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6739273226978061 / 10000000000000000 : ℝ)) (q := - (6748365965551843 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6748365965551843 / 10000000000000000 : ℚ)) + (r' := (6748365965551843 / 5000000000000000 : ℚ)) + (U := (-(1966423481665302052459 / 5000000000000000000000 : ℚ))) + (U' := (1499312419834697947541 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (6739273226978061 / 10000000000000000 : ℚ)) + (q := (6748365965551843 / 10000000000000000 : ℚ)) + (U := (-(1966423481665302052459 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_7 : Uω (aρ 7) (bρ 7) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4052,25 +3505,21 @@ lemma U_624_7 : have hlg : Real.log (2605555928203611 / 4000000000000000 : ℝ) ≤ (-(2143241501416554488787 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2605555928203611 / 4000000000000000 : ℝ) = - (2605555928203611 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2605555928203611 / 2000000000000000 : ℚ)) - (U := (1322494400083445511213 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2605555928203611 / 2000000000000000 : ℝ) ≤ - (1322494400083445511213 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (649398231765243 / 1000000000000000 : ℝ)) (q := - (2605555928203611 / 4000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2605555928203611 / 4000000000000000 : ℚ)) + (r' := (2605555928203611 / 2000000000000000 : ℚ)) + (U := (-(2143241501416554488787 / 5000000000000000000000 : ℚ))) + (U' := (1322494400083445511213 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (649398231765243 / 1000000000000000 : ℚ)) + (q := (2605555928203611 / 4000000000000000 : ℚ)) + (U := (-(2143241501416554488787 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_8 : Uω (aρ 8) (bρ 8) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4078,25 +3527,21 @@ lemma U_624_8 : have hlg : Real.log (12419270215629507 / 20000000000000000 : ℝ) ≤ (-(4764829573210770707701 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12419270215629507 / 20000000000000000 : ℝ) = - (12419270215629507 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12419270215629507 / 10000000000000000 : ℚ)) - (U := (2166642229789229292299 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12419270215629507 / 10000000000000000 : ℝ) ≤ - (2166642229789229292299 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3084507271801941 / 5000000000000000 : ℝ)) (q := - (12419270215629507 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12419270215629507 / 20000000000000000 : ℚ)) + (r' := (12419270215629507 / 10000000000000000 : ℚ)) + (U := (-(4764829573210770707701 / 10000000000000000000000 : ℚ))) + (U' := (2166642229789229292299 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (3084507271801941 / 5000000000000000 : ℚ)) + (q := (12419270215629507 / 20000000000000000 : ℚ)) + (U := (-(4764829573210770707701 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_9 : Uω (aρ 9) (bρ 9) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4104,25 +3549,21 @@ lemma U_624_9 : have hlg : Real.log (5831633460616669 / 10000000000000000 : ℝ) ≤ (-(5392879496913676081697 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5831633460616669 / 10000000000000000 : ℝ) = - (5831633460616669 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5831633460616669 / 5000000000000000 : ℚ)) - (U := (1538592306086323918303 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5831633460616669 / 5000000000000000 : ℝ) ≤ - (1538592306086323918303 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5753976877567713 / 10000000000000000 : ℝ)) (q := - (5831633460616669 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5831633460616669 / 10000000000000000 : ℚ)) + (r' := (5831633460616669 / 5000000000000000 : ℚ)) + (U := (-(5392879496913676081697 / 10000000000000000000000 : ℚ))) + (U' := (1538592306086323918303 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (5753976877567713 / 10000000000000000 : ℚ)) + (q := (5831633460616669 / 10000000000000000 : ℚ)) + (U := (-(5392879496913676081697 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_10 : Uω (aρ 10) (bρ 10) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4130,26 +3571,21 @@ lemma U_624_10 : have hlg : Real.log (2690454805563697 / 5000000000000000 : ℝ) ≤ (-(1549319150378315990693 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2690454805563697 / 5000000000000000 : ℝ) = - (2690454805563697 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2690454805563697 / 2500000000000000 : ℚ)) - (U := (183548800371684009307 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2690454805563697 / 2500000000000000 : ℝ) ≤ - (183548800371684009307 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5241088212084163 / 10000000000000000 : ℝ)) (q := - (2690454805563697 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2690454805563697 / 5000000000000000 : ℚ)) + (r' := (2690454805563697 / 2500000000000000 : ℚ)) + (U := (-(1549319150378315990693 / 2500000000000000000000 : ℚ))) + (U' := (183548800371684009307 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (5241088212084163 / 10000000000000000 : ℚ)) + (q := (2690454805563697 / 5000000000000000 : ℚ)) + (U := (-(1549319150378315990693 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_11 : Uω (aρ 11) (bρ 11) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4157,26 +3593,21 @@ lemma U_624_11 : have hlg : Real.log (9727785845026523 / 20000000000000000 : ℝ) ≤ (-(7207459623385319839303 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9727785845026523 / 20000000000000000 : ℝ) = - (9727785845026523 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9727785845026523 / 5000000000000000 : ℚ)) - (U := (6655483982614680160697 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9727785845026523 / 5000000000000000 : ℝ) ≤ - (6655483982614680160697 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2312765730530449 / 5000000000000000 : ℝ)) (q := - (9727785845026523 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9727785845026523 / 20000000000000000 : ℚ)) + (r' := (9727785845026523 / 5000000000000000 : ℚ)) + (U := (-(7207459623385319839303 / 10000000000000000000000 : ℚ))) + (U' := (6655483982614680160697 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (2312765730530449 / 5000000000000000 : ℚ)) + (q := (9727785845026523 / 20000000000000000 : ℚ)) + (U := (-(7207459623385319839303 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_12 : Uω (aρ 12) (bρ 12) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4184,26 +3615,21 @@ lemma U_624_12 : have hlg : Real.log (8583199208577703 / 20000000000000000 : ℝ) ≤ (-(1691851121799353991287 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8583199208577703 / 20000000000000000 : ℝ) = - (8583199208577703 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8583199208577703 / 5000000000000000 : ℚ)) - (U := (1080737599400646008713 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8583199208577703 / 5000000000000000 : ℝ) ≤ - (1080737599400646008713 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1952322460648539 / 5000000000000000 : ℝ)) (q := - (8583199208577703 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8583199208577703 / 20000000000000000 : ℚ)) + (r' := (8583199208577703 / 5000000000000000 : ℚ)) + (U := (-(1691851121799353991287 / 2000000000000000000000 : ℚ))) + (U' := (1080737599400646008713 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (1952322460648539 / 5000000000000000 : ℚ)) + (q := (8583199208577703 / 20000000000000000 : ℚ)) + (U := (-(1691851121799353991287 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_13 : Uω (aρ 13) (bρ 13) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4211,26 +3637,21 @@ lemma U_624_13 : have hlg : Real.log (1838310021227563 / 5000000000000000 : ℝ) ≤ (-(2501478072666182089101 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1838310021227563 / 5000000000000000 : ℝ) = - (1838310021227563 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1838310021227563 / 1250000000000000 : ℚ)) - (U := (964257828833817910899 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1838310021227563 / 1250000000000000 : ℝ) ≤ - (964257828833817910899 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3074067539224627 / 10000000000000000 : ℝ)) (q := - (1838310021227563 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1838310021227563 / 5000000000000000 : ℚ)) + (r' := (1838310021227563 / 1250000000000000 : ℚ)) + (U := (-(2501478072666182089101 / 2500000000000000000000 : ℚ))) + (U' := (964257828833817910899 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (3074067539224627 / 10000000000000000 : ℚ)) + (q := (1838310021227563 / 5000000000000000 : ℚ)) + (U := (-(2501478072666182089101 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_14 : Uω (aρ 14) (bρ 14) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4238,26 +3659,21 @@ lemma U_624_14 : have hlg : Real.log (6046726360687117 / 20000000000000000 : ℝ) ≤ (-(11962152448444704526753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6046726360687117 / 20000000000000000 : ℝ) = - (6046726360687117 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6046726360687117 / 5000000000000000 : ℚ)) - (U := (1900791157555295473247 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6046726360687117 / 5000000000000000 : ℝ) ≤ - (1900791157555295473247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (527870275011623 / 2500000000000000 : ℝ)) (q := - (6046726360687117 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6046726360687117 / 20000000000000000 : ℚ)) + (r' := (6046726360687117 / 5000000000000000 : ℚ)) + (U := (-(11962152448444704526753 / 10000000000000000000000 : ℚ))) + (U' := (1900791157555295473247 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (527870275011623 / 2500000000000000 : ℚ)) + (q := (6046726360687117 / 20000000000000000 : ℚ)) + (U := (-(11962152448444704526753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_15 : Uω (aρ 15) (bρ 15) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4265,26 +3681,21 @@ lemma U_624_15 : have hlg : Real.log (4506977895184479 / 20000000000000000 : ℝ) ≤ (-(14901054336295950917693 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4506977895184479 / 20000000000000000 : ℝ) = - (4506977895184479 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4506977895184479 / 2500000000000000 : ℚ)) - (U := (5893361072704049082307 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4506977895184479 / 2500000000000000 : ℝ) ≤ - (5893361072704049082307 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (415652955979427 / 5000000000000000 : ℝ)) (q := - (4506977895184479 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4506977895184479 / 20000000000000000 : ℚ)) + (r' := (4506977895184479 / 2500000000000000 : ℚ)) + (U := (-(14901054336295950917693 / 10000000000000000000000 : ℚ))) + (U' := (5893361072704049082307 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11610952826577 / 16000000000000 : ℚ)) + (s := (415652955979427 / 5000000000000000 : ℚ)) + (q := (4506977895184479 / 20000000000000000 : ℚ)) + (U := (-(14901054336295950917693 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_624_16 : Uω (aρ 16) (bρ 16) (11610952826577 / 16000000000000 : ℝ) ≤ @@ -4382,25 +3793,21 @@ lemma U_625_1 : have hlg : Real.log (5761479859975443 / 8000000000000000 : ℝ) ≤ (-(3282471795757911769263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5761479859975443 / 8000000000000000 : ℝ) = - (5761479859975443 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5761479859975443 / 4000000000000000 : ℚ)) - (U := (3649000007242088230737 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5761479859975443 / 4000000000000000 : ℝ) ≤ - (3649000007242088230737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (90022842210799 / 125000000000000 : ℝ)) (q := - (5761479859975443 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5761479859975443 / 8000000000000000 : ℚ)) + (r' := (5761479859975443 / 4000000000000000 : ℚ)) + (U := (-(3282471795757911769263 / 10000000000000000000000 : ℚ))) + (U' := (3649000007242088230737 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (90022842210799 / 125000000000000 : ℚ)) + (q := (5761479859975443 / 8000000000000000 : ℚ)) + (U := (-(3282471795757911769263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_2 : Uω (aρ 2) (bρ 2) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4408,25 +3815,21 @@ lemma U_625_2 : have hlg : Real.log (5742364365647849 / 8000000000000000 : ℝ) ≤ (-(1657852527543002467351 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5742364365647849 / 8000000000000000 : ℝ) = - (5742364365647849 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5742364365647849 / 4000000000000000 : ℚ)) - (U := (1807883373956997532649 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5742364365647849 / 4000000000000000 : ℝ) ≤ - (1807883373956997532649 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1435561530710987 / 2000000000000000 : ℝ)) (q := - (5742364365647849 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5742364365647849 / 8000000000000000 : ℚ)) + (r' := (5742364365647849 / 4000000000000000 : ℚ)) + (U := (-(1657852527543002467351 / 5000000000000000000000 : ℚ))) + (U' := (1807883373956997532649 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (1435561530710987 / 2000000000000000 : ℚ)) + (q := (5742364365647849 / 8000000000000000 : ℚ)) + (U := (-(1657852527543002467351 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_3 : Uω (aρ 3) (bρ 3) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4434,25 +3837,21 @@ lemma U_625_3 : have hlg : Real.log (28520753473823387 / 40000000000000000 : ℝ) ≤ (-(845618598796519162513 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28520753473823387 / 40000000000000000 : ℝ) = - (28520753473823387 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28520753473823387 / 20000000000000000 : ℚ)) - (U := (887249351953480837487 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28520753473823387 / 20000000000000000 : ℝ) ≤ - (887249351953480837487 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3564834791348503 / 5000000000000000 : ℝ)) (q := - (28520753473823387 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28520753473823387 / 40000000000000000 : ℚ)) + (r' := (28520753473823387 / 20000000000000000 : ℚ)) + (U := (-(845618598796519162513 / 2500000000000000000000 : ℚ))) + (U' := (887249351953480837487 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (3564834791348503 / 5000000000000000 : ℚ)) + (q := (28520753473823387 / 40000000000000000 : ℚ)) + (U := (-(845618598796519162513 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_4 : Uω (aρ 4) (bρ 4) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4460,25 +3859,21 @@ lemma U_625_4 : have hlg : Real.log (5640736715494749 / 8000000000000000 : ℝ) ≤ (-(3494268611257336033207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5640736715494749 / 8000000000000000 : ℝ) = - (5640736715494749 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5640736715494749 / 4000000000000000 : ℚ)) - (U := (3437203191742663966793 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5640736715494749 / 4000000000000000 : ℝ) ≤ - (3437203191742663966793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1409885763117437 / 2000000000000000 : ℝ)) (q := - (5640736715494749 / 8000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5640736715494749 / 8000000000000000 : ℚ)) + (r' := (5640736715494749 / 4000000000000000 : ℚ)) + (U := (-(3494268611257336033207 / 10000000000000000000000 : ℚ))) + (U' := (3437203191742663966793 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (1409885763117437 / 2000000000000000 : ℚ)) + (q := (5640736715494749 / 8000000000000000 : ℚ)) + (U := (-(3494268611257336033207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_5 : Uω (aρ 5) (bρ 5) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4486,25 +3881,21 @@ lemma U_625_5 : have hlg : Real.log (27721523108848051 / 40000000000000000 : ℝ) ≤ (-(458337918543920478139 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27721523108848051 / 40000000000000000 : ℝ) = - (27721523108848051 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27721523108848051 / 20000000000000000 : ℚ)) - (U := (408096056831079521861 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27721523108848051 / 20000000000000000 : ℝ) ≤ - (408096056831079521861 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3463269250304669 / 5000000000000000 : ℝ)) (q := - (27721523108848051 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27721523108848051 / 40000000000000000 : ℚ)) + (r' := (27721523108848051 / 20000000000000000 : ℚ)) + (U := (-(458337918543920478139 / 1250000000000000000000 : ℚ))) + (U' := (408096056831079521861 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (3463269250304669 / 5000000000000000 : ℚ)) + (q := (27721523108848051 / 40000000000000000 : ℚ)) + (U := (-(458337918543920478139 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_6 : Uω (aρ 6) (bρ 6) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4512,25 +3903,21 @@ lemma U_625_6 : have hlg : Real.log (27031611087384427 / 40000000000000000 : ℝ) ≤ (-(3918724916650439724693 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27031611087384427 / 40000000000000000 : ℝ) = - (27031611087384427 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27031611087384427 / 20000000000000000 : ℚ)) - (U := (3012746886349560275307 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27031611087384427 / 20000000000000000 : ℝ) ≤ - (3012746886349560275307 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3374411432508763 / 5000000000000000 : ℝ)) (q := - (27031611087384427 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27031611087384427 / 40000000000000000 : ℚ)) + (r' := (27031611087384427 / 20000000000000000 : ℚ)) + (U := (-(3918724916650439724693 / 10000000000000000000000 : ℚ))) + (U' := (3012746886349560275307 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (3374411432508763 / 5000000000000000 : ℚ)) + (q := (27031611087384427 / 40000000000000000 : ℚ)) + (U := (-(3918724916650439724693 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_7 : Uω (aρ 7) (bρ 7) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4538,25 +3925,21 @@ lemma U_625_7 : have hlg : Real.log (5218754358567231 / 8000000000000000 : ℝ) ≤ (-(4271827966286515829487 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5218754358567231 / 8000000000000000 : ℝ) = - (5218754358567231 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5218754358567231 / 4000000000000000 : ℚ)) - (U := (2659643836713484170513 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5218754358567231 / 4000000000000000 : ℝ) ≤ - (2659643836713484170513 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (650356459850339 / 1000000000000000 : ℝ)) (q := - (5218754358567231 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5218754358567231 / 8000000000000000 : ℚ)) + (r' := (5218754358567231 / 4000000000000000 : ℚ)) + (U := (-(4271827966286515829487 / 10000000000000000000000 : ℚ))) + (U' := (2659643836713484170513 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (650356459850339 / 1000000000000000 : ℚ)) + (q := (5218754358567231 / 8000000000000000 : ℚ)) + (U := (-(4271827966286515829487 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_8 : Uω (aρ 8) (bρ 8) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4564,25 +3947,21 @@ lemma U_625_8 : have hlg : Real.log (4975377357387353 / 8000000000000000 : ℝ) ≤ (-(2374701614773647720401 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4975377357387353 / 8000000000000000 : ℝ) = - (4975377357387353 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4975377357387353 / 4000000000000000 : ℚ)) - (U := (1091034286726352279599 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4975377357387353 / 4000000000000000 : ℝ) ≤ - (1091034286726352279599 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1235732749378739 / 2000000000000000 : ℝ)) (q := - (4975377357387353 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4975377357387353 / 8000000000000000 : ℚ)) + (r' := (4975377357387353 / 4000000000000000 : ℚ)) + (U := (-(2374701614773647720401 / 5000000000000000000000 : ℚ))) + (U' := (1091034286726352279599 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (1235732749378739 / 2000000000000000 : ℚ)) + (q := (4975377357387353 / 8000000000000000 : ℚ)) + (U := (-(2374701614773647720401 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_9 : Uω (aρ 9) (bρ 9) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4590,25 +3969,21 @@ lemma U_625_9 : have hlg : Real.log (23365143027897899 / 40000000000000000 : ℝ) ≤ (-(5376341562609795843151 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23365143027897899 / 40000000000000000 : ℝ) = - (23365143027897899 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23365143027897899 / 20000000000000000 : ℚ)) - (U := (1555130240390204156849 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23365143027897899 / 20000000000000000 : ℝ) ≤ - (1555130240390204156849 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2881878747867131 / 5000000000000000 : ℝ)) (q := - (23365143027897899 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23365143027897899 / 40000000000000000 : ℚ)) + (r' := (23365143027897899 / 20000000000000000 : ℚ)) + (U := (-(5376341562609795843151 / 10000000000000000000000 : ℚ))) + (U' := (1555130240390204156849 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (2881878747867131 / 5000000000000000 : ℚ)) + (q := (23365143027897899 / 40000000000000000 : ℚ)) + (U := (-(5376341562609795843151 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_10 : Uω (aρ 10) (bρ 10) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4616,26 +3991,21 @@ lemma U_625_10 : have hlg : Real.log (21562748770038979 / 40000000000000000 : ℝ) ≤ (-(6179122219677369954149 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21562748770038979 / 40000000000000000 : ℝ) = - (21562748770038979 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21562748770038979 / 20000000000000000 : ℚ)) - (U := (752349583322630045851 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21562748770038979 / 20000000000000000 : ℝ) ≤ - (752349583322630045851 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2625559700149901 / 5000000000000000 : ℝ)) (q := - (21562748770038979 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21562748770038979 / 40000000000000000 : ℚ)) + (r' := (21562748770038979 / 20000000000000000 : ℚ)) + (U := (-(6179122219677369954149 / 10000000000000000000000 : ℚ))) + (U' := (752349583322630045851 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (2625559700149901 / 5000000000000000 : ℚ)) + (q := (21562748770038979 / 40000000000000000 : ℚ)) + (U := (-(6179122219677369954149 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_11 : Uω (aρ 11) (bρ 11) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4643,26 +4013,21 @@ lemma U_625_11 : have hlg : Real.log (19495626493545693 / 40000000000000000 : ℝ) ≤ (-(7186892955616715097121 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19495626493545693 / 40000000000000000 : ℝ) = - (19495626493545693 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19495626493545693 / 10000000000000000 : ℚ)) - (U := (6676050650383284902879 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19495626493545693 / 10000000000000000 : ℝ) ≤ - (6676050650383284902879 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4636034888258159 / 10000000000000000 : ℝ)) (q := - (19495626493545693 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19495626493545693 / 40000000000000000 : ℚ)) + (r' := (19495626493545693 / 10000000000000000 : ℚ)) + (U := (-(7186892955616715097121 / 10000000000000000000000 : ℚ))) + (U' := (6676050650383284902879 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (4636034888258159 / 10000000000000000 : ℚ)) + (q := (19495626493545693 / 40000000000000000 : ℚ)) + (U := (-(7186892955616715097121 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_12 : Uω (aρ 12) (bρ 12) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4670,26 +4035,21 @@ lemma U_625_12 : have hlg : Real.log (17208259569819893 / 40000000000000000 : ℝ) ≤ (-(8434899774897159942441 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17208259569819893 / 40000000000000000 : ℝ) = - (17208259569819893 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17208259569819893 / 10000000000000000 : ℚ)) - (U := (5428043831102840057559 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17208259569819893 / 10000000000000000 : ℝ) ≤ - (5428043831102840057559 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3916051523080259 / 10000000000000000 : ℝ)) (q := - (17208259569819893 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17208259569819893 / 40000000000000000 : ℚ)) + (r' := (17208259569819893 / 10000000000000000 : ℚ)) + (U := (-(8434899774897159942441 / 10000000000000000000000 : ℚ))) + (U' := (5428043831102840057559 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (3916051523080259 / 10000000000000000 : ℚ)) + (q := (17208259569819893 / 40000000000000000 : ℚ)) + (U := (-(8434899774897159942441 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_13 : Uω (aρ 13) (bρ 13) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4697,26 +4057,21 @@ lemma U_625_13 : have hlg : Real.log (14752015750445453 / 40000000000000000 : ℝ) ≤ (-(2493749297745844288991 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14752015750445453 / 40000000000000000 : ℝ) = - (14752015750445453 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14752015750445453 / 10000000000000000 : ℚ)) - (U := (971986603754155711009 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14752015750445453 / 10000000000000000 : ℝ) ≤ - (971986603754155711009 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3087311354988039 / 10000000000000000 : ℝ)) (q := - (14752015750445453 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14752015750445453 / 40000000000000000 : ℚ)) + (r' := (14752015750445453 / 10000000000000000 : ℚ)) + (U := (-(2493749297745844288991 / 2500000000000000000000 : ℚ))) + (U' := (971986603754155711009 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (3087311354988039 / 10000000000000000 : ℚ)) + (q := (14752015750445453 / 40000000000000000 : ℚ)) + (U := (-(2493749297745844288991 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_14 : Uω (aρ 14) (bρ 14) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4724,26 +4079,21 @@ lemma U_625_14 : have hlg : Real.log (2429579132447089 / 8000000000000000 : ℝ) ≤ (-(11917234953315698604143 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2429579132447089 / 8000000000000000 : ℝ) = - (2429579132447089 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2429579132447089 / 2000000000000000 : ℚ)) - (U := (1945708652684301395857 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2429579132447089 / 2000000000000000 : ℝ) ≤ - (1945708652684301395857 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (425835719185607 / 2000000000000000 : ℝ)) (q := - (2429579132447089 / 8000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2429579132447089 / 8000000000000000 : ℚ)) + (r' := (2429579132447089 / 2000000000000000 : ℚ)) + (U := (-(11917234953315698604143 / 10000000000000000000000 : ℚ))) + (U' := (1945708652684301395857 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (425835719185607 / 2000000000000000 : ℚ)) + (q := (2429579132447089 / 8000000000000000 : ℚ)) + (U := (-(11917234953315698604143 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_15 : Uω (aρ 15) (bρ 15) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4751,26 +4101,21 @@ lemma U_625_15 : have hlg : Real.log (9115297916670169 / 40000000000000000 : ℝ) ≤ (-(739462680758528667917 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9115297916670169 / 40000000000000000 : ℝ) = - (9115297916670169 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9115297916670169 / 5000000000000000 : ℚ)) - (U := (300258089691471332083 / 500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9115297916670169 / 5000000000000000 : ℝ) ≤ - (300258089691471332083 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (872453000560397 / 10000000000000000 : ℝ)) (q := - (9115297916670169 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9115297916670169 / 40000000000000000 : ℚ)) + (r' := (9115297916670169 / 5000000000000000 : ℚ)) + (U := (-(739462680758528667917 / 500000000000000000000 : ℚ))) + (U' := (300258089691471332083 / 500000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23252382371711 / 32000000000000 : ℚ)) + (s := (872453000560397 / 10000000000000000 : ℚ)) + (q := (9115297916670169 / 40000000000000000 : ℚ)) + (U := (-(739462680758528667917 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_625_16 : Uω (aρ 16) (bρ 16) (23252382371711 / 32000000000000 : ℝ) ≤ @@ -4867,25 +4212,21 @@ lemma U_626_1 : have hlg : Real.log (7211373829165401 / 10000000000000000 : ℝ) ≤ (-(3269256146281007372917 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7211373829165401 / 10000000000000000 : ℝ) = - (7211373829165401 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7211373829165401 / 5000000000000000 : ℚ)) - (U := (3662215656718992627083 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7211373829165401 / 5000000000000000 : ℝ) ≤ - (3662215656718992627083 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1802837852676763 / 2500000000000000 : ℝ)) (q := - (7211373829165401 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7211373829165401 / 10000000000000000 : ℚ)) + (r' := (7211373829165401 / 5000000000000000 : ℚ)) + (U := (-(3269256146281007372917 / 10000000000000000000000 : ℚ))) + (U' := (3662215656718992627083 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (1802837852676763 / 2500000000000000 : ℚ)) + (q := (7211373829165401 / 10000000000000000 : ℚ)) + (U := (-(3269256146281007372917 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_2 : Uω (aρ 2) (bρ 2) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -4893,25 +4234,21 @@ lemma U_626_2 : have hlg : Real.log (449217476716509 / 625000000000000 : ℝ) ≤ (-(3302445210544198461269 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (449217476716509 / 625000000000000 : ℝ) = - (449217476716509 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (449217476716509 / 312500000000000 : ℚ)) - (U := (3629026592455801538731 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (449217476716509 / 312500000000000 : ℝ) ≤ - (3629026592455801538731 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3593666009907269 / 5000000000000000 : ℝ)) (q := - (449217476716509 / 625000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (449217476716509 / 625000000000000 : ℚ)) + (r' := (449217476716509 / 312500000000000 : ℚ)) + (U := (-(3302445210544198461269 / 10000000000000000000000 : ℚ))) + (U' := (3629026592455801538731 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (3593666009907269 / 5000000000000000 : ℚ)) + (q := (449217476716509 / 625000000000000 : ℚ)) + (U := (-(3302445210544198461269 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_3 : Uω (aρ 3) (bρ 3) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -4919,25 +4256,21 @@ lemma U_626_3 : have hlg : Real.log (7139713035086143 / 10000000000000000 : ℝ) ≤ (-(842281270886748966641 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7139713035086143 / 10000000000000000 : ℝ) = - (7139713035086143 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7139713035086143 / 5000000000000000 : ℚ)) - (U := (890586679863251033359 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7139713035086143 / 5000000000000000 : ℝ) ≤ - (890586679863251033359 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (892399367676067 / 1250000000000000 : ℝ)) (q := - (7139713035086143 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7139713035086143 / 10000000000000000 : ℚ)) + (r' := (7139713035086143 / 5000000000000000 : ℚ)) + (U := (-(842281270886748966641 / 2500000000000000000000 : ℚ))) + (U' := (890586679863251033359 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (892399367676067 / 1250000000000000 : ℚ)) + (q := (7139713035086143 / 10000000000000000 : ℚ)) + (U := (-(842281270886748966641 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_4 : Uω (aρ 4) (bρ 4) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -4945,25 +4278,21 @@ lemma U_626_4 : have hlg : Real.log (14120893764074217 / 20000000000000000 : ℝ) ≤ (-(3480767454931998022547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14120893764074217 / 20000000000000000 : ℝ) = - (14120893764074217 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14120893764074217 / 10000000000000000 : ℚ)) - (U := (3450704348068001977453 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14120893764074217 / 10000000000000000 : ℝ) ≤ - (3450704348068001977453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7058956816375467 / 10000000000000000 : ℝ)) (q := - (14120893764074217 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14120893764074217 / 20000000000000000 : ℚ)) + (r' := (14120893764074217 / 10000000000000000 : ℚ)) + (U := (-(3480767454931998022547 / 10000000000000000000000 : ℚ))) + (U' := (3450704348068001977453 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (7058956816375467 / 10000000000000000 : ℚ)) + (q := (14120893764074217 / 20000000000000000 : ℚ)) + (U := (-(3480767454931998022547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_5 : Uω (aρ 5) (bρ 5) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -4971,25 +4300,21 @@ lemma U_626_5 : have hlg : Real.log (13879820055248543 / 20000000000000000 : ℝ) ≤ (-(3652962826186939902803 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13879820055248543 / 20000000000000000 : ℝ) = - (13879820055248543 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13879820055248543 / 10000000000000000 : ℚ)) - (U := (3278508976813060097197 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13879820055248543 / 10000000000000000 : ℝ) ≤ - (3278508976813060097197 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6936073026884793 / 10000000000000000 : ℝ)) (q := - (13879820055248543 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13879820055248543 / 20000000000000000 : ℚ)) + (r' := (13879820055248543 / 10000000000000000 : ℚ)) + (U := (-(3652962826186939902803 / 10000000000000000000000 : ℚ))) + (U' := (3278508976813060097197 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (6936073026884793 / 10000000000000000 : ℚ)) + (q := (13879820055248543 / 20000000000000000 : ℚ)) + (U := (-(3652962826186939902803 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_6 : Uω (aρ 6) (bρ 6) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -4997,25 +4322,21 @@ lemma U_626_6 : have hlg : Real.log (1353487908385273 / 2000000000000000 : ℝ) ≤ (-(1952311419290875189301 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1353487908385273 / 2000000000000000 : ℝ) = - (1353487908385273 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1353487908385273 / 1000000000000000 : ℚ)) - (U := (1513424482209124810699 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1353487908385273 / 1000000000000000 : ℝ) ≤ - (1513424482209124810699 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (337918621531449 / 500000000000000 : ℝ)) (q := - (1353487908385273 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1353487908385273 / 2000000000000000 : ℚ)) + (r' := (1353487908385273 / 1000000000000000 : ℚ)) + (U := (-(1952311419290875189301 / 5000000000000000000000 : ℚ))) + (U' := (1513424482209124810699 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (337918621531449 / 500000000000000 : ℚ)) + (q := (1353487908385273 / 2000000000000000 : ℚ)) + (U := (-(1952311419290875189301 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_7 : Uω (aρ 7) (bρ 7) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5023,25 +4344,21 @@ lemma U_626_7 : have hlg : Real.log (3266497995194277 / 5000000000000000 : ℝ) ≤ (-(4257194506230267187757 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3266497995194277 / 5000000000000000 : ℝ) = - (3266497995194277 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3266497995194277 / 2500000000000000 : ℚ)) - (U := (2674277296769732812243 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3266497995194277 / 2500000000000000 : ℝ) ≤ - (2674277296769732812243 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3256573354156679 / 5000000000000000 : ℝ)) (q := - (3266497995194277 / 5000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3266497995194277 / 5000000000000000 : ℚ)) + (r' := (3266497995194277 / 2500000000000000 : ℚ)) + (U := (-(4257194506230267187757 / 10000000000000000000000 : ℚ))) + (U' := (2674277296769732812243 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (3256573354156679 / 5000000000000000 : ℚ)) + (q := (3266497995194277 / 5000000000000000 : ℚ)) + (U := (-(4257194506230267187757 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_8 : Uω (aρ 8) (bρ 8) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5049,25 +4366,21 @@ lemma U_626_8 : have hlg : Real.log (12457616183312499 / 20000000000000000 : ℝ) ≤ (-(4734000957894396568091 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12457616183312499 / 20000000000000000 : ℝ) = - (12457616183312499 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12457616183312499 / 10000000000000000 : ℚ)) - (U := (2197470845105603431909 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12457616183312499 / 10000000000000000 : ℝ) ≤ - (2197470845105603431909 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6188312562188749 / 10000000000000000 : ℝ)) (q := - (12457616183312499 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12457616183312499 / 20000000000000000 : ℚ)) + (r' := (12457616183312499 / 10000000000000000 : ℚ)) + (U := (-(4734000957894396568091 / 10000000000000000000000 : ℚ))) + (U' := (2197470845105603431909 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (6188312562188749 / 10000000000000000 : ℚ)) + (q := (12457616183312499 / 20000000000000000 : ℚ)) + (U := (-(4734000957894396568091 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_9 : Uω (aρ 9) (bρ 9) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5075,25 +4388,21 @@ lemma U_626_9 : have hlg : Real.log (11701875248542423 / 20000000000000000 : ℝ) ≤ (-(2679915833401137352107 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11701875248542423 / 20000000000000000 : ℝ) = - (11701875248542423 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11701875248542423 / 10000000000000000 : ℚ)) - (U := (785820068098862647893 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11701875248542423 / 10000000000000000 : ℝ) ≤ - (785820068098862647893 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5773537255778673 / 10000000000000000 : ℝ)) (q := - (11701875248542423 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11701875248542423 / 20000000000000000 : ℚ)) + (r' := (11701875248542423 / 10000000000000000 : ℚ)) + (U := (-(2679915833401137352107 / 5000000000000000000000 : ℚ))) + (U' := (785820068098862647893 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (5773537255778673 / 10000000000000000 : ℚ)) + (q := (11701875248542423 / 20000000000000000 : ℚ)) + (U := (-(2679915833401137352107 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_10 : Uω (aρ 10) (bρ 10) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5101,26 +4410,21 @@ lemma U_626_10 : have hlg : Real.log (10800927662522133 / 20000000000000000 : ℝ) ≤ (-(6161002481746330224137 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10800927662522133 / 20000000000000000 : ℝ) = - (10800927662522133 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10800927662522133 / 10000000000000000 : ℚ)) - (U := (770469321253669775863 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10800927662522133 / 10000000000000000 : ℝ) ≤ - (770469321253669775863 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5261148703253383 / 10000000000000000 : ℝ)) (q := - (10800927662522133 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10800927662522133 / 20000000000000000 : ℚ)) + (r' := (10800927662522133 / 10000000000000000 : ℚ)) + (U := (-(6161002481746330224137 / 10000000000000000000000 : ℚ))) + (U' := (770469321253669775863 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (5261148703253383 / 10000000000000000 : ℚ)) + (q := (10800927662522133 / 20000000000000000 : ℚ)) + (U := (-(6161002481746330224137 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_11 : Uω (aρ 11) (bρ 11) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5128,25 +4432,21 @@ lemma U_626_11 : have hlg : Real.log (195356728538063 / 400000000000000 : ℝ) ≤ (-(7166372821784453306367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (195356728538063 / 400000000000000 : ℝ) = - (195356728538063 / 100000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (195356728538063 / 100000000000000 : ℚ)) - (U := (6696570784215546693633 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (195356728538063 / 100000000000000 : ℝ) ≤ - (6696570784215546693633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23232670469197 / 50000000000000 : ℝ)) (q := - (195356728538063 / 400000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (195356728538063 / 400000000000000 : ℚ)) + (r' := (195356728538063 / 100000000000000 : ℚ)) + (U := (-(7166372821784453306367 / 10000000000000000000000 : ℚ))) + (U' := (6696570784215546693633 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (23232670469197 / 50000000000000 : ℚ)) + (q := (195356728538063 / 400000000000000 : ℚ)) + (U := (-(7166372821784453306367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_12 : Uω (aρ 12) (bρ 12) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5154,26 +4454,21 @@ lemma U_626_12 : have hlg : Real.log (8625050328156639 / 20000000000000000 : ℝ) ≤ (-(4205307374925527529399 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8625050328156639 / 20000000000000000 : ℝ) = - (8625050328156639 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8625050328156639 / 5000000000000000 : ℚ)) - (U := (2726164428074472470601 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8625050328156639 / 5000000000000000 : ℝ) ≤ - (2726164428074472470601 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3927448091777889 / 10000000000000000 : ℝ)) (q := - (8625050328156639 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8625050328156639 / 20000000000000000 : ℚ)) + (r' := (8625050328156639 / 5000000000000000 : ℚ)) + (U := (-(4205307374925527529399 / 5000000000000000000000 : ℚ))) + (U' := (2726164428074472470601 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (3927448091777889 / 10000000000000000 : ℚ)) + (q := (8625050328156639 / 20000000000000000 : ℚ)) + (U := (-(4205307374925527529399 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_13 : Uω (aρ 13) (bρ 13) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5181,26 +4476,21 @@ lemma U_626_13 : have hlg : Real.log (7398748350124519 / 20000000000000000 : ℝ) ≤ (-(497210714502570725607 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7398748350124519 / 20000000000000000 : ℝ) = - (7398748350124519 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7398748350124519 / 5000000000000000 : ℚ)) - (U := (195936465797429274393 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7398748350124519 / 5000000000000000 : ℝ) ≤ - (195936465797429274393 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3100527855340769 / 10000000000000000 : ℝ)) (q := - (7398748350124519 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7398748350124519 / 20000000000000000 : ℚ)) + (r' := (7398748350124519 / 5000000000000000 : ℚ)) + (U := (-(497210714502570725607 / 500000000000000000000 : ℚ))) + (U' := (195936465797429274393 / 500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (3100527855340769 / 10000000000000000 : ℚ)) + (q := (7398748350124519 / 20000000000000000 : ℚ)) + (U := (-(497210714502570725607 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_14 : Uω (aρ 14) (bρ 14) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5208,26 +4498,21 @@ lemma U_626_14 : have hlg : Real.log (6101065662292823 / 20000000000000000 : ℝ) ≤ (-(5936344091881768530959 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6101065662292823 / 20000000000000000 : ℝ) = - (6101065662292823 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6101065662292823 / 5000000000000000 : ℚ)) - (U := (995127711118231469041 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6101065662292823 / 5000000000000000 : ℝ) ≤ - (995127711118231469041 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2146772452554073 / 10000000000000000 : ℝ)) (q := - (6101065662292823 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6101065662292823 / 20000000000000000 : ℚ)) + (r' := (6101065662292823 / 5000000000000000 : ℚ)) + (U := (-(5936344091881768530959 / 5000000000000000000000 : ℚ))) + (U' := (995127711118231469041 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (2146772452554073 / 10000000000000000 : ℚ)) + (q := (6101065662292823 / 20000000000000000 : ℚ)) + (U := (-(5936344091881768530959 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_15 : Uω (aρ 15) (bρ 15) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5235,26 +4520,21 @@ lemma U_626_15 : have hlg : Real.log (2303282209888357 / 10000000000000000 : ℝ) ≤ (-(14682499387665634183519 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2303282209888357 / 10000000000000000 : ℝ) = - (2303282209888357 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2303282209888357 / 1250000000000000 : ℚ)) - (U := (6111916021334365816481 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (2303282209888357 / 1250000000000000 : ℝ) ≤ - (6111916021334365816481 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (227961121863241 / 2500000000000000 : ℝ)) (q := - (2303282209888357 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2303282209888357 / 10000000000000000 : ℚ)) + (r' := (2303282209888357 / 1250000000000000 : ℚ)) + (U := (-(14682499387665634183519 / 10000000000000000000000 : ℚ))) + (U' := (6111916021334365816481 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (5820714772567 / 8000000000000 : ℚ)) + (s := (227961121863241 / 2500000000000000 : ℚ)) + (q := (2303282209888357 / 10000000000000000 : ℚ)) + (U := (-(14682499387665634183519 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_626_16 : Uω (aρ 16) (bρ 16) (5820714772567 / 8000000000000 : ℝ) ≤ @@ -5351,25 +4631,21 @@ lemma U_627_1 : have hlg : Real.log (28883591333133169 / 40000000000000000 : ℝ) ≤ (-(3256057939202933221281 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28883591333133169 / 40000000000000000 : ℝ) = - (28883591333133169 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28883591333133169 / 20000000000000000 : ℚ)) - (U := (3675413863797066778719 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28883591333133169 / 20000000000000000 : ℝ) ≤ - (3675413863797066778719 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1805218861098443 / 2500000000000000 : ℝ)) (q := - (28883591333133169 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28883591333133169 / 40000000000000000 : ℚ)) + (r' := (28883591333133169 / 20000000000000000 : ℚ)) + (U := (-(3256057939202933221281 / 10000000000000000000000 : ℚ))) + (U' := (3675413863797066778719 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (1805218861098443 / 2500000000000000 : ℚ)) + (q := (28883591333133169 / 40000000000000000 : ℚ)) + (U := (-(3256057939202933221281 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_2 : Uω (aρ 2) (bρ 2) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5377,25 +4653,21 @@ lemma U_627_2 : have hlg : Real.log (28788015189400381 / 40000000000000000 : ℝ) ≤ (-(3289202925789912456111 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28788015189400381 / 40000000000000000 : ℝ) = - (28788015189400381 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28788015189400381 / 20000000000000000 : ℚ)) - (U := (3642268877210087543889 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28788015189400381 / 20000000000000000 : ℝ) ≤ - (3642268877210087543889 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3598428192518689 / 5000000000000000 : ℝ)) (q := - (28788015189400381 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28788015189400381 / 40000000000000000 : ℚ)) + (r' := (28788015189400381 / 20000000000000000 : ℚ)) + (U := (-(3289202925789912456111 / 10000000000000000000000 : ℚ))) + (U' := (3642268877210087543889 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (3598428192518689 / 5000000000000000 : ℚ)) + (q := (28788015189400381 / 40000000000000000 : ℚ)) + (U := (-(3289202925789912456111 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_3 : Uω (aρ 3) (bρ 3) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5403,25 +4675,21 @@ lemma U_627_3 : have hlg : Real.log (28596950799488947 / 40000000000000000 : ℝ) ≤ (-(671158714228988945661 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28596950799488947 / 40000000000000000 : ℝ) = - (28596950799488947 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28596950799488947 / 20000000000000000 : ℚ)) - (U := (715135646371011054339 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28596950799488947 / 20000000000000000 : ℝ) ≤ - (715135646371011054339 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7148720296431661 / 10000000000000000 : ℝ)) (q := - (28596950799488947 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28596950799488947 / 40000000000000000 : ℚ)) + (r' := (28596950799488947 / 20000000000000000 : ℚ)) + (U := (-(671158714228988945661 / 2000000000000000000000 : ℚ))) + (U' := (715135646371011054339 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (7148720296431661 / 10000000000000000 : ℚ)) + (q := (28596950799488947 / 40000000000000000 : ℚ)) + (U := (-(671158714228988945661 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_4 : Uω (aρ 4) (bρ 4) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5429,25 +4697,21 @@ lemma U_627_4 : have hlg : Real.log (28279891457118949 / 40000000000000000 : ℝ) ≤ (-(3467284509829511449131 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28279891457118949 / 40000000000000000 : ℝ) = - (28279891457118949 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28279891457118949 / 20000000000000000 : ℚ)) - (U := (3464187293170488550869 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28279891457118949 / 20000000000000000 : ℝ) ≤ - (3464187293170488550869 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3534242403155831 / 5000000000000000 : ℝ)) (q := - (28279891457118949 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28279891457118949 / 40000000000000000 : ℚ)) + (r' := (28279891457118949 / 20000000000000000 : ℚ)) + (U := (-(3467284509829511449131 / 10000000000000000000000 : ℚ))) + (U' := (3464187293170488550869 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (3534242403155831 / 5000000000000000 : ℚ)) + (q := (28279891457118949 / 40000000000000000 : ℚ)) + (U := (-(3467284509829511449131 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_5 : Uω (aρ 5) (bρ 5) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5455,25 +4719,21 @@ lemma U_627_5 : have hlg : Real.log (27797757054238993 / 40000000000000000 : ℝ) ≤ (-(1819620589572607906299 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27797757054238993 / 40000000000000000 : ℝ) = - (27797757054238993 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27797757054238993 / 20000000000000000 : ℚ)) - (U := (1646115311927392093701 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27797757054238993 / 20000000000000000 : ℝ) ≤ - (1646115311927392093701 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1736401881051671 / 2500000000000000 : ℝ)) (q := - (27797757054238993 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27797757054238993 / 40000000000000000 : ℚ)) + (r' := (27797757054238993 / 20000000000000000 : ℚ)) + (U := (-(1819620589572607906299 / 5000000000000000000000 : ℚ))) + (U' := (1646115311927392093701 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (1736401881051671 / 2500000000000000 : ℚ)) + (q := (27797757054238993 / 40000000000000000 : ℚ)) + (U := (-(1819620589572607906299 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_6 : Uω (aρ 6) (bρ 6) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5481,25 +4741,21 @@ lemma U_627_6 : have hlg : Real.log (27107905103783649 / 40000000000000000 : ℝ) ≤ (-(243158792036402207847 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27107905103783649 / 40000000000000000 : ℝ) = - (27107905103783649 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27107905103783649 / 20000000000000000 : ℚ)) - (U := (190058195651097792153 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27107905103783649 / 20000000000000000 : ℝ) ≤ - (190058195651097792153 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1691980481029753 / 2500000000000000 : ℝ)) (q := - (27107905103783649 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27107905103783649 / 40000000000000000 : ℚ)) + (r' := (27107905103783649 / 20000000000000000 : ℚ)) + (U := (-(243158792036402207847 / 625000000000000000000 : ℚ))) + (U' := (190058195651097792153 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (1691980481029753 / 2500000000000000 : ℚ)) + (q := (27107905103783649 / 40000000000000000 : ℚ)) + (U := (-(243158792036402207847 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_7 : Uω (aρ 7) (bρ 7) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5507,25 +4763,21 @@ lemma U_627_7 : have hlg : Real.log (26170195789697881 / 40000000000000000 : ℝ) ≤ (-(4242582558841379302559 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26170195789697881 / 40000000000000000 : ℝ) = - (26170195789697881 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26170195789697881 / 20000000000000000 : ℚ)) - (U := (2688889244158620697441 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26170195789697881 / 20000000000000000 : ℝ) ≤ - (2688889244158620697441 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (203835270244879 / 312500000000000 : ℝ)) (q := - (26170195789697881 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26170195789697881 / 40000000000000000 : ℚ)) + (r' := (26170195789697881 / 20000000000000000 : ℚ)) + (U := (-(4242582558841379302559 / 10000000000000000000000 : ℚ))) + (U' := (2688889244158620697441 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (203835270244879 / 312500000000000 : ℚ)) + (q := (26170195789697881 / 40000000000000000 : ℚ)) + (U := (-(4242582558841379302559 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_8 : Uω (aρ 8) (bρ 8) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5533,25 +4785,21 @@ lemma U_627_8 : have hlg : Real.log (24953577173947831 / 40000000000000000 : ℝ) ≤ (-(4718622682281668301957 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24953577173947831 / 40000000000000000 : ℝ) = - (24953577173947831 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24953577173947831 / 20000000000000000 : ℚ)) - (U := (2212849120718331698043 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24953577173947831 / 20000000000000000 : ℝ) ≤ - (2212849120718331698043 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6197960991301103 / 10000000000000000 : ℝ)) (q := - (24953577173947831 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24953577173947831 / 40000000000000000 : ℚ)) + (r' := (24953577173947831 / 20000000000000000 : ℚ)) + (U := (-(4718622682281668301957 / 10000000000000000000000 : ℚ))) + (U' := (2212849120718331698043 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (6197960991301103 / 10000000000000000 : ℚ)) + (q := (24953577173947831 / 40000000000000000 : ℚ)) + (U := (-(4718622682281668301957 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_9 : Uω (aρ 9) (bρ 9) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5559,25 +4807,21 @@ lemma U_627_9 : have hlg : Real.log (937694250349367 / 1600000000000000 : ℝ) ≤ (-(2671674856068678912033 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (937694250349367 / 1600000000000000 : ℝ) = - (937694250349367 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (937694250349367 / 800000000000000 : ℚ)) - (U := (794061045431321087967 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (937694250349367 / 800000000000000 : ℝ) ≤ - (794061045431321087967 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (231332646482171 / 400000000000000 : ℝ)) (q := - (937694250349367 / 1600000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (937694250349367 / 1600000000000000 : ℚ)) + (r' := (937694250349367 / 800000000000000 : ℚ)) + (U := (-(2671674856068678912033 / 5000000000000000000000 : ℚ))) + (U' := (794061045431321087967 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (231332646482171 / 400000000000000 : ℚ)) + (q := (937694250349367 / 1600000000000000 : ℚ)) + (U := (-(2671674856068678912033 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_10 : Uω (aρ 10) (bρ 10) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5585,26 +4829,21 @@ lemma U_627_10 : have hlg : Real.log (4328191626209523 / 8000000000000000 : ℝ) ≤ (-(1535729312323613446291 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4328191626209523 / 8000000000000000 : ℝ) = - (4328191626209523 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4328191626209523 / 4000000000000000 : ℚ)) - (U := (197138638426386553709 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4328191626209523 / 4000000000000000 : ℝ) ≤ - (197138638426386553709 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1054235226341199 / 2000000000000000 : ℝ)) (q := - (4328191626209523 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4328191626209523 / 8000000000000000 : ℚ)) + (r' := (4328191626209523 / 4000000000000000 : ℚ)) + (U := (-(1535729312323613446291 / 2500000000000000000000 : ℚ))) + (U' := (197138638426386553709 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (1054235226341199 / 2000000000000000 : ℚ)) + (q := (4328191626209523 / 8000000000000000 : ℚ)) + (U := (-(1535729312323613446291 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_11 : Uω (aρ 11) (bρ 11) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5612,26 +4851,21 @@ lemma U_627_11 : have hlg : Real.log (19575710827940307 / 40000000000000000 : ℝ) ≤ (-(3572949496635842197997 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19575710827940307 / 40000000000000000 : ℝ) = - (19575710827940307 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19575710827940307 / 10000000000000000 : ℚ)) - (U := (3358522306364157802003 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19575710827940307 / 10000000000000000 : ℝ) ≤ - (3358522306364157802003 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4657029106357341 / 10000000000000000 : ℝ)) (q := - (19575710827940307 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19575710827940307 / 40000000000000000 : ℚ)) + (r' := (19575710827940307 / 10000000000000000 : ℚ)) + (U := (-(3572949496635842197997 / 5000000000000000000000 : ℚ))) + (U' := (3358522306364157802003 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (4657029106357341 / 10000000000000000 : ℚ)) + (q := (19575710827940307 / 40000000000000000 : ℚ)) + (U := (-(3572949496635842197997 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_12 : Uω (aρ 12) (bρ 12) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5639,26 +4873,21 @@ lemma U_627_12 : have hlg : Real.log (3458384370162619 / 8000000000000000 : ℝ) ≤ (-(262075001932125642291 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3458384370162619 / 8000000000000000 : ℝ) = - (3458384370162619 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3458384370162619 / 2000000000000000 : ℚ)) - (U := (171141985755374357709 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3458384370162619 / 2000000000000000 : ℝ) ≤ - (171141985755374357709 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (787766942895747 / 2000000000000000 : ℝ)) (q := - (3458384370162619 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3458384370162619 / 8000000000000000 : ℚ)) + (r' := (3458384370162619 / 2000000000000000 : ℚ)) + (U := (-(262075001932125642291 / 312500000000000000000 : ℚ))) + (U' := (171141985755374357709 / 312500000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (787766942895747 / 2000000000000000 : ℚ)) + (q := (3458384370162619 / 8000000000000000 : ℚ)) + (U := (-(262075001932125642291 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_13 : Uω (aρ 13) (bρ 13) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5666,26 +4895,21 @@ lemma U_627_13 : have hlg : Real.log (14842923714890069 / 40000000000000000 : ℝ) ≤ (-(2478390548579272769413 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14842923714890069 / 40000000000000000 : ℝ) = - (14842923714890069 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14842923714890069 / 10000000000000000 : ℚ)) - (U := (987345352920727230587 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14842923714890069 / 10000000000000000 : ℝ) ≤ - (987345352920727230587 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1556858694056111 / 5000000000000000 : ℝ)) (q := - (14842923714890069 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14842923714890069 / 40000000000000000 : ℚ)) + (r' := (14842923714890069 / 10000000000000000 : ℚ)) + (U := (-(2478390548579272769413 / 2500000000000000000000 : ℚ))) + (U' := (987345352920727230587 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (1556858694056111 / 5000000000000000 : ℚ)) + (q := (14842923714890069 / 40000000000000000 : ℚ)) + (U := (-(2478390548579272769413 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_14 : Uω (aρ 14) (bρ 14) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5693,26 +4917,21 @@ lemma U_627_14 : have hlg : Real.log (12256164763485383 / 40000000000000000 : ℝ) ≤ (-(11828503971903031566869 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12256164763485383 / 40000000000000000 : ℝ) = - (12256164763485383 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12256164763485383 / 10000000000000000 : ℚ)) - (U := (2034439634096968433131 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12256164763485383 / 10000000000000000 : ℝ) ≤ - (2034439634096968433131 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2164265197454879 / 10000000000000000 : ℝ)) (q := - (12256164763485383 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12256164763485383 / 40000000000000000 : ℚ)) + (r' := (12256164763485383 / 10000000000000000 : ℚ)) + (U := (-(11828503971903031566869 / 10000000000000000000000 : ℚ))) + (U' := (2034439634096968433131 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (2164265197454879 / 10000000000000000 : ℚ)) + (q := (12256164763485383 / 40000000000000000 : ℚ)) + (U := (-(11828503971903031566869 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_15 : Uω (aρ 15) (bρ 15) (932533432353 / 1280000000000 : ℝ) ≤ @@ -5720,26 +4939,21 @@ lemma U_627_15 : have hlg : Real.log (9307885521012117 / 40000000000000000 : ℝ) ≤ (-(1458017506958502499819 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9307885521012117 / 40000000000000000 : ℝ) = - (9307885521012117 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9307885521012117 / 5000000000000000 : ℚ)) - (U := (621424033941497500181 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9307885521012117 / 5000000000000000 : ℝ) ≤ - (621424033941497500181 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (474849426816623 / 5000000000000000 : ℝ)) (q := - (9307885521012117 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9307885521012117 / 40000000000000000 : ℚ)) + (r' := (9307885521012117 / 5000000000000000 : ℚ)) + (U := (-(1458017506958502499819 / 1000000000000000000000 : ℚ))) + (U' := (621424033941497500181 / 1000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (932533432353 / 1280000000000 : ℚ)) + (s := (474849426816623 / 5000000000000000 : ℚ)) + (q := (9307885521012117 / 40000000000000000 : ℚ)) + (U := (-(1458017506958502499819 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_627_16 : Uω (aρ 16) (bρ 16) (932533432353 / 1280000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U52.lean b/LeanPool/Zeta5Irrational/Table/U52.lean index e0f87e4a1e..58c955327a 100644 --- a/LeanPool/Zeta5Irrational/Table/U52.lean +++ b/LeanPool/Zeta5Irrational/Table/U52.lean @@ -24,25 +24,21 @@ lemma U_628_1 : have hlg : Real.log (3615210918661643 / 5000000000000000 : ℝ) ≤ (-(3242877128542114788709 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3615210918661643 / 5000000000000000 : ℝ) = - (3615210918661643 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3615210918661643 / 2500000000000000 : ℚ)) - (U := (3688594674457885211291 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3615210918661643 / 2500000000000000 : ℝ) ≤ - (3688594674457885211291 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7230399477924697 / 10000000000000000 : ℝ)) (q := - (3615210918661643 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3615210918661643 / 5000000000000000 : ℚ)) + (r' := (3615210918661643 / 2500000000000000 : ℚ)) + (U := (-(3242877128542114788709 / 10000000000000000000000 : ℚ))) + (U' := (3688594674457885211291 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (7230399477924697 / 10000000000000000 : ℚ)) + (q := (3615210918661643 / 5000000000000000 : ℚ)) + (U := (-(3242877128542114788709 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_2 : Uω (aρ 2) (bρ 2) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_628_2 : have hlg : Real.log (14413055933439441 / 20000000000000000 : ℝ) ≤ (-(1637989077187245085489 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14413055933439441 / 20000000000000000 : ℝ) = - (14413055933439441 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14413055933439441 / 10000000000000000 : ℚ)) - (U := (1827746824312754914511 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14413055933439441 / 10000000000000000 : ℝ) ≤ - (1827746824312754914511 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3603190374613783 / 5000000000000000 : ℝ)) (q := - (14413055933439441 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14413055933439441 / 20000000000000000 : ℚ)) + (r' := (14413055933439441 / 10000000000000000 : ℚ)) + (U := (-(1637989077187245085489 / 5000000000000000000000 : ℚ))) + (U' := (1827746824312754914511 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (3603190374613783 / 5000000000000000 : ℚ)) + (q := (14413055933439441 / 20000000000000000 : ℚ)) + (U := (-(1637989077187245085489 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_3 : Uω (aρ 3) (bρ 3) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_628_3 : have hlg : Real.log (14317524725642981 / 20000000000000000 : ℝ) ≤ (-(3342479810571222740781 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14317524725642981 / 20000000000000000 : ℝ) = - (14317524725642981 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14317524725642981 / 10000000000000000 : ℚ)) - (U := (3588991992428777259219 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14317524725642981 / 10000000000000000 : ℝ) ≤ - (3588991992428777259219 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3579122823890553 / 5000000000000000 : ℝ)) (q := - (14317524725642981 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14317524725642981 / 20000000000000000 : ℚ)) + (r' := (14317524725642981 / 10000000000000000 : ℚ)) + (U := (-(3342479810571222740781 / 10000000000000000000000 : ℚ))) + (U' := (3588991992428777259219 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (3579122823890553 / 5000000000000000 : ℚ)) + (q := (14317524725642981 / 20000000000000000 : ℚ)) + (U := (-(3342479810571222740781 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_4 : Uω (aρ 4) (bρ 4) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_628_4 : have hlg : Real.log (14158997682236471 / 20000000000000000 : ℝ) ≤ (-(3453819726866507349207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14158997682236471 / 20000000000000000 : ℝ) = - (14158997682236471 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14158997682236471 / 10000000000000000 : ℚ)) - (U := (3477652076133492650793 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14158997682236471 / 10000000000000000 : ℝ) ≤ - (3477652076133492650793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1769503196359899 / 2500000000000000 : ℝ)) (q := - (14158997682236471 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14158997682236471 / 20000000000000000 : ℚ)) + (r' := (14158997682236471 / 10000000000000000 : ℚ)) + (U := (-(3453819726866507349207 / 10000000000000000000000 : ℚ))) + (U' := (3477652076133492650793 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (1769503196359899 / 2500000000000000 : ℚ)) + (q := (14158997682236471 / 20000000000000000 : ℚ)) + (U := (-(3453819726866507349207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_5 : Uω (aρ 5) (bρ 5) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_628_5 : have hlg : Real.log (6958968485077981 / 10000000000000000 : ℝ) ≤ (-(3625538355383480504909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6958968485077981 / 10000000000000000 : ℝ) = - (6958968485077981 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6958968485077981 / 5000000000000000 : ℚ)) - (U := (3305933447616519495091 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6958968485077981 / 5000000000000000 : ℝ) ≤ - (3305933447616519495091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6955141992694087 / 10000000000000000 : ℝ)) (q := - (6958968485077981 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6958968485077981 / 10000000000000000 : ℚ)) + (r' := (6958968485077981 / 5000000000000000 : ℚ)) + (U := (-(3625538355383480504909 / 10000000000000000000000 : ℚ))) + (U' := (3305933447616519495091 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (6955141992694087 / 10000000000000000 : ℚ)) + (q := (6958968485077981 / 10000000000000000 : ℚ)) + (U := (-(3625538355383480504909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_6 : Uω (aρ 6) (bρ 6) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_628_6 : have hlg : Real.log (2714605189622871 / 4000000000000000 : ℝ) ≤ (-(193823918117542028053 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2714605189622871 / 4000000000000000 : ℝ) = - (2714605189622871 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2714605189622871 / 2000000000000000 : ℚ)) - (U := (152749672032457971947 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2714605189622871 / 2000000000000000 : ℝ) ≤ - (152749672032457971947 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (42359195911203 / 62500000000000 : ℝ)) (q := - (2714605189622871 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2714605189622871 / 4000000000000000 : ℚ)) + (r' := (2714605189622871 / 2000000000000000 : ℚ)) + (U := (-(193823918117542028053 / 500000000000000000000 : ℚ))) + (U' := (152749672032457971947 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (42359195911203 / 62500000000000 : ℚ)) + (q := (2714605189622871 / 4000000000000000 : ℚ)) + (U := (-(193823918117542028053 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_7 : Uω (aρ 7) (bρ 7) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_628_7 : have hlg : Real.log (6552101819691467 / 10000000000000000 : ℝ) ≤ (-(132124751893165640127 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6552101819691467 / 10000000000000000 : ℝ) = - (6552101819691467 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6552101819691467 / 5000000000000000 : ℚ)) - (U := (84483741950584359873 / 312500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6552101819691467 / 5000000000000000 : ℝ) ≤ - (84483741950584359873 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6532310417821059 / 10000000000000000 : ℝ)) (q := - (6552101819691467 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6552101819691467 / 10000000000000000 : ℚ)) + (r' := (6552101819691467 / 5000000000000000 : ℚ)) + (U := (-(132124751893165640127 / 312500000000000000000 : ℚ))) + (U' := (84483741950584359873 / 312500000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (6532310417821059 / 10000000000000000 : ℚ)) + (q := (6552101819691467 / 10000000000000000 : ℚ)) + (U := (-(132124751893165640127 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_8 : Uω (aρ 8) (bρ 8) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_628_8 : have hlg : Real.log (1561995075781669 / 2500000000000000 : ℝ) ≤ (-(4703268327102192686097 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1561995075781669 / 2500000000000000 : ℝ) = - (1561995075781669 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1561995075781669 / 1250000000000000 : ℚ)) - (U := (2228203475897807313903 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1561995075781669 / 1250000000000000 : ℝ) ≤ - (2228203475897807313903 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6207609036031477 / 10000000000000000 : ℝ)) (q := - (1561995075781669 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1561995075781669 / 2500000000000000 : ℚ)) + (r' := (1561995075781669 / 1250000000000000 : ℚ)) + (U := (-(4703268327102192686097 / 10000000000000000000000 : ℚ))) + (U' := (2228203475897807313903 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (6207609036031477 / 10000000000000000 : ℚ)) + (q := (1561995075781669 / 2500000000000000 : ℚ)) + (U := (-(4703268327102192686097 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_9 : Uω (aρ 9) (bρ 9) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -232,24 +200,21 @@ lemma U_628_9 : have hlg : Real.log (23480960321493 / 40000000000000 : ℝ) ≤ (-(5326895601779464101117 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23480960321493 / 40000000000000 : ℝ) = (23480960321493 / 20000000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23480960321493 / 20000000000000 : ℚ)) - (U := (1604576201220535898883 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23480960321493 / 20000000000000 : ℝ) ≤ - (1604576201220535898883 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (46344753751077 / 80000000000000 : ℝ)) (q := - (23480960321493 / 40000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23480960321493 / 40000000000000 : ℚ)) + (r' := (23480960321493 / 20000000000000 : ℚ)) + (U := (-(5326895601779464101117 / 10000000000000000000000 : ℚ))) + (U' := (1604576201220535898883 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (46344753751077 / 80000000000000 : ℚ)) + (q := (23480960321493 / 40000000000000 : ℚ)) + (U := (-(5326895601779464101117 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_10 : Uω (aρ 10) (bρ 10) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -257,26 +222,21 @@ lemma U_628_10 : have hlg : Real.log (1084002860470187 / 2000000000000000 : ℝ) ≤ (-(3062433192379457887933 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1084002860470187 / 2000000000000000 : ℝ) = - (1084002860470187 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1084002860470187 / 1000000000000000 : ℚ)) - (U := (403302709120542112067 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1084002860470187 / 1000000000000000 : ℝ) ≤ - (403302709120542112067 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1056240339266999 / 2000000000000000 : ℝ)) (q := - (1084002860470187 / 2000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1084002860470187 / 2000000000000000 : ℚ)) + (r' := (1084002860470187 / 1000000000000000 : ℚ)) + (U := (-(3062433192379457887933 / 5000000000000000000000 : ℚ))) + (U' := (403302709120542112067 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (1056240339266999 / 2000000000000000 : ℚ)) + (q := (1084002860470187 / 2000000000000000 : ℚ)) + (U := (-(3062433192379457887933 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_11 : Uω (aρ 11) (bρ 11) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -284,26 +244,21 @@ lemma U_628_11 : have hlg : Real.log (4903935118129209 / 10000000000000000 : ℝ) ≤ (-(7125471243255631514223 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4903935118129209 / 10000000000000000 : ℝ) = - (4903935118129209 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4903935118129209 / 2500000000000000 : ℚ)) - (U := (6737472362744368485777 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4903935118129209 / 2500000000000000 : ℝ) ≤ - (6737472362744368485777 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4667519954096543 / 10000000000000000 : ℝ)) (q := - (4903935118129209 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4903935118129209 / 10000000000000000 : ℚ)) + (r' := (4903935118129209 / 2500000000000000 : ℚ)) + (U := (-(7125471243255631514223 / 10000000000000000000000 : ℚ))) + (U' := (6737472362744368485777 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (4667519954096543 / 10000000000000000 : ℚ)) + (q := (4903935118129209 / 10000000000000000 : ℚ)) + (U := (-(7125471243255631514223 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_12 : Uω (aρ 12) (bρ 12) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -311,26 +266,21 @@ lemma U_628_12 : have hlg : Real.log (8666861662668721 / 20000000000000000 : ℝ) ≤ (-(8362255243951402653027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8666861662668721 / 20000000000000000 : ℝ) = - (8666861662668721 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8666861662668721 / 5000000000000000 : ℚ)) - (U := (5500688362048597346973 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8666861662668721 / 5000000000000000 : ℝ) ≤ - (5500688362048597346973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1975105738595923 / 5000000000000000 : ℝ)) (q := - (8666861662668721 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8666861662668721 / 20000000000000000 : ℚ)) + (r' := (8666861662668721 / 5000000000000000 : ℚ)) + (U := (-(8362255243951402653027 / 10000000000000000000000 : ℚ))) + (U' := (5500688362048597346973 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (1975105738595923 / 5000000000000000 : ℚ)) + (q := (8666861662668721 / 20000000000000000 : ℚ)) + (U := (-(8362255243951402653027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_13 : Uω (aρ 13) (bρ 13) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -338,26 +288,21 @@ lemma U_628_13 : have hlg : Real.log (1488829747688233 / 4000000000000000 : ℝ) ≤ (-(9883039534702144509293 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1488829747688233 / 4000000000000000 : ℝ) = - (1488829747688233 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1488829747688233 / 1000000000000000 : ℚ)) - (U := (3979904071297855490707 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1488829747688233 / 1000000000000000 : ℝ) ≤ - (3979904071297855490707 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (312688029455929 / 1000000000000000 : ℝ)) (q := - (1488829747688233 / 4000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1488829747688233 / 4000000000000000 : ℚ)) + (r' := (1488829747688233 / 1000000000000000 : ℚ)) + (U := (-(9883039534702144509293 / 10000000000000000000000 : ℚ))) + (U' := (3979904071297855490707 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (312688029455929 / 1000000000000000 : ℚ)) + (q := (1488829747688233 / 4000000000000000 : ℚ)) + (U := (-(9883039534702144509293 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_14 : Uω (aρ 14) (bρ 14) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -365,26 +310,21 @@ lemma U_628_14 : have hlg : Real.log (6155000421638059 / 20000000000000000 : ℝ) ≤ (-(589233722447172838279 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6155000421638059 / 20000000000000000 : ℝ) = - (6155000421638059 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6155000421638059 / 5000000000000000 : ℚ)) - (U := (103913457852827161721 / 500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6155000421638059 / 5000000000000000 : ℝ) ≤ - (103913457852827161721 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (68176851962537 / 312500000000000 : ℝ)) (q := - (6155000421638059 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6155000421638059 / 20000000000000000 : ℚ)) + (r' := (6155000421638059 / 5000000000000000 : ℚ)) + (U := (-(589233722447172838279 / 500000000000000000000 : ℚ))) + (U' := (103913457852827161721 / 500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (68176851962537 / 312500000000000 : ℚ)) + (q := (6155000421638059 / 20000000000000000 : ℚ)) + (U := (-(589233722447172838279 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_15 : Uω (aρ 15) (bρ 15) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -392,26 +332,21 @@ lemma U_628_15 : have hlg : Real.log (2349980500237737 / 10000000000000000 : ℝ) ≤ (-(7240890309318723000821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2349980500237737 / 10000000000000000 : ℝ) = - (2349980500237737 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2349980500237737 / 1250000000000000 : ℚ)) - (U := (3156317395181276999179 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2349980500237737 / 1250000000000000 : ℝ) ≤ - (3156317395181276999179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (986193119053599 / 10000000000000000 : ℝ)) (q := - (2349980500237737 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2349980500237737 / 10000000000000000 : ℚ)) + (r' := (2349980500237737 / 1250000000000000 : ℚ)) + (U := (-(7240890309318723000821 / 5000000000000000000000 : ℚ))) + (U' := (3156317395181276999179 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11671906263691 / 16000000000000 : ℚ)) + (s := (986193119053599 / 10000000000000000 : ℚ)) + (q := (2349980500237737 / 10000000000000000 : ℚ)) + (U := (-(7240890309318723000821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_628_16 : Uω (aρ 16) (bρ 16) (11671906263691 / 16000000000000 : ℝ) ≤ @@ -508,25 +443,21 @@ lemma U_629_1 : have hlg : Real.log (28959783365142761 / 40000000000000000 : ℝ) ≤ (-(645942733699712492987 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28959783365142761 / 40000000000000000 : ℝ) = - (28959783365142761 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28959783365142761 / 20000000000000000 : ℚ)) - (U := (740351626900287507013 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28959783365142761 / 20000000000000000 : ℝ) ≤ - (740351626900287507013 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7239923511300443 / 10000000000000000 : ℝ)) (q := - (28959783365142761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28959783365142761 / 40000000000000000 : ℚ)) + (r' := (28959783365142761 / 20000000000000000 : ℚ)) + (U := (-(645942733699712492987 / 2000000000000000000000 : ℚ))) + (U' := (740351626900287507013 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (7239923511300443 / 10000000000000000 : ℚ)) + (q := (28959783365142761 / 40000000000000000 : ℚ)) + (U := (-(645942733699712492987 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_2 : Uω (aρ 2) (bρ 2) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -534,25 +465,21 @@ lemma U_629_2 : have hlg : Real.log (28864208542300257 / 40000000000000000 : ℝ) ≤ (-(815692712508334048631 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28864208542300257 / 40000000000000000 : ℝ) = - (28864208542300257 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28864208542300257 / 20000000000000000 : ℚ)) - (U := (917175238241665951369 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28864208542300257 / 20000000000000000 : ℝ) ≤ - (917175238241665951369 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7215905112389191 / 10000000000000000 : ℝ)) (q := - (28864208542300257 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28864208542300257 / 40000000000000000 : ℚ)) + (r' := (28864208542300257 / 20000000000000000 : ℚ)) + (U := (-(815692712508334048631 / 2500000000000000000000 : ℚ))) + (U' := (917175238241665951369 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (7215905112389191 / 10000000000000000 : ℚ)) + (q := (28864208542300257 / 40000000000000000 : ℚ)) + (U := (-(815692712508334048631 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_3 : Uω (aρ 3) (bρ 3) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -560,25 +487,21 @@ lemma U_629_3 : have hlg : Real.log (28673148095764909 / 40000000000000000 : ℝ) ≤ (-(832295938651579155123 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28673148095764909 / 40000000000000000 : ℝ) = - (28673148095764909 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28673148095764909 / 20000000000000000 : ℚ)) - (U := (900572012098420844877 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28673148095764909 / 20000000000000000 : ℝ) ≤ - (900572012098420844877 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7167770995471517 / 10000000000000000 : ℝ)) (q := - (28673148095764909 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28673148095764909 / 40000000000000000 : ℚ)) + (r' := (28673148095764909 / 20000000000000000 : ℚ)) + (U := (-(832295938651579155123 / 2500000000000000000000 : ℚ))) + (U' := (900572012098420844877 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (7167770995471517 / 10000000000000000 : ℚ)) + (q := (28673148095764909 / 40000000000000000 : ℚ)) + (U := (-(832295938651579155123 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_4 : Uω (aρ 4) (bρ 4) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -586,25 +509,21 @@ lemma U_629_4 : have hlg : Real.log (28356099250297589 / 40000000000000000 : ℝ) ≤ (-(3440373057157870478887 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28356099250297589 / 40000000000000000 : ℝ) = - (28356099250297589 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28356099250297589 / 20000000000000000 : ℚ)) - (U := (3491098745842129521113 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28356099250297589 / 20000000000000000 : ℝ) ≤ - (3491098745842129521113 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7087540753802857 / 10000000000000000 : ℝ)) (q := - (28356099250297589 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28356099250297589 / 40000000000000000 : ℚ)) + (r' := (28356099250297589 / 20000000000000000 : ℚ)) + (U := (-(3440373057157870478887 / 10000000000000000000000 : ℚ))) + (U' := (3491098745842129521113 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (7087540753802857 / 10000000000000000 : ℚ)) + (q := (28356099250297589 / 40000000000000000 : ℚ)) + (U := (-(3440373057157870478887 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_5 : Uω (aρ 5) (bρ 5) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -612,25 +531,21 @@ lemma U_629_5 : have hlg : Real.log (27873990768952717 / 40000000000000000 : ℝ) ≤ (-(722370860654510914959 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27873990768952717 / 40000000000000000 : ℝ) = - (27873990768952717 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27873990768952717 / 20000000000000000 : ℚ)) - (U := (663923499945489085041 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27873990768952717 / 20000000000000000 : ℝ) ≤ - (663923499945489085041 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6964676432465421 / 10000000000000000 : ℝ)) (q := - (27873990768952717 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27873990768952717 / 40000000000000000 : ℚ)) + (r' := (27873990768952717 / 20000000000000000 : ℚ)) + (U := (-(722370860654510914959 / 2000000000000000000000 : ℚ))) + (U' := (663923499945489085041 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (6964676432465421 / 10000000000000000 : ℚ)) + (q := (27873990768952717 / 40000000000000000 : ℚ)) + (U := (-(722370860654510914959 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_6 : Uω (aρ 6) (bρ 6) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -638,25 +553,21 @@ lemma U_629_6 : have hlg : Real.log (1087367941825877 / 1600000000000000 : ℝ) ≤ (-(965608962956098136493 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1087367941825877 / 1600000000000000 : ℝ) = - (1087367941825877 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1087367941825877 / 800000000000000 : ℚ)) - (U := (767258987793901863507 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1087367941825877 / 800000000000000 : ℝ) ≤ - (767258987793901863507 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (271480827838101 / 400000000000000 : ℝ)) (q := - (1087367941825877 / 1600000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1087367941825877 / 1600000000000000 : ℚ)) + (r' := (1087367941825877 / 800000000000000 : ℚ)) + (U := (-(965608962956098136493 / 2500000000000000000000 : ℚ))) + (U' := (767258987793901863507 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (271480827838101 / 400000000000000 : ℚ)) + (q := (1087367941825877 / 1600000000000000 : ℚ)) + (U := (-(965608962956098136493 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_7 : Uω (aρ 7) (bρ 7) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -664,25 +575,21 @@ lemma U_629_7 : have hlg : Real.log (26246618430248087 / 40000000000000000 : ℝ) ≤ (-(105335573704855377237 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26246618430248087 / 40000000000000000 : ℝ) = - (26246618430248087 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26246618430248087 / 20000000000000000 : ℚ)) - (U := (67951221370144622763 / 250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26246618430248087 / 20000000000000000 : ℝ) ≤ - (67951221370144622763 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3270946009506553 / 5000000000000000 : ℝ)) (q := - (26246618430248087 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26246618430248087 / 40000000000000000 : ℚ)) + (r' := (26246618430248087 / 20000000000000000 : ℚ)) + (U := (-(105335573704855377237 / 250000000000000000000 : ℚ))) + (U' := (67951221370144622763 / 250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (3270946009506553 / 5000000000000000 : ℚ)) + (q := (26246618430248087 / 40000000000000000 : ℚ)) + (U := (-(105335573704855377237 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_8 : Uω (aρ 8) (bρ 8) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -690,25 +597,21 @@ lemma U_629_8 : have hlg : Real.log (25030264485880559 / 40000000000000000 : ℝ) ≤ (-(4687937817110196890423 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25030264485880559 / 40000000000000000 : ℝ) = - (25030264485880559 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25030264485880559 / 20000000000000000 : ℚ)) - (U := (2243533985889803109577 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25030264485880559 / 20000000000000000 : ℝ) ≤ - (2243533985889803109577 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3108628349084671 / 5000000000000000 : ℝ)) (q := - (25030264485880559 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25030264485880559 / 40000000000000000 : ℚ)) + (r' := (25030264485880559 / 20000000000000000 : ℚ)) + (U := (-(4687937817110196890423 / 10000000000000000000000 : ℚ))) + (U' := (2243533985889803109577 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (3108628349084671 / 5000000000000000 : ℚ)) + (q := (25030264485880559 / 40000000000000000 : ℚ)) + (U := (-(4687937817110196890423 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_9 : Uω (aρ 9) (bρ 9) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -716,25 +619,21 @@ lemma U_629_9 : have hlg : Real.log (4703912538789881 / 8000000000000000 : ℝ) ≤ (-(5310469239407437719787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4703912538789881 / 8000000000000000 : ℝ) = - (4703912538789881 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4703912538789881 / 4000000000000000 : ℚ)) - (U := (1621002563592562280213 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4703912538789881 / 4000000000000000 : ℝ) ≤ - (1621002563592562280213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1160574286112753 / 2000000000000000 : ℝ)) (q := - (4703912538789881 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4703912538789881 / 8000000000000000 : ℚ)) + (r' := (4703912538789881 / 4000000000000000 : ℚ)) + (U := (-(5310469239407437719787 / 10000000000000000000000 : ℚ))) + (U' := (1621002563592562280213 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (1160574286112753 / 2000000000000000 : ℚ)) + (q := (4703912538789881 / 8000000000000000 : ℚ)) + (U := (-(5310469239407437719787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_10 : Uω (aρ 10) (bρ 10) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -742,26 +641,21 @@ lemma U_629_10 : have hlg : Real.log (21719152581301551 / 40000000000000000 : ℝ) ≤ (-(3053424875716178132791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21719152581301551 / 40000000000000000 : ℝ) = - (21719152581301551 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21719152581301551 / 20000000000000000 : ℚ)) - (U := (412311025783821867209 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21719152581301551 / 20000000000000000 : ℝ) ≤ - (412311025783821867209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2645612703867419 / 5000000000000000 : ℝ)) (q := - (21719152581301551 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21719152581301551 / 40000000000000000 : ℚ)) + (r' := (21719152581301551 / 20000000000000000 : ℚ)) + (U := (-(3053424875716178132791 / 5000000000000000000000 : ℚ))) + (U' := (412311025783821867209 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (2645612703867419 / 5000000000000000 : ℚ)) + (q := (21719152581301551 / 40000000000000000 : ℚ)) + (U := (-(3053424875716178132791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_11 : Uω (aρ 11) (bρ 11) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -769,26 +663,21 @@ lemma U_629_11 : have hlg : Real.log (19655761843575217 / 40000000000000000 : ℝ) ≤ (-(1421017869337593465473 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19655761843575217 / 40000000000000000 : ℝ) = - (19655761843575217 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19655761843575217 / 10000000000000000 : ℚ)) - (U := (1351570851862406534527 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19655761843575217 / 10000000000000000 : ℝ) ≤ - (1351570851862406534527 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4678006665076671 / 10000000000000000 : ℝ)) (q := - (19655761843575217 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19655761843575217 / 40000000000000000 : ℚ)) + (r' := (19655761843575217 / 10000000000000000 : ℚ)) + (U := (-(1421017869337593465473 / 2000000000000000000000 : ℚ))) + (U' := (1351570851862406534527 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (4678006665076671 / 10000000000000000 : ℚ)) + (q := (19655761843575217 / 40000000000000000 : ℚ)) + (U := (-(1421017869337593465473 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_12 : Uω (aρ 12) (bρ 12) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -796,26 +685,21 @@ lemma U_629_12 : have hlg : Real.log (3475101049956067 / 8000000000000000 : ℝ) ≤ (-(833817983441931326163 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3475101049956067 / 8000000000000000 : ℝ) = - (3475101049956067 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3475101049956067 / 2000000000000000 : ℚ)) - (U := (552476377158068673837 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3475101049956067 / 2000000000000000 : ℝ) ≤ - (552476377158068673837 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (396157846486423 / 1000000000000000 : ℝ)) (q := - (3475101049956067 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3475101049956067 / 8000000000000000 : ℚ)) + (r' := (3475101049956067 / 2000000000000000 : ℚ)) + (U := (-(833817983441931326163 / 1000000000000000000000 : ℚ))) + (U' := (552476377158068673837 / 1000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (396157846486423 / 1000000000000000 : ℚ)) + (q := (3475101049956067 / 8000000000000000 : ℚ)) + (U := (-(833817983441931326163 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_13 : Uω (aρ 13) (bρ 13) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -823,26 +707,21 @@ lemma U_629_13 : have hlg : Real.log (2986723731185781 / 8000000000000000 : ℝ) ≤ (-(12315806207499133563 / 12500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2986723731185781 / 8000000000000000 : ℝ) = - (2986723731185781 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2986723731185781 / 2000000000000000 : ℚ)) - (U := (5012873300000866437 / 12500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2986723731185781 / 2000000000000000 : ℝ) ≤ - (5012873300000866437 / 12500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (628003381906703 / 2000000000000000 : ℝ)) (q := - (2986723731185781 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2986723731185781 / 8000000000000000 : ℚ)) + (r' := (2986723731185781 / 2000000000000000 : ℚ)) + (U := (-(12315806207499133563 / 12500000000000000000 : ℚ))) + (U' := (5012873300000866437 / 12500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (628003381906703 / 2000000000000000 : ℚ)) + (q := (2986723731185781 / 8000000000000000 : ℚ)) + (U := (-(12315806207499133563 / 12500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_14 : Uω (aρ 14) (bρ 14) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -850,26 +729,21 @@ lemma U_629_14 : have hlg : Real.log (2472728849475393 / 8000000000000000 : ℝ) ≤ (-(469647681200431082067 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2472728849475393 / 8000000000000000 : ℝ) = - (2472728849475393 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2472728849475393 / 2000000000000000 : ℚ)) - (U := (84870063039568917933 / 400000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (2472728849475393 / 2000000000000000 : ℝ) ≤ - (84870063039568917933 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (439791398060509 / 2000000000000000 : ℝ)) (q := - (2472728849475393 / 8000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2472728849475393 / 8000000000000000 : ℚ)) + (r' := (2472728849475393 / 2000000000000000 : ℚ)) + (U := (-(469647681200431082067 / 400000000000000000000 : ℚ))) + (U' := (84870063039568917933 / 400000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (439791398060509 / 2000000000000000 : ℚ)) + (q := (2472728849475393 / 8000000000000000 : ℚ)) + (U := (-(469647681200431082067 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_15 : Uω (aρ 15) (bρ 15) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -877,26 +751,21 @@ lemma U_629_15 : have hlg : Real.log (9489529854871201 / 40000000000000000 : ℝ) ≤ (-(14386903830489276582459 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9489529854871201 / 40000000000000000 : ℝ) = - (9489529854871201 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9489529854871201 / 5000000000000000 : ℚ)) - (U := (6407511578510723417541 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9489529854871201 / 5000000000000000 : ℝ) ≤ - (6407511578510723417541 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1021473071464663 / 10000000000000000 : ℝ)) (q := - (9489529854871201 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9489529854871201 / 40000000000000000 : ℚ)) + (r' := (9489529854871201 / 5000000000000000 : ℚ)) + (U := (-(14386903830489276582459 / 10000000000000000000000 : ℚ))) + (U' := (6407511578510723417541 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23374289245939 / 32000000000000 : ℚ)) + (s := (1021473071464663 / 10000000000000000 : ℚ)) + (q := (9489529854871201 / 40000000000000000 : ℚ)) + (U := (-(14386903830489276582459 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_629_16 : Uω (aρ 16) (bρ 16) (23374289245939 / 32000000000000 : ℝ) ≤ @@ -991,25 +860,21 @@ lemma U_630_1 : have hlg : Real.log (14498939690341621 / 20000000000000000 : ℝ) ≤ (-(3216567513452919317099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14498939690341621 / 20000000000000000 : ℝ) = - (14498939690341621 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14498939690341621 / 10000000000000000 : ℚ)) - (U := (3714904289547080682901 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14498939690341621 / 10000000000000000 : ℝ) ≤ - (3714904289547080682901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7249447544521621 / 10000000000000000 : ℝ)) (q := - (14498939690341621 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14498939690341621 / 20000000000000000 : ℚ)) + (r' := (14498939690341621 / 10000000000000000 : ℚ)) + (U := (-(3216567513452919317099 / 10000000000000000000000 : ℚ))) + (U' := (3714904289547080682901 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (7249447544521621 / 10000000000000000 : ℚ)) + (q := (14498939690341621 / 20000000000000000 : ℚ)) + (U := (-(3216567513452919317099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_2 : Uω (aρ 2) (bρ 2) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1017,25 +882,21 @@ lemma U_630_2 : have hlg : Real.log (14451152607836319 / 20000000000000000 : ℝ) ≤ (-(1624790483342472992419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14451152607836319 / 20000000000000000 : ℝ) = - (14451152607836319 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14451152607836319 / 10000000000000000 : ℚ)) - (U := (1840945418157527007581 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14451152607836319 / 10000000000000000 : ℝ) ≤ - (1840945418157527007581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7225429474526319 / 10000000000000000 : ℝ)) (q := - (14451152607836319 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14451152607836319 / 20000000000000000 : ℚ)) + (r' := (14451152607836319 / 10000000000000000 : ℚ)) + (U := (-(1624790483342472992419 / 5000000000000000000000 : ℚ))) + (U' := (1840945418157527007581 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (7225429474526319 / 10000000000000000 : ℚ)) + (q := (14451152607836319 / 20000000000000000 : ℚ)) + (U := (-(1624790483342472992419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_3 : Uω (aρ 3) (bρ 3) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1043,25 +904,21 @@ lemma U_630_3 : have hlg : Real.log (7177811683238731 / 10000000000000000 : ℝ) ≤ (-(1657952678109447268993 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7177811683238731 / 10000000000000000 : ℝ) = - (7177811683238731 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7177811683238731 / 5000000000000000 : ℚ)) - (U := (1807783223390552731007 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7177811683238731 / 5000000000000000 : ℝ) ≤ - (1807783223390552731007 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3588648169758731 / 5000000000000000 : ℝ)) (q := - (7177811683238731 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7177811683238731 / 10000000000000000 : ℚ)) + (r' := (7177811683238731 / 5000000000000000 : ℚ)) + (U := (-(1657952678109447268993 / 5000000000000000000000 : ℚ))) + (U' := (1807783223390552731007 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (3588648169758731 / 5000000000000000 : ℚ)) + (q := (7177811683238731 / 10000000000000000 : ℚ)) + (U := (-(1657952678109447268993 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_4 : Uω (aρ 4) (bρ 4) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1069,25 +926,21 @@ lemma U_630_4 : have hlg : Real.log (7098550778669901 / 10000000000000000 : ℝ) ≤ (-(3426944452015668801577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7098550778669901 / 10000000000000000 : ℝ) = - (7098550778669901 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7098550778669901 / 5000000000000000 : ℚ)) - (U := (3504527350984331198423 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7098550778669901 / 5000000000000000 : ℝ) ≤ - (3504527350984331198423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3548534355722401 / 5000000000000000 : ℝ)) (q := - (7098550778669901 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7098550778669901 / 10000000000000000 : ℚ)) + (r' := (7098550778669901 / 5000000000000000 : ℚ)) + (U := (-(3426944452015668801577 / 10000000000000000000000 : ℚ))) + (U' := (3504527350984331198423 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (3548534355722401 / 5000000000000000 : ℚ)) + (q := (7098550778669901 / 10000000000000000 : ℚ)) + (U := (-(3426944452015668801577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_5 : Uω (aρ 5) (bρ 5) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1095,25 +948,21 @@ lemma U_630_5 : have hlg : Real.log (13956053770198459 / 20000000000000000 : ℝ) ≤ (-(1799094485697806630207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13956053770198459 / 20000000000000000 : ℝ) = - (13956053770198459 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13956053770198459 / 10000000000000000 : ℚ)) - (U := (1666641415802193369793 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13956053770198459 / 10000000000000000 : ℝ) ≤ - (1666641415802193369793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6974210843638459 / 10000000000000000 : ℝ)) (q := - (13956053770198459 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13956053770198459 / 20000000000000000 : ℚ)) + (r' := (13956053770198459 / 10000000000000000 : ℚ)) + (U := (-(1799094485697806630207 / 5000000000000000000000 : ℚ))) + (U' := (1666641415802193369793 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (6974210843638459 / 10000000000000000 : ℚ)) + (q := (13956053770198459 / 20000000000000000 : ℚ)) + (U := (-(1799094485697806630207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_6 : Uω (aρ 6) (bρ 6) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1121,25 +970,21 @@ lemma U_630_6 : have hlg : Real.log (13611172526320581 / 20000000000000000 : ℝ) ≤ (-(38484130851782445057 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13611172526320581 / 20000000000000000 : ℝ) = - (13611172526320581 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13611172526320581 / 10000000000000000 : ℚ)) - (U := (30830587178217554943 / 100000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13611172526320581 / 10000000000000000 : ℝ) ≤ - (30830587178217554943 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6796569974900581 / 10000000000000000 : ℝ)) (q := - (13611172526320581 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13611172526320581 / 20000000000000000 : ℚ)) + (r' := (13611172526320581 / 10000000000000000 : ℚ)) + (U := (-(38484130851782445057 / 100000000000000000000 : ℚ))) + (U' := (30830587178217554943 / 100000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (6796569974900581 / 10000000000000000 : ℚ)) + (q := (13611172526320581 / 20000000000000000 : ℚ)) + (U := (-(38484130851782445057 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_7 : Uω (aρ 7) (bρ 7) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1147,25 +992,21 @@ lemma U_630_7 : have hlg : Real.log (13142414622812853 / 20000000000000000 : ℝ) ≤ (-(524859394838169808527 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13142414622812853 / 20000000000000000 : ℝ) = - (13142414622812853 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13142414622812853 / 10000000000000000 : ℚ)) - (U := (341574580536830191473 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13142414622812853 / 10000000000000000 : ℝ) ≤ - (341574580536830191473 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6551473452152853 / 10000000000000000 : ℝ)) (q := - (13142414622812853 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13142414622812853 / 20000000000000000 : ℚ)) + (r' := (13142414622812853 / 10000000000000000 : ℚ)) + (U := (-(524859394838169808527 / 1250000000000000000000 : ℚ))) + (U' := (341574580536830191473 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (6551473452152853 / 10000000000000000 : ℚ)) + (q := (13142414622812853 / 20000000000000000 : ℚ)) + (U := (-(524859394838169808527 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_8 : Uω (aρ 8) (bρ 8) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1173,25 +1014,21 @@ lemma U_630_8 : have hlg : Real.log (1253430349881301 / 2000000000000000 : ℝ) ≤ (-(4672631077418728873253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1253430349881301 / 2000000000000000 : ℝ) = - (1253430349881301 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1253430349881301 / 1000000000000000 : ℚ)) - (U := (2258840725581271126747 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1253430349881301 / 1000000000000000 : ℝ) ≤ - (2258840725581271126747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (622690397949301 / 1000000000000000 : ℝ)) (q := - (1253430349881301 / 2000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1253430349881301 / 2000000000000000 : ℚ)) + (r' := (1253430349881301 / 1000000000000000 : ℚ)) + (U := (-(4672631077418728873253 / 10000000000000000000000 : ℚ))) + (U' := (2258840725581271126747 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (622690397949301 / 1000000000000000 : ℚ)) + (q := (1253430349881301 / 2000000000000000 : ℚ)) + (U := (-(4672631077418728873253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_9 : Uω (aρ 9) (bρ 9) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1199,25 +1036,21 @@ lemma U_630_9 : have hlg : Real.log (11779081692316477 / 20000000000000000 : ℝ) ≤ (-(529407052921083357707 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11779081692316477 / 20000000000000000 : ℝ) = - (11779081692316477 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11779081692316477 / 10000000000000000 : ℚ)) - (U := (163740127378916642293 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11779081692316477 / 10000000000000000 : ℝ) ≤ - (163740127378916642293 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5812647801356477 / 10000000000000000 : ℝ)) (q := - (11779081692316477 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11779081692316477 / 20000000000000000 : ℚ)) + (r' := (11779081692316477 / 10000000000000000 : ℚ)) + (U := (-(529407052921083357707 / 1000000000000000000000 : ℚ))) + (U' := (163740127378916642293 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (5812647801356477 / 10000000000000000 : ℚ)) + (q := (11779081692316477 / 20000000000000000 : ℚ)) + (U := (-(529407052921083357707 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_10 : Uω (aρ 10) (bρ 10) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1225,26 +1058,21 @@ lemma U_630_10 : have hlg : Real.log (10879122133882899 / 20000000000000000 : ℝ) ≤ (-(3044433606727779236829 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10879122133882899 / 20000000000000000 : ℝ) = - (10879122133882899 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10879122133882899 / 10000000000000000 : ℚ)) - (U := (421302294772220763171 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10879122133882899 / 10000000000000000 : ℝ) ≤ - (421302294772220763171 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5301247276417899 / 10000000000000000 : ℝ)) (q := - (10879122133882899 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10879122133882899 / 20000000000000000 : ℚ)) + (r' := (10879122133882899 / 10000000000000000 : ℚ)) + (U := (-(3044433606727779236829 / 5000000000000000000000 : ℚ))) + (U' := (421302294772220763171 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (5301247276417899 / 10000000000000000 : ℚ)) + (q := (10879122133882899 / 20000000000000000 : ℚ)) + (U := (-(3044433606727779236829 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_11 : Uω (aρ 11) (bρ 11) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1252,26 +1080,21 @@ lemma U_630_11 : have hlg : Real.log (1969577499663141 / 4000000000000000 : ℝ) ≤ (-(7084753080275469726601 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1969577499663141 / 4000000000000000 : ℝ) = - (1969577499663141 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1969577499663141 / 1000000000000000 : ℚ)) - (U := (6778190525724530273399 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1969577499663141 / 1000000000000000 : ℝ) ≤ - (6778190525724530273399 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (937697853411141 / 2000000000000000 : ℝ)) (q := - (1969577499663141 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1969577499663141 / 4000000000000000 : ℚ)) + (r' := (1969577499663141 / 1000000000000000 : ℚ)) + (U := (-(7084753080275469726601 / 10000000000000000000000 : ℚ))) + (U' := (6778190525724530273399 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (937697853411141 / 2000000000000000 : ℚ)) + (q := (1969577499663141 / 4000000000000000 : ℚ)) + (U := (-(7084753080275469726601 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_12 : Uω (aρ 12) (bρ 12) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1279,26 +1102,21 @@ lemma U_630_12 : have hlg : Real.log (2177158473993287 / 5000000000000000 : ℝ) ≤ (-(1662834675285439792897 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2177158473993287 / 5000000000000000 : ℝ) = - (2177158473993287 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2177158473993287 / 1250000000000000 : ℚ)) - (U := (1109754045914560207103 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2177158473993287 / 1250000000000000 : ℝ) ≤ - (1109754045914560207103 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (993233940349537 / 2500000000000000 : ℝ)) (q := - (2177158473993287 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2177158473993287 / 5000000000000000 : ℚ)) + (r' := (2177158473993287 / 1250000000000000 : ℚ)) + (U := (-(1662834675285439792897 / 2000000000000000000000 : ℚ))) + (U' := (1109754045914560207103 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (993233940349537 / 2500000000000000 : ℚ)) + (q := (2177158473993287 / 5000000000000000 : ℚ)) + (U := (-(1662834675285439792897 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_13 : Uω (aρ 13) (bρ 13) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1306,26 +1124,21 @@ lemma U_630_13 : have hlg : Real.log (7489443954622891 / 20000000000000000 : ℝ) ≤ (-(9822377166288816452343 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7489443954622891 / 20000000000000000 : ℝ) = - (7489443954622891 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7489443954622891 / 5000000000000000 : ℚ)) - (U := (4040566439711183547657 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7489443954622891 / 5000000000000000 : ℝ) ≤ - (4040566439711183547657 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3153127561642891 / 10000000000000000 : ℝ)) (q := - (7489443954622891 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7489443954622891 / 20000000000000000 : ℚ)) + (r' := (7489443954622891 / 5000000000000000 : ℚ)) + (U := (-(9822377166288816452343 / 10000000000000000000000 : ℚ))) + (U' := (4040566439711183547657 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (3153127561642891 / 10000000000000000 : ℚ)) + (q := (7489443954622891 / 20000000000000000 : ℚ)) + (U := (-(9822377166288816452343 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_14 : Uω (aρ 14) (bρ 14) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1333,25 +1146,21 @@ lemma U_630_14 : have hlg : Real.log (310427487186159 / 1000000000000000 : ℝ) ≤ (-(5849024699973716311919 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (310427487186159 / 1000000000000000 : ℝ) = - (310427487186159 / 250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (310427487186159 / 250000000000000 : ℚ)) - (U := (1082447103026283688081 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (310427487186159 / 250000000000000 : ℝ) ≤ - (1082447103026283688081 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (110808031789409 / 500000000000000 : ℝ)) (q := - (310427487186159 / 1000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (310427487186159 / 1000000000000000 : ℚ)) + (r' := (310427487186159 / 250000000000000 : ℚ)) + (U := (-(5849024699973716311919 / 5000000000000000000000 : ℚ))) + (U' := (1082447103026283688081 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (110808031789409 / 500000000000000 : ℚ)) + (q := (310427487186159 / 1000000000000000 : ℚ)) + (U := (-(5849024699973716311919 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_15 : Uω (aρ 15) (bρ 15) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1359,26 +1168,21 @@ lemma U_630_15 : have hlg : Real.log (4788476294669653 / 20000000000000000 : ℝ) ≤ (-(7147600066389320593217 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (4788476294669653 / 20000000000000000 : ℝ) = - (4788476294669653 / 2500000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4788476294669653 / 2500000000000000 : ℚ)) - (U := (3249607638110679406783 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4788476294669653 / 2500000000000000 : ℝ) ≤ - (3249607638110679406783 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1055660464149653 / 10000000000000000 : ℝ)) (q := - (4788476294669653 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4788476294669653 / 20000000000000000 : ℚ)) + (r' := (4788476294669653 / 2500000000000000 : ℚ)) + (U := (-(7147600066389320593217 / 5000000000000000000000 : ℚ))) + (U' := (3249607638110679406783 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (1462797872781 / 2000000000000 : ℚ)) + (s := (1055660464149653 / 10000000000000000 : ℚ)) + (q := (4788476294669653 / 20000000000000000 : ℚ)) + (U := (-(7147600066389320593217 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_630_16 : Uω (aρ 16) (bρ 16) (1462797872781 / 2000000000000 : ℝ) ≤ @@ -1475,25 +1279,21 @@ lemma U_631_1 : have hlg : Real.log (29035975395915803 / 40000000000000000 : ℝ) ≤ (-(3203438617965511292341 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29035975395915803 / 40000000000000000 : ℝ) = - (29035975395915803 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29035975395915803 / 20000000000000000 : ℚ)) - (U := (3728033185034488707659 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29035975395915803 / 20000000000000000 : ℝ) ≤ - (3728033185034488707659 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7258971577588839 / 10000000000000000 : ℝ)) (q := - (29035975395915803 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29035975395915803 / 40000000000000000 : ℚ)) + (r' := (29035975395915803 / 20000000000000000 : ℚ)) + (U := (-(3203438617965511292341 / 10000000000000000000000 : ℚ))) + (U' := (3728033185034488707659 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (7258971577588839 / 10000000000000000 : ℚ)) + (q := (29035975395915803 / 40000000000000000 : ℚ)) + (U := (-(3203438617965511292341 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_2 : Uω (aρ 2) (bρ 2) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1501,25 +1301,21 @@ lemma U_631_2 : have hlg : Real.log (28940401887004121 / 40000000000000000 : ℝ) ≤ (-(3236408458429937679207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28940401887004121 / 40000000000000000 : ℝ) = - (28940401887004121 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28940401887004121 / 20000000000000000 : ℚ)) - (U := (3695063344570062320793 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28940401887004121 / 20000000000000000 : ℝ) ≤ - (3695063344570062320793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3617476917821499 / 5000000000000000 : ℝ)) (q := - (28940401887004121 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28940401887004121 / 40000000000000000 : ℚ)) + (r' := (28940401887004121 / 20000000000000000 : ℚ)) + (U := (-(3236408458429937679207 / 10000000000000000000000 : ℚ))) + (U' := (3695063344570062320793 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (3617476917821499 / 5000000000000000 : ℚ)) + (q := (28940401887004121 / 40000000000000000 : ℚ)) + (U := (-(3236408458429937679207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_3 : Uω (aρ 3) (bρ 3) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1527,25 +1323,21 @@ lemma U_631_3 : have hlg : Real.log (28749345362884991 / 40000000000000000 : ℝ) ≤ (-(132105782742592253447 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28749345362884991 / 40000000000000000 : ℝ) = - (28749345362884991 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28749345362884991 / 20000000000000000 : ℚ)) - (U := (145153089377407746553 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28749345362884991 / 20000000000000000 : ℝ) ≤ - (145153089377407746553 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7186821679933433 / 10000000000000000 : ℝ)) (q := - (28749345362884991 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28749345362884991 / 40000000000000000 : ℚ)) + (r' := (28749345362884991 / 20000000000000000 : ℚ)) + (U := (-(132105782742592253447 / 400000000000000000000 : ℚ))) + (U' := (145153089377407746553 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (7186821679933433 / 10000000000000000 : ℚ)) + (q := (28749345362884991 / 40000000000000000 : ℚ)) + (U := (-(132105782742592253447 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_4 : Uω (aρ 4) (bρ 4) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1553,25 +1345,21 @@ lemma U_631_4 : have hlg : Real.log (28432306957705233 / 40000000000000000 : ℝ) ≤ (-(3413533862948097198867 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28432306957705233 / 40000000000000000 : ℝ) = - (28432306957705233 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28432306957705233 / 20000000000000000 : ℚ)) - (U := (3517937940051902801133 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28432306957705233 / 20000000000000000 : ℝ) ≤ - (3517937940051902801133 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3553298329204277 / 5000000000000000 : ℝ)) (q := - (28432306957705233 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28432306957705233 / 40000000000000000 : ℚ)) + (r' := (28432306957705233 / 20000000000000000 : ℚ)) + (U := (-(3413533862948097198867 / 10000000000000000000000 : ℚ))) + (U' := (3517937940051902801133 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (3553298329204277 / 5000000000000000 : ℚ)) + (q := (28432306957705233 / 40000000000000000 : ℚ)) + (U := (-(3413533862948097198867 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_5 : Uω (aρ 5) (bρ 5) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1579,25 +1367,21 @@ lemma U_631_5 : have hlg : Real.log (27950224254878789 / 40000000000000000 : ℝ) ≤ (-(3584542308547022505337 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27950224254878789 / 40000000000000000 : ℝ) = - (27950224254878789 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27950224254878789 / 20000000000000000 : ℚ)) - (U := (3346929494452977494663 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27950224254878789 / 20000000000000000 : ℝ) ≤ - (3346929494452977494663 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1745936306582583 / 2500000000000000 : ℝ)) (q := - (27950224254878789 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27950224254878789 / 40000000000000000 : ℚ)) + (r' := (27950224254878789 / 20000000000000000 : ℚ)) + (U := (-(3584542308547022505337 / 10000000000000000000000 : ℚ))) + (U' := (3346929494452977494663 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (1745936306582583 / 2500000000000000 : ℚ)) + (q := (27950224254878789 / 40000000000000000 : ℚ)) + (U := (-(3584542308547022505337 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_6 : Uω (aρ 6) (bρ 6) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1605,25 +1389,21 @@ lemma U_631_6 : have hlg : Real.log (27260491417810903 / 40000000000000000 : ℝ) ≤ (-(3834410006823929320503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27260491417810903 / 40000000000000000 : ℝ) = - (27260491417810903 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27260491417810903 / 20000000000000000 : ℚ)) - (U := (3097061796176070679497 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27260491417810903 / 20000000000000000 : ℝ) ≤ - (3097061796176070679497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6806119182936389 / 10000000000000000 : ℝ)) (q := - (27260491417810903 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27260491417810903 / 40000000000000000 : ℚ)) + (r' := (27260491417810903 / 20000000000000000 : ℚ)) + (U := (-(3834410006823929320503 / 10000000000000000000000 : ℚ))) + (U' := (3097061796176070679497 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (6806119182936389 / 10000000000000000 : ℚ)) + (q := (27260491417810903 / 40000000000000000 : ℚ)) + (U := (-(3834410006823929320503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_7 : Uω (aρ 7) (bρ 7) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1631,25 +1411,21 @@ lemma U_631_7 : have hlg : Real.log (26323039726371219 / 40000000000000000 : ℝ) ≤ (-(836869725883868706071 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26323039726371219 / 40000000000000000 : ℝ) = - (26323039726371219 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26323039726371219 / 20000000000000000 : ℚ)) - (U := (549424634716131293929 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26323039726371219 / 20000000000000000 : ℝ) ≤ - (549424634716131293929 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6561054717976547 / 10000000000000000 : ℝ)) (q := - (26323039726371219 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26323039726371219 / 40000000000000000 : ℚ)) + (r' := (26323039726371219 / 20000000000000000 : ℚ)) + (U := (-(836869725883868706071 / 2000000000000000000000 : ℚ))) + (U' := (549424634716131293929 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (6561054717976547 / 10000000000000000 : ℚ)) + (q := (26323039726371219 / 40000000000000000 : ℚ)) + (U := (-(836869725883868706071 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_8 : Uω (aρ 8) (bρ 8) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1657,25 +1433,21 @@ lemma U_631_8 : have hlg : Real.log (25106948751277561 / 40000000000000000 : ℝ) ≤ (-(931469606699471203557 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25106948751277561 / 40000000000000000 : ℝ) = - (25106948751277561 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25106948751277561 / 20000000000000000 : ℚ)) - (U := (454824753900528796443 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (25106948751277561 / 20000000000000000 : ℝ) ≤ - (454824753900528796443 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3118275440884859 / 5000000000000000 : ℝ)) (q := - (25106948751277561 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25106948751277561 / 40000000000000000 : ℚ)) + (r' := (25106948751277561 / 20000000000000000 : ℚ)) + (U := (-(931469606699471203557 / 2000000000000000000000 : ℚ))) + (U' := (454824753900528796443 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (3118275440884859 / 5000000000000000 : ℚ)) + (q := (25106948751277561 / 40000000000000000 : ℚ)) + (U := (-(931469606699471203557 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_9 : Uω (aρ 9) (bρ 9) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1683,25 +1455,21 @@ lemma U_631_9 : have hlg : Real.log (4719352480403037 / 8000000000000000 : ℝ) ≤ (-(5277699375886241265793 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4719352480403037 / 8000000000000000 : ℝ) = - (4719352480403037 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4719352480403037 / 4000000000000000 : ℚ)) - (U := (1653772427113758734207 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4719352480403037 / 4000000000000000 : ℝ) ≤ - (1653772427113758734207 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (582242333549853 / 1000000000000000 : ℝ)) (q := - (4719352480403037 / 8000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4719352480403037 / 8000000000000000 : ℚ)) + (r' := (4719352480403037 / 4000000000000000 : ℚ)) + (U := (-(5277699375886241265793 / 10000000000000000000000 : ℚ))) + (U' := (1653772427113758734207 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (582242333549853 / 1000000000000000 : ℚ)) + (q := (4719352480403037 / 8000000000000000 : ℚ)) + (U := (-(5277699375886241265793 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_10 : Uω (aρ 10) (bρ 10) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1709,26 +1477,21 @@ lemma U_631_10 : have hlg : Real.log (21797332289658697 / 40000000000000000 : ℝ) ≤ (-(758864829476275798249 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21797332289658697 / 40000000000000000 : ℝ) = - (21797332289658697 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21797332289658697 / 20000000000000000 : ℚ)) - (U := (107569145898724201751 / 1250000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21797332289658697 / 20000000000000000 : ℝ) ≤ - (107569145898724201751 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2655633656407643 / 5000000000000000 : ℝ)) (q := - (21797332289658697 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21797332289658697 / 40000000000000000 : ℚ)) + (r' := (21797332289658697 / 20000000000000000 : ℚ)) + (U := (-(758864829476275798249 / 1250000000000000000000 : ℚ))) + (U' := (107569145898724201751 / 1250000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (2655633656407643 / 5000000000000000 : ℚ)) + (q := (21797332289658697 / 40000000000000000 : ℚ)) + (U := (-(758864829476275798249 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_11 : Uω (aρ 11) (bρ 11) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1736,26 +1499,21 @@ lemma U_631_11 : have hlg : Real.log (19735779986684331 / 40000000000000000 : ℝ) ≤ (-(7064462222460948975133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19735779986684331 / 40000000000000000 : ℝ) = - (19735779986684331 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19735779986684331 / 10000000000000000 : ℚ)) - (U := (6798481383539051024867 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19735779986684331 / 10000000000000000 : ℝ) ≤ - (6798481383539051024867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4698967787533103 / 10000000000000000 : ℝ)) (q := - (19735779986684331 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19735779986684331 / 40000000000000000 : ℚ)) + (r' := (19735779986684331 / 10000000000000000 : ℚ)) + (U := (-(7064462222460948975133 / 10000000000000000000000 : ℚ))) + (U' := (6798481383539051024867 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (4698967787533103 / 10000000000000000 : ℚ)) + (q := (19735779986684331 / 40000000000000000 : ℚ)) + (U := (-(7064462222460948975133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_12 : Uω (aρ 12) (bρ 12) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1763,26 +1521,21 @@ lemma U_631_12 : have hlg : Real.log (17459011117584283 / 40000000000000000 : ℝ) ≤ (-(8290235418091904679413 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17459011117584283 / 40000000000000000 : ℝ) = - (17459011117584283 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17459011117584283 / 10000000000000000 : ℚ)) - (U := (5572708187908095320587 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17459011117584283 / 10000000000000000 : ℝ) ≤ - (5572708187908095320587 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3984283449668079 / 10000000000000000 : ℝ)) (q := - (17459011117584283 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17459011117584283 / 40000000000000000 : ℚ)) + (r' := (17459011117584283 / 10000000000000000 : ℚ)) + (U := (-(8290235418091904679413 / 10000000000000000000000 : ℚ))) + (U' := (5572708187908095320587 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (3984283449668079 / 10000000000000000 : ℚ)) + (q := (17459011117584283 / 40000000000000000 : ℚ)) + (U := (-(8290235418091904679413 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_13 : Uω (aρ 13) (bρ 13) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1790,26 +1543,21 @@ lemma U_631_13 : have hlg : Real.log (15024105881875133 / 40000000000000000 : ℝ) ≤ (-(9792234836373217187103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15024105881875133 / 40000000000000000 : ℝ) = - (15024105881875133 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15024105881875133 / 10000000000000000 : ℚ)) - (U := (4070708769626782812897 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15024105881875133 / 10000000000000000 : ℝ) ≤ - (4070708769626782812897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (395776571676063 / 1250000000000000 : ℝ)) (q := - (15024105881875133 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15024105881875133 / 40000000000000000 : ℚ)) + (r' := (15024105881875133 / 10000000000000000 : ℚ)) + (U := (-(9792234836373217187103 / 10000000000000000000000 : ℚ))) + (U' := (4070708769626782812897 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (395776571676063 / 1250000000000000 : ℚ)) + (q := (15024105881875133 / 40000000000000000 : ℚ)) + (U := (-(9792234836373217187103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_14 : Uω (aρ 14) (bρ 14) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1817,26 +1565,21 @@ lemma U_631_14 : have hlg : Real.log (12470370911958191 / 40000000000000000 : ℝ) ≤ (-(2913809875003440331781 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12470370911958191 / 40000000000000000 : ℝ) = - (12470370911958191 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12470370911958191 / 10000000000000000 : ℚ)) - (U := (551926026496559668219 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12470370911958191 / 10000000000000000 : ℝ) ≤ - (551926026496559668219 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2233272373495033 / 10000000000000000 : ℝ)) (q := - (12470370911958191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12470370911958191 / 40000000000000000 : ℚ)) + (r' := (12470370911958191 / 10000000000000000 : ℚ)) + (U := (-(2913809875003440331781 / 2500000000000000000000 : ℚ))) + (U' := (551926026496559668219 / 2500000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (2233272373495033 / 10000000000000000 : ℚ)) + (q := (12470370911958191 / 40000000000000000 : ℚ)) + (U := (-(2913809875003440331781 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_15 : Uω (aρ 15) (bρ 15) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1844,26 +1587,21 @@ lemma U_631_15 : have hlg : Real.log (9662396035747569 / 40000000000000000 : ℝ) ≤ (-(221974656099820521723 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9662396035747569 / 40000000000000000 : ℝ) = - (9662396035747569 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9662396035747569 / 5000000000000000 : ℚ)) - (U := (102938084665804478277 / 156250000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9662396035747569 / 5000000000000000 : ℝ) ≤ - (102938084665804478277 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (544429106402361 / 5000000000000000 : ℝ)) (q := - (9662396035747569 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9662396035747569 / 40000000000000000 : ℚ)) + (r' := (9662396035747569 / 5000000000000000 : ℚ)) + (U := (-(221974656099820521723 / 156250000000000000000 : ℚ))) + (U' := (102938084665804478277 / 156250000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23435242683053 / 32000000000000 : ℚ)) + (s := (544429106402361 / 5000000000000000 : ℚ)) + (q := (9662396035747569 / 40000000000000000 : ℚ)) + (U := (-(221974656099820521723 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_631_16 : Uω (aρ 16) (bρ 16) (23435242683053 / 32000000000000 : ℝ) ≤ @@ -1961,25 +1699,21 @@ lemma U_632_1 : have hlg : Real.log (14537035705420829 / 20000000000000000 : ℝ) ≤ (-(1595163468387701664069 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14537035705420829 / 20000000000000000 : ℝ) = - (14537035705420829 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14537035705420829 / 10000000000000000 : ℚ)) - (U := (1870572433112298335931 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14537035705420829 / 10000000000000000 : ℝ) ≤ - (1870572433112298335931 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (454280975656419 / 625000000000000 : ℝ)) (q := - (14537035705420829 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14537035705420829 / 20000000000000000 : ℚ)) + (r' := (14537035705420829 / 10000000000000000 : ℚ)) + (U := (-(1595163468387701664069 / 5000000000000000000000 : ℚ))) + (U' := (1870572433112298335931 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (454280975656419 / 625000000000000 : ℚ)) + (q := (14537035705420829 / 20000000000000000 : ℚ)) + (U := (-(1595163468387701664069 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_2 : Uω (aρ 2) (bρ 2) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -1987,25 +1721,21 @@ lemma U_632_2 : have hlg : Real.log (905578079884461 / 1250000000000000 : ℝ) ≤ (-(3223253279550098399567 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (905578079884461 / 1250000000000000 : ℝ) = - (905578079884461 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (905578079884461 / 625000000000000 : ℚ)) - (U := (3708218523449901600433 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (905578079884461 / 625000000000000 : ℝ) ≤ - (3708218523449901600433 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7244478195743251 / 10000000000000000 : ℝ)) (q := - (905578079884461 / 1250000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (905578079884461 / 1250000000000000 : ℚ)) + (r' := (905578079884461 / 625000000000000 : ℚ)) + (U := (-(3223253279550098399567 / 10000000000000000000000 : ℚ))) + (U' := (3708218523449901600433 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (7244478195743251 / 10000000000000000 : ℚ)) + (q := (905578079884461 / 1250000000000000 : ℚ)) + (U := (-(3223253279550098399567 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_3 : Uω (aρ 3) (bρ 3) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2013,25 +1743,21 @@ lemma U_632_3 : have hlg : Real.log (14393721992791967 / 20000000000000000 : ℝ) ≤ (-(3289401344986094540583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14393721992791967 / 20000000000000000 : ℝ) = - (14393721992791967 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14393721992791967 / 10000000000000000 : ℚ)) - (U := (3642070458013905459417 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14393721992791967 / 10000000000000000 : ℝ) ≤ - (3642070458013905459417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3598173508366921 / 5000000000000000 : ℝ)) (q := - (14393721992791967 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14393721992791967 / 20000000000000000 : ℚ)) + (r' := (14393721992791967 / 10000000000000000 : ℚ)) + (U := (-(3289401344986094540583 / 10000000000000000000000 : ℚ))) + (U' := (3642070458013905459417 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (3598173508366921 / 5000000000000000 : ℚ)) + (q := (14393721992791967 / 20000000000000000 : ℚ)) + (U := (-(3289401344986094540583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_4 : Uω (aρ 4) (bρ 4) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2039,25 +1765,21 @@ lemma U_632_4 : have hlg : Real.log (889700336858133 / 1250000000000000 : ℝ) ≤ (-(680028248331685089271 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (889700336858133 / 1250000000000000 : ℝ) = - (889700336858133 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (889700336858133 / 625000000000000 : ℚ)) - (U := (706266112268314910729 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (889700336858133 / 625000000000000 : ℝ) ≤ - (706266112268314910729 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7116124594737003 / 10000000000000000 : ℝ)) (q := - (889700336858133 / 1250000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (889700336858133 / 1250000000000000 : ℚ)) + (r' := (889700336858133 / 625000000000000 : ℚ)) + (U := (-(680028248331685089271 / 2000000000000000000000 : ℚ))) + (U' := (706266112268314910729 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (7116124594737003 / 10000000000000000 : ℚ)) + (q := (889700336858133 / 1250000000000000 : ℚ)) + (U := (-(680028248331685089271 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_5 : Uω (aρ 5) (bρ 5) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2065,25 +1787,21 @@ lemma U_632_5 : have hlg : Real.log (6997085228157827 / 10000000000000000 : ℝ) ≤ (-(1785457131865592913579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6997085228157827 / 10000000000000000 : ℝ) = - (6997085228157827 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6997085228157827 / 5000000000000000 : ℚ)) - (U := (1680278769634407086421 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6997085228157827 / 5000000000000000 : ℝ) ≤ - (1680278769634407086421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6993279580657529 / 10000000000000000 : ℝ)) (q := - (6997085228157827 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6997085228157827 / 10000000000000000 : ℚ)) + (r' := (6997085228157827 / 5000000000000000 : ℚ)) + (U := (-(1785457131865592913579 / 5000000000000000000000 : ℚ))) + (U' := (1680278769634407086421 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (6993279580657529 / 10000000000000000 : ℚ)) + (q := (6997085228157827 / 10000000000000000 : ℚ)) + (U := (-(1785457131865592913579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_6 : Uω (aρ 6) (bρ 6) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2091,25 +1809,21 @@ lemma U_632_6 : have hlg : Real.log (3412329705219033 / 5000000000000000 : ℝ) ≤ (-(1910213280704012408157 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3412329705219033 / 5000000000000000 : ℝ) = - (3412329705219033 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3412329705219033 / 2500000000000000 : ℚ)) - (U := (1555522620795987591843 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3412329705219033 / 2500000000000000 : ℝ) ≤ - (1555522620795987591843 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6815668320358007 / 10000000000000000 : ℝ)) (q := - (3412329705219033 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3412329705219033 / 5000000000000000 : ℚ)) + (r' := (3412329705219033 / 2500000000000000 : ℚ)) + (U := (-(1910213280704012408157 / 5000000000000000000000 : ℚ))) + (U' := (1555522620795987591843 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (6815668320358007 / 10000000000000000 : ℚ)) + (q := (3412329705219033 / 5000000000000000 : ℚ)) + (U := (-(1910213280704012408157 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_7 : Uω (aρ 7) (bρ 7) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2117,25 +1831,21 @@ lemma U_632_7 : have hlg : Real.log (13180624936974249 / 20000000000000000 : ℝ) ≤ (-(4169843297918505665339 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13180624936974249 / 20000000000000000 : ℝ) = - (13180624936974249 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13180624936974249 / 10000000000000000 : ℚ)) - (U := (2761628505081494334661 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13180624936974249 / 10000000000000000 : ℝ) ≤ - (2761628505081494334661 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1642658954304031 / 2500000000000000 : ℝ)) (q := - (13180624936974249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13180624936974249 / 20000000000000000 : ℚ)) + (r' := (13180624936974249 / 10000000000000000 : ℚ)) + (U := (-(4169843297918505665339 / 10000000000000000000000 : ℚ))) + (U' := (2761628505081494334661 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (1642658954304031 / 2500000000000000 : ℚ)) + (q := (13180624936974249 / 20000000000000000 : ℚ)) + (U := (-(4169843297918505665339 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_8 : Uω (aρ 8) (bρ 8) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2143,25 +1853,21 @@ lemma U_632_8 : have hlg : Real.log (157158060939673 / 250000000000000 : ℝ) ≤ (-(2321044305584939681371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (157158060939673 / 250000000000000 : ℝ) = - (157158060939673 / 125000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (157158060939673 / 125000000000000 : ℚ)) - (U := (1144691595915060318629 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (157158060939673 / 125000000000000 : ℝ) ≤ - (1144691595915060318629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1249239481351143 / 2000000000000000 : ℝ)) (q := - (157158060939673 / 250000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (157158060939673 / 250000000000000 : ℚ)) + (r' := (157158060939673 / 125000000000000 : ℚ)) + (U := (-(2321044305584939681371 / 5000000000000000000000 : ℚ))) + (U' := (1144691595915060318629 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (1249239481351143 / 2000000000000000 : ℚ)) + (q := (157158060939673 / 250000000000000 : ℚ)) + (U := (-(2321044305584939681371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_9 : Uω (aρ 9) (bρ 9) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2169,25 +1875,21 @@ lemma U_632_9 : have hlg : Real.log (11817679877255061 / 20000000000000000 : ℝ) ≤ (-(5261355684633632966319 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11817679877255061 / 20000000000000000 : ℝ) = - (11817679877255061 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11817679877255061 / 10000000000000000 : ℚ)) - (U := (1670116118366367033681 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11817679877255061 / 10000000000000000 : ℝ) ≤ - (1670116118366367033681 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (729024754649617 / 1250000000000000 : ℝ)) (q := - (11817679877255061 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11817679877255061 / 20000000000000000 : ℚ)) + (r' := (11817679877255061 / 10000000000000000 : ℚ)) + (U := (-(5261355684633632966319 / 10000000000000000000000 : ℚ))) + (U' := (1670116118366367033681 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (729024754649617 / 1250000000000000 : ℚ)) + (q := (11817679877255061 / 20000000000000000 : ℚ)) + (U := (-(5261355684633632966319 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_10 : Uω (aρ 10) (bρ 10) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2195,26 +1897,21 @@ lemma U_632_10 : have hlg : Real.log (10918208333840763 / 20000000000000000 : ℝ) ≤ (-(6053003884311726330449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10918208333840763 / 20000000000000000 : ℝ) = - (10918208333840763 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10918208333840763 / 10000000000000000 : ℚ)) - (U := (878467918688273669551 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10918208333840763 / 10000000000000000 : ℝ) ≤ - (878467918688273669551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2660642763638819 / 5000000000000000 : ℝ)) (q := - (10918208333840763 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10918208333840763 / 20000000000000000 : ℚ)) + (r' := (10918208333840763 / 10000000000000000 : ℚ)) + (U := (-(6053003884311726330449 / 10000000000000000000000 : ℚ))) + (U' := (878467918688273669551 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (2660642763638819 / 5000000000000000 : ℚ)) + (q := (10918208333840763 / 20000000000000000 : ℚ)) + (U := (-(6053003884311726330449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_11 : Uω (aρ 11) (bρ 11) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2222,26 +1919,21 @@ lemma U_632_11 : have hlg : Real.log (1977577686822209 / 4000000000000000 : ℝ) ≤ (-(7044216553404438458349 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1977577686822209 / 4000000000000000 : ℝ) = - (1977577686822209 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1977577686822209 / 1000000000000000 : ℚ)) - (U := (6818727052595561541651 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1977577686822209 / 1000000000000000 : ℝ) ≤ - (6818727052595561541651 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117736056343823 / 250000000000000 : ℝ)) (q := - (1977577686822209 / 4000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1977577686822209 / 4000000000000000 : ℚ)) + (r' := (1977577686822209 / 1000000000000000 : ℚ)) + (U := (-(7044216553404438458349 / 10000000000000000000000 : ℚ))) + (U' := (6818727052595561541651 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (117736056343823 / 250000000000000 : ℚ)) + (q := (1977577686822209 / 4000000000000000 : ℚ)) + (U := (-(7044216553404438458349 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_12 : Uω (aρ 12) (bρ 12) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2249,26 +1941,21 @@ lemma U_632_12 : have hlg : Real.log (8750367695210443 / 20000000000000000 : ℝ) ≤ (-(4133182756188624599249 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8750367695210443 / 20000000000000000 : ℝ) = - (8750367695210443 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8750367695210443 / 5000000000000000 : ℚ)) - (U := (2798289046811375400751 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8750367695210443 / 5000000000000000 : ℝ) ≤ - (2798289046811375400751 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1997810805768659 / 5000000000000000 : ℝ)) (q := - (8750367695210443 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8750367695210443 / 20000000000000000 : ℚ)) + (r' := (8750367695210443 / 5000000000000000 : ℚ)) + (U := (-(4133182756188624599249 / 5000000000000000000000 : ℚ))) + (U' := (2798289046811375400751 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (1997810805768659 / 5000000000000000 : ℚ)) + (q := (8750367695210443 / 20000000000000000 : ℚ)) + (U := (-(4133182756188624599249 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_13 : Uω (aρ 13) (bρ 13) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2276,26 +1963,21 @@ lemma U_632_13 : have hlg : Real.log (7534636603494341 / 20000000000000000 : ℝ) ≤ (-(9762216699229738464429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7534636603494341 / 20000000000000000 : ℝ) = - (7534636603494341 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7534636603494341 / 5000000000000000 : ℚ)) - (U := (4100726906770261535571 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7534636603494341 / 5000000000000000 : ℝ) ≤ - (4100726906770261535571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (397409032677027 / 1250000000000000 : ℝ)) (q := - (7534636603494341 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7534636603494341 / 20000000000000000 : ℚ)) + (r' := (7534636603494341 / 5000000000000000 : ℚ)) + (U := (-(9762216699229738464429 / 10000000000000000000000 : ℚ))) + (U' := (4100726906770261535571 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (397409032677027 / 1250000000000000 : ℚ)) + (q := (7534636603494341 / 20000000000000000 : ℚ)) + (U := (-(9762216699229738464429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_14 : Uω (aρ 14) (bρ 14) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2303,26 +1985,21 @@ lemma U_632_14 : have hlg : Real.log (6261731357118699 / 20000000000000000 : ℝ) ≤ (-(11612755515422022468479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6261731357118699 / 20000000000000000 : ℝ) = - (6261731357118699 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6261731357118699 / 5000000000000000 : ℚ)) - (U := (2250188090577977531521 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6261731357118699 / 5000000000000000 : ℝ) ≤ - (2250188090577977531521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1125147150042787 / 5000000000000000 : ℝ)) (q := - (6261731357118699 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6261731357118699 / 20000000000000000 : ℚ)) + (r' := (6261731357118699 / 5000000000000000 : ℚ)) + (U := (-(11612755515422022468479 / 10000000000000000000000 : ℚ))) + (U' := (2250188090577977531521 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (1125147150042787 / 5000000000000000 : ℚ)) + (q := (6261731357118699 / 20000000000000000 : ℚ)) + (U := (-(11612755515422022468479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_15 : Uω (aρ 15) (bρ 15) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2330,26 +2007,21 @@ lemma U_632_15 : have hlg : Real.log (2436509005779369 / 10000000000000000 : ℝ) ≤ (-(2824037625449027245121 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2436509005779369 / 10000000000000000 : ℝ) = - (2436509005779369 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2436509005779369 / 1250000000000000 : ℚ)) - (U := (1334845456350972754879 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2436509005779369 / 1250000000000000 : ℝ) ≤ - (1334845456350972754879 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1121154231940613 / 10000000000000000 : ℝ)) (q := - (2436509005779369 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2436509005779369 / 10000000000000000 : ℚ)) + (r' := (2436509005779369 / 1250000000000000 : ℚ)) + (U := (-(2824037625449027245121 / 2000000000000000000000 : ℚ))) + (U' := (1334845456350972754879 / 2000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (2346571940161 / 3200000000000 : ℚ)) + (s := (1121154231940613 / 10000000000000000 : ℚ)) + (q := (2436509005779369 / 10000000000000000 : ℚ)) + (U := (-(2824037625449027245121 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_632_16 : Uω (aρ 16) (bρ 16) (2346571940161 / 3200000000000 : ℝ) ≤ @@ -2447,25 +2119,21 @@ lemma U_633_1 : have hlg : Real.log (29112167425462007 / 40000000000000000 : ℝ) ≤ (-(1588616212399733649147 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29112167425462007 / 40000000000000000 : ℝ) = - (29112167425462007 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29112167425462007 / 20000000000000000 : ℚ)) - (U := (1877119689100266350853 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29112167425462007 / 20000000000000000 : ℝ) ≤ - (1877119689100266350853 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (909752455407977 / 1250000000000000 : ℝ)) (q := - (29112167425462007 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29112167425462007 / 40000000000000000 : ℚ)) + (r' := (29112167425462007 / 20000000000000000 : ℚ)) + (U := (-(1588616212399733649147 / 5000000000000000000000 : ℚ))) + (U' := (1877119689100266350853 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (909752455407977 / 1250000000000000 : ℚ)) + (q := (29112167425462007 / 40000000000000000 : ℚ)) + (U := (-(1588616212399733649147 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_2 : Uω (aρ 2) (bρ 2) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2473,25 +2141,21 @@ lemma U_633_2 : have hlg : Real.log (29016595223576541 / 40000000000000000 : ℝ) ≤ (-(3210115384507427481169 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29016595223576541 / 40000000000000000 : ℝ) = - (29016595223576541 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29016595223576541 / 20000000000000000 : ℚ)) - (U := (3721356418492572518831 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29016595223576541 / 20000000000000000 : ℝ) ≤ - (3721356418492572518831 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7254002554831083 / 10000000000000000 : ℝ)) (q := - (29016595223576541 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29016595223576541 / 40000000000000000 : ℚ)) + (r' := (29016595223576541 / 20000000000000000 : ℚ)) + (U := (-(3210115384507427481169 / 10000000000000000000000 : ℚ))) + (U' := (3721356418492572518831 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (7254002554831083 / 10000000000000000 : ℚ)) + (q := (29016595223576541 / 40000000000000000 : ℚ)) + (U := (-(3210115384507427481169 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_3 : Uω (aρ 3) (bρ 3) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2499,25 +2163,21 @@ lemma U_633_3 : have hlg : Real.log (28825542601080433 / 40000000000000000 : ℝ) ≤ (-(131047025560400143257 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28825542601080433 / 40000000000000000 : ℝ) = - (28825542601080433 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28825542601080433 / 20000000000000000 : ℚ)) - (U := (146211846559599856743 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28825542601080433 / 20000000000000000 : ℝ) ≤ - (146211846559599856743 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7205872349933029 / 10000000000000000 : ℝ)) (q := - (28825542601080433 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28825542601080433 / 40000000000000000 : ℚ)) + (r' := (28825542601080433 / 20000000000000000 : ℚ)) + (U := (-(131047025560400143257 / 400000000000000000000 : ℚ))) + (U' := (146211846559599856743 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (7205872349933029 / 10000000000000000 : ℚ)) + (q := (28825542601080433 / 40000000000000000 : ℚ)) + (U := (-(131047025560400143257 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_4 : Uω (aρ 4) (bρ 4) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2525,25 +2185,21 @@ lemma U_633_4 : have hlg : Real.log (28508514580030001 / 40000000000000000 : ℝ) ≤ (-(846691635010987255199 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28508514580030001 / 40000000000000000 : ℝ) = - (28508514580030001 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28508514580030001 / 20000000000000000 : ℚ)) - (U := (886176315739012744801 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28508514580030001 / 20000000000000000 : ℝ) ≤ - (886176315739012744801 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7125652520472813 / 10000000000000000 : ℝ)) (q := - (28508514580030001 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28508514580030001 / 40000000000000000 : ℚ)) + (r' := (28508514580030001 / 20000000000000000 : ℚ)) + (U := (-(846691635010987255199 / 2500000000000000000000 : ℚ))) + (U' := (886176315739012744801 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (7125652520472813 / 10000000000000000 : ℚ)) + (q := (28508514580030001 / 40000000000000000 : ℚ)) + (U := (-(846691635010987255199 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_5 : Uω (aρ 5) (bρ 5) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2551,25 +2207,21 @@ lemma U_633_5 : have hlg : Real.log (28026457513886189 / 40000000000000000 : ℝ) ≤ (-(3557304786161391909607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28026457513886189 / 40000000000000000 : ℝ) = - (28026457513886189 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28026457513886189 / 20000000000000000 : ℚ)) - (U := (3374167016838608090393 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28026457513886189 / 20000000000000000 : ℝ) ≤ - (3374167016838608090393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7002813906735907 / 10000000000000000 : ℝ)) (q := - (28026457513886189 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28026457513886189 / 40000000000000000 : ℚ)) + (r' := (28026457513886189 / 20000000000000000 : ℚ)) + (U := (-(3557304786161391909607 / 10000000000000000000000 : ℚ))) + (U' := (3374167016838608090393 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (7002813906735907 / 10000000000000000 : ℚ)) + (q := (28026457513886189 / 40000000000000000 : ℚ)) + (U := (-(3557304786161391909607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_6 : Uω (aρ 6) (bρ 6) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2577,25 +2229,21 @@ lemma U_633_6 : have hlg : Real.log (27336783725058021 / 40000000000000000 : ℝ) ≤ (-(3806462693810826226399 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27336783725058021 / 40000000000000000 : ℝ) = - (27336783725058021 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27336783725058021 / 20000000000000000 : ℚ)) - (U := (3125009109189173773601 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27336783725058021 / 20000000000000000 : ℝ) ≤ - (3125009109189173773601 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6825217387461823 / 10000000000000000 : ℝ)) (q := - (27336783725058021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27336783725058021 / 40000000000000000 : ℚ)) + (r' := (27336783725058021 / 20000000000000000 : ℚ)) + (U := (-(3806462693810826226399 / 10000000000000000000000 : ℚ))) + (U' := (3125009109189173773601 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (6825217387461823 / 10000000000000000 : ℚ)) + (q := (27336783725058021 / 40000000000000000 : ℚ)) + (U := (-(3806462693810826226399 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_7 : Uω (aρ 7) (bρ 7) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2603,25 +2251,21 @@ lemma U_633_7 : have hlg : Real.log (26399459689812871 / 40000000000000000 : ℝ) ≤ (-(2077679551030624965963 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26399459689812871 / 40000000000000000 : ℝ) = - (26399459689812871 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26399459689812871 / 20000000000000000 : ℚ)) - (U := (1388056350469375034037 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26399459689812871 / 20000000000000000 : ℝ) ≤ - (1388056350469375034037 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (411263546912453 / 625000000000000 : ℝ)) (q := - (26399459689812871 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26399459689812871 / 40000000000000000 : ℚ)) + (r' := (26399459689812871 / 20000000000000000 : ℚ)) + (U := (-(2077679551030624965963 / 5000000000000000000000 : ℚ))) + (U' := (1388056350469375034037 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (411263546912453 / 625000000000000 : ℚ)) + (q := (26399459689812871 / 40000000000000000 : ℚ)) + (U := (-(2077679551030624965963 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_8 : Uω (aρ 8) (bρ 8) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2629,25 +2273,21 @@ lemma U_633_8 : have hlg : Real.log (25183629998327079 / 40000000000000000 : ℝ) ≤ (-(4626852736612063300721 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25183629998327079 / 40000000000000000 : ℝ) = - (25183629998327079 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25183629998327079 / 20000000000000000 : ℚ)) - (U := (2304619066387936699279 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25183629998327079 / 20000000000000000 : ℝ) ≤ - (2304619066387936699279 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (95456597232 / 152587890625 : ℝ)) (q := - (25183629998327079 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25183629998327079 / 40000000000000000 : ℚ)) + (r' := (25183629998327079 / 20000000000000000 : ℚ)) + (U := (-(4626852736612063300721 / 10000000000000000000000 : ℚ))) + (U' := (2304619066387936699279 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (95456597232 / 152587890625 : ℚ)) + (q := (25183629998327079 / 40000000000000000 : ℚ)) + (U := (-(4626852736612063300721 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_9 : Uω (aρ 9) (bρ 9) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2655,25 +2295,21 @@ lemma U_633_9 : have hlg : Real.log (23673955450474761 / 40000000000000000 : ℝ) ≤ (-(5245039361152753413503 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23673955450474761 / 40000000000000000 : ℝ) = - (23673955450474761 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23673955450474761 / 20000000000000000 : ℚ)) - (U := (1686432441847246586497 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23673955450474761 / 20000000000000000 : ℝ) ≤ - (1686432441847246586497 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5841971910630193 / 10000000000000000 : ℝ)) (q := - (23673955450474761 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23673955450474761 / 40000000000000000 : ℚ)) + (r' := (23673955450474761 / 20000000000000000 : ℚ)) + (U := (-(5245039361152753413503 / 10000000000000000000000 : ℚ))) + (U' := (1686432441847246586497 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (5841971910630193 / 10000000000000000 : ℚ)) + (q := (23673955450474761 / 40000000000000000 : ℚ)) + (U := (-(5245039361152753413503 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_10 : Uω (aρ 10) (bρ 10) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2681,26 +2317,21 @@ lemma U_633_10 : have hlg : Real.log (21875497422376211 / 40000000000000000 : ℝ) ≤ (-(1508780706400550594719 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21875497422376211 / 40000000000000000 : ℝ) = - (21875497422376211 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21875497422376211 / 20000000000000000 : ℚ)) - (U := (224087244349449405281 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21875497422376211 / 20000000000000000 : ℝ) ≤ - (224087244349449405281 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2665650965037959 / 5000000000000000 : ℝ)) (q := - (21875497422376211 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21875497422376211 / 40000000000000000 : ℚ)) + (r' := (21875497422376211 / 20000000000000000 : ℚ)) + (U := (-(1508780706400550594719 / 2500000000000000000000 : ℚ))) + (U' := (224087244349449405281 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (2665650965037959 / 5000000000000000 : ℚ)) + (q := (21875497422376211 / 40000000000000000 : ℚ)) + (U := (-(1508780706400550594719 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_11 : Uω (aρ 11) (bρ 11) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2708,26 +2339,21 @@ lemma U_633_11 : have hlg : Real.log (19815765695228119 / 40000000000000000 : ℝ) ≤ (-(219500495467645514591 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19815765695228119 / 40000000000000000 : ℝ) = - (19815765695228119 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19815765695228119 / 10000000000000000 : ℚ)) - (U := (213716492219854485409 / 312500000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19815765695228119 / 10000000000000000 : ℝ) ≤ - (213716492219854485409 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (589989086588359 / 1250000000000000 : ℝ)) (q := - (19815765695228119 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19815765695228119 / 40000000000000000 : ℚ)) + (r' := (19815765695228119 / 10000000000000000 : ℚ)) + (U := (-(219500495467645514591 / 312500000000000000000 : ℚ))) + (U' := (213716492219854485409 / 312500000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (589989086588359 / 1250000000000000 : ℚ)) + (q := (19815765695228119 / 40000000000000000 : ℚ)) + (U := (-(219500495467645514591 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_12 : Uω (aρ 12) (bρ 12) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2735,26 +2361,21 @@ lemma U_633_12 : have hlg : Real.log (3508488154438577 / 8000000000000000 : ℝ) ≤ (-(1030320402127628943133 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3508488154438577 / 8000000000000000 : ℝ) = - (3508488154438577 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3508488154438577 / 2000000000000000 : ℚ)) - (U := (702547548622371056867 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (3508488154438577 / 2000000000000000 : ℝ) ≤ - (702547548622371056867 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (801390065574851 / 2000000000000000 : ℝ)) (q := - (3508488154438577 / 8000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3508488154438577 / 8000000000000000 : ℚ)) + (r' := (3508488154438577 / 2000000000000000 : ℚ)) + (U := (-(1030320402127628943133 / 1250000000000000000000 : ℚ))) + (U' := (702547548622371056867 / 1250000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (801390065574851 / 2000000000000000 : ℚ)) + (q := (3508488154438577 / 8000000000000000 : ℚ)) + (U := (-(1030320402127628943133 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_13 : Uω (aρ 13) (bρ 13) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2762,26 +2383,21 @@ lemma U_633_13 : have hlg : Real.log (3022878101236307 / 8000000000000000 : ℝ) ≤ (-(304135046858737321201 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3022878101236307 / 8000000000000000 : ℝ) = - (3022878101236307 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3022878101236307 / 2000000000000000 : ℚ)) - (U := (129081940828762678799 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3022878101236307 / 2000000000000000 : ℝ) ≤ - (129081940828762678799 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (159615346823179 / 500000000000000 : ℝ)) (q := - (3022878101236307 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3022878101236307 / 8000000000000000 : ℚ)) + (r' := (3022878101236307 / 2000000000000000 : ℚ)) + (U := (-(304135046858737321201 / 312500000000000000000 : ℚ))) + (U' := (129081940828762678799 / 312500000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (159615346823179 / 500000000000000 : ℚ)) + (q := (3022878101236307 / 8000000000000000 : ℚ)) + (U := (-(304135046858737321201 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_14 : Uω (aρ 14) (bρ 14) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2789,26 +2405,21 @@ lemma U_633_14 : have hlg : Real.log (12576378939996057 / 40000000000000000 : ℝ) ≤ (-(11570590863640125216681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12576378939996057 / 40000000000000000 : ℝ) = - (12576378939996057 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12576378939996057 / 10000000000000000 : ℚ)) - (U := (2292352742359874783319 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (12576378939996057 / 10000000000000000 : ℝ) ≤ - (2292352742359874783319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2267228438415841 / 10000000000000000 : ℝ)) (q := - (12576378939996057 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12576378939996057 / 40000000000000000 : ℚ)) + (r' := (12576378939996057 / 10000000000000000 : ℚ)) + (U := (-(11570590863640125216681 / 10000000000000000000000 : ℚ))) + (U' := (2292352742359874783319 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (2267228438415841 / 10000000000000000 : ℚ)) + (q := (12576378939996057 / 40000000000000000 : ℚ)) + (U := (-(11570590863640125216681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_15 : Uω (aρ 15) (bρ 15) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2816,26 +2427,21 @@ lemma U_633_15 : have hlg : Real.log (9828024152786267 / 40000000000000000 : ℝ) ≤ (-(7018207705648636198711 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9828024152786267 / 40000000000000000 : ℝ) = - (9828024152786267 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9828024152786267 / 5000000000000000 : ℚ)) - (U := (3378999998851363801289 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9828024152786267 / 5000000000000000 : ℝ) ≤ - (3378999998851363801289 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (576312161112973 / 5000000000000000 : ℝ)) (q := - (9828024152786267 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9828024152786267 / 40000000000000000 : ℚ)) + (r' := (9828024152786267 / 5000000000000000 : ℚ)) + (U := (-(7018207705648636198711 / 5000000000000000000000 : ℚ))) + (U' := (3378999998851363801289 / 5000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23496196120167 / 32000000000000 : ℚ)) + (s := (576312161112973 / 5000000000000000 : ℚ)) + (q := (9828024152786267 / 40000000000000000 : ℚ)) + (U := (-(7018207705648636198711 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_633_16 : Uω (aρ 16) (bρ 16) (23496196120167 / 32000000000000 : ℝ) ≤ @@ -2931,25 +2537,21 @@ lemma U_634_1 : have hlg : Real.log (583005268795561 / 800000000000000 : ℝ) ≤ (-(3164155037131447097627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (583005268795561 / 800000000000000 : ℝ) = - (583005268795561 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (583005268795561 / 400000000000000 : ℚ)) - (U := (3767316765868552902373 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (583005268795561 / 400000000000000 : ℝ) ≤ - (3767316765868552902373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (291501747034911 / 400000000000000 : ℝ)) (q := - (583005268795561 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (583005268795561 / 800000000000000 : ℚ)) + (r' := (583005268795561 / 400000000000000 : ℚ)) + (U := (-(3164155037131447097627 / 10000000000000000000000 : ℚ))) + (U' := (3767316765868552902373 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (291501747034911 / 400000000000000 : ℚ)) + (q := (583005268795561 / 800000000000000 : ℚ)) + (U := (-(3164155037131447097627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_2 : Uω (aρ 2) (bρ 2) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -2957,25 +2559,21 @@ lemma U_634_2 : have hlg : Real.log (7263672972208363 / 10000000000000000 : ℝ) ≤ (-(3196994727943193935909 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7263672972208363 / 10000000000000000 : ℝ) = - (7263672972208363 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7263672972208363 / 5000000000000000 : ℚ)) - (U := (3734477075056806064091 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7263672972208363 / 5000000000000000 : ℝ) ≤ - (3734477075056806064091 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1815881728227619 / 2500000000000000 : ℝ)) (q := - (7263672972208363 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7263672972208363 / 10000000000000000 : ℚ)) + (r' := (7263672972208363 / 5000000000000000 : ℚ)) + (U := (-(3196994727943193935909 / 10000000000000000000000 : ℚ))) + (U' := (3734477075056806064091 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (1815881728227619 / 2500000000000000 : ℚ)) + (q := (7263672972208363 / 10000000000000000 : ℚ)) + (U := (-(3196994727943193935909 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_3 : Uω (aρ 3) (bρ 3) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -2983,25 +2581,21 @@ lemma U_634_3 : have hlg : Real.log (7215910302350753 / 10000000000000000 : ℝ) ≤ (-(163148370217400263421 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7215910302350753 / 10000000000000000 : ℝ) = - (7215910302350753 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7215910302350753 / 5000000000000000 : ℚ)) - (U := (183425219932599736579 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7215910302350753 / 5000000000000000 : ℝ) ≤ - (183425219932599736579 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (901924709943157 / 1250000000000000 : ℝ)) (q := - (7215910302350753 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7215910302350753 / 10000000000000000 : ℚ)) + (r' := (7215910302350753 / 5000000000000000 : ℚ)) + (U := (-(163148370217400263421 / 500000000000000000000 : ℚ))) + (U' := (183425219932599736579 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (901924709943157 / 1250000000000000 : ℚ)) + (q := (7215910302350753 / 10000000000000000 : ℚ)) + (U := (-(163148370217400263421 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_4 : Uω (aρ 4) (bρ 4) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3009,25 +2603,21 @@ lemma U_634_4 : have hlg : Real.log (14273309179749669 / 20000000000000000 : ℝ) ≤ (-(3373409710194953931207 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14273309179749669 / 20000000000000000 : ℝ) = - (14273309179749669 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14273309179749669 / 10000000000000000 : ℚ)) - (U := (3558062092805046068793 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14273309179749669 / 10000000000000000 : ℝ) ≤ - (3558062092805046068793 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7135180435658419 / 10000000000000000 : ℝ)) (q := - (14273309179749669 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14273309179749669 / 20000000000000000 : ℚ)) + (r' := (14273309179749669 / 10000000000000000 : ℚ)) + (U := (-(3373409710194953931207 / 10000000000000000000000 : ℚ))) + (U' := (3558062092805046068793 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (7135180435658419 / 10000000000000000 : ℚ)) + (q := (14273309179749669 / 20000000000000000 : ℚ)) + (U := (-(3373409710194953931207 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_5 : Uω (aρ 5) (bρ 5) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3035,25 +2625,21 @@ lemma U_634_5 : have hlg : Real.log (7016143514718471 / 10000000000000000 : ℝ) ≤ (-(3543713825258676462001 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7016143514718471 / 10000000000000000 : ℝ) = - (7016143514718471 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7016143514718471 / 5000000000000000 : ℚ)) - (U := (3387757977741323537999 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7016143514718471 / 5000000000000000 : ℝ) ≤ - (3387757977741323537999 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1753087051170173 / 2500000000000000 : ℝ)) (q := - (7016143514718471 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7016143514718471 / 10000000000000000 : ℚ)) + (r' := (7016143514718471 / 5000000000000000 : ℚ)) + (U := (-(3543713825258676462001 / 10000000000000000000000 : ℚ))) + (U' := (3387757977741323537999 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (1753087051170173 / 2500000000000000 : ℚ)) + (q := (7016143514718471 / 10000000000000000 : ℚ)) + (U := (-(3543713825258676462001 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_6 : Uω (aρ 6) (bρ 6) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3061,25 +2647,21 @@ lemma U_634_6 : have hlg : Real.log (13687464834158817 / 20000000000000000 : ℝ) ≤ (-(3792518349145028688873 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13687464834158817 / 20000000000000000 : ℝ) = - (13687464834158817 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13687464834158817 / 10000000000000000 : ℚ)) - (U := (3138953453854971311127 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13687464834158817 / 10000000000000000 : ℝ) ≤ - (3138953453854971311127 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6834766384542567 / 10000000000000000 : ℝ)) (q := - (13687464834158817 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13687464834158817 / 20000000000000000 : ℚ)) + (r' := (13687464834158817 / 10000000000000000 : ℚ)) + (U := (-(3792518349145028688873 / 10000000000000000000000 : ℚ))) + (U' := (3138953453854971311127 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (6834766384542567 / 10000000000000000 : ℚ)) + (q := (13687464834158817 / 20000000000000000 : ℚ)) + (U := (-(3792518349145028688873 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_7 : Uω (aρ 7) (bρ 7) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3087,25 +2669,21 @@ lemma U_634_7 : have hlg : Real.log (13218834587705587 / 20000000000000000 : ℝ) ≤ (-(1035223994995105045411 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13218834587705587 / 20000000000000000 : ℝ) = - (13218834587705587 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13218834587705587 / 10000000000000000 : ℚ)) - (U := (697643955754894954589 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13218834587705587 / 10000000000000000 : ℝ) ≤ - (697643955754894954589 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6589797518849337 / 10000000000000000 : ℝ)) (q := - (13218834587705587 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13218834587705587 / 20000000000000000 : ℚ)) + (r' := (13218834587705587 / 10000000000000000 : ℚ)) + (U := (-(1035223994995105045411 / 2500000000000000000000 : ℚ))) + (U' := (697643955754894954589 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (6589797518849337 / 10000000000000000 : ℚ)) + (q := (13218834587705587 / 20000000000000000 : ℚ)) + (U := (-(1035223994995105045411 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_8 : Uω (aρ 8) (bρ 8) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3113,25 +2691,21 @@ lemma U_634_8 : have hlg : Real.log (3152746187335603 / 5000000000000000 : ℝ) ≤ (-(4611640336349390814731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3152746187335603 / 5000000000000000 : ℝ) = - (3152746187335603 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3152746187335603 / 2500000000000000 : ℚ)) - (U := (2319831466650609185269 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3152746187335603 / 2500000000000000 : ℝ) ≤ - (2319831466650609185269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3132744665913081 / 5000000000000000 : ℝ)) (q := - (3152746187335603 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3152746187335603 / 5000000000000000 : ℚ)) + (r' := (3152746187335603 / 2500000000000000 : ℚ)) + (U := (-(4611640336349390814731 / 10000000000000000000000 : ℚ))) + (U' := (2319831466650609185269 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (3132744665913081 / 5000000000000000 : ℚ)) + (q := (3152746187335603 / 5000000000000000 : ℚ)) + (U := (-(4611640336349390814731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_9 : Uω (aρ 9) (bρ 9) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3139,25 +2713,21 @@ lemma U_634_9 : have hlg : Real.log (5928137374552389 / 10000000000000000 : ℝ) ≤ (-(5228750311639540664367 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5928137374552389 / 10000000000000000 : ℝ) = - (5928137374552389 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5928137374552389 / 5000000000000000 : ℚ)) - (U := (1702721491360459335633 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (5928137374552389 / 5000000000000000 : ℝ) ≤ - (1702721491360459335633 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (365734059996783 / 625000000000000 : ℝ)) (q := - (5928137374552389 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5928137374552389 / 10000000000000000 : ℚ)) + (r' := (5928137374552389 / 5000000000000000 : ℚ)) + (U := (-(5228750311639540664367 / 10000000000000000000000 : ℚ))) + (U' := (1702721491360459335633 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (365734059996783 / 625000000000000 : ℚ)) + (q := (5928137374552389 / 10000000000000000 : ℚ)) + (U := (-(5228750311639540664367 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_10 : Uω (aρ 10) (bρ 10) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3165,26 +2735,21 @@ lemma U_634_10 : have hlg : Real.log (5478643643531723 / 10000000000000000 : ℝ) ≤ (-(6017275327143369276991 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5478643643531723 / 10000000000000000 : ℝ) = - (5478643643531723 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5478643643531723 / 5000000000000000 : ℚ)) - (U := (914196475856630723009 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (5478643643531723 / 5000000000000000 : ℝ) ≤ - (914196475856630723009 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1335329132850549 / 2500000000000000 : ℝ)) (q := - (5478643643531723 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5478643643531723 / 10000000000000000 : ℚ)) + (r' := (5478643643531723 / 5000000000000000 : ℚ)) + (U := (-(6017275327143369276991 / 10000000000000000000000 : ℚ))) + (U' := (914196475856630723009 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (1335329132850549 / 2500000000000000 : ℚ)) + (q := (5478643643531723 / 10000000000000000 : ℚ)) + (U := (-(6017275327143369276991 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_11 : Uω (aρ 11) (bρ 11) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3192,25 +2757,21 @@ lemma U_634_11 : have hlg : Real.log (620492078787101 / 1250000000000000 : ℝ) ≤ (-(437741244417544630727 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (620492078787101 / 1250000000000000 : ℝ) = - (620492078787101 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (620492078787101 / 312500000000000 : ℚ)) - (U := (428692730957455369273 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (620492078787101 / 312500000000000 : ℝ) ≤ - (428692730957455369273 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2365189565568683 / 5000000000000000 : ℝ)) (q := - (620492078787101 / 1250000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) (by norm_num [bρ_11]) - (by norm_num) (by norm_num [aρ_11, bρ_11]) (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (620492078787101 / 1250000000000000 : ℚ)) + (r' := (620492078787101 / 312500000000000 : ℚ)) + (U := (-(437741244417544630727 / 625000000000000000000 : ℚ))) + (U' := (428692730957455369273 / 625000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (2365189565568683 / 5000000000000000 : ℚ)) + (q := (620492078787101 / 1250000000000000 : ℚ)) + (U := (-(437741244417544630727 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_12 : Uω (aρ 12) (bρ 12) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3218,26 +2779,21 @@ lemma U_634_12 : have hlg : Real.log (8792063711339569 / 20000000000000000 : ℝ) ≤ (-(4109414047231730727419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8792063711339569 / 20000000000000000 : ℝ) = - (8792063711339569 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8792063711339569 / 5000000000000000 : ℚ)) - (U := (2822057755768269272581 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8792063711339569 / 5000000000000000 : ℝ) ≤ - (2822057755768269272581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4018269678568319 / 10000000000000000 : ℝ)) (q := - (8792063711339569 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8792063711339569 / 20000000000000000 : ℚ)) + (r' := (8792063711339569 / 5000000000000000 : ℚ)) + (U := (-(4109414047231730727419 / 5000000000000000000000 : ℚ))) + (U' := (2822057755768269272581 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (4018269678568319 / 10000000000000000 : ℚ)) + (q := (8792063711339569 / 20000000000000000 : ℚ)) + (U := (-(4109414047231730727419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_13 : Uω (aρ 13) (bρ 13) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3245,26 +2801,21 @@ lemma U_634_13 : have hlg : Real.log (1894932298719603 / 5000000000000000 : ℝ) ≤ (-(1940509600574714462243 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1894932298719603 / 5000000000000000 : ℝ) = - (1894932298719603 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1894932298719603 / 1250000000000000 : ℚ)) - (U := (832079120625285537757 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1894932298719603 / 1250000000000000 : ℝ) ≤ - (832079120625285537757 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1602658451851081 / 5000000000000000 : ℝ)) (q := - (1894932298719603 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1894932298719603 / 5000000000000000 : ℚ)) + (r' := (1894932298719603 / 1250000000000000 : ℚ)) + (U := (-(1940509600574714462243 / 2000000000000000000000 : ℚ))) + (U' := (832079120625285537757 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (1602658451851081 / 5000000000000000 : ℚ)) + (q := (1894932298719603 / 5000000000000000 : ℚ)) + (U := (-(1940509600574714462243 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_14 : Uω (aρ 14) (bρ 14) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3272,25 +2823,21 @@ lemma U_634_14 : have hlg : Real.log (157864043680091 / 500000000000000 : ℝ) ≤ (-(90068274870373059033 / 78125000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (157864043680091 / 500000000000000 : ℝ) = - (157864043680091 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (157864043680091 / 125000000000000 : ℚ)) - (U := (18235972051501940967 / 78125000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (157864043680091 / 125000000000000 : ℝ) ≤ - (18235972051501940967 / 78125000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228407674107239 / 1000000000000000 : ℝ)) (q := - (157864043680091 / 500000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (157864043680091 / 500000000000000 : ℚ)) + (r' := (157864043680091 / 125000000000000 : ℚ)) + (U := (-(90068274870373059033 / 78125000000000000000 : ℚ))) + (U' := (18235972051501940967 / 78125000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (228407674107239 / 1000000000000000 : ℚ)) + (q := (157864043680091 / 500000000000000 : ℚ)) + (U := (-(90068274870373059033 / 78125000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_15 : Uω (aρ 15) (bρ 15) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3298,26 +2845,21 @@ lemma U_634_15 : have hlg : Real.log (2477123054752717 / 10000000000000000 : ℝ) ≤ (-(13954872639935423773157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (2477123054752717 / 10000000000000000 : ℝ) = - (2477123054752717 / 1250000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2477123054752717 / 1250000000000000 : ℚ)) - (U := (6839542769064576226843 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (2477123054752717 / 1250000000000000 : ℝ) ≤ - (6839542769064576226843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (18489599699831 / 156250000000000 : ℝ)) (q := - (2477123054752717 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2477123054752717 / 10000000000000000 : ℚ)) + (r' := (2477123054752717 / 1250000000000000 : ℚ)) + (U := (-(13954872639935423773157 / 10000000000000000000000 : ℚ))) + (U' := (6839542769064576226843 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (5881668209681 / 8000000000000 : ℚ)) + (s := (18489599699831 / 156250000000000 : ℚ)) + (q := (2477123054752717 / 10000000000000000 : ℚ)) + (U := (-(13954872639935423773157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_634_16 : Uω (aρ 16) (bρ 16) (5881668209681 / 8000000000000 : ℝ) ≤ @@ -3413,25 +2955,21 @@ lemma U_635_1 : have hlg : Real.log (29188359453790979 / 40000000000000000 : ℝ) ≤ (-(630218945808207475073 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29188359453790979 / 40000000000000000 : ℝ) = - (29188359453790979 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29188359453790979 / 20000000000000000 : ℚ)) - (U := (756075414791792524927 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29188359453790979 / 20000000000000000 : ℝ) ≤ - (756075414791792524927 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7297067708330177 / 10000000000000000 : ℝ)) (q := - (29188359453790979 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29188359453790979 / 40000000000000000 : ℚ)) + (r' := (29188359453790979 / 20000000000000000 : ℚ)) + (U := (-(630218945808207475073 / 2000000000000000000000 : ℚ))) + (U' := (756075414791792524927 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (7297067708330177 / 10000000000000000 : ℚ)) + (q := (29188359453790979 / 40000000000000000 : ℚ)) + (U := (-(630218945808207475073 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_2 : Uω (aρ 2) (bρ 2) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3439,25 +2977,21 @@ lemma U_635_2 : have hlg : Real.log (29092788552081409 / 40000000000000000 : ℝ) ≤ (-(636778252935398947851 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29092788552081409 / 40000000000000000 : ℝ) = - (29092788552081409 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29092788552081409 / 20000000000000000 : ℚ)) - (U := (749516107664601052149 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29092788552081409 / 20000000000000000 : ℝ) ≤ - (749516107664601052149 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (454565704374087 / 625000000000000 : ℝ)) (q := - (29092788552081409 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29092788552081409 / 40000000000000000 : ℚ)) + (r' := (29092788552081409 / 20000000000000000 : ℚ)) + (U := (-(636778252935398947851 / 2000000000000000000000 : ℚ))) + (U' := (749516107664601052149 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (454565704374087 / 625000000000000 : ℚ)) + (q := (29092788552081409 / 40000000000000000 : ℚ)) + (U := (-(636778252935398947851 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_3 : Uω (aρ 3) (bρ 3) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3465,25 +2999,21 @@ lemma U_635_3 : have hlg : Real.log (28901739810580043 / 40000000000000000 : ℝ) ≤ (-(649955318978965030579 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28901739810580043 / 40000000000000000 : ℝ) = - (28901739810580043 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28901739810580043 / 20000000000000000 : ℚ)) - (U := (736339041621034969421 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28901739810580043 / 20000000000000000 : ℝ) ≤ - (736339041621034969421 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7224923005584709 / 10000000000000000 : ℝ)) (q := - (28901739810580043 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28901739810580043 / 40000000000000000 : ℚ)) + (r' := (28901739810580043 / 20000000000000000 : ℚ)) + (U := (-(649955318978965030579 / 2000000000000000000000 : ℚ))) + (U' := (736339041621034969421 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (7224923005584709 / 10000000000000000 : ℚ)) + (q := (28901739810580043 / 40000000000000000 : ℚ)) + (U := (-(649955318978965030579 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_4 : Uω (aρ 4) (bρ 4) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3491,25 +3021,21 @@ lemma U_635_4 : have hlg : Real.log (28584722117952679 / 40000000000000000 : ℝ) ≤ (-(672014140878737271299 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28584722117952679 / 40000000000000000 : ℝ) = - (28584722117952679 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28584722117952679 / 20000000000000000 : ℚ)) - (U := (714280219721262728701 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28584722117952679 / 20000000000000000 : ℝ) ≤ - (714280219721262728701 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7144708340336027 / 10000000000000000 : ℝ)) (q := - (28584722117952679 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28584722117952679 / 40000000000000000 : ℚ)) + (r' := (28584722117952679 / 20000000000000000 : ℚ)) + (U := (-(672014140878737271299 / 2000000000000000000000 : ℚ))) + (U' := (714280219721262728701 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (7144708340336027 / 10000000000000000 : ℚ)) + (q := (28584722117952679 / 40000000000000000 : ℚ)) + (U := (-(672014140878737271299 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_5 : Uω (aρ 5) (bρ 5) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3517,25 +3043,21 @@ lemma U_635_5 : have hlg : Real.log (28102690547823587 / 40000000000000000 : ℝ) ≤ (-(882535332662672776061 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28102690547823587 / 40000000000000000 : ℝ) = - (28102690547823587 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28102690547823587 / 20000000000000000 : ℚ)) - (U := (850332618087327223939 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28102690547823587 / 20000000000000000 : ℝ) ≤ - (850332618087327223939 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7021882474606481 / 10000000000000000 : ℝ)) (q := - (28102690547823587 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28102690547823587 / 40000000000000000 : ℚ)) + (r' := (28102690547823587 / 20000000000000000 : ℚ)) + (U := (-(882535332662672776061 / 2500000000000000000000 : ℚ))) + (U' := (850332618087327223939 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (7021882474606481 / 10000000000000000 : ℚ)) + (q := (28102690547823587 / 40000000000000000 : ℚ)) + (U := (-(882535332662672776061 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_6 : Uω (aρ 6) (bρ 6) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3543,25 +3065,21 @@ lemma U_635_6 : have hlg : Real.log (27413075472117267 / 40000000000000000 : ℝ) ≤ (-(1889296736377210212201 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27413075472117267 / 40000000000000000 : ℝ) = - (27413075472117267 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27413075472117267 / 20000000000000000 : ℚ)) - (U := (1576439165122789787799 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27413075472117267 / 20000000000000000 : ℝ) ≤ - (1576439165122789787799 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6844315311893321 / 10000000000000000 : ℝ)) (q := - (27413075472117267 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27413075472117267 / 40000000000000000 : ℚ)) + (r' := (27413075472117267 / 20000000000000000 : ℚ)) + (U := (-(1889296736377210212201 / 5000000000000000000000 : ℚ))) + (U' := (1576439165122789787799 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (6844315311893321 / 10000000000000000 : ℚ)) + (q := (27413075472117267 / 40000000000000000 : ℚ)) + (U := (-(1889296736377210212201 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_7 : Uω (aρ 7) (bρ 7) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3569,25 +3087,21 @@ lemma U_635_7 : have hlg : Real.log (5295175666436363 / 8000000000000000 : ℝ) ≤ (-(82529077401633511151 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5295175666436363 / 8000000000000000 : ℝ) = - (5295175666436363 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5295175666436363 / 4000000000000000 : ℚ)) - (U := (56100358658366488849 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5295175666436363 / 4000000000000000 : ℝ) ≤ - (56100358658366488849 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1319875624537119 / 2000000000000000 : ℝ)) (q := - (5295175666436363 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5295175666436363 / 8000000000000000 : ℚ)) + (r' := (5295175666436363 / 4000000000000000 : ℚ)) + (U := (-(82529077401633511151 / 200000000000000000000 : ℚ))) + (U' := (56100358658366488849 / 200000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (1319875624537119 / 2000000000000000 : ℚ)) + (q := (5295175666436363 / 8000000000000000 : ℚ)) + (U := (-(82529077401633511151 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_8 : Uω (aρ 8) (bρ 8) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3595,25 +3109,21 @@ lemma U_635_8 : have hlg : Real.log (25260308254868517 / 40000000000000000 : ℝ) ≤ (-(1149112834313707893071 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25260308254868517 / 40000000000000000 : ℝ) = - (25260308254868517 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25260308254868517 / 20000000000000000 : ℚ)) - (U := (583755116436292106929 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25260308254868517 / 20000000000000000 : ℝ) ≤ - (583755116436292106929 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3137567367684473 / 5000000000000000 : ℝ)) (q := - (25260308254868517 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25260308254868517 / 40000000000000000 : ℚ)) + (r' := (25260308254868517 / 20000000000000000 : ℚ)) + (U := (-(1149112834313707893071 / 2500000000000000000000 : ℚ))) + (U' := (583755116436292106929 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (3137567367684473 / 5000000000000000 : ℚ)) + (q := (25260308254868517 / 40000000000000000 : ℚ)) + (U := (-(1149112834313707893071 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_9 : Uω (aρ 9) (bρ 9) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3621,25 +3131,21 @@ lemma U_635_9 : have hlg : Real.log (23751141905958909 / 40000000000000000 : ℝ) ≤ (-(2606244221391287807851 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23751141905958909 / 40000000000000000 : ℝ) = - (23751141905958909 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23751141905958909 / 20000000000000000 : ℚ)) - (U := (859491680108712192149 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23751141905958909 / 20000000000000000 : ℝ) ≤ - (859491680108712192149 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2930758594637071 / 5000000000000000 : ℝ)) (q := - (23751141905958909 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23751141905958909 / 40000000000000000 : ℚ)) + (r' := (23751141905958909 / 20000000000000000 : ℚ)) + (U := (-(2606244221391287807851 / 5000000000000000000000 : ℚ))) + (U' := (859491680108712192149 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (2930758594637071 / 5000000000000000 : ℚ)) + (q := (23751141905958909 / 40000000000000000 : ℚ)) + (U := (-(2606244221391287807851 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_10 : Uω (aρ 10) (bρ 10) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3647,26 +3153,21 @@ lemma U_635_10 : have hlg : Real.log (21953648143161469 / 40000000000000000 : ℝ) ≤ (-(1499865314302420498799 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (21953648143161469 / 40000000000000000 : ℝ) = - (21953648143161469 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (21953648143161469 / 20000000000000000 : ℚ)) - (U := (233002636447579501201 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (21953648143161469 / 20000000000000000 : ℝ) ≤ - (233002636447579501201 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2675664670685211 / 5000000000000000 : ℝ)) (q := - (21953648143161469 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (21953648143161469 / 40000000000000000 : ℚ)) + (r' := (21953648143161469 / 20000000000000000 : ℚ)) + (U := (-(1499865314302420498799 / 2500000000000000000000 : ℚ))) + (U' := (233002636447579501201 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (2675664670685211 / 5000000000000000 : ℚ)) + (q := (21953648143161469 / 40000000000000000 : ℚ)) + (U := (-(1499865314302420498799 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_11 : Uω (aρ 11) (bρ 11) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3674,26 +3175,21 @@ lemma U_635_11 : have hlg : Real.log (3979143879818317 / 8000000000000000 : ℝ) ≤ (-(6983748505754081904723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3979143879818317 / 8000000000000000 : ℝ) = - (3979143879818317 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3979143879818317 / 2000000000000000 : ℚ)) - (U := (6879195100245918095277 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3979143879818317 / 2000000000000000 : ℝ) ≤ - (6879195100245918095277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (925945624129 / 1953125000000 : ℝ)) (q := - (3979143879818317 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3979143879818317 / 8000000000000000 : ℚ)) + (r' := (3979143879818317 / 2000000000000000 : ℚ)) + (U := (-(6983748505754081904723 / 10000000000000000000000 : ℚ))) + (U' := (6879195100245918095277 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (925945624129 / 1953125000000 : ℚ)) + (q := (3979143879818317 / 8000000000000000 : ℚ)) + (U := (-(6983748505754081904723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_12 : Uω (aρ 12) (bρ 12) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3701,26 +3197,21 @@ lemma U_635_12 : have hlg : Real.log (17625795499731837 / 40000000000000000 : ℝ) ≤ (-(1639031942355393550651 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17625795499731837 / 40000000000000000 : ℝ) = - (17625795499731837 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17625795499731837 / 10000000000000000 : ℚ)) - (U := (1133556778844606449349 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17625795499731837 / 10000000000000000 : ℝ) ≤ - (1133556778844606449349 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2014789871272803 / 5000000000000000 : ℝ)) (q := - (17625795499731837 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17625795499731837 / 40000000000000000 : ℚ)) + (r' := (17625795499731837 / 10000000000000000 : ℚ)) + (U := (-(1639031942355393550651 / 2000000000000000000000 : ℚ))) + (U' := (1133556778844606449349 / 2000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (2014789871272803 / 5000000000000000 : ℚ)) + (q := (17625795499731837 / 40000000000000000 : ℚ)) + (U := (-(1639031942355393550651 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_13 : Uω (aρ 13) (bρ 13) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3728,26 +3219,21 @@ lemma U_635_13 : have hlg : Real.log (3040895491400307 / 8000000000000000 : ℝ) ≤ (-(4836447497896644797437 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3040895491400307 / 8000000000000000 : ℝ) = - (3040895491400307 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3040895491400307 / 2000000000000000 : ℚ)) - (U := (2095024305103355202563 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3040895491400307 / 2000000000000000 : ℝ) ≤ - (2095024305103355202563 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (643660492555091 / 2000000000000000 : ℝ)) (q := - (3040895491400307 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3040895491400307 / 8000000000000000 : ℚ)) + (r' := (3040895491400307 / 2000000000000000 : ℚ)) + (U := (-(4836447497896644797437 / 5000000000000000000000 : ℚ))) + (U' := (2095024305103355202563 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (643660492555091 / 2000000000000000 : ℚ)) + (q := (3040895491400307 / 8000000000000000 : ℚ)) + (U := (-(4836447497896644797437 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_14 : Uω (aρ 14) (bρ 14) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3755,26 +3241,21 @@ lemma U_635_14 : have hlg : Real.log (12681700148751069 / 40000000000000000 : ℝ) ≤ (-(11487194324412495821493 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12681700148751069 / 40000000000000000 : ℝ) = - (12681700148751069 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12681700148751069 / 10000000000000000 : ℚ)) - (U := (2375749281587504178507 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12681700148751069 / 10000000000000000 : ℝ) ≤ - (2375749281587504178507 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1150420546847611 / 5000000000000000 : ℝ)) (q := - (12681700148751069 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12681700148751069 / 40000000000000000 : ℚ)) + (r' := (12681700148751069 / 10000000000000000 : ℚ)) + (U := (-(11487194324412495821493 / 10000000000000000000000 : ℚ))) + (U' := (2375749281587504178507 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (1150420546847611 / 5000000000000000 : ℚ)) + (q := (12681700148751069 / 40000000000000000 : ℚ)) + (U := (-(11487194324412495821493 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_15 : Uω (aρ 15) (bρ 15) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3782,26 +3263,21 @@ lemma U_635_15 : have hlg : Real.log (9987555644342411 / 40000000000000000 : ℝ) ≤ (-(346884892714684572593 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (9987555644342411 / 40000000000000000 : ℝ) = - (9987555644342411 / 5000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9987555644342411 / 5000000000000000 : ℚ)) - (U := (172975492510315427407 / 250000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (9987555644342411 / 5000000000000000 : ℝ) ≤ - (172975492510315427407 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1213342118905893 / 10000000000000000 : ℝ)) (q := - (9987555644342411 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9987555644342411 / 40000000000000000 : ℚ)) + (r' := (9987555644342411 / 5000000000000000 : ℚ)) + (U := (-(346884892714684572593 / 250000000000000000000 : ℚ))) + (U' := (172975492510315427407 / 250000000000000000000 : ℚ)) + 3 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23557149557281 / 32000000000000 : ℚ)) + (s := (1213342118905893 / 10000000000000000 : ℚ)) + (q := (9987555644342411 / 40000000000000000 : ℚ)) + (U := (-(346884892714684572593 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_635_16 : Uω (aρ 16) (bρ 16) (23557149557281 / 32000000000000 : ℝ) ≤ @@ -3897,25 +3373,21 @@ lemma U_636_1 : have hlg : Real.log (14613227733750989 / 20000000000000000 : ℝ) ≤ (-(627610291194593107191 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14613227733750989 / 20000000000000000 : ℝ) = - (14613227733750989 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14613227733750989 / 10000000000000000 : ℚ)) - (U := (758684069405406892809 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14613227733750989 / 10000000000000000 : ℝ) ≤ - (758684069405406892809 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3653295870318307 / 5000000000000000 : ℝ)) (q := - (14613227733750989 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14613227733750989 / 20000000000000000 : ℚ)) + (r' := (14613227733750989 / 10000000000000000 : ℚ)) + (U := (-(627610291194593107191 / 2000000000000000000000 : ℚ))) + (U' := (758684069405406892809 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (3653295870318307 / 5000000000000000 : ℚ)) + (q := (14613227733750989 / 20000000000000000 : ℚ)) + (U := (-(627610291194593107191 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_2 : Uω (aρ 2) (bρ 2) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -3923,25 +3395,21 @@ lemma U_636_2 : have hlg : Real.log (14565442606664147 / 20000000000000000 : ℝ) ≤ (-(634160989941164399659 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14565442606664147 / 20000000000000000 : ℝ) = - (14565442606664147 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14565442606664147 / 10000000000000000 : ℚ)) - (U := (752133370658835600341 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14565442606664147 / 10000000000000000 : ℝ) ≤ - (752133370658835600341 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1820643906514943 / 2500000000000000 : ℝ)) (q := - (14565442606664147 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14565442606664147 / 20000000000000000 : ℚ)) + (r' := (14565442606664147 / 10000000000000000 : ℚ)) + (U := (-(634160989941164399659 / 2000000000000000000000 : ℚ))) + (U' := (752133370658835600341 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1820643906514943 / 2500000000000000 : ℚ)) + (q := (14565442606664147 / 20000000000000000 : ℚ)) + (U := (-(634160989941164399659 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_3 : Uω (aρ 3) (bρ 3) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -3949,25 +3417,21 @@ lemma U_636_3 : have hlg : Real.log (14469919202319877 / 20000000000000000 : ℝ) ≤ (-(1618301582363736978203 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14469919202319877 / 20000000000000000 : ℝ) = - (14469919202319877 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14469919202319877 / 10000000000000000 : ℚ)) - (U := (1847434319136263021797 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14469919202319877 / 10000000000000000 : ℝ) ≤ - (1847434319136263021797 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3617224164032751 / 5000000000000000 : ℝ)) (q := - (14469919202319877 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14469919202319877 / 20000000000000000 : ℚ)) + (r' := (14469919202319877 / 10000000000000000 : ℚ)) + (U := (-(1618301582363736978203 / 5000000000000000000000 : ℚ))) + (U' := (1847434319136263021797 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (3617224164032751 / 5000000000000000 : ℚ)) + (q := (14469919202319877 / 20000000000000000 : ℚ)) + (U := (-(1618301582363736978203 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_4 : Uω (aρ 4) (bρ 4) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -3975,25 +3439,21 @@ lemma U_636_4 : have hlg : Real.log (14311412927736997 / 20000000000000000 : ℝ) ≤ (-(1673374737556661780137 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14311412927736997 / 20000000000000000 : ℝ) = - (14311412927736997 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14311412927736997 / 10000000000000000 : ℚ)) - (U := (1792361163943338219863 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14311412927736997 / 10000000000000000 : ℝ) ≤ - (1792361163943338219863 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3577118117273811 / 5000000000000000 : ℝ)) (q := - (14311412927736997 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14311412927736997 / 20000000000000000 : ℚ)) + (r' := (14311412927736997 / 10000000000000000 : ℚ)) + (U := (-(1673374737556661780137 / 5000000000000000000000 : ℚ))) + (U' := (1792361163943338219863 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (3577118117273811 / 5000000000000000 : ℚ)) + (q := (14311412927736997 / 20000000000000000 : ℚ)) + (U := (-(1673374737556661780137 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_5 : Uω (aρ 5) (bρ 5) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4001,25 +3461,21 @@ lemma U_636_5 : have hlg : Real.log (3517600872620407 / 5000000000000000 : ℝ) ≤ (-(3516587252170573535409 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3517600872620407 / 5000000000000000 : ℝ) = - (3517600872620407 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3517600872620407 / 2500000000000000 : ℚ)) - (U := (3414884550829426464591 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3517600872620407 / 2500000000000000 : ℝ) ≤ - (3414884550829426464591 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7031416716627253 / 10000000000000000 : ℝ)) (q := - (3517600872620407 / 5000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3517600872620407 / 5000000000000000 : ℚ)) + (r' := (3517600872620407 / 2500000000000000 : ℚ)) + (U := (-(3516587252170573535409 / 10000000000000000000000 : ℚ))) + (U' := (3414884550829426464591 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (7031416716627253 / 10000000000000000 : ℚ)) + (q := (3517600872620407 / 5000000000000000 : ℚ)) + (U := (-(3516587252170573535409 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_6 : Uω (aρ 6) (bρ 6) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4027,25 +3483,21 @@ lemma U_636_6 : have hlg : Real.log (13725610568519909 / 20000000000000000 : ℝ) ≤ (-(470586001276572675323 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13725610568519909 / 20000000000000000 : ℝ) = - (13725610568519909 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13725610568519909 / 10000000000000000 : ℚ)) - (U := (395847974098427324677 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13725610568519909 / 10000000000000000 : ℝ) ≤ - (395847974098427324677 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3426932084902767 / 5000000000000000 : ℝ)) (q := - (13725610568519909 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13725610568519909 / 20000000000000000 : ℚ)) + (r' := (13725610568519909 / 10000000000000000 : ℚ)) + (U := (-(470586001276572675323 / 1250000000000000000000 : ℚ))) + (U' := (395847974098427324677 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (3426932084902767 / 5000000000000000 : ℚ)) + (q := (13725610568519909 / 20000000000000000 : ℚ)) + (U := (-(470586001276572675323 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_7 : Uω (aρ 7) (bρ 7) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4053,25 +3505,21 @@ lemma U_636_7 : have hlg : Real.log (13257043580777419 / 20000000000000000 : ℝ) ≤ (-(822406542208375767147 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13257043580777419 / 20000000000000000 : ℝ) = - (13257043580777419 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13257043580777419 / 10000000000000000 : ℚ)) - (U := (563887818391624232853 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13257043580777419 / 10000000000000000 : ℝ) ≤ - (563887818391624232853 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1652239640705761 / 2500000000000000 : ℝ)) (q := - (13257043580777419 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13257043580777419 / 20000000000000000 : ℚ)) + (r' := (13257043580777419 / 10000000000000000 : ℚ)) + (U := (-(822406542208375767147 / 2000000000000000000000 : ℚ))) + (U' := (563887818391624232853 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1652239640705761 / 2500000000000000 : ℚ)) + (q := (13257043580777419 / 20000000000000000 : ℚ)) + (U := (-(822406542208375767147 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_8 : Uω (aρ 8) (bρ 8) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4079,25 +3527,21 @@ lemma U_636_8 : have hlg : Real.log (1581165391894029 / 2500000000000000 : ℝ) ≤ (-(4581285666546628779379 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1581165391894029 / 2500000000000000 : ℝ) = - (1581165391894029 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1581165391894029 / 1250000000000000 : ℚ)) - (U := (2350186136453371220621 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1581165391894029 / 1250000000000000 : ℝ) ≤ - (2350186136453371220621 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6284779768537857 / 10000000000000000 : ℝ)) (q := - (1581165391894029 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1581165391894029 / 2500000000000000 : ℚ)) + (r' := (1581165391894029 / 1250000000000000 : ℚ)) + (U := (-(4581285666546628779379 / 10000000000000000000000 : ℚ))) + (U' := (2350186136453371220621 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (6284779768537857 / 10000000000000000 : ℚ)) + (q := (1581165391894029 / 2500000000000000 : ℚ)) + (U := (-(4581285666546628779379 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_9 : Uω (aρ 9) (bρ 9) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4105,25 +3549,21 @@ lemma U_636_9 : have hlg : Real.log (594743317047791 / 1000000000000000 : ℝ) ≤ (-(5196253661759570077241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (594743317047791 / 1000000000000000 : ℝ) = - (594743317047791 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (594743317047791 / 500000000000000 : ℚ)) - (U := (1735218141240429922759 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (594743317047791 / 500000000000000 : ℝ) ≤ - (1735218141240429922759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1174257720540289 / 2000000000000000 : ℝ)) (q := - (594743317047791 / 1000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (594743317047791 / 1000000000000000 : ℚ)) + (r' := (594743317047791 / 500000000000000 : ℚ)) + (U := (-(5196253661759570077241 / 10000000000000000000000 : ℚ))) + (U' := (1735218141240429922759 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1174257720540289 / 2000000000000000 : ℚ)) + (q := (594743317047791 / 1000000000000000 : ℚ)) + (U := (-(5196253661759570077241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_10 : Uω (aρ 10) (bρ 10) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4131,26 +3571,21 @@ lemma U_636_10 : have hlg : Real.log (10996359074776561 / 20000000000000000 : ℝ) ≤ (-(5981680484881463733891 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10996359074776561 / 20000000000000000 : ℝ) = - (10996359074776561 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10996359074776561 / 10000000000000000 : ℚ)) - (U := (949791318118536266109 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10996359074776561 / 10000000000000000 : ℝ) ≤ - (949791318118536266109 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2680670185008593 / 5000000000000000 : ℝ)) (q := - (10996359074776561 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10996359074776561 / 20000000000000000 : ℚ)) + (r' := (10996359074776561 / 10000000000000000 : ℚ)) + (U := (-(5981680484881463733891 / 10000000000000000000000 : ℚ))) + (U' := (949791318118536266109 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (2680670185008593 / 5000000000000000 : ℚ)) + (q := (10996359074776561 / 20000000000000000 : ℚ)) + (U := (-(5981680484881463733891 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_11 : Uω (aρ 11) (bρ 11) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4158,26 +3593,21 @@ lemma U_636_11 : have hlg : Real.log (9967842190723267 / 20000000000000000 : ℝ) ≤ (-(278547257081232514053 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9967842190723267 / 20000000000000000 : ℝ) = - (9967842190723267 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9967842190723267 / 5000000000000000 : ℚ)) - (U := (275970487158767485947 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9967842190723267 / 5000000000000000 : ℝ) ≤ - (275970487158767485947 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1187825028042223 / 2500000000000000 : ℝ)) (q := - (9967842190723267 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9967842190723267 / 20000000000000000 : ℚ)) + (r' := (9967842190723267 / 5000000000000000 : ℚ)) + (U := (-(278547257081232514053 / 400000000000000000000 : ℚ))) + (U' := (275970487158767485947 / 400000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1187825028042223 / 2500000000000000 : ℚ)) + (q := (9967842190723267 / 20000000000000000 : ℚ)) + (U := (-(278547257081232514053 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_12 : Uω (aρ 12) (bρ 12) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4185,26 +3615,21 @@ lemma U_636_12 : have hlg : Real.log (1766744515930713 / 4000000000000000 : ℝ) ≤ (-(817155764059736202051 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1766744515930713 / 4000000000000000 : ℝ) = - (1766744515930713 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1766744515930713 / 1000000000000000 : ℚ)) - (U := (569138596540263797949 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1766744515930713 / 1000000000000000 : ℝ) ≤ - (569138596540263797949 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (404088059778419 / 1000000000000000 : ℝ)) (q := - (1766744515930713 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1766744515930713 / 4000000000000000 : ℚ)) + (r' := (1766744515930713 / 1000000000000000 : ℚ)) + (U := (-(817155764059736202051 / 1000000000000000000000 : ℚ))) + (U' := (569138596540263797949 / 1000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (404088059778419 / 1000000000000000 : ℚ)) + (q := (1766744515930713 / 4000000000000000 : ℚ)) + (U := (-(817155764059736202051 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_13 : Uω (aρ 13) (bρ 13) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4212,26 +3637,21 @@ lemma U_636_13 : have hlg : Real.log (7624724148226917 / 20000000000000000 : ℝ) ≤ (-(9643361284767544950333 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7624724148226917 / 20000000000000000 : ℝ) = - (7624724148226917 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7624724148226917 / 5000000000000000 : ℚ)) - (U := (4219582321232455049667 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7624724148226917 / 5000000000000000 : ℝ) ≤ - (4219582321232455049667 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1615631953976271 / 5000000000000000 : ℝ)) (q := - (7624724148226917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7624724148226917 / 20000000000000000 : ℚ)) + (r' := (7624724148226917 / 5000000000000000 : ℚ)) + (U := (-(9643361284767544950333 / 10000000000000000000000 : ℚ))) + (U' := (4219582321232455049667 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1615631953976271 / 5000000000000000 : ℚ)) + (q := (7624724148226917 / 20000000000000000 : ℚ)) + (U := (-(9643361284767544950333 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_14 : Uω (aρ 14) (bρ 14) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4239,26 +3659,21 @@ lemma U_636_14 : have hlg : Real.log (1273411254666331 / 4000000000000000 : ℝ) ≤ (-(457838013503125911517 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1273411254666331 / 4000000000000000 : ℝ) = - (1273411254666331 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1273411254666331 / 1000000000000000 : ℚ)) - (U := (96679730736874088483 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1273411254666331 / 1000000000000000 : ℝ) ≤ - (96679730736874088483 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (57938082952557 / 250000000000000 : ℝ)) (q := - (1273411254666331 / 4000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1273411254666331 / 4000000000000000 : ℚ)) + (r' := (1273411254666331 / 1000000000000000 : ℚ)) + (U := (-(457838013503125911517 / 400000000000000000000 : ℚ))) + (U' := (96679730736874088483 / 400000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (57938082952557 / 250000000000000 : ℚ)) + (q := (1273411254666331 / 4000000000000000 : ℚ)) + (U := (-(457838013503125911517 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_15 : Uω (aρ 15) (bρ 15) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4266,26 +3681,21 @@ lemma U_636_15 : have hlg : Real.log (2516329046367611 / 10000000000000000 : ℝ) ≤ (-(6898919903209831485569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2516329046367611 / 10000000000000000 : ℝ) = - (2516329046367611 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2516329046367611 / 2500000000000000 : ℚ)) - (U := (32551899790168514431 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (2516329046367611 / 2500000000000000 : ℝ) ≤ - (32551899790168514431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1242698414920847 / 10000000000000000 : ℝ)) (q := - (2516329046367611 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2516329046367611 / 10000000000000000 : ℚ)) + (r' := (2516329046367611 / 2500000000000000 : ℚ)) + (U := (-(6898919903209831485569 / 5000000000000000000000 : ℚ))) + (U' := (32551899790168514431 / 5000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11793813137919 / 16000000000000 : ℚ)) + (s := (1242698414920847 / 10000000000000000 : ℚ)) + (q := (2516329046367611 / 10000000000000000 : ℚ)) + (U := (-(6898919903209831485569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_636_16 : Uω (aρ 16) (bρ 16) (11793813137919 / 16000000000000 : ℝ) ≤ @@ -4381,25 +3791,21 @@ lemma U_637_1 : have hlg : Real.log (1170582059236489 / 1600000000000000 : ℝ) ≤ (-(195314073346629939723 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1170582059236489 / 1600000000000000 : ℝ) = - (1170582059236489 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1170582059236489 / 800000000000000 : ℚ)) - (U := (237902914340870060277 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1170582059236489 / 800000000000000 : ℝ) ≤ - (237902914340870060277 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (292644630911707 / 400000000000000 : ℝ)) (q := - (1170582059236489 / 1600000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1170582059236489 / 1600000000000000 : ℚ)) + (r' := (1170582059236489 / 800000000000000 : ℚ)) + (U := (-(195314073346629939723 / 625000000000000000000 : ℚ))) + (U' := (237902914340870060277 / 625000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (292644630911707 / 400000000000000 : ℚ)) + (q := (1170582059236489 / 1600000000000000 : ℚ)) + (U := (-(195314073346629939723 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_2 : Uω (aρ 2) (bρ 2) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4407,25 +3813,21 @@ lemma U_637_2 : have hlg : Real.log (29168981872581949 / 40000000000000000 : ℝ) ≤ (-(25261885905625078749 / 80000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29168981872581949 / 40000000000000000 : ℝ) = - (29168981872581949 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29168981872581949 / 20000000000000000 : ℚ)) - (U := (30189888518374921251 / 80000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29168981872581949 / 20000000000000000 : ℝ) ≤ - (30189888518374921251 / 80000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7292099981137537 / 10000000000000000 : ℝ)) (q := - (29168981872581949 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29168981872581949 / 40000000000000000 : ℚ)) + (r' := (29168981872581949 / 20000000000000000 : ℚ)) + (U := (-(25261885905625078749 / 80000000000000000000 : ℚ))) + (U' := (30189888518374921251 / 80000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (7292099981137537 / 10000000000000000 : ℚ)) + (q := (29168981872581949 / 40000000000000000 : ℚ)) + (U := (-(25261885905625078749 / 80000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_3 : Uω (aρ 3) (bρ 3) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4433,25 +3835,21 @@ lemma U_637_3 : have hlg : Real.log (28977936991610221 / 40000000000000000 : ℝ) ≤ (-(3223447068104290737667 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28977936991610221 / 40000000000000000 : ℝ) = - (28977936991610221 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28977936991610221 / 20000000000000000 : ℚ)) - (U := (3708024734895709262333 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (28977936991610221 / 20000000000000000 : ℝ) ≤ - (3708024734895709262333 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7243973647001673 / 10000000000000000 : ℝ)) (q := - (28977936991610221 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28977936991610221 / 40000000000000000 : ℚ)) + (r' := (28977936991610221 / 20000000000000000 : ℚ)) + (U := (-(3223447068104290737667 / 10000000000000000000000 : ℚ))) + (U' := (3708024734895709262333 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (7243973647001673 / 10000000000000000 : ℚ)) + (q := (28977936991610221 / 40000000000000000 : ℚ)) + (U := (-(3223447068104290737667 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_4 : Uω (aρ 4) (bρ 4) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4459,25 +3857,21 @@ lemma U_637_4 : have hlg : Real.log (28660929572146799 / 40000000000000000 : ℝ) ≤ (-(166672298750848071597 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28660929572146799 / 40000000000000000 : ℝ) = - (28660929572146799 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28660929572146799 / 20000000000000000 : ℚ)) - (U := (179901291399151928403 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28660929572146799 / 20000000000000000 : ℝ) ≤ - (179901291399151928403 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3581882059167481 / 5000000000000000 : ℝ)) (q := - (28660929572146799 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28660929572146799 / 40000000000000000 : ℚ)) + (r' := (28660929572146799 / 20000000000000000 : ℚ)) + (U := (-(166672298750848071597 / 500000000000000000000 : ℚ))) + (U' := (179901291399151928403 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (3581882059167481 / 5000000000000000 : ℚ)) + (q := (28660929572146799 / 40000000000000000 : ℚ)) + (U := (-(166672298750848071597 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_5 : Uω (aρ 5) (bρ 5) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4485,25 +3879,21 @@ lemma U_637_5 : have hlg : Real.log (28178923358519609 / 40000000000000000 : ℝ) ≤ (-(3503051539855834598479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28178923358519609 / 40000000000000000 : ℝ) = - (28178923358519609 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28178923358519609 / 20000000000000000 : ℚ)) - (U := (3428420263144165401521 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28178923358519609 / 20000000000000000 : ℝ) ≤ - (3428420263144165401521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7040950930856367 / 10000000000000000 : ℝ)) (q := - (28178923358519609 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28178923358519609 / 40000000000000000 : ℚ)) + (r' := (28178923358519609 / 20000000000000000 : ℚ)) + (U := (-(3503051539855834598479 / 10000000000000000000000 : ℚ))) + (U' := (3428420263144165401521 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (7040950930856367 / 10000000000000000 : ℚ)) + (q := (28178923358519609 / 40000000000000000 : ℚ)) + (U := (-(3503051539855834598479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_6 : Uω (aρ 6) (bρ 6) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4511,25 +3901,21 @@ lemma U_637_6 : have hlg : Real.log (27489366663664929 / 40000000000000000 : ℝ) ≤ (-(750160381464319673849 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27489366663664929 / 40000000000000000 : ℝ) = - (27489366663664929 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27489366663664929 / 20000000000000000 : ℚ)) - (U := (636133979135680326151 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27489366663664929 / 20000000000000000 : ℝ) ≤ - (636133979135680326151 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6863412958569027 / 10000000000000000 : ℝ)) (q := - (27489366663664929 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27489366663664929 / 40000000000000000 : ℚ)) + (r' := (27489366663664929 / 20000000000000000 : ℚ)) + (U := (-(750160381464319673849 / 2000000000000000000000 : ℚ))) + (U' := (636133979135680326151 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (6863412958569027 / 10000000000000000 : ℚ)) + (q := (27489366663664929 / 40000000000000000 : ℚ)) + (U := (-(750160381464319673849 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_7 : Uω (aρ 7) (bρ 7) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4537,25 +3923,21 @@ lemma U_637_7 : have hlg : Real.log (5310459132990397 / 8000000000000000 : ℝ) ≤ (-(1024408110451874314823 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5310459132990397 / 8000000000000000 : ℝ) = - (5310459132990397 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5310459132990397 / 4000000000000000 : ℚ)) - (U := (708459840298125685177 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5310459132990397 / 4000000000000000 : ℝ) ≤ - (708459840298125685177 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1323707767994511 / 2000000000000000 : ℝ)) (q := - (5310459132990397 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5310459132990397 / 8000000000000000 : ℚ)) + (r' := (5310459132990397 / 4000000000000000 : ℚ)) + (U := (-(1024408110451874314823 / 2500000000000000000000 : ℚ))) + (U' := (708459840298125685177 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (1323707767994511 / 2000000000000000 : ℚ)) + (q := (5310459132990397 / 8000000000000000 : ℚ)) + (U := (-(1024408110451874314823 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_8 : Uω (aρ 8) (bρ 8) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4563,25 +3945,21 @@ lemma U_637_8 : have hlg : Real.log (25336983548397839 / 40000000000000000 : ℝ) ≤ (-(2283071625893052422273 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25336983548397839 / 40000000000000000 : ℝ) = - (25336983548397839 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25336983548397839 / 20000000000000000 : ℚ)) - (U := (1182664275606947577727 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25336983548397839 / 20000000000000000 : ℝ) ≤ - (1182664275606947577727 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3147212216517741 / 5000000000000000 : ℝ)) (q := - (25336983548397839 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25336983548397839 / 40000000000000000 : ℚ)) + (r' := (25336983548397839 / 20000000000000000 : ℚ)) + (U := (-(2283071625893052422273 / 5000000000000000000000 : ℚ))) + (U' := (1182664275606947577727 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (3147212216517741 / 5000000000000000 : ℚ)) + (q := (25336983548397839 / 40000000000000000 : ℚ)) + (U := (-(2283071625893052422273 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_9 : Uω (aρ 9) (bρ 9) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4589,25 +3967,21 @@ lemma U_637_9 : have hlg : Real.log (23828321834201471 / 40000000000000000 : ℝ) ≤ (-(647505734529234841183 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23828321834201471 / 40000000000000000 : ℝ) = - (23828321834201471 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23828321834201471 / 20000000000000000 : ℚ)) - (U := (218928240845765158817 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23828321834201471 / 20000000000000000 : ℝ) ≤ - (218928240845765158817 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2940529602148649 / 5000000000000000 : ℝ)) (q := - (23828321834201471 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23828321834201471 / 40000000000000000 : ℚ)) + (r' := (23828321834201471 / 20000000000000000 : ℚ)) + (U := (-(647505734529234841183 / 1250000000000000000000 : ℚ))) + (U' := (218928240845765158817 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (2940529602148649 / 5000000000000000 : ℚ)) + (q := (23828321834201471 / 40000000000000000 : ℚ)) + (U := (-(647505734529234841183 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_10 : Uω (aρ 10) (bρ 10) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4615,26 +3989,21 @@ lemma U_637_10 : have hlg : Real.log (22031784613221831 / 40000000000000000 : ℝ) ≤ (-(2981966440019059832977 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22031784613221831 / 40000000000000000 : ℝ) = - (22031784613221831 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22031784613221831 / 20000000000000000 : ℚ)) - (U := (483769461480940167023 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22031784613221831 / 20000000000000000 : ℝ) ≤ - (483769461480940167023 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2685674813651239 / 5000000000000000 : ℝ)) (q := - (22031784613221831 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22031784613221831 / 40000000000000000 : ℚ)) + (r' := (22031784613221831 / 20000000000000000 : ℚ)) + (U := (-(2981966440019059832977 / 5000000000000000000000 : ℚ))) + (U' := (483769461480940167023 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (2685674813651239 / 5000000000000000 : ℚ)) + (q := (22031784613221831 / 40000000000000000 : ℚ)) + (U := (-(2981966440019059832977 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_11 : Uω (aρ 11) (bρ 11) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4642,26 +4011,21 @@ lemma U_637_11 : have hlg : Real.log (19975641520276431 / 40000000000000000 : ℝ) ≤ (-(1388731692596799573783 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19975641520276431 / 40000000000000000 : ℝ) = - (19975641520276431 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19975641520276431 / 10000000000000000 : ℚ)) - (U := (1383857028603200426217 / 2000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (19975641520276431 / 10000000000000000 : ℝ) ≤ - (1383857028603200426217 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2380877353517389 / 5000000000000000 : ℝ)) (q := - (19975641520276431 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19975641520276431 / 40000000000000000 : ℚ)) + (r' := (19975641520276431 / 10000000000000000 : ℚ)) + (U := (-(1388731692596799573783 / 2000000000000000000000 : ℚ))) + (U' := (1383857028603200426217 / 2000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (2380877353517389 / 5000000000000000 : ℚ)) + (q := (19975641520276431 / 40000000000000000 : ℚ)) + (U := (-(1388731692596799573783 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_12 : Uω (aρ 12) (bρ 12) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4669,26 +4033,21 @@ lemma U_637_12 : have hlg : Real.log (17709076555495139 / 40000000000000000 : ℝ) ≤ (-(4074010728528158471861 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17709076555495139 / 40000000000000000 : ℝ) = - (17709076555495139 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17709076555495139 / 10000000000000000 : ℚ)) - (U := (2857461074471841528139 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17709076555495139 / 10000000000000000 : ℝ) ≤ - (2857461074471841528139 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1013043080332283 / 2500000000000000 : ℝ)) (q := - (17709076555495139 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17709076555495139 / 40000000000000000 : ℚ)) + (r' := (17709076555495139 / 10000000000000000 : ℚ)) + (U := (-(4074010728528158471861 / 5000000000000000000000 : ℚ))) + (U' := (2857461074471841528139 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (1013043080332283 / 2500000000000000 : ℚ)) + (q := (17709076555495139 / 40000000000000000 : ℚ)) + (U := (-(4074010728528158471861 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_13 : Uω (aρ 13) (bρ 13) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4696,26 +4055,21 @@ lemma U_637_13 : have hlg : Real.log (15294371486162191 / 40000000000000000 : ℝ) ≤ (-(2403486424000805781369 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15294371486162191 / 40000000000000000 : ℝ) = - (15294371486162191 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15294371486162191 / 10000000000000000 : ℚ)) - (U := (1062249477499194218631 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15294371486162191 / 10000000000000000 : ℝ) ≤ - (1062249477499194218631 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1622100764128829 / 5000000000000000 : ℝ)) (q := - (15294371486162191 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15294371486162191 / 40000000000000000 : ℚ)) + (r' := (15294371486162191 / 10000000000000000 : ℚ)) + (U := (-(2403486424000805781369 / 2500000000000000000000 : ℚ))) + (U' := (1062249477499194218631 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (1622100764128829 / 5000000000000000 : ℚ)) + (q := (15294371486162191 / 40000000000000000 : ℚ)) + (U := (-(2403486424000805781369 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_14 : Uω (aρ 14) (bρ 14) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4723,26 +4077,21 @@ lemma U_637_14 : have hlg : Real.log (12786364210016413 / 40000000000000000 : ℝ) ≤ (-(11405001465921323028451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12786364210016413 / 40000000000000000 : ℝ) = - (12786364210016413 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12786364210016413 / 10000000000000000 : ℚ)) - (U := (2457942140078676971549 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12786364210016413 / 10000000000000000 : ℝ) ≤ - (2457942140078676971549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2334125175229769 / 10000000000000000 : ℝ)) (q := - (12786364210016413 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12786364210016413 / 40000000000000000 : ℚ)) + (r' := (12786364210016413 / 10000000000000000 : ℚ)) + (U := (-(11405001465921323028451 / 10000000000000000000000 : ℚ))) + (U' := (2457942140078676971549 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (2334125175229769 / 10000000000000000 : ℚ)) + (q := (12786364210016413 / 40000000000000000 : ℚ)) + (U := (-(11405001465921323028451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_15 : Uω (aρ 15) (bρ 15) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4750,26 +4099,21 @@ lemma U_637_15 : have hlg : Real.log (10141864090335721 / 40000000000000000 : ℝ) ≤ (-(857629773117390833237 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10141864090335721 / 40000000000000000 : ℝ) = - (10141864090335721 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10141864090335721 / 10000000000000000 : ℚ)) - (U := (8804202257609166763 / 625000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10141864090335721 / 10000000000000000 : ℝ) ≤ - (8804202257609166763 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1271448392804423 / 10000000000000000 : ℝ)) (q := - (10141864090335721 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10141864090335721 / 40000000000000000 : ℚ)) + (r' := (10141864090335721 / 10000000000000000 : ℚ)) + (U := (-(857629773117390833237 / 625000000000000000000 : ℚ))) + (U' := (8804202257609166763 / 625000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (4723620598879 / 6400000000000 : ℚ)) + (s := (1271448392804423 / 10000000000000000 : ℚ)) + (q := (10141864090335721 / 40000000000000000 : ℚ)) + (U := (-(857629773117390833237 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_637_16 : Uω (aρ 16) (bρ 16) (4723620598879 / 6400000000000 : ℝ) ≤ @@ -4865,25 +4209,21 @@ lemma U_638_1 : have hlg : Real.log (1831415468376431 / 2500000000000000 : ℝ) ≤ (-(622403167510487586771 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1831415468376431 / 2500000000000000 : ℝ) = - (1831415468376431 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1831415468376431 / 1250000000000000 : ℚ)) - (U := (763891193089512413229 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1831415468376431 / 1250000000000000 : ℝ) ≤ - (763891193089512413229 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1831409951199737 / 2500000000000000 : ℝ)) (q := - (1831415468376431 / 2500000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1831415468376431 / 2500000000000000 : ℚ)) + (r' := (1831415468376431 / 1250000000000000 : ℚ)) + (U := (-(622403167510487586771 / 2000000000000000000000 : ℚ))) + (U' := (763891193089512413229 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1831409951199737 / 2500000000000000 : ℚ)) + (q := (1831415468376431 / 2500000000000000 : ℚ)) + (U := (-(622403167510487586771 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_2 : Uω (aρ 2) (bρ 2) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -4891,25 +4231,21 @@ lemma U_638_2 : have hlg : Real.log (2920707852985017 / 4000000000000000 : ℝ) ≤ (-(1572341792758970059237 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2920707852985017 / 4000000000000000 : ℝ) = - (2920707852985017 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2920707852985017 / 2000000000000000 : ℚ)) - (U := (1893394108741029940763 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2920707852985017 / 2000000000000000 : ℝ) ≤ - (1893394108741029940763 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1460324867044517 / 2000000000000000 : ℝ)) (q := - (2920707852985017 / 4000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2920707852985017 / 4000000000000000 : ℚ)) + (r' := (2920707852985017 / 2000000000000000 : ℚ)) + (U := (-(1572341792758970059237 / 5000000000000000000000 : ℚ))) + (U' := (1893394108741029940763 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1460324867044517 / 2000000000000000 : ℚ)) + (q := (2920707852985017 / 4000000000000000 : ℚ)) + (U := (-(1572341792758970059237 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_3 : Uω (aρ 3) (bρ 3) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -4917,25 +4253,21 @@ lemma U_638_3 : have hlg : Real.log (2901603557151937 / 4000000000000000 : ℝ) ≤ (-(802577064865997302589 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2901603557151937 / 4000000000000000 : ℝ) = - (2901603557151937 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2901603557151937 / 2000000000000000 : ℚ)) - (U := (930290885884002697411 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2901603557151937 / 2000000000000000 : ℝ) ≤ - (930290885884002697411 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1450699792481437 / 2000000000000000 : ℝ)) (q := - (2901603557151937 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2901603557151937 / 4000000000000000 : ℚ)) + (r' := (2901603557151937 / 2000000000000000 : ℚ)) + (U := (-(802577064865997302589 / 2500000000000000000000 : ℚ))) + (U' := (930290885884002697411 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1450699792481437 / 2000000000000000 : ℚ)) + (q := (2901603557151937 / 4000000000000000 : ℚ)) + (U := (-(802577064865997302589 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_4 : Uω (aρ 4) (bρ 4) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -4943,25 +4275,21 @@ lemma U_638_4 : have hlg : Real.log (14349516634027087 / 20000000000000000 : ℝ) ≤ (-(20751000980978739367 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14349516634027087 / 20000000000000000 : ℝ) = - (14349516634027087 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14349516634027087 / 10000000000000000 : ℚ)) - (U := (22570697787771260633 / 62500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14349516634027087 / 10000000000000000 : ℝ) ≤ - (22570697787771260633 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7173291991739587 / 10000000000000000 : ℝ)) (q := - (14349516634027087 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14349516634027087 / 20000000000000000 : ℚ)) + (r' := (14349516634027087 / 10000000000000000 : ℚ)) + (U := (-(20751000980978739367 / 62500000000000000000 : ℚ))) + (U' := (22570697787771260633 / 62500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (7173291991739587 / 10000000000000000 : ℚ)) + (q := (14349516634027087 / 20000000000000000 : ℚ)) + (U := (-(20751000980978739367 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_5 : Uω (aρ 5) (bρ 5) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -4969,25 +4297,21 @@ lemma U_638_5 : have hlg : Real.log (1410851984035907 / 2000000000000000 : ℝ) ≤ (-(872383535986811447349 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1410851984035907 / 2000000000000000 : ℝ) = - (1410851984035907 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1410851984035907 / 1000000000000000 : ℚ)) - (U := (860484414763188552651 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1410851984035907 / 1000000000000000 : ℝ) ≤ - (860484414763188552651 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (705048511740657 / 1000000000000000 : ℝ)) (q := - (1410851984035907 / 2000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1410851984035907 / 2000000000000000 : ℚ)) + (r' := (1410851984035907 / 1000000000000000 : ℚ)) + (U := (-(872383535986811447349 / 2500000000000000000000 : ℚ))) + (U' := (860484414763188552651 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (705048511740657 / 1000000000000000 : ℚ)) + (q := (1410851984035907 / 2000000000000000 : ℚ)) + (U := (-(872383535986811447349 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_6 : Uω (aρ 6) (bρ 6) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -4995,25 +4319,21 @@ lemma U_638_6 : have hlg : Real.log (430117375821391 / 625000000000000 : ℝ) ≤ (-(3736935110110778650981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (430117375821391 / 625000000000000 : ℝ) = - (430117375821391 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (430117375821391 / 312500000000000 : ℚ)) - (U := (3194536692889221349019 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (430117375821391 / 312500000000000 : ℝ) ≤ - (3194536692889221349019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1718240419618003 / 2500000000000000 : ℝ)) (q := - (430117375821391 / 625000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (430117375821391 / 625000000000000 : ℚ)) + (r' := (430117375821391 / 312500000000000 : ℚ)) + (U := (-(3736935110110778650981 / 10000000000000000000000 : ℚ))) + (U' := (3194536692889221349019 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1718240419618003 / 2500000000000000 : ℚ)) + (q := (430117375821391 / 625000000000000 : ℚ)) + (U := (-(3736935110110778650981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_7 : Uω (aρ 7) (bρ 7) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5021,24 +4341,21 @@ lemma U_638_7 : have hlg : Real.log (106362015375147 / 160000000000000 : ℝ) ≤ (-(81665060031860360223 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (106362015375147 / 160000000000000 : ℝ) = (106362015375147 / 80000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (106362015375147 / 80000000000000 : ℚ)) - (U := (56964376028139639777 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (106362015375147 / 80000000000000 : ℝ) ≤ - (56964376028139639777 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (53024951638727 / 80000000000000 : ℝ)) (q := - (106362015375147 / 160000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (106362015375147 / 160000000000000 : ℚ)) + (r' := (106362015375147 / 80000000000000 : ℚ)) + (U := (-(81665060031860360223 / 200000000000000000000 : ℚ))) + (U' := (56964376028139639777 / 200000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (53024951638727 / 80000000000000 : ℚ)) + (q := (106362015375147 / 160000000000000 : ℚ)) + (U := (-(81665060031860360223 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_8 : Uω (aρ 8) (bρ 8) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5046,25 +4363,21 @@ lemma U_638_8 : have hlg : Real.log (1585957505783303 / 2500000000000000 : ℝ) ≤ (-(1137756005218871002723 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1585957505783303 / 2500000000000000 : ℝ) = - (1585957505783303 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1585957505783303 / 1250000000000000 : ℚ)) - (U := (595111945531128997277 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (1585957505783303 / 1250000000000000 : ℝ) ≤ - (595111945531128997277 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1576017182638481 / 2500000000000000 : ℝ)) (q := - (1585957505783303 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1585957505783303 / 2500000000000000 : ℚ)) + (r' := (1585957505783303 / 1250000000000000 : ℚ)) + (U := (-(1137756005218871002723 / 2500000000000000000000 : ℚ))) + (U' := (595111945531128997277 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1576017182638481 / 2500000000000000 : ℚ)) + (q := (1585957505783303 / 2500000000000000 : ℚ)) + (U := (-(1137756005218871002723 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_9 : Uω (aρ 9) (bρ 9) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5072,25 +4385,21 @@ lemma U_638_9 : have hlg : Real.log (11933454685453741 / 20000000000000000 : ℝ) ≤ (-(1290966248587763081941 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11933454685453741 / 20000000000000000 : ℝ) = - (11933454685453741 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11933454685453741 / 10000000000000000 : ℚ)) - (U := (441901702162236918059 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11933454685453741 / 10000000000000000 : ℝ) ≤ - (441901702162236918059 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5890828998101241 / 10000000000000000 : ℝ)) (q := - (11933454685453741 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11933454685453741 / 20000000000000000 : ℚ)) + (r' := (11933454685453741 / 10000000000000000 : ℚ)) + (U := (-(1290966248587763081941 / 2500000000000000000000 : ℚ))) + (U' := (441901702162236918059 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (5890828998101241 / 10000000000000000 : ℚ)) + (q := (11933454685453741 / 20000000000000000 : ℚ)) + (U := (-(1290966248587763081941 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_10 : Uω (aρ 10) (bρ 10) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5098,26 +4407,21 @@ lemma U_638_10 : have hlg : Real.log (1379427972120991 / 2500000000000000 : ℝ) ≤ (-(2973109156675716891163 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1379427972120991 / 2500000000000000 : ℝ) = - (1379427972120991 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1379427972120991 / 1250000000000000 : ℚ)) - (U := (492626744824283108837 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (1379427972120991 / 1250000000000000 : ℝ) ≤ - (492626744824283108837 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1345339280777607 / 2500000000000000 : ℝ)) (q := - (1379427972120991 / 2500000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1379427972120991 / 2500000000000000 : ℚ)) + (r' := (1379427972120991 / 1250000000000000 : ℚ)) + (U := (-(2973109156675716891163 / 5000000000000000000000 : ℚ))) + (U' := (492626744824283108837 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1345339280777607 / 2500000000000000 : ℚ)) + (q := (1379427972120991 / 2500000000000000 : ℚ)) + (U := (-(2973109156675716891163 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_11 : Uω (aρ 11) (bρ 11) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5125,26 +4429,21 @@ lemma U_638_11 : have hlg : Real.log (10007795433565161 / 20000000000000000 : ℝ) ≤ (-(6923679406295921670647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10007795433565161 / 20000000000000000 : ℝ) = - (10007795433565161 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10007795433565161 / 10000000000000000 : ℚ)) - (U := (7792396704078329353 / 10000000000000000000000 : ℚ)) - 2 (by decide +kernel)) : - Real.log (10007795433565161 / 10000000000000000 : ℝ) ≤ - (7792396704078329353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4772205405912661 / 10000000000000000 : ℝ)) (q := - (10007795433565161 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10007795433565161 / 20000000000000000 : ℚ)) + (r' := (10007795433565161 / 10000000000000000 : ℚ)) + (U := (-(6923679406295921670647 / 10000000000000000000000 : ℚ))) + (U' := (7792396704078329353 / 10000000000000000000000 : ℚ)) + 1 2 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (4772205405912661 / 10000000000000000 : ℚ)) + (q := (10007795433565161 / 20000000000000000 : ℚ)) + (U := (-(6923679406295921670647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_12 : Uω (aρ 12) (bρ 12) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5152,26 +4451,21 @@ lemma U_638_12 : have hlg : Real.log (4437672460137349 / 10000000000000000 : ℝ) ≤ (-(4062275370857562616801 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4437672460137349 / 10000000000000000 : ℝ) = - (4437672460137349 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4437672460137349 / 2500000000000000 : ℚ)) - (U := (2869196432142437383199 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4437672460137349 / 2500000000000000 : ℝ) ≤ - (2869196432142437383199 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2031727494653599 / 5000000000000000 : ℝ)) (q := - (4437672460137349 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4437672460137349 / 10000000000000000 : ℚ)) + (r' := (4437672460137349 / 2500000000000000 : ℚ)) + (U := (-(4062275370857562616801 / 5000000000000000000000 : ℚ))) + (U' := (2869196432142437383199 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (2031727494653599 / 5000000000000000 : ℚ)) + (q := (4437672460137349 / 10000000000000000 : ℚ)) + (U := (-(4062275370857562616801 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_13 : Uω (aρ 13) (bρ 13) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5179,25 +4473,21 @@ lemma U_638_13 : have hlg : Real.log (958702974621041 / 2500000000000000 : ℝ) ≤ (-(2396161768732546289149 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (958702974621041 / 2500000000000000 : ℝ) = - (958702974621041 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (958702974621041 / 625000000000000 : ℚ)) - (U := (1069574132767453710851 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (958702974621041 / 625000000000000 : ℝ) ≤ - (1069574132767453710851 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (814278901898957 / 2500000000000000 : ℝ)) (q := - (958702974621041 / 2500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (958702974621041 / 2500000000000000 : ℚ)) + (r' := (958702974621041 / 625000000000000 : ℚ)) + (U := (-(2396161768732546289149 / 2500000000000000000000 : ℚ))) + (U' := (1069574132767453710851 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (814278901898957 / 2500000000000000 : ℚ)) + (q := (958702974621041 / 2500000000000000 : ℚ)) + (U := (-(2396161768732546289149 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_14 : Uω (aρ 14) (bρ 14) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5205,24 +4495,21 @@ lemma U_638_14 : have hlg : Real.log (80240365902861 / 250000000000000 : ℝ) ≤ (-(11364342135936268109407 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (80240365902861 / 250000000000000 : ℝ) = (80240365902861 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80240365902861 / 62500000000000 : ℚ)) - (U := (2498601470063731890593 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (80240365902861 / 62500000000000 : ℝ) ≤ - (2498601470063731890593 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117532418395069 / 500000000000000 : ℝ)) (q := - (80240365902861 / 250000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80240365902861 / 250000000000000 : ℚ)) + (r' := (80240365902861 / 62500000000000 : ℚ)) + (U := (-(11364342135936268109407 / 10000000000000000000000 : ℚ))) + (U' := (2498601470063731890593 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (117532418395069 / 500000000000000 : ℚ)) + (q := (80240365902861 / 250000000000000 : ℚ)) + (U := (-(11364342135936268109407 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_15 : Uω (aρ 15) (bρ 15) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5230,26 +4517,21 @@ lemma U_638_15 : have hlg : Real.log (5108639918318627 / 20000000000000000 : ℝ) ≤ (-(13647990650442621606171 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5108639918318627 / 20000000000000000 : ℝ) = - (5108639918318627 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5108639918318627 / 5000000000000000 : ℚ)) - (U := (214952955557378393829 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5108639918318627 / 5000000000000000 : ℝ) ≤ - (214952955557378393829 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1299632291406127 / 10000000000000000 : ℝ)) (q := - (5108639918318627 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5108639918318627 / 20000000000000000 : ℚ)) + (r' := (5108639918318627 / 5000000000000000 : ℚ)) + (U := (-(13647990650442621606171 / 10000000000000000000000 : ℚ))) + (U' := (214952955557378393829 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (2956072464119 / 4000000000000 : ℚ)) + (s := (1299632291406127 / 10000000000000000 : ℚ)) + (q := (5108639918318627 / 20000000000000000 : ℚ)) + (U := (-(13647990650442621606171 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_638_16 : Uω (aρ 16) (bρ 16) (2956072464119 / 4000000000000 : ℝ) ≤ @@ -5344,25 +4626,21 @@ lemma U_639_1 : have hlg : Real.log (5868148701367031 / 8000000000000000 : ℝ) ≤ (-(3099023403956418114027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5868148701367031 / 8000000000000000 : ℝ) = - (5868148701367031 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5868148701367031 / 4000000000000000 : ℚ)) - (U := (3832448399043581885973 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5868148701367031 / 4000000000000000 : ℝ) ≤ - (3832448399043581885973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1467032767331203 / 2000000000000000 : ℝ)) (q := - (5868148701367031 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5868148701367031 / 8000000000000000 : ℚ)) + (r' := (5868148701367031 / 4000000000000000 : ℚ)) + (U := (-(3099023403956418114027 / 10000000000000000000000 : ℚ))) + (U' := (3832448399043581885973 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (1467032767331203 / 2000000000000000 : ℚ)) + (q := (5868148701367031 / 8000000000000000 : ℚ)) + (U := (-(3099023403956418114027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_2 : Uω (aρ 2) (bρ 2) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5370,25 +4648,21 @@ lemma U_639_2 : have hlg : Real.log (29245175185140721 / 40000000000000000 : ℝ) ≤ (-(3131648447173872218449 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29245175185140721 / 40000000000000000 : ℝ) = - (29245175185140721 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29245175185140721 / 20000000000000000 : ℚ)) - (U := (3799823355826127781551 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29245175185140721 / 20000000000000000 : ℝ) ≤ - (3799823355826127781551 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3655574344159399 / 5000000000000000 : ℝ)) (q := - (29245175185140721 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29245175185140721 / 40000000000000000 : ℚ)) + (r' := (29245175185140721 / 20000000000000000 : ℚ)) + (U := (-(3131648447173872218449 / 10000000000000000000000 : ℚ))) + (U' := (3799823355826127781551 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (3655574344159399 / 5000000000000000 : ℚ)) + (q := (29245175185140721 / 40000000000000000 : ℚ)) + (U := (-(3131648447173872218449 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_3 : Uω (aρ 3) (bρ 3) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5396,25 +4670,21 @@ lemma U_639_3 : have hlg : Real.log (29054134144394987 / 40000000000000000 : ℝ) ≤ (-(3197186693424707257857 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29054134144394987 / 40000000000000000 : ℝ) = - (29054134144394987 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29054134144394987 / 20000000000000000 : ℚ)) - (U := (3734285109575292742143 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29054134144394987 / 20000000000000000 : ℝ) ≤ - (3734285109575292742143 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7263024274295931 / 10000000000000000 : ℝ)) (q := - (29054134144394987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29054134144394987 / 40000000000000000 : ℚ)) + (r' := (29054134144394987 / 20000000000000000 : ℚ)) + (U := (-(3197186693424707257857 / 10000000000000000000000 : ℚ))) + (U' := (3734285109575292742143 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (7263024274295931 / 10000000000000000 : ℚ)) + (q := (29054134144394987 / 40000000000000000 : ℚ)) + (U := (-(3197186693424707257857 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_4 : Uω (aρ 4) (bρ 4) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5422,25 +4692,21 @@ lemma U_639_4 : have hlg : Real.log (28737136943278751 / 40000000000000000 : ℝ) ≤ (-(3306891973972135931103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28737136943278751 / 40000000000000000 : ℝ) = - (28737136943278751 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28737136943278751 / 20000000000000000 : ℚ)) - (U := (3624579829027864068897 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28737136943278751 / 20000000000000000 : ℝ) ≤ - (3624579829027864068897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7182819854802813 / 10000000000000000 : ℝ)) (q := - (28737136943278751 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28737136943278751 / 40000000000000000 : ℚ)) + (r' := (28737136943278751 / 20000000000000000 : ℚ)) + (U := (-(3306891973972135931103 / 10000000000000000000000 : ℚ))) + (U' := (3624579829027864068897 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (7182819854802813 / 10000000000000000 : ℚ)) + (q := (28737136943278751 / 40000000000000000 : ℚ)) + (U := (-(3306891973972135931103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_5 : Uω (aρ 5) (bρ 5) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5448,25 +4714,21 @@ lemma U_639_5 : have hlg : Real.log (28255155947783119 / 40000000000000000 : ℝ) ≤ (-(54313047107620936833 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28255155947783119 / 40000000000000000 : ℝ) = - (28255155947783119 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28255155947783119 / 20000000000000000 : ℚ)) - (U := (53991199814254063167 / 156250000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28255155947783119 / 20000000000000000 : ℝ) ≤ - (53991199814254063167 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7060019276389997 / 10000000000000000 : ℝ)) (q := - (28255155947783119 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28255155947783119 / 40000000000000000 : ℚ)) + (r' := (28255155947783119 / 20000000000000000 : ℚ)) + (U := (-(54313047107620936833 / 156250000000000000000 : ℚ))) + (U' := (53991199814254063167 / 156250000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (7060019276389997 / 10000000000000000 : ℚ)) + (q := (28255155947783119 / 40000000000000000 : ℚ)) + (U := (-(54313047107620936833 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_6 : Uω (aρ 6) (bρ 6) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5474,25 +4736,21 @@ lemma U_639_6 : have hlg : Real.log (27565657304325319 / 40000000000000000 : ℝ) ≤ (-(3723087564835383075901 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27565657304325319 / 40000000000000000 : ℝ) = - (27565657304325319 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27565657304325319 / 20000000000000000 : ℚ)) - (U := (3208384238164616924099 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27565657304325319 / 20000000000000000 : ℝ) ≤ - (3208384238164616924099 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6882510329801097 / 10000000000000000 : ℝ)) (q := - (27565657304325319 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27565657304325319 / 40000000000000000 : ℚ)) + (r' := (27565657304325319 / 20000000000000000 : ℚ)) + (U := (-(3723087564835383075901 / 10000000000000000000000 : ℚ))) + (U' := (3208384238164616924099 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (6882510329801097 / 10000000000000000 : ℚ)) + (q := (27565657304325319 / 40000000000000000 : ℚ)) + (U := (-(3723087564835383075901 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_7 : Uω (aρ 7) (bρ 7) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5500,25 +4758,21 @@ lemma U_639_7 : have hlg : Real.log (26628711699464443 / 40000000000000000 : ℝ) ≤ (-(2034447164939685717283 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26628711699464443 / 40000000000000000 : ℝ) = - (26628711699464443 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26628711699464443 / 20000000000000000 : ℚ)) - (U := (1431288736560314282717 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26628711699464443 / 20000000000000000 : ℝ) ≤ - (1431288736560314282717 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6637698908130659 / 10000000000000000 : ℝ)) (q := - (26628711699464443 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26628711699464443 / 40000000000000000 : ℚ)) + (r' := (26628711699464443 / 20000000000000000 : ℚ)) + (U := (-(2034447164939685717283 / 5000000000000000000000 : ℚ))) + (U' := (1431288736560314282717 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (6637698908130659 / 10000000000000000 : ℚ)) + (q := (26628711699464443 / 40000000000000000 : ℚ)) + (U := (-(2034447164939685717283 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_8 : Uω (aρ 8) (bρ 8) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5526,25 +4780,21 @@ lemma U_639_8 : have hlg : Real.log (25413655906072891 / 40000000000000000 : ℝ) ≤ (-(2267963951027866300151 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25413655906072891 / 40000000000000000 : ℝ) = - (25413655906072891 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25413655906072891 / 20000000000000000 : ℚ)) - (U := (1197771950472133699849 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25413655906072891 / 20000000000000000 : ℝ) ≤ - (1197771950472133699849 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6313712662774883 / 10000000000000000 : ℝ)) (q := - (25413655906072891 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25413655906072891 / 40000000000000000 : ℚ)) + (r' := (25413655906072891 / 20000000000000000 : ℚ)) + (U := (-(2267963951027866300151 / 5000000000000000000000 : ℚ))) + (U' := (1197771950472133699849 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (6313712662774883 / 10000000000000000 : ℚ)) + (q := (25413655906072891 / 40000000000000000 : ℚ)) + (U := (-(2267963951027866300151 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_9 : Uω (aρ 9) (bρ 9) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5552,25 +4802,21 @@ lemma U_639_9 : have hlg : Real.log (23905495300054583 / 40000000000000000 : ℝ) ≤ (-(5147710924735413315221 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23905495300054583 / 40000000000000000 : ℝ) = - (23905495300054583 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23905495300054583 / 20000000000000000 : ℚ)) - (U := (1783760878264586684779 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23905495300054583 / 20000000000000000 : ℝ) ≤ - (1783760878264586684779 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5900597988125729 / 10000000000000000 : ℝ)) (q := - (23905495300054583 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23905495300054583 / 40000000000000000 : ℚ)) + (r' := (23905495300054583 / 20000000000000000 : ℚ)) + (U := (-(5147710924735413315221 / 10000000000000000000000 : ℚ))) + (U' := (1783760878264586684779 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (5900597988125729 / 10000000000000000 : ℚ)) + (q := (23905495300054583 / 40000000000000000 : ℚ)) + (U := (-(5147710924735413315221 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_10 : Uω (aρ 10) (bρ 10) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5578,26 +4824,21 @@ lemma U_639_10 : have hlg : Real.log (22109906991313217 / 40000000000000000 : ℝ) ≤ (-(2964268328139464888913 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22109906991313217 / 40000000000000000 : ℝ) = - (22109906991313217 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22109906991313217 / 20000000000000000 : ℚ)) - (U := (501467573360535111087 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (22109906991313217 / 20000000000000000 : ℝ) ≤ - (501467573360535111087 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2695681433625023 / 5000000000000000 : ℝ)) (q := - (22109906991313217 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22109906991313217 / 40000000000000000 : ℚ)) + (r' := (22109906991313217 / 20000000000000000 : ℚ)) + (U := (-(2964268328139464888913 / 5000000000000000000000 : ℚ))) + (U' := (501467573360535111087 / 5000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (2695681433625023 / 5000000000000000 : ℚ)) + (q := (22109906991313217 / 40000000000000000 : ℚ)) + (U := (-(2964268328139464888913 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_11 : Uω (aρ 11) (bρ 11) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5605,26 +4846,21 @@ lemma U_639_11 : have hlg : Real.log (20055532473087563 / 40000000000000000 : ℝ) ≤ (-(6903744043443189821783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20055532473087563 / 40000000000000000 : ℝ) = - (20055532473087563 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20055532473087563 / 20000000000000000 : ℚ)) - (U := (27727759556810178217 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20055532473087563 / 20000000000000000 : ℝ) ≤ - (27727759556810178217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4782652234342219 / 10000000000000000 : ℝ)) (q := - (20055532473087563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20055532473087563 / 40000000000000000 : ℚ)) + (r' := (20055532473087563 / 20000000000000000 : ℚ)) + (U := (-(6903744043443189821783 / 10000000000000000000000 : ℚ))) + (U' := (27727759556810178217 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (4782652234342219 / 10000000000000000 : ℚ)) + (q := (20055532473087563 / 40000000000000000 : ℚ)) + (U := (-(6903744043443189821783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_12 : Uω (aρ 12) (bρ 12) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5632,26 +4868,21 @@ lemma U_639_12 : have hlg : Real.log (17792285164915683 / 40000000000000000 : ℝ) ≤ (-(4050572539749861997181 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17792285164915683 / 40000000000000000 : ℝ) = - (17792285164915683 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17792285164915683 / 10000000000000000 : ℚ)) - (U := (2880899263250138002819 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17792285164915683 / 10000000000000000 : ℝ) ≤ - (2880899263250138002819 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4074728676941279 / 10000000000000000 : ℝ)) (q := - (17792285164915683 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17792285164915683 / 40000000000000000 : ℚ)) + (r' := (17792285164915683 / 10000000000000000 : ℚ)) + (U := (-(4050572539749861997181 / 5000000000000000000000 : ℚ))) + (U' := (2880899263250138002819 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (4074728676941279 / 10000000000000000 : ℚ)) + (q := (17792285164915683 / 40000000000000000 : ℚ)) + (U := (-(4050572539749861997181 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_13 : Uω (aρ 13) (bρ 13) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5659,26 +4890,21 @@ lemma U_639_13 : have hlg : Real.log (15384077177592513 / 40000000000000000 : ℝ) ≤ (-(1194433035719959725449 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15384077177592513 / 40000000000000000 : ℝ) = - (15384077177592513 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15384077177592513 / 10000000000000000 : ℚ)) - (U := (538434915030040274551 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15384077177592513 / 10000000000000000 : ℝ) ≤ - (538434915030040274551 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1635003212437347 / 5000000000000000 : ℝ)) (q := - (15384077177592513 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15384077177592513 / 40000000000000000 : ℚ)) + (r' := (15384077177592513 / 10000000000000000 : ℚ)) + (U := (-(1194433035719959725449 / 1250000000000000000000 : ℚ))) + (U' := (538434915030040274551 / 1250000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (1635003212437347 / 5000000000000000 : ℚ)) + (q := (15384077177592513 / 40000000000000000 : ℚ)) + (U := (-(1194433035719959725449 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_14 : Uω (aρ 14) (bρ 14) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5686,26 +4912,21 @@ lemma U_639_14 : have hlg : Real.log (12890398844629933 / 40000000000000000 : ℝ) ≤ (-(11323966949471001526601 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12890398844629933 / 40000000000000000 : ℝ) = - (12890398844629933 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12890398844629933 / 10000000000000000 : ℚ)) - (U := (2538976656528998473399 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12890398844629933 / 10000000000000000 : ℝ) ≤ - (2538976656528998473399 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (591773635859601 / 2500000000000000 : ℝ)) (q := - (12890398844629933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12890398844629933 / 40000000000000000 : ℚ)) + (r' := (12890398844629933 / 10000000000000000 : ℚ)) + (U := (-(11323966949471001526601 / 10000000000000000000000 : ℚ))) + (U' := (2538976656528998473399 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (591773635859601 / 2500000000000000 : ℚ)) + (q := (12890398844629933 / 40000000000000000 : ℚ)) + (U := (-(11323966949471001526601 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_15 : Uω (aρ 15) (bρ 15) (23679056431509 / 32000000000000 : ℝ) ≤ @@ -5713,26 +4934,21 @@ lemma U_639_15 : have hlg : Real.log (10291635546897611 / 40000000000000000 : ℝ) ≤ (-(3393869927754534575737 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10291635546897611 / 40000000000000000 : ℝ) = - (10291635546897611 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10291635546897611 / 10000000000000000 : ℚ)) - (U := (71865973745465424263 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10291635546897611 / 10000000000000000 : ℝ) ≤ - (71865973745465424263 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1327286171987243 / 10000000000000000 : ℝ)) (q := - (10291635546897611 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10291635546897611 / 40000000000000000 : ℚ)) + (r' := (10291635546897611 / 10000000000000000 : ℚ)) + (U := (-(3393869927754534575737 / 2500000000000000000000 : ℚ))) + (U' := (71865973745465424263 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23679056431509 / 32000000000000 : ℚ)) + (s := (1327286171987243 / 10000000000000000 : ℚ)) + (q := (10291635546897611 / 40000000000000000 : ℚ)) + (U := (-(3393869927754534575737 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_639_16 : Uω (aρ 16) (bρ 16) (23679056431509 / 32000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U53.lean b/LeanPool/Zeta5Irrational/Table/U53.lean index 82b347250b..f4a2a97b52 100644 --- a/LeanPool/Zeta5Irrational/Table/U53.lean +++ b/LeanPool/Zeta5Irrational/Table/U53.lean @@ -24,25 +24,21 @@ lemma U_640_1 : have hlg : Real.log (14689419759675083 / 20000000000000000 : ℝ) ≤ (-(617209565778762565663 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14689419759675083 / 20000000000000000 : ℝ) = - (14689419759675083 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14689419759675083 / 10000000000000000 : ℚ)) - (U := (769084794821237434337 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14689419759675083 / 10000000000000000 : ℝ) ≤ - (769084794821237434337 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3672343934182229 / 5000000000000000 : ℝ)) (q := - (14689419759675083 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14689419759675083 / 20000000000000000 : ℚ)) + (r' := (14689419759675083 / 10000000000000000 : ℚ)) + (U := (-(617209565778762565663 / 2000000000000000000000 : ℚ))) + (U' := (769084794821237434337 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (3672343934182229 / 5000000000000000 : ℚ)) + (q := (14689419759675083 / 20000000000000000 : ℚ)) + (U := (-(617209565778762565663 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_2 : Uω (aρ 2) (bρ 2) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_640_2 : have hlg : Real.log (732081795961533 / 1000000000000000 : ℝ) ≤ (-(1559315139434144244523 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (732081795961533 / 1000000000000000 : ℝ) = - (732081795961533 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (732081795961533 / 500000000000000 : ℚ)) - (U := (1906420762065855755477 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (732081795961533 / 500000000000000 : ℝ) ≤ - (1906420762065855755477 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1464134608086007 / 2000000000000000 : ℝ)) (q := - (732081795961533 / 1000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (732081795961533 / 1000000000000000 : ℚ)) + (r' := (732081795961533 / 500000000000000 : ℚ)) + (U := (-(1559315139434144244523 / 5000000000000000000000 : ℚ))) + (U' := (1906420762065855755477 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (1464134608086007 / 2000000000000000 : ℚ)) + (q := (732081795961533 / 1000000000000000 : ℚ)) + (U := (-(1559315139434144244523 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_3 : Uω (aρ 3) (bρ 3) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_640_3 : have hlg : Real.log (14546116355132353 / 20000000000000000 : ℝ) ≤ (-(796020581195767598923 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14546116355132353 / 20000000000000000 : ℝ) = - (14546116355132353 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14546116355132353 / 10000000000000000 : ℚ)) - (U := (936847369554232401077 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14546116355132353 / 10000000000000000 : ℝ) ≤ - (936847369554232401077 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (56816793614701 / 78125000000000 : ℝ)) (q := - (14546116355132353 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14546116355132353 / 20000000000000000 : ℚ)) + (r' := (14546116355132353 / 10000000000000000 : ℚ)) + (U := (-(796020581195767598923 / 2500000000000000000000 : ℚ))) + (U' := (936847369554232401077 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (56816793614701 / 78125000000000 : ℚ)) + (q := (14546116355132353 / 20000000000000000 : ℚ)) + (U := (-(796020581195767598923 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_4 : Uω (aρ 4) (bρ 4) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_640_4 : have hlg : Real.log (3596905074737841 / 5000000000000000 : ℝ) ≤ (-(3293641379290378129919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3596905074737841 / 5000000000000000 : ℝ) = - (3596905074737841 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3596905074737841 / 2500000000000000 : ℚ)) - (U := (3637830423709621870081 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3596905074737841 / 2500000000000000 : ℝ) ≤ - (3637830423709621870081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7192347707565739 / 10000000000000000 : ℝ)) (q := - (3596905074737841 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3596905074737841 / 5000000000000000 : ℚ)) + (r' := (3596905074737841 / 2500000000000000 : ℚ)) + (U := (-(3293641379290378129919 / 10000000000000000000000 : ℚ))) + (U' := (3637830423709621870081 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (7192347707565739 / 10000000000000000 : ℚ)) + (q := (3596905074737841 / 5000000000000000 : ℚ)) + (U := (-(3293641379290378129919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_5 : Uω (aρ 5) (bρ 5) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_640_5 : have hlg : Real.log (7073318039984403 / 10000000000000000 : ℝ) ≤ (-(3462554103321312357713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7073318039984403 / 10000000000000000 : ℝ) = - (7073318039984403 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7073318039984403 / 5000000000000000 : ℚ)) - (U := (3468917699678687642287 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7073318039984403 / 5000000000000000 : ℝ) ≤ - (3468917699678687642287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7069553407918181 / 10000000000000000 : ℝ)) (q := - (7073318039984403 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7073318039984403 / 10000000000000000 : ℚ)) + (r' := (7073318039984403 / 5000000000000000 : ℚ)) + (U := (-(3462554103321312357713 / 10000000000000000000000 : ℚ))) + (U' := (3468917699678687642287 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (7069553407918181 / 10000000000000000 : ℚ)) + (q := (7073318039984403 / 10000000000000000 : ℚ)) + (U := (-(3462554103321312357713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_6 : Uω (aρ 6) (bρ 6) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_640_6 : have hlg : Real.log (6900950604875963 / 10000000000000000 : ℝ) ≤ (-(1854629608987680224327 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6900950604875963 / 10000000000000000 : ℝ) = - (6900950604875963 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6900950604875963 / 5000000000000000 : ℚ)) - (U := (1611106292512319775673 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6900950604875963 / 5000000000000000 : ℝ) ≤ - (1611106292512319775673 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6892058912841301 / 10000000000000000 : ℝ)) (q := - (6900950604875963 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6900950604875963 / 10000000000000000 : ℚ)) + (r' := (6900950604875963 / 5000000000000000 : ℚ)) + (U := (-(1854629608987680224327 / 5000000000000000000000 : ℚ))) + (U' := (1611106292512319775673 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (6892058912841301 / 10000000000000000 : ℚ)) + (q := (6900950604875963 / 10000000000000000 : ℚ)) + (U := (-(1854629608987680224327 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_7 : Uω (aρ 7) (bρ 7) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_640_7 : have hlg : Real.log (13333459616691127 / 20000000000000000 : ℝ) ≤ (-(4054556366412365688859 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13333459616691127 / 20000000000000000 : ℝ) = - (13333459616691127 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13333459616691127 / 10000000000000000 : ℚ)) - (U := (2876915436587634311141 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13333459616691127 / 10000000000000000 : ℝ) ≤ - (2876915436587634311141 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3323639350270251 / 5000000000000000 : ℝ)) (q := - (13333459616691127 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13333459616691127 / 20000000000000000 : ℚ)) + (r' := (13333459616691127 / 10000000000000000 : ℚ)) + (U := (-(4054556366412365688859 / 10000000000000000000000 : ℚ))) + (U' := (2876915436587634311141 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (3323639350270251 / 5000000000000000 : ℚ)) + (q := (13333459616691127 / 20000000000000000 : ℚ)) + (U := (-(4054556366412365688859 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_8 : Uω (aρ 8) (bρ 8) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_640_8 : have hlg : Real.log (318149887404509 / 500000000000000 : ℝ) ≤ (-(141276713247013046609 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (318149887404509 / 500000000000000 : ℝ) = - (318149887404509 / 250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (318149887404509 / 250000000000000 : ℚ)) - (U := (75331780596736953391 / 312500000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (318149887404509 / 250000000000000 : ℝ) ≤ - (75331780596736953391 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1264671246273947 / 2000000000000000 : ℝ)) (q := - (318149887404509 / 500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (318149887404509 / 500000000000000 : ℚ)) + (r' := (318149887404509 / 250000000000000 : ℚ)) + (U := (-(141276713247013046609 / 312500000000000000000 : ℚ))) + (U' := (75331780596736953391 / 312500000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (1264671246273947 / 2000000000000000 : ℚ)) + (q := (318149887404509 / 500000000000000 : ℚ)) + (U := (-(141276713247013046609 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_9 : Uω (aρ 9) (bρ 9) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_640_9 : have hlg : Real.log (11972039814806983 / 20000000000000000 : ℝ) ≤ (-(160361986765208395623 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11972039814806983 / 20000000000000000 : ℝ) = - (11972039814806983 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11972039814806983 / 10000000000000000 : ℚ)) - (U := (56246507078541604377 / 312500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11972039814806983 / 10000000000000000 : ℝ) ≤ - (56246507078541604377 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2955183089178179 / 5000000000000000 : ℝ)) (q := - (11972039814806983 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11972039814806983 / 20000000000000000 : ℚ)) + (r' := (11972039814806983 / 10000000000000000 : ℚ)) + (U := (-(160361986765208395623 / 312500000000000000000 : ℚ))) + (U' := (56246507078541604377 / 312500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (2955183089178179 / 5000000000000000 : ℚ)) + (q := (11972039814806983 / 20000000000000000 : ℚ)) + (U := (-(160361986765208395623 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_10 : Uω (aρ 10) (bρ 10) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_640_10 : have hlg : Real.log (5537240736205787 / 10000000000000000 : ℝ) ≤ (-(1477721945264326746369 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5537240736205787 / 10000000000000000 : ℝ) = - (5537240736205787 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5537240736205787 / 5000000000000000 : ℚ)) - (U := (255146005485673253631 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5537240736205787 / 5000000000000000 : ℝ) ≤ - (255146005485673253631 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5401366869455949 / 10000000000000000 : ℝ)) (q := - (5537240736205787 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5537240736205787 / 10000000000000000 : ℚ)) + (r' := (5537240736205787 / 5000000000000000 : ℚ)) + (U := (-(1477721945264326746369 / 2500000000000000000000 : ℚ))) + (U' := (255146005485673253631 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (5401366869455949 / 10000000000000000 : ℚ)) + (q := (5537240736205787 / 10000000000000000 : ℚ)) + (U := (-(1477721945264326746369 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_11 : Uω (aρ 11) (bρ 11) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_640_11 : have hlg : Real.log (10047733194381673 / 20000000000000000 : ℝ) ≤ (-(430240760642288933031 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10047733194381673 / 20000000000000000 : ℝ) = - (10047733194381673 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10047733194381673 / 10000000000000000 : ℚ)) - (U := (2976227045211066969 / 625000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (10047733194381673 / 10000000000000000 : ℝ) ≤ - (2976227045211066969 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (599136902203881 / 1250000000000000 : ℝ)) (q := - (10047733194381673 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10047733194381673 / 20000000000000000 : ℚ)) + (r' := (10047733194381673 / 10000000000000000 : ℚ)) + (U := (-(430240760642288933031 / 625000000000000000000 : ℚ))) + (U' := (2976227045211066969 / 625000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (599136902203881 / 1250000000000000 : ℚ)) + (q := (10047733194381673 / 20000000000000000 : ℚ)) + (U := (-(430240760642288933031 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_12 : Uω (aρ 12) (bρ 12) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_640_12 : have hlg : Real.log (1114616417328769 / 2500000000000000 : ℝ) ≤ (-(4038902029818474039807 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1114616417328769 / 2500000000000000 : ℝ) = - (1114616417328769 / 625000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1114616417328769 / 625000000000000 : ℚ)) - (U := (2892569773181525960193 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1114616417328769 / 625000000000000 : ℝ) ≤ - (2892569773181525960193 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4085993458564527 / 10000000000000000 : ℝ)) (q := - (1114616417328769 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1114616417328769 / 2500000000000000 : ℚ)) + (r' := (1114616417328769 / 625000000000000 : ℚ)) + (U := (-(4038902029818474039807 / 5000000000000000000000 : ℚ))) + (U' := (2892569773181525960193 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (4085993458564527 / 10000000000000000 : ℚ)) + (q := (1114616417328769 / 2500000000000000 : ℚ)) + (U := (-(4038902029818474039807 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_13 : Uω (aρ 13) (bρ 13) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -339,25 +288,21 @@ lemma U_640_13 : have hlg : Real.log (192860759814833 / 500000000000000 : ℝ) ≤ (-(9526396211055741483633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (192860759814833 / 500000000000000 : ℝ) = - (192860759814833 / 125000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192860759814833 / 125000000000000 : ℚ)) - (U := (4336547394944258516367 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (192860759814833 / 125000000000000 : ℝ) ≤ - (4336547394944258516367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (656574850824539 / 2000000000000000 : ℝ)) (q := - (192860759814833 / 500000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192860759814833 / 500000000000000 : ℚ)) + (r' := (192860759814833 / 125000000000000 : ℚ)) + (U := (-(9526396211055741483633 / 10000000000000000000000 : ℚ))) + (U' := (4336547394944258516367 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (656574850824539 / 2000000000000000 : ℚ)) + (q := (192860759814833 / 500000000000000 : ℚ)) + (U := (-(9526396211055741483633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_14 : Uω (aρ 14) (bρ 14) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -365,26 +310,21 @@ lemma U_640_14 : have hlg : Real.log (3235547074773687 / 10000000000000000 : ℝ) ≤ (-(11283870676060941852289 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3235547074773687 / 10000000000000000 : ℝ) = - (3235547074773687 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3235547074773687 / 2500000000000000 : ℚ)) - (U := (2579072929939058147711 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3235547074773687 / 2500000000000000 : ℝ) ≤ - (2579072929939058147711 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2383465296121749 / 10000000000000000 : ℝ)) (q := - (3235547074773687 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3235547074773687 / 10000000000000000 : ℚ)) + (r' := (3235547074773687 / 2500000000000000 : ℚ)) + (U := (-(11283870676060941852289 / 10000000000000000000000 : ℚ))) + (U' := (2579072929939058147711 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (2383465296121749 / 10000000000000000 : ℚ)) + (q := (3235547074773687 / 10000000000000000 : ℚ)) + (U := (-(11283870676060941852289 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_15 : Uω (aρ 15) (bρ 15) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -392,26 +332,21 @@ lemma U_640_15 : have hlg : Real.log (5182498075348999 / 20000000000000000 : ℝ) ≤ (-(3376112697703459964891 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5182498075348999 / 20000000000000000 : ℝ) = - (5182498075348999 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5182498075348999 / 5000000000000000 : ℚ)) - (U := (89623203796540035109 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5182498075348999 / 5000000000000000 : ℝ) ≤ - (89623203796540035109 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (677221249669187 / 5000000000000000 : ℝ)) (q := - (5182498075348999 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5182498075348999 / 20000000000000000 : ℚ)) + (r' := (5182498075348999 / 5000000000000000 : ℚ)) + (U := (-(3376112697703459964891 / 2500000000000000000000 : ℚ))) + (U' := (89623203796540035109 / 2500000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11854766575033 / 16000000000000 : ℚ)) + (s := (677221249669187 / 5000000000000000 : ℚ)) + (q := (5182498075348999 / 20000000000000000 : ℚ)) + (U := (-(3376112697703459964891 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_640_16 : Uω (aρ 16) (bρ 16) (11854766575033 / 16000000000000 : ℝ) ≤ @@ -508,25 +443,21 @@ lemma U_641_1 : have hlg : Real.log (29416935531569081 / 40000000000000000 : ℝ) ≤ (-(3073089068670948228763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29416935531569081 / 40000000000000000 : ℝ) = - (29416935531569081 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29416935531569081 / 20000000000000000 : ℚ)) - (U := (3858382734329051771237 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29416935531569081 / 20000000000000000 : ℝ) ≤ - (3858382734329051771237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7354211899924853 / 10000000000000000 : ℝ)) (q := - (29416935531569081 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29416935531569081 / 40000000000000000 : ℚ)) + (r' := (29416935531569081 / 20000000000000000 : ℚ)) + (U := (-(3073089068670948228763 / 10000000000000000000000 : ℚ))) + (U' := (3858382734329051771237 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (7354211899924853 / 10000000000000000 : ℚ)) + (q := (29416935531569081 / 40000000000000000 : ℚ)) + (U := (-(3073089068670948228763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_2 : Uω (aρ 2) (bρ 2) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -534,25 +465,21 @@ lemma U_641_2 : have hlg : Real.log (5864273697963929 / 8000000000000000 : ℝ) ≤ (-(3105629036471363676813 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5864273697963929 / 8000000000000000 : ℝ) = - (5864273697963929 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5864273697963929 / 4000000000000000 : ℚ)) - (U := (3825842766528636323187 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5864273697963929 / 4000000000000000 : ℝ) ≤ - (3825842766528636323187 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1466039478312027 / 2000000000000000 : ℝ)) (q := - (5864273697963929 / 8000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5864273697963929 / 8000000000000000 : ℚ)) + (r' := (5864273697963929 / 4000000000000000 : ℚ)) + (U := (-(3105629036471363676813 / 10000000000000000000000 : ℚ))) + (U' := (3825842766528636323187 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (1466039478312027 / 2000000000000000 : ℚ)) + (q := (5864273697963929 / 8000000000000000 : ℚ)) + (U := (-(3105629036471363676813 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_3 : Uω (aρ 3) (bρ 3) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -560,25 +487,21 @@ lemma U_641_3 : have hlg : Real.log (29130331269156021 / 40000000000000000 : ℝ) ≤ (-(1585497554256626544711 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29130331269156021 / 40000000000000000 : ℝ) = - (29130331269156021 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29130331269156021 / 20000000000000000 : ℚ)) - (U := (1880238347243373455289 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29130331269156021 / 20000000000000000 : ℝ) ≤ - (1880238347243373455289 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7282074887578323 / 10000000000000000 : ℝ)) (q := - (29130331269156021 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29130331269156021 / 40000000000000000 : ℚ)) + (r' := (29130331269156021 / 20000000000000000 : ℚ)) + (U := (-(1585497554256626544711 / 5000000000000000000000 : ℚ))) + (U' := (1880238347243373455289 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (7282074887578323 / 10000000000000000 : ℚ)) + (q := (29130331269156021 / 40000000000000000 : ℚ)) + (U := (-(1585497554256626544711 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_4 : Uω (aρ 4) (bρ 4) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -586,25 +509,21 @@ lemma U_641_4 : have hlg : Real.log (28813344232007867 / 40000000000000000 : ℝ) ≤ (-(3280408326324041502759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28813344232007867 / 40000000000000000 : ℝ) = - (28813344232007867 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28813344232007867 / 20000000000000000 : ℚ)) - (U := (3651063476675958497241 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28813344232007867 / 20000000000000000 : ℝ) ≤ - (3651063476675958497241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3600937775034623 / 5000000000000000 : ℝ)) (q := - (28813344232007867 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28813344232007867 / 40000000000000000 : ℚ)) + (r' := (28813344232007867 / 20000000000000000 : ℚ)) + (U := (-(3280408326324041502759 / 10000000000000000000000 : ℚ))) + (U' := (3651063476675958497241 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (3600937775034623 / 5000000000000000 : ℚ)) + (q := (28813344232007867 / 40000000000000000 : ℚ)) + (U := (-(3280408326324041502759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_5 : Uω (aρ 5) (bρ 5) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -612,25 +531,21 @@ lemma U_641_5 : have hlg : Real.log (28331388317403481 / 40000000000000000 : ℝ) ≤ (-(1724545680045968091771 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28331388317403481 / 40000000000000000 : ℝ) = - (28331388317403481 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28331388317403481 / 20000000000000000 : ℚ)) - (U := (1741190221454031908229 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28331388317403481 / 20000000000000000 : ℝ) ≤ - (1741190221454031908229 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7079087512102053 / 10000000000000000 : ℝ)) (q := - (28331388317403481 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28331388317403481 / 40000000000000000 : ℚ)) + (r' := (28331388317403481 / 20000000000000000 : ℚ)) + (U := (-(1724545680045968091771 / 5000000000000000000000 : ℚ))) + (U' := (1741190221454031908229 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (7079087512102053 / 10000000000000000 : ℚ)) + (q := (28331388317403481 / 40000000000000000 : ℚ)) + (U := (-(1724545680045968091771 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_6 : Uω (aρ 6) (bρ 6) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -638,25 +553,21 @@ lemma U_641_6 : have hlg : Real.log (27641947398671501 / 40000000000000000 : ℝ) ≤ (-(3695450016234095153087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27641947398671501 / 40000000000000000 : ℝ) = - (27641947398671501 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27641947398671501 / 20000000000000000 : ℚ)) - (U := (3236021786765904846913 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27641947398671501 / 20000000000000000 : ℝ) ≤ - (3236021786765904846913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6901607427876063 / 10000000000000000 : ℝ)) (q := - (27641947398671501 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27641947398671501 / 40000000000000000 : ℚ)) + (r' := (27641947398671501 / 20000000000000000 : ℚ)) + (U := (-(3695450016234095153087 / 10000000000000000000000 : ℚ))) + (U' := (3236021786765904846913 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (6901607427876063 / 10000000000000000 : ℚ)) + (q := (27641947398671501 / 40000000000000000 : ℚ)) + (U := (-(3695450016234095153087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_7 : Uω (aρ 7) (bρ 7) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -664,25 +575,21 @@ lemma U_641_7 : have hlg : Real.log (26705126446929301 / 40000000000000000 : ℝ) ≤ (-(808047810240227746469 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26705126446929301 / 40000000000000000 : ℝ) = - (26705126446929301 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26705126446929301 / 20000000000000000 : ℚ)) - (U := (578246550359772253531 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26705126446929301 / 20000000000000000 : ℝ) ≤ - (578246550359772253531 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6656858332764963 / 10000000000000000 : ℝ)) (q := - (26705126446929301 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26705126446929301 / 40000000000000000 : ℚ)) + (r' := (26705126446929301 / 20000000000000000 : ℚ)) + (U := (-(808047810240227746469 / 2000000000000000000000 : ℚ))) + (U' := (578246550359772253531 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (6656858332764963 / 10000000000000000 : ℚ)) + (q := (26705126446929301 / 40000000000000000 : ℚ)) + (U := (-(808047810240227746469 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_8 : Uω (aρ 8) (bρ 8) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -690,25 +597,21 @@ lemma U_641_8 : have hlg : Real.log (5098065070943721 / 8000000000000000 : ℝ) ≤ (-(4505804715333577953633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5098065070943721 / 8000000000000000 : ℝ) = - (5098065070943721 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5098065070943721 / 4000000000000000 : ℚ)) - (U := (2425667087666422046367 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (5098065070943721 / 4000000000000000 : ℝ) ≤ - (2425667087666422046367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1266599887599923 / 2000000000000000 : ℝ)) (q := - (5098065070943721 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5098065070943721 / 8000000000000000 : ℚ)) + (r' := (5098065070943721 / 4000000000000000 : ℚ)) + (U := (-(4505804715333577953633 / 10000000000000000000000 : ℚ))) + (U' := (2425667087666422046367 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (1266599887599923 / 2000000000000000 : ℚ)) + (q := (5098065070943721 / 8000000000000000 : ℚ)) + (U := (-(4505804715333577953633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_9 : Uω (aρ 9) (bρ 9) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -716,25 +619,21 @@ lemma U_641_9 : have hlg : Real.log (23982662367503569 / 40000000000000000 : ℝ) ≤ (-(5115482859176546188077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23982662367503569 / 40000000000000000 : ℝ) = - (23982662367503569 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23982662367503569 / 20000000000000000 : ℚ)) - (U := (1815988943823453811923 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23982662367503569 / 20000000000000000 : ℝ) ≤ - (1815988943823453811923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5920133572752097 / 10000000000000000 : ℝ)) (q := - (23982662367503569 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23982662367503569 / 40000000000000000 : ℚ)) + (r' := (23982662367503569 / 20000000000000000 : ℚ)) + (U := (-(5115482859176546188077 / 10000000000000000000000 : ℚ))) + (U' := (1815988943823453811923 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (5920133572752097 / 10000000000000000 : ℚ)) + (q := (23982662367503569 / 40000000000000000 : ℚ)) + (U := (-(5115482859176546188077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_10 : Uω (aρ 10) (bρ 10) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -742,26 +641,21 @@ lemma U_641_10 : have hlg : Real.log (22188015433787531 / 40000000000000000 : ℝ) ≤ (-(736658945086993470021 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22188015433787531 / 40000000000000000 : ℝ) = - (22188015433787531 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22188015433787531 / 20000000000000000 : ℚ)) - (U := (129775030288006529979 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (22188015433787531 / 20000000000000000 : ℝ) ≤ - (129775030288006529979 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2705684569694539 / 5000000000000000 : ℝ)) (q := - (22188015433787531 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22188015433787531 / 40000000000000000 : ℚ)) + (r' := (22188015433787531 / 20000000000000000 : ℚ)) + (U := (-(736658945086993470021 / 1250000000000000000000 : ℚ))) + (U' := (129775030288006529979 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (2705684569694539 / 5000000000000000 : ℚ)) + (q := (22188015433787531 / 40000000000000000 : ℚ)) + (U := (-(736658945086993470021 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_11 : Uω (aρ 11) (bρ 11) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -769,26 +663,21 @@ lemma U_641_11 : have hlg : Real.log (20135392664314169 / 40000000000000000 : ℝ) ≤ (-(6864003581606836853937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20135392664314169 / 40000000000000000 : ℝ) = - (20135392664314169 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20135392664314169 / 20000000000000000 : ℚ)) - (U := (67468221393163146063 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20135392664314169 / 20000000000000000 : ℝ) ≤ - (67468221393163146063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4803534380857397 / 10000000000000000 : ℝ)) (q := - (20135392664314169 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20135392664314169 / 40000000000000000 : ℚ)) + (r' := (20135392664314169 / 20000000000000000 : ℚ)) + (U := (-(6864003581606836853937 / 10000000000000000000000 : ℚ))) + (U' := (67468221393163146063 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (4803534380857397 / 10000000000000000 : ℚ)) + (q := (20135392664314169 / 40000000000000000 : ℚ)) + (U := (-(6864003581606836853937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_12 : Uω (aρ 12) (bρ 12) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -796,25 +685,21 @@ lemma U_641_12 : have hlg : Real.log (715016900979913 / 1600000000000000 : ℝ) ≤ (-(4027263637795985554169 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (715016900979913 / 1600000000000000 : ℝ) = - (715016900979913 / 400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (715016900979913 / 400000000000000 : ℚ)) - (U := (2904208165204014445831 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (715016900979913 / 400000000000000 : ℝ) ≤ - (2904208165204014445831 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (163889976305369 / 400000000000000 : ℝ)) (q := - (715016900979913 / 1600000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (715016900979913 / 1600000000000000 : ℚ)) + (r' := (715016900979913 / 400000000000000 : ℚ)) + (U := (-(4027263637795985554169 / 5000000000000000000000 : ℚ))) + (U' := (2904208165204014445831 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (163889976305369 / 400000000000000 : ℚ)) + (q := (715016900979913 / 1600000000000000 : ℚ)) + (U := (-(4027263637795985554169 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_13 : Uω (aρ 13) (bρ 13) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -822,26 +707,21 @@ lemma U_641_13 : have hlg : Real.log (15473598955246807 / 40000000000000000 : ℝ) ≤ (-(9497441751319171954421 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15473598955246807 / 40000000000000000 : ℝ) = - (15473598955246807 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15473598955246807 / 10000000000000000 : ℚ)) - (U := (4365501854680828045579 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15473598955246807 / 10000000000000000 : ℝ) ≤ - (4365501854680828045579 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (823929841150929 / 2500000000000000 : ℝ)) (q := - (15473598955246807 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15473598955246807 / 40000000000000000 : ℚ)) + (r' := (15473598955246807 / 10000000000000000 : ℚ)) + (U := (-(9497441751319171954421 / 10000000000000000000000 : ℚ))) + (U' := (4365501854680828045579 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (823929841150929 / 2500000000000000 : ℚ)) + (q := (15473598955246807 / 40000000000000000 : ℚ)) + (U := (-(9497441751319171954421 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_14 : Uω (aρ 14) (bρ 14) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -849,26 +729,21 @@ lemma U_641_14 : have hlg : Real.log (12993829994981327 / 40000000000000000 : ℝ) ≤ (-(1124404824568891011653 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12993829994981327 / 40000000000000000 : ℝ) = - (12993829994981327 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12993829994981327 / 10000000000000000 : ℚ)) - (U := (261889536031108988347 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12993829994981327 / 10000000000000000 : ℝ) ≤ - (261889536031108988347 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (299970271189497 / 1250000000000000 : ℝ)) (q := - (12993829994981327 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12993829994981327 / 40000000000000000 : ℚ)) + (r' := (12993829994981327 / 10000000000000000 : ℚ)) + (U := (-(1124404824568891011653 / 1000000000000000000000 : ℚ))) + (U' := (261889536031108988347 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (299970271189497 / 1250000000000000 : ℚ)) + (q := (12993829994981327 / 40000000000000000 : ℚ)) + (U := (-(1124404824568891011653 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_15 : Uω (aρ 15) (bρ 15) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -876,26 +751,21 @@ lemma U_641_15 : have hlg : Real.log (10437420347172571 / 40000000000000000 : ℝ) ≤ (-(13434819948548071133851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10437420347172571 / 40000000000000000 : ℝ) = - (10437420347172571 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10437420347172571 / 10000000000000000 : ℚ)) - (U := (428123657451928866149 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (10437420347172571 / 10000000000000000 : ℝ) ≤ - (428123657451928866149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (690565311513299 / 5000000000000000 : ℝ)) (q := - (10437420347172571 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10437420347172571 / 40000000000000000 : ℚ)) + (r' := (10437420347172571 / 10000000000000000 : ℚ)) + (U := (-(13434819948548071133851 / 10000000000000000000000 : ℚ))) + (U' := (428123657451928866149 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23740009868623 / 32000000000000 : ℚ)) + (s := (690565311513299 / 5000000000000000 : ℚ)) + (q := (10437420347172571 / 40000000000000000 : ℚ)) + (U := (-(13434819948548071133851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_641_16 : Uω (aρ 16) (bρ 16) (23740009868623 / 32000000000000 : ℝ) ≤ @@ -993,25 +863,21 @@ lemma U_642_1 : have hlg : Real.log (589100630869861 / 800000000000000 : ℝ) ≤ (-(3060147079763797147191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (589100630869861 / 800000000000000 : ℝ) = - (589100630869861 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (589100630869861 / 400000000000000 : ℚ)) - (U := (3871324723236202852809 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (589100630869861 / 400000000000000 : ℝ) ≤ - (3871324723236202852809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (294549437253511 / 400000000000000 : ℝ)) (q := - (589100630869861 / 800000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (589100630869861 / 800000000000000 : ℚ)) + (r' := (589100630869861 / 400000000000000 : ℚ)) + (U := (-(3060147079763797147191 / 10000000000000000000000 : ℚ))) + (U' := (3871324723236202852809 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (294549437253511 / 400000000000000 : ℚ)) + (q := (589100630869861 / 800000000000000 : ℚ)) + (U := (-(3060147079763797147191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_2 : Uω (aρ 2) (bρ 2) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1019,25 +885,21 @@ lemma U_642_2 : have hlg : Real.log (14679732569611667 / 20000000000000000 : ℝ) ≤ (-(3092644676025192306147 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14679732569611667 / 20000000000000000 : ℝ) = - (14679732569611667 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14679732569611667 / 10000000000000000 : ℚ)) - (U := (3838827126974807693853 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14679732569611667 / 10000000000000000 : ℝ) ≤ - (3838827126974807693853 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7339721741712917 / 10000000000000000 : ℝ)) (q := - (14679732569611667 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14679732569611667 / 20000000000000000 : ℚ)) + (r' := (14679732569611667 / 10000000000000000 : ℚ)) + (U := (-(3092644676025192306147 / 10000000000000000000000 : ℚ))) + (U' := (3838827126974807693853 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (7339721741712917 / 10000000000000000 : ℚ)) + (q := (14679732569611667 / 20000000000000000 : ℚ)) + (U := (-(3092644676025192306147 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_3 : Uω (aρ 3) (bρ 3) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1045,25 +907,21 @@ lemma U_642_3 : have hlg : Real.log (14584214910548139 / 20000000000000000 : ℝ) ≤ (-(3157924999766053070299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14584214910548139 / 20000000000000000 : ℝ) = - (14584214910548139 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14584214910548139 / 10000000000000000 : ℚ)) - (U := (3773546803233946929701 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14584214910548139 / 10000000000000000 : ℝ) ≤ - (3773546803233946929701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7291600188999389 / 10000000000000000 : ℝ)) (q := - (14584214910548139 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14584214910548139 / 20000000000000000 : ℚ)) + (r' := (14584214910548139 / 10000000000000000 : ℚ)) + (U := (-(3157924999766053070299 / 10000000000000000000000 : ℚ))) + (U' := (3773546803233946929701 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (7291600188999389 / 10000000000000000 : ℚ)) + (q := (14584214910548139 / 20000000000000000 : ℚ)) + (U := (-(3157924999766053070299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_4 : Uω (aρ 4) (bρ 4) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1071,25 +929,21 @@ lemma U_642_4 : have hlg : Real.log (3606430980709437 / 5000000000000000 : ℝ) ≤ (-(1633596384335385696813 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3606430980709437 / 5000000000000000 : ℝ) = - (3606430980709437 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3606430980709437 / 2500000000000000 : ℚ)) - (U := (1832139517164614303187 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3606430980709437 / 2500000000000000 : ℝ) ≤ - (1832139517164614303187 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3605701691176999 / 5000000000000000 : ℝ)) (q := - (3606430980709437 / 5000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3606430980709437 / 5000000000000000 : ℚ)) + (r' := (3606430980709437 / 2500000000000000 : ℚ)) + (U := (-(1633596384335385696813 / 5000000000000000000000 : ℚ))) + (U' := (1832139517164614303187 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (3605701691176999 / 5000000000000000 : ℚ)) + (q := (3606430980709437 / 5000000000000000 : ℚ)) + (U := (-(1633596384335385696813 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_5 : Uω (aρ 5) (bρ 5) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1097,25 +951,21 @@ lemma U_642_5 : have hlg : Real.log (7092376105100347 / 10000000000000000 : ℝ) ≤ (-(1717823368121241994069 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7092376105100347 / 10000000000000000 : ℝ) = - (7092376105100347 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7092376105100347 / 5000000000000000 : ℚ)) - (U := (1747912533378758005931 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7092376105100347 / 5000000000000000 : ℝ) ≤ - (1747912533378758005931 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (886077698631493 / 1250000000000000 : ℝ)) (q := - (7092376105100347 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7092376105100347 / 10000000000000000 : ℚ)) + (r' := (7092376105100347 / 5000000000000000 : ℚ)) + (U := (-(1717823368121241994069 / 5000000000000000000000 : ℚ))) + (U' := (1747912533378758005931 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (886077698631493 / 1250000000000000 : ℚ)) + (q := (7092376105100347 / 10000000000000000 : ℚ)) + (U := (-(1717823368121241994069 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_6 : Uω (aρ 6) (bρ 6) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1123,25 +973,21 @@ lemma U_642_6 : have hlg : Real.log (2768009224239201 / 4000000000000000 : ℝ) ≤ (-(736331981307432108431 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2768009224239201 / 4000000000000000 : ℝ) = - (2768009224239201 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2768009224239201 / 2000000000000000 : ℚ)) - (U := (649962379292567891569 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (2768009224239201 / 2000000000000000 : ℝ) ≤ - (649962379292567891569 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1382231175037451 / 2000000000000000 : ℝ)) (q := - (2768009224239201 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2768009224239201 / 4000000000000000 : ℚ)) + (r' := (2768009224239201 / 2000000000000000 : ℚ)) + (U := (-(736331981307432108431 / 2000000000000000000000 : ℚ))) + (U' := (649962379292567891569 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (1382231175037451 / 2000000000000000 : ℚ)) + (q := (2768009224239201 / 4000000000000000 : ℚ)) + (U := (-(736331981307432108431 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_7 : Uω (aρ 7) (bρ 7) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1149,25 +995,21 @@ lemma U_642_7 : have hlg : Real.log (267433333414867 / 400000000000000 : ℝ) ≤ (-(805188464903322653011 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (267433333414867 / 400000000000000 : ℝ) = - (267433333414867 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (267433333414867 / 200000000000000 : ℚ)) - (U := (581105895696677346989 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (267433333414867 / 200000000000000 : ℝ) ≤ - (581105895696677346989 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (33332189027473 / 50000000000000 : ℝ)) (q := - (267433333414867 / 400000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (267433333414867 / 400000000000000 : ℚ)) + (r' := (267433333414867 / 200000000000000 : ℚ)) + (U := (-(805188464903322653011 / 2000000000000000000000 : ℚ))) + (U' := (581105895696677346989 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (33332189027473 / 50000000000000 : ℚ)) + (q := (267433333414867 / 400000000000000 : ℚ)) + (U := (-(805188464903322653011 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_8 : Uω (aρ 8) (bρ 8) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1175,25 +1017,21 @@ lemma U_642_8 : have hlg : Real.log (6382164749112121 / 10000000000000000 : ℝ) ≤ (-(4490777505587620117577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6382164749112121 / 10000000000000000 : ℝ) = - (6382164749112121 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6382164749112121 / 5000000000000000 : ℚ)) - (U := (2440694297412379882423 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6382164749112121 / 5000000000000000 : ℝ) ≤ - (2440694297412379882423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1585660571078873 / 2500000000000000 : ℝ)) (q := - (6382164749112121 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6382164749112121 / 10000000000000000 : ℚ)) + (r' := (6382164749112121 / 5000000000000000 : ℚ)) + (U := (-(4490777505587620117577 / 10000000000000000000000 : ℚ))) + (U' := (2440694297412379882423 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (1585660571078873 / 2500000000000000 : ℚ)) + (q := (6382164749112121 / 10000000000000000 : ℚ)) + (U := (-(4490777505587620117577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_9 : Uω (aρ 9) (bρ 9) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1201,25 +1039,21 @@ lemma U_642_9 : have hlg : Real.log (6005310880397129 / 10000000000000000 : ℝ) ≤ (-(2549704341422734584063 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6005310880397129 / 10000000000000000 : ℝ) = - (6005310880397129 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6005310880397129 / 5000000000000000 : ℚ)) - (U := (916031560077265415937 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6005310880397129 / 5000000000000000 : ℝ) ≤ - (916031560077265415937 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1482475043811377 / 2500000000000000 : ℝ)) (q := - (6005310880397129 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6005310880397129 / 10000000000000000 : ℚ)) + (r' := (6005310880397129 / 5000000000000000 : ℚ)) + (U := (-(2549704341422734584063 / 5000000000000000000000 : ℚ))) + (U' := (916031560077265415937 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (1482475043811377 / 2500000000000000 : ℚ)) + (q := (6005310880397129 / 10000000000000000 : ℚ)) + (U := (-(2549704341422734584063 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_10 : Uω (aρ 10) (bρ 10) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1227,26 +1061,21 @@ lemma U_642_10 : have hlg : Real.log (2778383059672791 / 5000000000000000 : ℝ) ≤ (-(5875687868970487449787 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2778383059672791 / 5000000000000000 : ℝ) = - (2778383059672791 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2778383059672791 / 2500000000000000 : ℚ)) - (U := (1055783934029512550213 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2778383059672791 / 2500000000000000 : ℝ) ≤ - (1055783934029512550213 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2710684843318707 / 5000000000000000 : ℝ)) (q := - (2778383059672791 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2778383059672791 / 5000000000000000 : ℚ)) + (r' := (2778383059672791 / 2500000000000000 : ℚ)) + (U := (-(5875687868970487449787 / 10000000000000000000000 : ℚ))) + (U' := (1055783934029512550213 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (2710684843318707 / 5000000000000000 : ℚ)) + (q := (2778383059672791 / 5000000000000000 : ℚ)) + (U := (-(5875687868970487449787 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_11 : Uω (aρ 11) (bρ 11) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1254,26 +1083,21 @@ lemma U_642_11 : have hlg : Real.log (5043827837360799 / 10000000000000000 : ℝ) ≤ (-(3422099036893664444543 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5043827837360799 / 10000000000000000 : ℝ) = - (5043827837360799 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5043827837360799 / 5000000000000000 : ℚ)) - (U := (43636864606335555457 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5043827837360799 / 5000000000000000 : ℝ) ≤ - (43636864606335555457 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (300873109304553 / 625000000000000 : ℝ)) (q := - (5043827837360799 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5043827837360799 / 10000000000000000 : ℚ)) + (r' := (5043827837360799 / 5000000000000000 : ℚ)) + (U := (-(3422099036893664444543 / 5000000000000000000000 : ℚ))) + (U' := (43636864606335555457 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (300873109304553 / 625000000000000 : ℚ)) + (q := (5043827837360799 / 10000000000000000 : ℚ)) + (U := (-(3422099036893664444543 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_12 : Uω (aρ 12) (bρ 12) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1281,26 +1105,21 @@ lemma U_642_12 : have hlg : Real.log (4479241212954563 / 10000000000000000 : ℝ) ≤ (-(31372321582058323511 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4479241212954563 / 10000000000000000 : ℝ) = - (4479241212954563 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4479241212954563 / 2500000000000000 : ℚ)) - (U := (22779801878879176489 / 39062500000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4479241212954563 / 2500000000000000 : ℝ) ≤ - (22779801878879176489 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (128390518648293 / 312500000000000 : ℝ)) (q := - (4479241212954563 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4479241212954563 / 10000000000000000 : ℚ)) + (r' := (4479241212954563 / 2500000000000000 : ℚ)) + (U := (-(31372321582058323511 / 39062500000000000000 : ℚ))) + (U' := (22779801878879176489 / 39062500000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (128390518648293 / 312500000000000 : ℚ)) + (q := (4479241212954563 / 10000000000000000 : ℚ)) + (U := (-(31372321582058323511 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_13 : Uω (aρ 13) (bρ 13) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1308,26 +1127,21 @@ lemma U_642_13 : have hlg : Real.log (7759146108497097 / 20000000000000000 : ℝ) ≤ (-(4734299912291785360331 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7759146108497097 / 20000000000000000 : ℝ) = - (7759146108497097 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7759146108497097 / 5000000000000000 : ℚ)) - (U := (2197171890708214639669 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7759146108497097 / 5000000000000000 : ℝ) ≤ - (2197171890708214639669 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3308542020928347 / 10000000000000000 : ℝ)) (q := - (7759146108497097 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7759146108497097 / 20000000000000000 : ℚ)) + (r' := (7759146108497097 / 5000000000000000 : ℚ)) + (U := (-(4734299912291785360331 / 5000000000000000000000 : ℚ))) + (U' := (2197171890708214639669 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (3308542020928347 / 10000000000000000 : ℚ)) + (q := (7759146108497097 / 20000000000000000 : ℚ)) + (U := (-(4734299912291785360331 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_14 : Uω (aρ 14) (bρ 14) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1335,25 +1149,21 @@ lemma U_642_14 : have hlg : Real.log (407666466324277 / 1250000000000000 : ℝ) ≤ (-(2240898948388567398827 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (407666466324277 / 1250000000000000 : ℝ) = - (407666466324277 / 312500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (407666466324277 / 312500000000000 : ℚ)) - (U := (531689772811432601173 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (407666466324277 / 312500000000000 : ℝ) ≤ - (531689772811432601173 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1207993329332341 / 5000000000000000 : ℝ)) (q := - (407666466324277 / 1250000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (407666466324277 / 1250000000000000 : ℚ)) + (r' := (407666466324277 / 312500000000000 : ℚ)) + (U := (-(2240898948388567398827 / 2000000000000000000000 : ℚ))) + (U' := (531689772811432601173 / 2000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (1207993329332341 / 5000000000000000 : ℚ)) + (q := (407666466324277 / 1250000000000000 : ℚ)) + (U := (-(2240898948388567398827 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_15 : Uω (aρ 15) (bρ 15) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1361,26 +1171,21 @@ lemma U_642_15 : have hlg : Real.log (5254480704081081 / 20000000000000000 : ℝ) ≤ (-(13366510929828003237353 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (5254480704081081 / 20000000000000000 : ℝ) = - (5254480704081081 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5254480704081081 / 5000000000000000 : ℚ)) - (U := (496432676171996762647 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (5254480704081081 / 5000000000000000 : ℝ) ≤ - (496432676171996762647 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1407377178972331 / 10000000000000000 : ℝ)) (q := - (5254480704081081 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5254480704081081 / 20000000000000000 : ℚ)) + (r' := (5254480704081081 / 5000000000000000 : ℚ)) + (U := (-(13366510929828003237353 / 10000000000000000000000 : ℚ))) + (U' := (496432676171996762647 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (1188524329359 / 1600000000000 : ℚ)) + (s := (1407377178972331 / 10000000000000000 : ℚ)) + (q := (5254480704081081 / 20000000000000000 : ℚ)) + (U := (-(13366510929828003237353 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_642_16 : Uω (aρ 16) (bρ 16) (1188524329359 / 1600000000000 : ℝ) ≤ @@ -1477,25 +1282,21 @@ lemma U_643_1 : have hlg : Real.log (5898625511024643 / 8000000000000000 : ℝ) ≤ (-(1523610909408552015951 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5898625511024643 / 8000000000000000 : ℝ) = - (5898625511024643 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5898625511024643 / 4000000000000000 : ℚ)) - (U := (1942124992091447984049 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5898625511024643 / 4000000000000000 : ℝ) ≤ - (1942124992091447984049 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1474651992520759 / 2000000000000000 : ℝ)) (q := - (5898625511024643 / 8000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5898625511024643 / 8000000000000000 : ℚ)) + (r' := (5898625511024643 / 4000000000000000 : ℚ)) + (U := (-(1523610909408552015951 / 5000000000000000000000 : ℚ))) + (U' := (1942124992091447984049 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (1474651992520759 / 2000000000000000 : ℚ)) + (q := (5898625511024643 / 8000000000000000 : ℚ)) + (U := (-(1523610909408552015951 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_2 : Uω (aρ 2) (bρ 2) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1503,25 +1304,21 @@ lemma U_643_2 : have hlg : Real.log (29397561786679987 / 40000000000000000 : ℝ) ≤ (-(1539838576871448098047 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (29397561786679987 / 40000000000000000 : ℝ) = - (29397561786679987 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29397561786679987 / 20000000000000000 : ℚ)) - (U := (1925897324628551901953 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (29397561786679987 / 20000000000000000 : ℝ) ≤ - (1925897324628551901953 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7349246090892181 / 10000000000000000 : ℝ)) (q := - (29397561786679987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29397561786679987 / 40000000000000000 : ℚ)) + (r' := (29397561786679987 / 20000000000000000 : ℚ)) + (U := (-(1539838576871448098047 / 5000000000000000000000 : ℚ))) + (U' := (1925897324628551901953 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (7349246090892181 / 10000000000000000 : ℚ)) + (q := (29397561786679987 / 40000000000000000 : ℚ)) + (U := (-(1539838576871448098047 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_3 : Uω (aρ 3) (bρ 3) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1529,25 +1326,21 @@ lemma U_643_3 : have hlg : Real.log (5841305673222537 / 8000000000000000 : ℝ) ≤ (-(628974390773593105421 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5841305673222537 / 8000000000000000 : ℝ) = - (5841305673222537 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5841305673222537 / 4000000000000000 : ℚ)) - (U := (757319969826406894579 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (5841305673222537 / 4000000000000000 : ℝ) ≤ - (757319969826406894579 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (730112548695853 / 1000000000000000 : ℝ)) (q := - (5841305673222537 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5841305673222537 / 8000000000000000 : ℚ)) + (r' := (5841305673222537 / 4000000000000000 : ℚ)) + (U := (-(628974390773593105421 / 2000000000000000000000 : ℚ))) + (U' := (757319969826406894579 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (730112548695853 / 1000000000000000 : ℚ)) + (q := (5841305673222537 / 8000000000000000 : ℚ)) + (U := (-(628974390773593105421 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_4 : Uω (aρ 4) (bρ 4) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1555,25 +1348,21 @@ lemma U_643_4 : have hlg : Real.log (28889551438986517 / 40000000000000000 : ℝ) ≤ (-(813498665028040558633 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28889551438986517 / 40000000000000000 : ℝ) = - (28889551438986517 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28889551438986517 / 20000000000000000 : ℚ)) - (U := (919369285721959441367 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28889551438986517 / 20000000000000000 : ℝ) ≤ - (919369285721959441367 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3610465602230223 / 5000000000000000 : ℝ)) (q := - (28889551438986517 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28889551438986517 / 40000000000000000 : ℚ)) + (r' := (28889551438986517 / 20000000000000000 : ℚ)) + (U := (-(813498665028040558633 / 2500000000000000000000 : ℚ))) + (U' := (919369285721959441367 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (3610465602230223 / 5000000000000000 : ℚ)) + (q := (28889551438986517 / 40000000000000000 : ℚ)) + (U := (-(813498665028040558633 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_5 : Uω (aρ 5) (bρ 5) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1581,25 +1370,21 @@ lemma U_643_5 : have hlg : Real.log (5681524093830163 / 8000000000000000 : ℝ) ≤ (-(1711110091506825365049 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5681524093830163 / 8000000000000000 : ℝ) = - (5681524093830163 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5681524093830163 / 4000000000000000 : ℚ)) - (U := (1754625809993174634951 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5681524093830163 / 4000000000000000 : ℝ) ≤ - (1754625809993174634951 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1419631127775519 / 2000000000000000 : ℝ)) (q := - (5681524093830163 / 8000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5681524093830163 / 8000000000000000 : ℚ)) + (r' := (5681524093830163 / 4000000000000000 : ℚ)) + (U := (-(1711110091506825365049 / 5000000000000000000000 : ℚ))) + (U' := (1754625809993174634951 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (1419631127775519 / 2000000000000000 : ℚ)) + (q := (5681524093830163 / 8000000000000000 : ℚ)) + (U := (-(1711110091506825365049 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_6 : Uω (aρ 6) (bρ 6) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1607,25 +1392,21 @@ lemma U_643_6 : have hlg : Real.log (27718236951226001 / 40000000000000000 : ℝ) ≤ (-(3667888836031086007881 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27718236951226001 / 40000000000000000 : ℝ) = - (27718236951226001 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27718236951226001 / 20000000000000000 : ℚ)) - (U := (3263582966968913992119 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27718236951226001 / 20000000000000000 : ℝ) ≤ - (3263582966968913992119 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1730176063763797 / 2500000000000000 : ℝ)) (q := - (27718236951226001 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27718236951226001 / 40000000000000000 : ℚ)) + (r' := (27718236951226001 / 20000000000000000 : ℚ)) + (U := (-(3667888836031086007881 / 10000000000000000000000 : ℚ))) + (U' := (3263582966968913992119 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (1730176063763797 / 2500000000000000 : ℚ)) + (q := (27718236951226001 / 40000000000000000 : ℚ)) + (U := (-(3667888836031086007881 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_7 : Uω (aρ 7) (bρ 7) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1633,25 +1414,21 @@ lemma U_643_7 : have hlg : Real.log (26781539918427609 / 40000000000000000 : ℝ) ≤ (-(501458265861246567413 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26781539918427609 / 40000000000000000 : ℝ) = - (26781539918427609 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26781539918427609 / 20000000000000000 : ℚ)) - (U := (364975709513753432587 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26781539918427609 / 20000000000000000 : ℝ) ≤ - (364975709513753432587 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (834502139926999 / 1250000000000000 : ℝ)) (q := - (26781539918427609 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26781539918427609 / 40000000000000000 : ℚ)) + (r' := (26781539918427609 / 20000000000000000 : ℚ)) + (U := (-(501458265861246567413 / 1250000000000000000000 : ℚ))) + (U' := (364975709513753432587 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (834502139926999 / 1250000000000000 : ℚ)) + (q := (26781539918427609 / 40000000000000000 : ℚ)) + (U := (-(501458265861246567413 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_8 : Uω (aρ 8) (bρ 8) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1659,25 +1436,21 @@ lemma U_643_8 : have hlg : Real.log (25566991920832123 / 40000000000000000 : ℝ) ≤ (-(4475773124241223698507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25566991920832123 / 40000000000000000 : ℝ) = - (25566991920832123 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25566991920832123 / 20000000000000000 : ℚ)) - (U := (2455698678758776301493 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25566991920832123 / 20000000000000000 : ℝ) ≤ - (2455698678758776301493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6352284771958249 / 10000000000000000 : ℝ)) (q := - (25566991920832123 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25566991920832123 / 40000000000000000 : ℚ)) + (r' := (25566991920832123 / 20000000000000000 : ℚ)) + (U := (-(4475773124241223698507 / 10000000000000000000000 : ℚ))) + (U' := (2455698678758776301493 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (6352284771958249 / 10000000000000000 : ℚ)) + (q := (25566991920832123 / 40000000000000000 : ℚ)) + (U := (-(4475773124241223698507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_9 : Uω (aρ 9) (bρ 9) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1685,25 +1458,21 @@ lemma U_643_9 : have hlg : Real.log (24059823099681563 / 40000000000000000 : ℝ) ≤ (-(1270840239499814070163 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (24059823099681563 / 40000000000000000 : ℝ) = - (24059823099681563 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24059823099681563 / 20000000000000000 : ℚ)) - (U := (462027711250185929837 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24059823099681563 / 20000000000000000 : ℝ) ≤ - (462027711250185929837 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5939665989742969 / 10000000000000000 : ℝ)) (q := - (24059823099681563 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24059823099681563 / 40000000000000000 : ℚ)) + (r' := (24059823099681563 / 20000000000000000 : ℚ)) + (U := (-(1270840239499814070163 / 2500000000000000000000 : ℚ))) + (U' := (462027711250185929837 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (5939665989742969 / 10000000000000000 : ℚ)) + (q := (24059823099681563 / 40000000000000000 : ℚ)) + (U := (-(1270840239499814070163 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_10 : Uω (aρ 10) (bρ 10) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1711,25 +1480,21 @@ lemma U_643_10 : have hlg : Real.log (890644403785559 / 1600000000000000 : ℝ) ≤ (-(292906829020823116481 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (890644403785559 / 1600000000000000 : ℝ) = - (890644403785559 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (890644403785559 / 800000000000000 : ℚ)) - (U := (53666761129176883519 / 500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (890644403785559 / 800000000000000 : ℝ) ≤ - (53666761129176883519 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (217254740828667 / 400000000000000 : ℝ)) (q := - (890644403785559 / 1600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) (by norm_num [bρ_10]) - (by norm_num) (by norm_num [aρ_10, bρ_10]) (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (890644403785559 / 1600000000000000 : ℚ)) + (r' := (890644403785559 / 800000000000000 : ℚ)) + (U := (-(292906829020823116481 / 500000000000000000000 : ℚ))) + (U' := (53666761129176883519 / 500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (217254740828667 / 400000000000000 : ℚ)) + (q := (890644403785559 / 1600000000000000 : ℚ)) + (U := (-(292906829020823116481 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_11 : Uω (aρ 11) (bρ 11) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1737,26 +1502,21 @@ lemma U_643_11 : have hlg : Real.log (20215222493405561 / 40000000000000000 : ℝ) ≤ (-(106631803823411271099 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20215222493405561 / 40000000000000000 : ℝ) = - (20215222493405561 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20215222493405561 / 20000000000000000 : ℚ)) - (U := (1672443098463728901 / 156250000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (20215222493405561 / 20000000000000000 : ℝ) ≤ - (1672443098463728901 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (603050168288121 / 1250000000000000 : ℝ)) (q := - (20215222493405561 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20215222493405561 / 40000000000000000 : ℚ)) + (r' := (20215222493405561 / 20000000000000000 : ℚ)) + (U := (-(106631803823411271099 / 156250000000000000000 : ℚ))) + (U' := (1672443098463728901 / 156250000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (603050168288121 / 1250000000000000 : ℚ)) + (q := (20215222493405561 / 40000000000000000 : ℚ)) + (U := (-(106631803823411271099 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_12 : Uω (aρ 12) (bρ 12) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1764,26 +1524,21 @@ lemma U_643_12 : have hlg : Real.log (17958489802713691 / 40000000000000000 : ℝ) ≤ (-(1601632961928138856129 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17958489802713691 / 40000000000000000 : ℝ) = - (17958489802713691 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17958489802713691 / 10000000000000000 : ℚ)) - (U := (1170955759271861143871 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17958489802713691 / 10000000000000000 : ℝ) ≤ - (1170955759271861143871 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4119735097644033 / 10000000000000000 : ℝ)) (q := - (17958489802713691 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17958489802713691 / 40000000000000000 : ℚ)) + (r' := (17958489802713691 / 10000000000000000 : ℚ)) + (U := (-(1601632961928138856129 / 2000000000000000000000 : ℚ))) + (U' := (1170955759271861143871 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (4119735097644033 / 10000000000000000 : ℚ)) + (q := (17958489802713691 / 40000000000000000 : ℚ)) + (U := (-(1601632961928138856129 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_13 : Uω (aρ 13) (bρ 13) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1791,26 +1546,21 @@ lemma U_643_13 : have hlg : Real.log (3112588218111867 / 8000000000000000 : ℝ) ≤ (-(4719934683011539956371 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3112588218111867 / 8000000000000000 : ℝ) = - (3112588218111867 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3112588218111867 / 2000000000000000 : ℚ)) - (U := (2211537119988460043629 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3112588218111867 / 2000000000000000 : ℝ) ≤ - (2211537119988460043629 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (664268496632371 / 2000000000000000 : ℝ)) (q := - (3112588218111867 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3112588218111867 / 8000000000000000 : ℚ)) + (r' := (3112588218111867 / 2000000000000000 : ℚ)) + (U := (-(4719934683011539956371 / 5000000000000000000000 : ℚ))) + (U' := (2211537119988460043629 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (664268496632371 / 2000000000000000 : ℚ)) + (q := (3112588218111867 / 8000000000000000 : ℚ)) + (U := (-(4719934683011539956371 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_14 : Uω (aρ 14) (bρ 14) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1818,26 +1568,21 @@ lemma U_643_14 : have hlg : Real.log (13096681978477213 / 40000000000000000 : ℝ) ≤ (-(2791301348886200293647 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13096681978477213 / 40000000000000000 : ℝ) = - (13096681978477213 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13096681978477213 / 10000000000000000 : ℚ)) - (U := (674434552613799706353 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13096681978477213 / 10000000000000000 : ℝ) ≤ - (674434552613799706353 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1216070106082897 / 5000000000000000 : ℝ)) (q := - (13096681978477213 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13096681978477213 / 40000000000000000 : ℚ)) + (r' := (13096681978477213 / 10000000000000000 : ℚ)) + (U := (-(2791301348886200293647 / 2500000000000000000000 : ℚ))) + (U' := (674434552613799706353 / 2500000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (1216070106082897 / 5000000000000000 : ℚ)) + (q := (13096681978477213 / 40000000000000000 : ℚ)) + (U := (-(2791301348886200293647 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_15 : Uω (aρ 15) (bρ 15) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1845,26 +1590,21 @@ lemma U_643_15 : have hlg : Real.log (10579667853113777 / 40000000000000000 : ℝ) ≤ (-(13299454215022681784837 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (10579667853113777 / 40000000000000000 : ℝ) = - (10579667853113777 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10579667853113777 / 10000000000000000 : ℚ)) - (U := (563489390977318215163 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10579667853113777 / 10000000000000000 : ℝ) ≤ - (563489390977318215163 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (358301606724769 / 2500000000000000 : ℝ)) (q := - (10579667853113777 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10579667853113777 / 40000000000000000 : ℚ)) + (r' := (10579667853113777 / 10000000000000000 : ℚ)) + (U := (-(13299454215022681784837 / 10000000000000000000000 : ℚ))) + (U' := (563489390977318215163 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (23800963305737 / 32000000000000 : ℚ)) + (s := (358301606724769 / 2500000000000000 : ℚ)) + (q := (10579667853113777 / 40000000000000000 : ℚ)) + (U := (-(13299454215022681784837 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_643_16 : Uω (aρ 16) (bρ 16) (23800963305737 / 32000000000000 : ℝ) ≤ @@ -1960,25 +1700,21 @@ lemma U_644_1 : have hlg : Real.log (7382805891615179 / 10000000000000000 : ℝ) ≤ (-(3034313242643511466231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7382805891615179 / 10000000000000000 : ℝ) = - (7382805891615179 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7382805891615179 / 5000000000000000 : ℚ)) - (U := (3897158560356488533769 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7382805891615179 / 5000000000000000 : ℝ) ≤ - (3897158560356488533769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7382783993723483 / 10000000000000000 : ℝ)) (q := - (7382805891615179 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7382805891615179 / 10000000000000000 : ℚ)) + (r' := (7382805891615179 / 5000000000000000 : ℚ)) + (U := (-(3034313242643511466231 / 10000000000000000000000 : ℚ))) + (U' := (3897158560356488533769 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (7382783993723483 / 10000000000000000 : ℚ)) + (q := (7382805891615179 / 10000000000000000 : ℚ)) + (U := (-(3034313242643511466231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_2 : Uω (aρ 2) (bρ 2) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -1986,25 +1722,21 @@ lemma U_644_2 : have hlg : Real.log (14717829216098583 / 20000000000000000 : ℝ) ≤ (-(766681606501934609241 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14717829216098583 / 20000000000000000 : ℝ) = - (14717829216098583 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14717829216098583 / 10000000000000000 : ℚ)) - (U := (966186344248065390759 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14717829216098583 / 10000000000000000 : ℝ) ≤ - (966186344248065390759 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1839692609775427 / 2500000000000000 : ℝ)) (q := - (14717829216098583 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14717829216098583 / 20000000000000000 : ℚ)) + (r' := (14717829216098583 / 10000000000000000 : ℚ)) + (U := (-(766681606501934609241 / 2500000000000000000000 : ℚ))) + (U' := (966186344248065390759 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (1839692609775427 / 2500000000000000 : ℚ)) + (q := (14717829216098583 / 20000000000000000 : ℚ)) + (U := (-(766681606501934609241 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_3 : Uω (aρ 3) (bρ 3) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2012,25 +1744,21 @@ lemma U_644_3 : have hlg : Real.log (14622313452116153 / 20000000000000000 : ℝ) ≤ (-(3131835926320268809229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14622313452116153 / 20000000000000000 : ℝ) = - (14622313452116153 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14622313452116153 / 10000000000000000 : ℚ)) - (U := (3799635876679731190771 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (14622313452116153 / 10000000000000000 : ℝ) ≤ - (3799635876679731190771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3655325390734639 / 5000000000000000 : ℝ)) (q := - (14622313452116153 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14622313452116153 / 20000000000000000 : ℚ)) + (r' := (14622313452116153 / 10000000000000000 : ℚ)) + (U := (-(3131835926320268809229 / 10000000000000000000000 : ℚ))) + (U' := (3799635876679731190771 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (3655325390734639 / 5000000000000000 : ℚ)) + (q := (14622313452116153 / 20000000000000000 : ℚ)) + (U := (-(3131835926320268809229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_4 : Uω (aρ 4) (bρ 4) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2038,25 +1766,21 @@ lemma U_644_4 : have hlg : Real.log (14463827506010701 / 20000000000000000 : ℝ) ≤ (-(810203488653197127289 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14463827506010701 / 20000000000000000 : ℝ) = - (14463827506010701 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14463827506010701 / 10000000000000000 : ℚ)) - (U := (922664462096802872711 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14463827506010701 / 10000000000000000 : ℝ) ≤ - (922664462096802872711 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3615229508214413 / 5000000000000000 : ℝ)) (q := - (14463827506010701 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14463827506010701 / 20000000000000000 : ℚ)) + (r' := (14463827506010701 / 10000000000000000 : ℚ)) + (U := (-(810203488653197127289 / 2500000000000000000000 : ℚ))) + (U' := (922664462096802872711 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (3615229508214413 / 5000000000000000 : ℚ)) + (q := (14463827506010701 / 20000000000000000 : ℚ)) + (U := (-(810203488653197127289 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_5 : Uω (aρ 5) (bρ 5) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2064,25 +1788,21 @@ lemma U_644_5 : have hlg : Real.log (14222868231935033 / 20000000000000000 : ℝ) ≤ (-(852202912960722596749 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14222868231935033 / 20000000000000000 : ℝ) = - (14222868231935033 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14222868231935033 / 10000000000000000 : ℚ)) - (U := (880665037789277403251 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14222868231935033 / 10000000000000000 : ℝ) ≤ - (880665037789277403251 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3553844830844079 / 5000000000000000 : ℝ)) (q := - (14222868231935033 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14222868231935033 / 20000000000000000 : ℚ)) + (r' := (14222868231935033 / 10000000000000000 : ℚ)) + (U := (-(852202912960722596749 / 2500000000000000000000 : ℚ))) + (U' := (880665037789277403251 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (3553844830844079 / 5000000000000000 : ℚ)) + (q := (14222868231935033 / 20000000000000000 : ℚ)) + (U := (-(852202912960722596749 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_6 : Uω (aρ 6) (bρ 6) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2090,25 +1810,21 @@ lemma U_644_6 : have hlg : Real.log (6939095381432753 / 10000000000000000 : ℝ) ≤ (-(3654136752082123200103 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6939095381432753 / 10000000000000000 : ℝ) = - (6939095381432753 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6939095381432753 / 5000000000000000 : ℚ)) - (U := (3277335050917876799897 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (6939095381432753 / 5000000000000000 : ℝ) ≤ - (3277335050917876799897 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6930252567758631 / 10000000000000000 : ℝ)) (q := - (6939095381432753 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6939095381432753 / 10000000000000000 : ℚ)) + (r' := (6939095381432753 / 5000000000000000 : ℚ)) + (U := (-(3654136752082123200103 / 10000000000000000000000 : ℚ))) + (U' := (3277335050917876799897 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (6930252567758631 / 10000000000000000 : ℚ)) + (q := (6939095381432753 / 10000000000000000 : ℚ)) + (U := (-(3654136752082123200103 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_7 : Uω (aρ 7) (bρ 7) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2116,25 +1832,21 @@ lemma U_644_7 : have hlg : Real.log (13409873089558651 / 20000000000000000 : ℝ) ≤ (-(3997410399111135964581 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13409873089558651 / 20000000000000000 : ℝ) = - (13409873089558651 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13409873089558651 / 10000000000000000 : ℚ)) - (U := (2934061403888864035419 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13409873089558651 / 10000000000000000 : ℝ) ≤ - (2934061403888864035419 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (13057805225023 / 19531250000000 : ℝ)) (q := - (13409873089558651 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13409873089558651 / 20000000000000000 : ℚ)) + (r' := (13409873089558651 / 10000000000000000 : ℚ)) + (U := (-(3997410399111135964581 / 10000000000000000000000 : ℚ))) + (U' := (2934061403888864035419 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (13057805225023 / 19531250000000 : ℚ)) + (q := (13409873089558651 / 20000000000000000 : ℚ)) + (U := (-(3997410399111135964581 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_8 : Uω (aρ 8) (bρ 8) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2142,25 +1854,21 @@ lemma U_644_8 : have hlg : Real.log (3200665516391409 / 5000000000000000 : ℝ) ≤ (-(178431660047890653203 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3200665516391409 / 5000000000000000 : ℝ) = - (3200665516391409 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3200665516391409 / 2500000000000000 : ℚ)) - (U := (98827212072109346797 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3200665516391409 / 2500000000000000 : ℝ) ≤ - (98827212072109346797 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6361926902558761 / 10000000000000000 : ℝ)) (q := - (3200665516391409 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3200665516391409 / 5000000000000000 : ℚ)) + (r' := (3200665516391409 / 2500000000000000 : ℚ)) + (U := (-(178431660047890653203 / 400000000000000000000 : ℚ))) + (U' := (98827212072109346797 / 400000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (6361926902558761 / 10000000000000000 : ℚ)) + (q := (3200665516391409 / 5000000000000000 : ℚ)) + (U := (-(178431660047890653203 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_9 : Uω (aρ 9) (bρ 9) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2168,25 +1876,21 @@ lemma U_644_9 : have hlg : Real.log (1204920055477177 / 2000000000000000 : ℝ) ≤ (-(633417449450731358873 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1204920055477177 / 2000000000000000 : ℝ) = - (1204920055477177 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1204920055477177 / 1000000000000000 : ℚ)) - (U := (233016525924268641127 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (1204920055477177 / 1000000000000000 : ℝ) ≤ - (233016525924268641127 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1189886204024979 / 2000000000000000 : ℝ)) (q := - (1204920055477177 / 2000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1204920055477177 / 2000000000000000 : ℚ)) + (r' := (1204920055477177 / 1000000000000000 : ℚ)) + (U := (-(633417449450731358873 / 1250000000000000000000 : ℚ))) + (U' := (233016525924268641127 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (1189886204024979 / 2000000000000000 : ℚ)) + (q := (1204920055477177 / 2000000000000000 : ℚ)) + (U := (-(633417449450731358873 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_10 : Uω (aρ 10) (bρ 10) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2194,26 +1898,21 @@ lemma U_644_10 : have hlg : Real.log (5576288076111443 / 10000000000000000 : ℝ) ≤ (-(2920308785161509705411 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5576288076111443 / 10000000000000000 : ℝ) = - (5576288076111443 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5576288076111443 / 5000000000000000 : ℚ)) - (U := (545427116338490294589 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5576288076111443 / 5000000000000000 : ℝ) ≤ - (545427116338490294589 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5441365651071011 / 10000000000000000 : ℝ)) (q := - (5576288076111443 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5576288076111443 / 10000000000000000 : ℚ)) + (r' := (5576288076111443 / 5000000000000000 : ℚ)) + (U := (-(2920308785161509705411 / 5000000000000000000000 : ℚ))) + (U' := (545427116338490294589 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (5441365651071011 / 10000000000000000 : ℚ)) + (q := (5576288076111443 / 10000000000000000 : ℚ)) + (U := (-(2920308785161509705411 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_11 : Uω (aρ 11) (bρ 11) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2221,26 +1920,21 @@ lemma U_644_11 : have hlg : Real.log (5063781536253397 / 10000000000000000 : ℝ) ≤ (-(3402357746865413340039 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5063781536253397 / 10000000000000000 : ℝ) = - (5063781536253397 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5063781536253397 / 5000000000000000 : ℚ)) - (U := (63378154634586659961 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (5063781536253397 / 5000000000000000 : ℝ) ≤ - (63378154634586659961 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4834829197559919 / 10000000000000000 : ℝ)) (q := - (5063781536253397 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5063781536253397 / 10000000000000000 : ℚ)) + (r' := (5063781536253397 / 5000000000000000 : ℚ)) + (U := (-(3402357746865413340039 / 5000000000000000000000 : ℚ))) + (U' := (63378154634586659961 / 5000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (4834829197559919 / 10000000000000000 : ℚ)) + (q := (5063781536253397 / 10000000000000000 : ℚ)) + (U := (-(3402357746865413340039 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_12 : Uω (aρ 12) (bρ 12) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2248,26 +1942,21 @@ lemma U_644_12 : have hlg : Real.log (4499999379751123 / 10000000000000000 : ℝ) ≤ (-(3992539167654871337849 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4499999379751123 / 10000000000000000 : ℝ) = - (4499999379751123 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4499999379751123 / 2500000000000000 : ℚ)) - (U := (2938932635345128662151 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4499999379751123 / 2500000000000000 : ℝ) ≤ - (2938932635345128662151 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4130964981240371 / 10000000000000000 : ℝ)) (q := - (4499999379751123 / 10000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4499999379751123 / 10000000000000000 : ℚ)) + (r' := (4499999379751123 / 2500000000000000 : ℚ)) + (U := (-(3992539167654871337849 / 5000000000000000000000 : ℚ))) + (U' := (2938932635345128662151 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (4130964981240371 / 10000000000000000 : ℚ)) + (q := (4499999379751123 / 10000000000000000 : ℚ)) + (U := (-(3992539167654871337849 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_13 : Uω (aρ 13) (bρ 13) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2275,26 +1964,21 @@ lemma U_644_13 : have hlg : Real.log (1950943260898971 / 5000000000000000 : ℝ) ≤ (-(9411249327571361579049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1950943260898971 / 5000000000000000 : ℝ) = - (1950943260898971 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1950943260898971 / 1250000000000000 : ℚ)) - (U := (4451694278428638420951 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1950943260898971 / 1250000000000000 : ℝ) ≤ - (4451694278428638420951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3334121006929009 / 10000000000000000 : ℝ)) (q := - (1950943260898971 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1950943260898971 / 5000000000000000 : ℚ)) + (r' := (1950943260898971 / 1250000000000000 : ℚ)) + (U := (-(9411249327571361579049 / 10000000000000000000000 : ℚ))) + (U' := (4451694278428638420951 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (3334121006929009 / 10000000000000000 : ℚ)) + (q := (1950943260898971 / 5000000000000000 : ℚ)) + (U := (-(9411249327571361579049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_14 : Uω (aρ 14) (bρ 14) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2302,26 +1986,21 @@ lemma U_644_14 : have hlg : Real.log (6573948985756573 / 20000000000000000 : ℝ) ≤ (-(5563087789113514828389 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6573948985756573 / 20000000000000000 : ℝ) = - (6573948985756573 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6573948985756573 / 5000000000000000 : ℚ)) - (U := (1368384013886485171611 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6573948985756573 / 5000000000000000 : ℝ) ≤ - (1368384013886485171611 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1224112117067349 / 5000000000000000 : ℝ)) (q := - (6573948985756573 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6573948985756573 / 20000000000000000 : ℚ)) + (r' := (6573948985756573 / 5000000000000000 : ℚ)) + (U := (-(5563087789113514828389 / 5000000000000000000000 : ℚ))) + (U' := (1368384013886485171611 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (1224112117067349 / 5000000000000000 : ℚ)) + (q := (6573948985756573 / 20000000000000000 : ℚ)) + (U := (-(5563087789113514828389 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_15 : Uω (aρ 15) (bρ 15) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2329,26 +2008,21 @@ lemma U_644_15 : have hlg : Real.log (2662396004972763 / 10000000000000000 : ℝ) ≤ (-(13233586213666000565321 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2662396004972763 / 10000000000000000 : ℝ) = - (2662396004972763 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2662396004972763 / 2500000000000000 : ℚ)) - (U := (629357392333999434679 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (2662396004972763 / 2500000000000000 : ℝ) ≤ - (629357392333999434679 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1458640535738651 / 10000000000000000 : ℝ)) (q := - (2662396004972763 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2662396004972763 / 10000000000000000 : ℚ)) + (r' := (2662396004972763 / 2500000000000000 : ℚ)) + (U := (-(13233586213666000565321 / 10000000000000000000000 : ℚ))) + (U' := (629357392333999434679 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (11915720012147 / 16000000000000 : ℚ)) + (s := (1458640535738651 / 10000000000000000 : ℚ)) + (q := (2662396004972763 / 10000000000000000 : ℚ)) + (U := (-(13233586213666000565321 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_644_16 : Uω (aρ 16) (bρ 16) (11915720012147 / 16000000000000 : ℝ) ≤ @@ -2445,25 +2119,21 @@ lemma U_645_1 : have hlg : Real.log (7401853897065559 / 10000000000000000 : ℝ) ≤ (-(1504272986350256580489 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7401853897065559 / 10000000000000000 : ℝ) = - (7401853897065559 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7401853897065559 / 5000000000000000 : ℚ)) - (U := (1961462915149743419511 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7401853897065559 / 5000000000000000 : ℝ) ≤ - (1961462915149743419511 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3700916027763059 / 5000000000000000 : ℝ)) (q := - (7401853897065559 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7401853897065559 / 10000000000000000 : ℚ)) + (r' := (7401853897065559 / 5000000000000000 : ℚ)) + (U := (-(1504272986350256580489 / 5000000000000000000000 : ℚ))) + (U' := (1961462915149743419511 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (3700916027763059 / 5000000000000000 : ℚ)) + (q := (7401853897065559 / 10000000000000000 : ℚ)) + (U := (-(1504272986350256580489 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_2 : Uω (aρ 2) (bρ 2) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2471,25 +2141,21 @@ lemma U_645_2 : have hlg : Real.log (1475592585872157 / 2000000000000000 : ℝ) ≤ (-(3040875180557327393003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1475592585872157 / 2000000000000000 : ℝ) = - (1475592585872157 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1475592585872157 / 1000000000000000 : ℚ)) - (U := (3890596622442672606997 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1475592585872157 / 1000000000000000 : ℝ) ≤ - (3890596622442672606997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (737781913262657 / 1000000000000000 : ℝ)) (q := - (1475592585872157 / 2000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1475592585872157 / 2000000000000000 : ℚ)) + (r' := (1475592585872157 / 1000000000000000 : ℚ)) + (U := (-(3040875180557327393003 / 10000000000000000000000 : ℚ))) + (U' := (3890596622442672606997 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (737781913262657 / 1000000000000000 : ℚ)) + (q := (1475592585872157 / 2000000000000000 : ℚ)) + (U := (-(3040875180557327393003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_3 : Uω (aρ 3) (bρ 3) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2497,25 +2163,21 @@ lemma U_645_3 : have hlg : Real.log (1466041197994437 / 2000000000000000 : ℝ) ≤ (-(388226843643701977613 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1466041197994437 / 2000000000000000 : ℝ) = - (1466041197994437 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1466041197994437 / 1000000000000000 : ℚ)) - (U := (478207131731298022387 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1466041197994437 / 1000000000000000 : ℝ) ≤ - (478207131731298022387 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (732970136019937 / 1000000000000000 : ℝ)) (q := - (1466041197994437 / 2000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1466041197994437 / 2000000000000000 : ℚ)) + (r' := (1466041197994437 / 1000000000000000 : ℚ)) + (U := (-(388226843643701977613 / 1250000000000000000000 : ℚ))) + (U' := (478207131731298022387 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (732970136019937 / 1000000000000000 : ℚ)) + (q := (1466041197994437 / 2000000000000000 : ℚ)) + (U := (-(388226843643701977613 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_4 : Uω (aρ 4) (bρ 4) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2523,25 +2185,21 @@ lemma U_645_4 : have hlg : Real.log (580077241951651 / 800000000000000 : ℝ) ≤ (-(1607252284779575578089 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (580077241951651 / 800000000000000 : ℝ) = - (580077241951651 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (580077241951651 / 400000000000000 : ℚ)) - (U := (1858483616720424421911 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (580077241951651 / 400000000000000 : ℝ) ≤ - (1858483616720424421911 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (289980584404451 / 400000000000000 : ℝ)) (q := - (580077241951651 / 800000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (580077241951651 / 800000000000000 : ℚ)) + (r' := (580077241951651 / 400000000000000 : ℚ)) + (U := (-(1607252284779575578089 / 5000000000000000000000 : ℚ))) + (U' := (1858483616720424421911 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (289980584404451 / 400000000000000 : ℚ)) + (q := (580077241951651 / 800000000000000 : ℚ)) + (U := (-(1607252284779575578089 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_5 : Uω (aρ 5) (bρ 5) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2549,25 +2207,21 @@ lemma U_645_5 : have hlg : Real.log (142609841460427 / 200000000000000 : ℝ) ≤ (-(3382048462402861285543 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (142609841460427 / 200000000000000 : ℝ) = - (142609841460427 / 100000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (142609841460427 / 100000000000000 : ℚ)) - (U := (3549423340597138714457 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (142609841460427 / 100000000000000 : ℝ) ≤ - (3549423340597138714457 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (71267576266977 / 100000000000000 : ℝ)) (q := - (142609841460427 / 200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (142609841460427 / 200000000000000 : ℚ)) + (r' := (142609841460427 / 100000000000000 : ℚ)) + (U := (-(3382048462402861285543 / 10000000000000000000000 : ℚ))) + (U' := (3549423340597138714457 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (71267576266977 / 100000000000000 : ℚ)) + (q := (142609841460427 / 200000000000000 : ℚ)) + (U := (-(3382048462402861285543 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_6 : Uω (aρ 6) (bρ 6) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2575,25 +2229,21 @@ lemma U_645_6 : have hlg : Real.log (3479083784246109 / 5000000000000000 : ℝ) ≤ (-(3626689334411872943689 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3479083784246109 / 5000000000000000 : ℝ) = - (3479083784246109 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3479083784246109 / 2500000000000000 : ℚ)) - (U := (3304782468588127056311 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3479083784246109 / 2500000000000000 : ℝ) ≤ - (3304782468588127056311 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1737337248194859 / 2500000000000000 : ℝ)) (q := - (3479083784246109 / 5000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3479083784246109 / 5000000000000000 : ℚ)) + (r' := (3479083784246109 / 2500000000000000 : ℚ)) + (U := (-(3626689334411872943689 / 10000000000000000000000 : ℚ))) + (U' := (3304782468588127056311 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (1737337248194859 / 2500000000000000 : ℚ)) + (q := (3479083784246109 / 5000000000000000 : ℚ)) + (U := (-(3626689334411872943689 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_7 : Uω (aρ 7) (bρ 7) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2601,25 +2251,21 @@ lemma U_645_7 : have hlg : Real.log (420252464955703 / 625000000000000 : ℝ) ≤ (-(496120014692653319329 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (420252464955703 / 625000000000000 : ℝ) = - (420252464955703 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (420252464955703 / 312500000000000 : ℚ)) - (U := (370313960682346680671 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (420252464955703 / 312500000000000 : ℝ) ≤ - (370313960682346680671 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (838094264392187 / 1250000000000000 : ℝ)) (q := - (420252464955703 / 625000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (420252464955703 / 625000000000000 : ℚ)) + (r' := (420252464955703 / 312500000000000 : ℚ)) + (U := (-(496120014692653319329 / 1250000000000000000000 : ℚ))) + (U' := (370313960682346680671 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (838094264392187 / 1250000000000000 : ℚ)) + (q := (420252464955703 / 625000000000000 : ℚ)) + (U := (-(496120014692653319329 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_8 : Uω (aρ 8) (bρ 8) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2627,25 +2273,21 @@ lemma U_645_8 : have hlg : Real.log (6420496605605981 / 10000000000000000 : ℝ) ≤ (-(4430896251256838405569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6420496605605981 / 10000000000000000 : ℝ) = - (6420496605605981 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6420496605605981 / 5000000000000000 : ℚ)) - (U := (2500575551743161594431 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6420496605605981 / 5000000000000000 : ℝ) ≤ - (2500575551743161594431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3190605049553481 / 5000000000000000 : ℝ)) (q := - (6420496605605981 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6420496605605981 / 10000000000000000 : ℚ)) + (r' := (6420496605605981 / 5000000000000000 : ℚ)) + (U := (-(4430896251256838405569 / 10000000000000000000000 : ℚ))) + (U' := (2500575551743161594431 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (3190605049553481 / 5000000000000000 : ℚ)) + (q := (6420496605605981 / 10000000000000000 : ℚ)) + (U := (-(4430896251256838405569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_9 : Uω (aρ 9) (bρ 9) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2653,25 +2295,21 @@ lemma U_645_9 : have hlg : Real.log (6043888113840151 / 10000000000000000 : ℝ) ≤ (-(2517687802170217421033 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6043888113840151 / 10000000000000000 : ℝ) = - (6043888113840151 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6043888113840151 / 5000000000000000 : ℚ)) - (U := (948048099329782578967 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (6043888113840151 / 5000000000000000 : ℝ) ≤ - (948048099329782578967 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2984479371967651 / 5000000000000000 : ℝ)) (q := - (6043888113840151 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6043888113840151 / 10000000000000000 : ℚ)) + (r' := (6043888113840151 / 5000000000000000 : ℚ)) + (U := (-(2517687802170217421033 / 5000000000000000000000 : ℚ))) + (U' := (948048099329782578967 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (2984479371967651 / 5000000000000000 : ℚ)) + (q := (6043888113840151 / 10000000000000000 : ℚ)) + (U := (-(2517687802170217421033 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_10 : Uω (aρ 10) (bρ 10) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2679,26 +2317,21 @@ lemma U_645_10 : have hlg : Real.log (2797903322069447 / 5000000000000000 : ℝ) ≤ (-(2902837945202620132743 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2797903322069447 / 5000000000000000 : ℝ) = - (2797903322069447 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2797903322069447 / 2500000000000000 : ℚ)) - (U := (562897956297379867257 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2797903322069447 / 2500000000000000 : ℝ) ≤ - (562897956297379867257 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1365338709506947 / 2500000000000000 : ℝ)) (q := - (2797903322069447 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2797903322069447 / 5000000000000000 : ℚ)) + (r' := (2797903322069447 / 2500000000000000 : ℚ)) + (U := (-(2902837945202620132743 / 5000000000000000000000 : ℚ))) + (U' := (562897956297379867257 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (1365338709506947 / 2500000000000000 : ℚ)) + (q := (2797903322069447 / 5000000000000000 : ℚ)) + (U := (-(2902837945202620132743 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_11 : Uω (aρ 11) (bρ 11) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2706,26 +2339,21 @@ lemma U_645_11 : have hlg : Real.log (1016745558211633 / 2000000000000000 : ℝ) ≤ (-(1691350707796066750917 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1016745558211633 / 2000000000000000 : ℝ) = - (1016745558211633 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1016745558211633 / 1000000000000000 : ℚ)) - (U := (41517242953933249083 / 2500000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (1016745558211633 / 1000000000000000 : ℝ) ≤ - (41517242953933249083 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (485567375807133 / 1000000000000000 : ℝ)) (q := - (1016745558211633 / 2000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1016745558211633 / 2000000000000000 : ℚ)) + (r' := (1016745558211633 / 1000000000000000 : ℚ)) + (U := (-(1691350707796066750917 / 2500000000000000000000 : ℚ))) + (U' := (41517242953933249083 / 2500000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (485567375807133 / 1000000000000000 : ℚ)) + (q := (1016745558211633 / 2000000000000000 : ℚ)) + (U := (-(1691350707796066750917 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_12 : Uω (aρ 12) (bρ 12) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2733,26 +2361,21 @@ lemma U_645_12 : have hlg : Real.log (9041480903424091 / 20000000000000000 : ℝ) ≤ (-(3969546476480306766289 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (9041480903424091 / 20000000000000000 : ℝ) = - (9041480903424091 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9041480903424091 / 5000000000000000 : ℚ)) - (U := (2961925326519693233711 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9041480903424091 / 5000000000000000 : ℝ) ≤ - (2961925326519693233711 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4153399176064091 / 10000000000000000 : ℝ)) (q := - (9041480903424091 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9041480903424091 / 20000000000000000 : ℚ)) + (r' := (9041480903424091 / 5000000000000000 : ℚ)) + (U := (-(3969546476480306766289 / 5000000000000000000000 : ℚ))) + (U' := (2961925326519693233711 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (4153399176064091 / 10000000000000000 : ℚ)) + (q := (9041480903424091 / 20000000000000000 : ℚ)) + (U := (-(3969546476480306766289 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_13 : Uω (aρ 13) (bρ 13) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2760,26 +2383,21 @@ lemma U_645_13 : have hlg : Real.log (1569662645146701 / 4000000000000000 : ℝ) ≤ (-(935433640031612922849 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1569662645146701 / 4000000000000000 : ℝ) = - (1569662645146701 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1569662645146701 / 1000000000000000 : ℚ)) - (U := (450860720568387077151 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1569662645146701 / 1000000000000000 : ℝ) ≤ - (450860720568387077151 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (671922647993701 / 2000000000000000 : ℝ)) (q := - (1569662645146701 / 4000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1569662645146701 / 4000000000000000 : ℚ)) + (r' := (1569662645146701 / 1000000000000000 : ℚ)) + (U := (-(935433640031612922849 / 1000000000000000000000 : ℚ))) + (U' := (450860720568387077151 / 1000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (671922647993701 / 2000000000000000 : ℚ)) + (q := (1569662645146701 / 4000000000000000 : ℚ)) + (U := (-(935433640031612922849 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_14 : Uω (aρ 14) (bρ 14) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2787,26 +2405,21 @@ lemma U_645_14 : have hlg : Real.log (3312480894648137 / 10000000000000000 : ℝ) ≤ (-(1104887668831840048521 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3312480894648137 / 10000000000000000 : ℝ) = - (3312480894648137 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3312480894648137 / 2500000000000000 : ℚ)) - (U := (281406691768159951479 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3312480894648137 / 2500000000000000 : ℝ) ≤ - (281406691768159951479 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1240094544288137 / 5000000000000000 : ℝ)) (q := - (3312480894648137 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3312480894648137 / 10000000000000000 : ℚ)) + (r' := (3312480894648137 / 2500000000000000 : ℚ)) + (U := (-(1104887668831840048521 / 1000000000000000000000 : ℚ))) + (U' := (281406691768159951479 / 1000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (1240094544288137 / 5000000000000000 : ℚ)) + (q := (3312480894648137 / 10000000000000000 : ℚ)) + (U := (-(1104887668831840048521 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_15 : Uω (aρ 15) (bρ 15) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2814,24 +2427,21 @@ lemma U_645_15 : have hlg : Real.log (67420030040337 / 250000000000000 : ℝ) ≤ (-(6552593809832138435991 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (67420030040337 / 250000000000000 : ℝ) = (67420030040337 / 62500000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (67420030040337 / 62500000000000 : ℚ)) - (U := (378877993167861564009 / 5000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (67420030040337 / 62500000000000 : ℝ) ≤ - (378877993167861564009 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (37710074498049 / 250000000000000 : ℝ)) (q := - (67420030040337 / 250000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [bρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (67420030040337 / 250000000000000 : ℚ)) + (r' := (67420030040337 / 62500000000000 : ℚ)) + (U := (-(6552593809832138435991 / 5000000000000000000000 : ℚ))) + (U' := (378877993167861564009 / 5000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (746637295669 / 1000000000000 : ℚ)) + (s := (37710074498049 / 250000000000000 : ℚ)) + (q := (67420030040337 / 250000000000000 : ℚ)) + (U := (-(6552593809832138435991 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_645_16 : Uω (aρ 16) (bρ 16) (746637295669 / 1000000000000 : ℝ) ≤ @@ -2929,25 +2539,21 @@ lemma U_646_1 : have hlg : Real.log (949004006820246619 / 1280000000000000000 : ℝ) ≤ (-(2992023359028118615229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (949004006820246619 / 1280000000000000000 : ℝ) = - (949004006820246619 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (949004006820246619 / 640000000000000000 : ℚ)) - (U := (3939448443971881384771 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (949004006820246619 / 640000000000000000 : ℝ) ≤ - (3939448443971881384771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7414071997801871 / 10000000000000000 : ℝ)) (q := - (949004006820246619 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (949004006820246619 / 1280000000000000000 : ℚ)) + (r' := (949004006820246619 / 640000000000000000 : ℚ)) + (U := (-(2992023359028118615229 / 10000000000000000000000 : ℚ))) + (U' := (3939448443971881384771 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (7414071997801871 / 10000000000000000 : ℚ)) + (q := (949004006820246619 / 1280000000000000000 : ℚ)) + (U := (-(2992023359028118615229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_2 : Uω (aρ 2) (bρ 2) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -2955,25 +2561,21 @@ lemma U_646_2 : have hlg : Real.log (37837839552948499 / 51200000000000000 : ℝ) ≤ (-(3024298834984676636863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (37837839552948499 / 51200000000000000 : ℝ) = - (37837839552948499 / 25600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37837839552948499 / 25600000000000000 : ℚ)) - (U := (3907172968015323363137 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (37837839552948499 / 25600000000000000 : ℝ) ≤ - (3907172968015323363137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (295602379164641 / 400000000000000 : ℝ)) (q := - (37837839552948499 / 51200000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37837839552948499 / 51200000000000000 : ℚ)) + (r' := (37837839552948499 / 25600000000000000 : ℚ)) + (U := (-(3024298834984676636863 / 10000000000000000000000 : ℚ))) + (U' := (3907172968015323363137 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (295602379164641 / 400000000000000 : ℚ)) + (q := (37837839552948499 / 51200000000000000 : ℚ)) + (U := (-(3024298834984676636863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_3 : Uω (aρ 3) (bρ 3) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -2981,25 +2583,21 @@ lemma U_646_3 : have hlg : Real.log (187966635556047583 / 256000000000000000 : ℝ) ≤ (-(3089129675859665067647 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (187966635556047583 / 256000000000000000 : ℝ) = - (187966635556047583 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (187966635556047583 / 128000000000000000 : ℚ)) - (U := (3842342127140334932353 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (187966635556047583 / 128000000000000000 : ℝ) ≤ - (3842342127140334932353 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1468388582582347 / 2000000000000000 : ℝ)) (q := - (187966635556047583 / 256000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (187966635556047583 / 256000000000000000 : ℚ)) + (r' := (187966635556047583 / 128000000000000000 : ℚ)) + (U := (-(3089129675859665067647 / 10000000000000000000000 : ℚ))) + (U' := (3842342127140334932353 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (1468388582582347 / 2000000000000000 : ℚ)) + (q := (187966635556047583 / 256000000000000000 : ℚ)) + (U := (-(3089129675859665067647 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_4 : Uω (aρ 4) (bρ 4) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3007,25 +2605,21 @@ lemma U_646_4 : have hlg : Real.log (929690603533680987 / 1280000000000000000 : ℝ) ≤ (-(3197635102305245452937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (929690603533680987 / 1280000000000000000 : ℝ) = - (929690603533680987 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (929690603533680987 / 640000000000000000 : ℚ)) - (U := (3733836700694754547063 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (929690603533680987 / 640000000000000000 : ℝ) ≤ - (3733836700694754547063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7261759371374283 / 10000000000000000 : ℝ)) (q := - (929690603533680987 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (929690603533680987 / 1280000000000000000 : ℚ)) + (r' := (929690603533680987 / 640000000000000000 : ℚ)) + (U := (-(3197635102305245452937 / 10000000000000000000000 : ℚ))) + (U' := (3733836700694754547063 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (7261759371374283 / 10000000000000000 : ℚ)) + (q := (929690603533680987 / 1280000000000000000 : ℚ)) + (U := (-(3197635102305245452937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_5 : Uω (aρ 5) (bρ 5) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3033,25 +2627,21 @@ lemma U_646_5 : have hlg : Real.log (914270508277011163 / 1280000000000000000 : ℝ) ≤ (-(3364888680715927873629 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (914270508277011163 / 1280000000000000000 : ℝ) = - (914270508277011163 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (914270508277011163 / 640000000000000000 : ℚ)) - (U := (3566583122284072126371 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (914270508277011163 / 640000000000000000 : ℝ) ≤ - (3566583122284072126371 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7139010302323817 / 10000000000000000 : ℝ)) (q := - (914270508277011163 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (914270508277011163 / 1280000000000000000 : ℚ)) + (r' := (914270508277011163 / 640000000000000000 : ℚ)) + (U := (-(3364888680715927873629 / 10000000000000000000000 : ℚ))) + (U' := (3566583122284072126371 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (7139010302323817 / 10000000000000000 : ℚ)) + (q := (914270508277011163 / 1280000000000000000 : ℚ)) + (U := (-(3364888680715927873629 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_6 : Uω (aρ 6) (bρ 6) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3059,25 +2649,21 @@ lemma U_646_6 : have hlg : Real.log (892214136760683483 / 1280000000000000000 : ℝ) ≤ (-(902272973128295129753 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (892214136760683483 / 1280000000000000000 : ℝ) = - (892214136760683483 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (892214136760683483 / 640000000000000000 : ℚ)) - (U := (830594977621704870247 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (892214136760683483 / 640000000000000000 : ℝ) ≤ - (830594977621704870247 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6961619872521197 / 10000000000000000 : ℝ)) (q := - (892214136760683483 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (892214136760683483 / 1280000000000000000 : ℚ)) + (r' := (892214136760683483 / 640000000000000000 : ℚ)) + (U := (-(902272973128295129753 / 2500000000000000000000 : ℚ))) + (U' := (830594977621704870247 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (6961619872521197 / 10000000000000000 : ℚ)) + (q := (892214136760683483 / 1280000000000000000 : ℚ)) + (U := (-(902272973128295129753 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_7 : Uω (aρ 7) (bρ 7) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3085,25 +2671,21 @@ lemma U_646_7 : have hlg : Real.log (172449649957237919 / 256000000000000000 : ℝ) ≤ (-(3950721346605848420679 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (172449649957237919 / 256000000000000000 : ℝ) = - (172449649957237919 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (172449649957237919 / 128000000000000000 : ℚ)) - (U := (2980750456394151579321 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (172449649957237919 / 128000000000000000 : ℝ) ≤ - (2980750456394151579321 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (671706426930473 / 1000000000000000 : ℝ)) (q := - (172449649957237919 / 256000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (172449649957237919 / 256000000000000000 : ℚ)) + (r' := (172449649957237919 / 128000000000000000 : ℚ)) + (U := (-(3950721346605848420679 / 10000000000000000000000 : ℚ))) + (U' := (2980750456394151579321 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (671706426930473 / 1000000000000000 : ℚ)) + (q := (172449649957237919 / 256000000000000000 : ℚ)) + (U := (-(3950721346605848420679 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_8 : Uω (aρ 8) (bρ 8) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3111,25 +2693,21 @@ lemma U_646_8 : have hlg : Real.log (823399895872270299 / 1280000000000000000 : ℝ) ≤ (-(1102933434446520637007 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (823399895872270299 / 1280000000000000000 : ℝ) = - (823399895872270299 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (823399895872270299 / 640000000000000000 : ℚ)) - (U := (629934516303479362993 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (823399895872270299 / 640000000000000000 : ℝ) ≤ - (629934516303479362993 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6393600390739741 / 10000000000000000 : ℝ)) (q := - (823399895872270299 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (823399895872270299 / 1280000000000000000 : ℚ)) + (r' := (823399895872270299 / 640000000000000000 : ℚ)) + (U := (-(1102933434446520637007 / 2500000000000000000000 : ℚ))) + (U' := (629934516303479362993 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (6393600390739741 / 10000000000000000 : ℚ)) + (q := (823399895872270299 / 1280000000000000000 : ℚ)) + (U := (-(1102933434446520637007 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_9 : Uω (aρ 9) (bρ 9) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3137,25 +2715,21 @@ lemma U_646_9 : have hlg : Real.log (775204008300344347 / 1280000000000000000 : ℝ) ≤ (-(5014891254244500333307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (775204008300344347 / 1280000000000000000 : ℝ) = - (775204008300344347 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (775204008300344347 / 640000000000000000 : ℚ)) - (U := (1916580548755499666693 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (775204008300344347 / 640000000000000000 : ℝ) ≤ - (1916580548755499666693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2990752637894199 / 5000000000000000 : ℝ)) (q := - (775204008300344347 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (775204008300344347 / 1280000000000000000 : ℚ)) + (r' := (775204008300344347 / 640000000000000000 : ℚ)) + (U := (-(5014891254244500333307 / 10000000000000000000000 : ℚ))) + (U' := (1916580548755499666693 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (2990752637894199 / 5000000000000000 : ℚ)) + (q := (775204008300344347 / 1280000000000000000 : ℚ)) + (U := (-(5014891254244500333307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_10 : Uω (aρ 10) (bρ 10) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3163,26 +2737,21 @@ lemma U_646_10 : have hlg : Real.log (28714737430711059 / 51200000000000000 : ℝ) ≤ (-(2891645207438468629941 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28714737430711059 / 51200000000000000 : ℝ) = - (28714737430711059 / 25600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28714737430711059 / 25600000000000000 : ℚ)) - (U := (574090694061531370059 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (28714737430711059 / 25600000000000000 : ℝ) ≤ - (574090694061531370059 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (218967839538481 / 400000000000000 : ℝ)) (q := - (28714737430711059 / 51200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28714737430711059 / 51200000000000000 : ℚ)) + (r' := (28714737430711059 / 25600000000000000 : ℚ)) + (U := (-(2891645207438468629941 / 5000000000000000000000 : ℚ))) + (U' := (574090694061531370059 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (218967839538481 / 400000000000000 : ℚ)) + (q := (28714737430711059 / 51200000000000000 : ℚ)) + (U := (-(2891645207438468629941 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_11 : Uω (aρ 11) (bρ 11) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3190,26 +2759,21 @@ lemma U_646_11 : have hlg : Real.log (652357249560574811 / 1280000000000000000 : ℝ) ≤ (-(6740230160113358478249 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (652357249560574811 / 1280000000000000000 : ℝ) = - (652357249560574811 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (652357249560574811 / 640000000000000000 : ℚ)) - (U := (191241642886641521751 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (652357249560574811 / 640000000000000000 : ℝ) ≤ - (191241642886641521751 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4869060330179499 / 10000000000000000 : ℝ)) (q := - (652357249560574811 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (652357249560574811 / 1280000000000000000 : ℚ)) + (r' := (652357249560574811 / 640000000000000000 : ℚ)) + (U := (-(6740230160113358478249 / 10000000000000000000000 : ℚ))) + (U' := (191241642886641521751 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (4869060330179499 / 10000000000000000 : ℚ)) + (q := (652357249560574811 / 1280000000000000000 : ℚ)) + (U := (-(6740230160113358478249 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_12 : Uω (aρ 12) (bρ 12) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3217,26 +2781,21 @@ lemma U_646_12 : have hlg : Real.log (580359603050208539 / 1280000000000000000 : ℝ) ≤ (-(3954837198590898932649 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (580359603050208539 / 1280000000000000000 : ℝ) = - (580359603050208539 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (580359603050208539 / 320000000000000000 : ℚ)) - (U := (2976634604409101067351 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (580359603050208539 / 320000000000000000 : ℝ) ≤ - (2976634604409101067351 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2083898600070013 / 5000000000000000 : ℝ)) (q := - (580359603050208539 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (580359603050208539 / 1280000000000000000 : ℚ)) + (r' := (580359603050208539 / 320000000000000000 : ℚ)) + (U := (-(3954837198590898932649 / 5000000000000000000000 : ℚ))) + (U' := (2976634604409101067351 / 5000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (2083898600070013 / 5000000000000000 : ℚ)) + (q := (580359603050208539 / 1280000000000000000 : ℚ)) + (U := (-(3954837198590898932649 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_13 : Uω (aρ 13) (bρ 13) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3244,26 +2803,21 @@ lemma U_646_13 : have hlg : Real.log (100824180191920607 / 256000000000000000 : ℝ) ≤ (-(9317992342333403447889 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (100824180191920607 / 256000000000000000 : ℝ) = - (100824180191920607 / 64000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (100824180191920607 / 64000000000000000 : ℚ)) - (U := (4544951263666596552111 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (100824180191920607 / 64000000000000000 : ℝ) ≤ - (4544951263666596552111 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (675189844313863 / 2000000000000000 : ℝ)) (q := - (100824180191920607 / 256000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (100824180191920607 / 256000000000000000 : ℚ)) + (r' := (100824180191920607 / 64000000000000000 : ℚ)) + (U := (-(9317992342333403447889 / 10000000000000000000000 : ℚ))) + (U' := (4544951263666596552111 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (675189844313863 / 2000000000000000 : ℚ)) + (q := (100824180191920607 / 256000000000000000 : ℚ)) + (U := (-(9317992342333403447889 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_14 : Uω (aρ 14) (bρ 14) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3271,26 +2825,21 @@ lemma U_646_14 : have hlg : Real.log (85217313779522783 / 256000000000000000 : ℝ) ≤ (-(10999728173947622292111 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (85217313779522783 / 256000000000000000 : ℝ) = - (85217313779522783 / 64000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85217313779522783 / 64000000000000000 : ℚ)) - (U := (2863215432052377707889 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (85217313779522783 / 64000000000000000 : ℝ) ≤ - (2863215432052377707889 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (500118013629147 / 2000000000000000 : ℝ)) (q := - (85217313779522783 / 256000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85217313779522783 / 256000000000000000 : ℚ)) + (r' := (85217313779522783 / 64000000000000000 : ℚ)) + (U := (-(10999728173947622292111 / 10000000000000000000000 : ℚ))) + (U' := (2863215432052377707889 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (500118013629147 / 2000000000000000 : ℚ)) + (q := (85217313779522783 / 256000000000000000 : ℚ)) + (U := (-(10999728173947622292111 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_15 : Uω (aρ 15) (bρ 15) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3298,26 +2847,21 @@ lemma U_646_15 : have hlg : Real.log (347974045552011739 / 1280000000000000000 : ℝ) ≤ (-(3256218652869368476347 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (347974045552011739 / 1280000000000000000 : ℝ) = - (347974045552011739 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (347974045552011739 / 320000000000000000 : ℚ)) - (U := (209517248630631523653 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (347974045552011739 / 320000000000000000 : ℝ) ≤ - (209517248630631523653 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1539655168285701 / 10000000000000000 : ℝ)) (q := - (347974045552011739 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (347974045552011739 / 1280000000000000000 : ℚ)) + (r' := (347974045552011739 / 320000000000000000 : ℚ)) + (U := (-(3256218652869368476347 / 2500000000000000000000 : ℚ))) + (U' := (209517248630631523653 / 2500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (1539655168285701 / 10000000000000000 : ℚ)) + (q := (347974045552011739 / 1280000000000000000 : ℚ)) + (U := (-(3256218652869368476347 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646_16 : Uω (aρ 16) (bρ 16) (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3325,26 +2869,21 @@ lemma U_646_16 : have hlg : Real.log (259046679374740763 / 1280000000000000000 : ℝ) ≤ (-(3195214162855050481337 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (259046679374740763 / 1280000000000000000 : ℝ) = - (259046679374740763 / 160000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (259046679374740763 / 160000000000000000 : ℚ)) - (U := (963668918944949518663 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (259046679374740763 / 160000000000000000 : ℝ) ≤ - (963668918944949518663 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (151268361637921 / 5000000000000000 : ℝ)) (q := - (259046679374740763 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (259046679374740763 / 1280000000000000000 : ℚ)) + (r' := (259046679374740763 / 160000000000000000 : ℚ)) + (U := (-(3195214162855050481337 / 2000000000000000000000 : ℚ))) + (U' := (963668918944949518663 / 2000000000000000000000 : ℚ)) + 3 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (765809953469387 / 1024000000000000 : ℚ)) + (s := (151268361637921 / 5000000000000000 : ℚ)) + (q := (259046679374740763 / 1280000000000000000 : ℚ)) + (U := (-(3195214162855050481337 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_646 : Uρ (765809953469387 / 1024000000000000 : ℝ) ≤ @@ -3450,25 +2989,21 @@ lemma U_647_1 : have hlg : Real.log (475285357400443739 / 640000000000000000 : ℝ) ≤ (-(2975528000166417994777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (475285357400443739 / 640000000000000000 : ℝ) = - (475285357400443739 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (475285357400443739 / 320000000000000000 : ℚ)) - (U := (3955943802833582005223 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (475285357400443739 / 320000000000000000 : ℝ) ≤ - (3955943802833582005223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3713155969919951 / 5000000000000000 : ℝ)) (q := - (475285357400443739 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (475285357400443739 / 640000000000000000 : ℚ)) + (r' := (475285357400443739 / 320000000000000000 : ℚ)) + (U := (-(2975528000166417994777 / 10000000000000000000000 : ℚ))) + (U' := (3955943802833582005223 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (3713155969919951 / 5000000000000000 : ℚ)) + (q := (475285357400443739 / 640000000000000000 : ℚ)) + (U := (-(2975528000166417994777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_2 : Uω (aρ 2) (bρ 2) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3476,25 +3011,21 @@ lemma U_647_2 : have hlg : Real.log (473756361294213403 / 640000000000000000 : ℝ) ≤ (-(3007749922533249645921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (473756361294213403 / 640000000000000000 : ℝ) = - (473756361294213403 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (473756361294213403 / 320000000000000000 : ℚ)) - (U := (3923721880466750354079 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (473756361294213403 / 320000000000000000 : ℝ) ≤ - (3923721880466750354079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1850574956007551 / 2500000000000000 : ℝ)) (q := - (473756361294213403 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (473756361294213403 / 640000000000000000 : ℚ)) + (r' := (473756361294213403 / 320000000000000000 : ℚ)) + (U := (-(3007749922533249645921 / 10000000000000000000000 : ℚ))) + (U' := (3923721880466750354079 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (1850574956007551 / 2500000000000000 : ℚ)) + (q := (473756361294213403 / 640000000000000000 : ℚ)) + (U := (-(3007749922533249645921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_3 : Uω (aρ 3) (bρ 3) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3502,25 +3033,21 @@ lemma U_647_3 : have hlg : Real.log (470699994242783899 / 640000000000000000 : ℝ) ≤ (-(3072472399178550156159 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (470699994242783899 / 640000000000000000 : ℝ) = - (470699994242783899 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (470699994242783899 / 320000000000000000 : ℚ)) - (U := (3858999403821449843841 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (470699994242783899 / 320000000000000000 : ℝ) ≤ - (3858999403821449843841 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (919273057502879 / 1250000000000000 : ℝ)) (q := - (470699994242783899 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (470699994242783899 / 640000000000000000 : ℚ)) + (r' := (470699994242783899 / 320000000000000000 : ℚ)) + (U := (-(3072472399178550156159 / 10000000000000000000000 : ℚ))) + (U' := (3858999403821449843841 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (919273057502879 / 1250000000000000 : ℚ)) + (q := (470699994242783899 / 640000000000000000 : ℚ)) + (U := (-(3072472399178550156159 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_4 : Uω (aρ 4) (bρ 4) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3528,25 +3055,21 @@ lemma U_647_4 : have hlg : Real.log (465628809445522491 / 640000000000000000 : ℝ) ≤ (-(3180794056339040181553 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (465628809445522491 / 640000000000000000 : ℝ) = - (465628809445522491 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (465628809445522491 / 320000000000000000 : ℚ)) - (U := (3750677746660959818447 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (465628809445522491 / 320000000000000000 : ℝ) ≤ - (3750677746660959818447 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7274004116173613 / 10000000000000000 : ℝ)) (q := - (465628809445522491 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (465628809445522491 / 640000000000000000 : ℚ)) + (r' := (465628809445522491 / 320000000000000000 : ℚ)) + (U := (-(3180794056339040181553 / 10000000000000000000000 : ℚ))) + (U' := (3750677746660959818447 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (7274004116173613 / 10000000000000000 : ℚ)) + (q := (465628809445522491 / 640000000000000000 : ℚ)) + (U := (-(3180794056339040181553 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_5 : Uω (aρ 5) (bρ 5) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3554,25 +3077,21 @@ lemma U_647_5 : have hlg : Real.log (457919014200195963 / 640000000000000000 : ℝ) ≤ (-(1673879162526766033253 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (457919014200195963 / 640000000000000000 : ℝ) = - (457919014200195963 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (457919014200195963 / 320000000000000000 : ℚ)) - (U := (1791856738973233966747 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (457919014200195963 / 320000000000000000 : ℝ) ≤ - (1791856738973233966747 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7151262934092159 / 10000000000000000 : ℝ)) (q := - (457919014200195963 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (457919014200195963 / 640000000000000000 : ℚ)) + (r' := (457919014200195963 / 320000000000000000 : ℚ)) + (U := (-(1673879162526766033253 / 5000000000000000000000 : ℚ))) + (U' := (1791856738973233966747 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (7151262934092159 / 10000000000000000 : ℚ)) + (q := (457919014200195963 / 640000000000000000 : ℚ)) + (U := (-(1673879162526766033253 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_6 : Uω (aρ 6) (bρ 6) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3580,25 +3099,21 @@ lemma U_647_6 : have hlg : Real.log (446891408889576027 / 640000000000000000 : ℝ) ≤ (-(1795762720630881838427 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (446891408889576027 / 640000000000000000 : ℝ) = - (446891408889576027 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (446891408889576027 / 320000000000000000 : ℚ)) - (U := (1669973180869118161573 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (446891408889576027 / 320000000000000000 : ℝ) ≤ - (1669973180869118161573 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3486945321637643 / 5000000000000000 : ℝ)) (q := - (446891408889576027 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (446891408889576027 / 640000000000000000 : ℚ)) + (r' := (446891408889576027 / 320000000000000000 : ℚ)) + (U := (-(1795762720630881838427 / 5000000000000000000000 : ℚ))) + (U' := (1669973180869118161573 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (3486945321637643 / 5000000000000000 : ℚ)) + (q := (446891408889576027 / 640000000000000000 : ℚ)) + (U := (-(1795762720630881838427 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_7 : Uω (aρ 7) (bρ 7) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3606,25 +3121,21 @@ lemma U_647_7 : have hlg : Real.log (431909717466452347 / 640000000000000000 : ℝ) ≤ (-(983128992591838766227 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (431909717466452347 / 640000000000000000 : ℝ) = - (431909717466452347 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (431909717466452347 / 320000000000000000 : ℚ)) - (U := (749738958158161233773 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (431909717466452347 / 320000000000000000 : ℝ) ≤ - (749738958158161233773 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6729374167062671 / 10000000000000000 : ℝ)) (q := - (431909717466452347 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (431909717466452347 / 640000000000000000 : ℚ)) + (r' := (431909717466452347 / 320000000000000000 : ℚ)) + (U := (-(983128992591838766227 / 2500000000000000000000 : ℚ))) + (U' := (749738958158161233773 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (6729374167062671 / 10000000000000000 : ℚ)) + (q := (431909717466452347 / 640000000000000000 : ℚ)) + (U := (-(983128992591838766227 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_8 : Uω (aρ 8) (bρ 8) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3632,25 +3143,21 @@ lemma U_647_8 : have hlg : Real.log (412488094606284123 / 640000000000000000 : ℝ) ≤ (-(4392608322960627458259 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (412488094606284123 / 640000000000000000 : ℝ) = - (412488094606284123 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (412488094606284123 / 320000000000000000 : ℚ)) - (U := (2538863480039372541741 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (412488094606284123 / 320000000000000000 : ℝ) ≤ - (2538863480039372541741 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3202995052011207 / 5000000000000000 : ℝ)) (q := - (412488094606284123 / 640000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (412488094606284123 / 640000000000000000 : ℚ)) + (r' := (412488094606284123 / 320000000000000000 : ℚ)) + (U := (-(4392608322960627458259 / 10000000000000000000000 : ℚ))) + (U' := (2538863480039372541741 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (3202995052011207 / 5000000000000000 : ℚ)) + (q := (412488094606284123 / 640000000000000000 : ℚ)) + (U := (-(4392608322960627458259 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_9 : Uω (aρ 9) (bρ 9) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3658,25 +3165,21 @@ lemma U_647_9 : have hlg : Real.log (388395128435461531 / 640000000000000000 : ℝ) ≤ (-(998889964806808706123 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (388395128435461531 / 640000000000000000 : ℝ) = - (388395128435461531 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (388395128435461531 / 320000000000000000 : ℚ)) - (U := (387404395793191293877 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (388395128435461531 / 320000000000000000 : ℝ) ≤ - (387404395793191293877 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (374628158721513 / 625000000000000 : ℝ)) (q := - (388395128435461531 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (388395128435461531 / 640000000000000000 : ℚ)) + (r' := (388395128435461531 / 320000000000000000 : ℚ)) + (U := (-(998889964806808706123 / 2000000000000000000000 : ℚ))) + (U' := (387404395793191293877 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (374628158721513 / 625000000000000 : ℚ)) + (q := (388395128435461531 / 640000000000000000 : ℚ)) + (U := (-(998889964806808706123 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_10 : Uω (aρ 10) (bρ 10) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3684,26 +3187,21 @@ lemma U_647_10 : have hlg : Real.log (359736722593189947 / 640000000000000000 : ℝ) ≤ (-(5760957383230505686231 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (359736722593189947 / 640000000000000000 : ℝ) = - (359736722593189947 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (359736722593189947 / 320000000000000000 : ℚ)) - (U := (1170514419769494313769 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (359736722593189947 / 320000000000000000 : ℝ) ≤ - (1170514419769494313769 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5487034390468221 / 10000000000000000 : ℝ)) (q := - (359736722593189947 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (359736722593189947 / 640000000000000000 : ℚ)) + (r' := (359736722593189947 / 320000000000000000 : ℚ)) + (U := (-(5760957383230505686231 / 10000000000000000000000 : ℚ))) + (U' := (1170514419769494313769 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (5487034390468221 / 10000000000000000 : ℚ)) + (q := (359736722593189947 / 640000000000000000 : ℚ)) + (U := (-(5760957383230505686231 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_11 : Uω (aρ 11) (bρ 11) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3711,26 +3209,21 @@ lemma U_647_11 : have hlg : Real.log (326998478334935771 / 640000000000000000 : ℝ) ≤ (-(3357563293086641684171 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (326998478334935771 / 640000000000000000 : ℝ) = - (326998478334935771 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (326998478334935771 / 320000000000000000 : ℚ)) - (U := (108172608413358315829 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (326998478334935771 / 320000000000000000 : ℝ) ≤ - (108172608413358315829 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2441220441801389 / 5000000000000000 : ℝ)) (q := - (326998478334935771 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (326998478334935771 / 640000000000000000 : ℚ)) + (r' := (326998478334935771 / 320000000000000000 : ℚ)) + (U := (-(3357563293086641684171 / 5000000000000000000000 : ℚ))) + (U' := (108172608413358315829 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (2441220441801389 / 5000000000000000 : ℚ)) + (q := (326998478334935771 / 640000000000000000 : ℚ)) + (U := (-(3357563293086641684171 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_12 : Uω (aρ 12) (bρ 12) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3738,26 +3231,21 @@ lemma U_647_12 : have hlg : Real.log (58206354853245951 / 128000000000000000 : ℝ) ≤ (-(1970089311762010817417 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58206354853245951 / 128000000000000000 : ℝ) = - (58206354853245951 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58206354853245951 / 32000000000000000 : ℚ)) - (U := (1495646589737989182583 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (58206354853245951 / 32000000000000000 : ℝ) ≤ - (1495646589737989182583 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (836436295628143 / 2000000000000000 : ℝ)) (q := - (58206354853245951 / 128000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58206354853245951 / 128000000000000000 : ℚ)) + (r' := (58206354853245951 / 32000000000000000 : ℚ)) + (U := (-(1970089311762010817417 / 2500000000000000000000 : ℚ))) + (U' := (1495646589737989182583 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (836436295628143 / 2000000000000000 : ℚ)) + (q := (58206354853245951 / 128000000000000000 : ℚ)) + (U := (-(1970089311762010817417 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_13 : Uω (aρ 13) (bρ 13) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3765,26 +3253,21 @@ lemma U_647_13 : have hlg : Real.log (252973773579265531 / 640000000000000000 : ℝ) ≤ (-(1856364708443179756327 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (252973773579265531 / 640000000000000000 : ℝ) = - (252973773579265531 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (252973773579265531 / 160000000000000000 : ℚ)) - (U := (916224012756820243673 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (252973773579265531 / 160000000000000000 : ℝ) ≤ - (916224012756820243673 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3392250698268083 / 10000000000000000 : ℝ)) (q := - (252973773579265531 / 640000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (252973773579265531 / 640000000000000000 : ℚ)) + (r' := (252973773579265531 / 160000000000000000 : ℚ)) + (U := (-(1856364708443179756327 / 2000000000000000000000 : ℚ))) + (U' := (916224012756820243673 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (3392250698268083 / 10000000000000000 : ℚ)) + (q := (252973773579265531 / 640000000000000000 : ℚ)) + (U := (-(1856364708443179756327 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_14 : Uω (aρ 14) (bρ 14) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3792,26 +3275,21 @@ lemma U_647_14 : have hlg : Real.log (42816882045091679 / 128000000000000000 : ℝ) ≤ (-(10950977982772224991237 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (42816882045091679 / 128000000000000000 : ℝ) = - (42816882045091679 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42816882045091679 / 32000000000000000 : ℚ)) - (U := (2911965623227775008763 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (42816882045091679 / 32000000000000000 : ℝ) ≤ - (2911965623227775008763 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (252088537850661 / 1000000000000000 : ℝ)) (q := - (42816882045091679 / 128000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42816882045091679 / 128000000000000000 : ℚ)) + (r' := (42816882045091679 / 32000000000000000 : ℚ)) + (U := (-(10950977982772224991237 / 10000000000000000000000 : ℚ))) + (U' := (2911965623227775008763 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (252088537850661 / 1000000000000000 : ℚ)) + (q := (42816882045091679 / 128000000000000000 : ℚ)) + (U := (-(10950977982772224991237 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_15 : Uω (aρ 15) (bρ 15) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3819,26 +3297,21 @@ lemma U_647_15 : have hlg : Real.log (7014476874257139 / 25600000000000000 : ℝ) ≤ (-(80913513290171031217 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7014476874257139 / 25600000000000000 : ℝ) = - (7014476874257139 / 6400000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7014476874257139 / 6400000000000000 : ℚ)) - (U := (5729884247328968783 / 62500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (7014476874257139 / 6400000000000000 : ℝ) ≤ - (5729884247328968783 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (62815235775577 / 400000000000000 : ℝ)) (q := - (7014476874257139 / 25600000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7014476874257139 / 25600000000000000 : ℚ)) + (r' := (7014476874257139 / 6400000000000000 : ℚ)) + (U := (-(80913513290171031217 / 62500000000000000000 : ℚ))) + (U' := (5729884247328968783 / 62500000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (62815235775577 / 400000000000000 : ℚ)) + (q := (7014476874257139 / 25600000000000000 : ℚ)) + (U := (-(80913513290171031217 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647_16 : Uω (aρ 16) (bρ 16) (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3846,26 +3319,21 @@ lemma U_647_16 : have hlg : Real.log (5357451598432147 / 25600000000000000 : ℝ) ≤ (-(7820519683689689857467 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (5357451598432147 / 25600000000000000 : ℝ) = - (5357451598432147 / 3200000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5357451598432147 / 3200000000000000 : ℚ)) - (U := (2576688020810310142533 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (5357451598432147 / 3200000000000000 : ℝ) ≤ - (2576688020810310142533 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8564030983223 / 200000000000000 : ℝ)) (q := - (5357451598432147 / 25600000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5357451598432147 / 25600000000000000 : ℚ)) + (r' := (5357451598432147 / 3200000000000000 : ℚ)) + (U := (-(7820519683689689857467 / 5000000000000000000000 : ℚ))) + (U' := (2576688020810310142533 / 5000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (383531658086859 / 512000000000000 : ℚ)) + (s := (8564030983223 / 200000000000000 : ℚ)) + (q := (5357451598432147 / 25600000000000000 : ℚ)) + (U := (-(7820519683689689857467 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_647 : Uρ (383531658086859 / 512000000000000 : ℝ) ≤ @@ -3965,25 +3433,21 @@ lemma U_648_1 : have hlg : Real.log (190427484553277853 / 256000000000000000 : ℝ) ≤ (-(1479529903173407912513 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (190427484553277853 / 256000000000000000 : ℝ) = - (190427484553277853 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (190427484553277853 / 128000000000000000 : ℚ)) - (U := (1986205998326592087487 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (190427484553277853 / 128000000000000000 : ℝ) ≤ - (1986205998326592087487 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1487710376328277 / 2000000000000000 : ℝ)) (q := - (190427484553277853 / 256000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (190427484553277853 / 256000000000000000 : ℚ)) + (r' := (190427484553277853 / 128000000000000000 : ℚ)) + (U := (-(1479529903173407912513 / 5000000000000000000000 : ℚ))) + (U' := (1986205998326592087487 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (1487710376328277 / 2000000000000000 : ℚ)) + (q := (190427484553277853 / 256000000000000000 : ℚ)) + (U := (-(1479529903173407912513 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_2 : Uω (aρ 2) (bρ 2) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -3991,25 +3455,21 @@ lemma U_648_2 : have hlg : Real.log (949079456252822801 / 1280000000000000000 : ℝ) ≤ (-(1495614176274166129169 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (949079456252822801 / 1280000000000000000 : ℝ) = - (949079456252822801 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (949079456252822801 / 640000000000000000 : ℚ)) - (U := (1970121725225833870831 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (949079456252822801 / 640000000000000000 : ℝ) ≤ - (1970121725225833870831 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7414540167376909 / 10000000000000000 : ℝ)) (q := - (949079456252822801 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (949079456252822801 / 1280000000000000000 : ℚ)) + (r' := (949079456252822801 / 640000000000000000 : ℚ)) + (U := (-(1495614176274166129169 / 5000000000000000000000 : ℚ))) + (U' := (1970121725225833870831 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (7414540167376909 / 10000000000000000 : ℚ)) + (q := (949079456252822801 / 1280000000000000000 : ℚ)) + (U := (-(1495614176274166129169 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_3 : Uω (aρ 3) (bρ 3) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4017,25 +3477,21 @@ lemma U_648_3 : have hlg : Real.log (942966798834216401 / 1280000000000000000 : ℝ) ≤ (-(1527921413315886781817 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (942966798834216401 / 1280000000000000000 : ℝ) = - (942966798834216401 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (942966798834216401 / 640000000000000000 : ℚ)) - (U := (1937814488184113218183 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (942966798834216401 / 640000000000000000 : ℝ) ≤ - (1937814488184113218183 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (230200812548787 / 312500000000000 : ℝ)) (q := - (942966798834216401 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (942966798834216401 / 1280000000000000000 : ℚ)) + (r' := (942966798834216401 / 640000000000000000 : ℚ)) + (U := (-(1527921413315886781817 / 5000000000000000000000 : ℚ))) + (U' := (1937814488184113218183 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (230200812548787 / 312500000000000 : ℚ)) + (q := (942966798834216401 / 1280000000000000000 : ℚ)) + (U := (-(1527921413315886781817 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_4 : Uω (aρ 4) (bρ 4) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4043,25 +3499,21 @@ lemma U_648_4 : have hlg : Real.log (932824633200045713 / 1280000000000000000 : ℝ) ≤ (-(1581990668008304209843 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (932824633200045713 / 1280000000000000000 : ℝ) = - (932824633200045713 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (932824633200045713 / 640000000000000000 : ℚ)) - (U := (1883745233491695790157 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (932824633200045713 / 640000000000000000 : ℝ) ≤ - (1883745233491695790157 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7286248844592267 / 10000000000000000 : ℝ)) (q := - (932824633200045713 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (932824633200045713 / 1280000000000000000 : ℚ)) + (r' := (932824633200045713 / 640000000000000000 : ℚ)) + (U := (-(1581990668008304209843 / 5000000000000000000000 : ℚ))) + (U' := (1883745233491695790157 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (7286248844592267 / 10000000000000000 : ℚ)) + (q := (932824633200045713 / 1280000000000000000 : ℚ)) + (U := (-(1581990668008304209843 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_5 : Uω (aρ 5) (bρ 5) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4069,25 +3521,21 @@ lemma U_648_5 : have hlg : Real.log (917405545731278097 / 1280000000000000000 : ℝ) ≤ (-(3330657294562922625271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (917405545731278097 / 1280000000000000000 : ℝ) = - (917405545731278097 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (917405545731278097 / 640000000000000000 : ℚ)) - (U := (3600814508437077374729 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (917405545731278097 / 640000000000000000 : ℝ) ≤ - (3600814508437077374729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7163515522227773 / 10000000000000000 : ℝ)) (q := - (917405545731278097 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (917405545731278097 / 1280000000000000000 : ℚ)) + (r' := (917405545731278097 / 640000000000000000 : ℚ)) + (U := (-(3330657294562922625271 / 10000000000000000000000 : ℚ))) + (U' := (3600814508437077374729 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (7163515522227773 / 10000000000000000 : ℚ)) + (q := (917405545731278097 / 1280000000000000000 : ℚ)) + (U := (-(3330657294562922625271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_6 : Uω (aρ 6) (bρ 6) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4095,25 +3543,21 @@ lemma U_648_6 : have hlg : Real.log (895351491859164177 / 1280000000000000000 : ℝ) ≤ (-(714797974284375681511 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (895351491859164177 / 1280000000000000000 : ℝ) = - (895351491859164177 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (895351491859164177 / 640000000000000000 : ℚ)) - (U := (671496386315624318489 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (895351491859164177 / 640000000000000000 : ℝ) ≤ - (671496386315624318489 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6986161305615993 / 10000000000000000 : ℝ)) (q := - (895351491859164177 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (895351491859164177 / 1280000000000000000 : ℚ)) + (r' := (895351491859164177 / 640000000000000000 : ℚ)) + (U := (-(714797974284375681511 / 2000000000000000000000 : ℚ))) + (U' := (671496386315624318489 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (6986161305615993 / 10000000000000000 : ℚ)) + (q := (895351491859164177 / 1280000000000000000 : ℚ)) + (U := (-(714797974284375681511 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_7 : Uω (aρ 7) (bρ 7) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4121,25 +3565,21 @@ lemma U_648_7 : have hlg : Real.log (865390603759317137 / 1280000000000000000 : ℝ) ≤ (-(489292983258718903463 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (865390603759317137 / 1280000000000000000 : ℝ) = - (865390603759317137 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (865390603759317137 / 640000000000000000 : ℚ)) - (U := (377140992116281096537 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (865390603759317137 / 640000000000000000 : ℝ) ≤ - (377140992116281096537 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6741683809815883 / 10000000000000000 : ℝ)) (q := - (865390603759317137 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (865390603759317137 / 1280000000000000000 : ℚ)) + (r' := (865390603759317137 / 640000000000000000 : ℚ)) + (U := (-(489292983258718903463 / 1250000000000000000000 : ℚ))) + (U' := (377140992116281096537 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (6741683809815883 / 10000000000000000 : ℚ)) + (q := (865390603759317137 / 1280000000000000000 : ℚ)) + (U := (-(489292983258718903463 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_8 : Uω (aρ 8) (bρ 8) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4147,25 +3587,21 @@ lemma U_648_8 : have hlg : Real.log (826552445752811537 / 1280000000000000000 : ℝ) ≤ (-(4373519861695254145247 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (826552445752811537 / 1280000000000000000 : ℝ) = - (826552445752811537 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (826552445752811537 / 640000000000000000 : ℚ)) - (U := (2557951941304745854753 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (826552445752811537 / 640000000000000000 : ℝ) ≤ - (2557951941304745854753 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6418379242304233 / 10000000000000000 : ℝ)) (q := - (826552445752811537 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (826552445752811537 / 1280000000000000000 : ℚ)) + (r' := (826552445752811537 / 640000000000000000 : ℚ)) + (U := (-(4373519861695254145247 / 10000000000000000000000 : ℚ))) + (U' := (2557951941304745854753 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (6418379242304233 / 10000000000000000 : ℚ)) + (q := (826552445752811537 / 1280000000000000000 : ℚ)) + (U := (-(4373519861695254145247 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_9 : Uω (aρ 9) (bρ 9) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4173,25 +3609,21 @@ lemma U_648_9 : have hlg : Real.log (778376424791792401 / 1280000000000000000 : ℝ) ≤ (-(2487025564965771604759 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (778376424791792401 / 1280000000000000000 : ℝ) = - (778376424791792401 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (778376424791792401 / 640000000000000000 : ℚ)) - (U := (978710336534228395241 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (778376424791792401 / 640000000000000000 : ℝ) ≤ - (978710336534228395241 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6006594543148309 / 10000000000000000 : ℝ)) (q := - (778376424791792401 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (778376424791792401 / 1280000000000000000 : ℚ)) + (r' := (778376424791792401 / 640000000000000000 : ℚ)) + (U := (-(2487025564965771604759 / 5000000000000000000000 : ℚ))) + (U' := (978710336534228395241 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (6006594543148309 / 10000000000000000 : ℚ)) + (q := (778376424791792401 / 1280000000000000000 : ℚ)) + (U := (-(2487025564965771604759 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_10 : Uω (aρ 10) (bρ 10) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4199,26 +3631,21 @@ lemma U_648_10 : have hlg : Real.log (721078279937399953 / 1280000000000000000 : ℝ) ≤ (-(1434669134801156281813 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (721078279937399953 / 1280000000000000000 : ℝ) = - (721078279937399953 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (721078279937399953 / 640000000000000000 : ℚ)) - (U := (298198815948843718187 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (721078279937399953 / 640000000000000000 : ℝ) ≤ - (298198815948843718187 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5499870063293427 / 10000000000000000 : ℝ)) (q := - (721078279937399953 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (721078279937399953 / 1280000000000000000 : ℚ)) + (r' := (721078279937399953 / 640000000000000000 : ℚ)) + (U := (-(1434669134801156281813 / 2500000000000000000000 : ℚ))) + (U' := (298198815948843718187 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (5499870063293427 / 10000000000000000 : ℚ)) + (q := (721078279937399953 / 1280000000000000000 : ℚ)) + (U := (-(1434669134801156281813 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_11 : Uω (aρ 11) (bρ 11) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4226,26 +3653,21 @@ lemma U_648_11 : have hlg : Real.log (655636281741624337 / 1280000000000000000 : ℝ) ≤ (-(3345045850188347560643 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (655636281741624337 / 1280000000000000000 : ℝ) = - (655636281741624337 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (655636281741624337 / 640000000000000000 : ℚ)) - (U := (120690051311652439357 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (655636281741624337 / 640000000000000000 : ℝ) ≤ - (120690051311652439357 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4895815467689433 / 10000000000000000 : ℝ)) (q := - (655636281741624337 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (655636281741624337 / 1280000000000000000 : ℚ)) + (r' := (655636281741624337 / 640000000000000000 : ℚ)) + (U := (-(3345045850188347560643 / 5000000000000000000000 : ℚ))) + (U' := (120690051311652439357 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (4895815467689433 / 10000000000000000 : ℚ)) + (q := (655636281741624337 / 1280000000000000000 : ℚ)) + (U := (-(3345045850188347560643 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_12 : Uω (aρ 12) (bρ 12) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4253,26 +3675,21 @@ lemma U_648_12 : have hlg : Real.log (116753324662457309 / 256000000000000000 : ℝ) ≤ (-(245348147203090920197 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (116753324662457309 / 256000000000000000 : ℝ) = - (116753324662457309 / 64000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (116753324662457309 / 64000000000000000 : ℚ)) - (U := (187868840484409079803 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (116753324662457309 / 64000000000000000 : ℝ) ≤ - (187868840484409079803 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (419655215141603 / 1000000000000000 : ℝ)) (q := - (116753324662457309 / 256000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (116753324662457309 / 256000000000000000 : ℚ)) + (r' := (116753324662457309 / 64000000000000000 : ℚ)) + (U := (-(245348147203090920197 / 312500000000000000000 : ℚ))) + (U' := (187868840484409079803 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (419655215141603 / 1000000000000000 : ℚ)) + (q := (116753324662457309 / 256000000000000000 : ℚ)) + (U := (-(245348147203090920197 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_13 : Uω (aρ 13) (bρ 13) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4280,26 +3697,21 @@ lemma U_648_13 : have hlg : Real.log (507772016727975633 / 1280000000000000000 : ℝ) ≤ (-(9245827955184049930021 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (507772016727975633 / 1280000000000000000 : ℝ) = - (507772016727975633 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (507772016727975633 / 320000000000000000 : ℚ)) - (U := (4617115650815950069979 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (507772016727975633 / 320000000000000000 : ℝ) ≤ - (4617115650815950069979 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (852129541282793 / 2500000000000000 : ℝ)) (q := - (507772016727975633 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (507772016727975633 / 1280000000000000000 : ℚ)) + (r' := (507772016727975633 / 320000000000000000 : ℚ)) + (U := (-(9245827955184049930021 / 10000000000000000000000 : ℚ))) + (U' := (4617115650815950069979 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (852129541282793 / 2500000000000000 : ℚ)) + (q := (507772016727975633 / 1280000000000000000 : ℚ)) + (U := (-(9245827955184049930021 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_14 : Uω (aρ 14) (bρ 14) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4307,26 +3719,21 @@ lemma U_648_14 : have hlg : Real.log (86048894243380189 / 256000000000000000 : ℝ) ≤ (-(10902617715487759439317 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (86048894243380189 / 256000000000000000 : ℝ) = - (86048894243380189 / 64000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86048894243380189 / 64000000000000000 : ℚ)) - (U := (2960325890512240560683 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (86048894243380189 / 64000000000000000 : ℝ) ≤ - (2960325890512240560683 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (254107755156563 / 1000000000000000 : ℝ)) (q := - (86048894243380189 / 256000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86048894243380189 / 256000000000000000 : ℚ)) + (r' := (86048894243380189 / 64000000000000000 : ℚ)) + (U := (-(10902617715487759439317 / 10000000000000000000000 : ℚ))) + (U' := (2960325890512240560683 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (254107755156563 / 1000000000000000 : ℚ)) + (q := (86048894243380189 / 256000000000000000 : ℚ)) + (U := (-(10902617715487759439317 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_15 : Uω (aρ 15) (bρ 15) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4334,26 +3741,21 @@ lemma U_648_15 : have hlg : Real.log (353441888679318097 / 1280000000000000000 : ℝ) ≤ (-(12868962730306120814047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (353441888679318097 / 1280000000000000000 : ℝ) = - (353441888679318097 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (353441888679318097 / 320000000000000000 : ℚ)) - (U := (993980875693879185953 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (353441888679318097 / 320000000000000000 : ℝ) ≤ - (993980875693879185953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (800305238415449 / 5000000000000000 : ℝ)) (q := - (353441888679318097 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (353441888679318097 / 1280000000000000000 : ℚ)) + (r' := (353441888679318097 / 320000000000000000 : ℚ)) + (U := (-(12868962730306120814047 / 10000000000000000000000 : ℚ))) + (U' := (993980875693879185953 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (800305238415449 / 5000000000000000 : ℚ)) + (q := (353441888679318097 / 1280000000000000000 : ℚ)) + (U := (-(12868962730306120814047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648_16 : Uω (aρ 16) (bρ 16) (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4361,26 +3763,21 @@ lemma U_648_16 : have hlg : Real.log (274842454963529489 / 1280000000000000000 : ℝ) ≤ (-(3076834627347482851323 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (274842454963529489 / 1280000000000000000 : ℝ) = - (274842454963529489 / 160000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (274842454963529489 / 160000000000000000 : ℚ)) - (U := (1082048454452517148677 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (274842454963529489 / 160000000000000000 : ℝ) ≤ - (1082048454452517148677 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (524865976531701 / 10000000000000000 : ℝ)) (q := - (274842454963529489 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (274842454963529489 / 1280000000000000000 : ℚ)) + (r' := (274842454963529489 / 160000000000000000 : ℚ)) + (U := (-(3076834627347482851323 / 2000000000000000000000 : ℚ))) + (U' := (1082048454452517148677 / 2000000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (768316678878049 / 1024000000000000 : ℚ)) + (s := (524865976531701 / 10000000000000000 : ℚ)) + (q := (274842454963529489 / 1280000000000000000 : ℚ)) + (U := (-(3076834627347482851323 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_648 : Uρ (768316678878049 / 1024000000000000 : ℝ) ≤ @@ -4485,25 +3882,21 @@ lemma U_649_1 : have hlg : Real.log (238426032679206651 / 320000000000000000 : ℝ) ≤ (-(1471309344121746862427 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (238426032679206651 / 320000000000000000 : ℝ) = - (238426032679206651 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (238426032679206651 / 160000000000000000 : ℚ)) - (U := (1994426557378253137573 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (238426032679206651 / 160000000000000000 : ℝ) ≤ - (1994426557378253137573 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3725395911603743 / 5000000000000000 : ℝ)) (q := - (238426032679206651 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (238426032679206651 / 320000000000000000 : ℚ)) + (r' := (238426032679206651 / 160000000000000000 : ℚ)) + (U := (-(1471309344121746862427 / 5000000000000000000000 : ℚ))) + (U' := (1994426557378253137573 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (3725395911603743 / 5000000000000000 : ℚ)) + (q := (238426032679206651 / 320000000000000000 : ℚ)) + (U := (-(1471309344121746862427 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_2 : Uω (aρ 2) (bρ 2) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4511,25 +3904,21 @@ lemma U_649_2 : have hlg : Real.log (237661547454349131 / 320000000000000000 : ℝ) ≤ (-(2974734034823848649063 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (237661547454349131 / 320000000000000000 : ℝ) = - (237661547454349131 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (237661547454349131 / 160000000000000000 : ℚ)) - (U := (3956737768176151350937 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (237661547454349131 / 160000000000000000 : ℝ) ≤ - (3956737768176151350937 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7426780509163891 / 10000000000000000 : ℝ)) (q := - (237661547454349131 / 320000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (237661547454349131 / 320000000000000000 : ℚ)) + (r' := (237661547454349131 / 160000000000000000 : ℚ)) + (U := (-(2974734034823848649063 / 10000000000000000000000 : ℚ))) + (U' := (3956737768176151350937 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (7426780509163891 / 10000000000000000 : ℚ)) + (q := (237661547454349131 / 320000000000000000 : ℚ)) + (U := (-(2974734034823848649063 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_3 : Uω (aρ 3) (bρ 3) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4537,25 +3926,21 @@ lemma U_649_3 : have hlg : Real.log (47226680441397951 / 64000000000000000 : ℝ) ≤ (-(3039240866205603229829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47226680441397951 / 64000000000000000 : ℝ) = - (47226680441397951 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47226680441397951 / 32000000000000000 : ℚ)) - (U := (3892230936794396770171 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47226680441397951 / 32000000000000000 : ℝ) ≤ - (3892230936794396770171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (737866753755393 / 1000000000000000 : ℝ)) (q := - (47226680441397951 / 64000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47226680441397951 / 64000000000000000 : ℚ)) + (r' := (47226680441397951 / 32000000000000000 : ℚ)) + (U := (-(3039240866205603229829 / 10000000000000000000000 : ℚ))) + (U' := (3892230936794396770171 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (737866753755393 / 1000000000000000 : ℚ)) + (q := (47226680441397951 / 64000000000000000 : ℚ)) + (U := (-(3039240866205603229829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_4 : Uω (aρ 4) (bρ 4) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4563,25 +3948,21 @@ lemma U_649_4 : have hlg : Real.log (233597911616489947 / 320000000000000000 : ℝ) ≤ (-(1573598423088097864679 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (233597911616489947 / 320000000000000000 : ℝ) = - (233597911616489947 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (233597911616489947 / 160000000000000000 : ℚ)) - (U := (1892137478411902135321 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (233597911616489947 / 160000000000000000 : ℝ) ≤ - (1892137478411902135321 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1824623389178173 / 2500000000000000 : ℝ)) (q := - (233597911616489947 / 320000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (233597911616489947 / 320000000000000000 : ℚ)) + (r' := (233597911616489947 / 160000000000000000 : ℚ)) + (U := (-(1573598423088097864679 / 5000000000000000000000 : ℚ))) + (U' := (1892137478411902135321 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (1824623389178173 / 2500000000000000 : ℚ)) + (q := (233597911616489947 / 320000000000000000 : ℚ)) + (U := (-(1573598423088097864679 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_5 : Uω (aρ 5) (bρ 5) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4589,25 +3970,21 @@ lemma U_649_5 : have hlg : Real.log (229743265070993531 / 320000000000000000 : ℝ) ≤ (-(82839637222737004547 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (229743265070993531 / 320000000000000000 : ℝ) = - (229743265070993531 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (229743265070993531 / 160000000000000000 : ℚ)) - (U := (90447157852262995453 / 250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (229743265070993531 / 160000000000000000 : ℝ) ≤ - (90447157852262995453 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3587884033477083 / 5000000000000000 : ℝ)) (q := - (229743265070993531 / 320000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (229743265070993531 / 320000000000000000 : ℚ)) + (r' := (229743265070993531 / 160000000000000000 : ℚ)) + (U := (-(82839637222737004547 / 250000000000000000000 : ℚ))) + (U' := (90447157852262995453 / 250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (3587884033477083 / 5000000000000000 : ℚ)) + (q := (229743265070993531 / 320000000000000000 : ℚ)) + (U := (-(82839637222737004547 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_6 : Uω (aρ 6) (bρ 6) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4615,25 +3992,21 @@ lemma U_649_6 : have hlg : Real.log (224230039759304091 / 320000000000000000 : ℝ) ≤ (-(3556485074335744005427 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (224230039759304091 / 320000000000000000 : ℝ) = - (224230039759304091 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (224230039759304091 / 160000000000000000 : ℚ)) - (U := (3374986728664255994573 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (224230039759304091 / 160000000000000000 : ℝ) ≤ - (3374986728664255994573 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (874803982514197 / 1250000000000000 : ℝ)) (q := - (224230039759304091 / 320000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (224230039759304091 / 320000000000000000 : ℚ)) + (r' := (224230039759304091 / 160000000000000000 : ℚ)) + (U := (-(3556485074335744005427 / 10000000000000000000000 : ℚ))) + (U' := (3374986728664255994573 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (874803982514197 / 1250000000000000 : ℚ)) + (q := (224230039759304091 / 320000000000000000 : ℚ)) + (U := (-(3556485074335744005427 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_7 : Uω (aρ 7) (bρ 7) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4641,25 +4014,21 @@ lemma U_649_7 : have hlg : Real.log (43348087817733087 / 64000000000000000 : ℝ) ≤ (-(3896204911636402043661 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43348087817733087 / 64000000000000000 : ℝ) = - (43348087817733087 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43348087817733087 / 32000000000000000 : ℚ)) - (U := (3035266891363597956339 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (43348087817733087 / 32000000000000000 : ℝ) ≤ - (3035266891363597956339 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (337699659947933 / 500000000000000 : ℝ)) (q := - (43348087817733087 / 64000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43348087817733087 / 64000000000000000 : ℚ)) + (r' := (43348087817733087 / 32000000000000000 : ℚ)) + (U := (-(3896204911636402043661 / 10000000000000000000000 : ℚ))) + (U' := (3035266891363597956339 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (337699659947933 / 500000000000000 : ℚ)) + (q := (43348087817733087 / 64000000000000000 : ℚ)) + (U := (-(3896204911636402043661 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_8 : Uω (aρ 8) (bρ 8) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4667,25 +4036,21 @@ lemma U_649_8 : have hlg : Real.log (207032166426422683 / 320000000000000000 : ℝ) ≤ (-(4354468209763952836931 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (207032166426422683 / 320000000000000000 : ℝ) = - (207032166426422683 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (207032166426422683 / 160000000000000000 : ℚ)) - (U := (2577003593236047163069 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (207032166426422683 / 160000000000000000 : ℝ) ≤ - (2577003593236047163069 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (803845976113561 / 1250000000000000 : ℝ)) (q := - (207032166426422683 / 320000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (207032166426422683 / 320000000000000000 : ℚ)) + (r' := (207032166426422683 / 160000000000000000 : ℚ)) + (U := (-(4354468209763952836931 / 10000000000000000000000 : ℚ))) + (U' := (2577003593236047163069 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (803845976113561 / 1250000000000000 : ℚ)) + (q := (207032166426422683 / 320000000000000000 : ℚ)) + (U := (-(4354468209763952836931 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_9 : Uω (aρ 9) (bρ 9) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4693,25 +4058,21 @@ lemma U_649_9 : have hlg : Real.log (194990628141794779 / 320000000000000000 : ℝ) ≤ (-(990738997872693485211 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (194990628141794779 / 320000000000000000 : ℝ) = - (194990628141794779 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (194990628141794779 / 160000000000000000 : ℚ)) - (U := (395555362727306514789 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (194990628141794779 / 160000000000000000 : ℝ) ≤ - (395555362727306514789 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1504784323619811 / 2500000000000000 : ℝ)) (q := - (194990628141794779 / 320000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (194990628141794779 / 320000000000000000 : ℚ)) + (r' := (194990628141794779 / 160000000000000000 : ℚ)) + (U := (-(990738997872693485211 / 2000000000000000000000 : ℚ))) + (U' := (395555362727306514789 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (1504784323619811 / 2500000000000000 : ℚ)) + (q := (194990628141794779 / 320000000000000000 : ℚ)) + (U := (-(990738997872693485211 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_10 : Uω (aρ 10) (bρ 10) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4719,26 +4080,21 @@ lemma U_649_10 : have hlg : Real.log (180670735310228651 / 320000000000000000 : ℝ) ≤ (-(142911190712137077017 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (180670735310228651 / 320000000000000000 : ℝ) = - (180670735310228651 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (180670735310228651 / 160000000000000000 : ℚ)) - (U := (30375604362862922983 / 250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (180670735310228651 / 160000000000000000 : ℝ) ≤ - (30375604362862922983 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5512703026001361 / 10000000000000000 : ℝ)) (q := - (180670735310228651 / 320000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (180670735310228651 / 320000000000000000 : ℚ)) + (r' := (180670735310228651 / 160000000000000000 : ℚ)) + (U := (-(142911190712137077017 / 250000000000000000000 : ℚ))) + (U' := (30375604362862922983 / 250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (5512703026001361 / 10000000000000000 : ℚ)) + (q := (180670735310228651 / 320000000000000000 : ℚ)) + (U := (-(142911190712137077017 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_11 : Uω (aρ 11) (bρ 11) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4746,26 +4102,21 @@ lemma U_649_11 : have hlg : Real.log (164318806974575771 / 320000000000000000 : ℝ) ≤ (-(1666281274396531617289 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (164318806974575771 / 320000000000000000 : ℝ) = - (164318806974575771 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (164318806974575771 / 160000000000000000 : ℚ)) - (U := (66586676353468382711 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (164318806974575771 / 160000000000000000 : ℝ) ≤ - (66586676353468382711 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (613648016403507 / 1250000000000000 : ℝ)) (q := - (164318806974575771 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (164318806974575771 / 320000000000000000 : ℚ)) + (r' := (164318806974575771 / 160000000000000000 : ℚ)) + (U := (-(1666281274396531617289 / 2500000000000000000000 : ℚ))) + (U' := (66586676353468382711 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (613648016403507 / 1250000000000000 : ℚ)) + (q := (164318806974575771 / 320000000000000000 : ℚ)) + (U := (-(1666281274396531617289 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_12 : Uω (aρ 12) (bρ 12) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4773,26 +4124,21 @@ lemma U_649_12 : have hlg : Real.log (29273441815204607 / 64000000000000000 : ℝ) ≤ (-(1955506001388691126887 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29273441815204607 / 64000000000000000 : ℝ) = - (29273441815204607 / 16000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29273441815204607 / 16000000000000000 : ℚ)) - (U := (1510229900111308873113 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (29273441815204607 / 16000000000000000 : ℝ) ≤ - (1510229900111308873113 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (421090935925351 / 1000000000000000 : ℝ)) (q := - (29273441815204607 / 64000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29273441815204607 / 64000000000000000 : ℚ)) + (r' := (29273441815204607 / 16000000000000000 : ℚ)) + (U := (-(1955506001388691126887 / 2500000000000000000000 : ℚ))) + (U' := (1510229900111308873113 / 2500000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (421090935925351 / 1000000000000000 : ℚ)) + (q := (29273441815204607 / 64000000000000000 : ℚ)) + (U := (-(1955506001388691126887 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_13 : Uω (aρ 13) (bρ 13) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4800,26 +4146,21 @@ lemma U_649_13 : have hlg : Real.log (127398585171176907 / 320000000000000000 : ℝ) ≤ (-(9210003576042587965751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (127398585171176907 / 320000000000000000 : ℝ) = - (127398585171176907 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (127398585171176907 / 80000000000000000 : ℚ)) - (U := (4652940029957412034249 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (127398585171176907 / 80000000000000000 : ℝ) ≤ - (4652940029957412034249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3424752106795627 / 10000000000000000 : ℝ)) (q := - (127398585171176907 / 320000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (127398585171176907 / 320000000000000000 : ℚ)) + (r' := (127398585171176907 / 80000000000000000 : ℚ)) + (U := (-(9210003576042587965751 / 10000000000000000000000 : ℚ))) + (U' := (4652940029957412034249 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (3424752106795627 / 10000000000000000 : ℚ)) + (q := (127398585171176907 / 320000000000000000 : ℚ)) + (U := (-(9210003576042587965751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_14 : Uω (aρ 14) (bρ 14) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4827,26 +4168,21 @@ lemma U_649_14 : have hlg : Real.log (108078419329204123 / 320000000000000000 : ℝ) ≤ (-(2170927853472496869607 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (108078419329204123 / 320000000000000000 : ℝ) = - (108078419329204123 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (108078419329204123 / 80000000000000000 : ℚ)) - (U := (601660867727503130393 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (108078419329204123 / 80000000000000000 : ℝ) ≤ - (601660867727503130393 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (160073064169833 / 625000000000000 : ℝ)) (q := - (108078419329204123 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (108078419329204123 / 320000000000000000 : ℚ)) + (r' := (108078419329204123 / 80000000000000000 : ℚ)) + (U := (-(2170927853472496869607 / 2000000000000000000000 : ℚ))) + (U' := (601660867727503130393 / 2000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (160073064169833 / 625000000000000 : ℚ)) + (q := (108078419329204123 / 320000000000000000 : ℚ)) + (U := (-(2170927853472496869607 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_15 : Uω (aρ 15) (bρ 15) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4854,26 +4190,21 @@ lemma U_649_15 : have hlg : Real.log (17806497336238479 / 64000000000000000 : ℝ) ≤ (-(12793196732551274176083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17806497336238479 / 64000000000000000 : ℝ) = - (17806497336238479 / 16000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17806497336238479 / 16000000000000000 : ℚ)) - (U := (1069746873448725823917 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (17806497336238479 / 16000000000000000 : ℝ) ≤ - (1069746873448725823917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (326074302726319 / 2000000000000000 : ℝ)) (q := - (17806497336238479 / 64000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17806497336238479 / 64000000000000000 : ℚ)) + (r' := (17806497336238479 / 16000000000000000 : ℚ)) + (U := (-(12793196732551274176083 / 10000000000000000000000 : ℚ))) + (U' := (1069746873448725823917 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (326074302726319 / 2000000000000000 : ℚ)) + (q := (17806497336238479 / 64000000000000000 : ℚ)) + (U := (-(12793196732551274176083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649_16 : Uω (aρ 16) (bρ 16) (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4881,26 +4212,21 @@ lemma U_649_16 : have hlg : Real.log (70213511395988331 / 320000000000000000 : ℝ) ≤ (-(758390116236913319073 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (70213511395988331 / 320000000000000000 : ℝ) = - (70213511395988331 / 40000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70213511395988331 / 40000000000000000 : ℚ)) - (U := (281330654213086680927 / 500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70213511395988331 / 40000000000000000 : ℝ) ≤ - (281330654213086680927 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (606557209816341 / 10000000000000000 : ℝ)) (q := - (70213511395988331 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70213511395988331 / 320000000000000000 : ℚ)) + (r' := (70213511395988331 / 40000000000000000 : ℚ)) + (U := (-(758390116236913319073 / 500000000000000000000 : ℚ))) + (U' := (281330654213086680927 / 500000000000000000000 : ℚ)) + 3 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (38478502079119 / 51200000000000 : ℚ)) + (s := (606557209816341 / 10000000000000000 : ℚ)) + (q := (70213511395988331 / 320000000000000000 : ℚ)) + (U := (-(758390116236913319073 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_649 : Uρ (38478502079119 / 51200000000000 : ℝ) ≤ @@ -4991,25 +4317,21 @@ lemma U_650_1 : have hlg : Real.log (955270838652273607 / 1280000000000000000 : ℝ) ≤ (-(1463102278485251628801 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (955270838652273607 / 1280000000000000000 : ℝ) = - (955270838652273607 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (955270838652273607 / 640000000000000000 : ℚ)) - (U := (2002633623014748371199 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (955270838652273607 / 640000000000000000 : ℝ) ≤ - (2002633623014748371199 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7463031764539363 / 10000000000000000 : ℝ)) (q := - (955270838652273607 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (955270838652273607 / 1280000000000000000 : ℚ)) + (r' := (955270838652273607 / 640000000000000000 : ℚ)) + (U := (-(1463102278485251628801 / 5000000000000000000000 : ℚ))) + (U' := (2002633623014748371199 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (7463031764539363 / 10000000000000000 : ℚ)) + (q := (955270838652273607 / 1280000000000000000 : ℚ)) + (U := (-(1463102278485251628801 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_2 : Uω (aρ 2) (bρ 2) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5017,25 +4339,21 @@ lemma U_650_2 : have hlg : Real.log (952212923282640711 / 1280000000000000000 : ℝ) ≤ (-(1479133439799703354753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (952212923282640711 / 1280000000000000000 : ℝ) = - (952212923282640711 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (952212923282640711 / 640000000000000000 : ℚ)) - (U := (1986602461700296645247 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (952212923282640711 / 640000000000000000 : ℝ) ≤ - (1986602461700296645247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7439020849398849 / 10000000000000000 : ℝ)) (q := - (952212923282640711 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (952212923282640711 / 1280000000000000000 : ℚ)) + (r' := (952212923282640711 / 640000000000000000 : ℚ)) + (U := (-(1479133439799703354753 / 5000000000000000000000 : ℚ))) + (U' := (1986602461700296645247 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (7439020849398849 / 10000000000000000 : ℚ)) + (q := (952212923282640711 / 1280000000000000000 : ℚ)) + (U := (-(1479133439799703354753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_3 : Uω (aρ 3) (bρ 3) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5043,25 +4361,21 @@ lemma U_650_3 : have hlg : Real.log (946100418468559111 / 1280000000000000000 : ℝ) ≤ (-(1511333213172008917413 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (946100418468559111 / 1280000000000000000 : ℝ) = - (946100418468559111 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (946100418468559111 / 640000000000000000 : ℚ)) - (U := (1954402688327991082587 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (946100418468559111 / 640000000000000000 : ℝ) ≤ - (1954402688327991082587 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (923863633503603 / 1250000000000000 : ℝ)) (q := - (946100418468559111 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (946100418468559111 / 1280000000000000000 : ℚ)) + (r' := (946100418468559111 / 640000000000000000 : ℚ)) + (U := (-(1511333213172008917413 / 5000000000000000000000 : ℚ))) + (U' := (1954402688327991082587 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (923863633503603 / 1250000000000000 : ℚ)) + (q := (946100418468559111 / 1280000000000000000 : ℚ)) + (U := (-(1511333213172008917413 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_4 : Uω (aρ 4) (bρ 4) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5069,25 +4383,21 @@ lemma U_650_4 : have hlg : Real.log (187191731738805659 / 256000000000000000 : ℝ) ≤ (-(3130440492134986453193 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (187191731738805659 / 256000000000000000 : ℝ) = - (187191731738805659 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (187191731738805659 / 128000000000000000 : ℚ)) - (U := (3801031310865013546807 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (187191731738805659 / 128000000000000000 : ℝ) ≤ - (3801031310865013546807 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (365536912630839 / 500000000000000 : ℝ)) (q := - (187191731738805659 / 256000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (187191731738805659 / 256000000000000000 : ℚ)) + (r' := (187191731738805659 / 128000000000000000 : ℚ)) + (U := (-(3130440492134986453193 / 10000000000000000000000 : ℚ))) + (U' := (3801031310865013546807 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (365536912630839 / 500000000000000 : ℚ)) + (q := (187191731738805659 / 256000000000000000 : ℚ)) + (U := (-(3130440492134986453193 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_5 : Uω (aρ 5) (bρ 5) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5095,25 +4405,21 @@ lemma U_650_5 : have hlg : Real.log (920540572072686919 / 1280000000000000000 : ℝ) ≤ (-(1648271404136584240029 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (920540572072686919 / 1280000000000000000 : ℝ) = - (920540572072686919 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (920540572072686919 / 640000000000000000 : ℚ)) - (U := (1817464497363415759971 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (920540572072686919 / 640000000000000000 : ℝ) ≤ - (1817464497363415759971 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7188020568493321 / 10000000000000000 : ℝ)) (q := - (920540572072686919 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (920540572072686919 / 1280000000000000000 : ℚ)) + (r' := (920540572072686919 / 640000000000000000 : ℚ)) + (U := (-(1648271404136584240029 / 5000000000000000000000 : ℚ))) + (U' := (1817464497363415759971 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (7188020568493321 / 10000000000000000 : ℚ)) + (q := (920540572072686919 / 1280000000000000000 : ℚ)) + (U := (-(1648271404136584240029 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_6 : Uω (aρ 6) (bρ 6) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5121,25 +4427,21 @@ lemma U_650_6 : have hlg : Real.log (179697763869909851 / 256000000000000000 : ℝ) ≤ (-(1769505470959731984053 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (179697763869909851 / 256000000000000000 : ℝ) = - (179697763869909851 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (179697763869909851 / 128000000000000000 : ℚ)) - (U := (1696230430540268015947 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (179697763869909851 / 128000000000000000 : ℝ) ≤ - (1696230430540268015947 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1402140461466859 / 2000000000000000 : ℝ)) (q := - (179697763869909851 / 256000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (179697763869909851 / 256000000000000000 : ℚ)) + (r' := (179697763869909851 / 128000000000000000 : ℚ)) + (U := (-(1769505470959731984053 / 5000000000000000000000 : ℚ))) + (U' := (1696230430540268015947 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (1402140461466859 / 2000000000000000 : ℚ)) + (q := (179697763869909851 / 256000000000000000 : ℚ)) + (U := (-(1769505470959731984053 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_7 : Uω (aρ 7) (bρ 7) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5147,25 +4449,21 @@ lemma U_650_7 : have hlg : Real.log (173706578561504411 / 256000000000000000 : ℝ) ≤ (-(387809898566500223647 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (173706578561504411 / 256000000000000000 : ℝ) = - (173706578561504411 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (173706578561504411 / 128000000000000000 : ℚ)) - (U := (305337281733499776353 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (173706578561504411 / 128000000000000000 : ℝ) ≤ - (305337281733499776353 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (84578779198439 / 125000000000000 : ℝ)) (q := - (173706578561504411 / 256000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (173706578561504411 / 256000000000000000 : ℚ)) + (r' := (173706578561504411 / 128000000000000000 : ℚ)) + (U := (-(387809898566500223647 / 1000000000000000000000 : ℚ))) + (U' := (305337281733499776353 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (84578779198439 / 125000000000000 : ℚ)) + (q := (173706578561504411 / 256000000000000000 : ℚ)) + (U := (-(387809898566500223647 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_8 : Uω (aρ 8) (bρ 8) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5173,25 +4471,21 @@ lemma U_650_8 : have hlg : Real.log (829704849282250631 / 1280000000000000000 : ℝ) ≤ (-(867090644758616515783 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (829704849282250631 / 1280000000000000000 : ℝ) = - (829704849282250631 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (829704849282250631 / 640000000000000000 : ℚ)) - (U := (519203715841383484217 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (829704849282250631 / 640000000000000000 : ℝ) ≤ - (519203715841383484217 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3221577903566377 / 5000000000000000 : ℝ)) (q := - (829704849282250631 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (829704849282250631 / 1280000000000000000 : ℚ)) + (r' := (829704849282250631 / 640000000000000000 : ℚ)) + (U := (-(867090644758616515783 / 2000000000000000000000 : ℚ))) + (U' := (519203715841383484217 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (3221577903566377 / 5000000000000000 : ℚ)) + (q := (829704849282250631 / 1280000000000000000 : ℚ)) + (U := (-(867090644758616515783 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_9 : Uω (aρ 9) (bρ 9) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5199,25 +4493,21 @@ lemma U_650_9 : have hlg : Real.log (781548520697065799 / 1280000000000000000 : ℝ) ≤ (-(4933381220949565653991 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (781548520697065799 / 1280000000000000000 : ℝ) = - (781548520697065799 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (781548520697065799 / 640000000000000000 : ℚ)) - (U := (1998090582050434346009 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (781548520697065799 / 640000000000000000 : ℝ) ≤ - (1998090582050434346009 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6031678801349241 / 10000000000000000 : ℝ)) (q := - (781548520697065799 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (781548520697065799 / 1280000000000000000 : ℚ)) + (r' := (781548520697065799 / 640000000000000000 : ℚ)) + (U := (-(4933381220949565653991 / 10000000000000000000000 : ℚ))) + (U' := (1998090582050434346009 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (6031678801349241 / 10000000000000000 : ℚ)) + (q := (781548520697065799 / 1280000000000000000 : ℚ)) + (U := (-(4933381220949565653991 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_10 : Uω (aρ 10) (bρ 10) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5225,26 +4515,21 @@ lemma U_650_10 : have hlg : Real.log (724287430305411079 / 1280000000000000000 : ℝ) ≤ (-(2847135199343223354549 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (724287430305411079 / 1280000000000000000 : ℝ) = - (724287430305411079 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (724287430305411079 / 640000000000000000 : ℚ)) - (U := (618600702156776645451 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (724287430305411079 / 640000000000000000 : ℝ) ≤ - (618600702156776645451 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1381383324368659 / 2500000000000000 : ℝ)) (q := - (724287430305411079 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (724287430305411079 / 1280000000000000000 : ℚ)) + (r' := (724287430305411079 / 640000000000000000 : ℚ)) + (U := (-(2847135199343223354549 / 5000000000000000000000 : ℚ))) + (U' := (618600702156776645451 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (1381383324368659 / 2500000000000000 : ℚ)) + (q := (724287430305411079 / 1280000000000000000 : ℚ)) + (U := (-(2847135199343223354549 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_11 : Uω (aρ 11) (bρ 11) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5252,26 +4537,21 @@ lemma U_650_11 : have hlg : Real.log (131782759645416603 / 256000000000000000 : ℝ) ≤ (-(1328045275292720239523 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (131782759645416603 / 256000000000000000 : ℝ) = - (131782759645416603 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (131782759645416603 / 128000000000000000 : ℚ)) - (U := (58249085307279760477 / 2000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (131782759645416603 / 128000000000000000 : ℝ) ≤ - (58249085307279760477 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (61531836530697 / 125000000000000 : ℝ)) (q := - (131782759645416603 / 256000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (131782759645416603 / 256000000000000000 : ℚ)) + (r' := (131782759645416603 / 128000000000000000 : ℚ)) + (U := (-(1328045275292720239523 / 2000000000000000000000 : ℚ))) + (U' := (58249085307279760477 / 2000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (61531836530697 / 125000000000000 : ℚ)) + (q := (131782759645416603 / 256000000000000000 : ℚ)) + (U := (-(1328045275292720239523 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_12 : Uω (aρ 12) (bρ 12) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5279,26 +4559,21 @@ lemma U_650_12 : have hlg : Real.log (587170196292819527 / 1280000000000000000 : ℝ) ≤ (-(7793006360136964195467 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (587170196292819527 / 1280000000000000000 : ℝ) = - (587170196292819527 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (587170196292819527 / 320000000000000000 : ℚ)) - (U := (6069937245863035804533 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (587170196292819527 / 320000000000000000 : ℝ) ≤ - (6069937245863035804533 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4225253238917893 / 10000000000000000 : ℝ)) (q := - (587170196292819527 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (587170196292819527 / 1280000000000000000 : ℚ)) + (r' := (587170196292819527 / 320000000000000000 : ℚ)) + (U := (-(7793006360136964195467 / 10000000000000000000000 : ℚ))) + (U' := (6069937245863035804533 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (4225253238917893 / 10000000000000000 : ℚ)) + (q := (587170196292819527 / 1280000000000000000 : ℚ)) + (U := (-(7793006360136964195467 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_13 : Uω (aρ 13) (bρ 13) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5306,26 +4581,21 @@ lemma U_650_13 : have hlg : Real.log (511414549396843719 / 1280000000000000000 : ℝ) ≤ (-(9174348438106759670099 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (511414549396843719 / 1280000000000000000 : ℝ) = - (511414549396843719 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (511414549396843719 / 320000000000000000 : ℚ)) - (U := (4688595167893240329901 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (511414549396843719 / 320000000000000000 : ℝ) ≤ - (4688595167893240329901 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3440952997763271 / 10000000000000000 : ℝ)) (q := - (511414549396843719 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (511414549396843719 / 1280000000000000000 : ℚ)) + (r' := (511414549396843719 / 320000000000000000 : ℚ)) + (U := (-(9174348438106759670099 / 10000000000000000000000 : ℚ))) + (U' := (4688595167893240329901 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (3440952997763271 / 10000000000000000 : ℚ)) + (q := (511414549396843719 / 1280000000000000000 : ℚ)) + (U := (-(9174348438106759670099 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_14 : Uω (aρ 14) (bρ 14) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5333,26 +4603,21 @@ lemma U_650_14 : have hlg : Real.log (86875317848878747 / 256000000000000000 : ℝ) ≤ (-(10807034813892791887537 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (86875317848878747 / 256000000000000000 : ℝ) = - (86875317848878747 / 64000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86875317848878747 / 64000000000000000 : ℚ)) - (U := (3055908792107208112463 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (86875317848878747 / 64000000000000000 : ℝ) ≤ - (3055908792107208112463 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8066131735707 / 31250000000000 : ℝ)) (q := - (86875317848878747 / 256000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86875317848878747 / 256000000000000000 : ℚ)) + (r' := (86875317848878747 / 64000000000000000 : ℚ)) + (U := (-(10807034813892791887537 / 10000000000000000000000 : ℚ))) + (U' := (3055908792107208112463 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (8066131735707 / 31250000000000 : ℚ)) + (q := (86875317848878747 / 256000000000000000 : ℚ)) + (U := (-(10807034813892791887537 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_15 : Uω (aρ 15) (bρ 15) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5360,26 +4625,21 @@ lemma U_650_15 : have hlg : Real.log (358789631010213383 / 1280000000000000000 : ℝ) ≤ (-(12718791257063904718547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (358789631010213383 / 1280000000000000000 : ℝ) = - (358789631010213383 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (358789631010213383 / 320000000000000000 : ℚ)) - (U := (1144152348936095281453 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (358789631010213383 / 320000000000000000 : ℝ) ≤ - (1144152348936095281453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (414922302608043 / 2500000000000000 : ℝ)) (q := - (358789631010213383 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (358789631010213383 / 1280000000000000000 : ℚ)) + (r' := (358789631010213383 / 320000000000000000 : ℚ)) + (U := (-(12718791257063904718547 / 10000000000000000000000 : ℚ))) + (U' := (1144152348936095281453 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (414922302608043 / 2500000000000000 : ℚ)) + (q := (358789631010213383 / 1280000000000000000 : ℚ)) + (U := (-(12718791257063904718547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650_16 : Uω (aρ 16) (bρ 16) (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5387,26 +4647,21 @@ lemma U_650_16 : have hlg : Real.log (57250953781302043 / 256000000000000000 : ℝ) ≤ (-(936083213417966146663 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (57250953781302043 / 256000000000000000 : ℝ) = - (57250953781302043 / 32000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57250953781302043 / 32000000000000000 : ℚ)) - (U := (363567749644533853337 / 625000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (57250953781302043 / 32000000000000000 : ℝ) ≤ - (363567749644533853337 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (67870364157181 / 1000000000000000 : ℝ)) (q := - (57250953781302043 / 256000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57250953781302043 / 256000000000000000 : ℚ)) + (r' := (57250953781302043 / 32000000000000000 : ℚ)) + (U := (-(936083213417966146663 / 625000000000000000000 : ℚ))) + (U' := (363567749644533853337 / 625000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (770823404286711 / 1024000000000000 : ℚ)) + (s := (67870364157181 / 1000000000000000 : ℚ)) + (q := (57250953781302043 / 256000000000000000 : ℚ)) + (U := (-(936083213417966146663 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_650 : Uρ (770823404286711 / 1024000000000000 : ℝ) ≤ @@ -5511,25 +4766,21 @@ lemma U_651_1 : have hlg : Real.log (478418773286401937 / 640000000000000000 : ℝ) ≤ (-(1454908662039441301187 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (478418773286401937 / 640000000000000000 : ℝ) = - (478418773286401937 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (478418773286401937 / 320000000000000000 : ℚ)) - (U := (2010827239460558698813 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (478418773286401937 / 320000000000000000 : ℝ) ≤ - (2010827239460558698813 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3737635852819083 / 5000000000000000 : ℝ)) (q := - (478418773286401937 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (478418773286401937 / 640000000000000000 : ℚ)) + (r' := (478418773286401937 / 320000000000000000 : ℚ)) + (U := (-(1454908662039441301187 / 5000000000000000000000 : ℚ))) + (U' := (2010827239460558698813 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (3737635852819083 / 5000000000000000 : ℚ)) + (q := (478418773286401937 / 640000000000000000 : ℚ)) + (U := (-(1454908662039441301187 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_2 : Uω (aρ 2) (bρ 2) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5537,25 +4788,21 @@ lemma U_651_2 : have hlg : Real.log (476889828324522417 / 640000000000000000 : ℝ) ≤ (-(2941826797557366372611 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (476889828324522417 / 640000000000000000 : ℝ) = - (476889828324522417 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (476889828324522417 / 320000000000000000 : ℚ)) - (U := (3989645005442633627389 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (476889828324522417 / 320000000000000000 : ℝ) ≤ - (3989645005442633627389 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7451261188089431 / 10000000000000000 : ℝ)) (q := - (476889828324522417 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (476889828324522417 / 640000000000000000 : ℚ)) + (r' := (476889828324522417 / 320000000000000000 : ℚ)) + (U := (-(2941826797557366372611 / 10000000000000000000000 : ℚ))) + (U' := (3989645005442633627389 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (7451261188089431 / 10000000000000000 : ℚ)) + (q := (476889828324522417 / 640000000000000000 : ℚ)) + (U := (-(2941826797557366372611 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_3 : Uω (aρ 3) (bρ 3) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5563,25 +4810,21 @@ lemma U_651_3 : have hlg : Real.log (473833613878884241 / 640000000000000000 : ℝ) ≤ (-(150305970797283732639 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (473833613878884241 / 640000000000000000 : ℝ) = - (473833613878884241 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (473833613878884241 / 320000000000000000 : ℚ)) - (U := (196267619352716267361 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (473833613878884241 / 320000000000000000 : ℝ) ≤ - (196267619352716267361 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3701575296506619 / 5000000000000000 : ℝ)) (q := - (473833613878884241 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (473833613878884241 / 640000000000000000 : ℚ)) + (r' := (473833613878884241 / 320000000000000000 : ℚ)) + (U := (-(150305970797283732639 / 500000000000000000000 : ℚ))) + (U' := (196267619352716267361 / 500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (3701575296506619 / 5000000000000000 : ℚ)) + (q := (473833613878884241 / 640000000000000000 : ℚ)) + (U := (-(150305970797283732639 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_4 : Uω (aρ 4) (bρ 4) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5589,25 +4832,21 @@ lemma U_651_4 : have hlg : Real.log (468762834944728689 / 640000000000000000 : ℝ) ≤ (-(3113712179685890930111 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (468762834944728689 / 640000000000000000 : ℝ) = - (468762834944728689 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (468762834944728689 / 320000000000000000 : ℚ)) - (U := (3817759623314109069889 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (468762834944728689 / 320000000000000000 : ℝ) ≤ - (3817759623314109069889 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7322982932385877 / 10000000000000000 : ℝ)) (q := - (468762834944728689 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (468762834944728689 / 640000000000000000 : ℚ)) + (r' := (468762834944728689 / 320000000000000000 : ℚ)) + (U := (-(3113712179685890930111 / 10000000000000000000000 : ℚ))) + (U' := (3817759623314109069889 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (7322982932385877 / 10000000000000000 : ℚ)) + (q := (468762834944728689 / 640000000000000000 : ℚ)) + (U := (-(3113712179685890930111 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_5 : Uω (aρ 5) (bρ 5) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5615,25 +4854,21 @@ lemma U_651_5 : have hlg : Real.log (461054040555763377 / 640000000000000000 : ℝ) ≤ (-(3279529153345017258651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (461054040555763377 / 640000000000000000 : ℝ) = - (461054040555763377 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (461054040555763377 / 320000000000000000 : ℚ)) - (U := (3651942649654982741349 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (461054040555763377 / 320000000000000000 : ℝ) ≤ - (3651942649654982741349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7200273027065711 / 10000000000000000 : ℝ)) (q := - (461054040555763377 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (461054040555763377 / 640000000000000000 : ℚ)) + (r' := (461054040555763377 / 320000000000000000 : ℚ)) + (U := (-(3279529153345017258651 / 10000000000000000000000 : ℚ))) + (U' := (3651942649654982741349 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (7200273027065711 / 10000000000000000 : ℚ)) + (q := (461054040555763377 / 640000000000000000 : ℚ)) + (U := (-(3279529153345017258651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_6 : Uω (aρ 6) (bρ 6) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5641,25 +4876,21 @@ lemma U_651_6 : have hlg : Real.log (450028736416075057 / 640000000000000000 : ℝ) ≤ (-(880391841664744773029 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (450028736416075057 / 640000000000000000 : ℝ) = - (450028736416075057 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (450028736416075057 / 320000000000000000 : ℚ)) - (U := (852476109085255226971 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (450028736416075057 / 320000000000000000 : ℝ) ≤ - (852476109085255226971 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7022972647840451 / 10000000000000000 : ℝ)) (q := - (450028736416075057 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (450028736416075057 / 640000000000000000 : ℚ)) + (r' := (450028736416075057 / 320000000000000000 : ℚ)) + (U := (-(880391841664744773029 / 2500000000000000000000 : ℚ))) + (U' := (852476109085255226971 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (7022972647840451 / 10000000000000000 : ℚ)) + (q := (450028736416075057 / 640000000000000000 : ℚ)) + (U := (-(880391841664744773029 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_7 : Uω (aρ 7) (bρ 7) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5667,25 +4898,21 @@ lemma U_651_7 : have hlg : Real.log (17402080264116729 / 25600000000000000 : ℝ) ≤ (-(772005193484518130031 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17402080264116729 / 25600000000000000 : ℝ) = - (17402080264116729 / 12800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17402080264116729 / 12800000000000000 : ℚ)) - (U := (614289167115481869969 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (17402080264116729 / 12800000000000000 : ℝ) ≤ - (614289167115481869969 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (67786112219393 / 100000000000000 : ℝ)) (q := - (17402080264116729 / 25600000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17402080264116729 / 25600000000000000 : ℚ)) + (r' := (17402080264116729 / 12800000000000000 : ℚ)) + (U := (-(772005193484518130031 / 2000000000000000000000 : ℚ))) + (U' := (614289167115481869969 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (67786112219393 / 100000000000000 : ℚ)) + (q := (17402080264116729 / 25600000000000000 : ℚ)) + (U := (-(772005193484518130031 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_8 : Uω (aρ 8) (bρ 8) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5693,25 +4920,21 @@ lemma U_651_8 : have hlg : Real.log (83128099669190653 / 128000000000000000 : ℝ) ≤ (-(4316474761254591827999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (83128099669190653 / 128000000000000000 : ℝ) = - (83128099669190653 / 64000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (83128099669190653 / 64000000000000000 : ℚ)) - (U := (2614997041745408172001 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (83128099669190653 / 64000000000000000 : ℝ) ≤ - (2614997041745408172001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1291108648049829 / 2000000000000000 : ℝ)) (q := - (83128099669190653 / 128000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (83128099669190653 / 128000000000000000 : ℚ)) + (r' := (83128099669190653 / 64000000000000000 : ℚ)) + (U := (-(4316474761254591827999 / 10000000000000000000000 : ℚ))) + (U' := (2614997041745408172001 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (1291108648049829 / 2000000000000000 : ℚ)) + (q := (83128099669190653 / 128000000000000000 : ℚ)) + (U := (-(4316474761254591827999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_9 : Uω (aρ 9) (bρ 9) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5719,25 +4942,21 @@ lemma U_651_9 : have hlg : Real.log (391567224838617969 / 640000000000000000 : ℝ) ≤ (-(2456554822246143235107 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (391567224838617969 / 640000000000000000 : ℝ) = - (391567224838617969 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (391567224838617969 / 320000000000000000 : ℚ)) - (U := (1009181079253856764893 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (391567224838617969 / 320000000000000000 : ℝ) ≤ - (1009181079253856764893 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6044219071504917 / 10000000000000000 : ℝ)) (q := - (391567224838617969 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (391567224838617969 / 640000000000000000 : ℚ)) + (r' := (391567224838617969 / 320000000000000000 : ℚ)) + (U := (-(2456554822246143235107 / 5000000000000000000000 : ℚ))) + (U' := (1009181079253856764893 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (6044219071504917 / 10000000000000000 : ℚ)) + (q := (391567224838617969 / 640000000000000000 : ℚ)) + (U := (-(2456554822246143235107 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_10 : Uω (aρ 10) (bρ 10) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5745,26 +4964,21 @@ lemma U_651_10 : have hlg : Real.log (362945874163962929 / 640000000000000000 : ℝ) ≤ (-(5672144599328013069273 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (362945874163962929 / 640000000000000000 : ℝ) = - (362945874163962929 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (362945874163962929 / 320000000000000000 : ℚ)) - (U := (1259327203671986930727 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (362945874163962929 / 320000000000000000 : ℝ) ≤ - (1259327203671986930727 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5538360896416947 / 10000000000000000 : ℝ)) (q := - (362945874163962929 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (362945874163962929 / 640000000000000000 : ℚ)) + (r' := (362945874163962929 / 320000000000000000 : ℚ)) + (U := (-(5672144599328013069273 / 10000000000000000000000 : ℚ))) + (U' := (1259327203671986930727 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (5538360896416947 / 10000000000000000 : ℚ)) + (q := (362945874163962929 / 640000000000000000 : ℚ)) + (U := (-(5672144599328013069273 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_11 : Uω (aρ 11) (bρ 11) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5772,26 +4986,21 @@ lemma U_651_11 : have hlg : Real.log (330275997890179633 / 640000000000000000 : ℝ) ≤ (-(66153951394211009971 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (330275997890179633 / 640000000000000000 : ℝ) = - (330275997890179633 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (330275997890179633 / 320000000000000000 : ℚ)) - (U := (3160766635788990029 / 100000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (330275997890179633 / 320000000000000000 : ℝ) ≤ - (3160766635788990029 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4935903889066219 / 10000000000000000 : ℝ)) (q := - (330275997890179633 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (330275997890179633 / 640000000000000000 : ℚ)) + (r' := (330275997890179633 / 320000000000000000 : ℚ)) + (U := (-(66153951394211009971 / 100000000000000000000 : ℚ))) + (U' := (3160766635788990029 / 100000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (4935903889066219 / 10000000000000000 : ℚ)) + (q := (330275997890179633 / 640000000000000000 : ℚ)) + (U := (-(66153951394211009971 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_12 : Uω (aρ 12) (bρ 12) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5799,26 +5008,21 @@ lemma U_651_12 : have hlg : Real.log (58887071193642237 / 128000000000000000 : ℝ) ≤ (-(7764087011892156874073 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58887071193642237 / 128000000000000000 : ℝ) = - (58887071193642237 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58887071193642237 / 32000000000000000 : ℚ)) - (U := (6098856594107843125927 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (58887071193642237 / 32000000000000000 : ℝ) ≤ - (6098856594107843125927 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (847916785137941 / 2000000000000000 : ℝ)) (q := - (58887071193642237 / 128000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58887071193642237 / 128000000000000000 : ℚ)) + (r' := (58887071193642237 / 32000000000000000 : ℚ)) + (U := (-(7764087011892156874073 / 10000000000000000000000 : ℚ))) + (U' := (6098856594107843125927 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (847916785137941 / 2000000000000000 : ℚ)) + (q := (58887071193642237 / 128000000000000000 : ℚ)) + (U := (-(7764087011892156874073 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_13 : Uω (aρ 13) (bρ 13) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5826,26 +5030,21 @@ lemma U_651_13 : have hlg : Real.log (51323267260200061 / 128000000000000000 : ℝ) ≤ (-(2284715153041468922039 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (51323267260200061 / 128000000000000000 : ℝ) = - (51323267260200061 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (51323267260200061 / 32000000000000000 : ℚ)) - (U := (1181020748458531077961 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (51323267260200061 / 32000000000000000 : ℝ) ≤ - (1181020748458531077961 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (691424260536873 / 2000000000000000 : ℝ)) (q := - (51323267260200061 / 128000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (51323267260200061 / 128000000000000000 : ℚ)) + (r' := (51323267260200061 / 32000000000000000 : ℚ)) + (U := (-(2284715153041468922039 / 2500000000000000000000 : ℚ))) + (U' := (1181020748458531077961 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (691424260536873 / 2000000000000000 : ℚ)) + (q := (51323267260200061 / 128000000000000000 : ℚ)) + (U := (-(2284715153041468922039 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_14 : Uω (aρ 14) (bρ 14) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5853,26 +5052,21 @@ lemma U_651_14 : have hlg : Real.log (218216676070397777 / 640000000000000000 : ℝ) ≤ (-(10759796797346239902829 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (218216676070397777 / 640000000000000000 : ℝ) = - (218216676070397777 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (218216676070397777 / 160000000000000000 : ℚ)) - (U := (3103146808653760097171 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (218216676070397777 / 160000000000000000 : ℝ) ≤ - (3103146808653760097171 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (650264801380759 / 2500000000000000 : ℝ)) (q := - (218216676070397777 / 640000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (218216676070397777 / 640000000000000000 : ℚ)) + (r' := (218216676070397777 / 160000000000000000 : ℚ)) + (U := (-(10759796797346239902829 / 10000000000000000000000 : ℚ))) + (U' := (3103146808653760097171 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (650264801380759 / 2500000000000000 : ℚ)) + (q := (218216676070397777 / 640000000000000000 : ℚ)) + (U := (-(10759796797346239902829 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_15 : Uω (aρ 15) (bρ 15) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5880,26 +5074,21 @@ lemma U_651_15 : have hlg : Real.log (180711209722183089 / 640000000000000000 : ℝ) ≤ (-(252913589034511244197 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (180711209722183089 / 640000000000000000 : ℝ) = - (180711209722183089 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (180711209722183089 / 160000000000000000 : ℚ)) - (U := (24345283085488755803 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (180711209722183089 / 160000000000000000 : ℝ) ≤ - (24345283085488755803 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1688586659556327 / 10000000000000000 : ℝ)) (q := - (180711209722183089 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (180711209722183089 / 640000000000000000 : ℚ)) + (r' := (180711209722183089 / 160000000000000000 : ℚ)) + (U := (-(252913589034511244197 / 200000000000000000000 : ℚ))) + (U' := (24345283085488755803 / 200000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (1688586659556327 / 10000000000000000 : ℚ)) + (q := (180711209722183089 / 640000000000000000 : ℚ)) + (U := (-(252913589034511244197 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651_16 : Uω (aρ 16) (bρ 16) (386038383495521 / 512000000000000 : ℝ) ≤ @@ -5907,26 +5096,21 @@ lemma U_651_16 : have hlg : Real.log (145611323094618033 / 640000000000000000 : ℝ) ≤ (-(7402636371640588000721 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (145611323094618033 / 640000000000000000 : ℝ) = - (145611323094618033 / 80000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145611323094618033 / 80000000000000000 : ℚ)) - (U := (2994571332859411999279 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (145611323094618033 / 80000000000000000 : ℝ) ≤ - (2994571332859411999279 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (744086853954919 / 10000000000000000 : ℝ)) (q := - (145611323094618033 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145611323094618033 / 640000000000000000 : ℚ)) + (r' := (145611323094618033 / 80000000000000000 : ℚ)) + (U := (-(7402636371640588000721 / 5000000000000000000000 : ℚ))) + (U' := (2994571332859411999279 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (386038383495521 / 512000000000000 : ℚ)) + (s := (744086853954919 / 10000000000000000 : ℚ)) + (q := (145611323094618033 / 640000000000000000 : ℚ)) + (U := (-(7402636371640588000721 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_651 : Uρ (386038383495521 / 512000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U54.lean b/LeanPool/Zeta5Irrational/Table/U54.lean index 489b709f22..2fe03b6596 100644 --- a/LeanPool/Zeta5Irrational/Table/U54.lean +++ b/LeanPool/Zeta5Irrational/Table/U54.lean @@ -24,25 +24,21 @@ lemma U_652_1 : have hlg : Real.log (191680850895698137 / 256000000000000000 : ℝ) ≤ (-(2893456901553794808471 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (191680850895698137 / 256000000000000000 : ℝ) = - (191680850895698137 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (191680850895698137 / 128000000000000000 : ℚ)) - (U := (4038014901446205191529 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (191680850895698137 / 128000000000000000 : ℝ) ≤ - (4038014901446205191529 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (93593895581313 / 125000000000000 : ℝ)) (q := - (191680850895698137 / 256000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (191680850895698137 / 256000000000000000 : ℚ)) + (r' := (191680850895698137 / 128000000000000000 : ℚ)) + (U := (-(2893456901553794808471 / 10000000000000000000000 : ℚ))) + (U' := (4038014901446205191529 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (93593895581313 / 125000000000000 : ℚ)) + (q := (191680850895698137 / 256000000000000000 : ℚ)) + (U := (-(2893456901553794808471 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_2 : Uω (aρ 2) (bρ 2) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_652_2 : have hlg : Real.log (191069277983419033 / 256000000000000000 : ℝ) ≤ (-(1462706849909965999691 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (191069277983419033 / 256000000000000000 : ℝ) = - (191069277983419033 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (191069277983419033 / 128000000000000000 : ℚ)) - (U := (2003029051590034000309 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (191069277983419033 / 128000000000000000 : ℝ) ≤ - (2003029051590034000309 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1492700305048647 / 2000000000000000 : ℝ)) (q := - (191069277983419033 / 256000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (191069277983419033 / 256000000000000000 : ℚ)) + (r' := (191069277983419033 / 128000000000000000 : ℚ)) + (U := (-(1462706849909965999691 / 5000000000000000000000 : ℚ))) + (U' := (2003029051590034000309 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1492700305048647 / 2000000000000000 : ℚ)) + (q := (191069277983419033 / 256000000000000000 : ℚ)) + (U := (-(1462706849909965999691 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_3 : Uω (aρ 3) (bρ 3) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_652_3 : have hlg : Real.log (189846807339465497 / 256000000000000000 : ℝ) ≤ (-(1494799872180451229579 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (189846807339465497 / 256000000000000000 : ℝ) = - (189846807339465497 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (189846807339465497 / 128000000000000000 : ℚ)) - (U := (1970936029319548770421 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (189846807339465497 / 128000000000000000 : ℝ) ≤ - (1970936029319548770421 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1483078422506873 / 2000000000000000 : ℝ)) (q := - (189846807339465497 / 256000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (189846807339465497 / 256000000000000000 : ℚ)) + (r' := (189846807339465497 / 128000000000000000 : ℚ)) + (U := (-(1494799872180451229579 / 5000000000000000000000 : ℚ))) + (U' := (1970936029319548770421 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1483078422506873 / 2000000000000000 : ℚ)) + (q := (189846807339465497 / 256000000000000000 : ℚ)) + (U := (-(1494799872180451229579 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_4 : Uω (aρ 4) (bρ 4) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_652_4 : have hlg : Real.log (187818536011483673 / 256000000000000000 : ℝ) ≤ (-(3097011815094364335053 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (187818536011483673 / 256000000000000000 : ℝ) = - (187818536011483673 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (187818536011483673 / 128000000000000000 : ℚ)) - (U := (3834459987905635664947 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (187818536011483673 / 128000000000000000 : ℝ) ≤ - (3834459987905635664947 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1467045519220157 / 2000000000000000 : ℝ)) (q := - (187818536011483673 / 256000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (187818536011483673 / 256000000000000000 : ℚ)) + (r' := (187818536011483673 / 128000000000000000 : ℚ)) + (U := (-(3097011815094364335053 / 10000000000000000000000 : ℚ))) + (U' := (3834459987905635664947 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1467045519220157 / 2000000000000000 : ℚ)) + (q := (187818536011483673 / 256000000000000000 : ℚ)) + (U := (-(3097011815094364335053 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_5 : Uω (aρ 5) (bρ 5) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_652_5 : have hlg : Real.log (923675587414507837 / 1280000000000000000 : ℝ) ≤ (-(3262544425323638530593 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (923675587414507837 / 1280000000000000000 : ℝ) = - (923675587414507837 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (923675587414507837 / 640000000000000000 : ℚ)) - (U := (3668927377676361469407 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (923675587414507837 / 640000000000000000 : ℝ) ≤ - (3668927377676361469407 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1803131360722577 / 2500000000000000 : ℝ)) (q := - (923675587414507837 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (923675587414507837 / 1280000000000000000 : ℚ)) + (r' := (923675587414507837 / 640000000000000000 : ℚ)) + (U := (-(3262544425323638530593 / 10000000000000000000000 : ℚ))) + (U' := (3668927377676361469407 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1803131360722577 / 2500000000000000 : ℚ)) + (q := (923675587414507837 / 1280000000000000000 : ℚ)) + (U := (-(3262544425323638530593 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_6 : Uω (aρ 6) (bρ 6) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_652_6 : have hlg : Real.log (901626119520754429 / 1280000000000000000 : ℝ) ≤ (-(1752077120803032959657 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (901626119520754429 / 1280000000000000000 : ℝ) = - (901626119520754429 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (901626119520754429 / 640000000000000000 : ℚ)) - (U := (1713658780696967040343 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (901626119520754429 / 640000000000000000 : ℝ) ≤ - (1713658780696967040343 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7035242882190411 / 10000000000000000 : ℝ)) (q := - (901626119520754429 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (901626119520754429 / 1280000000000000000 : ℚ)) + (r' := (901626119520754429 / 640000000000000000 : ℚ)) + (U := (-(1752077120803032959657 / 5000000000000000000000 : ℚ))) + (U' := (1713658780696967040343 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (7035242882190411 / 10000000000000000 : ℚ)) + (q := (901626119520754429 / 1280000000000000000 : ℚ)) + (U := (-(1752077120803032959657 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_7 : Uω (aρ 7) (bρ 7) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_652_7 : have hlg : Real.log (871675117636903997 / 1280000000000000000 : ℝ) ≤ (-(3841985736840612427921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (871675117636903997 / 1280000000000000000 : ℝ) = - (871675117636903997 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (871675117636903997 / 640000000000000000 : ℚ)) - (U := (3089486066159387572079 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (871675117636903997 / 640000000000000000 : ℝ) ≤ - (3089486066159387572079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (424432491157203 / 625000000000000 : ℝ)) (q := - (871675117636903997 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (871675117636903997 / 1280000000000000000 : ℚ)) + (r' := (871675117636903997 / 640000000000000000 : ℚ)) + (U := (-(3841985736840612427921 / 10000000000000000000000 : ℚ))) + (U' := (3089486066159387572079 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (424432491157203 / 625000000000000 : ℚ)) + (q := (871675117636903997 / 1280000000000000000 : ℚ)) + (U := (-(3841985736840612427921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_8 : Uω (aρ 8) (bρ 8) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_652_8 : have hlg : Real.log (832857108142459837 / 1280000000000000000 : ℝ) ≤ (-(4297532680459312403669 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (832857108142459837 / 1280000000000000000 : ℝ) = - (832857108142459837 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (832857108142459837 / 640000000000000000 : ℚ)) - (U := (2633939122540687596331 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (832857108142459837 / 640000000000000000 : ℝ) ≤ - (2633939122540687596331 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3233965055752279 / 5000000000000000 : ℝ)) (q := - (832857108142459837 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (832857108142459837 / 1280000000000000000 : ℚ)) + (r' := (832857108142459837 / 640000000000000000 : ℚ)) + (U := (-(4297532680459312403669 / 10000000000000000000000 : ℚ))) + (U' := (2633939122540687596331 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (3233965055752279 / 5000000000000000 : ℚ)) + (q := (832857108142459837 / 1280000000000000000 : ℚ)) + (U := (-(4297532680459312403669 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_9 : Uω (aρ 9) (bρ 9) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_652_9 : have hlg : Real.log (784720299999318333 / 1280000000000000000 : ℝ) ≤ (-(2446440040483157550377 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (784720299999318333 / 1280000000000000000 : ℝ) = - (784720299999318333 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (784720299999318333 / 640000000000000000 : ℚ)) - (U := (1019295861016842449623 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (784720299999318333 / 640000000000000000 : ℝ) ≤ - (1019295861016842449623 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1514189528156993 / 2500000000000000 : ℝ)) (q := - (784720299999318333 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (784720299999318333 / 1280000000000000000 : ℚ)) + (r' := (784720299999318333 / 640000000000000000 : ℚ)) + (U := (-(2446440040483157550377 / 5000000000000000000000 : ℚ))) + (U' := (1019295861016842449623 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1514189528156993 / 2500000000000000 : ℚ)) + (q := (784720299999318333 / 1280000000000000000 : ℚ)) + (U := (-(2446440040483157550377 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_10 : Uω (aρ 10) (bρ 10) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_652_10 : have hlg : Real.log (145499179298836569 / 256000000000000000 : ℝ) ≤ (-(5650069981818022359461 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (145499179298836569 / 256000000000000000 : ℝ) = - (145499179298836569 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145499179298836569 / 128000000000000000 : ℚ)) - (U := (1281401821181977640539 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (145499179298836569 / 128000000000000000 : ℝ) ≤ - (1281401821181977640539 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (555118584135523 / 1000000000000000 : ℝ)) (q := - (145499179298836569 / 256000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145499179298836569 / 256000000000000000 : ℚ)) + (r' := (145499179298836569 / 128000000000000000 : ℚ)) + (U := (-(5650069981818022359461 / 10000000000000000000000 : ℚ))) + (U' := (1281401821181977640539 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (555118584135523 / 1000000000000000 : ℚ)) + (q := (145499179298836569 / 256000000000000000 : ℚ)) + (U := (-(5650069981818022359461 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_11 : Uω (aρ 11) (bρ 11) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_652_11 : have hlg : Real.log (662189823576252669 / 1280000000000000000 : ℝ) ≤ (-(6590630992571855497951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (662189823576252669 / 1280000000000000000 : ℝ) = - (662189823576252669 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (662189823576252669 / 640000000000000000 : ℚ)) - (U := (340840810428144502049 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (662189823576252669 / 640000000000000000 : ℝ) ≤ - (340840810428144502049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4949255078217571 / 10000000000000000 : ℝ)) (q := - (662189823576252669 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (662189823576252669 / 1280000000000000000 : ℚ)) + (r' := (662189823576252669 / 640000000000000000 : ℚ)) + (U := (-(6590630992571855497951 / 10000000000000000000000 : ℚ))) + (U' := (340840810428144502049 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (4949255078217571 / 10000000000000000 : ℚ)) + (q := (662189823576252669 / 1280000000000000000 : ℚ)) + (U := (-(6590630992571855497951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_12 : Uω (aρ 12) (bρ 12) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_652_12 : have hlg : Real.log (590570391768275581 / 1280000000000000000 : ℝ) ≤ (-(7735265208020603162373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (590570391768275581 / 1280000000000000000 : ℝ) = - (590570391768275581 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (590570391768275581 / 320000000000000000 : ℚ)) - (U := (6127678397979396837627 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (590570391768275581 / 320000000000000000 : ℝ) ≤ - (6127678397979396837627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4253901552902929 / 10000000000000000 : ℝ)) (q := - (590570391768275581 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (590570391768275581 / 1280000000000000000 : ℚ)) + (r' := (590570391768275581 / 320000000000000000 : ℚ)) + (U := (-(7735265208020603162373 / 10000000000000000000000 : ℚ))) + (U' := (6127678397979396837627 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (4253901552902929 / 10000000000000000 : ℚ)) + (q := (590570391768275581 / 1280000000000000000 : ℚ)) + (U := (-(7735265208020603162373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_13 : Uω (aρ 13) (bρ 13) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -339,26 +288,21 @@ lemma U_652_13 : have hlg : Real.log (515048739424809981 / 1280000000000000000 : ℝ) ≤ (-(9103538205482609527087 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (515048739424809981 / 1280000000000000000 : ℝ) = - (515048739424809981 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (515048739424809981 / 320000000000000000 : ℚ)) - (U := (4759405400517390472913 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (515048739424809981 / 320000000000000000 : ℝ) ≤ - (4759405400517390472913 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3473257476631279 / 10000000000000000 : ℝ)) (q := - (515048739424809981 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (515048739424809981 / 1280000000000000000 : ℚ)) + (r' := (515048739424809981 / 320000000000000000 : ℚ)) + (U := (-(9103538205482609527087 / 10000000000000000000000 : ℚ))) + (U' := (4759405400517390472913 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (3473257476631279 / 10000000000000000 : ℚ)) + (q := (515048739424809981 / 1280000000000000000 : ℚ)) + (U := (-(9103538205482609527087 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_14 : Uω (aρ 14) (bρ 14) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -366,26 +310,21 @@ lemma U_652_14 : have hlg : Real.log (438484106052634813 / 1280000000000000000 : ℝ) ≤ (-(10712917914125938837233 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (438484106052634813 / 1280000000000000000 : ℝ) = - (438484106052634813 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (438484106052634813 / 320000000000000000 : ℚ)) - (U := (3150025691874061162767 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (438484106052634813 / 320000000000000000 : ℝ) ≤ - (3150025691874061162767 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1310431182618021 / 5000000000000000 : ℝ)) (q := - (438484106052634813 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (438484106052634813 / 1280000000000000000 : ℚ)) + (r' := (438484106052634813 / 320000000000000000 : ℚ)) + (U := (-(10712917914125938837233 / 10000000000000000000000 : ℚ))) + (U' := (3150025691874061162767 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (1310431182618021 / 5000000000000000 : ℚ)) + (q := (438484106052634813 / 1280000000000000000 : ℚ)) + (U := (-(10712917914125938837233 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_15 : Uω (aρ 15) (bρ 15) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -393,26 +332,21 @@ lemma U_652_15 : have hlg : Real.log (2912237359646401 / 10240000000000000 : ℝ) ≤ (-(1571724976514098835237 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2912237359646401 / 10240000000000000 : ℝ) = - (2912237359646401 / 2560000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2912237359646401 / 2560000000000000 : ℚ)) - (U := (161142974235901164763 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (2912237359646401 / 2560000000000000 : ℝ) ≤ - (161142974235901164763 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (858542539319 / 5000000000000 : ℝ)) (q := - (2912237359646401 / 10240000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2912237359646401 / 10240000000000000 : ℚ)) + (r' := (2912237359646401 / 2560000000000000 : ℚ)) + (U := (-(1571724976514098835237 / 1250000000000000000000 : ℚ))) + (U' := (161142974235901164763 / 1250000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (858542539319 / 5000000000000 : ℚ)) + (q := (2912237359646401 / 10240000000000000 : ℚ)) + (U := (-(1571724976514098835237 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652_16 : Uω (aρ 16) (bρ 16) (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -420,26 +354,21 @@ lemma U_652_16 : have hlg : Real.log (295863339134328381 / 1280000000000000000 : ℝ) ≤ (-(7323588502680710169883 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (295863339134328381 / 1280000000000000000 : ℝ) = - (295863339134328381 / 160000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (295863339134328381 / 160000000000000000 : ℚ)) - (U := (3073619201819289830117 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (295863339134328381 / 160000000000000000 : ℝ) ≤ - (3073619201819289830117 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (100544726382813 / 1250000000000000 : ℝ)) (q := - (295863339134328381 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (295863339134328381 / 1280000000000000000 : ℚ)) + (r' := (295863339134328381 / 160000000000000000 : ℚ)) + (U := (-(7323588502680710169883 / 5000000000000000000000 : ℚ))) + (U' := (3073619201819289830117 / 5000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (773330129695373 / 1024000000000000 : ℚ)) + (s := (100544726382813 / 1250000000000000 : ℚ)) + (q := (295863339134328381 / 1280000000000000000 : ℚ)) + (U := (-(7323588502680710169883 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_652 : Uρ (773330129695373 / 1024000000000000 : ℝ) ≤ @@ -545,25 +474,21 @@ lemma U_653_1 : have hlg : Real.log (119996370296175819 / 160000000000000000 : ℝ) ≤ (-(2877123201811696091637 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (119996370296175819 / 160000000000000000 : ℝ) = - (119996370296175819 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (119996370296175819 / 80000000000000000 : ℚ)) - (U := (4054348601188303908363 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (119996370296175819 / 80000000000000000 : ℝ) ≤ - (4054348601188303908363 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3749875793570559 / 5000000000000000 : ℝ)) (q := - (119996370296175819 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (119996370296175819 / 160000000000000000 : ℚ)) + (r' := (119996370296175819 / 80000000000000000 : ℚ)) + (U := (-(2877123201811696091637 / 10000000000000000000000 : ℚ))) + (U' := (4054348601188303908363 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (3749875793570559 / 5000000000000000 : ℚ)) + (q := (119996370296175819 / 160000000000000000 : ℚ)) + (U := (-(2877123201811696091637 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_2 : Uω (aρ 2) (bρ 2) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -571,25 +496,21 @@ lemma U_653_2 : have hlg : Real.log (119614140385909363 / 160000000000000000 : ℝ) ≤ (-(1454513748973133960733 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (119614140385909363 / 160000000000000000 : ℝ) = - (119614140385909363 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (119614140385909363 / 80000000000000000 : ℚ)) - (U := (2011222152526866039267 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (119614140385909363 / 80000000000000000 : ℝ) ≤ - (2011222152526866039267 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7475741860867811 / 10000000000000000 : ℝ)) (q := - (119614140385909363 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (119614140385909363 / 160000000000000000 : ℚ)) + (r' := (119614140385909363 / 80000000000000000 : ℚ)) + (U := (-(1454513748973133960733 / 5000000000000000000000 : ℚ))) + (U' := (2011222152526866039267 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (7475741860867811 / 10000000000000000 : ℚ)) + (q := (119614140385909363 / 160000000000000000 : ℚ)) + (U := (-(1454513748973133960733 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_3 : Uω (aρ 3) (bρ 3) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -597,25 +518,21 @@ lemma U_653_3 : have hlg : Real.log (118850105661120603 / 160000000000000000 : ℝ) ≤ (-(185819207586795205137 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (118850105661120603 / 160000000000000000 : ℝ) = - (118850105661120603 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (118850105661120603 / 80000000000000000 : ℚ)) - (U := (247397780100704794863 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (118850105661120603 / 80000000000000000 : ℝ) ≤ - (247397780100704794863 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (464227101663701 / 625000000000000 : ℝ)) (q := - (118850105661120603 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (118850105661120603 / 160000000000000000 : ℚ)) + (r' := (118850105661120603 / 80000000000000000 : ℚ)) + (U := (-(185819207586795205137 / 625000000000000000000 : ℚ))) + (U' := (247397780100704794863 / 625000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (464227101663701 / 625000000000000 : ℚ)) + (q := (118850105661120603 / 160000000000000000 : ℚ)) + (U := (-(185819207586795205137 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_4 : Uω (aρ 4) (bρ 4) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -623,25 +540,21 @@ lemma U_653_4 : have hlg : Real.log (117582461150381027 / 160000000000000000 : ℝ) ≤ (-(3080339305095248653731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (117582461150381027 / 160000000000000000 : ℝ) = - (117582461150381027 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (117582461150381027 / 80000000000000000 : ℚ)) - (U := (3851132497904751346269 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (117582461150381027 / 80000000000000000 : ℝ) ≤ - (3851132497904751346269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7347472243841769 / 10000000000000000 : ℝ)) (q := - (117582461150381027 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (117582461150381027 / 160000000000000000 : ℚ)) + (r' := (117582461150381027 / 80000000000000000 : ℚ)) + (U := (-(3080339305095248653731 / 10000000000000000000000 : ℚ))) + (U' := (3851132497904751346269 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (7347472243841769 / 10000000000000000 : ℚ)) + (q := (117582461150381027 / 160000000000000000 : ℚ)) + (U := (-(3080339305095248653731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_5 : Uω (aρ 5) (bρ 5) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -649,25 +562,21 @@ lemma U_653_5 : have hlg : Real.log (115655386374443651 / 160000000000000000 : ℝ) ≤ (-(64911770518235379883 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (115655386374443651 / 160000000000000000 : ℝ) = - (115655386374443651 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (115655386374443651 / 80000000000000000 : ℚ)) - (U := (73717665541764620117 / 200000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (115655386374443651 / 80000000000000000 : ℝ) ≤ - (73717665541764620117 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7224777816184597 / 10000000000000000 : ℝ)) (q := - (115655386374443651 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (115655386374443651 / 160000000000000000 : ℚ)) + (r' := (115655386374443651 / 80000000000000000 : ℚ)) + (U := (-(64911770518235379883 / 200000000000000000000 : ℚ))) + (U' := (73717665541764620117 / 200000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (7224777816184597 / 10000000000000000 : ℚ)) + (q := (115655386374443651 / 160000000000000000 : ℚ)) + (U := (-(64911770518235379883 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_6 : Uω (aρ 6) (bρ 6) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -675,25 +584,21 @@ lemma U_653_6 : have hlg : Real.log (22579868986271223 / 32000000000000000 : ℝ) ≤ (-(174338573018717726637 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22579868986271223 / 32000000000000000 : ℝ) = - (22579868986271223 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22579868986271223 / 16000000000000000 : ℚ)) - (U := (172235017131282273363 / 500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (22579868986271223 / 16000000000000000 : ℝ) ≤ - (172235017131282273363 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1409502602187731 / 2000000000000000 : ℝ)) (q := - (22579868986271223 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22579868986271223 / 32000000000000000 : ℚ)) + (r' := (22579868986271223 / 16000000000000000 : ℚ)) + (U := (-(174338573018717726637 / 500000000000000000000 : ℚ))) + (U' := (172235017131282273363 / 500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (1409502602187731 / 2000000000000000 : ℚ)) + (q := (22579868986271223 / 32000000000000000 : ℚ)) + (U := (-(174338573018717726637 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_7 : Uω (aρ 7) (bρ 7) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -701,25 +606,21 @@ lemma U_653_7 : have hlg : Real.log (109155775773423779 / 160000000000000000 : ℝ) ≤ (-(1911989087255013801439 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (109155775773423779 / 160000000000000000 : ℝ) = - (109155775773423779 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (109155775773423779 / 80000000000000000 : ℚ)) - (U := (1553746814244986198561 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (109155775773423779 / 80000000000000000 : ℝ) ≤ - (1553746814244986198561 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6803228246957113 / 10000000000000000 : ℝ)) (q := - (109155775773423779 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (109155775773423779 / 160000000000000000 : ℚ)) + (r' := (109155775773423779 / 80000000000000000 : ℚ)) + (U := (-(1911989087255013801439 / 5000000000000000000000 : ℚ))) + (U' := (1553746814244986198561 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (6803228246957113 / 10000000000000000 : ℚ)) + (q := (109155775773423779 / 160000000000000000 : ℚ)) + (U := (-(1911989087255013801439 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_8 : Uω (aρ 8) (bρ 8) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -727,25 +628,21 @@ lemma U_653_8 : have hlg : Real.log (20860829596002847 / 32000000000000000 : ℝ) ≤ (-(2139313420275157981527 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20860829596002847 / 32000000000000000 : ℝ) = - (20860829596002847 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20860829596002847 / 16000000000000000 : ℚ)) - (U := (1326422481224842018473 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (20860829596002847 / 16000000000000000 : ℝ) ≤ - (1326422481224842018473 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (162007910603023 / 250000000000000 : ℝ)) (q := - (20860829596002847 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20860829596002847 / 32000000000000000 : ℚ)) + (r' := (20860829596002847 / 16000000000000000 : ℚ)) + (U := (-(2139313420275157981527 / 5000000000000000000000 : ℚ))) + (U' := (1326422481224842018473 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (162007910603023 / 250000000000000 : ℚ)) + (q := (20860829596002847 / 32000000000000000 : ℚ)) + (U := (-(2139313420275157981527 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_9 : Uω (aρ 9) (bρ 9) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -753,25 +650,21 @@ lemma U_653_9 : have hlg : Real.log (786306072150831 / 1280000000000000 : ℝ) ≤ (-(1218173088127056917877 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (786306072150831 / 1280000000000000 : ℝ) = - (786306072150831 / 640000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (786306072150831 / 640000000000000 : ℚ)) - (U := (514694862622943082123 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (786306072150831 / 640000000000000 : ℝ) ≤ - (514694862622943082123 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48554367458687 / 80000000000000 : ℝ)) (q := - (786306072150831 / 1280000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (786306072150831 / 1280000000000000 : ℚ)) + (r' := (786306072150831 / 640000000000000 : ℚ)) + (U := (-(1218173088127056917877 / 2500000000000000000000 : ℚ))) + (U' := (514694862622943082123 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (48554367458687 / 80000000000000 : ℚ)) + (q := (786306072150831 / 1280000000000000 : ℚ)) + (U := (-(1218173088127056917877 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_10 : Uω (aρ 10) (bρ 10) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -779,26 +672,21 @@ lemma U_653_10 : have hlg : Real.log (91137484497341187 / 160000000000000000 : ℝ) ≤ (-(5628046299432133914873 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (91137484497341187 / 160000000000000000 : ℝ) = - (91137484497341187 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (91137484497341187 / 80000000000000000 : ℚ)) - (U := (1303425503567866085127 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (91137484497341187 / 80000000000000000 : ℝ) ≤ - (1303425503567866085127 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5564008150641789 / 10000000000000000 : ℝ)) (q := - (91137484497341187 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (91137484497341187 / 160000000000000000 : ℚ)) + (r' := (91137484497341187 / 80000000000000000 : ℚ)) + (U := (-(5628046299432133914873 / 10000000000000000000000 : ℚ))) + (U' := (1303425503567866085127 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (5564008150641789 / 10000000000000000 : ℚ)) + (q := (91137484497341187 / 160000000000000000 : ℚ)) + (U := (-(5628046299432133914873 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_11 : Uω (aρ 11) (bρ 11) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -806,26 +694,21 @@ lemma U_653_11 : have hlg : Real.log (82978410574888283 / 160000000000000000 : ℝ) ≤ (-(6565933545682449290393 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (82978410574888283 / 160000000000000000 : ℝ) = - (82978410574888283 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (82978410574888283 / 80000000000000000 : ℚ)) - (U := (365538257317550709607 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (82978410574888283 / 80000000000000000 : ℝ) ≤ - (365538257317550709607 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (310162533533761 / 625000000000000 : ℝ)) (q := - (82978410574888283 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (82978410574888283 / 160000000000000000 : ℚ)) + (r' := (82978410574888283 / 80000000000000000 : ℚ)) + (U := (-(6565933545682449290393 / 10000000000000000000000 : ℚ))) + (U' := (365538257317550709607 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (310162533533761 / 625000000000000 : ℚ)) + (q := (82978410574888283 / 160000000000000000 : ℚ)) + (U := (-(6565933545682449290393 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_12 : Uω (aρ 12) (bρ 12) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -833,26 +716,21 @@ lemma U_653_12 : have hlg : Real.log (74033655524941171 / 160000000000000000 : ℝ) ≤ (-(7706540205108390999763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (74033655524941171 / 160000000000000000 : ℝ) = - (74033655524941171 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (74033655524941171 / 40000000000000000 : ℚ)) - (U := (6156403400891609000237 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (74033655524941171 / 40000000000000000 : ℝ) ≤ - (6156403400891609000237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4268206251981787 / 10000000000000000 : ℝ)) (q := - (74033655524941171 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (74033655524941171 / 160000000000000000 : ℚ)) + (r' := (74033655524941171 / 40000000000000000 : ℚ)) + (U := (-(7706540205108390999763 / 10000000000000000000000 : ℚ))) + (U' := (6156403400891609000237 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (4268206251981787 / 10000000000000000 : ℚ)) + (q := (74033655524941171 / 160000000000000000 : ℚ)) + (U := (-(7706540205108390999763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_13 : Uω (aρ 13) (bρ 13) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -860,26 +738,21 @@ lemma U_653_13 : have hlg : Real.log (64607847299227699 / 160000000000000000 : ℝ) ≤ (-(2267094840206635581753 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (64607847299227699 / 160000000000000000 : ℝ) = - (64607847299227699 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64607847299227699 / 40000000000000000 : ℚ)) - (U := (1198641061293364418247 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64607847299227699 / 40000000000000000 : ℝ) ≤ - (1198641061293364418247 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3489361965362603 / 10000000000000000 : ℝ)) (q := - (64607847299227699 / 160000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64607847299227699 / 160000000000000000 : ℚ)) + (r' := (64607847299227699 / 40000000000000000 : ℚ)) + (U := (-(2267094840206635581753 / 2500000000000000000000 : ℚ))) + (U' := (1198641061293364418247 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (3489361965362603 / 10000000000000000 : ℚ)) + (q := (64607847299227699 / 160000000000000000 : ℚ)) + (U := (-(2267094840206635581753 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_14 : Uω (aρ 14) (bρ 14) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -887,26 +760,21 @@ lemma U_653_14 : have hlg : Real.log (55066123271789059 / 160000000000000000 : ℝ) ≤ (-(10666391102895760677611 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55066123271789059 / 160000000000000000 : ℝ) = - (55066123271789059 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55066123271789059 / 40000000000000000 : ℚ)) - (U := (3196552503104239322389 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55066123271789059 / 40000000000000000 : ℝ) ≤ - (3196552503104239322389 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2640573746977773 / 10000000000000000 : ℝ)) (q := - (55066123271789059 / 160000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55066123271789059 / 160000000000000000 : ℚ)) + (r' := (55066123271789059 / 40000000000000000 : ℚ)) + (U := (-(10666391102895760677611 / 10000000000000000000000 : ℚ))) + (U' := (3196552503104239322389 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (2640573746977773 / 10000000000000000 : ℚ)) + (q := (55066123271789059 / 160000000000000000 : ℚ)) + (U := (-(10666391102895760677611 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_15 : Uω (aρ 15) (bρ 15) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -914,26 +782,21 @@ lemma U_653_15 : have hlg : Real.log (45826579202610331 / 160000000000000000 : ℝ) ≤ (-(12503095599865301573741 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45826579202610331 / 160000000000000000 : ℝ) = - (45826579202610331 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45826579202610331 / 40000000000000000 : ℚ)) - (U := (1359848006134698426259 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45826579202610331 / 40000000000000000 : ℝ) ≤ - (1359848006134698426259 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (218150501968179 / 1250000000000000 : ℝ)) (q := - (45826579202610331 / 160000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45826579202610331 / 160000000000000000 : ℚ)) + (r' := (45826579202610331 / 40000000000000000 : ℚ)) + (U := (-(12503095599865301573741 / 10000000000000000000000 : ℚ))) + (U' := (1359848006134698426259 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (218150501968179 / 1250000000000000 : ℚ)) + (q := (45826579202610331 / 160000000000000000 : ℚ)) + (U := (-(12503095599865301573741 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653_16 : Uω (aρ 16) (bρ 16) (96822936549963 / 128000000000000 : ℝ) ≤ @@ -941,26 +804,21 @@ lemma U_653_16 : have hlg : Real.log (37530704140993003 / 160000000000000000 : ℝ) ≤ (-(14500144393995872475567 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (37530704140993003 / 160000000000000000 : ℝ) = - (37530704140993003 / 20000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37530704140993003 / 20000000000000000 : ℚ)) - (U := (6294271015004127524433 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37530704140993003 / 20000000000000000 : ℝ) ≤ - (6294271015004127524433 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (430295642276633 / 5000000000000000 : ℝ)) (q := - (37530704140993003 / 160000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37530704140993003 / 160000000000000000 : ℚ)) + (r' := (37530704140993003 / 20000000000000000 : ℚ)) + (U := (-(14500144393995872475567 / 10000000000000000000000 : ℚ))) + (U' := (6294271015004127524433 / 10000000000000000000000 : ℚ)) + 3 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (96822936549963 / 128000000000000 : ℚ)) + (s := (430295642276633 / 5000000000000000 : ℚ)) + (q := (37530704140993003 / 160000000000000000 : ℚ)) + (U := (-(14500144393995872475567 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_653 : Uρ (96822936549963 / 128000000000000 : ℝ) ≤ @@ -1054,25 +912,21 @@ lemma U_654_1 : have hlg : Real.log (192307534049124759 / 256000000000000000 : ℝ) ≤ (-(178801008606094785107 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (192307534049124759 / 256000000000000000 : ℝ) = - (192307534049124759 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (192307534049124759 / 128000000000000000 : ℚ)) - (U := (254415979081405214893 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (192307534049124759 / 128000000000000000 : ℝ) ≤ - (254415979081405214893 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (751199152754753 / 1000000000000000 : ℝ)) (q := - (192307534049124759 / 256000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (192307534049124759 / 256000000000000000 : ℚ)) + (r' := (192307534049124759 / 128000000000000000 : ℚ)) + (U := (-(178801008606094785107 / 625000000000000000000 : ℚ))) + (U' := (254415979081405214893 / 625000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (751199152754753 / 1000000000000000 : ℚ)) + (q := (192307534049124759 / 256000000000000000 : ℚ)) + (U := (-(178801008606094785107 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_2 : Uω (aρ 2) (bρ 2) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1080,25 +934,21 @@ lemma U_654_2 : have hlg : Real.log (958479856160063987 / 1280000000000000000 : ℝ) ≤ (-(180791756495602557493 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (958479856160063987 / 1280000000000000000 : ℝ) = - (958479856160063987 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (958479856160063987 / 640000000000000000 : ℚ)) - (U := (252425231191897442507 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (958479856160063987 / 640000000000000000 : ℝ) ≤ - (252425231191897442507 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3743991097485329 / 5000000000000000 : ℝ)) (q := - (958479856160063987 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (958479856160063987 / 1280000000000000000 : ℚ)) + (r' := (958479856160063987 / 640000000000000000 : ℚ)) + (U := (-(180791756495602557493 / 625000000000000000000 : ℚ))) + (U' := (252425231191897442507 / 625000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (3743991097485329 / 5000000000000000 : ℚ)) + (q := (958479856160063987 / 1280000000000000000 : ℚ)) + (U := (-(180791756495602557493 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_3 : Uω (aρ 3) (bρ 3) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1106,25 +956,21 @@ lemma U_654_3 : have hlg : Real.log (7618941228275183 / 10240000000000000 : ℝ) ≤ (-(2956642057273893298753 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7618941228275183 / 10240000000000000 : ℝ) = - (7618941228275183 / 5120000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7618941228275183 / 5120000000000000 : ℚ)) - (U := (3974829745726106701247 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7618941228275183 / 5120000000000000 : ℝ) ≤ - (3974829745726106701247 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59519001082357 / 80000000000000 : ℝ)) (q := - (7618941228275183 / 10240000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7618941228275183 / 10240000000000000 : ℚ)) + (r' := (7618941228275183 / 5120000000000000 : ℚ)) + (U := (-(2956642057273893298753 / 10000000000000000000000 : ℚ))) + (U' := (3974829745726106701247 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (59519001082357 / 80000000000000 : ℚ)) + (q := (7618941228275183 / 10240000000000000 : ℚ)) + (U := (-(2956642057273893298753 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_4 : Uω (aρ 4) (bρ 4) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1132,25 +978,21 @@ lemma U_654_4 : have hlg : Real.log (942226697331449523 / 1280000000000000000 : ℝ) ≤ (-(612738911377929143541 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (942226697331449523 / 1280000000000000000 : ℝ) = - (942226697331449523 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (942226697331449523 / 640000000000000000 : ℚ)) - (U := (773555449222070856459 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (942226697331449523 / 640000000000000000 : ℝ) ≤ - (773555449222070856459 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7359716875688557 / 10000000000000000 : ℝ)) (q := - (942226697331449523 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (942226697331449523 / 1280000000000000000 : ℚ)) + (r' := (942226697331449523 / 640000000000000000 : ℚ)) + (U := (-(612738911377929143541 / 2000000000000000000000 : ℚ))) + (U' := (773555449222070856459 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (7359716875688557 / 10000000000000000 : ℚ)) + (q := (942226697331449523 / 1280000000000000000 : ℚ)) + (U := (-(612738911377929143541 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_5 : Uω (aρ 5) (bρ 5) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1158,25 +1000,21 @@ lemma U_654_5 : have hlg : Real.log (926810591868475827 / 1280000000000000000 : ℝ) ≤ (-(3228661357312839731263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (926810591868475827 / 1280000000000000000 : ℝ) = - (926810591868475827 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (926810591868475827 / 640000000000000000 : ℚ)) - (U := (3702810445687160268737 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (926810591868475827 / 640000000000000000 : ℝ) ≤ - (3702810445687160268737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7237030147164593 / 10000000000000000 : ℝ)) (q := - (926810591868475827 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (926810591868475827 / 1280000000000000000 : ℚ)) + (r' := (926810591868475827 / 640000000000000000 : ℚ)) + (U := (-(3228661357312839731263 / 10000000000000000000000 : ℚ))) + (U' := (3702810445687160268737 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (7237030147164593 / 10000000000000000 : ℚ)) + (q := (926810591868475827 / 1280000000000000000 : ℚ)) + (U := (-(3228661357312839731263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_6 : Uω (aρ 6) (bρ 6) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1184,25 +1022,21 @@ lemma U_654_6 : have hlg : Real.log (904763392657673011 / 1280000000000000000 : ℝ) ≤ (-(1734709458567699032261 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (904763392657673011 / 1280000000000000000 : ℝ) = - (904763392657673011 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (904763392657673011 / 640000000000000000 : ℚ)) - (U := (1731026442932300967739 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (904763392657673011 / 640000000000000000 : ℝ) ≤ - (1731026442932300967739 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7059783034635799 / 10000000000000000 : ℝ)) (q := - (904763392657673011 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (904763392657673011 / 1280000000000000000 : ℚ)) + (r' := (904763392657673011 / 640000000000000000 : ℚ)) + (U := (-(1734709458567699032261 / 5000000000000000000000 : ℚ))) + (U' := (1731026442932300967739 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (7059783034635799 / 10000000000000000 : ℚ)) + (q := (904763392657673011 / 1280000000000000000 : ℚ)) + (U := (-(1734709458567699032261 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_7 : Uω (aρ 7) (bρ 7) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1210,25 +1044,21 @@ lemma U_654_7 : have hlg : Real.log (874817278943332787 / 1280000000000000000 : ℝ) ≤ (-(761200632335293118429 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (874817278943332787 / 1280000000000000000 : ℝ) = - (874817278943332787 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (874817278943332787 / 640000000000000000 : ℚ)) - (U := (625093728264706881571 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (874817278943332787 / 640000000000000000 : ℝ) ≤ - (625093728264706881571 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6815536388609233 / 10000000000000000 : ℝ)) (q := - (874817278943332787 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (874817278943332787 / 1280000000000000000 : ℚ)) + (r' := (874817278943332787 / 640000000000000000 : ℚ)) + (U := (-(761200632335293118429 / 2000000000000000000000 : ℚ))) + (U' := (625093728264706881571 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (6815536388609233 / 10000000000000000 : ℚ)) + (q := (874817278943332787 / 1280000000000000000 : ℚ)) + (U := (-(761200632335293118429 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_8 : Uω (aρ 8) (bρ 8) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1236,25 +1066,21 @@ lemma U_654_8 : have hlg : Real.log (33440368959579563 / 51200000000000000 : ℝ) ≤ (-(425975710149634223111 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (33440368959579563 / 51200000000000000 : ℝ) = - (33440368959579563 / 25600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33440368959579563 / 25600000000000000 : ℚ)) - (U := (267171470150365776889 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (33440368959579563 / 25600000000000000 : ℝ) ≤ - (267171470150365776889 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (259708087251817 / 400000000000000 : ℝ)) (q := - (33440368959579563 / 51200000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33440368959579563 / 51200000000000000 : ℚ)) + (r' := (33440368959579563 / 25600000000000000 : ℚ)) + (U := (-(425975710149634223111 / 1000000000000000000000 : ℚ))) + (U' := (267171470150365776889 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (259708087251817 / 400000000000000 : ℚ)) + (q := (33440368959579563 / 51200000000000000 : ℚ)) + (U := (-(425975710149634223111 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_9 : Uω (aρ 9) (bρ 9) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1262,25 +1088,21 @@ lemma U_654_9 : have hlg : Real.log (787891766615224371 / 1280000000000000000 : ℝ) ≤ (-(4852546282406263118157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (787891766615224371 / 1280000000000000000 : ℝ) = - (787891766615224371 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (787891766615224371 / 640000000000000000 : ℚ)) - (U := (2078925520593736881843 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (787891766615224371 / 640000000000000000 : ℝ) ≤ - (2078925520593736881843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6081832538182539 / 10000000000000000 : ℝ)) (q := - (787891766615224371 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (787891766615224371 / 1280000000000000000 : ℚ)) + (r' := (787891766615224371 / 640000000000000000 : ℚ)) + (U := (-(4852546282406263118157 / 10000000000000000000000 : ℚ))) + (U' := (2078925520593736881843 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (6081832538182539 / 10000000000000000 : ℚ)) + (q := (787891766615224371 / 1280000000000000000 : ℚ)) + (U := (-(4852546282406263118157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_10 : Uω (aρ 10) (bρ 10) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1288,26 +1110,21 @@ lemma U_654_10 : have hlg : Real.log (146140737589014167 / 256000000000000000 : ℝ) ≤ (-(2803036653647281027841 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (146140737589014167 / 256000000000000000 : ℝ) = - (146140737589014167 / 128000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (146140737589014167 / 128000000000000000 : ℚ)) - (U := (662699247852718972159 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (146140737589014167 / 128000000000000000 : ℝ) ≤ - (662699247852718972159 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (557682784245639 / 1000000000000000 : ℝ)) (q := - (146140737589014167 / 256000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (146140737589014167 / 256000000000000000 : ℚ)) + (r' := (146140737589014167 / 128000000000000000 : ℚ)) + (U := (-(2803036653647281027841 / 5000000000000000000000 : ℚ))) + (U' := (662699247852718972159 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (557682784245639 / 1000000000000000 : ℚ)) + (q := (146140737589014167 / 256000000000000000 : ℚ)) + (U := (-(2803036653647281027841 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_11 : Uω (aρ 11) (bρ 11) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1315,26 +1132,21 @@ lemma U_654_11 : have hlg : Real.log (665464381799973043 / 1280000000000000000 : ℝ) ≤ (-(817662801515715558399 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (665464381799973043 / 1280000000000000000 : ℝ) = - (665464381799973043 / 640000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (665464381799973043 / 640000000000000000 : ℚ)) - (U := (48771173859284441601 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (665464381799973043 / 640000000000000000 : ℝ) ≤ - (48771173859284441601 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4975940310144237 / 10000000000000000 : ℝ)) (q := - (665464381799973043 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (665464381799973043 / 1280000000000000000 : ℚ)) + (r' := (665464381799973043 / 640000000000000000 : ℚ)) + (U := (-(817662801515715558399 / 1250000000000000000000 : ℚ))) + (U' := (48771173859284441601 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (4975940310144237 / 10000000000000000 : ℚ)) + (q := (665464381799973043 / 1280000000000000000 : ℚ)) + (U := (-(817662801515715558399 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_12 : Uω (aρ 12) (bρ 12) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1342,26 +1154,21 @@ lemma U_654_12 : have hlg : Real.log (23758691100856299 / 51200000000000000 : ℝ) ≤ (-(239934727155107788411 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (23758691100856299 / 51200000000000000 : ℝ) = - (23758691100856299 / 12800000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23758691100856299 / 12800000000000000 : ℚ)) - (U := (193282260532392211589 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (23758691100856299 / 12800000000000000 : ℝ) ≤ - (193282260532392211589 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (85649963049533 / 200000000000000 : ℝ)) (q := - (23758691100856299 / 51200000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23758691100856299 / 51200000000000000 : ℚ)) + (r' := (23758691100856299 / 12800000000000000 : ℚ)) + (U := (-(239934727155107788411 / 312500000000000000000 : ℚ))) + (U' := (193282260532392211589 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (85649963049533 / 200000000000000 : ℚ)) + (q := (23758691100856299 / 51200000000000000 : ℚ)) + (U := (-(239934727155107788411 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_13 : Uω (aρ 13) (bρ 13) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1369,26 +1176,21 @@ lemma U_654_13 : have hlg : Real.log (518674817457819507 / 1280000000000000000 : ℝ) ≤ (-(2258345563885136111871 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (518674817457819507 / 1280000000000000000 : ℝ) = - (518674817457819507 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (518674817457819507 / 320000000000000000 : ℚ)) - (U := (1207390337614863888129 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (518674817457819507 / 320000000000000000 : ℝ) ≤ - (1207390337614863888129 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (438179400697261 / 1250000000000000 : ℝ)) (q := - (518674817457819507 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (518674817457819507 / 1280000000000000000 : ℚ)) + (r' := (518674817457819507 / 320000000000000000 : ℚ)) + (U := (-(2258345563885136111871 / 2500000000000000000000 : ℚ))) + (U' := (1207390337614863888129 / 2500000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (438179400697261 / 1250000000000000 : ℚ)) + (q := (518674817457819507 / 1280000000000000000 : ℚ)) + (U := (-(2258345563885136111871 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_14 : Uω (aρ 14) (bρ 14) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1396,26 +1198,21 @@ lemma U_654_14 : have hlg : Real.log (442568123075821491 / 1280000000000000000 : ℝ) ≤ (-(5310104766705545786437 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (442568123075821491 / 1280000000000000000 : ℝ) = - (442568123075821491 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (442568123075821491 / 320000000000000000 : ℚ)) - (U := (1621367036294454213563 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (442568123075821491 / 320000000000000000 : ℝ) ≤ - (1621367036294454213563 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2660195390904369 / 10000000000000000 : ℝ)) (q := - (442568123075821491 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (442568123075821491 / 1280000000000000000 : ℚ)) + (r' := (442568123075821491 / 320000000000000000 : ℚ)) + (U := (-(5310104766705545786437 / 5000000000000000000000 : ℚ))) + (U' := (1621367036294454213563 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (2660195390904369 / 10000000000000000 : ℚ)) + (q := (442568123075821491 / 1280000000000000000 : ℚ)) + (U := (-(5310104766705545786437 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_15 : Uω (aρ 15) (bρ 15) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1423,26 +1220,21 @@ lemma U_654_15 : have hlg : Real.log (369172466004084083 / 1280000000000000000 : ℝ) ≤ (-(12433514339998384626713 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (369172466004084083 / 1280000000000000000 : ℝ) = - (369172466004084083 / 320000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (369172466004084083 / 320000000000000000 : ℚ)) - (U := (1429429266001615373287 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (369172466004084083 / 320000000000000000 : ℝ) ≤ - (1429429266001615373287 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (55405047705421 / 312500000000000 : ℝ)) (q := - (369172466004084083 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (369172466004084083 / 1280000000000000000 : ℚ)) + (r' := (369172466004084083 / 320000000000000000 : ℚ)) + (U := (-(12433514339998384626713 / 10000000000000000000000 : ℚ))) + (U' := (1429429266001615373287 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (55405047705421 / 312500000000000 : ℚ)) + (q := (369172466004084083 / 1280000000000000000 : ℚ)) + (U := (-(12433514339998384626713 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654_16 : Uω (aρ 16) (bρ 16) (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1450,26 +1242,21 @@ lemma U_654_16 : have hlg : Real.log (304417265698092147 / 1280000000000000000 : ℝ) ≤ (-(14362160113274664036023 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (304417265698092147 / 1280000000000000000 : ℝ) = - (304417265698092147 / 160000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (304417265698092147 / 160000000000000000 : ℚ)) - (U := (6432255295725335963977 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (304417265698092147 / 160000000000000000 : ℝ) ≤ - (6432255295725335963977 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (228383293325587 / 2500000000000000 : ℝ)) (q := - (304417265698092147 / 1280000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (304417265698092147 / 1280000000000000000 : ℚ)) + (r' := (304417265698092147 / 160000000000000000 : ℚ)) + (U := (-(14362160113274664036023 / 10000000000000000000000 : ℚ))) + (U' := (6432255295725335963977 / 10000000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (155167371020807 / 204800000000000 : ℚ)) + (s := (228383293325587 / 2500000000000000 : ℚ)) + (q := (304417265698092147 / 1280000000000000000 : ℚ)) + (U := (-(14362160113274664036023 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_654 : Uρ (155167371020807 / 204800000000000 : ℝ) ≤ @@ -1569,25 +1356,21 @@ lemma U_655_1 : have hlg : Real.log (481552189053607047 / 640000000000000000 : ℝ) ≤ (-(44445869101279289721 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (481552189053607047 / 640000000000000000 : ℝ) = - (481552189053607047 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (481552189053607047 / 320000000000000000 : ℚ)) - (U := (63858377820595710279 / 156250000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (481552189053607047 / 320000000000000000 : ℝ) ≤ - (63858377820595710279 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1881057866931349 / 2500000000000000 : ℝ)) (q := - (481552189053607047 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (481552189053607047 / 640000000000000000 : ℚ)) + (r' := (481552189053607047 / 320000000000000000 : ℚ)) + (U := (-(44445869101279289721 / 156250000000000000000 : ℚ))) + (U' := (63858377820595710279 / 156250000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (1881057866931349 / 2500000000000000 : ℚ)) + (q := (481552189053607047 / 640000000000000000 : ℚ)) + (U := (-(44445869101279289721 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_2 : Uω (aρ 2) (bρ 2) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1595,25 +1378,21 @@ lemma U_655_2 : have hlg : Real.log (480023294567969607 / 640000000000000000 : ℝ) ≤ (-(2876335430194582704191 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (480023294567969607 / 640000000000000000 : ℝ) = - (480023294567969607 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (480023294567969607 / 320000000000000000 : ℚ)) - (U := (4055136372805417295809 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (480023294567969607 / 320000000000000000 : ℝ) ≤ - (4055136372805417295809 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3750111263779613 / 5000000000000000 : ℝ)) (q := - (480023294567969607 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (480023294567969607 / 640000000000000000 : ℚ)) + (r' := (480023294567969607 / 320000000000000000 : ℚ)) + (U := (-(2876335430194582704191 / 10000000000000000000000 : ℚ))) + (U' := (4055136372805417295809 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (3750111263779613 / 5000000000000000 : ℚ)) + (q := (480023294567969607 / 640000000000000000 : ℚ)) + (U := (-(2876335430194582704191 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_3 : Uω (aρ 3) (bρ 3) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1621,25 +1400,21 @@ lemma U_655_3 : have hlg : Real.log (476967230717666407 / 640000000000000000 : ℝ) ≤ (-(2940203862703970074569 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (476967230717666407 / 640000000000000000 : ℝ) = - (476967230717666407 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (476967230717666407 / 320000000000000000 : ℚ)) - (U := (3991267940296029925431 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (476967230717666407 / 320000000000000000 : ℝ) ≤ - (3991267940296029925431 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7452116638587251 / 10000000000000000 : ℝ)) (q := - (476967230717666407 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (476967230717666407 / 640000000000000000 : ℚ)) + (r' := (476967230717666407 / 320000000000000000 : ℚ)) + (U := (-(2940203862703970074569 / 10000000000000000000000 : ℚ))) + (U' := (3991267940296029925431 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (7452116638587251 / 10000000000000000 : ℚ)) + (q := (476967230717666407 / 640000000000000000 : ℚ)) + (U := (-(2940203862703970074569 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_4 : Uω (aρ 4) (bρ 4) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1647,25 +1422,21 @@ lemma U_655_4 : have hlg : Real.log (471896852223845543 / 640000000000000000 : ℝ) ≤ (-(3047077478141810132203 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (471896852223845543 / 640000000000000000 : ℝ) = - (471896852223845543 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (471896852223845543 / 320000000000000000 : ℚ)) - (U := (3884394324858189867797 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (471896852223845543 / 320000000000000000 : ℝ) ≤ - (3884394324858189867797 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7371961491720349 / 10000000000000000 : ℝ)) (q := - (471896852223845543 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (471896852223845543 / 640000000000000000 : ℚ)) + (r' := (471896852223845543 / 320000000000000000 : ℚ)) + (U := (-(3047077478141810132203 / 10000000000000000000000 : ℚ))) + (U' := (3884394324858189867797 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (7371961491720349 / 10000000000000000 : ℚ)) + (q := (471896852223845543 / 640000000000000000 : ℚ)) + (U := (-(3047077478141810132203 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_5 : Uω (aρ 5) (bρ 5) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1673,25 +1444,21 @@ lemma U_655_5 : have hlg : Real.log (464189045023509479 / 640000000000000000 : ℝ) ≤ (-(80294070555689559269 / 250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (464189045023509479 / 640000000000000000 : ℝ) = - (464189045023509479 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (464189045023509479 / 320000000000000000 : ℚ)) - (U := (92992724519310440731 / 250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (464189045023509479 / 320000000000000000 : ℝ) ≤ - (92992724519310440731 / 250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7249282436044847 / 10000000000000000 : ℝ)) (q := - (464189045023509479 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (464189045023509479 / 640000000000000000 : ℚ)) + (r' := (464189045023509479 / 320000000000000000 : ℚ)) + (U := (-(80294070555689559269 / 250000000000000000000 : ℚ))) + (U' := (92992724519310440731 / 250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (7249282436044847 / 10000000000000000 : ℚ)) + (q := (464189045023509479 / 640000000000000000 : ℚ)) + (U := (-(80294070555689559269 / 250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_6 : Uω (aρ 6) (bρ 6) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1699,25 +1466,21 @@ lemma U_655_6 : have hlg : Real.log (453166009588110663 / 640000000000000000 : ℝ) ≤ (-(1726048253307382550747 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (453166009588110663 / 640000000000000000 : ℝ) = - (453166009588110663 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (453166009588110663 / 320000000000000000 : ℚ)) - (U := (1739687648192617449253 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (453166009588110663 / 320000000000000000 : ℝ) ≤ - (1739687648192617449253 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3536026476914317 / 5000000000000000 : ℝ)) (q := - (453166009588110663 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (453166009588110663 / 640000000000000000 : ℚ)) + (r' := (453166009588110663 / 320000000000000000 : ℚ)) + (U := (-(1726048253307382550747 / 5000000000000000000000 : ℚ))) + (U' := (1739687648192617449253 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (3536026476914317 / 5000000000000000 : ℚ)) + (q := (453166009588110663 / 640000000000000000 : ℚ)) + (U := (-(1726048253307382550747 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_7 : Uω (aρ 7) (bρ 7) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1725,25 +1488,21 @@ lemma U_655_7 : have hlg : Real.log (438194167995073671 / 640000000000000000 : ℝ) ≤ (-(3788060580235419980457 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (438194167995073671 / 640000000000000000 : ℝ) = - (438194167995073671 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (438194167995073671 / 320000000000000000 : ℚ)) - (U := (3143411222764580019543 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (438194167995073671 / 320000000000000000 : ℝ) ≤ - (3143411222764580019543 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1706961071201557 / 2500000000000000 : ℝ)) (q := - (438194167995073671 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (438194167995073671 / 640000000000000000 : ℚ)) + (r' := (438194167995073671 / 320000000000000000 : ℚ)) + (U := (-(3788060580235419980457 / 10000000000000000000000 : ℚ))) + (U' := (3143411222764580019543 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (1706961071201557 / 2500000000000000 : ℚ)) + (q := (438194167995073671 / 640000000000000000 : ℚ)) + (U := (-(3788060580235419980457 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_8 : Uω (aρ 8) (bρ 8) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1751,25 +1510,21 @@ lemma U_655_8 : have hlg : Real.log (16751704575872767 / 25600000000000000 : ℝ) ≤ (-(4240923324085287446963 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16751704575872767 / 25600000000000000 : ℝ) = - (16751704575872767 / 12800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16751704575872767 / 12800000000000000 : ℚ)) - (U := (2690548478914712553037 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (16751704575872767 / 12800000000000000 : ℝ) ≤ - (2690548478914712553037 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (260203495448031 / 400000000000000 : ℝ)) (q := - (16751704575872767 / 25600000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16751704575872767 / 25600000000000000 : ℚ)) + (r' := (16751704575872767 / 12800000000000000 : ℚ)) + (U := (-(4240923324085287446963 / 10000000000000000000000 : ℚ))) + (U' := (2690548478914712553037 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (260203495448031 / 400000000000000 : ℚ)) + (q := (16751704575872767 / 25600000000000000 : ℚ)) + (U := (-(4240923324085287446963 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_9 : Uω (aρ 9) (bρ 9) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1777,25 +1532,21 @@ lemma U_655_9 : have hlg : Real.log (394738691935962311 / 640000000000000000 : ℝ) ≤ (-(966488339018040144383 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (394738691935962311 / 640000000000000000 : ℝ) = - (394738691935962311 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (394738691935962311 / 320000000000000000 : ℚ)) - (U := (419806021581959855617 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (394738691935962311 / 320000000000000000 : ℝ) ≤ - (419806021581959855617 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3047183968829499 / 5000000000000000 : ℝ)) (q := - (394738691935962311 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (394738691935962311 / 640000000000000000 : ℚ)) + (r' := (394738691935962311 / 320000000000000000 : ℚ)) + (U := (-(966488339018040144383 / 2000000000000000000000 : ℚ))) + (U' := (419806021581959855617 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (3047183968829499 / 5000000000000000 : ℚ)) + (q := (394738691935962311 / 640000000000000000 : ℚ)) + (U := (-(966488339018040144383 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_10 : Uω (aρ 10) (bρ 10) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1803,26 +1554,21 @@ lemma U_655_10 : have hlg : Real.log (14646146670916031 / 25600000000000000 : ℝ) ≤ (-(5584150762359065444067 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14646146670916031 / 25600000000000000 : ℝ) = - (14646146670916031 / 12800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14646146670916031 / 12800000000000000 : ℚ)) - (U := (1347321040640934555933 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (14646146670916031 / 12800000000000000 : ℝ) ≤ - (1347321040640934555933 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (223585797392333 / 400000000000000 : ℝ)) (q := - (14646146670916031 / 25600000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14646146670916031 / 25600000000000000 : ℚ)) + (r' := (14646146670916031 / 12800000000000000 : ℚ)) + (U := (-(5584150762359065444067 / 10000000000000000000000 : ℚ))) + (U' := (1347321040640934555933 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (223585797392333 / 400000000000000 : ℚ)) + (q := (14646146670916031 / 25600000000000000 : ℚ)) + (U := (-(5584150762359065444067 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_11 : Uω (aρ 11) (bρ 11) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1830,26 +1576,21 @@ lemma U_655_11 : have hlg : Real.log (333550559048547303 / 640000000000000000 : ℝ) ≤ (-(6516737208834470122621 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (333550559048547303 / 640000000000000000 : ℝ) = - (333550559048547303 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (333550559048547303 / 320000000000000000 : ℚ)) - (U := (414734594165529877379 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (333550559048547303 / 320000000000000000 : ℝ) ≤ - (414734594165529877379 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4989274444627279 / 10000000000000000 : ℝ)) (q := - (333550559048547303 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (333550559048547303 / 640000000000000000 : ℚ)) + (r' := (333550559048547303 / 320000000000000000 : ℚ)) + (U := (-(6516737208834470122621 / 10000000000000000000000 : ℚ))) + (U' := (414734594165529877379 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (4989274444627279 / 10000000000000000 : ℚ)) + (q := (333550559048547303 / 640000000000000000 : ℚ)) + (U := (-(6516737208834470122621 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_12 : Uω (aρ 12) (bρ 12) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1857,26 +1598,21 @@ lemma U_655_12 : have hlg : Real.log (297832249953725863 / 640000000000000000 : ℝ) ≤ (-(7649377674455245816967 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (297832249953725863 / 640000000000000000 : ℝ) = - (297832249953725863 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (297832249953725863 / 160000000000000000 : ℚ)) - (U := (6213565931544754183033 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (297832249953725863 / 160000000000000000 : ℝ) ≤ - (6213565931544754183033 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4296777382099109 / 10000000000000000 : ℝ)) (q := - (297832249953725863 / 640000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (297832249953725863 / 640000000000000000 : ℚ)) + (r' := (297832249953725863 / 160000000000000000 : ℚ)) + (U := (-(7649377674455245816967 / 10000000000000000000000 : ℚ))) + (U' := (6213565931544754183033 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (4296777382099109 / 10000000000000000 : ℚ)) + (q := (297832249953725863 / 640000000000000000 : ℚ)) + (U := (-(7649377674455245816967 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_13 : Uω (aρ 13) (bρ 13) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1884,26 +1620,21 @@ lemma U_655_13 : have hlg : Real.log (52048488400157723 / 128000000000000000 : ℝ) ≤ (-(8998545100638613692049 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (52048488400157723 / 128000000000000000 : ℝ) = - (52048488400157723 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52048488400157723 / 32000000000000000 : ℚ)) - (U := (4864398505361386307951 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (52048488400157723 / 32000000000000000 : ℝ) ≤ - (4864398505361386307951 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (176073881258241 / 500000000000000 : ℝ)) (q := - (52048488400157723 / 128000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52048488400157723 / 128000000000000000 : ℚ)) + (r' := (52048488400157723 / 32000000000000000 : ℚ)) + (U := (-(8998545100638613692049 / 10000000000000000000000 : ℚ))) + (U' := (4864398505361386307951 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (176073881258241 / 500000000000000 : ℚ)) + (q := (52048488400157723 / 128000000000000000 : ℚ)) + (U := (-(8998545100638613692049 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_14 : Uω (aρ 14) (bρ 14) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1911,26 +1642,21 @@ lemma U_655_14 : have hlg : Real.log (44460164291706619 / 128000000000000000 : ℝ) ≤ (-(10574366596004491116633 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44460164291706619 / 128000000000000000 : ℝ) = - (44460164291706619 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44460164291706619 / 32000000000000000 : ℚ)) - (U := (3288577009995508883367 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (44460164291706619 / 32000000000000000 : ℝ) ≤ - (3288577009995508883367 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (535945853652867 / 2000000000000000 : ℝ)) (q := - (44460164291706619 / 128000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44460164291706619 / 128000000000000000 : ℚ)) + (r' := (44460164291706619 / 32000000000000000 : ℚ)) + (U := (-(10574366596004491116633 / 10000000000000000000000 : ℚ))) + (U' := (3288577009995508883367 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (535945853652867 / 2000000000000000 : ℚ)) + (q := (44460164291706619 / 128000000000000000 : ℚ)) + (U := (-(10574366596004491116633 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_15 : Uω (aρ 15) (bρ 15) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1938,26 +1664,21 @@ lemma U_655_15 : have hlg : Real.log (185855118499611463 / 640000000000000000 : ℝ) ≤ (-(247300147688838586911 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (185855118499611463 / 640000000000000000 : ℝ) = - (185855118499611463 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (185855118499611463 / 160000000000000000 : ℚ)) - (U := (29958724431161413089 / 200000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (185855118499611463 / 160000000000000000 : ℝ) ≤ - (29958724431161413089 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (900187164106517 / 5000000000000000 : ℝ)) (q := - (185855118499611463 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (185855118499611463 / 640000000000000000 : ℚ)) + (r' := (185855118499611463 / 160000000000000000 : ℚ)) + (U := (-(247300147688838586911 / 200000000000000000000 : ℚ))) + (U' := (29958724431161413089 / 200000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (900187164106517 / 5000000000000000 : ℚ)) + (q := (185855118499611463 / 640000000000000000 : ℚ)) + (U := (-(247300147688838586911 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655_16 : Uω (aρ 16) (bρ 16) (388545108904183 / 512000000000000 : ℝ) ≤ @@ -1965,26 +1686,21 @@ lemma U_655_16 : have hlg : Real.log (154206482206035719 / 640000000000000000 : ℝ) ≤ (-(889484798547236706907 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (154206482206035719 / 640000000000000000 : ℝ) = - (154206482206035719 / 80000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (154206482206035719 / 80000000000000000 : ℚ)) - (U := (410166164515263293093 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (154206482206035719 / 80000000000000000 : ℝ) ≤ - (410166164515263293093 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (120465761943599 / 1250000000000000 : ℝ)) (q := - (154206482206035719 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (154206482206035719 / 640000000000000000 : ℚ)) + (r' := (154206482206035719 / 80000000000000000 : ℚ)) + (U := (-(889484798547236706907 / 625000000000000000000 : ℚ))) + (U' := (410166164515263293093 / 625000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (388545108904183 / 512000000000000 : ℚ)) + (s := (120465761943599 / 1250000000000000 : ℚ)) + (q := (154206482206035719 / 640000000000000000 : ℚ)) + (U := (-(889484798547236706907 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_655 : Uρ (388545108904183 / 512000000000000 : ℝ) ≤ @@ -2083,25 +1799,21 @@ lemma U_656_1 : have hlg : Real.log (241559448446699633 / 320000000000000000 : ℝ) ≤ (-(703013473485130443647 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (241559448446699633 / 320000000000000000 : ℝ) = - (241559448446699633 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (241559448446699633 / 160000000000000000 : ℚ)) - (U := (1029854477264869556353 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (241559448446699633 / 160000000000000000 : ℝ) ≤ - (1029854477264869556353 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3774355673699969 / 5000000000000000 : ℝ)) (q := - (241559448446699633 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (241559448446699633 / 320000000000000000 : ℚ)) + (r' := (241559448446699633 / 160000000000000000 : ℚ)) + (U := (-(703013473485130443647 / 2500000000000000000000 : ℚ))) + (U' := (1029854477264869556353 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (3774355673699969 / 5000000000000000 : ℚ)) + (q := (241559448446699633 / 320000000000000000 : ℚ)) + (U := (-(703013473485130443647 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_2 : Uω (aρ 2) (bρ 2) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2109,25 +1821,21 @@ lemma U_656_2 : have hlg : Real.log (48159002739941997 / 64000000000000000 : ℝ) ≤ (-(568749979081353075301 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48159002739941997 / 64000000000000000 : ℝ) = - (48159002739941997 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48159002739941997 / 32000000000000000 : ℚ)) - (U := (817544381518646924699 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (48159002739941997 / 32000000000000000 : ℝ) ≤ - (817544381518646924699 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1504940637644617 / 2000000000000000 : ℝ)) (q := - (48159002739941997 / 64000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48159002739941997 / 64000000000000000 : ℚ)) + (r' := (48159002739941997 / 32000000000000000 : ℚ)) + (U := (-(568749979081353075301 / 2000000000000000000000 : ℚ))) + (U' := (817544381518646924699 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (1504940637644617 / 2000000000000000 : ℚ)) + (q := (48159002739941997 / 64000000000000000 : ℚ)) + (U := (-(568749979081353075301 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_3 : Uω (aρ 3) (bρ 3) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2135,25 +1843,21 @@ lemma U_656_3 : have hlg : Real.log (239267019052619217 / 320000000000000000 : ℝ) ≤ (-(2907408327145662851251 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (239267019052619217 / 320000000000000000 : ℝ) = - (239267019052619217 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (239267019052619217 / 160000000000000000 : ℚ)) - (U := (4024063475854337148749 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (239267019052619217 / 160000000000000000 : ℝ) ≤ - (4024063475854337148749 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (934574953641239 / 1250000000000000 : ℝ)) (q := - (239267019052619217 / 320000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (239267019052619217 / 320000000000000000 : ℚ)) + (r' := (239267019052619217 / 160000000000000000 : ℚ)) + (U := (-(2907408327145662851251 / 10000000000000000000000 : ℚ))) + (U' := (4024063475854337148749 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (934574953641239 / 1250000000000000 : ℚ)) + (q := (239267019052619217 / 320000000000000000 : ℚ)) + (U := (-(2907408327145662851251 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_4 : Uω (aρ 4) (bρ 4) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2161,25 +1865,21 @@ lemma U_656_4 : have hlg : Real.log (47346385783190109 / 64000000000000000 : ℝ) ≤ (-(3013925961973787554127 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47346385783190109 / 64000000000000000 : ℝ) = - (47346385783190109 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47346385783190109 / 32000000000000000 : ℚ)) - (U := (3917545841026212445873 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47346385783190109 / 32000000000000000 : ℝ) ≤ - (3917545841026212445873 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (23113908364541 / 31250000000000 : ℝ)) (q := - (47346385783190109 / 64000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47346385783190109 / 64000000000000000 : ℚ)) + (r' := (47346385783190109 / 32000000000000000 : ℚ)) + (U := (-(3013925961973787554127 / 10000000000000000000000 : ℚ))) + (U' := (3917545841026212445873 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (23113908364541 / 31250000000000 : ℚ)) + (q := (47346385783190109 / 64000000000000000 : ℚ)) + (U := (-(3013925961973787554127 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_5 : Uω (aρ 5) (bρ 5) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2187,25 +1887,21 @@ lemma U_656_5 : have hlg : Real.log (232878269593854273 / 320000000000000000 : ℝ) ≤ (-(1589025632933657282791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (232878269593854273 / 320000000000000000 : ℝ) = - (232878269593854273 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (232878269593854273 / 160000000000000000 : ℚ)) - (U := (1876710268566342717209 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (232878269593854273 / 160000000000000000 : ℝ) ≤ - (1876710268566342717209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7273786888357103 / 10000000000000000 : ℝ)) (q := - (232878269593854273 / 320000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (232878269593854273 / 320000000000000000 : ℚ)) + (r' := (232878269593854273 / 160000000000000000 : ℚ)) + (U := (-(1589025632933657282791 / 5000000000000000000000 : ℚ))) + (U' := (1876710268566342717209 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (7273786888357103 / 10000000000000000 : ℚ)) + (q := (232878269593854273 / 320000000000000000 : ℚ)) + (U := (-(1589025632933657282791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_6 : Uω (aρ 6) (bρ 6) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2213,25 +1909,21 @@ lemma U_656_6 : have hlg : Real.log (227367313071814481 / 320000000000000000 : ℝ) ≤ (-(1708770832688818507607 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (227367313071814481 / 320000000000000000 : ℝ) = - (227367313071814481 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (227367313071814481 / 160000000000000000 : ℚ)) - (U := (1756965068811181492393 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (227367313071814481 / 160000000000000000 : ℝ) ≤ - (1756965068811181492393 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (443537030054351 / 625000000000000 : ℝ)) (q := - (227367313071814481 / 320000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (227367313071814481 / 320000000000000000 : ℚ)) + (r' := (227367313071814481 / 160000000000000000 : ℚ)) + (U := (-(1708770832688818507607 / 5000000000000000000000 : ℚ))) + (U' := (1756965068811181492393 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (443537030054351 / 625000000000000 : ℚ)) + (q := (227367313071814481 / 320000000000000000 : ℚ)) + (U := (-(1708770832688818507607 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_7 : Uω (aρ 7) (bρ 7) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2239,25 +1931,21 @@ lemma U_656_7 : have hlg : Real.log (43976520164748893 / 64000000000000000 : ℝ) ≤ (-(1876136121166841495429 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43976520164748893 / 64000000000000000 : ℝ) = - (43976520164748893 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43976520164748893 / 32000000000000000 : ℚ)) - (U := (1589599780333158504571 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (43976520164748893 / 32000000000000000 : ℝ) ≤ - (1589599780333158504571 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (171311483653131 / 250000000000000 : ℝ)) (q := - (43976520164748893 / 64000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43976520164748893 / 64000000000000000 : ℚ)) + (r' := (43976520164748893 / 32000000000000000 : ℚ)) + (U := (-(1876136121166841495429 / 5000000000000000000000 : ℚ))) + (U' := (1589599780333158504571 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (171311483653131 / 250000000000000 : ℚ)) + (q := (43976520164748893 / 64000000000000000 : ℚ)) + (U := (-(1876136121166841495429 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_8 : Uω (aρ 8) (bρ 8) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2265,25 +1953,21 @@ lemma U_656_8 : have hlg : Real.log (42036856658536173 / 64000000000000000 : ℝ) ≤ (-(420336310140069993621 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42036856658536173 / 64000000000000000 : ℝ) = - (42036856658536173 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42036856658536173 / 32000000000000000 : ℚ)) - (U := (272810870159930006379 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (42036856658536173 / 32000000000000000 : ℝ) ≤ - (272810870159930006379 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1305971230354753 / 2000000000000000 : ℝ)) (q := - (42036856658536173 / 64000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42036856658536173 / 64000000000000000 : ℚ)) + (r' := (42036856658536173 / 32000000000000000 : ℚ)) + (U := (-(420336310140069993621 / 1000000000000000000000 : ℚ))) + (U' := (272810870159930006379 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (1305971230354753 / 2000000000000000 : ℚ)) + (q := (42036856658536173 / 64000000000000000 : ℚ)) + (U := (-(420336310140069993621 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_9 : Uω (aρ 9) (bρ 9) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2291,25 +1975,21 @@ lemma U_656_9 : have hlg : Real.log (198162097165019857 / 320000000000000000 : ℝ) ≤ (-(2396178136091364650849 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (198162097165019857 / 320000000000000000 : ℝ) = - (198162097165019857 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (198162097165019857 / 160000000000000000 : ℚ)) - (U := (1069557765408635349151 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (198162097165019857 / 160000000000000000 : ℝ) ≤ - (1069557765408635349151 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (764929393394369 / 1250000000000000 : ℝ)) (q := - (198162097165019857 / 320000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (198162097165019857 / 320000000000000000 : ℚ)) + (r' := (198162097165019857 / 160000000000000000 : ℚ)) + (U := (-(2396178136091364650849 / 5000000000000000000000 : ℚ))) + (U' := (1069557765408635349151 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (764929393394369 / 1250000000000000 : ℚ)) + (q := (198162097165019857 / 320000000000000000 : ℚ)) + (U := (-(2396178136091364650849 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_10 : Uω (aρ 10) (bρ 10) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2317,26 +1997,21 @@ lemma U_656_10 : have hlg : Real.log (36775706510351901 / 64000000000000000 : ℝ) ≤ (-(692557006368090820231 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (36775706510351901 / 64000000000000000 : ℝ) = - (36775706510351901 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36775706510351901 / 32000000000000000 : ℚ)) - (U := (173876969006909179769 / 1250000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (36775706510351901 / 32000000000000000 : ℝ) ≤ - (173876969006909179769 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (280763569616059 / 500000000000000 : ℝ)) (q := - (36775706510351901 / 64000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36775706510351901 / 64000000000000000 : ℚ)) + (r' := (36775706510351901 / 32000000000000000 : ℚ)) + (U := (-(692557006368090820231 / 1250000000000000000000 : ℚ))) + (U' := (173876969006909179769 / 1250000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (280763569616059 / 500000000000000 : ℚ)) + (q := (36775706510351901 / 64000000000000000 : ℚ)) + (U := (-(692557006368090820231 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_11 : Uω (aρ 11) (bρ 11) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2344,26 +2019,21 @@ lemma U_656_11 : have hlg : Real.log (167593379872956993 / 320000000000000000 : ℝ) ≤ (-(6467803078306683504167 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (167593379872956993 / 320000000000000000 : ℝ) = - (167593379872956993 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (167593379872956993 / 160000000000000000 : ℚ)) - (U := (463668724693316495833 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (167593379872956993 / 160000000000000000 : ℝ) ≤ - (463668724693316495833 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5015925976101023 / 10000000000000000 : ℝ)) (q := - (167593379872956993 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (167593379872956993 / 320000000000000000 : ℚ)) + (r' := (167593379872956993 / 160000000000000000 : ℚ)) + (U := (-(6467803078306683504167 / 10000000000000000000000 : ℚ))) + (U' := (463668724693316495833 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (5015925976101023 / 10000000000000000 : ℚ)) + (q := (167593379872956993 / 320000000000000000 : ℚ)) + (U := (-(6467803078306683504167 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_12 : Uω (aρ 12) (bρ 12) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2371,26 +2041,21 @@ lemma U_656_12 : have hlg : Real.log (29952827199544909 / 64000000000000000 : ℝ) ≤ (-(237268551693682025271 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (29952827199544909 / 64000000000000000 : ℝ) = - (29952827199544909 / 16000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (29952827199544909 / 16000000000000000 : ℚ)) - (U := (195948435993817974729 / 312500000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (29952827199544909 / 16000000000000000 : ℝ) ≤ - (195948435993817974729 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (865059666116799 / 2000000000000000 : ℝ)) (q := - (29952827199544909 / 64000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (29952827199544909 / 64000000000000000 : ℚ)) + (r' := (29952827199544909 / 16000000000000000 : ℚ)) + (U := (-(237268551693682025271 / 312500000000000000000 : ℚ))) + (U' := (195948435993817974729 / 312500000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (865059666116799 / 2000000000000000 : ℚ)) + (q := (29952827199544909 / 64000000000000000 : ℚ)) + (U := (-(237268551693682025271 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_13 : Uω (aρ 13) (bρ 13) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2398,26 +2063,21 @@ lemma U_656_13 : have hlg : Real.log (131024801584548321 / 320000000000000000 : ℝ) ≤ (-(4464671824597859984033 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (131024801584548321 / 320000000000000000 : ℝ) = - (131024801584548321 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (131024801584548321 / 80000000000000000 : ℚ)) - (U := (2466799978402140015967 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (131024801584548321 / 80000000000000000 : ℝ) ≤ - (2466799978402140015967 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3553471671355481 / 10000000000000000 : ℝ)) (q := - (131024801584548321 / 320000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (131024801584548321 / 320000000000000000 : ℚ)) + (r' := (131024801584548321 / 80000000000000000 : ℚ)) + (U := (-(4464671824597859984033 / 5000000000000000000000 : ℚ))) + (U' := (2466799978402140015967 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (3553471671355481 / 10000000000000000 : ℚ)) + (q := (131024801584548321 / 320000000000000000 : ℚ)) + (U := (-(4464671824597859984033 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_14 : Uω (aρ 14) (bρ 14) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2425,26 +2085,21 @@ lemma U_656_14 : have hlg : Real.log (112163078801764561 / 320000000000000000 : ℝ) ≤ (-(163807362855826435447 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (112163078801764561 / 320000000000000000 : ℝ) = - (112163078801764561 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (112163078801764561 / 80000000000000000 : ℚ)) - (U := (52801130987923564553 / 156250000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (112163078801764561 / 80000000000000000 : ℝ) ≤ - (52801130987923564553 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (169908830154781 / 625000000000000 : ℝ)) (q := - (112163078801764561 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (112163078801764561 / 320000000000000000 : ℚ)) + (r' := (112163078801764561 / 80000000000000000 : ℚ)) + (U := (-(163807362855826435447 / 156250000000000000000 : ℚ))) + (U' := (52801130987923564553 / 156250000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (169908830154781 / 625000000000000 : ℚ)) + (q := (112163078801764561 / 320000000000000000 : ℚ)) + (U := (-(163807362855826435447 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_15 : Uω (aρ 15) (bρ 15) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2452,26 +2107,21 @@ lemma U_656_15 : have hlg : Real.log (94180874109960769 / 320000000000000000 : ℝ) ≤ (-(2446207738464103347739 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (94180874109960769 / 320000000000000000 : ℝ) = - (94180874109960769 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (94180874109960769 / 80000000000000000 : ℚ)) - (U := (326380982735896652261 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (94180874109960769 / 80000000000000000 : ℝ) ≤ - (326380982735896652261 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1854226766653759 / 10000000000000000 : ℝ)) (q := - (94180874109960769 / 320000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (94180874109960769 / 320000000000000000 : ℚ)) + (r' := (94180874109960769 / 80000000000000000 : ℚ)) + (U := (-(2446207738464103347739 / 2000000000000000000000 : ℚ))) + (U' := (326380982735896652261 / 2000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (1854226766653759 / 10000000000000000 : ℚ)) + (q := (94180874109960769 / 320000000000000000 : ℚ)) + (U := (-(2446207738464103347739 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656_16 : Uω (aρ 16) (bρ 16) (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2479,26 +2129,21 @@ lemma U_656_16 : have hlg : Real.log (78993868669915009 / 320000000000000000 : ℝ) ≤ (-(559580302932836820887 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 3 - (show - (78993868669915009 / 320000000000000000 : ℝ) = - (78993868669915009 / 40000000000000000 : ℝ) / 2 ^ 3 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (78993868669915009 / 40000000000000000 : ℚ)) - (U := (272196313427163179113 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (78993868669915009 / 40000000000000000 : ℝ) ≤ - (272196313427163179113 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1057410578160899 / 10000000000000000 : ℝ)) (q := - (78993868669915009 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (78993868669915009 / 320000000000000000 : ℚ)) + (r' := (78993868669915009 / 40000000000000000 : ℚ)) + (U := (-(559580302932836820887 / 400000000000000000000 : ℚ))) + (U' := (272196313427163179113 / 400000000000000000000 : ℚ)) + 3 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (194899235804257 / 256000000000000 : ℚ)) + (s := (1057410578160899 / 10000000000000000 : ℚ)) + (q := (78993868669915009 / 320000000000000000 : ℚ)) + (U := (-(559580302932836820887 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_656 : Uρ (194899235804257 / 256000000000000 : ℝ) ≤ @@ -2596,25 +2241,21 @@ lemma U_657_1 : have hlg : Real.log (96937120940872441 / 128000000000000000 : ℝ) ≤ (-(1389838665380847924577 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (96937120940872441 / 128000000000000000 : ℝ) = - (96937120940872441 / 64000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96937120940872441 / 64000000000000000 : ℚ)) - (U := (2075897236119152075423 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (96937120940872441 / 64000000000000000 : ℝ) ≤ - (2075897236119152075423 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1514638245234713 / 2000000000000000 : ℝ)) (q := - (96937120940872441 / 128000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96937120940872441 / 128000000000000000 : ℚ)) + (r' := (96937120940872441 / 64000000000000000 : ℚ)) + (U := (-(1389838665380847924577 / 5000000000000000000000 : ℚ))) + (U' := (2075897236119152075423 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (1514638245234713 / 2000000000000000 : ℚ)) + (q := (96937120940872441 / 128000000000000000 : ℚ)) + (U := (-(1389838665380847924577 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_2 : Uω (aρ 2) (bρ 2) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2622,25 +2263,21 @@ lemma U_657_2 : have hlg : Real.log (483156760039864957 / 640000000000000000 : ℝ) ≤ (-(2811270201498031012067 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (483156760039864957 / 640000000000000000 : ℝ) = - (483156760039864957 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (483156760039864957 / 320000000000000000 : ℚ)) - (U := (4120201601501968987933 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (483156760039864957 / 320000000000000000 : ℝ) ≤ - (4120201601501968987933 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3774591921459013 / 5000000000000000 : ℝ)) (q := - (483156760039864957 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (483156760039864957 / 640000000000000000 : ℚ)) + (r' := (483156760039864957 / 320000000000000000 : ℚ)) + (U := (-(2811270201498031012067 / 10000000000000000000000 : ℚ))) + (U' := (4120201601501968987933 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (3774591921459013 / 5000000000000000 : ℚ)) + (q := (483156760039864957 / 640000000000000000 : ℚ)) + (U := (-(2811270201498031012067 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_3 : Uω (aρ 3) (bρ 3) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2648,25 +2285,21 @@ lemma U_657_3 : have hlg : Real.log (480100844813911869 / 640000000000000000 : ℝ) ≤ (-(57494400179207807219 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (480100844813911869 / 640000000000000000 : ℝ) = - (480100844813911869 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (480100844813911869 / 320000000000000000 : ℚ)) - (U := (81135035880792192781 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (480100844813911869 / 320000000000000000 : ℝ) ≤ - (81135035880792192781 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (234408831201781 / 312500000000000 : ℝ)) (q := - (480100844813911869 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (480100844813911869 / 640000000000000000 : ℚ)) + (r' := (480100844813911869 / 320000000000000000 : ℚ)) + (U := (-(57494400179207807219 / 200000000000000000000 : ℚ))) + (U' := (81135035880792192781 / 200000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (234408831201781 / 312500000000000 : ℚ)) + (q := (480100844813911869 / 640000000000000000 : ℚ)) + (U := (-(57494400179207807219 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_4 : Uω (aρ 4) (bρ 4) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2674,25 +2307,21 @@ lemma U_657_4 : have hlg : Real.log (475030861445632029 / 640000000000000000 : ℝ) ≤ (-(1490442013525983607791 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (475030861445632029 / 640000000000000000 : ℝ) = - (475030861445632029 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (475030861445632029 / 320000000000000000 : ℚ)) - (U := (1975293887974016392209 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (475030861445632029 / 320000000000000000 : ℝ) ≤ - (1975293887974016392209 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7420939799263247 / 10000000000000000 : ℝ)) (q := - (475030861445632029 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (475030861445632029 / 640000000000000000 : ℚ)) + (r' := (475030861445632029 / 320000000000000000 : ℚ)) + (U := (-(1490442013525983607791 / 5000000000000000000000 : ℚ))) + (U' := (1975293887974016392209 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (7420939799263247 / 10000000000000000 : ℚ)) + (q := (475030861445632029 / 640000000000000000 : ℚ)) + (U := (-(1490442013525983607791 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_5 : Uω (aρ 5) (bρ 5) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2700,25 +2329,21 @@ lemma U_657_5 : have hlg : Real.log (467324028044376893 / 640000000000000000 : ℝ) ≤ (-(3144453088255461251677 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (467324028044376893 / 640000000000000000 : ℝ) = - (467324028044376893 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (467324028044376893 / 320000000000000000 : ℚ)) - (U := (3787018714744538748323 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (467324028044376893 / 320000000000000000 : ℝ) ≤ - (3787018714744538748323 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (114035799606391 / 156250000000000 : ℝ)) (q := - (467324028044376893 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (467324028044376893 / 640000000000000000 : ℚ)) + (r' := (467324028044376893 / 320000000000000000 : ℚ)) + (U := (-(3144453088255461251677 / 10000000000000000000000 : ℚ))) + (U' := (3787018714744538748323 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (114035799606391 / 156250000000000 : ℚ)) + (q := (467324028044376893 / 640000000000000000 : ℚ)) + (U := (-(3144453088255461251677 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_6 : Uω (aρ 6) (bρ 6) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2726,25 +2351,21 @@ lemma U_657_6 : have hlg : Real.log (456303229529549373 / 640000000000000000 : ℝ) ≤ (-(3383106105401640094821 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (456303229529549373 / 640000000000000000 : ℝ) = - (456303229529549373 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (456303229529549373 / 320000000000000000 : ℚ)) - (U := (3548365697598359905179 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (456303229529549373 / 320000000000000000 : ℝ) ≤ - (3548365697598359905179 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (890141449545083 / 1250000000000000 : ℝ)) (q := - (456303229529549373 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (456303229529549373 / 640000000000000000 : ℚ)) + (r' := (456303229529549373 / 320000000000000000 : ℚ)) + (U := (-(3383106105401640094821 / 10000000000000000000000 : ℚ))) + (U' := (3548365697598359905179 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (890141449545083 / 1250000000000000 : ℚ)) + (q := (456303229529549373 / 640000000000000000 : ℚ)) + (U := (-(3383106105401640094821 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_7 : Uω (aρ 7) (bρ 7) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2752,25 +2373,21 @@ lemma U_657_7 : have hlg : Real.log (441336204386488477 / 640000000000000000 : ℝ) ≤ (-(1858306114393186210517 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (441336204386488477 / 640000000000000000 : ℝ) = - (441336204386488477 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (441336204386488477 / 320000000000000000 : ℚ)) - (U := (1607429787106813789483 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (441336204386488477 / 320000000000000000 : ℝ) ≤ - (1607429787106813789483 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6877073441400011 / 10000000000000000 : ℝ)) (q := - (441336204386488477 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (441336204386488477 / 640000000000000000 : ℚ)) + (r' := (441336204386488477 / 320000000000000000 : ℚ)) + (U := (-(1858306114393186210517 / 5000000000000000000000 : ℚ))) + (U' := (1607429787106813789483 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (6877073441400011 / 10000000000000000 : ℚ)) + (q := (441336204386488477 / 640000000000000000 : ℚ)) + (U := (-(1858306114393186210517 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_8 : Uω (aρ 8) (bρ 8) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2778,25 +2395,21 @@ lemma U_657_8 : have hlg : Real.log (421944449282505021 / 640000000000000000 : ℝ) ≤ (-(2082972537469778711169 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (421944449282505021 / 640000000000000000 : ℝ) = - (421944449282505021 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (421944449282505021 / 320000000000000000 : ℚ)) - (U := (1382763364030221288831 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (421944449282505021 / 320000000000000000 : ℝ) ≤ - (1382763364030221288831 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (409663921608783 / 625000000000000 : ℝ)) (q := - (421944449282505021 / 640000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (421944449282505021 / 640000000000000000 : ℚ)) + (r' := (421944449282505021 / 320000000000000000 : ℚ)) + (U := (-(2082972537469778711169 / 5000000000000000000000 : ℚ))) + (U' := (1382763364030221288831 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (409663921608783 / 625000000000000 : ℚ)) + (q := (421944449282505021 / 640000000000000000 : ℚ)) + (U := (-(2082972537469778711169 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_9 : Uω (aρ 9) (bρ 9) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2804,25 +2417,21 @@ lemma U_657_9 : have hlg : Real.log (397909545135901917 / 640000000000000000 : ℝ) ≤ (-(4752434701677612012609 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (397909545135901917 / 640000000000000000 : ℝ) = - (397909545135901917 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (397909545135901917 / 320000000000000000 : ℚ)) - (U := (2179037101322387987391 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (397909545135901917 / 320000000000000000 : ℝ) ≤ - (2179037101322387987391 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6144497619519181 / 10000000000000000 : ℝ)) (q := - (397909545135901917 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (397909545135901917 / 640000000000000000 : ℚ)) + (r' := (397909545135901917 / 320000000000000000 : ℚ)) + (U := (-(4752434701677612012609 / 10000000000000000000000 : ℚ))) + (U' := (2179037101322387987391 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (6144497619519181 / 10000000000000000 : ℚ)) + (q := (397909545135901917 / 640000000000000000 : ℚ)) + (U := (-(4752434701677612012609 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_10 : Uω (aρ 10) (bρ 10) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2830,26 +2439,21 @@ lemma U_657_10 : have hlg : Real.log (369360137484945533 / 640000000000000000 : ℝ) ≤ (-(1374240064175814711503 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (369360137484945533 / 640000000000000000 : ℝ) = - (369360137484945533 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (369360137484945533 / 320000000000000000 : ℚ)) - (U := (358627886574185288497 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (369360137484945533 / 320000000000000000 : ℝ) ≤ - (358627886574185288497 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2820443831960897 / 5000000000000000 : ℝ)) (q := - (369360137484945533 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (369360137484945533 / 640000000000000000 : ℚ)) + (r' := (369360137484945533 / 320000000000000000 : ℚ)) + (U := (-(1374240064175814711503 / 2500000000000000000000 : ℚ))) + (U' := (358627886574185288497 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (2820443831960897 / 5000000000000000 : ℚ)) + (q := (369360137484945533 / 640000000000000000 : ℚ)) + (U := (-(1374240064175814711503 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_11 : Uω (aρ 11) (bρ 11) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2857,26 +2461,21 @@ lemma U_657_11 : have hlg : Real.log (67364451149068953 / 128000000000000000 : ℝ) ≤ (-(6419128159047950867803 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (67364451149068953 / 128000000000000000 : ℝ) = - (67364451149068953 / 64000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (67364451149068953 / 64000000000000000 : ℚ)) - (U := (512343643952049132197 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (67364451149068953 / 64000000000000000 : ℝ) ≤ - (512343643952049132197 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (504255548576427 / 1000000000000000 : ℝ)) (q := - (67364451149068953 / 128000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (67364451149068953 / 128000000000000000 : ℚ)) + (r' := (67364451149068953 / 64000000000000000 : ℚ)) + (U := (-(6419128159047950867803 / 10000000000000000000000 : ℚ))) + (U' := (512343643952049132197 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (504255548576427 / 1000000000000000 : ℚ)) + (q := (67364451149068953 / 128000000000000000 : ℚ)) + (U := (-(6419128159047950867803 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_12 : Uω (aρ 12) (bρ 12) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2884,26 +2483,21 @@ lemma U_657_12 : have hlg : Real.log (301222719783302717 / 640000000000000000 : ℝ) ≤ (-(942022814831744407111 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (301222719783302717 / 640000000000000000 : ℝ) = - (301222719783302717 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (301222719783302717 / 160000000000000000 : ℚ)) - (U := (790845135918255592889 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (301222719783302717 / 160000000000000000 : ℝ) ≤ - (790845135918255592889 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (17006914389201 / 39062500000000 : ℝ)) (q := - (301222719783302717 / 640000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (301222719783302717 / 640000000000000000 : ℚ)) + (r' := (301222719783302717 / 160000000000000000 : ℚ)) + (U := (-(942022814831744407111 / 1250000000000000000000 : ℚ))) + (U' := (790845135918255592889 / 1250000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (17006914389201 / 39062500000000 : ℚ)) + (q := (301222719783302717 / 640000000000000000 : ℚ)) + (U := (-(942022814831744407111 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_13 : Uω (aρ 13) (bρ 13) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2911,26 +2505,21 @@ lemma U_657_13 : have hlg : Real.log (263852976883560349 / 640000000000000000 : ℝ) ≤ (-(4430380667806009793779 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (263852976883560349 / 640000000000000000 : ℝ) = - (263852976883560349 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (263852976883560349 / 160000000000000000 : ℚ)) - (U := (2501091135193990206221 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (263852976883560349 / 160000000000000000 : ℝ) ≤ - (2501091135193990206221 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3585347359613507 / 10000000000000000 : ℝ)) (q := - (263852976883560349 / 640000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (263852976883560349 / 640000000000000000 : ℚ)) + (r' := (263852976883560349 / 160000000000000000 : ℚ)) + (U := (-(4430380667806009793779 / 5000000000000000000000 : ℚ))) + (U' := (2501091135193990206221 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (3585347359613507 / 10000000000000000 : ℚ)) + (q := (263852976883560349 / 640000000000000000 : ℚ)) + (U := (-(4430380667806009793779 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_14 : Uω (aρ 14) (bρ 14) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2938,26 +2527,21 @@ lemma U_657_14 : have hlg : Real.log (45268193150524441 / 128000000000000000 : ℝ) ≤ (-(5197128077412783468093 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (45268193150524441 / 128000000000000000 : ℝ) = - (45268193150524441 / 32000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45268193150524441 / 32000000000000000 : ℚ)) - (U := (1734343725587216531907 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (45268193150524441 / 32000000000000000 : ℝ) ≤ - (1734343725587216531907 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (275702429681669 / 1000000000000000 : ℝ)) (q := - (45268193150524441 / 128000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45268193150524441 / 128000000000000000 : ℚ)) + (r' := (45268193150524441 / 32000000000000000 : ℚ)) + (U := (-(5197128077412783468093 / 5000000000000000000000 : ℚ))) + (U' := (1734343725587216531907 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (275702429681669 / 1000000000000000 : ℚ)) + (q := (45268193150524441 / 128000000000000000 : ℚ)) + (U := (-(5197128077412783468093 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_15 : Uω (aρ 15) (bρ 15) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2965,26 +2549,21 @@ lemma U_657_15 : have hlg : Real.log (190829779040784189 / 640000000000000000 : ℝ) ≤ (-(12100863543607861278483 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (190829779040784189 / 640000000000000000 : ℝ) = - (190829779040784189 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (190829779040784189 / 160000000000000000 : ℚ)) - (U := (1762080062392138721517 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (190829779040784189 / 160000000000000000 : ℝ) ≤ - (1762080062392138721517 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (59589780921461 / 312500000000000 : ℝ)) (q := - (190829779040784189 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (190829779040784189 / 640000000000000000 : ℚ)) + (r' := (190829779040784189 / 160000000000000000 : ℚ)) + (U := (-(12100863543607861278483 / 10000000000000000000000 : ℚ))) + (U' := (1762080062392138721517 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (59589780921461 / 312500000000000 : ℚ)) + (q := (190829779040784189 / 640000000000000000 : ℚ)) + (U := (-(12100863543607861278483 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657_16 : Uω (aρ 16) (bρ 16) (78210366862569 / 102400000000000 : ℝ) ≤ @@ -2992,26 +2571,21 @@ lemma U_657_16 : have hlg : Real.log (161540954567697789 / 640000000000000000 : ℝ) ≤ (-(6883547383324041154463 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (161540954567697789 / 640000000000000000 : ℝ) = - (161540954567697789 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (161540954567697789 / 160000000000000000 : ℚ)) - (U := (47924419675958845537 / 5000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (161540954567697789 / 160000000000000000 : ℝ) ≤ - (47924419675958845537 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (571984438106401 / 5000000000000000 : ℝ)) (q := - (161540954567697789 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (161540954567697789 / 640000000000000000 : ℚ)) + (r' := (161540954567697789 / 160000000000000000 : ℚ)) + (U := (-(6883547383324041154463 / 5000000000000000000000 : ℚ))) + (U' := (47924419675958845537 / 5000000000000000000000 : ℚ)) + 2 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (78210366862569 / 102400000000000 : ℚ)) + (s := (571984438106401 / 5000000000000000 : ℚ)) + (q := (161540954567697789 / 640000000000000000 : ℚ)) + (U := (-(6883547383324041154463 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_657 : Uρ (78210366862569 / 102400000000000 : ℝ) ≤ @@ -3105,25 +2679,21 @@ lemma U_658_1 : have hlg : Real.log (60781539060846823 / 80000000000000000 : ℝ) ≤ (-(171712828384726161937 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (60781539060846823 / 80000000000000000 : ℝ) = - (60781539060846823 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (60781539060846823 / 40000000000000000 : ℚ)) - (U := (261504159302773838063 / 625000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (60781539060846823 / 40000000000000000 : ℝ) ≤ - (261504159302773838063 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7597671104054987 / 10000000000000000 : ℝ)) (q := - (60781539060846823 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (60781539060846823 / 80000000000000000 : ℚ)) + (r' := (60781539060846823 / 40000000000000000 : ℚ)) + (U := (-(171712828384726161937 / 625000000000000000000 : ℚ))) + (U' := (261504159302773838063 / 625000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (7597671104054987 / 10000000000000000 : ℚ)) + (q := (60781539060846823 / 80000000000000000 : ℚ)) + (U := (-(171712828384726161937 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_2 : Uω (aρ 2) (bρ 2) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3131,25 +2701,21 @@ lemma U_658_2 : have hlg : Real.log (60590436561394599 / 80000000000000000 : ℝ) ≤ (-(2778895663106141822649 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (60590436561394599 / 80000000000000000 : ℝ) = - (60590436561394599 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (60590436561394599 / 40000000000000000 : ℚ)) - (U := (4152576139893858177351 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (60590436561394599 / 40000000000000000 : ℝ) ≤ - (4152576139893858177351 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7573664491701931 / 10000000000000000 : ℝ)) (q := - (60590436561394599 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (60590436561394599 / 80000000000000000 : ℚ)) + (r' := (60590436561394599 / 40000000000000000 : ℚ)) + (U := (-(2778895663106141822649 / 10000000000000000000000 : ℚ))) + (U' := (4152576139893858177351 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (7573664491701931 / 10000000000000000 : ℚ)) + (q := (60590436561394599 / 80000000000000000 : ℚ)) + (U := (-(2778895663106141822649 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_3 : Uω (aρ 3) (bρ 3) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3157,25 +2723,21 @@ lemma U_658_3 : have hlg : Real.log (60208456356289091 / 80000000000000000 : ℝ) ≤ (-(2842138209295904021429 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (60208456356289091 / 80000000000000000 : ℝ) = - (60208456356289091 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (60208456356289091 / 40000000000000000 : ℚ)) - (U := (4089333593704095978571 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (60208456356289091 / 40000000000000000 : ℝ) ≤ - (4089333593704095978571 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3762782773387777 / 5000000000000000 : ℝ)) (q := - (60208456356289091 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (60208456356289091 / 80000000000000000 : ℚ)) + (r' := (60208456356289091 / 40000000000000000 : ℚ)) + (U := (-(2842138209295904021429 / 10000000000000000000000 : ℚ))) + (U' := (4089333593704095978571 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (3762782773387777 / 5000000000000000 : ℚ)) + (q := (60208456356289091 / 80000000000000000 : ℚ)) + (U := (-(2842138209295904021429 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_4 : Uω (aρ 4) (bρ 4) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3183,25 +2745,21 @@ lemma U_658_4 : have hlg : Real.log (59574732885589659 / 80000000000000000 : ℝ) ≤ (-(1473975475526614955667 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (59574732885589659 / 80000000000000000 : ℝ) = - (59574732885589659 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59574732885589659 / 40000000000000000 : ℚ)) - (U := (1991760425973385044333 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59574732885589659 / 40000000000000000 : ℝ) ≤ - (1991760425973385044333 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (116334825940089 / 156250000000000 : ℝ)) (q := - (59574732885589659 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59574732885589659 / 80000000000000000 : ℚ)) + (r' := (59574732885589659 / 40000000000000000 : ℚ)) + (U := (-(1473975475526614955667 / 5000000000000000000000 : ℚ))) + (U' := (1991760425973385044333 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (116334825940089 / 156250000000000 : ℚ)) + (q := (59574732885589659 / 80000000000000000 : ℚ)) + (U := (-(1473975475526614955667 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_5 : Uω (aρ 5) (bρ 5) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3209,25 +2767,21 @@ lemma U_658_5 : have hlg : Real.log (11722287791169907 / 16000000000000000 : ℝ) ≤ (-(12443870114242395501 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11722287791169907 / 16000000000000000 : ℝ) = - (11722287791169907 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11722287791169907 / 8000000000000000 : ℚ)) - (U := (15282017097757604499 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (11722287791169907 / 8000000000000000 : ℝ) ≤ - (15282017097757604499 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1464559059413133 / 2000000000000000 : ℝ)) (q := - (11722287791169907 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11722287791169907 / 16000000000000000 : ℚ)) + (r' := (11722287791169907 / 8000000000000000 : ℚ)) + (U := (-(12443870114242395501 / 40000000000000000000 : ℚ))) + (U' := (15282017097757604499 / 40000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (1464559059413133 / 2000000000000000 : ℚ)) + (q := (11722287791169907 / 16000000000000000 : ℚ)) + (U := (-(12443870114242395501 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_6 : Uω (aρ 6) (bρ 6) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3235,25 +2789,21 @@ lemma U_658_6 : have hlg : Real.log (57233977485193759 / 80000000000000000 : ℝ) ≤ (-(3348789004045531172871 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (57233977485193759 / 80000000000000000 : ℝ) = - (57233977485193759 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (57233977485193759 / 40000000000000000 : ℚ)) - (U := (3582682798954468827129 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (57233977485193759 / 40000000000000000 : ℝ) ≤ - (3582682798954468827129 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7145670304541721 / 10000000000000000 : ℝ)) (q := - (57233977485193759 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (57233977485193759 / 80000000000000000 : ℚ)) + (r' := (57233977485193759 / 40000000000000000 : ℚ)) + (U := (-(3348789004045531172871 / 10000000000000000000000 : ℚ))) + (U' := (3582682798954468827129 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (7145670304541721 / 10000000000000000 : ℚ)) + (q := (57233977485193759 / 80000000000000000 : ℚ)) + (U := (-(3348789004045531172871 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_7 : Uω (aρ 7) (bρ 7) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3261,25 +2811,21 @@ lemma U_658_7 : have hlg : Real.log (11072679413570503 / 16000000000000000 : ℝ) ≤ (-(3681079617672882922721 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11072679413570503 / 16000000000000000 : ℝ) = - (11072679413570503 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11072679413570503 / 8000000000000000 : ℚ)) - (U := (3250392185327117077279 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (11072679413570503 / 8000000000000000 : ℝ) ≤ - (3250392185327117077279 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (690168658096641 / 1000000000000000 : ℝ)) (q := - (11072679413570503 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11072679413570503 / 16000000000000000 : ℚ)) + (r' := (11072679413570503 / 8000000000000000 : ℚ)) + (U := (-(3681079617672882922721 / 10000000000000000000000 : ℚ))) + (U' := (3250392185327117077279 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (690168658096641 / 1000000000000000 : ℚ)) + (q := (11072679413570503 / 16000000000000000 : ℚ)) + (U := (-(3681079617672882922721 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_8 : Uω (aρ 8) (bρ 8) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3287,25 +2833,21 @@ lemma U_658_8 : have hlg : Real.log (52940032909125299 / 80000000000000000 : ℝ) ≤ (-(3225521999879289743 / 7812500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (52940032909125299 / 80000000000000000 : ℝ) = - (52940032909125299 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (52940032909125299 / 40000000000000000 : ℚ)) - (U := (2189690346214460257 / 7812500000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (52940032909125299 / 40000000000000000 : ℝ) ≤ - (2189690346214460257 / 7812500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3289693596312303 / 5000000000000000 : ℝ)) (q := - (52940032909125299 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (52940032909125299 / 80000000000000000 : ℚ)) + (r' := (52940032909125299 / 40000000000000000 : ℚ)) + (U := (-(3225521999879289743 / 7812500000000000000 : ℚ))) + (U' := (2189690346214460257 / 7812500000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (3289693596312303 / 5000000000000000 : ℚ)) + (q := (52940032909125299 / 80000000000000000 : ℚ)) + (U := (-(3225521999879289743 / 7812500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_9 : Uω (aρ 9) (bρ 9) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3313,25 +2855,21 @@ lemma U_658_9 : have hlg : Real.log (49936843275116379 / 80000000000000000 : ℝ) ≤ (-(4712675619102600426311 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49936843275116379 / 80000000000000000 : ℝ) = - (49936843275116379 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49936843275116379 / 40000000000000000 : ℚ)) - (U := (2218796183897399573689 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49936843275116379 / 40000000000000000 : ℝ) ≤ - (2218796183897399573689 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (771194426560297 / 1250000000000000 : ℝ)) (q := - (49936843275116379 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49936843275116379 / 80000000000000000 : ℚ)) + (r' := (49936843275116379 / 40000000000000000 : ℚ)) + (U := (-(4712675619102600426311 / 10000000000000000000000 : ℚ))) + (U' := (2218796183897399573689 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (771194426560297 / 1250000000000000 : ℚ)) + (q := (49936843275116379 / 80000000000000000 : ℚ)) + (U := (-(4712675619102600426311 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_10 : Uω (aρ 10) (bρ 10) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3339,26 +2877,21 @@ lemma U_658_10 : have hlg : Real.log (46370361042211667 / 80000000000000000 : ℝ) ≤ (-(2726830749623017945813 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46370361042211667 / 80000000000000000 : ℝ) = - (46370361042211667 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46370361042211667 / 40000000000000000 : ℚ)) - (U := (738905151876982054187 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (46370361042211667 / 40000000000000000 : ℝ) ≤ - (738905151876982054187 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2833246943875599 / 5000000000000000 : ℝ)) (q := - (46370361042211667 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46370361042211667 / 80000000000000000 : ℚ)) + (r' := (46370361042211667 / 40000000000000000 : ℚ)) + (U := (-(2726830749623017945813 / 5000000000000000000000 : ℚ))) + (U' := (738905151876982054187 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (2833246943875599 / 5000000000000000 : ℚ)) + (q := (46370361042211667 / 80000000000000000 : ℚ)) + (U := (-(2726830749623017945813 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_11 : Uω (aρ 11) (bρ 11) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3366,26 +2899,21 @@ lemma U_658_11 : have hlg : Real.log (42307132269084127 / 80000000000000000 : ℝ) ≤ (-(6370709510127633117299 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42307132269084127 / 80000000000000000 : ℝ) = - (42307132269084127 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42307132269084127 / 40000000000000000 : ℚ)) - (U := (560762292872366882701 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (42307132269084127 / 40000000000000000 : ℝ) ≤ - (560762292872366882701 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5069163320674313 / 10000000000000000 : ℝ)) (q := - (42307132269084127 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42307132269084127 / 80000000000000000 : ℚ)) + (r' := (42307132269084127 / 40000000000000000 : ℚ)) + (U := (-(6370709510127633117299 / 10000000000000000000000 : ℚ))) + (U' := (560762292872366882701 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (5069163320674313 / 10000000000000000 : ℚ)) + (q := (42307132269084127 / 80000000000000000 : ℚ)) + (U := (-(6370709510127633117299 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_12 : Uω (aρ 12) (bρ 12) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3393,26 +2921,21 @@ lemma U_658_12 : have hlg : Real.log (7572890600044083 / 16000000000000000 : ℝ) ≤ (-(7480138777450943837259 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7572890600044083 / 16000000000000000 : ℝ) = - (7572890600044083 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7572890600044083 / 4000000000000000 : ℚ)) - (U := (6382804828549056162741 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7572890600044083 / 4000000000000000 : ℝ) ≤ - (6382804828549056162741 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (876438720028677 / 2000000000000000 : ℝ)) (q := - (7572890600044083 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7572890600044083 / 16000000000000000 : ℚ)) + (r' := (7572890600044083 / 4000000000000000 : ℚ)) + (U := (-(7480138777450943837259 / 10000000000000000000000 : ℚ))) + (U' := (6382804828549056162741 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (876438720028677 / 2000000000000000 : ℚ)) + (q := (7572890600044083 / 16000000000000000 : ℚ)) + (U := (-(7480138777450943837259 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_13 : Uω (aρ 13) (bρ 13) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3420,26 +2943,21 @@ lemma U_658_13 : have hlg : Real.log (33206582909350039 / 80000000000000000 : ℝ) ≤ (-(8792784974843993706773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (33206582909350039 / 80000000000000000 : ℝ) = - (33206582909350039 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33206582909350039 / 20000000000000000 : ℚ)) - (U := (5070158631156006293227 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33206582909350039 / 20000000000000000 : ℝ) ≤ - (5070158631156006293227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3617107819020791 / 10000000000000000 : ℝ)) (q := - (33206582909350039 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33206582909350039 / 80000000000000000 : ℚ)) + (r' := (33206582909350039 / 20000000000000000 : ℚ)) + (U := (-(8792784974843993706773 / 10000000000000000000000 : ℚ))) + (U' := (5070158631156006293227 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (3617107819020791 / 10000000000000000 : ℚ)) + (q := (33206582909350039 / 80000000000000000 : ℚ)) + (U := (-(8792784974843993706773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_14 : Uω (aρ 14) (bρ 14) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3447,26 +2965,21 @@ lemma U_658_14 : have hlg : Real.log (28543210092723919 / 80000000000000000 : ℝ) ≤ (-(644129719662722860471 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28543210092723919 / 80000000000000000 : ℝ) = - (28543210092723919 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28543210092723919 / 20000000000000000 : ℚ)) - (U := (222304255712277139529 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28543210092723919 / 20000000000000000 : ℝ) ≤ - (222304255712277139529 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2795191899909261 / 10000000000000000 : ℝ)) (q := - (28543210092723919 / 80000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28543210092723919 / 80000000000000000 : ℚ)) + (r' := (28543210092723919 / 20000000000000000 : ℚ)) + (U := (-(644129719662722860471 / 625000000000000000000 : ℚ))) + (U' := (222304255712277139529 / 625000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (2795191899909261 / 10000000000000000 : ℚ)) + (q := (28543210092723919 / 80000000000000000 : ℚ)) + (U := (-(644129719662722860471 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_15 : Uω (aρ 15) (bρ 15) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3474,26 +2987,21 @@ lemma U_658_15 : have hlg : Real.log (24157790487552283 / 80000000000000000 : ℝ) ≤ (-(11974197185992771512583 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (24157790487552283 / 80000000000000000 : ℝ) = - (24157790487552283 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (24157790487552283 / 20000000000000000 : ℚ)) - (U := (1888746420007228487417 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (24157790487552283 / 20000000000000000 : ℝ) ≤ - (1888746420007228487417 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (244801284503919 / 1250000000000000 : ℝ)) (q := - (24157790487552283 / 80000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (24157790487552283 / 80000000000000000 : ℚ)) + (r' := (24157790487552283 / 20000000000000000 : ℚ)) + (U := (-(11974197185992771512583 / 10000000000000000000000 : ℚ))) + (U' := (1888746420007228487417 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (244801284503919 / 1250000000000000 : ℚ)) + (q := (24157790487552283 / 80000000000000000 : ℚ)) + (U := (-(11974197185992771512583 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658_16 : Uω (aρ 16) (bρ 16) (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3501,26 +3009,21 @@ lemma U_658_16 : have hlg : Real.log (20614313318481031 / 80000000000000000 : ℝ) ≤ (-(13560409783495217840437 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (20614313318481031 / 80000000000000000 : ℝ) = - (20614313318481031 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20614313318481031 / 20000000000000000 : ℚ)) - (U := (302533822504782159563 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20614313318481031 / 20000000000000000 : ℝ) ≤ - (302533822504782159563 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1224912635273539 / 10000000000000000 : ℝ)) (q := - (20614313318481031 / 80000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20614313318481031 / 80000000000000000 : ℚ)) + (r' := (20614313318481031 / 20000000000000000 : ℚ)) + (U := (-(13560409783495217840437 / 10000000000000000000000 : ℚ))) + (U' := (302533822504782159563 / 10000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (49038149627147 / 64000000000000 : ℚ)) + (s := (1224912635273539 / 10000000000000000 : ℚ)) + (q := (20614313318481031 / 80000000000000000 : ℚ)) + (U := (-(13560409783495217840437 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_658 : Uρ (49038149627147 / 64000000000000 : ℝ) ≤ @@ -3611,25 +3114,21 @@ lemma U_659_1 : have hlg : Real.log (487819020240911443 / 640000000000000000 : ℝ) ≤ (-(2715236991883287655507 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (487819020240911443 / 640000000000000000 : ℝ) = - (487819020240911443 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (487819020240911443 / 320000000000000000 : ℚ)) - (U := (4216234811116712344493 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (487819020240911443 / 320000000000000000 : ℝ) ≤ - (4216234811116712344493 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7622150981052799 / 10000000000000000 : ℝ)) (q := - (487819020240911443 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (487819020240911443 / 640000000000000000 : ℚ)) + (r' := (487819020240911443 / 320000000000000000 : ℚ)) + (U := (-(2715236991883287655507 / 10000000000000000000000 : ℚ))) + (U' := (4216234811116712344493 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (7622150981052799 / 10000000000000000 : ℚ)) + (q := (487819020240911443 / 640000000000000000 : ℚ)) + (U := (-(2715236991883287655507 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_2 : Uω (aρ 2) (bρ 2) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3637,25 +3136,21 @@ lemma U_659_2 : have hlg : Real.log (486290224755123731 / 640000000000000000 : ℝ) ≤ (-(10986502406018490339 / 40000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (486290224755123731 / 640000000000000000 : ℝ) = - (486290224755123731 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (486290224755123731 / 320000000000000000 : ℚ)) - (U := (16739384805981509661 / 40000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (486290224755123731 / 320000000000000000 : ℝ) ≤ - (16739384805981509661 / 40000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7598145134631933 / 10000000000000000 : ℝ)) (q := - (486290224755123731 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (486290224755123731 / 640000000000000000 : ℚ)) + (r' := (486290224755123731 / 320000000000000000 : ℚ)) + (U := (-(10986502406018490339 / 40000000000000000000 : ℚ))) + (U' := (16739384805981509661 / 40000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (7598145134631933 / 10000000000000000 : ℚ)) + (q := (486290224755123731 / 640000000000000000 : ℚ)) + (U := (-(10986502406018490339 / 40000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_3 : Uω (aρ 3) (bρ 3) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3663,25 +3158,21 @@ lemma U_659_3 : have hlg : Real.log (483234456220980979 / 640000000000000000 : ℝ) ≤ (-(2809662236111423922899 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (483234456220980979 / 640000000000000000 : ℝ) = - (483234456220980979 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (483234456220980979 / 320000000000000000 : ℚ)) - (U := (4121809566888576077101 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (483234456220980979 / 320000000000000000 : ℝ) ≤ - (4121809566888576077101 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1887512118572493 / 2500000000000000 : ℝ)) (q := - (483234456220980979 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (483234456220980979 / 640000000000000000 : ℚ)) + (r' := (483234456220980979 / 320000000000000000 : ℚ)) + (U := (-(2809662236111423922899 / 10000000000000000000000 : ℚ))) + (U' := (4121809566888576077101 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (1887512118572493 / 2500000000000000 : ℚ)) + (q := (483234456220980979 / 640000000000000000 : ℚ)) + (U := (-(2809662236111423922899 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_4 : Uω (aρ 4) (bρ 4) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3689,25 +3180,21 @@ lemma U_659_4 : have hlg : Real.log (478164862768577587 / 640000000000000000 : ℝ) ≤ (-(1457563009387830351699 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (478164862768577587 / 640000000000000000 : ℝ) = - (478164862768577587 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (478164862768577587 / 320000000000000000 : ℚ)) - (U := (2008172892112169648301 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (478164862768577587 / 320000000000000000 : ℝ) ≤ - (2008172892112169648301 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3734958929983683 / 5000000000000000 : ℝ)) (q := - (478164862768577587 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (478164862768577587 / 640000000000000000 : ℚ)) + (r' := (478164862768577587 / 320000000000000000 : ℚ)) + (U := (-(1457563009387830351699 / 5000000000000000000000 : ℚ))) + (U' := (2008172892112169648301 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (3734958929983683 / 5000000000000000 : ℚ)) + (q := (478164862768577587 / 640000000000000000 : ℚ)) + (U := (-(1457563009387830351699 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_5 : Uω (aρ 5) (bρ 5) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3715,25 +3202,21 @@ lemma U_659_5 : have hlg : Real.log (470458990047537363 / 640000000000000000 : ℝ) ≤ (-(3077593833591589989139 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (470458990047537363 / 640000000000000000 : ℝ) = - (470458990047537363 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (470458990047537363 / 320000000000000000 : ℚ)) - (U := (3853877969408410010861 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (470458990047537363 / 320000000000000000 : ℝ) ≤ - (3853877969408410010861 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7347299256769859 / 10000000000000000 : ℝ)) (q := - (470458990047537363 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (470458990047537363 / 640000000000000000 : ℚ)) + (r' := (470458990047537363 / 320000000000000000 : ℚ)) + (U := (-(3077593833591589989139 / 10000000000000000000000 : ℚ))) + (U' := (3853877969408410010861 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (7347299256769859 / 10000000000000000 : ℚ)) + (q := (470458990047537363 / 640000000000000000 : ℚ)) + (U := (-(3077593833591589989139 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_6 : Uω (aρ 6) (bρ 6) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3741,25 +3224,21 @@ lemma U_659_6 : have hlg : Real.log (459440397333449523 / 640000000000000000 : ℝ) ≤ (-(1657294773584553884893 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (459440397333449523 / 640000000000000000 : ℝ) = - (459440397333449523 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (459440397333449523 / 320000000000000000 : ℚ)) - (U := (1808441127915446115107 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (459440397333449523 / 320000000000000000 : ℝ) ≤ - (1808441127915446115107 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3585104304797307 / 5000000000000000 : ℝ)) (q := - (459440397333449523 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (459440397333449523 / 640000000000000000 : ℚ)) + (r' := (459440397333449523 / 320000000000000000 : ℚ)) + (U := (-(1657294773584553884893 / 5000000000000000000000 : ℚ))) + (U' := (1808441127915446115107 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (3585104304797307 / 5000000000000000 : ℚ)) + (q := (459440397333449523 / 640000000000000000 : ℚ)) + (U := (-(1657294773584553884893 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_7 : Uω (aρ 7) (bρ 7) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3767,25 +3246,21 @@ lemma U_659_7 : have hlg : Real.log (444478118442517427 / 640000000000000000 : ℝ) ≤ (-(729134699404871384131 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (444478118442517427 / 640000000000000000 : ℝ) = - (444478118442517427 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (444478118442517427 / 320000000000000000 : ℚ)) - (U := (657159661195128615869 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (444478118442517427 / 320000000000000000 : ℝ) ≤ - (657159661195128615869 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3463149387506493 / 5000000000000000 : ℝ)) (q := - (444478118442517427 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (444478118442517427 / 640000000000000000 : ℚ)) + (r' := (444478118442517427 / 320000000000000000 : ℚ)) + (U := (-(729134699404871384131 / 2000000000000000000000 : ℚ))) + (U' := (657159661195128615869 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (3463149387506493 / 5000000000000000 : ℚ)) + (q := (444478118442517427 / 640000000000000000 : ℚ)) + (U := (-(729134699404871384131 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_8 : Uω (aρ 8) (bρ 8) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3793,25 +3268,21 @@ lemma U_659_8 : have hlg : Real.log (425096009329768787 / 640000000000000000 : ℝ) ≤ (-(4091531283765524748763 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (425096009329768787 / 640000000000000000 : ℝ) = - (425096009329768787 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (425096009329768787 / 320000000000000000 : ℚ)) - (U := (2839940519234475251237 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (425096009329768787 / 320000000000000000 : ℝ) ≤ - (2839940519234475251237 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6604149516579591 / 10000000000000000 : ℝ)) (q := - (425096009329768787 / 640000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (425096009329768787 / 640000000000000000 : ℚ)) + (r' := (425096009329768787 / 320000000000000000 : ℚ)) + (U := (-(4091531283765524748763 / 10000000000000000000000 : ℚ))) + (U' := (2839940519234475251237 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (6604149516579591 / 10000000000000000 : ℚ)) + (q := (425096009329768787 / 640000000000000000 : ℚ)) + (U := (-(4091531283765524748763 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_9 : Uω (aρ 9) (bρ 9) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3819,25 +3290,21 @@ lemma U_659_9 : have hlg : Real.log (401079799342275667 / 640000000000000000 : ℝ) ≤ (-(2336538838658455572537 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (401079799342275667 / 640000000000000000 : ℝ) = - (401079799342275667 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (401079799342275667 / 320000000000000000 : ℚ)) - (U := (1129197062841544427463 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (401079799342275667 / 320000000000000000 : ℝ) ≤ - (1129197062841544427463 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6194608582830431 / 10000000000000000 : ℝ)) (q := - (401079799342275667 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (401079799342275667 / 640000000000000000 : ℚ)) + (r' := (401079799342275667 / 320000000000000000 : ℚ)) + (U := (-(2336538838658455572537 / 5000000000000000000000 : ℚ))) + (U' := (1129197062841544427463 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (6194608582830431 / 10000000000000000 : ℚ)) + (q := (401079799342275667 / 640000000000000000 : ℚ)) + (U := (-(2336538838658455572537 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_10 : Uω (aρ 10) (bρ 10) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3845,26 +3312,21 @@ lemma U_659_10 : have hlg : Real.log (372565322001013043 / 640000000000000000 : ℝ) ≤ (-(2705278962857846117447 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (372565322001013043 / 640000000000000000 : ℝ) = - (372565322001013043 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (372565322001013043 / 320000000000000000 : ℚ)) - (U := (760456938642153882553 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (372565322001013043 / 320000000000000000 : ℝ) ≤ - (760456938642153882553 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2846045099705487 / 5000000000000000 : ℝ)) (q := - (372565322001013043 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (372565322001013043 / 640000000000000000 : ℚ)) + (r' := (372565322001013043 / 320000000000000000 : ℚ)) + (U := (-(2705278962857846117447 / 5000000000000000000000 : ℚ))) + (U' := (760456938642153882553 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (2846045099705487 / 5000000000000000 : ℚ)) + (q := (372565322001013043 / 640000000000000000 : ℚ)) + (U := (-(2705278962857846117447 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_11 : Uω (aρ 11) (bρ 11) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3872,26 +3334,21 @@ lemma U_659_11 : have hlg : Real.log (340091177832826643 / 640000000000000000 : ℝ) ≤ (-(1580636060845473348809 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (340091177832826643 / 640000000000000000 : ℝ) = - (340091177832826643 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (340091177832826643 / 320000000000000000 : ℚ)) - (U := (152231889904526651191 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (340091177832826643 / 320000000000000000 : ℝ) ≤ - (152231889904526651191 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5095749820360149 / 10000000000000000 : ℝ)) (q := - (340091177832826643 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (340091177832826643 / 640000000000000000 : ℚ)) + (r' := (340091177832826643 / 320000000000000000 : ℚ)) + (U := (-(1580636060845473348809 / 2500000000000000000000 : ℚ))) + (U' := (152231889904526651191 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (5095749820360149 / 10000000000000000 : ℚ)) + (q := (340091177832826643 / 640000000000000000 : ℚ)) + (U := (-(1580636060845473348809 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_12 : Uω (aρ 12) (bρ 12) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3899,26 +3356,21 @@ lemma U_659_12 : have hlg : Real.log (304607014493012307 / 640000000000000000 : ℝ) ≤ (-(742445707098810187001 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (304607014493012307 / 640000000000000000 : ℝ) = - (304607014493012307 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (304607014493012307 / 160000000000000000 : ℚ)) - (U := (643848653501189812999 / 1000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (304607014493012307 / 160000000000000000 : ℝ) ≤ - (643848653501189812999 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4410569812675951 / 10000000000000000 : ℝ)) (q := - (304607014493012307 / 640000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (304607014493012307 / 640000000000000000 : ℚ)) + (r' := (304607014493012307 / 160000000000000000 : ℚ)) + (U := (-(742445707098810187001 / 1000000000000000000000 : ℚ))) + (U' := (643848653501189812999 / 1000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (4410569812675951 / 10000000000000000 : ℚ)) + (q := (304607014493012307 / 640000000000000000 : ℚ)) + (U := (-(742445707098810187001 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_13 : Uω (aρ 13) (bρ 13) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3926,26 +3378,21 @@ lemma U_659_13 : have hlg : Real.log (267448758631353747 / 640000000000000000 : ℝ) ≤ (-(8725401843653626065141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (267448758631353747 / 640000000000000000 : ℝ) = - (267448758631353747 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (267448758631353747 / 160000000000000000 : ℚ)) - (U := (5137541762346373934859 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (267448758631353747 / 160000000000000000 : ℝ) ≤ - (5137541762346373934859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3648756058594121 / 10000000000000000 : ℝ)) (q := - (267448758631353747 / 640000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (267448758631353747 / 640000000000000000 : ℚ)) + (r' := (267448758631353747 / 160000000000000000 : ℚ)) + (U := (-(8725401843653626065141 / 10000000000000000000000 : ℚ))) + (U' := (5137541762346373934859 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (3648756058594121 / 10000000000000000 : ℚ)) + (q := (267448758631353747 / 640000000000000000 : ℚ)) + (U := (-(8725401843653626065141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_14 : Uω (aρ 14) (bρ 14) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3953,26 +3400,21 @@ lemma U_659_14 : have hlg : Real.log (230340710504174291 / 640000000000000000 : ℝ) ≤ (-(5109543065045329487741 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (230340710504174291 / 640000000000000000 : ℝ) = - (230340710504174291 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (230340710504174291 / 160000000000000000 : ℚ)) - (U := (1821928737954670512259 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (230340710504174291 / 160000000000000000 : ℝ) ≤ - (1821928737954670512259 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2833056839664763 / 10000000000000000 : ℝ)) (q := - (230340710504174291 / 640000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (230340710504174291 / 640000000000000000 : ℚ)) + (r' := (230340710504174291 / 160000000000000000 : ℚ)) + (U := (-(5109543065045329487741 / 5000000000000000000000 : ℚ))) + (U' := (1821928737954670512259 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (2833056839664763 / 10000000000000000 : ℚ)) + (q := (230340710504174291 / 640000000000000000 : ℚ)) + (U := (-(5109543065045329487741 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_15 : Uω (aρ 15) (bρ 15) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -3980,26 +3422,21 @@ lemma U_659_15 : have hlg : Real.log (195662113945982771 / 640000000000000000 : ℝ) ≤ (-(5925394563411376445939 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (195662113945982771 / 640000000000000000 : ℝ) = - (195662113945982771 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (195662113945982771 / 160000000000000000 : ℚ)) - (U := (1006077239588623554061 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (195662113945982771 / 160000000000000000 : ℝ) ≤ - (1006077239588623554061 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1004461987318139 / 5000000000000000 : ℝ)) (q := - (195662113945982771 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (195662113945982771 / 640000000000000000 : ℚ)) + (r' := (195662113945982771 / 160000000000000000 : ℚ)) + (U := (-(5925394563411376445939 / 5000000000000000000000 : ℚ))) + (U' := (1006077239588623554061 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (1004461987318139 / 5000000000000000 : ℚ)) + (q := (195662113945982771 / 640000000000000000 : ℚ)) + (U := (-(5925394563411376445939 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659_16 : Uω (aρ 16) (bρ 16) (393558559721507 / 512000000000000 : ℝ) ≤ @@ -4007,26 +3444,21 @@ lemma U_659_16 : have hlg : Real.log (168141933781848243 / 640000000000000000 : ℝ) ≤ (-(6683298545853789424627 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (168141933781848243 / 640000000000000000 : ℝ) = - (168141933781848243 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (168141933781848243 / 160000000000000000 : ℚ)) - (U := (248173257146210575373 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (168141933781848243 / 160000000000000000 : ℝ) ≤ - (248173257146210575373 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (650644998008537 / 5000000000000000 : ℝ)) (q := - (168141933781848243 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (168141933781848243 / 640000000000000000 : ℚ)) + (r' := (168141933781848243 / 160000000000000000 : ℚ)) + (U := (-(6683298545853789424627 / 5000000000000000000000 : ℚ))) + (U' := (248173257146210575373 / 5000000000000000000000 : ℚ)) + 2 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (393558559721507 / 512000000000000 : ℚ)) + (s := (650644998008537 / 5000000000000000 : ℚ)) + (q := (168141933781848243 / 640000000000000000 : ℚ)) + (U := (-(6683298545853789424627 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_659 : Uρ (393558559721507 / 512000000000000 : ℝ) ≤ @@ -4126,25 +3558,21 @@ lemma U_660_1 : have hlg : Real.log (244692863983522167 / 320000000000000000 : ℝ) ≤ (-(2683171878172451050851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (244692863983522167 / 320000000000000000 : ℝ) = - (244692863983522167 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (244692863983522167 / 160000000000000000 : ℚ)) - (U := (4248299924827548949149 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (244692863983522167 / 160000000000000000 : ℝ) ≤ - (4248299924827548949149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7646630857175487 / 10000000000000000 : ℝ)) (q := - (244692863983522167 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (244692863983522167 / 320000000000000000 : ℚ)) + (r' := (244692863983522167 / 160000000000000000 : ℚ)) + (U := (-(2683171878172451050851 / 10000000000000000000000 : ℚ))) + (U' := (4248299924827548949149 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (7646630857175487 / 10000000000000000 : ℚ)) + (q := (244692863983522167 / 320000000000000000 : ℚ)) + (U := (-(2683171878172451050851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_2 : Uω (aρ 2) (bρ 2) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4152,25 +3580,21 @@ lemma U_660_2 : have hlg : Real.log (48785695683357067 / 64000000000000000 : ℝ) ≤ (-(1357229672258682030653 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48785695683357067 / 64000000000000000 : ℝ) = - (48785695683357067 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48785695683357067 / 32000000000000000 : ℚ)) - (U := (2108506229241317969347 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (48785695683357067 / 32000000000000000 : ℝ) ≤ - (2108506229241317969347 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1524525154352887 / 2000000000000000 : ℝ)) (q := - (48785695683357067 / 64000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48785695683357067 / 64000000000000000 : ℚ)) + (r' := (48785695683357067 / 32000000000000000 : ℚ)) + (U := (-(1357229672258682030653 / 5000000000000000000000 : ℚ))) + (U' := (2108506229241317969347 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (1524525154352887 / 2000000000000000 : ℚ)) + (q := (48785695683357067 / 64000000000000000 : ℚ)) + (U := (-(1357229672258682030653 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_3 : Uω (aρ 3) (bρ 3) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4178,25 +3602,21 @@ lemma U_660_3 : have hlg : Real.log (242400630466186087 / 320000000000000000 : ℝ) ≤ (-(1388645702044695172863 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (242400630466186087 / 320000000000000000 : ℝ) = - (242400630466186087 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (242400630466186087 / 160000000000000000 : ℚ)) - (U := (2077090199455304827137 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (242400630466186087 / 160000000000000000 : ℝ) ≤ - (2077090199455304827137 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3787265690600991 / 5000000000000000 : ℝ)) (q := - (242400630466186087 / 320000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (242400630466186087 / 320000000000000000 : ℚ)) + (r' := (242400630466186087 / 160000000000000000 : ℚ)) + (U := (-(1388645702044695172863 / 5000000000000000000000 : ℚ))) + (U' := (2077090199455304827137 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (3787265690600991 / 5000000000000000 : ℚ)) + (q := (242400630466186087 / 320000000000000000 : ℚ)) + (U := (-(1388645702044695172863 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_4 : Uω (aρ 4) (bρ 4) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4204,25 +3624,21 @@ lemma U_660_4 : have hlg : Real.log (239865930258189943 / 320000000000000000 : ℝ) ≤ (-(720602130511302706029 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (239865930258189943 / 320000000000000000 : ℝ) = - (239865930258189943 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (239865930258189943 / 160000000000000000 : ℚ)) - (U := (1012265820238697293971 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (239865930258189943 / 160000000000000000 : ℝ) ≤ - (1012265820238697293971 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7494406799267223 / 10000000000000000 : ℝ)) (q := - (239865930258189943 / 320000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (239865930258189943 / 320000000000000000 : ℚ)) + (r' := (239865930258189943 / 160000000000000000 : ℚ)) + (U := (-(720602130511302706029 / 2500000000000000000000 : ℚ))) + (U' := (1012265820238697293971 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (7494406799267223 / 10000000000000000 : ℚ)) + (q := (239865930258189943 / 320000000000000000 : ℚ)) + (U := (-(720602130511302706029 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_5 : Uω (aρ 5) (bρ 5) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4230,25 +3646,21 @@ lemma U_660_5 : have hlg : Real.log (47202646329847147 / 64000000000000000 : ℝ) ≤ (-(1522165628847763865193 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47202646329847147 / 64000000000000000 : ℝ) = - (47202646329847147 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47202646329847147 / 32000000000000000 : ℚ)) - (U := (1943570272652236134807 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47202646329847147 / 32000000000000000 : ℝ) ≤ - (1943570272652236134807 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1474360611108517 / 2000000000000000 : ℝ)) (q := - (47202646329847147 / 64000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47202646329847147 / 64000000000000000 : ℚ)) + (r' := (47202646329847147 / 32000000000000000 : ℚ)) + (U := (-(1522165628847763865193 / 5000000000000000000000 : ℚ))) + (U' := (1943570272652236134807 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (1474360611108517 / 2000000000000000 : ℚ)) + (q := (47202646329847147 / 64000000000000000 : ℚ)) + (U := (-(1522165628847763865193 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_6 : Uω (aρ 6) (bρ 6) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4256,25 +3668,21 @@ lemma U_660_6 : have hlg : Real.log (230504481008619239 / 320000000000000000 : ℝ) ≤ (-(20503168306351268131 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (230504481008619239 / 320000000000000000 : ℝ) = - (230504481008619239 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (230504481008619239 / 160000000000000000 : ℚ)) - (U := (22818530462398731869 / 62500000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (230504481008619239 / 160000000000000000 : ℝ) ≤ - (22818530462398731869 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3597373257822027 / 5000000000000000 : ℝ)) (q := - (230504481008619239 / 320000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (230504481008619239 / 320000000000000000 : ℚ)) + (r' := (230504481008619239 / 160000000000000000 : ℚ)) + (U := (-(20503168306351268131 / 62500000000000000000 : ℚ))) + (U' := (22818530462398731869 / 62500000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (3597373257822027 / 5000000000000000 : ℚ)) + (q := (230504481008619239 / 320000000000000000 : ℚ)) + (U := (-(20503168306351268131 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_7 : Uω (aρ 7) (bρ 7) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4282,25 +3690,21 @@ lemma U_660_7 : have hlg : Real.log (223024515203491959 / 320000000000000000 : ℝ) ≤ (-(1805196482340114028887 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (223024515203491959 / 320000000000000000 : ℝ) = - (223024515203491959 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (223024515203491959 / 160000000000000000 : ℚ)) - (U := (1660539419159885971113 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (223024515203491959 / 160000000000000000 : ℝ) ≤ - (1660539419159885971113 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6950910033583599 / 10000000000000000 : ℝ)) (q := - (223024515203491959 / 320000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (223024515203491959 / 320000000000000000 : ℚ)) + (r' := (223024515203491959 / 160000000000000000 : ℚ)) + (U := (-(1805196482340114028887 / 5000000000000000000000 : ℚ))) + (U' := (1660539419159885971113 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (6950910033583599 / 10000000000000000 : ℚ)) + (q := (223024515203491959 / 320000000000000000 : ℚ)) + (U := (-(1805196482340114028887 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_8 : Uω (aρ 8) (bρ 8) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4308,25 +3712,21 @@ lemma U_660_8 : have hlg : Real.log (42667168821410459 / 64000000000000000 : ℝ) ≤ (-(4054533386656685392731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (42667168821410459 / 64000000000000000 : ℝ) = - (42667168821410459 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (42667168821410459 / 32000000000000000 : ℚ)) - (U := (2876938416343314607269 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (42667168821410459 / 32000000000000000 : ℝ) ≤ - (2876938416343314607269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (165722743534903 / 250000000000000 : ℝ)) (q := - (42667168821410459 / 64000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (42667168821410459 / 64000000000000000 : ℚ)) + (r' := (42667168821410459 / 32000000000000000 : ℚ)) + (U := (-(4054533386656685392731 / 10000000000000000000000 : ℚ))) + (U' := (2876938416343314607269 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (165722743534903 / 250000000000000 : ℚ)) + (q := (42667168821410459 / 64000000000000000 : ℚ)) + (U := (-(4054533386656685392731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_9 : Uω (aρ 9) (bρ 9) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4334,25 +3734,21 @@ lemma U_660_9 : have hlg : Real.log (201332353173736791 / 320000000000000000 : ℝ) ≤ (-(1158409886553347536791 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (201332353173736791 / 320000000000000000 : ℝ) = - (201332353173736791 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (201332353173736791 / 160000000000000000 : ℚ)) - (U := (574458064196652463209 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (201332353173736791 / 160000000000000000 : ℝ) ≤ - (574458064196652463209 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6219657186423901 / 10000000000000000 : ℝ)) (q := - (201332353173736791 / 320000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (201332353173736791 / 320000000000000000 : ℚ)) + (r' := (201332353173736791 / 160000000000000000 : ℚ)) + (U := (-(1158409886553347536791 / 2500000000000000000000 : ℚ))) + (U' := (574458064196652463209 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (6219657186423901 / 10000000000000000 : ℚ)) + (q := (201332353173736791 / 320000000000000000 : ℚ)) + (U := (-(1158409886553347536791 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_10 : Uω (aρ 10) (bρ 10) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4360,26 +3756,21 @@ lemma U_660_10 : have hlg : Real.log (187083721367394247 / 320000000000000000 : ℝ) ≤ (-(5367647710234672246907 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (187083721367394247 / 320000000000000000 : ℝ) = - (187083721367394247 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (187083721367394247 / 160000000000000000 : ℚ)) - (U := (1563824092765327753093 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (187083721367394247 / 160000000000000000 : ℝ) ≤ - (1563824092765327753093 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1429419183005623 / 2500000000000000 : ℝ)) (q := - (187083721367394247 / 320000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (187083721367394247 / 320000000000000000 : ℚ)) + (r' := (187083721367394247 / 160000000000000000 : ℚ)) + (U := (-(5367647710234672246907 / 10000000000000000000000 : ℚ))) + (U' := (1563824092765327753093 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (1429419183005623 / 2500000000000000 : ℚ)) + (q := (187083721367394247 / 320000000000000000 : ℚ)) + (U := (-(5367647710234672246907 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_11 : Uω (aρ 11) (bρ 11) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4387,26 +3778,21 @@ lemma U_660_11 : have hlg : Real.log (170862312708270567 / 320000000000000000 : ℝ) ≤ (-(1568657380525846977687 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (170862312708270567 / 320000000000000000 : ℝ) = - (170862312708270567 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (170862312708270567 / 160000000000000000 : ℚ)) - (U := (164210570224153022313 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (170862312708270567 / 160000000000000000 : ℝ) ≤ - (164210570224153022313 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2561157658516131 / 5000000000000000 : ℝ)) (q := - (170862312708270567 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (170862312708270567 / 320000000000000000 : ℚ)) + (r' := (170862312708270567 / 160000000000000000 : ℚ)) + (U := (-(1568657380525846977687 / 2500000000000000000000 : ℚ))) + (U' := (164210570224153022313 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (2561157658516131 / 5000000000000000 : ℚ)) + (q := (170862312708270567 / 320000000000000000 : ℚ)) + (U := (-(1568657380525846977687 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_12 : Uω (aρ 12) (bρ 12) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4414,26 +3800,21 @@ lemma U_660_12 : have hlg : Real.log (153148460143557719 / 320000000000000000 : ℝ) ≤ (-(3684566083047103674919 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (153148460143557719 / 320000000000000000 : ℝ) = - (153148460143557719 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (153148460143557719 / 80000000000000000 : ℚ)) - (U := (3246905719952896325081 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (153148460143557719 / 80000000000000000 : ℝ) ≤ - (3246905719952896325081 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4438899628422709 / 10000000000000000 : ℝ)) (q := - (153148460143557719 / 320000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (153148460143557719 / 320000000000000000 : ℚ)) + (r' := (153148460143557719 / 80000000000000000 : ℚ)) + (U := (-(3684566083047103674919 / 5000000000000000000000 : ℚ))) + (U' := (3246905719952896325081 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (4438899628422709 / 10000000000000000 : ℚ)) + (q := (153148460143557719 / 320000000000000000 : ℚ)) + (U := (-(3684566083047103674919 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_13 : Uω (aρ 13) (bρ 13) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4441,26 +3822,21 @@ lemma U_660_13 : have hlg : Real.log (134620677797613799 / 320000000000000000 : ℝ) ≤ (-(4329299829043131844737 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (134620677797613799 / 320000000000000000 : ℝ) = - (134620677797613799 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (134620677797613799 / 80000000000000000 : ℚ)) - (U := (2602171973956868155263 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (134620677797613799 / 80000000000000000 : ℝ) ≤ - (2602171973956868155263 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1840147486698107 / 5000000000000000 : ℝ)) (q := - (134620677797613799 / 320000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (134620677797613799 / 320000000000000000 : ℚ)) + (r' := (134620677797613799 / 80000000000000000 : ℚ)) + (U := (-(4329299829043131844737 / 5000000000000000000000 : ℚ))) + (U' := (2602171973956868155263 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (1840147486698107 / 5000000000000000 : ℚ)) + (q := (134620677797613799 / 320000000000000000 : ℚ)) + (U := (-(4329299829043131844737 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_14 : Uω (aρ 14) (bρ 14) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4468,26 +3844,21 @@ lemma U_660_14 : have hlg : Real.log (116163219149155479 / 320000000000000000 : ℝ) ≤ (-(1013324731520483938837 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (116163219149155479 / 320000000000000000 : ℝ) = - (116163219149155479 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (116163219149155479 / 80000000000000000 : ℚ)) - (U := (372969629079516061163 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (116163219149155479 / 80000000000000000 : ℝ) ≤ - (372969629079516061163 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2870631092912569 / 10000000000000000 : ℝ)) (q := - (116163219149155479 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (116163219149155479 / 320000000000000000 : ℚ)) + (r' := (116163219149155479 / 80000000000000000 : ℚ)) + (U := (-(1013324731520483938837 / 1000000000000000000000 : ℚ))) + (U' := (372969629079516061163 / 1000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (2870631092912569 / 10000000000000000 : ℚ)) + (q := (116163219149155479 / 320000000000000000 : ℚ)) + (U := (-(1013324731520483938837 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_15 : Uω (aρ 15) (bρ 15) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4495,26 +3866,21 @@ lemma U_660_15 : have hlg : Real.log (99015780276553943 / 320000000000000000 : ℝ) ≤ (-(11730417611087330118851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (99015780276553943 / 320000000000000000 : ℝ) = - (99015780276553943 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (99015780276553943 / 80000000000000000 : ℚ)) - (U := (2132525994912669881149 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (99015780276553943 / 80000000000000000 : ℝ) ≤ - (2132525994912669881149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2058489440789973 / 10000000000000000 : ℝ)) (q := - (99015780276553943 / 320000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (99015780276553943 / 320000000000000000 : ℚ)) + (r' := (99015780276553943 / 80000000000000000 : ℚ)) + (U := (-(11730417611087330118851 / 10000000000000000000000 : ℚ))) + (U' := (2132525994912669881149 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (2058489440789973 / 10000000000000000 : ℚ)) + (q := (99015780276553943 / 320000000000000000 : ℚ)) + (U := (-(11730417611087330118851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660_16 : Uω (aρ 16) (bρ 16) (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4522,26 +3888,21 @@ lemma U_660_16 : have hlg : Real.log (85623806816932631 / 320000000000000000 : ℝ) ≤ (-(659178816886656724683 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (85623806816932631 / 320000000000000000 : ℝ) = - (85623806816932631 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (85623806816932631 / 80000000000000000 : ℚ)) - (U := (33968363413343275317 / 500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (85623806816932631 / 80000000000000000 : ℝ) ≤ - (33968363413343275317 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1373862751073641 / 10000000000000000 : ℝ)) (q := - (85623806816932631 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (85623806816932631 / 320000000000000000 : ℚ)) + (r' := (85623806816932631 / 80000000000000000 : ℚ)) + (U := (-(659178816886656724683 / 500000000000000000000 : ℚ))) + (U' := (33968363413343275317 / 500000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (197405961212919 / 256000000000000 : ℚ)) + (s := (1373862751073641 / 10000000000000000 : ℚ)) + (q := (85623806816932631 / 320000000000000000 : ℚ)) + (U := (-(659178816886656724683 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_660 : Uρ (197405961212919 / 256000000000000 : ℝ) ≤ @@ -4640,25 +4001,21 @@ lemma U_661_1 : have hlg : Real.log (490952435665441417 / 640000000000000000 : ℝ) ≤ (-(662802313408731620701 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (490952435665441417 / 640000000000000000 : ℝ) = - (490952435665441417 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (490952435665441417 / 320000000000000000 : ℚ)) - (U := (1070065637341268379299 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (490952435665441417 / 320000000000000000 : ℝ) ≤ - (1070065637341268379299 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7671110732431431 / 10000000000000000 : ℝ)) (q := - (490952435665441417 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (490952435665441417 / 640000000000000000 : ℚ)) + (r' := (490952435665441417 / 320000000000000000 : ℚ)) + (U := (-(662802313408731620701 / 2500000000000000000000 : ℚ))) + (U' := (1070065637341268379299 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (7671110732431431 / 10000000000000000 : ℚ)) + (q := (490952435665441417 / 640000000000000000 : ℚ)) + (U := (-(662802313408731620701 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_2 : Uω (aρ 2) (bρ 2) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4666,25 +4023,21 @@ lemma U_661_2 : have hlg : Real.log (489423688728279241 / 640000000000000000 : ℝ) ≤ (-(2682396226434606046731 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (489423688728279241 / 640000000000000000 : ℝ) = - (489423688728279241 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (489423688728279241 / 320000000000000000 : ℚ)) - (U := (4249075576565393953269 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (489423688728279241 / 320000000000000000 : ℝ) ≤ - (4249075576565393953269 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7647106403155113 / 10000000000000000 : ℝ)) (q := - (489423688728279241 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (489423688728279241 / 640000000000000000 : ℚ)) + (r' := (489423688728279241 / 320000000000000000 : ℚ)) + (U := (-(2682396226434606046731 / 10000000000000000000000 : ℚ))) + (U' := (4249075576565393953269 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (7647106403155113 / 10000000000000000 : ℚ)) + (q := (489423688728279241 / 640000000000000000 : ℚ)) + (U := (-(2682396226434606046731 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_3 : Uω (aρ 3) (bρ 3) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4692,25 +4045,21 @@ lemma U_661_3 : have hlg : Real.log (486368064990858537 / 640000000000000000 : ℝ) ≤ (-(54900500690973011711 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (486368064990858537 / 640000000000000000 : ℝ) = - (486368064990858537 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (486368064990858537 / 320000000000000000 : ℚ)) - (U := (83728935369026988289 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (486368064990858537 / 320000000000000000 : ℝ) ≤ - (83728935369026988289 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1899753566927679 / 2500000000000000 : ℝ)) (q := - (486368064990858537 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (486368064990858537 / 640000000000000000 : ℚ)) + (r' := (486368064990858537 / 320000000000000000 : ℚ)) + (U := (-(54900500690973011711 / 200000000000000000000 : ℚ))) + (U' := (83728935369026988289 / 200000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (1899753566927679 / 2500000000000000 : ℚ)) + (q := (486368064990858537 / 640000000000000000 : ℚ)) + (U := (-(54900500690973011711 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_4 : Uω (aρ 4) (bρ 4) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4718,25 +4067,21 @@ lemma U_661_4 : have hlg : Real.log (481298856347041321 / 640000000000000000 : ℝ) ≤ (-(2849797759623886644061 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (481298856347041321 / 640000000000000000 : ℝ) = - (481298856347041321 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (481298856347041321 / 320000000000000000 : ℚ)) - (U := (4081674043376113355939 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (481298856347041321 / 320000000000000000 : ℝ) ≤ - (4081674043376113355939 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1879723919664107 / 2500000000000000 : ℝ)) (q := - (481298856347041321 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (481298856347041321 / 640000000000000000 : ℚ)) + (r' := (481298856347041321 / 320000000000000000 : ℚ)) + (U := (-(2849797759623886644061 / 10000000000000000000000 : ℚ))) + (U' := (4081674043376113355939 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (1879723919664107 / 2500000000000000 : ℚ)) + (q := (481298856347041321 / 640000000000000000 : ℚ)) + (U := (-(2849797759623886644061 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_5 : Uω (aρ 5) (bρ 5) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4744,25 +4089,21 @@ lemma U_661_5 : have hlg : Real.log (94718786290156437 / 128000000000000000 : ℝ) ≤ (-(301117906265737937309 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (94718786290156437 / 128000000000000000 : ℝ) = - (94718786290156437 / 64000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (94718786290156437 / 64000000000000000 : ℚ)) - (U := (392029274034262062691 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (94718786290156437 / 64000000000000000 : ℝ) ≤ - (392029274034262062691 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (739630669498333 / 1000000000000000 : ℝ)) (q := - (94718786290156437 / 128000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (94718786290156437 / 128000000000000000 : ℚ)) + (r' := (94718786290156437 / 64000000000000000 : ℚ)) + (U := (-(301117906265737937309 / 1000000000000000000000 : ℚ))) + (U' := (392029274034262062691 / 1000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (739630669498333 / 1000000000000000 : ℚ)) + (q := (94718786290156437 / 128000000000000000 : ℚ)) + (U := (-(301117906265737937309 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_6 : Uω (aρ 6) (bρ 6) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4770,25 +4111,21 @@ lemma U_661_6 : have hlg : Real.log (462577514063111017 / 640000000000000000 : ℝ) ≤ (-(1623270176049848597967 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (462577514063111017 / 640000000000000000 : ℝ) = - (462577514063111017 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (462577514063111017 / 320000000000000000 : ℚ)) - (U := (1842465725450151402033 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (462577514063111017 / 320000000000000000 : ℝ) ≤ - (1842465725450151402033 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3609642013379303 / 5000000000000000 : ℝ)) (q := - (462577514063111017 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (462577514063111017 / 640000000000000000 : ℚ)) + (r' := (462577514063111017 / 320000000000000000 : ℚ)) + (U := (-(1623270176049848597967 / 5000000000000000000000 : ℚ))) + (U' := (1842465725450151402033 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (3609642013379303 / 5000000000000000 : ℚ)) + (q := (462577514063111017 / 640000000000000000 : ℚ)) + (U := (-(1623270176049848597967 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_7 : Uω (aρ 7) (bρ 7) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4796,25 +4133,21 @@ lemma U_661_7 : have hlg : Real.log (447619912753074921 / 640000000000000000 : ℝ) ≤ (-(3575237128147365079751 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (447619912753074921 / 640000000000000000 : ℝ) = - (447619912753074921 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (447619912753074921 / 320000000000000000 : ℚ)) - (U := (3356234674852634920249 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (447619912753074921 / 320000000000000000 : ℝ) ≤ - (3356234674852634920249 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3487760183289989 / 5000000000000000 : ℝ)) (q := - (447619912753074921 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (447619912753074921 / 640000000000000000 : ℚ)) + (r' := (447619912753074921 / 320000000000000000 : ℚ)) + (U := (-(3575237128147365079751 / 10000000000000000000000 : ℚ))) + (U' := (3356234674852634920249 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (3487760183289989 / 5000000000000000 : ℚ)) + (q := (447619912753074921 / 640000000000000000 : ℚ)) + (U := (-(3575237128147365079751 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_8 : Uω (aρ 8) (bρ 8) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4822,25 +4155,21 @@ lemma U_661_8 : have hlg : Real.log (428247300675913961 / 640000000000000000 : ℝ) ≤ (-(803534684119275944343 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (428247300675913961 / 640000000000000000 : ℝ) = - (428247300675913961 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (428247300675913961 / 320000000000000000 : ℚ)) - (U := (582759676480724055657 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (428247300675913961 / 320000000000000000 : ℝ) ≤ - (582759676480724055657 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3326833945254349 / 5000000000000000 : ℝ)) (q := - (428247300675913961 / 640000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (428247300675913961 / 640000000000000000 : ℚ)) + (r' := (428247300675913961 / 320000000000000000 : ℚ)) + (U := (-(803534684119275944343 / 2000000000000000000000 : ℚ))) + (U' := (582759676480724055657 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (3326833945254349 / 5000000000000000 : ℚ)) + (q := (428247300675913961 / 640000000000000000 : ℚ)) + (U := (-(803534684119275944343 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_9 : Uω (aρ 9) (bρ 9) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4848,25 +4177,21 @@ lemma U_661_9 : have hlg : Real.log (404249468975058729 / 640000000000000000 : ℝ) ≤ (-(459435991242715682401 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (404249468975058729 / 640000000000000000 : ℝ) = - (404249468975058729 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (404249468975058729 / 320000000000000000 : ℚ)) - (U := (233711189057284317599 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (404249468975058729 / 320000000000000000 : ℝ) ≤ - (233711189057284317599 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1561175319554243 / 2500000000000000 : ℝ)) (q := - (404249468975058729 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (404249468975058729 / 640000000000000000 : ℚ)) + (r' := (404249468975058729 / 320000000000000000 : ℚ)) + (U := (-(459435991242715682401 / 1000000000000000000000 : ℚ))) + (U' := (233711189057284317599 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (1561175319554243 / 2500000000000000 : ℚ)) + (q := (404249468975058729 / 640000000000000000 : ℚ)) + (U := (-(459435991242715682401 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_10 : Uω (aρ 10) (bρ 10) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4874,26 +4199,21 @@ lemma U_661_10 : have hlg : Real.log (375769254721378313 / 640000000000000000 : ℝ) ≤ (-(5324929053367865177511 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (375769254721378313 / 640000000000000000 : ℝ) = - (375769254721378313 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (375769254721378313 / 320000000000000000 : ℚ)) - (U := (1606542749632134822489 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (375769254721378313 / 320000000000000000 : ℝ) ≤ - (1606542749632134822489 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5743253616284459 / 10000000000000000 : ℝ)) (q := - (375769254721378313 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (375769254721378313 / 640000000000000000 : ℚ)) + (r' := (375769254721378313 / 320000000000000000 : ℚ)) + (U := (-(5324929053367865177511 / 10000000000000000000000 : ℚ))) + (U' := (1606542749632134822489 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (5743253616284459 / 10000000000000000 : ℚ)) + (q := (375769254721378313 / 640000000000000000 : ℚ)) + (U := (-(5324929053367865177511 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_11 : Uω (aρ 11) (bρ 11) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4901,26 +4221,21 @@ lemma U_661_11 : have hlg : Real.log (343357411306843081 / 640000000000000000 : ℝ) ≤ (-(15567406399431601151 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (343357411306843081 / 640000000000000000 : ℝ) = - (343357411306843081 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (343357411306843081 / 320000000000000000 : ℚ)) - (U := (1761273108068398849 / 25000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (343357411306843081 / 320000000000000000 : ℝ) ≤ - (1761273108068398849 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5148860135785233 / 10000000000000000 : ℝ)) (q := - (343357411306843081 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (343357411306843081 / 640000000000000000 : ℚ)) + (r' := (343357411306843081 / 320000000000000000 : ℚ)) + (U := (-(15567406399431601151 / 25000000000000000000 : ℚ))) + (U' := (1761273108068398849 / 25000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (5148860135785233 / 10000000000000000 : ℚ)) + (q := (343357411306843081 / 640000000000000000 : ℚ)) + (U := (-(15567406399431601151 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_12 : Uω (aρ 12) (bρ 12) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4928,26 +4243,21 @@ lemma U_661_12 : have hlg : Real.log (307985369630861833 / 640000000000000000 : ℝ) ≤ (-(3657079475934853258049 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (307985369630861833 / 640000000000000000 : ℝ) = - (307985369630861833 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (307985369630861833 / 160000000000000000 : ℚ)) - (U := (3274392327065146741951 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (307985369630861833 / 160000000000000000 : ℝ) ≤ - (3274392327065146741951 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4467183930095819 / 10000000000000000 : ℝ)) (q := - (307985369630861833 / 640000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (307985369630861833 / 640000000000000000 : ℚ)) + (r' := (307985369630861833 / 160000000000000000 : ℚ)) + (U := (-(3657079475934853258049 / 5000000000000000000000 : ℚ))) + (U' := (3274392327065146741951 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (4467183930095819 / 10000000000000000 : ℚ)) + (q := (307985369630861833 / 640000000000000000 : ℚ)) + (U := (-(3657079475934853258049 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_13 : Uω (aρ 13) (bρ 13) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4955,26 +4265,21 @@ lemma U_661_13 : have hlg : Real.log (271030543345022249 / 640000000000000000 : ℝ) ≤ (-(4296183276173925836353 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (271030543345022249 / 640000000000000000 : ℝ) = - (271030543345022249 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (271030543345022249 / 160000000000000000 : ℚ)) - (U := (2635288526826074163647 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (271030543345022249 / 160000000000000000 : ℝ) ≤ - (2635288526826074163647 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (927931837564583 / 2500000000000000 : ℝ)) (q := - (271030543345022249 / 640000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (271030543345022249 / 640000000000000000 : ℚ)) + (r' := (271030543345022249 / 160000000000000000 : ℚ)) + (U := (-(4296183276173925836353 / 5000000000000000000000 : ℚ))) + (U' := (2635288526826074163647 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (927931837564583 / 2500000000000000 : ℚ)) + (q := (271030543345022249 / 640000000000000000 : ℚ)) + (U := (-(4296183276173925836353 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_14 : Uω (aρ 14) (bρ 14) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -4982,26 +4287,21 @@ lemma U_661_14 : have hlg : Real.log (234303224706138217 / 640000000000000000 : ℝ) ≤ (-(5024260336321951904853 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (234303224706138217 / 640000000000000000 : ℝ) = - (234303224706138217 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (234303224706138217 / 160000000000000000 : ℚ)) - (U := (1907211466678048095147 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (234303224706138217 / 160000000000000000 : ℝ) ≤ - (1907211466678048095147 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1453962963919103 / 5000000000000000 : ℝ)) (q := - (234303224706138217 / 640000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (234303224706138217 / 640000000000000000 : ℚ)) + (r' := (234303224706138217 / 160000000000000000 : ℚ)) + (U := (-(5024260336321951904853 / 5000000000000000000000 : ℚ))) + (U' := (1907211466678048095147 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (1453962963919103 / 5000000000000000 : ℚ)) + (q := (234303224706138217 / 640000000000000000 : ℚ)) + (U := (-(5024260336321951904853 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_15 : Uω (aρ 15) (bρ 15) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -5009,26 +4309,21 @@ lemma U_661_15 : have hlg : Real.log (200372804993721609 / 640000000000000000 : ℝ) ≤ (-(11612885194558307579307 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (200372804993721609 / 640000000000000000 : ℝ) = - (200372804993721609 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (200372804993721609 / 160000000000000000 : ℚ)) - (U := (2250058411441692420693 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (200372804993721609 / 160000000000000000 : ℝ) ≤ - (2250058411441692420693 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2107173589240187 / 10000000000000000 : ℝ)) (q := - (200372804993721609 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (200372804993721609 / 640000000000000000 : ℚ)) + (r' := (200372804993721609 / 160000000000000000 : ℚ)) + (U := (-(11612885194558307579307 / 10000000000000000000000 : ℚ))) + (U' := (2250058411441692420693 / 10000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (2107173589240187 / 10000000000000000 : ℚ)) + (q := (200372804993721609 / 640000000000000000 : ℚ)) + (U := (-(11612885194558307579307 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661_16 : Uω (aρ 16) (bρ 16) (396065285130169 / 512000000000000 : ℝ) ≤ @@ -5036,26 +4331,21 @@ lemma U_661_16 : have hlg : Real.log (174249916260764873 / 640000000000000000 : ℝ) ≤ (-(13009776067628077066779 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (174249916260764873 / 640000000000000000 : ℝ) = - (174249916260764873 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (174249916260764873 / 160000000000000000 : ℚ)) - (U := (853167538371922933221 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (174249916260764873 / 160000000000000000 : ℝ) ≤ - (853167538371922933221 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1443204967845289 / 10000000000000000 : ℝ)) (q := - (174249916260764873 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (174249916260764873 / 640000000000000000 : ℚ)) + (r' := (174249916260764873 / 160000000000000000 : ℚ)) + (U := (-(13009776067628077066779 / 10000000000000000000000 : ℚ))) + (U' := (853167538371922933221 / 10000000000000000000000 : ℚ)) + 2 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (396065285130169 / 512000000000000 : ℚ)) + (s := (1443204967845289 / 10000000000000000 : ℚ)) + (q := (174249916260764873 / 640000000000000000 : ℚ)) + (U := (-(13009776067628077066779 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_661 : Uρ (396065285130169 / 512000000000000 : ℝ) ≤ @@ -5153,25 +4443,21 @@ lemma U_662_1 : have hlg : Real.log (123129785834091833 / 160000000000000000 : ℝ) ≤ (-(2619348465185242405921 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (123129785834091833 / 160000000000000000 : ℝ) = - (123129785834091833 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123129785834091833 / 80000000000000000 : ℚ)) - (U := (4312123337814757594079 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (123129785834091833 / 80000000000000000 : ℝ) ≤ - (4312123337814757594079 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7695590606828901 / 10000000000000000 : ℝ)) (q := - (123129785834091833 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123129785834091833 / 160000000000000000 : ℚ)) + (r' := (123129785834091833 / 80000000000000000 : ℚ)) + (U := (-(2619348465185242405921 / 10000000000000000000000 : ℚ))) + (U' := (4312123337814757594079 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (7695590606828901 / 10000000000000000 : ℚ)) + (q := (123129785834091833 / 160000000000000000 : ℚ)) + (U := (-(2619348465185242405921 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_2 : Uω (aρ 2) (bρ 2) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5179,25 +4465,21 @@ lemma U_662_2 : have hlg : Real.log (122747605110252121 / 160000000000000000 : ℝ) ≤ (-(530087117586050276873 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (122747605110252121 / 160000000000000000 : ℝ) = - (122747605110252121 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (122747605110252121 / 80000000000000000 : ℚ)) - (U := (856207243013949723127 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (122747605110252121 / 80000000000000000 : ℝ) ≤ - (856207243013949723127 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7671587028858937 / 10000000000000000 : ℝ)) (q := - (122747605110252121 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (122747605110252121 / 160000000000000000 : ℚ)) + (r' := (122747605110252121 / 80000000000000000 : ℚ)) + (U := (-(530087117586050276873 / 2000000000000000000000 : ℚ))) + (U' := (856207243013949723127 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (7671587028858937 / 10000000000000000 : ℚ)) + (q := (122747605110252121 / 160000000000000000 : ℚ)) + (U := (-(530087117586050276873 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_3 : Uω (aρ 3) (bρ 3) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5205,25 +4487,21 @@ lemma U_662_3 : have hlg : Real.log (121983717100682641 / 160000000000000000 : ℝ) ≤ (-(1356431227679515851249 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (121983717100682641 / 160000000000000000 : ℝ) = - (121983717100682641 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (121983717100682641 / 80000000000000000 : ℚ)) - (U := (2109304673820484148751 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (121983717100682641 / 80000000000000000 : ℝ) ≤ - (2109304673820484148751 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (476468570875797 / 625000000000000 : ℝ)) (q := - (121983717100682641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (121983717100682641 / 160000000000000000 : ℚ)) + (r' := (121983717100682641 / 80000000000000000 : ℚ)) + (U := (-(1356431227679515851249 / 5000000000000000000000 : ℚ))) + (U' := (2109304673820484148751 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (476468570875797 / 625000000000000 : ℚ)) + (q := (121983717100682641 / 160000000000000000 : ℚ)) + (U := (-(1356431227679515851249 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_4 : Uω (aρ 4) (bρ 4) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5231,25 +4509,21 @@ lemma U_662_4 : have hlg : Real.log (120716462569808329 / 160000000000000000 : ℝ) ≤ (-(56345860742388664727 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (120716462569808329 / 160000000000000000 : ℝ) = - (120716462569808329 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (120716462569808329 / 80000000000000000 : ℚ)) - (U := (82283575317611335273 / 200000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (120716462569808329 / 80000000000000000 : ℝ) ≤ - (82283575317611335273 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7543384498718463 / 10000000000000000 : ℝ)) (q := - (120716462569808329 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (120716462569808329 / 160000000000000000 : ℚ)) + (r' := (120716462569808329 / 80000000000000000 : ℚ)) + (U := (-(56345860742388664727 / 200000000000000000000 : ℚ))) + (U' := (82283575317611335273 / 200000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (7543384498718463 / 10000000000000000 : ℚ)) + (q := (120716462569808329 / 160000000000000000 : ℚ)) + (U := (-(56345860742388664727 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_5 : Uω (aρ 5) (bρ 5) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5257,25 +4531,21 @@ lemma U_662_5 : have hlg : Real.log (23758069727748837 / 32000000000000000 : ℝ) ≤ (-(1489068258800647595981 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23758069727748837 / 32000000000000000 : ℝ) = - (23758069727748837 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23758069727748837 / 16000000000000000 : ℚ)) - (U := (1976667642699352404019 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (23758069727748837 / 16000000000000000 : ℝ) ≤ - (1976667642699352404019 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1484162035334089 / 2000000000000000 : ℝ)) (q := - (23758069727748837 / 32000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23758069727748837 / 32000000000000000 : ℚ)) + (r' := (23758069727748837 / 16000000000000000 : ℚ)) + (U := (-(1489068258800647595981 / 5000000000000000000000 : ℚ))) + (U' := (1976667642699352404019 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (1484162035334089 / 2000000000000000 : ℚ)) + (q := (23758069727748837 / 32000000000000000 : ℚ)) + (U := (-(1489068258800647595981 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_6 : Uω (aρ 6) (bρ 6) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5283,25 +4553,21 @@ lemma U_662_6 : have hlg : Real.log (116036513399873761 / 160000000000000000 : ℝ) ≤ (-(401586128386062271131 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (116036513399873761 / 160000000000000000 : ℝ) = - (116036513399873761 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (116036513399873761 / 80000000000000000 : ℚ)) - (U := (464847846988937728869 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (116036513399873761 / 80000000000000000 : ℝ) ≤ - (464847846988937728869 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3621910573475821 / 5000000000000000 : ℝ)) (q := - (116036513399873761 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (116036513399873761 / 160000000000000000 : ℚ)) + (r' := (116036513399873761 / 80000000000000000 : ℚ)) + (U := (-(401586128386062271131 / 1250000000000000000000 : ℚ))) + (U' := (464847846988937728869 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (3621910573475821 / 5000000000000000 : ℚ)) + (q := (116036513399873761 / 160000000000000000 : ℚ)) + (U := (-(401586128386062271131 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_7 : Uω (aρ 7) (bρ 7) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5309,25 +4575,21 @@ lemma U_662_7 : have hlg : Real.log (112297691448294529 / 160000000000000000 : ℝ) ≤ (-(442525638057717244647 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (112297691448294529 / 160000000000000000 : ℝ) = - (112297691448294529 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (112297691448294529 / 80000000000000000 : ℚ)) - (U := (423908337317282755353 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (112297691448294529 / 80000000000000000 : ℝ) ≤ - (423908337317282755353 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3500064891882119 / 5000000000000000 : ℝ)) (q := - (112297691448294529 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (112297691448294529 / 160000000000000000 : ℚ)) + (r' := (112297691448294529 / 80000000000000000 : ℚ)) + (U := (-(442525638057717244647 / 1250000000000000000000 : ℚ))) + (U' := (423908337317282755353 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (3500064891882119 / 5000000000000000 : ℚ)) + (q := (112297691448294529 / 160000000000000000 : ℚ)) + (U := (-(442525638057717244647 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_8 : Uω (aρ 8) (bρ 8) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5335,25 +4597,21 @@ lemma U_662_8 : have hlg : Real.log (107455711863479641 / 160000000000000000 : ℝ) ≤ (-(39809503495964381451 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (107455711863479641 / 160000000000000000 : ℝ) = - (107455711863479641 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (107455711863479641 / 80000000000000000 : ℚ)) - (U := (29505214534035618549 / 100000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (107455711863479641 / 80000000000000000 : ℝ) ≤ - (29505214534035618549 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6678423987002377 / 10000000000000000 : ℝ)) (q := - (107455711863479641 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (107455711863479641 / 160000000000000000 : ℚ)) + (r' := (107455711863479641 / 80000000000000000 : ℚ)) + (U := (-(39809503495964381451 / 100000000000000000000 : ℚ))) + (U' := (29505214534035618549 / 100000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (6678423987002377 / 10000000000000000 : ℚ)) + (q := (107455711863479641 / 160000000000000000 : ℚ)) + (U := (-(39809503495964381451 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_9 : Uω (aρ 9) (bρ 9) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5361,25 +4619,21 @@ lemma U_662_9 : have hlg : Real.log (20291704447757669 / 32000000000000000 : ℝ) ≤ (-(455523747905055093527 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20291704447757669 / 32000000000000000 : ℝ) = - (20291704447757669 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20291704447757669 / 16000000000000000 : ℚ)) - (U := (237623432394944906473 / 1000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (20291704447757669 / 16000000000000000 : ℝ) ≤ - (237623432394944906473 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1253948182455193 / 2000000000000000 : ℝ)) (q := - (20291704447757669 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20291704447757669 / 32000000000000000 : ℚ)) + (r' := (20291704447757669 / 16000000000000000 : ℚ)) + (U := (-(455523747905055093527 / 1000000000000000000000 : ℚ))) + (U' := (237623432394944906473 / 1000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (1253948182455193 / 2000000000000000 : ℚ)) + (q := (20291704447757669 / 32000000000000000 : ℚ)) + (U := (-(455523747905055093527 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_10 : Uω (aρ 10) (bρ 10) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5387,26 +4641,21 @@ lemma U_662_10 : have hlg : Real.log (94342690516851393 / 160000000000000000 : ℝ) ≤ (-(1056480036319776071903 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (94342690516851393 / 160000000000000000 : ℝ) = - (94342690516851393 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (94342690516851393 / 80000000000000000 : ℚ)) - (U := (329814324280223928097 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (94342690516851393 / 80000000000000000 : ℝ) ≤ - (329814324280223928097 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2884410490264423 / 5000000000000000 : ℝ)) (q := - (94342690516851393 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (94342690516851393 / 160000000000000000 : ℚ)) + (r' := (94342690516851393 / 80000000000000000 : ℚ)) + (U := (-(1056480036319776071903 / 2000000000000000000000 : ℚ))) + (U' := (329814324280223928097 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (2884410490264423 / 5000000000000000 : ℚ)) + (q := (94342690516851393 / 160000000000000000 : ℚ)) + (U := (-(1056480036319776071903 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_11 : Uω (aρ 11) (bρ 11) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5414,26 +4663,21 @@ lemma U_662_11 : have hlg : Real.log (86247386421328329 / 160000000000000000 : ℝ) ≤ (-(1235908123765897962347 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (86247386421328329 / 160000000000000000 : ℝ) = - (86247386421328329 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86247386421328329 / 80000000000000000 : ℚ)) - (U := (150386236834102037653 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (86247386421328329 / 80000000000000000 : ℝ) ≤ - (150386236834102037653 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5175384594793463 / 10000000000000000 : ℝ)) (q := - (86247386421328329 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86247386421328329 / 160000000000000000 : ℚ)) + (r' := (86247386421328329 / 80000000000000000 : ℚ)) + (U := (-(1235908123765897962347 / 2000000000000000000000 : ℚ))) + (U' := (150386236834102037653 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (5175384594793463 / 10000000000000000 : ℚ)) + (q := (86247386421328329 / 160000000000000000 : ℚ)) + (U := (-(1235908123765897962347 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_12 : Uω (aρ 12) (bρ 12) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5441,26 +4685,21 @@ lemma U_662_12 : have hlg : Real.log (3096723900153329 / 6400000000000000 : ℝ) ≤ (-(7259532435704126432831 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3096723900153329 / 6400000000000000 : ℝ) = - (3096723900153329 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3096723900153329 / 1600000000000000 : ℚ)) - (U := (6603411170295873567169 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3096723900153329 / 1600000000000000 : ℝ) ≤ - (6603411170295873567169 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (179816943071663 / 400000000000000 : ℝ)) (q := - (3096723900153329 / 6400000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3096723900153329 / 6400000000000000 : ℚ)) + (r' := (3096723900153329 / 1600000000000000 : ℚ)) + (U := (-(7259532435704126432831 / 10000000000000000000000 : ℚ))) + (U' := (6603411170295873567169 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (179816943071663 / 400000000000000 : ℚ)) + (q := (3096723900153329 / 6400000000000000 : ℚ)) + (U := (-(7259532435704126432831 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_13 : Uω (aρ 13) (bρ 13) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5468,26 +4707,21 @@ lemma U_662_13 : have hlg : Real.log (13640820388378613 / 32000000000000000 : ℝ) ≤ (-(8526691058976463844233 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13640820388378613 / 32000000000000000 : ℝ) = - (13640820388378613 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13640820388378613 / 8000000000000000 : ℚ)) - (U := (5336252547023536155767 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (13640820388378613 / 8000000000000000 : ℝ) ≤ - (5336252547023536155767 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (748611174628811 / 2000000000000000 : ℝ)) (q := - (13640820388378613 / 32000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13640820388378613 / 32000000000000000 : ℚ)) + (r' := (13640820388378613 / 8000000000000000 : ℚ)) + (U := (-(8526691058976463844233 / 10000000000000000000000 : ℚ))) + (U' := (5336252547023536155767 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (748611174628811 / 2000000000000000 : ℚ)) + (q := (13640820388378613 / 32000000000000000 : ℚ)) + (U := (-(8526691058976463844233 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_14 : Uω (aρ 14) (bρ 14) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5495,26 +4729,21 @@ lemma U_662_14 : have hlg : Real.log (59067852357270697 / 160000000000000000 : ℝ) ≤ (-(4982434958219247805323 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59067852357270697 / 160000000000000000 : ℝ) = - (59067852357270697 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59067852357270697 / 40000000000000000 : ℚ)) - (U := (1949036844780752194677 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59067852357270697 / 40000000000000000 : ℝ) ≤ - (1949036844780752194677 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2944951960111259 / 10000000000000000 : ℝ)) (q := - (59067852357270697 / 160000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59067852357270697 / 160000000000000000 : ℚ)) + (r' := (59067852357270697 / 40000000000000000 : ℚ)) + (U := (-(4982434958219247805323 / 5000000000000000000000 : ℚ))) + (U' := (1949036844780752194677 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (2944951960111259 / 10000000000000000 : ℚ)) + (q := (59067852357270697 / 160000000000000000 : ℚ)) + (U := (-(4982434958219247805323 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_15 : Uω (aρ 15) (bρ 15) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5522,26 +4751,21 @@ lemma U_662_15 : have hlg : Real.log (50671939657254177 / 160000000000000000 : ℝ) ≤ (-(11498015157682552696681 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (50671939657254177 / 160000000000000000 : ℝ) = - (50671939657254177 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50671939657254177 / 40000000000000000 : ℚ)) - (U := (2364928448317447303319 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (50671939657254177 / 40000000000000000 : ℝ) ≤ - (2364928448317447303319 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1077518075012097 / 5000000000000000 : ℝ)) (q := - (50671939657254177 / 160000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50671939657254177 / 160000000000000000 : ℚ)) + (r' := (50671939657254177 / 40000000000000000 : ℚ)) + (U := (-(11498015157682552696681 / 10000000000000000000000 : ℚ))) + (U' := (2364928448317447303319 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (1077518075012097 / 5000000000000000 : ℚ)) + (q := (50671939657254177 / 160000000000000000 : ℚ)) + (U := (-(11498015157682552696681 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662_16 : Uω (aρ 16) (bρ 16) (794637295669 / 1024000000000 : ℝ) ≤ @@ -5549,26 +4773,21 @@ lemma U_662_16 : have hlg : Real.log (44290771968930889 / 160000000000000000 : ℝ) ≤ (-(50171776057069747423 / 39062500000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (44290771968930889 / 160000000000000000 : ℝ) = - (44290771968930889 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44290771968930889 / 40000000000000000 : ℚ)) - (U := (3980347403867752577 / 39062500000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44290771968930889 / 40000000000000000 : ℝ) ≤ - (3980347403867752577 / 39062500000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1509761840493783 / 10000000000000000 : ℝ)) (q := - (44290771968930889 / 160000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44290771968930889 / 160000000000000000 : ℚ)) + (r' := (44290771968930889 / 40000000000000000 : ℚ)) + (U := (-(50171776057069747423 / 39062500000000000000 : ℚ))) + (U' := (3980347403867752577 / 39062500000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (794637295669 / 1024000000000 : ℚ)) + (s := (1509761840493783 / 10000000000000000 : ℚ)) + (q := (44290771968930889 / 160000000000000000 : ℚ)) + (U := (-(50171776057069747423 / 39062500000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_662 : Uρ (794637295669 / 1024000000000 : ℝ) ≤ @@ -5659,25 +4878,21 @@ lemma U_663_1 : have hlg : Real.log (494085850980083391 / 640000000000000000 : ℝ) ≤ (-(1293794432980282284923 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (494085850980083391 / 640000000000000000 : ℝ) = - (494085850980083391 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (494085850980083391 / 320000000000000000 : ℚ)) - (U := (2171941468519717715077 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (494085850980083391 / 320000000000000000 : ℝ) ≤ - (2171941468519717715077 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7720070480376063 / 10000000000000000 : ℝ)) (q := - (494085850980083391 / 640000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (494085850980083391 / 640000000000000000 : ℚ)) + (r' := (494085850980083391 / 320000000000000000 : ℚ)) + (U := (-(1293794432980282284923 / 5000000000000000000000 : ℚ))) + (U' := (2171941468519717715077 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (7720070480376063 / 10000000000000000 : ℚ)) + (q := (494085850980083391 / 640000000000000000 : ℚ)) + (U := (-(1293794432980282284923 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_2 : Uω (aρ 2) (bρ 2) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5685,25 +4900,21 @@ lemma U_663_2 : have hlg : Real.log (492557151973494943 / 640000000000000000 : ℝ) ≤ (-(654644193995127234473 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (492557151973494943 / 640000000000000000 : ℝ) = - (492557151973494943 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (492557151973494943 / 320000000000000000 : ℚ)) - (U := (1078223756754872765527 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (492557151973494943 / 320000000000000000 : ℝ) ≤ - (1078223756754872765527 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3848033824465087 / 5000000000000000 : ℝ)) (q := - (492557151973494943 / 640000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (492557151973494943 / 640000000000000000 : ℚ)) + (r' := (492557151973494943 / 320000000000000000 : ℚ)) + (U := (-(654644193995127234473 / 2500000000000000000000 : ℚ))) + (U' := (1078223756754872765527 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (3848033824465087 / 5000000000000000 : ℚ)) + (q := (492557151973494943 / 640000000000000000 : ℚ)) + (U := (-(654644193995127234473 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_3 : Uω (aρ 3) (bρ 3) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5711,25 +4922,21 @@ lemma U_663_3 : have hlg : Real.log (489501671174198047 / 640000000000000000 : ℝ) ≤ (-(2680803000857294788523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (489501671174198047 / 640000000000000000 : ℝ) = - (489501671174198047 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (489501671174198047 / 320000000000000000 : ℚ)) - (U := (4250668802142705211477 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (489501671174198047 / 320000000000000000 : ℝ) ≤ - (4250668802142705211477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3823989990151073 / 5000000000000000 : ℝ)) (q := - (489501671174198047 / 640000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (489501671174198047 / 640000000000000000 : ℚ)) + (r' := (489501671174198047 / 320000000000000000 : ℚ)) + (U := (-(2680803000857294788523 / 10000000000000000000000 : ℚ))) + (U' := (4250668802142705211477 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (3823989990151073 / 5000000000000000 : ℚ)) + (q := (489501671174198047 / 640000000000000000 : ℚ)) + (U := (-(2680803000857294788523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_4 : Uω (aρ 4) (bρ 4) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5737,25 +4944,21 @@ lemma U_663_4 : have hlg : Real.log (484432842331385599 / 640000000000000000 : ℝ) ≤ (-(2784893666896482135699 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (484432842331385599 / 640000000000000000 : ℝ) = - (484432842331385599 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (484432842331385599 / 320000000000000000 : ℚ)) - (U := (4146578136103517864301 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (484432842331385599 / 320000000000000000 : ℝ) ≤ - (4146578136103517864301 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7567873260029257 / 10000000000000000 : ℝ)) (q := - (484432842331385599 / 640000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (484432842331385599 / 640000000000000000 : ℚ)) + (r' := (484432842331385599 / 320000000000000000 : ℚ)) + (U := (-(2784893666896482135699 / 10000000000000000000000 : ℚ))) + (U' := (4146578136103517864301 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (7567873260029257 / 10000000000000000 : ℚ)) + (q := (484432842331385599 / 640000000000000000 : ℚ)) + (U := (-(2784893666896482135699 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_5 : Uω (aρ 5) (bρ 5) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5763,25 +4966,21 @@ lemma U_663_5 : have hlg : Real.log (476728852660897087 / 640000000000000000 : ℝ) ≤ (-(368150362361694042147 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (476728852660897087 / 640000000000000000 : ℝ) = - (476728852660897087 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (476728852660897087 / 320000000000000000 : ℚ)) - (U := (498283613013305957853 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (476728852660897087 / 320000000000000000 : ℝ) ≤ - (498283613013305957853 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7445313502161491 / 10000000000000000 : ℝ)) (q := - (476728852660897087 / 640000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (476728852660897087 / 640000000000000000 : ℚ)) + (r' := (476728852660897087 / 320000000000000000 : ℚ)) + (U := (-(368150362361694042147 / 1250000000000000000000 : ℚ))) + (U' := (498283613013305957853 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (7445313502161491 / 10000000000000000 : ℚ)) + (q := (476728852660897087 / 640000000000000000 : ℚ)) + (U := (-(368150362361694042147 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_6 : Uω (aρ 6) (bρ 6) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5789,25 +4988,21 @@ lemma U_663_6 : have hlg : Real.log (465714580753082303 / 640000000000000000 : ℝ) ≤ (-(1589476086348222504551 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (465714580753082303 / 640000000000000000 : ℝ) = - (465714580753082303 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (465714580753082303 / 320000000000000000 : ℚ)) - (U := (1876259815151777495449 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (465714580753082303 / 320000000000000000 : ℝ) ≤ - (1876259815151777495449 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7268357880182279 / 10000000000000000 : ℝ)) (q := - (465714580753082303 / 640000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (465714580753082303 / 640000000000000000 : ℚ)) + (r' := (465714580753082303 / 320000000000000000 : ℚ)) + (U := (-(1589476086348222504551 / 5000000000000000000000 : ℚ))) + (U' := (1876259815151777495449 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (7268357880182279 / 10000000000000000 : ℚ)) + (q := (465714580753082303 / 640000000000000000 : ℚ)) + (U := (-(1589476086348222504551 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_7 : Uω (aρ 7) (bρ 7) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5815,25 +5010,21 @@ lemma U_663_7 : have hlg : Real.log (450761589835292159 / 640000000000000000 : ℝ) ≤ (-(3505296020052566257047 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (450761589835292159 / 640000000000000000 : ℝ) = - (450761589835292159 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (450761589835292159 / 320000000000000000 : ℚ)) - (U := (3426175782947433742953 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (450761589835292159 / 320000000000000000 : ℝ) ≤ - (3426175782947433742953 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7024738294761337 / 10000000000000000 : ℝ)) (q := - (450761589835292159 / 640000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (450761589835292159 / 640000000000000000 : ℚ)) + (r' := (450761589835292159 / 320000000000000000 : ℚ)) + (U := (-(3505296020052566257047 / 10000000000000000000000 : ℚ))) + (U' := (3426175782947433742953 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (7024738294761337 / 10000000000000000 : ℚ)) + (q := (450761589835292159 / 640000000000000000 : ℚ)) + (U := (-(3505296020052566257047 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_8 : Uω (aρ 8) (bρ 8) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5841,25 +5032,21 @@ lemma U_663_8 : have hlg : Real.log (86279665855173267 / 128000000000000000 : ℝ) ≤ (-(493045393677593413659 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (86279665855173267 / 128000000000000000 : ℝ) = - (86279665855173267 / 64000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (86279665855173267 / 64000000000000000 : ℚ)) - (U := (373388581697406586341 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (86279665855173267 / 64000000000000000 : ℝ) ≤ - (373388581697406586341 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (83789725670241 / 125000000000000 : ℝ)) (q := - (86279665855173267 / 128000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (86279665855173267 / 128000000000000000 : ℚ)) + (r' := (86279665855173267 / 64000000000000000 : ℚ)) + (U := (-(493045393677593413659 / 1250000000000000000000 : ℚ))) + (U' := (373388581697406586341 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (83789725670241 / 125000000000000 : ℚ)) + (q := (86279665855173267 / 128000000000000000 : ℚ)) + (U := (-(493045393677593413659 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_9 : Uω (aρ 9) (bρ 9) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5867,25 +5054,21 @@ lemma U_663_9 : have hlg : Real.log (407418567990045727 / 640000000000000000 : ℝ) ≤ (-(903254193070843639721 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (407418567990045727 / 640000000000000000 : ℝ) = - (407418567990045727 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (407418567990045727 / 320000000000000000 : ℚ)) - (U := (483040167529156360279 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (407418567990045727 / 320000000000000000 : ℝ) ≤ - (483040167529156360279 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3147388070898693 / 5000000000000000 : ℝ)) (q := - (407418567990045727 / 640000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (407418567990045727 / 640000000000000000 : ℚ)) + (r' := (407418567990045727 / 320000000000000000 : ℚ)) + (U := (-(903254193070843639721 / 2000000000000000000000 : ℚ))) + (U' := (483040167529156360279 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (3147388070898693 / 5000000000000000 : ℚ)) + (q := (407418567990045727 / 640000000000000000 : ℚ)) + (U := (-(903254193070843639721 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_10 : Uω (aρ 10) (bρ 10) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5893,26 +5076,21 @@ lemma U_663_10 : have hlg : Real.log (378971968805497247 / 640000000000000000 : ℝ) ≤ (-(5240059346819541959201 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (378971968805497247 / 640000000000000000 : ℝ) = - (378971968805497247 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (378971968805497247 / 320000000000000000 : ℚ)) - (U := (1691412456180458040799 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (378971968805497247 / 320000000000000000 : ℝ) ≤ - (1691412456180458040799 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2897189475387623 / 5000000000000000 : ℝ)) (q := - (378971968805497247 / 640000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (378971968805497247 / 640000000000000000 : ℚ)) + (r' := (378971968805497247 / 320000000000000000 : ℚ)) + (U := (-(5240059346819541959201 / 10000000000000000000000 : ℚ))) + (U' := (1691412456180458040799 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (2897189475387623 / 5000000000000000 : ℚ)) + (q := (378971968805497247 / 640000000000000000 : ℚ)) + (U := (-(5240059346819541959201 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_11 : Uω (aρ 11) (bρ 11) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5920,26 +5098,21 @@ lemma U_663_11 : have hlg : Real.log (346621038518138783 / 640000000000000000 : ℝ) ≤ (-(6132361009483060921937 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (346621038518138783 / 640000000000000000 : ℝ) = - (346621038518138783 / 320000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (346621038518138783 / 320000000000000000 : ℚ)) - (U := (799110793516939078063 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (346621038518138783 / 320000000000000000 : ℝ) ≤ - (799110793516939078063 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2600944502750147 / 5000000000000000 : ℝ)) (q := - (346621038518138783 / 640000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (346621038518138783 / 640000000000000000 : ℚ)) + (r' := (346621038518138783 / 320000000000000000 : ℚ)) + (U := (-(6132361009483060921937 / 10000000000000000000000 : ℚ))) + (U' := (799110793516939078063 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (2600944502750147 / 5000000000000000 : ℚ)) + (q := (346621038518138783 / 640000000000000000 : ℚ)) + (U := (-(6132361009483060921937 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_12 : Uω (aρ 12) (bρ 12) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5947,26 +5120,21 @@ lemma U_663_12 : have hlg : Real.log (311358008202268671 / 640000000000000000 : ℝ) ≤ (-(1441049547891940481097 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (311358008202268671 / 640000000000000000 : ℝ) = - (311358008202268671 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (311358008202268671 / 160000000000000000 : ℚ)) - (U := (1331539173308059518903 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (311358008202268671 / 160000000000000000 : ℝ) ≤ - (1331539173308059518903 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4523619404814353 / 10000000000000000 : ℝ)) (q := - (311358008202268671 / 640000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (311358008202268671 / 640000000000000000 : ℚ)) + (r' := (311358008202268671 / 160000000000000000 : ℚ)) + (U := (-(1441049547891940481097 / 2000000000000000000000 : ℚ))) + (U' := (1331539173308059518903 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (4523619404814353 / 10000000000000000 : ℚ)) + (q := (311358008202268671 / 640000000000000000 : ℚ)) + (U := (-(1441049547891940481097 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_13 : Uω (aρ 13) (bρ 13) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -5974,26 +5142,21 @@ lemma U_663_13 : have hlg : Real.log (274599031618965983 / 640000000000000000 : ℝ) ≤ (-(2115390522553072752363 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (274599031618965983 / 640000000000000000 : ℝ) = - (274599031618965983 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (274599031618965983 / 160000000000000000 : ℚ)) - (U := (1350345378946927247637 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (274599031618965983 / 160000000000000000 : ℝ) ≤ - (1350345378946927247637 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (471785391022643 / 1250000000000000 : ℝ)) (q := - (274599031618965983 / 640000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (274599031618965983 / 640000000000000000 : ℚ)) + (r' := (274599031618965983 / 160000000000000000 : ℚ)) + (U := (-(2115390522553072752363 / 2500000000000000000000 : ℚ))) + (U' := (1350345378946927247637 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (471785391022643 / 1250000000000000 : ℚ)) + (q := (274599031618965983 / 640000000000000000 : ℚ)) + (U := (-(2115390522553072752363 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_14 : Uω (aρ 14) (bρ 14) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -6001,26 +5164,21 @@ lemma U_663_14 : have hlg : Real.log (238231312906570783 / 640000000000000000 : ℝ) ≤ (-(9882260711854623304547 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (238231312906570783 / 640000000000000000 : ℝ) = - (238231312906570783 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (238231312906570783 / 160000000000000000 : ℚ)) - (U := (3980682894145376695453 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (238231312906570783 / 160000000000000000 : ℝ) ≤ - (3980682894145376695453 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1490859601731897 / 5000000000000000 : ℝ)) (q := - (238231312906570783 / 640000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (238231312906570783 / 640000000000000000 : ℚ)) + (r' := (238231312906570783 / 160000000000000000 : ℚ)) + (U := (-(9882260711854623304547 / 10000000000000000000000 : ℚ))) + (U' := (3980682894145376695453 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (1490859601731897 / 5000000000000000 : ℚ)) + (q := (238231312906570783 / 640000000000000000 : ℚ)) + (U := (-(9882260711854623304547 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_15 : Uω (aρ 15) (bρ 15) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -6028,26 +5186,21 @@ lemma U_663_15 : have hlg : Real.log (204978135744948383 / 640000000000000000 : ℝ) ≤ (-(11385648572861481335083 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (204978135744948383 / 640000000000000000 : ℝ) = - (204978135744948383 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (204978135744948383 / 160000000000000000 : ℚ)) - (U := (2477295033138518664917 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (204978135744948383 / 160000000000000000 : ℝ) ≤ - (2477295033138518664917 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1101065347289047 / 5000000000000000 : ℝ)) (q := - (204978135744948383 / 640000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (204978135744948383 / 640000000000000000 : ℚ)) + (r' := (204978135744948383 / 160000000000000000 : ℚ)) + (U := (-(11385648572861481335083 / 10000000000000000000000 : ℚ))) + (U' := (2477295033138518664917 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (1101065347289047 / 5000000000000000 : ℚ)) + (q := (204978135744948383 / 640000000000000000 : ℚ)) + (U := (-(11385648572861481335083 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663_16 : Uω (aρ 16) (bρ 16) (398572010538831 / 512000000000000 : ℝ) ≤ @@ -6055,26 +5208,21 @@ lemma U_663_16 : have hlg : Real.log (179998437324363327 / 640000000000000000 : ℝ) ≤ (-(3171300016281540266367 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (179998437324363327 / 640000000000000000 : ℝ) = - (179998437324363327 / 160000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (179998437324363327 / 160000000000000000 : ℚ)) - (U := (294435885218459733633 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (179998437324363327 / 160000000000000000 : ℝ) ≤ - (294435885218459733633 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1573886770444811 / 10000000000000000 : ℝ)) (q := - (179998437324363327 / 640000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (179998437324363327 / 640000000000000000 : ℚ)) + (r' := (179998437324363327 / 160000000000000000 : ℚ)) + (U := (-(3171300016281540266367 / 2500000000000000000000 : ℚ))) + (U' := (294435885218459733633 / 2500000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (398572010538831 / 512000000000000 : ℚ)) + (s := (1573886770444811 / 10000000000000000 : ℚ)) + (q := (179998437324363327 / 640000000000000000 : ℚ)) + (U := (-(3171300016281540266367 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_663 : Uρ (398572010538831 / 512000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U55.lean b/LeanPool/Zeta5Irrational/Table/U55.lean index 6c4a39c811..2e69350d05 100644 --- a/LeanPool/Zeta5Irrational/Table/U55.lean +++ b/LeanPool/Zeta5Irrational/Table/U55.lean @@ -24,25 +24,21 @@ lemma U_664_1 : have hlg : Real.log (247826279298423837 / 320000000000000000 : ℝ) ≤ (-(1277964907620946027673 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (247826279298423837 / 320000000000000000 : ℝ) = - (247826279298423837 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (247826279298423837 / 160000000000000000 : ℚ)) - (U := (2187770993879053972327 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (247826279298423837 / 160000000000000000 : ℝ) ≤ - (2187770993879053972327 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3872275176540491 / 5000000000000000 : ℝ)) (q := - (247826279298423837 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (247826279298423837 / 320000000000000000 : ℚ)) + (r' := (247826279298423837 / 160000000000000000 : ℚ)) + (U := (-(1277964907620946027673 / 5000000000000000000000 : ℚ))) + (U' := (2187770993879053972327 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (3872275176540491 / 5000000000000000 : ℚ)) + (q := (247826279298423837 / 320000000000000000 : ℚ)) + (U := (-(1277964907620946027673 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_2 : Uω (aρ 2) (bρ 2) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_664_2 : have hlg : Real.log (49412388332745321 / 64000000000000000 : ℝ) ≤ (-(103472765751352777257 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49412388332745321 / 64000000000000000 : ℝ) = - (49412388332745321 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49412388332745321 / 32000000000000000 : ℚ)) - (U := (173786106368647222743 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (49412388332745321 / 32000000000000000 : ℝ) ≤ - (173786106368647222743 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1544109652684481 / 2000000000000000 : ℝ)) (q := - (49412388332745321 / 64000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49412388332745321 / 64000000000000000 : ℚ)) + (r' := (49412388332745321 / 32000000000000000 : ℚ)) + (U := (-(103472765751352777257 / 400000000000000000000 : ℚ))) + (U' := (173786106368647222743 / 400000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (1544109652684481 / 2000000000000000 : ℚ)) + (q := (49412388332745321 / 64000000000000000 : ℚ)) + (U := (-(103472765751352777257 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_3 : Uω (aρ 3) (bρ 3) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_664_3 : have hlg : Real.log (245534236655695789 / 320000000000000000 : ℝ) ≤ (-(2648846011764422714851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (245534236655695789 / 320000000000000000 : ℝ) = - (245534236655695789 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (245534236655695789 / 160000000000000000 : ℚ)) - (U := (4282625791235577285149 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (245534236655695789 / 160000000000000000 : ℝ) ≤ - (4282625791235577285149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7672462806770479 / 10000000000000000 : ℝ)) (q := - (245534236655695789 / 320000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (245534236655695789 / 320000000000000000 : ℚ)) + (r' := (245534236655695789 / 160000000000000000 : ℚ)) + (U := (-(2648846011764422714851 / 10000000000000000000000 : ℚ))) + (U' := (4282625791235577285149 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (7672462806770479 / 10000000000000000 : ℚ)) + (q := (245534236655695789 / 320000000000000000 : ℚ)) + (U := (-(2648846011764422714851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_4 : Uω (aρ 4) (bρ 4) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_664_4 : have hlg : Real.log (242999916260845037 / 320000000000000000 : ℝ) ≤ (-(2752598967989138191723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (242999916260845037 / 320000000000000000 : ℝ) = - (242999916260845037 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (242999916260845037 / 160000000000000000 : ℚ)) - (U := (4178872835010861808277 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (242999916260845037 / 160000000000000000 : ℝ) ≤ - (4178872835010861808277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7592361963157307 / 10000000000000000 : ℝ)) (q := - (242999916260845037 / 320000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (242999916260845037 / 320000000000000000 : ℚ)) + (r' := (242999916260845037 / 160000000000000000 : ℚ)) + (U := (-(2752598967989138191723 / 10000000000000000000000 : ℚ))) + (U' := (4178872835010861808277 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (7592361963157307 / 10000000000000000 : ℚ)) + (q := (242999916260845037 / 320000000000000000 : ℚ)) + (U := (-(2752598967989138191723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_5 : Uω (aρ 5) (bρ 5) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_664_5 : have hlg : Real.log (47829630581773097 / 64000000000000000 : ℝ) ≤ (-(291237749004709474387 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47829630581773097 / 64000000000000000 : ℝ) = - (47829630581773097 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47829630581773097 / 32000000000000000 : ℚ)) - (U := (401909431295290525613 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47829630581773097 / 32000000000000000 : ℝ) ≤ - (401909431295290525613 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1493963334598717 / 2000000000000000 : ℝ)) (q := - (47829630581773097 / 64000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47829630581773097 / 64000000000000000 : ℚ)) + (r' := (47829630581773097 / 32000000000000000 : ℚ)) + (U := (-(291237749004709474387 / 1000000000000000000000 : ℚ))) + (U' := (401909431295290525613 / 1000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (1493963334598717 / 2000000000000000 : ℚ)) + (q := (47829630581773097 / 64000000000000000 : ℚ)) + (U := (-(291237749004709474387 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_6 : Uω (aρ 6) (bρ 6) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_664_6 : have hlg : Real.log (233641547824428733 / 320000000000000000 : ℝ) ≤ (-(3145329015573109930877 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (233641547824428733 / 320000000000000000 : ℝ) = - (233641547824428733 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (233641547824428733 / 160000000000000000 : ℚ)) - (U := (3786142787426890069123 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (233641547824428733 / 160000000000000000 : ℝ) ≤ - (3786142787426890069123 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (113951472349317 / 156250000000000 : ℝ)) (q := - (233641547824428733 / 320000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (233641547824428733 / 320000000000000000 : ℚ)) + (r' := (233641547824428733 / 160000000000000000 : ℚ)) + (U := (-(3145329015573109930877 / 10000000000000000000000 : ℚ))) + (U' := (3786142787426890069123 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (113951472349317 / 156250000000000 : ℚ)) + (q := (233641547824428733 / 320000000000000000 : ℚ)) + (U := (-(3145329015573109930877 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_7 : Uω (aρ 7) (bρ 7) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_664_7 : have hlg : Real.log (226166192591551821 / 320000000000000000 : ℝ) ≤ (-(3470509010608891617659 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (226166192591551821 / 320000000000000000 : ℝ) = - (226166192591551821 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (226166192591551821 / 160000000000000000 : ℚ)) - (U := (3460962792391108382341 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (226166192591551821 / 160000000000000000 : ℝ) ≤ - (3460962792391108382341 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7049345909061481 / 10000000000000000 : ℝ)) (q := - (226166192591551821 / 320000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (226166192591551821 / 320000000000000000 : ℚ)) + (r' := (226166192591551821 / 160000000000000000 : ℚ)) + (U := (-(3470509010608891617659 / 10000000000000000000000 : ℚ))) + (U' := (3460962792391108382341 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (7049345909061481 / 10000000000000000 : ℚ)) + (q := (226166192591551821 / 320000000000000000 : ℚ)) + (U := (-(3470509010608891617659 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_8 : Uω (aρ 8) (bρ 8) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_664_8 : have hlg : Real.log (216486873429367757 / 320000000000000000 : ℝ) ≤ (-(1953955403703193484059 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (216486873429367757 / 320000000000000000 : ℝ) = - (216486873429367757 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (216486873429367757 / 160000000000000000 : ℚ)) - (U := (1511780497796806515941 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (216486873429367757 / 160000000000000000 : ℝ) ≤ - (1511780497796806515941 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6727930112764977 / 10000000000000000 : ℝ)) (q := - (216486873429367757 / 320000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (216486873429367757 / 320000000000000000 : ℚ)) + (r' := (216486873429367757 / 160000000000000000 : ℚ)) + (U := (-(1953955403703193484059 / 5000000000000000000000 : ℚ))) + (U' := (1511780497796806515941 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (6727930112764977 / 10000000000000000 : ℚ)) + (q := (216486873429367757 / 320000000000000000 : ℚ)) + (U := (-(1953955403703193484059 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_9 : Uω (aρ 9) (bρ 9) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_664_9 : have hlg : Real.log (204501453877376573 / 320000000000000000 : ℝ) ≤ (-(4477459106514180083733 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (204501453877376573 / 320000000000000000 : ℝ) = - (204501453877376573 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (204501453877376573 / 160000000000000000 : ℚ)) - (U := (2454012696485819916267 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (204501453877376573 / 160000000000000000 : ℝ) ≤ - (2454012696485819916267 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (789975877390691 / 1250000000000000 : ℝ)) (q := - (204501453877376573 / 320000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (204501453877376573 / 320000000000000000 : ℚ)) + (r' := (204501453877376573 / 160000000000000000 : ℚ)) + (U := (-(4477459106514180083733 / 10000000000000000000000 : ℚ))) + (U' := (2454012696485819916267 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (789975877390691 / 1250000000000000 : ℚ)) + (q := (204501453877376573 / 320000000000000000 : ℚ)) + (U := (-(4477459106514180083733 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_10 : Uω (aρ 10) (bρ 10) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_664_10 : have hlg : Real.log (38057287889597513 / 64000000000000000 : ℝ) ≤ (-(1299476206458049317223 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (38057287889597513 / 64000000000000000 : ℝ) = - (38057287889597513 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (38057287889597513 / 32000000000000000 : ℚ)) - (U := (433391744291950682777 / 2500000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (38057287889597513 / 32000000000000000 : ℝ) ≤ - (433391744291950682777 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1163985530156743 / 2000000000000000 : ℝ)) (q := - (38057287889597513 / 64000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (38057287889597513 / 64000000000000000 : ℚ)) + (r' := (38057287889597513 / 32000000000000000 : ℚ)) + (U := (-(1299476206458049317223 / 2500000000000000000000 : ℚ))) + (U' := (433391744291950682777 / 2500000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (1163985530156743 / 2000000000000000 : ℚ)) + (q := (38057287889597513 / 64000000000000000 : ℚ)) + (U := (-(1299476206458049317223 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_11 : Uω (aρ 11) (bρ 11) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_664_11 : have hlg : Real.log (174125949780980637 / 320000000000000000 : ℝ) ≤ (-(6085421088558797644903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (174125949780980637 / 320000000000000000 : ℝ) = - (174125949780980637 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (174125949780980637 / 160000000000000000 : ℚ)) - (U := (846050714441202355097 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (174125949780980637 / 160000000000000000 : ℝ) ≤ - (846050714441202355097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2614186836400391 / 5000000000000000 : ℝ)) (q := - (174125949780980637 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (174125949780980637 / 320000000000000000 : ℚ)) + (r' := (174125949780980637 / 160000000000000000 : ℚ)) + (U := (-(6085421088558797644903 / 10000000000000000000000 : ℚ))) + (U' := (846050714441202355097 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (2614186836400391 / 5000000000000000 : ℚ)) + (q := (174125949780980637 / 320000000000000000 : ℚ)) + (U := (-(6085421088558797644903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_12 : Uω (aρ 12) (bρ 12) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -312,26 +266,21 @@ lemma U_664_12 : have hlg : Real.log (156521125124646877 / 320000000000000000 : ℝ) ≤ (-(3575650047906401257211 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (156521125124646877 / 320000000000000000 : ℝ) = - (156521125124646877 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (156521125124646877 / 80000000000000000 : ℚ)) - (U := (3355821755093598742789 / 5000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (156521125124646877 / 80000000000000000 : ℝ) ≤ - (3355821755093598742789 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2275886114232461 / 5000000000000000 : ℝ)) (q := - (156521125124646877 / 320000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (156521125124646877 / 320000000000000000 : ℚ)) + (r' := (156521125124646877 / 80000000000000000 : ℚ)) + (U := (-(3575650047906401257211 / 5000000000000000000000 : ℚ))) + (U' := (3355821755093598742789 / 5000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (2275886114232461 / 5000000000000000 : ℚ)) + (q := (156521125124646877 / 320000000000000000 : ℚ)) + (U := (-(3575650047906401257211 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_13 : Uω (aρ 13) (bρ 13) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -339,26 +288,21 @@ lemma U_664_13 : have hlg : Real.log (27637849467573129 / 64000000000000000 : ℝ) ≤ (-(4198484460239256737569 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (27637849467573129 / 64000000000000000 : ℝ) = - (27637849467573129 / 16000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27637849467573129 / 16000000000000000 : ℚ)) - (U := (2732987342760743262431 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (27637849467573129 / 16000000000000000 : ℝ) ≤ - (2732987342760743262431 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (761082321677219 / 2000000000000000 : ℝ)) (q := - (27637849467573129 / 64000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27637849467573129 / 64000000000000000 : ℚ)) + (r' := (27637849467573129 / 16000000000000000 : ℚ)) + (U := (-(4198484460239256737569 / 5000000000000000000000 : ℚ))) + (U' := (2732987342760743262431 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (761082321677219 / 2000000000000000 : ℚ)) + (q := (27637849467573129 / 64000000000000000 : ℚ)) + (U := (-(4198484460239256737569 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_14 : Uω (aρ 14) (bρ 14) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -366,26 +310,21 @@ lemma U_664_14 : have hlg : Real.log (120091618888945197 / 320000000000000000 : ℝ) ≤ (-(1960132106122831270009 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (120091618888945197 / 320000000000000000 : ℝ) = - (120091618888945197 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (120091618888945197 / 80000000000000000 : ℚ)) - (U := (812456615077168729991 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (120091618888945197 / 80000000000000000 : ℝ) ≤ - (812456615077168729991 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3018237115373567 / 10000000000000000 : ℝ)) (q := - (120091618888945197 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (120091618888945197 / 320000000000000000 : ℚ)) + (r' := (120091618888945197 / 80000000000000000 : ℚ)) + (U := (-(1960132106122831270009 / 2000000000000000000000 : ℚ))) + (U' := (812456615077168729991 / 2000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (3018237115373567 / 10000000000000000 : ℚ)) + (q := (120091618888945197 / 320000000000000000 : ℚ)) + (U := (-(1960132106122831270009 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_15 : Uω (aρ 15) (bρ 15) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -393,25 +332,21 @@ lemma U_664_15 : have hlg : Real.log (165796384488381 / 512000000000000 : ℝ) ≤ (-(225512837703902044943 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (165796384488381 / 512000000000000 : ℝ) = - (165796384488381 / 128000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (165796384488381 / 128000000000000 : ℚ)) - (U := (51746034416097955057 / 200000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (165796384488381 / 128000000000000 : ℝ) ≤ - (51746034416097955057 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3597608770091 / 16000000000000 : ℝ)) (q := - (165796384488381 / 512000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [bρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (165796384488381 / 512000000000000 : ℚ)) + (r' := (165796384488381 / 128000000000000 : ℚ)) + (U := (-(225512837703902044943 / 200000000000000000000 : ℚ))) + (U' := (51746034416097955057 / 200000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (3597608770091 / 16000000000000 : ℚ)) + (q := (165796384488381 / 512000000000000 : ℚ)) + (U := (-(225512837703902044943 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664_16 : Uω (aρ 16) (bρ 16) (199912686621581 / 256000000000000 : ℝ) ≤ @@ -419,26 +354,21 @@ lemma U_664_16 : have hlg : Real.log (91382558574823133 / 320000000000000000 : ℝ) ≤ (-(1253266360243979778637 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (91382558574823133 / 320000000000000000 : ℝ) = - (91382558574823133 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (91382558574823133 / 80000000000000000 : ℚ)) - (U := (133028000356020221363 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (91382558574823133 / 80000000000000000 : ℝ) ≤ - (133028000356020221363 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (817932887332969 / 5000000000000000 : ℝ)) (q := - (91382558574823133 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (91382558574823133 / 320000000000000000 : ℚ)) + (r' := (91382558574823133 / 80000000000000000 : ℚ)) + (U := (-(1253266360243979778637 / 1000000000000000000000 : ℚ))) + (U' := (133028000356020221363 / 1000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (199912686621581 / 256000000000000 : ℚ)) + (s := (817932887332969 / 5000000000000000 : ℚ)) + (q := (91382558574823133 / 320000000000000000 : ℚ)) + (U := (-(1253266360243979778637 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_664 : Uρ (199912686621581 / 256000000000000 : ℝ) ≤ @@ -538,25 +468,21 @@ lemma U_665_1 : have hlg : Real.log (31174123359408541 / 40000000000000000 : ℝ) ≤ (-(249291082670160325427 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (31174123359408541 / 40000000000000000 : ℝ) = - (31174123359408541 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31174123359408541 / 20000000000000000 : ℚ)) - (U := (443856097629839674573 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31174123359408541 / 20000000000000000 : ℝ) ≤ - (443856097629839674573 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7793510095995833 / 10000000000000000 : ℝ)) (q := - (31174123359408541 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31174123359408541 / 40000000000000000 : ℚ)) + (r' := (31174123359408541 / 20000000000000000 : ℚ)) + (U := (-(249291082670160325427 / 1000000000000000000000 : ℚ))) + (U' := (443856097629839674573 / 1000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (7793510095995833 / 10000000000000000 : ℚ)) + (q := (31174123359408541 / 40000000000000000 : ℚ)) + (U := (-(249291082670160325427 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_2 : Uω (aρ 2) (bρ 2) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -564,25 +490,21 @@ lemma U_665_2 : have hlg : Real.log (31078584094158457 / 40000000000000000 : ℝ) ≤ (-(252360486208296023661 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (31078584094158457 / 40000000000000000 : ℝ) = - (31078584094158457 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31078584094158457 / 20000000000000000 : ℚ)) - (U := (440786694091703976339 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31078584094158457 / 20000000000000000 : ℝ) ≤ - (440786694091703976339 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7769509475880791 / 10000000000000000 : ℝ)) (q := - (31078584094158457 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31078584094158457 / 40000000000000000 : ℚ)) + (r' := (31078584094158457 / 20000000000000000 : ℚ)) + (U := (-(252360486208296023661 / 1000000000000000000000 : ℚ))) + (U' := (440786694091703976339 / 1000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (7769509475880791 / 10000000000000000 : ℚ)) + (q := (31078584094158457 / 40000000000000000 : ℚ)) + (U := (-(252360486208296023661 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_3 : Uω (aρ 3) (bρ 3) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -590,25 +512,21 @@ lemma U_665_3 : have hlg : Real.log (30887629731693159 / 40000000000000000 : ℝ) ≤ (-(2585236824123272191887 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (30887629731693159 / 40000000000000000 : ℝ) = - (30887629731693159 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30887629731693159 / 20000000000000000 : ℚ)) - (U := (4346234978876727808113 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30887629731693159 / 20000000000000000 : ℝ) ≤ - (4346234978876727808113 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3860714200499071 / 5000000000000000 : ℝ)) (q := - (30887629731693159 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30887629731693159 / 40000000000000000 : ℚ)) + (r' := (30887629731693159 / 20000000000000000 : ℚ)) + (U := (-(2585236824123272191887 / 10000000000000000000000 : ℚ))) + (U' := (4346234978876727808113 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (3860714200499071 / 5000000000000000 : ℚ)) + (q := (30887629731693159 / 40000000000000000 : ℚ)) + (U := (-(2585236824123272191887 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_4 : Uω (aρ 4) (bρ 4) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -616,25 +534,21 @@ lemma U_665_4 : have hlg : Real.log (30570862961772313 / 40000000000000000 : ℝ) ≤ (-(1344160446545207092199 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (30570862961772313 / 40000000000000000 : ℝ) = - (30570862961772313 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30570862961772313 / 20000000000000000 : ℚ)) - (U := (2121575454954792907801 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30570862961772313 / 20000000000000000 : ℝ) ≤ - (2121575454954792907801 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7641339197102719 / 10000000000000000 : ℝ)) (q := - (30570862961772313 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30570862961772313 / 40000000000000000 : ℚ)) + (r' := (30570862961772313 / 20000000000000000 : ℚ)) + (U := (-(1344160446545207092199 / 5000000000000000000000 : ℚ))) + (U' := (2121575454954792907801 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (7641339197102719 / 10000000000000000 : ℚ)) + (q := (30570862961772313 / 40000000000000000 : ℚ)) + (U := (-(1344160446545207092199 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_5 : Uω (aρ 5) (bρ 5) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -642,25 +556,21 @@ lemma U_665_5 : have hlg : Real.log (30089449842355157 / 40000000000000000 : ℝ) ≤ (-(355881058895171594713 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (30089449842355157 / 40000000000000000 : ℝ) = - (30089449842355157 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30089449842355157 / 20000000000000000 : ℚ)) - (U := (510552916479828405287 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30089449842355157 / 20000000000000000 : ℝ) ≤ - (510552916479828405287 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7518822556729141 / 10000000000000000 : ℝ)) (q := - (30089449842355157 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30089449842355157 / 40000000000000000 : ℚ)) + (r' := (30089449842355157 / 20000000000000000 : ℚ)) + (U := (-(355881058895171594713 / 1250000000000000000000 : ℚ))) + (U' := (510552916479828405287 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (7518822556729141 / 10000000000000000 : ℚ)) + (q := (30089449842355157 / 40000000000000000 : ℚ)) + (U := (-(355881058895171594713 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_6 : Uω (aρ 6) (bρ 6) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -668,25 +578,21 @@ lemma U_665_6 : have hlg : Real.log (1176050222896367 / 1600000000000000 : ℝ) ≤ (-(3078420738767238145273 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1176050222896367 / 1600000000000000 : ℝ) = - (1176050222896367 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1176050222896367 / 800000000000000 : ℚ)) - (U := (3853051064232761854727 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1176050222896367 / 800000000000000 : ℝ) ≤ - (3853051064232761854727 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (146839315937923 / 200000000000000 : ℝ)) (q := - (1176050222896367 / 1600000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1176050222896367 / 1600000000000000 : ℚ)) + (r' := (1176050222896367 / 800000000000000 : ℚ)) + (U := (-(3078420738767238145273 / 10000000000000000000000 : ℚ))) + (U' := (3853051064232761854727 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (146839315937923 / 200000000000000 : ℚ)) + (q := (1176050222896367 / 1600000000000000 : ℚ)) + (U := (-(3078420738767238145273 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_7 : Uω (aρ 7) (bρ 7) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -694,25 +600,21 @@ lemma U_665_7 : have hlg : Real.log (5693423637368201 / 8000000000000000 : ℝ) ≤ (-(340129780488928500307 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5693423637368201 / 8000000000000000 : ℝ) = - (5693423637368201 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5693423637368201 / 4000000000000000 : ℚ)) - (U := (353017399811071499693 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5693423637368201 / 4000000000000000 : ℝ) ≤ - (353017399811071499693 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1419711696974413 / 2000000000000000 : ℝ)) (q := - (5693423637368201 / 8000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5693423637368201 / 8000000000000000 : ℚ)) + (r' := (5693423637368201 / 4000000000000000 : ℚ)) + (U := (-(340129780488928500307 / 1000000000000000000000 : ℚ))) + (U' := (353017399811071499693 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1419711696974413 / 2000000000000000 : ℚ)) + (q := (5693423637368201 / 8000000000000000 : ℚ)) + (U := (-(340129780488928500307 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_8 : Uω (aρ 8) (bρ 8) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -720,25 +622,21 @@ lemma U_665_8 : have hlg : Real.log (27257774507655987 / 40000000000000000 : ℝ) ≤ (-(3835406704026617134509 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (27257774507655987 / 40000000000000000 : ℝ) = - (27257774507655987 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (27257774507655987 / 20000000000000000 : ℚ)) - (U := (3096065098973382865491 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (27257774507655987 / 20000000000000000 : ℝ) ≤ - (3096065098973382865491 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1694357074154889 / 2500000000000000 : ℝ)) (q := - (27257774507655987 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (27257774507655987 / 40000000000000000 : ℚ)) + (r' := (27257774507655987 / 20000000000000000 : ℚ)) + (U := (-(3835406704026617134509 / 10000000000000000000000 : ℚ))) + (U' := (3096065098973382865491 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1694357074154889 / 2500000000000000 : ℚ)) + (q := (27257774507655987 / 40000000000000000 : ℚ)) + (U := (-(3835406704026617134509 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_9 : Uω (aρ 9) (bρ 9) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -746,25 +644,21 @@ lemma U_665_9 : have hlg : Real.log (25760698502538297 / 40000000000000000 : ℝ) ≤ (-(4400294372036981046643 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25760698502538297 / 40000000000000000 : ℝ) = - (25760698502538297 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25760698502538297 / 20000000000000000 : ℚ)) - (U := (2531177430963018953357 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25760698502538297 / 20000000000000000 : ℝ) ≤ - (2531177430963018953357 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6369855922420711 / 10000000000000000 : ℝ)) (q := - (25760698502538297 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25760698502538297 / 40000000000000000 : ℚ)) + (r' := (25760698502538297 / 20000000000000000 : ℚ)) + (U := (-(4400294372036981046643 / 10000000000000000000000 : ℚ))) + (U' := (2531177430963018953357 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (6369855922420711 / 10000000000000000 : ℚ)) + (q := (25760698502538297 / 40000000000000000 : ℚ)) + (U := (-(4400294372036981046643 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_10 : Uω (aρ 10) (bρ 10) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -772,26 +666,21 @@ lemma U_665_10 : have hlg : Real.log (23985864038979301 / 40000000000000000 : ℝ) ≤ (-(2557073977047964558419 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23985864038979301 / 40000000000000000 : ℝ) = - (23985864038979301 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23985864038979301 / 20000000000000000 : ℚ)) - (U := (908661924452035441581 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (23985864038979301 / 20000000000000000 : ℝ) ≤ - (908661924452035441581 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5870997724136213 / 10000000000000000 : ℝ)) (q := - (23985864038979301 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23985864038979301 / 40000000000000000 : ℚ)) + (r' := (23985864038979301 / 20000000000000000 : ℚ)) + (U := (-(2557073977047964558419 / 5000000000000000000000 : ℚ))) + (U' := (908661924452035441581 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (5870997724136213 / 10000000000000000 : ℚ)) + (q := (23985864038979301 / 40000000000000000 : ℚ)) + (U := (-(2557073977047964558419 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_11 : Uω (aρ 11) (bρ 11) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -799,26 +688,21 @@ lemma U_665_11 : have hlg : Real.log (4393897053689701 / 8000000000000000 : ℝ) ≤ (-(5992249965690502151559 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4393897053689701 / 8000000000000000 : ℝ) = - (4393897053689701 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4393897053689701 / 4000000000000000 : ℚ)) - (U := (939221837309497848441 / 10000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (4393897053689701 / 4000000000000000 : ℝ) ≤ - (939221837309497848441 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1056256993015163 / 2000000000000000 : ℝ)) (q := - (4393897053689701 / 8000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4393897053689701 / 8000000000000000 : ℚ)) + (r' := (4393897053689701 / 4000000000000000 : ℚ)) + (U := (-(5992249965690502151559 / 10000000000000000000000 : ℚ))) + (U' := (939221837309497848441 / 10000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1056256993015163 / 2000000000000000 : ℚ)) + (q := (4393897053689701 / 8000000000000000 : ℚ)) + (U := (-(5992249965690502151559 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_12 : Uω (aρ 12) (bρ 12) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -826,26 +710,21 @@ lemma U_665_12 : have hlg : Real.log (19775419173586063 / 40000000000000000 : ℝ) ≤ (-(1408879486035550407403 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (19775419173586063 / 40000000000000000 : ℝ) = - (19775419173586063 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19775419173586063 / 10000000000000000 : ℚ)) - (U := (1363709235164449592597 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19775419173586063 / 10000000000000000 : ℝ) ≤ - (1363709235164449592597 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2303976007164797 / 5000000000000000 : ℝ)) (q := - (19775419173586063 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19775419173586063 / 40000000000000000 : ℚ)) + (r' := (19775419173586063 / 10000000000000000 : ℚ)) + (U := (-(1408879486035550407403 / 2000000000000000000000 : ℚ))) + (U' := (1363709235164449592597 / 2000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (2303976007164797 / 5000000000000000 : ℚ)) + (q := (19775419173586063 / 40000000000000000 : ℚ)) + (U := (-(1408879486035550407403 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_13 : Uω (aρ 13) (bρ 13) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -853,26 +732,21 @@ lemma U_665_13 : have hlg : Real.log (17495515216103551 / 40000000000000000 : ℝ) ≤ (-(4134674394368595173987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17495515216103551 / 40000000000000000 : ℝ) = - (17495515216103551 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17495515216103551 / 10000000000000000 : ℚ)) - (U := (2796797408631404826013 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17495515216103551 / 10000000000000000 : ℝ) ≤ - (2796797408631404826013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1933690888591669 / 5000000000000000 : ℝ)) (q := - (17495515216103551 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17495515216103551 / 40000000000000000 : ℚ)) + (r' := (17495515216103551 / 10000000000000000 : ℚ)) + (U := (-(4134674394368595173987 / 5000000000000000000000 : ℚ))) + (U' := (2796797408631404826013 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1933690888591669 / 5000000000000000 : ℚ)) + (q := (17495515216103551 / 40000000000000000 : ℚ)) + (U := (-(4134674394368595173987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_14 : Uω (aρ 14) (bρ 14) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -880,26 +754,21 @@ lemma U_665_14 : have hlg : Real.log (15254017567212007 / 40000000000000000 : ℝ) ≤ (-(9640365382064048121153 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15254017567212007 / 40000000000000000 : ℝ) = - (15254017567212007 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15254017567212007 / 10000000000000000 : ℚ)) - (U := (4222578223935951878847 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15254017567212007 / 10000000000000000 : ℝ) ≤ - (4222578223935951878847 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1545280118891283 / 5000000000000000 : ℝ)) (q := - (15254017567212007 / 40000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15254017567212007 / 40000000000000000 : ℚ)) + (r' := (15254017567212007 / 10000000000000000 : ℚ)) + (U := (-(9640365382064048121153 / 10000000000000000000000 : ℚ))) + (U' := (4222578223935951878847 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1545280118891283 / 5000000000000000 : ℚ)) + (q := (15254017567212007 / 40000000000000000 : ℚ)) + (U := (-(9640365382064048121153 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_15 : Uω (aρ 15) (bρ 15) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -907,26 +776,21 @@ lemma U_665_15 : have hlg : Real.log (13232283235222089 / 40000000000000000 : ℝ) ≤ (-(442487964087878460311 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (13232283235222089 / 40000000000000000 : ℝ) = - (13232283235222089 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13232283235222089 / 10000000000000000 : ℚ)) - (U := (112029780152121539689 / 400000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (13232283235222089 / 10000000000000000 : ℝ) ≤ - (112029780152121539689 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2339266349202607 / 10000000000000000 : ℝ)) (q := - (13232283235222089 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13232283235222089 / 40000000000000000 : ℚ)) + (r' := (13232283235222089 / 10000000000000000 : ℚ)) + (U := (-(442487964087878460311 / 400000000000000000000 : ℚ))) + (U' := (112029780152121539689 / 400000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (2339266349202607 / 10000000000000000 : ℚ)) + (q := (13232283235222089 / 40000000000000000 : ℚ)) + (U := (-(442487964087878460311 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665_16 : Uω (aρ 16) (bρ 16) (25145756165739 / 32000000000000 : ℝ) ≤ @@ -934,26 +798,21 @@ lemma U_665_16 : have hlg : Real.log (11757583533052329 / 40000000000000000 : ℝ) ≤ (-(12243810141211648147373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (11757583533052329 / 40000000000000000 : ℝ) = - (11757583533052329 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11757583533052329 / 10000000000000000 : ℚ)) - (U := (1619133464788351852627 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11757583533052329 / 10000000000000000 : ℝ) ≤ - (1619133464788351852627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1754288149627727 / 10000000000000000 : ℝ)) (q := - (11757583533052329 / 40000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11757583533052329 / 40000000000000000 : ℚ)) + (r' := (11757583533052329 / 10000000000000000 : ℚ)) + (U := (-(12243810141211648147373 / 10000000000000000000000 : ℚ))) + (U' := (1619133464788351852627 / 10000000000000000000000 : ℚ)) + 2 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (25145756165739 / 32000000000000 : ℚ)) + (s := (1754288149627727 / 10000000000000000 : ℚ)) + (q := (11757583533052329 / 40000000000000000 : ℚ)) + (U := (-(12243810141211648147373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_665 : Uρ (25145756165739 / 32000000000000 : ℝ) ≤ @@ -1046,25 +905,21 @@ lemma U_666_1 : have hlg : Real.log (250959694399717187 / 320000000000000000 : ℝ) ≤ (-(2430286493772126347773 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (250959694399717187 / 320000000000000000 : ℝ) = - (250959694399717187 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (250959694399717187 / 160000000000000000 : ℚ)) - (U := (4501185309227873652227 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (250959694399717187 / 160000000000000000 : ℝ) ≤ - (4501185309227873652227 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7842469835635957 / 10000000000000000 : ℝ)) (q := - (250959694399717187 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (250959694399717187 / 320000000000000000 : ℚ)) + (r' := (250959694399717187 / 160000000000000000 : ℚ)) + (U := (-(2430286493772126347773 / 10000000000000000000000 : ℚ))) + (U' := (4501185309227873652227 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (7842469835635957 / 10000000000000000 : ℚ)) + (q := (250959694399717187 / 320000000000000000 : ℚ)) + (U := (-(2430286493772126347773 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_2 : Uω (aρ 2) (bρ 2) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1072,25 +927,21 @@ lemma U_666_2 : have hlg : Real.log (250195403495771923 / 320000000000000000 : ℝ) ≤ (-(49215753797925468473 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (250195403495771923 / 320000000000000000 : ℝ) = - (250195403495771923 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (250195403495771923 / 160000000000000000 : ℚ)) - (U := (89413682262074531527 / 200000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (250195403495771923 / 160000000000000000 : ℝ) ≤ - (89413682262074531527 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3909235333324689 / 5000000000000000 : ℝ)) (q := - (250195403495771923 / 320000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (250195403495771923 / 320000000000000000 : ℚ)) + (r' := (250195403495771923 / 160000000000000000 : ℚ)) + (U := (-(49215753797925468473 / 200000000000000000000 : ℚ))) + (U' := (89413682262074531527 / 200000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (3909235333324689 / 5000000000000000 : ℚ)) + (q := (250195403495771923 / 320000000000000000 : ℚ)) + (U := (-(49215753797925468473 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_3 : Uω (aρ 3) (bρ 3) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1098,25 +949,21 @@ lemma U_666_3 : have hlg : Real.log (248667837818667059 / 320000000000000000 : ℝ) ≤ (-(1261014871413616783293 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (248667837818667059 / 320000000000000000 : ℝ) = - (248667837818667059 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (248667837818667059 / 160000000000000000 : ℚ)) - (U := (2204721030086383216707 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (248667837818667059 / 160000000000000000 : ℝ) ≤ - (2204721030086383216707 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1942598479545081 / 2500000000000000 : ℝ)) (q := - (248667837818667059 / 320000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (248667837818667059 / 320000000000000000 : ℚ)) + (r' := (248667837818667059 / 160000000000000000 : ℚ)) + (U := (-(1261014871413616783293 / 5000000000000000000000 : ℚ))) + (U' := (2204721030086383216707 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (1942598479545081 / 2500000000000000 : ℚ)) + (q := (248667837818667059 / 320000000000000000 : ℚ)) + (U := (-(1261014871413616783293 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_4 : Uω (aρ 4) (bρ 4) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1124,25 +971,21 @@ lemma U_666_4 : have hlg : Real.log (246133887510078227 / 320000000000000000 : ℝ) ≤ (-(656113373712938037237 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (246133887510078227 / 320000000000000000 : ℝ) = - (246133887510078227 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (246133887510078227 / 160000000000000000 : ℚ)) - (U := (1076754577037061962763 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (246133887510078227 / 160000000000000000 : ℝ) ≤ - (1076754577037061962763 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3845158102479261 / 5000000000000000 : ℝ)) (q := - (246133887510078227 / 320000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (246133887510078227 / 320000000000000000 : ℚ)) + (r' := (246133887510078227 / 160000000000000000 : ℚ)) + (U := (-(656113373712938037237 / 2500000000000000000000 : ℚ))) + (U' := (1076754577037061962763 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (3845158102479261 / 5000000000000000 : ℚ)) + (q := (246133887510078227 / 320000000000000000 : ℚ)) + (U := (-(656113373712938037237 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_5 : Uω (aρ 5) (bρ 5) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1150,25 +993,21 @@ lemma U_666_5 : have hlg : Real.log (242283034957824227 / 320000000000000000 : ℝ) ≤ (-(1391071934225770335259 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (242283034957824227 / 320000000000000000 : ℝ) = - (242283034957824227 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (242283034957824227 / 160000000000000000 : ℚ)) - (U := (2074663967274229664741 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (242283034957824227 / 160000000000000000 : ℝ) ≤ - (2074663967274229664741 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7567827839777647 / 10000000000000000 : ℝ)) (q := - (242283034957824227 / 320000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (242283034957824227 / 320000000000000000 : ℚ)) + (r' := (242283034957824227 / 160000000000000000 : ℚ)) + (U := (-(1391071934225770335259 / 5000000000000000000000 : ℚ))) + (U' := (2074663967274229664741 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (7567827839777647 / 10000000000000000 : ℚ)) + (q := (242283034957824227 / 320000000000000000 : ℚ)) + (U := (-(1391071934225770335259 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_6 : Uω (aρ 6) (bρ 6) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1176,25 +1015,21 @@ lemma U_666_6 : have hlg : Real.log (236778517547688323 / 320000000000000000 : ℝ) ≤ (-(1505979082273865270421 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (236778517547688323 / 320000000000000000 : ℝ) = - (236778517547688323 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (236778517547688323 / 160000000000000000 : ℚ)) - (U := (1959756819226134729579 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (236778517547688323 / 160000000000000000 : ℝ) ≤ - (1959756819226134729579 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7391035876784153 / 10000000000000000 : ℝ)) (q := - (236778517547688323 / 320000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (236778517547688323 / 320000000000000000 : ℚ)) + (r' := (236778517547688323 / 160000000000000000 : ℚ)) + (U := (-(1505979082273865270421 / 5000000000000000000000 : ℚ))) + (U' := (1959756819226134729579 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (7391035876784153 / 10000000000000000 : ℚ)) + (q := (236778517547688323 / 320000000000000000 : ℚ)) + (U := (-(1505979082273865270421 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_7 : Uω (aρ 7) (bρ 7) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1202,25 +1037,21 @@ lemma U_666_7 : have hlg : Real.log (45861528555831351 / 64000000000000000 : ℝ) ≤ (-(208285297068072753121 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45861528555831351 / 64000000000000000 : ℝ) = - (45861528555831351 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45861528555831351 / 32000000000000000 : ℚ)) - (U := (224931690619427246879 / 625000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (45861528555831351 / 32000000000000000 : ℝ) ≤ - (224931690619427246879 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (714776758451093 / 1000000000000000 : ℝ)) (q := - (45861528555831351 / 64000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45861528555831351 / 64000000000000000 : ℚ)) + (r' := (45861528555831351 / 32000000000000000 : ℚ)) + (U := (-(208285297068072753121 / 625000000000000000000 : ℚ))) + (U' := (224931690619427246879 / 625000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (714776758451093 / 1000000000000000 : ℚ)) + (q := (45861528555831351 / 64000000000000000 : ℚ)) + (U := (-(208285297068072753121 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_8 : Uω (aρ 8) (bρ 8) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1228,25 +1059,21 @@ lemma U_666_8 : have hlg : Real.log (219637394386552531 / 320000000000000000 : ℝ) ≤ (-(37634301630337236271 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (219637394386552531 / 320000000000000000 : ℝ) = - (219637394386552531 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (219637394386552531 / 160000000000000000 : ℚ)) - (U := (31680416399662763729 / 100000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (219637394386552531 / 160000000000000000 : ℝ) ≤ - (31680416399662763729 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3413459355656583 / 5000000000000000 : ℝ)) (q := - (219637394386552531 / 320000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (219637394386552531 / 320000000000000000 : ℚ)) + (r' := (219637394386552531 / 160000000000000000 : ℚ)) + (U := (-(37634301630337236271 / 100000000000000000000 : ℚ))) + (U' := (31680416399662763729 / 100000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (3413459355656583 / 5000000000000000 : ℚ)) + (q := (219637394386552531 / 320000000000000000 : ℚ)) + (U := (-(37634301630337236271 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_9 : Uω (aρ 9) (bρ 9) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1254,25 +1081,21 @@ lemma U_666_9 : have hlg : Real.log (41533890668800807 / 64000000000000000 : ℝ) ≤ (-(864746693025047178221 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (41533890668800807 / 64000000000000000 : ℝ) = - (41533890668800807 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (41533890668800807 / 32000000000000000 : ℚ)) - (U := (521547667574952821779 / 2000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (41533890668800807 / 32000000000000000 : ℝ) ≤ - (521547667574952821779 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1283977604902777 / 2000000000000000 : ℝ)) (q := - (41533890668800807 / 64000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (41533890668800807 / 64000000000000000 : ℚ)) + (r' := (41533890668800807 / 32000000000000000 : ℚ)) + (U := (-(864746693025047178221 / 2000000000000000000000 : ℚ))) + (U' := (521547667574952821779 / 2000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (1283977604902777 / 2000000000000000 : ℚ)) + (q := (41533890668800807 / 64000000000000000 : ℚ)) + (U := (-(864746693025047178221 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_10 : Uω (aρ 10) (bρ 10) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1280,26 +1103,21 @@ lemma U_666_10 : have hlg : Real.log (193486814774151011 / 320000000000000000 : ℝ) ≤ (-(31444476630483468137 / 62500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (193486814774151011 / 320000000000000000 : ℝ) = - (193486814774151011 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (193486814774151011 / 160000000000000000 : ℚ)) - (U := (11877222138266531863 / 62500000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (193486814774151011 / 160000000000000000 : ℝ) ≤ - (11877222138266531863 / 62500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5922032147393071 / 10000000000000000 : ℝ)) (q := - (193486814774151011 / 320000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (193486814774151011 / 320000000000000000 : ℚ)) + (r' := (193486814774151011 / 160000000000000000 : ℚ)) + (U := (-(31444476630483468137 / 62500000000000000000 : ℚ))) + (U' := (11877222138266531863 / 62500000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (5922032147393071 / 10000000000000000 : ℚ)) + (q := (193486814774151011 / 320000000000000000 : ℚ)) + (U := (-(31444476630483468137 / 62500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_11 : Uω (aρ 11) (bρ 11) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1307,26 +1125,21 @@ lemma U_666_11 : have hlg : Real.log (177384606978711139 / 320000000000000000 : ℝ) ≤ (-(2950003497771861187207 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (177384606978711139 / 320000000000000000 : ℝ) = - (177384606978711139 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (177384606978711139 / 160000000000000000 : ℚ)) - (U := (515732403728138812793 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (177384606978711139 / 160000000000000000 : ℝ) ≤ - (515732403728138812793 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5334120786383079 / 10000000000000000 : ℝ)) (q := - (177384606978711139 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (177384606978711139 / 320000000000000000 : ℚ)) + (r' := (177384606978711139 / 160000000000000000 : ℚ)) + (U := (-(2950003497771861187207 / 5000000000000000000000 : ℚ))) + (U' := (515732403728138812793 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (5334120786383079 / 10000000000000000 : ℚ)) + (q := (177384606978711139 / 320000000000000000 : ℚ)) + (U := (-(2950003497771861187207 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_12 : Uω (aρ 12) (bρ 12) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1334,26 +1147,21 @@ lemma U_666_12 : have hlg : Real.log (159882977435271507 / 320000000000000000 : ℝ) ≤ (-(3469394193332567164563 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (159882977435271507 / 320000000000000000 : ℝ) = - (159882977435271507 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (159882977435271507 / 80000000000000000 : ℚ)) - (U := (3462077609667432835437 / 5000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (159882977435271507 / 80000000000000000 : ℝ) ≤ - (3462077609667432835437 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2331984518301551 / 5000000000000000 : ℝ)) (q := - (159882977435271507 / 320000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (159882977435271507 / 320000000000000000 : ℚ)) + (r' := (159882977435271507 / 80000000000000000 : ℚ)) + (U := (-(3469394193332567164563 / 5000000000000000000000 : ℚ))) + (U' := (3462077609667432835437 / 5000000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (2331984518301551 / 5000000000000000 : ℚ)) + (q := (159882977435271507 / 320000000000000000 : ℚ)) + (U := (-(3469394193332567164563 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_13 : Uω (aρ 13) (bρ 13) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1361,26 +1169,21 @@ lemma U_666_13 : have hlg : Real.log (141733118963215363 / 320000000000000000 : ℝ) ≤ (-(8143751499644154206229 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (141733118963215363 / 320000000000000000 : ℝ) = - (141733118963215363 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (141733118963215363 / 80000000000000000 : ℚ)) - (U := (5719192106355845793771 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (141733118963215363 / 80000000000000000 : ℝ) ≤ - (5719192106355845793771 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3928984623694593 / 10000000000000000 : ℝ)) (q := - (141733118963215363 / 320000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (141733118963215363 / 320000000000000000 : ℚ)) + (r' := (141733118963215363 / 80000000000000000 : ℚ)) + (U := (-(8143751499644154206229 / 10000000000000000000000 : ℚ))) + (U' := (5719192106355845793771 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (3928984623694593 / 10000000000000000 : ℚ)) + (q := (141733118963215363 / 320000000000000000 : ℚ)) + (U := (-(8143751499644154206229 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_14 : Uω (aρ 14) (bρ 14) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1388,26 +1191,21 @@ lemma U_666_14 : have hlg : Real.log (123958325876728179 / 320000000000000000 : ℝ) ≤ (-(9483755677962245212443 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (123958325876728179 / 320000000000000000 : ℝ) = - (123958325876728179 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123958325876728179 / 80000000000000000 : ℚ)) - (U := (4379187928037754787557 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (123958325876728179 / 80000000000000000 : ℝ) ≤ - (4379187928037754787557 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (98812104401067 / 312500000000000 : ℝ)) (q := - (123958325876728179 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123958325876728179 / 320000000000000000 : ℚ)) + (r' := (123958325876728179 / 80000000000000000 : ℚ)) + (U := (-(9483755677962245212443 / 10000000000000000000000 : ℚ))) + (U' := (4379187928037754787557 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (98812104401067 / 312500000000000 : ℚ)) + (q := (123958325876728179 / 320000000000000000 : ℚ)) + (U := (-(9483755677962245212443 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_15 : Uω (aρ 15) (bρ 15) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1415,26 +1213,21 @@ lemma U_666_15 : have hlg : Real.log (108055316856504243 / 320000000000000000 : ℝ) ≤ (-(5428388530800015652507 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (108055316856504243 / 320000000000000000 : ℝ) = - (108055316856504243 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (108055316856504243 / 80000000000000000 : ℚ)) - (U := (1503083272199984347493 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (108055316856504243 / 80000000000000000 : ℝ) ≤ - (1503083272199984347493 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (606905638621287 / 2500000000000000 : ℝ)) (q := - (108055316856504243 / 320000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (108055316856504243 / 320000000000000000 : ℚ)) + (r' := (108055316856504243 / 80000000000000000 : ℚ)) + (U := (-(5428388530800015652507 / 5000000000000000000000 : ℚ))) + (U' := (1503083272199984347493 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (606905638621287 / 2500000000000000 : ℚ)) + (q := (108055316856504243 / 320000000000000000 : ℚ)) + (U := (-(5428388530800015652507 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666_16 : Uω (aρ 16) (bρ 16) (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1442,26 +1235,21 @@ lemma U_666_16 : have hlg : Real.log (96639275845260099 / 320000000000000000 : ℝ) ≤ (-(748334846524065932333 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (96639275845260099 / 320000000000000000 : ℝ) = - (96639275845260099 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96639275845260099 / 80000000000000000 : ℚ)) - (U := (118099128850934067667 / 625000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (96639275845260099 / 80000000000000000 : ℝ) ≤ - (118099128850934067667 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1866491642792389 / 10000000000000000 : ℝ)) (q := - (96639275845260099 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96639275845260099 / 320000000000000000 : ℚ)) + (r' := (96639275845260099 / 80000000000000000 : ℚ)) + (U := (-(748334846524065932333 / 625000000000000000000 : ℚ))) + (U' := (118099128850934067667 / 625000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (202419412030243 / 256000000000000 : ℚ)) + (s := (1866491642792389 / 10000000000000000 : ℚ)) + (q := (96639275845260099 / 320000000000000000 : ℚ)) + (U := (-(748334846524065932333 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_666 : Uρ (202419412030243 / 256000000000000 : ℝ) ≤ @@ -1558,25 +1346,21 @@ lemma U_667_1 : have hlg : Real.log (25252640187274563 / 32000000000000000 : ℝ) ≤ (-(1184025952061820073691 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25252640187274563 / 32000000000000000 : ℝ) = - (25252640187274563 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25252640187274563 / 16000000000000000 : ℚ)) - (U := (2281709949438179926309 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (25252640187274563 / 16000000000000000 : ℝ) ≤ - (2281709949438179926309 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1578285914412461 / 2000000000000000 : ℝ)) (q := - (25252640187274563 / 32000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25252640187274563 / 32000000000000000 : ℚ)) + (r' := (25252640187274563 / 16000000000000000 : ℚ)) + (U := (-(1184025952061820073691 / 5000000000000000000000 : ℚ))) + (U' := (2281709949438179926309 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1578285914412461 / 2000000000000000 : ℚ)) + (q := (25252640187274563 / 32000000000000000 : ℚ)) + (U := (-(1184025952061820073691 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_2 : Uω (aρ 2) (bρ 2) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1584,25 +1368,21 @@ lemma U_667_2 : have hlg : Real.log (25176213389771851 / 32000000000000000 : ℝ) ≤ (-(149897666808250901199 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25176213389771851 / 32000000000000000 : ℝ) = - (25176213389771851 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25176213389771851 / 16000000000000000 : ℚ)) - (U := (283319320879249098801 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (25176213389771851 / 16000000000000000 : ℝ) ≤ - (283319320879249098801 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (786743183613311 / 1000000000000000 : ℝ)) (q := - (25176213389771851 / 32000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25176213389771851 / 32000000000000000 : ℚ)) + (r' := (25176213389771851 / 16000000000000000 : ℚ)) + (U := (-(149897666808250901199 / 625000000000000000000 : ℚ))) + (U' := (283319320879249098801 / 625000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (786743183613311 / 1000000000000000 : ℚ)) + (q := (25176213389771851 / 32000000000000000 : ℚ)) + (U := (-(149897666808250901199 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_3 : Uω (aρ 3) (bρ 3) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1610,25 +1390,21 @@ lemma U_667_3 : have hlg : Real.log (125117318287109767 / 160000000000000000 : ℝ) ≤ (-(2459219715338930544141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (125117318287109767 / 160000000000000000 : ℝ) = - (125117318287109767 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (125117318287109767 / 80000000000000000 : ℚ)) - (U := (4472252087661069455859 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (125117318287109767 / 80000000000000000 : ℝ) ≤ - (4472252087661069455859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (977419919970553 / 1250000000000000 : ℝ)) (q := - (125117318287109767 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (125117318287109767 / 160000000000000000 : ℚ)) + (r' := (125117318287109767 / 80000000000000000 : ℚ)) + (U := (-(2459219715338930544141 / 10000000000000000000000 : ℚ))) + (U' := (4472252087661069455859 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (977419919970553 / 1250000000000000 : ℚ)) + (q := (125117318287109767 / 160000000000000000 : ℚ)) + (U := (-(2459219715338930544141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_4 : Uω (aρ 4) (bρ 4) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1636,25 +1412,21 @@ lemma U_667_4 : have hlg : Real.log (123850433888610727 / 160000000000000000 : ℝ) ≤ (-(2560991557050394938723 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (123850433888610727 / 160000000000000000 : ℝ) = - (123850433888610727 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (123850433888610727 / 80000000000000000 : ℚ)) - (U := (4370480245949605061277 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (123850433888610727 / 80000000000000000 : ℝ) ≤ - (4370480245949605061277 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1934823247754261 / 2500000000000000 : ℝ)) (q := - (123850433888610727 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (123850433888610727 / 160000000000000000 : ℚ)) + (r' := (123850433888610727 / 80000000000000000 : ℚ)) + (U := (-(2560991557050394938723 / 10000000000000000000000 : ℚ))) + (U' := (4370480245949605061277 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1934823247754261 / 2500000000000000 : ℚ)) + (q := (123850433888610727 / 160000000000000000 : ℚ)) + (U := (-(2560991557050394938723 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_5 : Uω (aρ 5) (bρ 5) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1662,25 +1434,21 @@ lemma U_667_5 : have hlg : Real.log (121925230875660191 / 160000000000000000 : ℝ) ≤ (-(1358829098960116310293 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (121925230875660191 / 160000000000000000 : ℝ) = - (121925230875660191 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (121925230875660191 / 80000000000000000 : ℚ)) - (U := (2106906802539883689707 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (121925230875660191 / 80000000000000000 : ℝ) ≤ - (2106906802539883689707 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7616832533733227 / 10000000000000000 : ℝ)) (q := - (121925230875660191 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (121925230875660191 / 160000000000000000 : ℚ)) + (r' := (121925230875660191 / 80000000000000000 : ℚ)) + (U := (-(1358829098960116310293 / 5000000000000000000000 : ℚ))) + (U' := (2106906802539883689707 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (7616832533733227 / 10000000000000000 : ℚ)) + (q := (121925230875660191 / 160000000000000000 : ℚ)) + (U := (-(1358829098960116310293 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_6 : Uω (aρ 6) (bρ 6) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1688,25 +1456,21 @@ lemma U_667_6 : have hlg : Real.log (23834696720031283 / 32000000000000000 : ℝ) ≤ (-(2945935381077970403423 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23834696720031283 / 32000000000000000 : ℝ) = - (23834696720031283 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23834696720031283 / 16000000000000000 : ℚ)) - (U := (3985536421922029596577 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (23834696720031283 / 16000000000000000 : ℝ) ≤ - (3985536421922029596577 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1488020899887051 / 2000000000000000 : ℝ)) (q := - (23834696720031283 / 32000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23834696720031283 / 32000000000000000 : ℚ)) + (r' := (23834696720031283 / 16000000000000000 : ℚ)) + (U := (-(2945935381077970403423 / 10000000000000000000000 : ℚ))) + (U' := (3985536421922029596577 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1488020899887051 / 2000000000000000 : ℚ)) + (q := (23834696720031283 / 32000000000000000 : ℚ)) + (U := (-(2945935381077970403423 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_7 : Uω (aρ 7) (bρ 7) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1714,25 +1478,21 @@ lemma U_667_7 : have hlg : Real.log (115439142792856383 / 160000000000000000 : ℝ) ≤ (-(130572130440057185229 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (115439142792856383 / 160000000000000000 : ℝ) = - (115439142792856383 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (115439142792856383 / 80000000000000000 : ℚ)) - (U := (146686741679942814771 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (115439142792856383 / 80000000000000000 : ℝ) ≤ - (146686741679942814771 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7196973279282751 / 10000000000000000 : ℝ)) (q := - (115439142792856383 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (115439142792856383 / 160000000000000000 : ℚ)) + (r' := (115439142792856383 / 80000000000000000 : ℚ)) + (U := (-(130572130440057185229 / 400000000000000000000 : ℚ))) + (U' := (146686741679942814771 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (7196973279282751 / 10000000000000000 : ℚ)) + (q := (115439142792856383 / 160000000000000000 : ℚ)) + (U := (-(130572130440057185229 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_8 : Uω (aρ 8) (bρ 8) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1740,25 +1500,21 @@ lemma U_667_8 : have hlg : Real.log (22121247108923667 / 32000000000000000 : ℝ) ≤ (-(1845986741144000437987 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22121247108923667 / 32000000000000000 : ℝ) = - (22121247108923667 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22121247108923667 / 16000000000000000 : ℚ)) - (U := (1619749160355999562013 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (22121247108923667 / 16000000000000000 : ℝ) ≤ - (1619749160355999562013 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1375280304918599 / 2000000000000000 : ℝ)) (q := - (22121247108923667 / 32000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22121247108923667 / 32000000000000000 : ℚ)) + (r' := (22121247108923667 / 16000000000000000 : ℚ)) + (U := (-(1845986741144000437987 / 5000000000000000000000 : ℚ))) + (U' := (1619749160355999562013 / 5000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1375280304918599 / 2000000000000000 : ℚ)) + (q := (22121247108923667 / 32000000000000000 : ℚ)) + (U := (-(1845986741144000437987 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_9 : Uω (aρ 9) (bρ 9) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1766,25 +1522,21 @@ lemma U_667_9 : have hlg : Real.log (20925305608484907 / 32000000000000000 : ℝ) ≤ (-(2123883406626890648073 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20925305608484907 / 32000000000000000 : ℝ) = - (20925305608484907 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20925305608484907 / 16000000000000000 : ℚ)) - (U := (1341852494873109351927 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (20925305608484907 / 16000000000000000 : ℝ) ≤ - (1341852494873109351927 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (646990371517877 / 1000000000000000 : ℝ)) (q := - (20925305608484907 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20925305608484907 / 32000000000000000 : ℚ)) + (r' := (20925305608484907 / 16000000000000000 : ℚ)) + (U := (-(2123883406626890648073 / 5000000000000000000000 : ℚ))) + (U' := (1341852494873109351927 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (646990371517877 / 1000000000000000 : ℚ)) + (q := (20925305608484907 / 32000000000000000 : ℚ)) + (U := (-(2123883406626890648073 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_10 : Uω (aρ 10) (bρ 10) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1792,26 +1544,21 @@ lemma U_667_10 : have hlg : Real.log (19508616145571099 / 32000000000000000 : ℝ) ≤ (-(618599601174517764213 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19508616145571099 / 32000000000000000 : ℝ) = - (19508616145571099 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19508616145571099 / 16000000000000000 : ℚ)) - (U := (247834374200482235787 / 1250000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (19508616145571099 / 16000000000000000 : ℝ) ≤ - (247834374200482235787 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1166607780147 / 1953125000000 : ℝ)) (q := - (19508616145571099 / 32000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19508616145571099 / 32000000000000000 : ℚ)) + (r' := (19508616145571099 / 16000000000000000 : ℚ)) + (U := (-(618599601174517764213 / 1250000000000000000000 : ℚ))) + (U' := (247834374200482235787 / 1250000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1166607780147 / 1953125000000 : ℚ)) + (q := (19508616145571099 / 32000000000000000 : ℚ)) + (U := (-(618599601174517764213 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_11 : Uω (aρ 11) (bρ 11) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1819,26 +1566,21 @@ lemma U_667_11 : have hlg : Real.log (89506079902867479 / 160000000000000000 : ℝ) ≤ (-(1452168150311807516473 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (89506079902867479 / 160000000000000000 : ℝ) = - (89506079902867479 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (89506079902867479 / 80000000000000000 : ℚ)) - (U := (280699800438192483527 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (89506079902867479 / 80000000000000000 : ℝ) ≤ - (280699800438192483527 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2693441678717069 / 5000000000000000 : ℝ)) (q := - (89506079902867479 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (89506079902867479 / 160000000000000000 : ℚ)) + (r' := (89506079902867479 / 80000000000000000 : ℚ)) + (U := (-(1452168150311807516473 / 2500000000000000000000 : ℚ))) + (U' := (280699800438192483527 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (2693441678717069 / 5000000000000000 : ℚ)) + (q := (89506079902867479 / 160000000000000000 : ℚ)) + (U := (-(1452168150311807516473 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_12 : Uω (aρ 12) (bρ 12) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1846,26 +1588,21 @@ lemma U_667_12 : have hlg : Real.log (80780044994235911 / 160000000000000000 : ℝ) ≤ (-(6834438478415439925663 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (80780044994235911 / 160000000000000000 : ℝ) = - (80780044994235911 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (80780044994235911 / 80000000000000000 : ℚ)) - (U := (97033324584560074337 / 10000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (80780044994235911 / 80000000000000000 : ℝ) ≤ - (97033324584560074337 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (147494659079381 / 312500000000000 : ℝ)) (q := - (80780044994235911 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (80780044994235911 / 160000000000000000 : ℚ)) + (r' := (80780044994235911 / 80000000000000000 : ℚ)) + (U := (-(6834438478415439925663 / 10000000000000000000000 : ℚ))) + (U' := (97033324584560074337 / 10000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (147494659079381 / 312500000000000 : ℚ)) + (q := (80780044994235911 / 160000000000000000 : ℚ)) + (U := (-(6834438478415439925663 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_13 : Uω (aρ 13) (bρ 13) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1873,26 +1610,21 @@ lemma U_667_13 : have hlg : Real.log (14349651124315259 / 32000000000000000 : ℝ) ≤ (-(802010272264151745109 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (14349651124315259 / 32000000000000000 : ℝ) = - (14349651124315259 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14349651124315259 / 8000000000000000 : ℚ)) - (U := (584284088335848254891 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (14349651124315259 / 8000000000000000 : ℝ) ≤ - (584284088335848254891 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (199511858027637 / 500000000000000 : ℝ)) (q := - (14349651124315259 / 32000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14349651124315259 / 32000000000000000 : ℚ)) + (r' := (14349651124315259 / 8000000000000000 : ℚ)) + (U := (-(802010272264151745109 / 1000000000000000000000 : ℚ))) + (U' := (584284088335848254891 / 1000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (199511858027637 / 500000000000000 : ℚ)) + (q := (14349651124315259 / 32000000000000000 : ℚ)) + (U := (-(802010272264151745109 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_14 : Uω (aρ 14) (bρ 14) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1900,26 +1632,21 @@ lemma U_667_14 : have hlg : Real.log (12587112524091627 / 32000000000000000 : ℝ) ≤ (-(4665312136517286567177 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (12587112524091627 / 32000000000000000 : ℝ) = - (12587112524091627 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12587112524091627 / 8000000000000000 : ℚ)) - (U := (2266159666482713432823 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12587112524091627 / 8000000000000000 : ℝ) ≤ - (2266159666482713432823 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (323257782045797 / 1000000000000000 : ℝ)) (q := - (12587112524091627 / 32000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12587112524091627 / 32000000000000000 : ℚ)) + (r' := (12587112524091627 / 8000000000000000 : ℚ)) + (U := (-(4665312136517286567177 / 5000000000000000000000 : ℚ))) + (U' := (2266159666482713432823 / 5000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (323257782045797 / 1000000000000000 : ℚ)) + (q := (12587112524091627 / 32000000000000000 : ℚ)) + (U := (-(4665312136517286567177 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_15 : Uω (aρ 15) (bρ 15) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1927,26 +1654,21 @@ lemma U_667_15 : have hlg : Real.log (55108975179349567 / 160000000000000000 : ℝ) ≤ (-(10658612229026117417291 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (55108975179349567 / 160000000000000000 : ℝ) = - (55108975179349567 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55108975179349567 / 40000000000000000 : ℚ)) - (U := (3204331376973882582709 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55108975179349567 / 40000000000000000 : ℝ) ≤ - (3204331376973882582709 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2513827667734399 / 10000000000000000 : ℝ)) (q := - (55108975179349567 / 160000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55108975179349567 / 160000000000000000 : ℚ)) + (r' := (55108975179349567 / 40000000000000000 : ℚ)) + (U := (-(10658612229026117417291 / 10000000000000000000000 : ℚ))) + (U' := (3204331376973882582709 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (2513827667734399 / 10000000000000000 : ℚ)) + (q := (55108975179349567 / 160000000000000000 : ℚ)) + (U := (-(10658612229026117417291 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667_16 : Uω (aρ 16) (bρ 16) (101836387367287 / 128000000000000 : ℝ) ≤ @@ -1954,26 +1676,21 @@ lemma U_667_16 : have hlg : Real.log (49567678580104111 / 160000000000000000 : ℝ) ≤ (-(5859174174619187689721 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (49567678580104111 / 160000000000000000 : ℝ) = - (49567678580104111 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49567678580104111 / 40000000000000000 : ℚ)) - (U := (1072297628380812310279 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49567678580104111 / 40000000000000000 : ℝ) ≤ - (1072297628380812310279 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1973537244338717 / 10000000000000000 : ℝ)) (q := - (49567678580104111 / 160000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49567678580104111 / 160000000000000000 : ℚ)) + (r' := (49567678580104111 / 40000000000000000 : ℚ)) + (U := (-(5859174174619187689721 / 5000000000000000000000 : ℚ))) + (U' := (1072297628380812310279 / 5000000000000000000000 : ℚ)) + 2 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (101836387367287 / 128000000000000 : ℚ)) + (s := (1973537244338717 / 10000000000000000 : ℚ)) + (q := (49567678580104111 / 160000000000000000 : ℚ)) + (U := (-(5859174174619187689721 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_667 : Uρ (101836387367287 / 128000000000000 : ℝ) ≤ @@ -2074,25 +1791,21 @@ lemma U_668_1 : have hlg : Real.log (254093109295304793 / 320000000000000000 : ℝ) ≤ (-(28827527957205322453 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (254093109295304793 / 320000000000000000 : ℝ) = - (254093109295304793 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (254093109295304793 / 160000000000000000 : ℚ)) - (U := (57815869580294677547 / 125000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (254093109295304793 / 160000000000000000 : ℝ) ≤ - (57815869580294677547 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7940389305334323 / 10000000000000000 : ℝ)) (q := - (254093109295304793 / 320000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (254093109295304793 / 320000000000000000 : ℚ)) + (r' := (254093109295304793 / 160000000000000000 : ℚ)) + (U := (-(28827527957205322453 / 125000000000000000000 : ℚ))) + (U' := (57815869580294677547 / 125000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (7940389305334323 / 10000000000000000 : ℚ)) + (q := (254093109295304793 / 320000000000000000 : ℚ)) + (U := (-(28827527957205322453 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_2 : Uω (aρ 2) (bρ 2) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2100,25 +1813,21 @@ lemma U_668_2 : have hlg : Real.log (253328863965426249 / 320000000000000000 : ℝ) ≤ (-(46726498663784903531 / 200000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (253328863965426249 / 320000000000000000 : ℝ) = - (253328863965426249 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (253328863965426249 / 160000000000000000 : ℚ)) - (U := (91902937396215096469 / 200000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (253328863965426249 / 160000000000000000 : ℝ) ≤ - (91902937396215096469 / 200000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3958196492363457 / 5000000000000000 : ℝ)) (q := - (253328863965426249 / 320000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (253328863965426249 / 320000000000000000 : ℚ)) + (r' := (253328863965426249 / 160000000000000000 : ℚ)) + (U := (-(46726498663784903531 / 200000000000000000000 : ℚ))) + (U' := (91902937396215096469 / 200000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (3958196492363457 / 5000000000000000 : ℚ)) + (q := (253328863965426249 / 320000000000000000 : ℚ)) + (U := (-(46726498663784903531 / 200000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_3 : Uω (aρ 3) (bρ 3) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2126,25 +1835,21 @@ lemma U_668_3 : have hlg : Real.log (50360286828556901 / 64000000000000000 : ℝ) ≤ (-(2396801783767159707439 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (50360286828556901 / 64000000000000000 : ℝ) = - (50360286828556901 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (50360286828556901 / 32000000000000000 : ℚ)) - (U := (4534670019232840292561 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (50360286828556901 / 32000000000000000 : ℝ) ≤ - (4534670019232840292561 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1573664945432361 / 2000000000000000 : ℝ)) (q := - (50360286828556901 / 64000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (50360286828556901 / 64000000000000000 : ℚ)) + (r' := (50360286828556901 / 32000000000000000 : ℚ)) + (U := (-(2396801783767159707439 / 10000000000000000000000 : ℚ))) + (U' := (4534670019232840292561 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (1573664945432361 / 2000000000000000 : ℚ)) + (q := (50360286828556901 / 64000000000000000 : ℚ)) + (U := (-(2396801783767159707439 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_4 : Uω (aρ 4) (bρ 4) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2152,25 +1857,21 @@ lemma U_668_4 : have hlg : Real.log (249267844562557577 / 320000000000000000 : ℝ) ≤ (-(312241245281524448941 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (249267844562557577 / 320000000000000000 : ℝ) = - (249267844562557577 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (249267844562557577 / 160000000000000000 : ℚ)) - (U := (554192730093475551059 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (249267844562557577 / 160000000000000000 : ℝ) ≤ - (554192730093475551059 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3894134779731311 / 5000000000000000 : ℝ)) (q := - (249267844562557577 / 320000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (249267844562557577 / 320000000000000000 : ℚ)) + (r' := (249267844562557577 / 160000000000000000 : ℚ)) + (U := (-(312241245281524448941 / 1250000000000000000000 : ℚ))) + (U' := (554192730093475551059 / 1250000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (3894134779731311 / 5000000000000000 : ℚ)) + (q := (249267844562557577 / 320000000000000000 : ℚ)) + (U := (-(312241245281524448941 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_5 : Uω (aρ 5) (bρ 5) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2178,25 +1879,21 @@ lemma U_668_5 : have hlg : Real.log (49083575860018021 / 64000000000000000 : ℝ) ≤ (-(663396520318592504421 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49083575860018021 / 64000000000000000 : ℝ) = - (49083575860018021 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49083575860018021 / 32000000000000000 : ℚ)) - (U := (1069471430431407495579 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (49083575860018021 / 32000000000000000 : ℝ) ≤ - (1069471430431407495579 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1533167329978681 / 2000000000000000 : ℝ)) (q := - (49083575860018021 / 64000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49083575860018021 / 64000000000000000 : ℚ)) + (r' := (49083575860018021 / 32000000000000000 : ℚ)) + (U := (-(663396520318592504421 / 2500000000000000000000 : ℚ))) + (U' := (1069471430431407495579 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (1533167329978681 / 2000000000000000 : ℚ)) + (q := (49083575860018021 / 64000000000000000 : ℚ)) + (U := (-(663396520318592504421 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_6 : Uω (aρ 6) (bρ 6) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2204,25 +1901,21 @@ lemma U_668_6 : have hlg : Real.log (47983078799087621 / 64000000000000000 : ℝ) ≤ (-(115213863744958042733 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (47983078799087621 / 64000000000000000 : ℝ) = - (47983078799087621 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (47983078799087621 / 32000000000000000 : ℚ)) - (U := (162045008375041957267 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (47983078799087621 / 32000000000000000 : ℝ) ≤ - (162045008375041957267 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1497834338698531 / 2000000000000000 : ℝ)) (q := - (47983078799087621 / 64000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (47983078799087621 / 64000000000000000 : ℚ)) + (r' := (47983078799087621 / 32000000000000000 : ℚ)) + (U := (-(115213863744958042733 / 400000000000000000000 : ℚ))) + (U' := (162045008375041957267 / 400000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (1497834338698531 / 2000000000000000 : ℚ)) + (q := (47983078799087621 / 64000000000000000 : ℚ)) + (U := (-(115213863744958042733 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_7 : Uω (aρ 7) (bρ 7) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2230,25 +1923,21 @@ lemma U_668_7 : have hlg : Real.log (232448875024204217 / 320000000000000000 : ℝ) ≤ (-(3196506870553017259521 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (232448875024204217 / 320000000000000000 : ℝ) = - (232448875024204217 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (232448875024204217 / 160000000000000000 : ℚ)) - (U := (3734964932446982740479 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (232448875024204217 / 160000000000000000 : ℝ) ≤ - (3734964932446982740479 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7246175638550537 / 10000000000000000 : ℝ)) (q := - (232448875024204217 / 320000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (232448875024204217 / 320000000000000000 : ℚ)) + (r' := (232448875024204217 / 160000000000000000 : ℚ)) + (U := (-(3196506870553017259521 / 10000000000000000000000 : ℚ))) + (U' := (3734964932446982740479 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (7246175638550537 / 10000000000000000 : ℚ)) + (q := (232448875024204217 / 320000000000000000 : ℚ)) + (U := (-(3196506870553017259521 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_8 : Uω (aρ 8) (bρ 8) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2256,25 +1945,21 @@ lemma U_668_8 : have hlg : Real.log (222787428776145417 / 320000000000000000 : ℝ) ≤ (-(3621029128780322054959 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (222787428776145417 / 320000000000000000 : ℝ) = - (222787428776145417 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (222787428776145417 / 160000000000000000 : ℚ)) - (U := (3310442674219677945041 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (222787428776145417 / 160000000000000000 : ℝ) ≤ - (3310442674219677945041 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3462938449693431 / 5000000000000000 : ℝ)) (q := - (222787428776145417 / 320000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (222787428776145417 / 320000000000000000 : ℚ)) + (r' := (222787428776145417 / 160000000000000000 : ℚ)) + (U := (-(3621029128780322054959 / 10000000000000000000000 : ℚ))) + (U' := (3310442674219677945041 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (3462938449693431 / 5000000000000000 : ℚ)) + (q := (222787428776145417 / 320000000000000000 : ℚ)) + (U := (-(3621029128780322054959 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_9 : Uω (aρ 9) (bρ 9) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2282,25 +1967,21 @@ lemma U_668_9 : have hlg : Real.log (210836402285843529 / 320000000000000000 : ℝ) ≤ (-(2086192537048560607821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (210836402285843529 / 320000000000000000 : ℝ) = - (210836402285843529 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (210836402285843529 / 160000000000000000 : ℚ)) - (U := (1379543364451439392179 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (210836402285843529 / 160000000000000000 : ℝ) ≤ - (1379543364451439392179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3259951686051497 / 5000000000000000 : ℝ)) (q := - (210836402285843529 / 320000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (210836402285843529 / 320000000000000000 : ℚ)) + (r' := (210836402285843529 / 160000000000000000 : ℚ)) + (U := (-(2086192537048560607821 / 5000000000000000000000 : ℚ))) + (U' := (1379543364451439392179 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (3259951686051497 / 5000000000000000 : ℚ)) + (q := (210836402285843529 / 320000000000000000 : ℚ)) + (U := (-(2086192537048560607821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_10 : Uω (aρ 10) (bρ 10) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2308,26 +1989,21 @@ lemma U_668_10 : have hlg : Real.log (39336993294475941 / 64000000000000000 : ℝ) ≤ (-(4867177017714833062951 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (39336993294475941 / 64000000000000000 : ℝ) = - (39336993294475941 / 32000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (39336993294475941 / 32000000000000000 : ℚ)) - (U := (2064294785285166937049 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (39336993294475941 / 32000000000000000 : ℝ) ≤ - (2064294785285166937049 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1204799533451301 / 2000000000000000 : ℝ)) (q := - (39336993294475941 / 64000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (39336993294475941 / 64000000000000000 : ℚ)) + (r' := (39336993294475941 / 32000000000000000 : ℚ)) + (U := (-(4867177017714833062951 / 10000000000000000000000 : ℚ))) + (U' := (2064294785285166937049 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (1204799533451301 / 2000000000000000 : ℚ)) + (q := (39336993294475941 / 64000000000000000 : ℚ)) + (U := (-(4867177017714833062951 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_11 : Uω (aρ 11) (bρ 11) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2335,26 +2011,21 @@ lemma U_668_11 : have hlg : Real.log (180638574733142217 / 320000000000000000 : ℝ) ≤ (-(571822785259138887833 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (180638574733142217 / 320000000000000000 : ℝ) = - (180638574733142217 / 160000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (180638574733142217 / 160000000000000000 : ℚ)) - (U := (121324395040861112167 / 1000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (180638574733142217 / 160000000000000000 : ℝ) ≤ - (121324395040861112167 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2719787404879581 / 5000000000000000 : ℝ)) (q := - (180638574733142217 / 320000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (180638574733142217 / 320000000000000000 : ℚ)) + (r' := (180638574733142217 / 160000000000000000 : ℚ)) + (U := (-(571822785259138887833 / 1000000000000000000000 : ℚ))) + (U' := (121324395040861112167 / 1000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (2719787404879581 / 5000000000000000 : ℚ)) + (q := (180638574733142217 / 320000000000000000 : ℚ)) + (U := (-(571822785259138887833 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_12 : Uω (aρ 12) (bρ 12) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2362,26 +2033,21 @@ lemma U_668_12 : have hlg : Real.log (6529391167203393 / 12800000000000000 : ℝ) ≤ (-(420707167491835697151 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6529391167203393 / 12800000000000000 : ℝ) = - (6529391167203393 / 6400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6529391167203393 / 6400000000000000 : ℚ)) - (U := (12509820195664302849 / 625000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (6529391167203393 / 6400000000000000 : ℝ) ≤ - (12509820195664302849 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (191021507375123 / 400000000000000 : ℝ)) (q := - (6529391167203393 / 12800000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6529391167203393 / 12800000000000000 : ℚ)) + (r' := (6529391167203393 / 6400000000000000 : ℚ)) + (U := (-(420707167491835697151 / 625000000000000000000 : ℚ))) + (U' := (12509820195664302849 / 625000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (191021507375123 / 400000000000000 : ℚ)) + (q := (6529391167203393 / 12800000000000000 : ℚ)) + (U := (-(420707167491835697151 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_13 : Uω (aρ 13) (bρ 13) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2389,26 +2055,21 @@ lemma U_668_13 : have hlg : Real.log (145254552806008569 / 320000000000000000 : ℝ) ≤ (-(1579666510826825980323 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (145254552806008569 / 320000000000000000 : ℝ) = - (145254552806008569 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (145254552806008569 / 80000000000000000 : ℚ)) - (U := (1192922210373174019677 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (145254552806008569 / 80000000000000000 : ℝ) ≤ - (1192922210373174019677 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4051155277593309 / 10000000000000000 : ℝ)) (q := - (145254552806008569 / 320000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (145254552806008569 / 320000000000000000 : ℚ)) + (r' := (145254552806008569 / 80000000000000000 : ℚ)) + (U := (-(1579666510826825980323 / 2000000000000000000000 : ℚ))) + (U' := (1192922210373174019677 / 2000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (4051155277593309 / 10000000000000000 : ℚ)) + (q := (145254552806008569 / 320000000000000000 : ℚ)) + (U := (-(1579666510826825980323 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_14 : Uω (aρ 14) (bρ 14) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2416,26 +2077,21 @@ lemma U_668_14 : have hlg : Real.log (127771397037108601 / 320000000000000000 : ℝ) ≤ (-(1836156577461968690781 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (127771397037108601 / 320000000000000000 : ℝ) = - (127771397037108601 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (127771397037108601 / 80000000000000000 : ℚ)) - (U := (936432143738031309219 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (127771397037108601 / 80000000000000000 : ℝ) ≤ - (936432143738031309219 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3302385327082061 / 10000000000000000 : ℝ)) (q := - (127771397037108601 / 320000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (127771397037108601 / 320000000000000000 : ℚ)) + (r' := (127771397037108601 / 80000000000000000 : ℚ)) + (U := (-(1836156577461968690781 / 2000000000000000000000 : ℚ))) + (U' := (936432143738031309219 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (3302385327082061 / 10000000000000000 : ℚ)) + (q := (127771397037108601 / 320000000000000000 : ℚ)) + (U := (-(1836156577461968690781 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_15 : Uω (aρ 15) (bρ 15) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2443,26 +2099,21 @@ lemma U_668_15 : have hlg : Real.log (112349592456445801 / 320000000000000000 : ℝ) ≤ (-(5233528120475439557461 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (112349592456445801 / 320000000000000000 : ℝ) = - (112349592456445801 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (112349592456445801 / 80000000000000000 : ℚ)) - (U := (1697943682524560442539 / 5000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (112349592456445801 / 80000000000000000 : ℝ) ≤ - (1697943682524560442539 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (649523954551409 / 2500000000000000 : ℝ)) (q := - (112349592456445801 / 320000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (112349592456445801 / 320000000000000000 : ℚ)) + (r' := (112349592456445801 / 80000000000000000 : ℚ)) + (U := (-(5233528120475439557461 / 5000000000000000000000 : ℚ))) + (U' := (1697943682524560442539 / 5000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (649523954551409 / 2500000000000000 : ℚ)) + (q := (112349592456445801 / 320000000000000000 : ℚ)) + (U := (-(5233528120475439557461 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668_16 : Uω (aρ 16) (bρ 16) (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2470,26 +2121,21 @@ lemma U_668_16 : have hlg : Real.log (101561679294659737 / 320000000000000000 : ℝ) ≤ (-(11476547035735173474157 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (101561679294659737 / 320000000000000000 : ℝ) = - (101561679294659737 / 80000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (101561679294659737 / 80000000000000000 : ℚ)) - (U := (2386396570264826525843 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (101561679294659737 / 80000000000000000 : ℝ) ≤ - (2386396570264826525843 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2076222897104007 / 10000000000000000 : ℝ)) (q := - (101561679294659737 / 320000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (101561679294659737 / 320000000000000000 : ℚ)) + (r' := (101561679294659737 / 80000000000000000 : ℚ)) + (U := (-(11476547035735173474157 / 10000000000000000000000 : ℚ))) + (U' := (2386396570264826525843 / 10000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (40985227487781 / 51200000000000 : ℚ)) + (s := (2076222897104007 / 10000000000000000 : ℚ)) + (q := (101561679294659737 / 320000000000000000 : ℚ)) + (U := (-(11476547035735173474157 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_668 : Uρ (40985227487781 / 51200000000000 : ℝ) ≤ @@ -2580,25 +2226,21 @@ lemma U_669_1 : have hlg : Real.log (63914954167080633 / 80000000000000000 : ℝ) ≤ (-(2244732758859609584141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (63914954167080633 / 80000000000000000 : ℝ) = - (63914954167080633 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63914954167080633 / 40000000000000000 : ℚ)) - (U := (4686739044140390415859 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63914954167080633 / 40000000000000000 : ℝ) ≤ - (4686739044140390415859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3994674517755001 / 5000000000000000 : ℝ)) (q := - (63914954167080633 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63914954167080633 / 80000000000000000 : ℚ)) + (r' := (63914954167080633 / 40000000000000000 : ℚ)) + (U := (-(2244732758859609584141 / 10000000000000000000000 : ℚ))) + (U' := (4686739044140390415859 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (3994674517755001 / 5000000000000000 : ℚ)) + (q := (63914954167080633 / 80000000000000000 : ℚ)) + (U := (-(2244732758859609584141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_2 : Uω (aρ 2) (bρ 2) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2606,25 +2248,21 @@ lemma U_669_2 : have hlg : Real.log (63723898426264653 / 80000000000000000 : ℝ) ≤ (-(227466970668141009613 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (63723898426264653 / 80000000000000000 : ℝ) = - (63723898426264653 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63723898426264653 / 40000000000000000 : ℚ)) - (U := (465680209631858990387 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63723898426264653 / 40000000000000000 : ℝ) ≤ - (465680209631858990387 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7965354112816007 / 10000000000000000 : ℝ)) (q := - (63723898426264653 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63723898426264653 / 80000000000000000 : ℚ)) + (r' := (63723898426264653 / 40000000000000000 : ℚ)) + (U := (-(227466970668141009613 / 1000000000000000000000 : ℚ))) + (U' := (465680209631858990387 / 1000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (7965354112816007 / 10000000000000000 : ℚ)) + (q := (63723898426264653 / 80000000000000000 : ℚ)) + (U := (-(227466970668141009613 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_3 : Uω (aρ 3) (bρ 3) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2632,25 +2270,21 @@ lemma U_669_3 : have hlg : Real.log (63342057636596289 / 80000000000000000 : ℝ) ≤ (-(2334771082517334658739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (63342057636596289 / 80000000000000000 : ℝ) = - (63342057636596289 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63342057636596289 / 40000000000000000 : ℚ)) - (U := (4596700720482665341261 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63342057636596289 / 40000000000000000 : ℝ) ≤ - (4596700720482665341261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1979322505437229 / 2500000000000000 : ℝ)) (q := - (63342057636596289 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63342057636596289 / 80000000000000000 : ℚ)) + (r' := (63342057636596289 / 40000000000000000 : ℚ)) + (U := (-(2334771082517334658739 / 10000000000000000000000 : ℚ))) + (U' := (4596700720482665341261 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (1979322505437229 / 2500000000000000 : ℚ)) + (q := (63342057636596289 / 80000000000000000 : ℚ)) + (U := (-(2334771082517334658739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_4 : Uω (aρ 4) (bρ 4) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2658,25 +2292,21 @@ lemma U_669_4 : have hlg : Real.log (62708704482840553 / 80000000000000000 : ℝ) ≤ (-(304407961166478728341 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (62708704482840553 / 80000000000000000 : ℝ) = - (62708704482840553 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62708704482840553 / 40000000000000000 : ℚ)) - (U := (562026014208521271659 / 1250000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62708704482840553 / 40000000000000000 : ℝ) ≤ - (562026014208521271659 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3918622957187491 / 5000000000000000 : ℝ)) (q := - (62708704482840553 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62708704482840553 / 80000000000000000 : ℚ)) + (r' := (62708704482840553 / 40000000000000000 : ℚ)) + (U := (-(304407961166478728341 / 1250000000000000000000 : ℚ))) + (U' := (562026014208521271659 / 1250000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (3918622957187491 / 5000000000000000 : ℚ)) + (q := (62708704482840553 / 80000000000000000 : ℚ)) + (U := (-(304407961166478728341 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_5 : Uω (aρ 5) (bρ 5) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2684,25 +2314,21 @@ lemma U_669_5 : have hlg : Real.log (2469852877802989 / 3200000000000000 : ℝ) ≤ (-(647480560805871238739 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2469852877802989 / 3200000000000000 : ℝ) = - (2469852877802989 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2469852877802989 / 1600000000000000 : ℚ)) - (U := (1085387389944128761261 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (2469852877802989 / 1600000000000000 : ℝ) ≤ - (1085387389944128761261 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (308593607970741 / 400000000000000 : ℝ)) (q := - (2469852877802989 / 3200000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2469852877802989 / 3200000000000000 : ℚ)) + (r' := (2469852877802989 / 1600000000000000 : ℚ)) + (U := (-(647480560805871238739 / 2500000000000000000000 : ℚ))) + (U' := (1085387389944128761261 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (308593607970741 / 400000000000000 : ℚ)) + (q := (2469852877802989 / 3200000000000000 : ℚ)) + (U := (-(647480560805871238739 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_6 : Uω (aρ 6) (bρ 6) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2710,25 +2336,21 @@ lemma U_669_6 : have hlg : Real.log (12074189918970493 / 16000000000000000 : ℝ) ≤ (-(87974566296101048461 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12074189918970493 / 16000000000000000 : ℝ) = - (12074189918970493 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12074189918970493 / 8000000000000000 : ℚ)) - (U := (128633927547648951539 / 312500000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (12074189918970493 / 8000000000000000 : ℝ) ≤ - (128633927547648951539 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (47113984292831 / 62500000000000 : ℝ)) (q := - (12074189918970493 / 16000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12074189918970493 / 16000000000000000 : ℚ)) + (r' := (12074189918970493 / 8000000000000000 : ℚ)) + (U := (-(87974566296101048461 / 312500000000000000000 : ℚ))) + (U' := (128633927547648951539 / 312500000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (47113984292831 / 62500000000000 : ℚ)) + (q := (12074189918970493 / 16000000000000000 : ℚ)) + (U := (-(87974566296101048461 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_7 : Uω (aρ 7) (bρ 7) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2736,25 +2358,21 @@ lemma U_669_7 : have hlg : Real.log (58504853043606353 / 80000000000000000 : ℝ) ≤ (-(391146157008232414821 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (58504853043606353 / 80000000000000000 : ℝ) = - (58504853043606353 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58504853043606353 / 40000000000000000 : ℚ)) - (U := (475287818366767585179 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58504853043606353 / 40000000000000000 : ℝ) ≤ - (475287818366767585179 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (911921841225179 / 1250000000000000 : ℝ)) (q := - (58504853043606353 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58504853043606353 / 80000000000000000 : ℚ)) + (r' := (58504853043606353 / 40000000000000000 : ℚ)) + (U := (-(391146157008232414821 / 1250000000000000000000 : ℚ))) + (U' := (475287818366767585179 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (911921841225179 / 1250000000000000 : ℚ)) + (q := (58504853043606353 / 80000000000000000 : ℚ)) + (U := (-(391146157008232414821 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_8 : Uω (aρ 8) (bρ 8) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2762,25 +2380,21 @@ lemma U_669_8 : have hlg : Real.log (56090567494944313 / 80000000000000000 : ℝ) ≤ (-(355058973366974848083 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (56090567494944313 / 80000000000000000 : ℝ) = - (56090567494944313 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56090567494944313 / 40000000000000000 : ℚ)) - (U := (338088206933025151917 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56090567494944313 / 40000000000000000 : ℝ) ≤ - (338088206933025151917 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3487672496987961 / 5000000000000000 : ℝ)) (q := - (56090567494944313 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56090567494944313 / 80000000000000000 : ℚ)) + (r' := (56090567494944313 / 40000000000000000 : ℚ)) + (U := (-(355058973366974848083 / 1000000000000000000000 : ℚ))) + (U' := (338088206933025151917 / 1000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (3487672496987961 / 5000000000000000 : ℚ)) + (q := (56090567494944313 / 80000000000000000 : ℚ)) + (U := (-(355058973366974848083 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_9 : Uω (aρ 9) (bρ 9) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2788,25 +2402,21 @@ lemma U_669_9 : have hlg : Real.log (53104874451030497 / 80000000000000000 : ℝ) ≤ (-(1024394782019966389091 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (53104874451030497 / 80000000000000000 : ℝ) = - (53104874451030497 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (53104874451030497 / 40000000000000000 : ℚ)) - (U := (708473168730033610909 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (53104874451030497 / 40000000000000000 : ℝ) ≤ - (708473168730033610909 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1642471840339367 / 2500000000000000 : ℝ)) (q := - (53104874451030497 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (53104874451030497 / 80000000000000000 : ℚ)) + (r' := (53104874451030497 / 40000000000000000 : ℚ)) + (U := (-(1024394782019966389091 / 2500000000000000000000 : ℚ))) + (U' := (708473168730033610909 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (1642471840339367 / 2500000000000000 : ℚ)) + (q := (53104874451030497 / 80000000000000000 : ℚ)) + (U := (-(1024394782019966389091 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_10 : Uω (aρ 10) (bρ 10) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2814,26 +2424,21 @@ lemma U_669_10 : have hlg : Real.log (49570810864276341 / 80000000000000000 : ℝ) ≤ (-(11965611613780661111 / 25000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (49570810864276341 / 80000000000000000 : ℝ) = - (49570810864276341 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (49570810864276341 / 40000000000000000 : ℚ)) - (U := (5363067893719338889 / 25000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (49570810864276341 / 40000000000000000 : ℝ) ≤ - (5363067893719338889 / 25000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6074930498163929 / 10000000000000000 : ℝ)) (q := - (49570810864276341 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (49570810864276341 / 80000000000000000 : ℚ)) + (r' := (49570810864276341 / 40000000000000000 : ℚ)) + (U := (-(11965611613780661111 / 25000000000000000000 : ℚ))) + (U' := (5363067893719338889 / 25000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (6074930498163929 / 10000000000000000 : ℚ)) + (q := (49570810864276341 / 80000000000000000 : ℚ)) + (U := (-(11965611613780661111 / 25000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_11 : Uω (aρ 11) (bρ 11) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2841,26 +2446,21 @@ lemma U_669_11 : have hlg : Real.log (45565971127884609 / 80000000000000000 : ℝ) ≤ (-(5628654436701494422077 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (45565971127884609 / 80000000000000000 : ℝ) = - (45565971127884609 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (45565971127884609 / 40000000000000000 : ℚ)) - (U := (1302817366298505577923 / 10000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (45565971127884609 / 40000000000000000 : ℝ) ≤ - (1302817366298505577923 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1373049297567749 / 2500000000000000 : ℝ)) (q := - (45565971127884609 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (45565971127884609 / 80000000000000000 : ℚ)) + (r' := (45565971127884609 / 40000000000000000 : ℚ)) + (U := (-(5628654436701494422077 / 10000000000000000000000 : ℚ))) + (U' := (1302817366298505577923 / 10000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (1373049297567749 / 2500000000000000 : ℚ)) + (q := (45565971127884609 / 80000000000000000 : ℚ)) + (U := (-(5628654436701494422077 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_12 : Uω (aρ 12) (bρ 12) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2868,26 +2468,21 @@ lemma U_669_12 : have hlg : Real.log (1649071288432777 / 3200000000000000 : ℝ) ≤ (-(6629385355911510922651 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1649071288432777 / 3200000000000000 : ℝ) = - (1649071288432777 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1649071288432777 / 1600000000000000 : ℚ)) - (U := (302086447088489077349 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1649071288432777 / 1600000000000000 : ℝ) ≤ - (302086447088489077349 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (48311000576897 / 100000000000000 : ℝ)) (q := - (1649071288432777 / 3200000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1649071288432777 / 3200000000000000 : ℚ)) + (r' := (1649071288432777 / 1600000000000000 : ℚ)) + (U := (-(6629385355911510922651 / 10000000000000000000000 : ℚ))) + (U' := (302086447088489077349 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (48311000576897 / 100000000000000 : ℚ)) + (q := (1649071288432777 / 3200000000000000 : ℚ)) + (U := (-(6629385355911510922651 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_13 : Uω (aρ 13) (bρ 13) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2895,26 +2490,21 @@ lemma U_669_13 : have hlg : Real.log (36751870368632741 / 80000000000000000 : ℝ) ≤ (-(972296894257070220027 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36751870368632741 / 80000000000000000 : ℝ) = - (36751870368632741 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36751870368632741 / 20000000000000000 : ℚ)) - (U := (760571056492929779973 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36751870368632741 / 20000000000000000 : ℝ) ≤ - (760571056492929779973 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4111753838738029 / 10000000000000000 : ℝ)) (q := - (36751870368632741 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36751870368632741 / 80000000000000000 : ℚ)) + (r' := (36751870368632741 / 20000000000000000 : ℚ)) + (U := (-(972296894257070220027 / 1250000000000000000000 : ℚ))) + (U' := (760571056492929779973 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (4111753838738029 / 10000000000000000 : ℚ)) + (q := (36751870368632741 / 80000000000000000 : ℚ)) + (U := (-(972296894257070220027 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_14 : Uω (aρ 14) (bρ 14) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2922,26 +2512,21 @@ lemma U_669_14 : have hlg : Real.log (6482995971853097 / 16000000000000000 : ℝ) ≤ (-(9034059768671761378607 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6482995971853097 / 16000000000000000 : ℝ) = - (6482995971853097 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6482995971853097 / 4000000000000000 : ℚ)) - (U := (4828883837328238621393 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (6482995971853097 / 4000000000000000 : ℝ) ≤ - (4828883837328238621393 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (674291699288243 / 2000000000000000 : ℝ)) (q := - (6482995971853097 / 16000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6482995971853097 / 16000000000000000 : ℚ)) + (r' := (6482995971853097 / 4000000000000000 : ℚ)) + (U := (-(9034059768671761378607 / 10000000000000000000000 : ℚ))) + (U' := (4828883837328238621393 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (674291699288243 / 2000000000000000 : ℚ)) + (q := (6482995971853097 / 16000000000000000 : ℚ)) + (U := (-(9034059768671761378607 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_15 : Uω (aρ 15) (bρ 15) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2949,26 +2534,21 @@ lemma U_669_15 : have hlg : Real.log (28613291501051061 / 80000000000000000 : ℝ) ≤ (-(10281552864863602885801 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (28613291501051061 / 80000000000000000 : ℝ) = - (28613291501051061 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28613291501051061 / 20000000000000000 : ℚ)) - (U := (3581390741136397114199 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28613291501051061 / 20000000000000000 : ℝ) ≤ - (3581390741136397114199 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2680609684302609 / 10000000000000000 : ℝ)) (q := - (28613291501051061 / 80000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28613291501051061 / 80000000000000000 : ℚ)) + (r' := (28613291501051061 / 20000000000000000 : ℚ)) + (U := (-(10281552864863602885801 / 10000000000000000000000 : ℚ))) + (U' := (3581390741136397114199 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (2680609684302609 / 10000000000000000 : ℚ)) + (q := (28613291501051061 / 80000000000000000 : ℚ)) + (U := (-(10281552864863602885801 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669_16 : Uω (aρ 16) (bρ 16) (51544875035809 / 64000000000000 : ℝ) ≤ @@ -2976,26 +2556,21 @@ lemma U_669_16 : have hlg : Real.log (25982030816194973 / 80000000000000000 : ℝ) ≤ (-(5623107287608835128659 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (25982030816194973 / 80000000000000000 : ℝ) = - (25982030816194973 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25982030816194973 / 20000000000000000 : ℚ)) - (U := (1308364515391164871341 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25982030816194973 / 20000000000000000 : ℝ) ≤ - (1308364515391164871341 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2175166164598587 / 10000000000000000 : ℝ)) (q := - (25982030816194973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25982030816194973 / 80000000000000000 : ℚ)) + (r' := (25982030816194973 / 20000000000000000 : ℚ)) + (U := (-(5623107287608835128659 / 5000000000000000000000 : ℚ))) + (U' := (1308364515391164871341 / 5000000000000000000000 : ℚ)) + 2 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (51544875035809 / 64000000000000 : ℚ)) + (s := (2175166164598587 / 10000000000000000 : ℚ)) + (q := (25982030816194973 / 80000000000000000 : ℚ)) + (U := (-(5623107287608835128659 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_669 : Uρ (51544875035809 / 64000000000000 : ℝ) ≤ @@ -3086,25 +2661,21 @@ lemma U_670_1 : have hlg : Real.log (129396615634666397 / 160000000000000000 : ℝ) ≤ (-(2122915875407152198241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (129396615634666397 / 160000000000000000 : ℝ) = - (129396615634666397 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (129396615634666397 / 80000000000000000 : ℚ)) - (U := (4808555927592847801759 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (129396615634666397 / 80000000000000000 : ℝ) ≤ - (4808555927592847801759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2021817121699321 / 2500000000000000 : ℝ)) (q := - (129396615634666397 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (129396615634666397 / 160000000000000000 : ℚ)) + (r' := (129396615634666397 / 80000000000000000 : ℚ)) + (U := (-(2122915875407152198241 / 10000000000000000000000 : ℚ))) + (U' := (4808555927592847801759 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (2021817121699321 / 2500000000000000 : ℚ)) + (q := (129396615634666397 / 160000000000000000 : ℚ)) + (U := (-(2122915875407152198241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_2 : Uω (aρ 2) (bρ 2) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3112,25 +2683,21 @@ lemma U_670_2 : have hlg : Real.log (129014526112001253 / 160000000000000000 : ℝ) ≤ (-(2152488114323455304571 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (129014526112001253 / 160000000000000000 : ℝ) = - (129014526112001253 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (129014526112001253 / 80000000000000000 : ℚ)) - (U := (4778983688676544695429 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (129014526112001253 / 80000000000000000 : ℝ) ≤ - (4778983688676544695429 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8063276308974141 / 10000000000000000 : ℝ)) (q := - (129014526112001253 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (129014526112001253 / 160000000000000000 : ℚ)) + (r' := (129014526112001253 / 80000000000000000 : ℚ)) + (U := (-(2152488114323455304571 / 10000000000000000000000 : ℚ))) + (U' := (4778983688676544695429 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (8063276308974141 / 10000000000000000 : ℚ)) + (q := (129014526112001253 / 160000000000000000 : ℚ)) + (U := (-(2152488114323455304571 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_3 : Uω (aρ 3) (bρ 3) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3138,25 +2705,21 @@ lemma U_670_3 : have hlg : Real.log (128250909972047621 / 160000000000000000 : ℝ) ≤ (-(2211852356495572801771 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (128250909972047621 / 160000000000000000 : ℝ) = - (128250909972047621 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (128250909972047621 / 80000000000000000 : ℚ)) - (U := (4719619446504427198229 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (128250909972047621 / 80000000000000000 : ℝ) ≤ - (4719619446504427198229 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8015220397829937 / 10000000000000000 : ℝ)) (q := - (128250909972047621 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (128250909972047621 / 160000000000000000 : ℚ)) + (r' := (128250909972047621 / 80000000000000000 : ℚ)) + (U := (-(2211852356495572801771 / 10000000000000000000000 : ℚ))) + (U' := (4719619446504427198229 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (8015220397829937 / 10000000000000000 : ℚ)) + (q := (128250909972047621 / 160000000000000000 : ℚ)) + (U := (-(2211852356495572801771 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_4 : Uω (aρ 4) (bρ 4) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3164,25 +2727,21 @@ lemma U_670_4 : have hlg : Real.log (126984377336210149 / 160000000000000000 : ℝ) ≤ (-(23110974918272984411 / 100000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (126984377336210149 / 160000000000000000 : ℝ) = - (126984377336210149 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (126984377336210149 / 80000000000000000 : ℚ)) - (U := (46203743111727015589 / 100000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (126984377336210149 / 80000000000000000 : ℝ) ≤ - (46203743111727015589 / 100000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7935197999415253 / 10000000000000000 : ℝ)) (q := - (126984377336210149 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (126984377336210149 / 160000000000000000 : ℚ)) + (r' := (126984377336210149 / 80000000000000000 : ℚ)) + (U := (-(23110974918272984411 / 100000000000000000000 : ℚ))) + (U' := (46203743111727015589 / 100000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (7935197999415253 / 10000000000000000 : ℚ)) + (q := (126984377336210149 / 160000000000000000 : ℚ)) + (U := (-(23110974918272984411 / 100000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_5 : Uω (aρ 5) (bρ 5) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3190,25 +2749,21 @@ lemma U_670_5 : have hlg : Real.log (125060039108793597 / 160000000000000000 : ℝ) ≤ (-(2463798801145355917777 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (125060039108793597 / 160000000000000000 : ℝ) = - (125060039108793597 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (125060039108793597 / 80000000000000000 : ℚ)) - (U := (4467673001854644082223 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (125060039108793597 / 80000000000000000 : ℝ) ≤ - (4467673001854644082223 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (488302852520199 / 625000000000000 : ℝ)) (q := - (125060039108793597 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (125060039108793597 / 160000000000000000 : ℚ)) + (r' := (125060039108793597 / 80000000000000000 : ℚ)) + (U := (-(2463798801145355917777 / 10000000000000000000000 : ℚ))) + (U' := (4467673001854644082223 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (488302852520199 / 625000000000000 : ℚ)) + (q := (125060039108793597 / 160000000000000000 : ℚ)) + (U := (-(2463798801145355917777 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_6 : Uω (aρ 6) (bρ 6) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3216,25 +2771,21 @@ lemma U_670_6 : have hlg : Real.log (122310270820928029 / 160000000000000000 : ℝ) ≤ (-(671531988149197401087 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (122310270820928029 / 160000000000000000 : ℝ) = - (122310270820928029 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (122310270820928029 / 80000000000000000 : ℚ)) - (U := (1061335962600802598913 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (122310270820928029 / 80000000000000000 : ℝ) ≤ - (1061335962600802598913 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1909091244869997 / 2500000000000000 : ℝ)) (q := - (122310270820928029 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (122310270820928029 / 160000000000000000 : ℚ)) + (r' := (122310270820928029 / 80000000000000000 : ℚ)) + (U := (-(671531988149197401087 / 2500000000000000000000 : ℚ))) + (U' := (1061335962600802598913 / 2500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (1909091244869997 / 2500000000000000 : ℚ)) + (q := (122310270820928029 / 160000000000000000 : ℚ)) + (U := (-(671531988149197401087 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_7 : Uω (aρ 7) (bρ 7) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3242,25 +2793,21 @@ lemma U_670_7 : have hlg : Real.log (118580166892592797 / 160000000000000000 : ℝ) ≤ (-(1497922846347504928719 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (118580166892592797 / 160000000000000000 : ℝ) = - (118580166892592797 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (118580166892592797 / 80000000000000000 : ℚ)) - (U := (1967813055152495071281 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (118580166892592797 / 80000000000000000 : ℝ) ≤ - (1967813055152495071281 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1848440842299521 / 2500000000000000 : ℝ)) (q := - (118580166892592797 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (118580166892592797 / 160000000000000000 : ℚ)) + (r' := (118580166892592797 / 80000000000000000 : ℚ)) + (U := (-(1497922846347504928719 / 5000000000000000000000 : ℚ))) + (U' := (1967813055152495071281 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (1848440842299521 / 2500000000000000 : ℚ)) + (q := (118580166892592797 / 160000000000000000 : ℚ)) + (U := (-(1497922846347504928719 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_8 : Uω (aρ 8) (bρ 8) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3268,25 +2815,21 @@ lemma U_670_8 : have hlg : Real.log (113755806355612957 / 160000000000000000 : ℝ) ≤ (-(426399641951322608969 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (113755806355612957 / 160000000000000000 : ℝ) = - (113755806355612957 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (113755806355612957 / 80000000000000000 : ℚ)) - (U := (440034333423677391031 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (113755806355612957 / 80000000000000000 : ℝ) ≤ - (440034333423677391031 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1768564988353901 / 2500000000000000 : ℝ)) (q := - (113755806355612957 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (113755806355612957 / 160000000000000000 : ℚ)) + (r' := (113755806355612957 / 80000000000000000 : ℚ)) + (U := (-(426399641951322608969 / 1250000000000000000000 : ℚ))) + (U' := (440034333423677391031 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (1768564988353901 / 2500000000000000 : ℚ)) + (q := (113755806355612957 / 160000000000000000 : ℚ)) + (U := (-(426399641951322608969 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_9 : Uω (aρ 9) (bρ 9) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3294,25 +2837,21 @@ lemma U_670_9 : have hlg : Real.log (107792479667179109 / 160000000000000000 : ℝ) ≤ (-(3949659208324676186013 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (107792479667179109 / 160000000000000000 : ℝ) = - (107792479667179109 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (107792479667179109 / 80000000000000000 : ℚ)) - (U := (2981812594675323813987 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (107792479667179109 / 80000000000000000 : ℝ) ≤ - (2981812594675323813987 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6669809745721373 / 10000000000000000 : ℝ)) (q := - (107792479667179109 / 160000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) - (by norm_num [bρ_9]) (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (107792479667179109 / 160000000000000000 : ℚ)) + (r' := (107792479667179109 / 80000000000000000 : ℚ)) + (U := (-(3949659208324676186013 / 10000000000000000000000 : ℚ))) + (U' := (2981812594675323813987 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (6669809745721373 / 10000000000000000 : ℚ)) + (q := (107792479667179109 / 160000000000000000 : ℚ)) + (U := (-(3949659208324676186013 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_10 : Uω (aρ 10) (bρ 10) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3320,26 +2859,21 @@ lemma U_670_10 : have hlg : Real.log (100739132785923661 / 160000000000000000 : ℝ) ≤ (-(4626394831317498006823 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (100739132785923661 / 160000000000000000 : ℝ) = - (100739132785923661 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (100739132785923661 / 80000000000000000 : ℚ)) - (U := (2305076971682501993177 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (100739132785923661 / 80000000000000000 : ℝ) ≤ - (2305076971682501993177 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3088350209529721 / 5000000000000000 : ℝ)) (q := - (100739132785923661 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (100739132785923661 / 160000000000000000 : ℚ)) + (r' := (100739132785923661 / 80000000000000000 : ℚ)) + (U := (-(4626394831317498006823 / 10000000000000000000000 : ℚ))) + (U' := (2305076971682501993177 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (3088350209529721 / 5000000000000000 : ℚ)) + (q := (100739132785923661 / 160000000000000000 : ℚ)) + (U := (-(4626394831317498006823 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_11 : Uω (aρ 11) (bρ 11) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3347,26 +2881,21 @@ lemma U_670_11 : have hlg : Real.log (92755656630473309 / 160000000000000000 : ℝ) ≤ (-(2726025637081969480721 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (92755656630473309 / 160000000000000000 : ℝ) = - (92755656630473309 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (92755656630473309 / 80000000000000000 : ℚ)) - (U := (739710264418030519279 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (92755656630473309 / 80000000000000000 : ℝ) ≤ - (739710264418030519279 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1399310631458287 / 2500000000000000 : ℝ)) (q := - (92755656630473309 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (92755656630473309 / 160000000000000000 : ℚ)) + (r' := (92755656630473309 / 80000000000000000 : ℚ)) + (U := (-(2726025637081969480721 / 5000000000000000000000 : ℚ))) + (U' := (739710264418030519279 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (1399310631458287 / 2500000000000000 : ℚ)) + (q := (92755656630473309 / 160000000000000000 : ℚ)) + (U := (-(2726025637081969480721 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_12 : Uω (aρ 12) (bρ 12) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3374,26 +2903,21 @@ lemma U_670_12 : have hlg : Real.log (84122562513276669 / 160000000000000000 : ℝ) ≤ (-(1607247505027276502399 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (84122562513276669 / 160000000000000000 : ℝ) = - (84122562513276669 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (84122562513276669 / 80000000000000000 : ℚ)) - (U := (125620445722723497601 / 2500000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (84122562513276669 / 80000000000000000 : ℝ) ≤ - (125620445722723497601 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (617725732233571 / 1250000000000000 : ℝ)) (q := - (84122562513276669 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (84122562513276669 / 160000000000000000 : ℚ)) + (r' := (84122562513276669 / 80000000000000000 : ℚ)) + (U := (-(1607247505027276502399 / 2500000000000000000000 : ℚ))) + (U' := (125620445722723497601 / 2500000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (617725732233571 / 1250000000000000 : ℚ)) + (q := (84122562513276669 / 160000000000000000 : ℚ)) + (U := (-(1607247505027276502399 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_13 : Uω (aρ 13) (bρ 13) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3401,26 +2925,21 @@ lemma U_670_13 : have hlg : Real.log (75249438756350077 / 160000000000000000 : ℝ) ≤ (-(7543653695001394939451 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (75249438756350077 / 160000000000000000 : ℝ) = - (75249438756350077 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (75249438756350077 / 40000000000000000 : ℚ)) - (U := (6319289910998605060549 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (75249438756350077 / 40000000000000000 : ℝ) ≤ - (6319289910998605060549 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (66125736403871 / 156250000000000 : ℝ)) (q := - (75249438756350077 / 160000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (75249438756350077 / 160000000000000000 : ℚ)) + (r' := (75249438756350077 / 40000000000000000 : ℚ)) + (U := (-(7543653695001394939451 / 10000000000000000000000 : ℚ))) + (U' := (6319289910998605060549 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (66125736403871 / 156250000000000 : ℚ)) + (q := (75249438756350077 / 160000000000000000 : ℚ)) + (U := (-(7543653695001394939451 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_14 : Uω (aρ 14) (bρ 14) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3428,26 +2947,21 @@ lemma U_670_14 : have hlg : Real.log (2668089704939989 / 6400000000000000 : ℝ) ≤ (-(8749352398163579758549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (2668089704939989 / 6400000000000000 : ℝ) = - (2668089704939989 / 1600000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2668089704939989 / 1600000000000000 : ℚ)) - (U := (5113591207836420241451 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2668089704939989 / 1600000000000000 : ℝ) ≤ - (5113591207836420241451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (70151497965729 / 200000000000000 : ℝ)) (q := - (2668089704939989 / 6400000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2668089704939989 / 6400000000000000 : ℚ)) + (r' := (2668089704939989 / 1600000000000000 : ℚ)) + (U := (-(8749352398163579758549 / 10000000000000000000000 : ℚ))) + (U' := (5113591207836420241451 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (70151497965729 / 200000000000000 : ℚ)) + (q := (2668089704939989 / 6400000000000000 : ℚ)) + (U := (-(8749352398163579758549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_15 : Uω (aρ 15) (bρ 15) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3455,26 +2969,21 @@ lemma U_670_15 : have hlg : Real.log (59292919606829613 / 160000000000000000 : ℝ) ≤ (-(2481709788466278231419 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (59292919606829613 / 160000000000000000 : ℝ) = - (59292919606829613 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59292919606829613 / 40000000000000000 : ℚ)) - (U := (984026113033721768581 / 2500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59292919606829613 / 40000000000000000 : ℝ) ≤ - (984026113033721768581 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1420491399308843 / 5000000000000000 : ℝ)) (q := - (59292919606829613 / 160000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59292919606829613 / 160000000000000000 : ℚ)) + (r' := (59292919606829613 / 40000000000000000 : ℚ)) + (U := (-(2481709788466278231419 / 2500000000000000000000 : ℚ))) + (U' := (984026113033721768581 / 2500000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (1420491399308843 / 5000000000000000 : ℚ)) + (q := (59292919606829613 / 160000000000000000 : ℚ)) + (U := (-(2481709788466278231419 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670_16 : Uω (aρ 16) (bρ 16) (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3482,26 +2991,21 @@ lemma U_670_16 : have hlg : Real.log (54255590911517429 / 160000000000000000 : ℝ) ≤ (-(1081467769326687780553 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (54255590911517429 / 160000000000000000 : ℝ) = - (54255590911517429 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (54255590911517429 / 40000000000000000 : ℚ)) - (U := (304826591273312219447 / 1000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (54255590911517429 / 40000000000000000 : ℝ) ≤ - (304826591273312219447 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2363688363213663 / 10000000000000000 : ℝ)) (q := - (54255590911517429 / 160000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (54255590911517429 / 160000000000000000 : ℚ)) + (r' := (54255590911517429 / 40000000000000000 : ℚ)) + (U := (-(1081467769326687780553 / 1000000000000000000000 : ℚ))) + (U' := (304826591273312219447 / 1000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (104343112775949 / 128000000000000 : ℚ)) + (s := (2363688363213663 / 10000000000000000 : ℚ)) + (q := (54255590911517429 / 160000000000000000 : ℚ)) + (U := (-(1081467769326687780553 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_670 : Uρ (104343112775949 / 128000000000000 : ℝ) ≤ @@ -3601,25 +3105,21 @@ lemma U_671_1 : have hlg : Real.log (16370415355172451 / 20000000000000000 : ℝ) ≤ (-(500641273210134050889 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16370415355172451 / 20000000000000000 : ℝ) = - (16370415355172451 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16370415355172451 / 10000000000000000 : ℚ)) - (U := (1232226677539865949111 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16370415355172451 / 10000000000000000 : ℝ) ≤ - (1232226677539865949111 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (15986695168673 / 19531250000000 : ℝ)) (q := - (16370415355172451 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16370415355172451 / 20000000000000000 : ℚ)) + (r' := (16370415355172451 / 10000000000000000 : ℚ)) + (U := (-(500641273210134050889 / 2500000000000000000000 : ℚ))) + (U' := (1232226677539865949111 / 2500000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (15986695168673 / 19531250000000 : ℚ)) + (q := (16370415355172451 / 20000000000000000 : ℚ)) + (U := (-(500641273210134050889 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_2 : Uω (aρ 2) (bρ 2) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3627,25 +3127,21 @@ lemma U_671_2 : have hlg : Real.log (8161328421903959 / 10000000000000000 : ℝ) ≤ (-(1015890701030451598891 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8161328421903959 / 10000000000000000 : ℝ) = - (8161328421903959 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8161328421903959 / 5000000000000000 : ℚ)) - (U := (2449845200469548401109 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8161328421903959 / 5000000000000000 : ℝ) ≤ - (2449845200469548401109 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8161198427506043 / 10000000000000000 : ℝ)) (q := - (8161328421903959 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8161328421903959 / 10000000000000000 : ℚ)) + (r' := (8161328421903959 / 5000000000000000 : ℚ)) + (U := (-(1015890701030451598891 / 5000000000000000000000 : ℚ))) + (U' := (2449845200469548401109 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (8161198427506043 / 10000000000000000 : ℚ)) + (q := (8161328421903959 / 10000000000000000 : ℚ)) + (U := (-(1015890701030451598891 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_3 : Uω (aρ 3) (bρ 3) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3653,25 +3149,21 @@ lemma U_671_3 : have hlg : Real.log (8113606404156209 / 10000000000000000 : ℝ) ≤ (-(1045213186822443644979 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8113606404156209 / 10000000000000000 : ℝ) = - (8113606404156209 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8113606404156209 / 5000000000000000 : ℚ)) - (U := (2420522714677556355021 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8113606404156209 / 5000000000000000 : ℝ) ≤ - (2420522714677556355021 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8113150498360543 / 10000000000000000 : ℝ)) (q := - (8113606404156209 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8113606404156209 / 10000000000000000 : ℚ)) + (r' := (8113606404156209 / 5000000000000000 : ℚ)) + (U := (-(1045213186822443644979 / 5000000000000000000000 : ℚ))) + (U' := (2420522714677556355021 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (8113150498360543 / 10000000000000000 : ℚ)) + (q := (8113606404156209 / 10000000000000000 : ℚ)) + (U := (-(1045213186822443644979 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_4 : Uω (aρ 4) (bρ 4) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3679,25 +3171,21 @@ lemma U_671_4 : have hlg : Real.log (8034458702845387 / 10000000000000000 : ℝ) ≤ (-(2188454632258100397817 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8034458702845387 / 10000000000000000 : ℝ) = - (8034458702845387 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8034458702845387 / 5000000000000000 : ℚ)) - (U := (4743017170741899602183 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (8034458702845387 / 5000000000000000 : ℝ) ≤ - (4743017170741899602183 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8033149276803899 / 10000000000000000 : ℝ)) (q := - (8034458702845387 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8034458702845387 / 10000000000000000 : ℚ)) + (r' := (8034458702845387 / 5000000000000000 : ℚ)) + (U := (-(2188454632258100397817 / 10000000000000000000000 : ℚ))) + (U' := (4743017170741899602183 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (8033149276803899 / 10000000000000000 : ℚ)) + (q := (8034458702845387 / 10000000000000000 : ℚ)) + (U := (-(2188454632258100397817 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_5 : Uω (aρ 5) (bρ 5) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3705,23 +3193,21 @@ lemma U_671_5 : have hlg : Real.log (15457448387817 / 19531250000000 : ℝ) ≤ (-(2339247632052252958919 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show (15457448387817 / 19531250000000 : ℝ) = (15457448387817 / 9765625000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15457448387817 / 9765625000000 : ℚ)) - (U := (4592224170947747041081 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (15457448387817 / 9765625000000 : ℝ) ≤ - (4592224170947747041081 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7910848939572733 / 10000000000000000 : ℝ)) (q := - (15457448387817 / 19531250000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15457448387817 / 19531250000000 : ℚ)) + (r' := (15457448387817 / 9765625000000 : ℚ)) + (U := (-(2339247632052252958919 / 10000000000000000000000 : ℚ))) + (U' := (4592224170947747041081 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (7910848939572733 / 10000000000000000 : ℚ)) + (q := (15457448387817 / 19531250000000 : ℚ)) + (U := (-(2339247632052252958919 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_6 : Uω (aρ 6) (bρ 6) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3729,25 +3215,21 @@ lemma U_671_6 : have hlg : Real.log (7742412510432781 / 10000000000000000 : ℝ) ≤ (-(127935879922268966083 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7742412510432781 / 10000000000000000 : ℝ) = - (7742412510432781 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7742412510432781 / 5000000000000000 : ℚ)) - (U := (218637710227731033917 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7742412510432781 / 5000000000000000 : ℝ) ≤ - (218637710227731033917 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7734487186453687 / 10000000000000000 : ℝ)) (q := - (7742412510432781 / 10000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7742412510432781 / 10000000000000000 : ℚ)) + (r' := (7742412510432781 / 5000000000000000 : ℚ)) + (U := (-(127935879922268966083 / 500000000000000000000 : ℚ))) + (U' := (218637710227731033917 / 500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (7734487186453687 / 10000000000000000 : ℚ)) + (q := (7742412510432781 / 10000000000000000 : ℚ)) + (U := (-(127935879922268966083 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_7 : Uω (aρ 7) (bρ 7) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3755,25 +3237,21 @@ lemma U_671_7 : have hlg : Real.log (15018816155841109 / 20000000000000000 : ℝ) ≤ (-(143214223958901012311 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (15018816155841109 / 20000000000000000 : ℝ) = - (15018816155841109 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15018816155841109 / 10000000000000000 : ℚ)) - (U := (203359366191098987689 / 500000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15018816155841109 / 10000000000000000 : ℝ) ≤ - (203359366191098987689 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3746069851094617 / 5000000000000000 : ℝ)) (q := - (15018816155841109 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15018816155841109 / 20000000000000000 : ℚ)) + (r' := (15018816155841109 / 10000000000000000 : ℚ)) + (U := (-(143214223958901012311 / 500000000000000000000 : ℚ))) + (U' := (203359366191098987689 / 500000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (3746069851094617 / 5000000000000000 : ℚ)) + (q := (15018816155841109 / 20000000000000000 : ℚ)) + (U := (-(143214223958901012311 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_8 : Uω (aρ 8) (bρ 8) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3781,25 +3259,21 @@ lemma U_671_8 : have hlg : Real.log (1802035298080953 / 2500000000000000 : ℝ) ≤ (-(3273739843396933459351 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1802035298080953 / 2500000000000000 : ℝ) = - (1802035298080953 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1802035298080953 / 1250000000000000 : ℚ)) - (U := (3657731959603066540649 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1802035298080953 / 1250000000000000 : ℝ) ≤ - (3657731959603066540649 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7173147582335749 / 10000000000000000 : ℝ)) (q := - (1802035298080953 / 2500000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1802035298080953 / 2500000000000000 : ℚ)) + (r' := (1802035298080953 / 1250000000000000 : ℚ)) + (U := (-(3273739843396933459351 / 10000000000000000000000 : ℚ))) + (U' := (3657731959603066540649 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (7173147582335749 / 10000000000000000 : ℚ)) + (q := (1802035298080953 / 2500000000000000 : ℚ)) + (U := (-(3273739843396933459351 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_9 : Uω (aρ 9) (bρ 9) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3807,25 +3281,21 @@ lemma U_671_9 : have hlg : Real.log (13671842754950423 / 20000000000000000 : ℝ) ≤ (-(3803938287939391401999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13671842754950423 / 20000000000000000 : ℝ) = - (13671842754950423 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13671842754950423 / 10000000000000000 : ℚ)) - (U := (3127533515060608598001 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13671842754950423 / 10000000000000000 : ℝ) ≤ - (3127533515060608598001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1692418395249637 / 2500000000000000 : ℝ)) (q := - (13671842754950423 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13671842754950423 / 20000000000000000 : ℚ)) + (r' := (13671842754950423 / 10000000000000000 : ℚ)) + (U := (-(3803938287939391401999 / 10000000000000000000000 : ℚ))) + (U' := (3127533515060608598001 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (1692418395249637 / 2500000000000000 : ℚ)) + (q := (13671842754950423 / 20000000000000000 : ℚ)) + (U := (-(3803938287939391401999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_10 : Uω (aρ 10) (bρ 10) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3833,26 +3303,21 @@ lemma U_671_10 : have hlg : Real.log (3197989499534529 / 5000000000000000 : ℝ) ≤ (-(4469155812153975488917 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3197989499534529 / 5000000000000000 : ℝ) = - (3197989499534529 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3197989499534529 / 2500000000000000 : ℚ)) - (U := (2462315990846024511083 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3197989499534529 / 2500000000000000 : ℝ) ≤ - (2462315990846024511083 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6278347857681241 / 10000000000000000 : ℝ)) (q := - (3197989499534529 / 5000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3197989499534529 / 5000000000000000 : ℚ)) + (r' := (3197989499534529 / 2500000000000000 : ℚ)) + (U := (-(4469155812153975488917 / 10000000000000000000000 : ℚ))) + (U' := (2462315990846024511083 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (6278347857681241 / 10000000000000000 : ℚ)) + (q := (3197989499534529 / 5000000000000000 : ℚ)) + (U := (-(4469155812153975488917 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_11 : Uω (aρ 11) (bρ 11) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3860,26 +3325,21 @@ lemma U_671_11 : have hlg : Real.log (11797167717509879 / 20000000000000000 : ℝ) ≤ (-(5278727945726234280523 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11797167717509879 / 20000000000000000 : ℝ) = - (11797167717509879 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11797167717509879 / 10000000000000000 : ℚ)) - (U := (1652743857273765719477 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (11797167717509879 / 10000000000000000 : ℝ) ≤ - (1652743857273765719477 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1425508550814501 / 2500000000000000 : ℝ)) (q := - (11797167717509879 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11797167717509879 / 20000000000000000 : ℚ)) + (r' := (11797167717509879 / 10000000000000000 : ℚ)) + (U := (-(5278727945726234280523 / 10000000000000000000000 : ℚ))) + (U' := (1652743857273765719477 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (1425508550814501 / 2500000000000000 : ℚ)) + (q := (11797167717509879 / 20000000000000000 : ℚ)) + (U := (-(5278727945726234280523 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_12 : Uω (aρ 12) (bρ 12) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3887,26 +3347,21 @@ lemma U_671_12 : have hlg : Real.log (10723417062856459 / 20000000000000000 : ℝ) ≤ (-(1558256031449427925669 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10723417062856459 / 20000000000000000 : ℝ) = - (10723417062856459 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10723417062856459 / 10000000000000000 : ℚ)) - (U := (174611919300572074331 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (10723417062856459 / 10000000000000000 : ℝ) ≤ - (174611919300572074331 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (315748977830599 / 625000000000000 : ℝ)) (q := - (10723417062856459 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10723417062856459 / 20000000000000000 : ℚ)) + (r' := (10723417062856459 / 10000000000000000 : ℚ)) + (U := (-(1558256031449427925669 / 2500000000000000000000 : ℚ))) + (U' := (174611919300572074331 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (315748977830599 / 625000000000000 : ℚ)) + (q := (10723417062856459 / 20000000000000000 : ℚ)) + (U := (-(1558256031449427925669 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_13 : Uω (aρ 13) (bρ 13) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3914,24 +3369,21 @@ lemma U_671_13 : have hlg : Real.log (96232701758961 / 200000000000000 : ℝ) ≤ (-(7315481309970044122373 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (96232701758961 / 200000000000000 : ℝ) = (96232701758961 / 50000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (96232701758961 / 50000000000000 : ℚ)) - (U := (6547462296029955877627 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (96232701758961 / 50000000000000 : ℝ) ≤ - (6547462296029955877627 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (174048739996969 / 400000000000000 : ℝ)) (q := - (96232701758961 / 200000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) (by norm_num [bρ_13]) - (by norm_num) (by norm_num [aρ_13, bρ_13]) (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (96232701758961 / 200000000000000 : ℚ)) + (r' := (96232701758961 / 50000000000000 : ℚ)) + (U := (-(7315481309970044122373 / 10000000000000000000000 : ℚ))) + (U' := (6547462296029955877627 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (174048739996969 / 400000000000000 : ℚ)) + (q := (96232701758961 / 200000000000000 : ℚ)) + (U := (-(7315481309970044122373 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_14 : Uω (aρ 14) (bρ 14) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3939,26 +3391,21 @@ lemma U_671_14 : have hlg : Real.log (8569361431673801 / 20000000000000000 : ℝ) ≤ (-(132427977383954035777 / 156250000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (8569361431673801 / 20000000000000000 : ℝ) = - (8569361431673801 / 5000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8569361431673801 / 5000000000000000 : ℚ)) - (U := (84180516459795964223 / 156250000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8569361431673801 / 5000000000000000 : ℝ) ≤ - (84180516459795964223 / 156250000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1820618520373463 / 5000000000000000 : ℝ)) (q := - (8569361431673801 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8569361431673801 / 20000000000000000 : ℚ)) + (r' := (8569361431673801 / 5000000000000000 : ℚ)) + (U := (-(132427977383954035777 / 156250000000000000000 : ℚ))) + (U' := (84180516459795964223 / 156250000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (1820618520373463 / 5000000000000000 : ℚ)) + (q := (8569361431673801 / 20000000000000000 : ℚ)) + (U := (-(132427977383954035777 / 156250000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_15 : Uω (aρ 15) (bρ 15) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3966,26 +3413,21 @@ lemma U_671_15 : have hlg : Real.log (1532905499401413 / 4000000000000000 : ℝ) ≤ (-(4795647034182452320199 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1532905499401413 / 4000000000000000 : ℝ) = - (1532905499401413 / 1000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1532905499401413 / 1000000000000000 : ℚ)) - (U := (2135824768817547679801 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1532905499401413 / 1000000000000000 : ℝ) ≤ - (2135824768817547679801 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (299597638349519 / 1000000000000000 : ℝ)) (q := - (1532905499401413 / 4000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1532905499401413 / 4000000000000000 : ℚ)) + (r' := (1532905499401413 / 1000000000000000 : ℚ)) + (U := (-(4795647034182452320199 / 5000000000000000000000 : ℚ))) + (U' := (2135824768817547679801 / 5000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (299597638349519 / 1000000000000000 : ℚ)) + (q := (1532905499401413 / 4000000000000000 : ℚ)) + (U := (-(4795647034182452320199 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671_16 : Uω (aρ 16) (bρ 16) (2639911887007 / 3200000000000 : ℝ) ≤ @@ -3993,26 +3435,21 @@ lemma U_671_16 : have hlg : Real.log (1764550262759391 / 5000000000000000 : ℝ) ≤ (-(10415420626330915702817 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (1764550262759391 / 5000000000000000 : ℝ) = - (1764550262759391 / 1250000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1764550262759391 / 1250000000000000 : ℚ)) - (U := (3447522979669084297183 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (1764550262759391 / 1250000000000000 : ℝ) ≤ - (3447522979669084297183 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2542021589035689 / 10000000000000000 : ℝ)) (q := - (1764550262759391 / 5000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1764550262759391 / 5000000000000000 : ℚ)) + (r' := (1764550262759391 / 1250000000000000 : ℚ)) + (U := (-(10415420626330915702817 / 10000000000000000000000 : ℚ))) + (U' := (3447522979669084297183 / 10000000000000000000000 : ℚ)) + 2 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (2639911887007 / 3200000000000 : ℚ)) + (s := (2542021589035689 / 10000000000000000 : ℚ)) + (q := (1764550262759391 / 5000000000000000 : ℚ)) + (U := (-(10415420626330915702817 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_671 : Uρ (2639911887007 / 3200000000000 : ℝ) ≤ @@ -4105,25 +3542,21 @@ lemma U_672_1 : have hlg : Real.log (132530029957627211 / 160000000000000000 : ℝ) ≤ (-(235455692546499870873 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (132530029957627211 / 160000000000000000 : ℝ) = - (132530029957627211 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (132530029957627211 / 80000000000000000 : ℚ)) - (U := (630978282828500129127 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (132530029957627211 / 80000000000000000 : ℝ) ≤ - (630978282828500129127 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8283107354615667 / 10000000000000000 : ℝ)) (q := - (132530029957627211 / 160000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) - (by norm_num [bρ_1]) (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (132530029957627211 / 160000000000000000 : ℚ)) + (r' := (132530029957627211 / 80000000000000000 : ℚ)) + (U := (-(235455692546499870873 / 1250000000000000000000 : ℚ))) + (U' := (630978282828500129127 / 1250000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (8283107354615667 / 10000000000000000 : ℚ)) + (q := (132530029957627211 / 160000000000000000 : ℚ)) + (U := (-(235455692546499870873 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_2 : Uω (aρ 2) (bρ 2) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4131,25 +3564,21 @@ lemma U_672_2 : have hlg : Real.log (132147982790004099 / 160000000000000000 : ℝ) ≤ (-(191251438587919057173 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (132147982790004099 / 160000000000000000 : ℝ) = - (132147982790004099 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (132147982790004099 / 80000000000000000 : ℚ)) - (U := (501895741712080942827 / 1000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (132147982790004099 / 80000000000000000 : ℝ) ≤ - (501895741712080942827 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4129560235586389 / 5000000000000000 : ℝ)) (q := - (132147982790004099 / 160000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) - (by norm_num [bρ_2]) (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (132147982790004099 / 160000000000000000 : ℚ)) + (r' := (132147982790004099 / 80000000000000000 : ℚ)) + (U := (-(191251438587919057173 / 1000000000000000000000 : ℚ))) + (U' := (501895741712080942827 / 1000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (4129560235586389 / 5000000000000000 : ℚ)) + (q := (132147982790004099 / 160000000000000000 : ℚ)) + (U := (-(191251438587919057173 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_3 : Uω (aρ 3) (bρ 3) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4157,25 +3586,21 @@ lemma U_672_3 : have hlg : Real.log (131384492835420723 / 160000000000000000 : ℝ) ≤ (-(123153581774262376029 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (131384492835420723 / 160000000000000000 : ℝ) = - (131384492835420723 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (131384492835420723 / 80000000000000000 : ℚ)) - (U := (310063405913237623971 / 625000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (131384492835420723 / 80000000000000000 : ℝ) ≤ - (310063405913237623971 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (513192520824991 / 625000000000000 : ℝ)) (q := - (131384492835420723 / 160000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) - (by norm_num [bρ_3]) (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (131384492835420723 / 160000000000000000 : ℚ)) + (r' := (131384492835420723 / 80000000000000000 : ℚ)) + (U := (-(123153581774262376029 / 625000000000000000000 : ℚ))) + (U' := (310063405913237623971 / 625000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (513192520824991 / 625000000000000 : ℚ)) + (q := (131384492835420723 / 160000000000000000 : ℚ)) + (U := (-(123153581774262376029 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_4 : Uω (aρ 4) (bρ 4) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4183,25 +3608,21 @@ lemma U_672_4 : have hlg : Real.log (130118294927134203 / 160000000000000000 : ℝ) ≤ (-(413459634607695491819 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (130118294927134203 / 160000000000000000 : ℝ) = - (130118294927134203 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (130118294927134203 / 80000000000000000 : ℚ)) - (U := (972834725992304508181 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (130118294927134203 / 80000000000000000 : ℝ) ≤ - (972834725992304508181 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8131099775729041 / 10000000000000000 : ℝ)) (q := - (130118294927134203 / 160000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) - (by norm_num [bρ_4]) (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (130118294927134203 / 160000000000000000 : ℚ)) + (r' := (130118294927134203 / 80000000000000000 : ℚ)) + (U := (-(413459634607695491819 / 2000000000000000000000 : ℚ))) + (U' := (972834725992304508181 / 2000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (8131099775729041 / 10000000000000000 : ℚ)) + (q := (130118294927134203 / 160000000000000000 : ℚ)) + (U := (-(413459634607695491819 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_5 : Uω (aρ 5) (bρ 5) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4209,25 +3630,21 @@ lemma U_672_5 : have hlg : Real.log (128194778771775299 / 160000000000000000 : ℝ) ≤ (-(2216229985259282885979 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (128194778771775299 / 160000000000000000 : ℝ) = - (128194778771775299 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (128194778771775299 / 80000000000000000 : ℚ)) - (U := (4715241817740717114021 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (128194778771775299 / 80000000000000000 : ℝ) ≤ - (4715241817740717114021 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4004425087822089 / 5000000000000000 : ℝ)) (q := - (128194778771775299 / 160000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) - (by norm_num [bρ_5]) (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (128194778771775299 / 160000000000000000 : ℚ)) + (r' := (128194778771775299 / 80000000000000000 : ℚ)) + (U := (-(2216229985259282885979 / 10000000000000000000000 : ℚ))) + (U' := (4715241817740717114021 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (4004425087822089 / 5000000000000000 : ℚ)) + (q := (128194778771775299 / 160000000000000000 : ℚ)) + (U := (-(2216229985259282885979 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_6 : Uω (aρ 6) (bρ 6) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4235,25 +3652,21 @@ lemma U_672_6 : have hlg : Real.log (125446888816866827 / 160000000000000000 : ℝ) ≤ (-(486582685306763027307 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (125446888816866827 / 160000000000000000 : ℝ) = - (125446888816866827 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (125446888816866827 / 80000000000000000 : ℚ)) - (U := (899711675293236972693 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (125446888816866827 / 80000000000000000 : ℝ) ≤ - (899711675293236972693 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7832604306420619 / 10000000000000000 : ℝ)) (q := - (125446888816866827 / 160000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) - (by norm_num [bρ_6]) (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (125446888816866827 / 160000000000000000 : ℚ)) + (r' := (125446888816866827 / 80000000000000000 : ℚ)) + (U := (-(486582685306763027307 / 2000000000000000000000 : ℚ))) + (U' := (899711675293236972693 / 2000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (7832604306420619 / 10000000000000000 : ℚ)) + (q := (125446888816866827 / 160000000000000000 : ℚ)) + (U := (-(486582685306763027307 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_7 : Uω (aρ 7) (bρ 7) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4261,25 +3674,21 @@ lemma U_672_7 : have hlg : Real.log (121720796977537651 / 160000000000000000 : ℝ) ≤ (-(341804927920539353553 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (121720796977537651 / 160000000000000000 : ℝ) = - (121720796977537651 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (121720796977537651 / 80000000000000000 : ℚ)) - (U := (524629047454460646447 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (121720796977537651 / 80000000000000000 : ℝ) ≤ - (524629047454460646447 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (948813025908059 / 1250000000000000 : ℝ)) (q := - (121720796977537651 / 160000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) - (by norm_num [bρ_7]) (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (121720796977537651 / 160000000000000000 : ℚ)) + (r' := (121720796977537651 / 80000000000000000 : ℚ)) + (U := (-(341804927920539353553 / 1250000000000000000000 : ℚ))) + (U' := (524629047454460646447 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (948813025908059 / 1250000000000000 : ℚ)) + (q := (121720796977537651 / 160000000000000000 : ℚ)) + (U := (-(341804927920539353553 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_8 : Uω (aρ 8) (bρ 8) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4287,25 +3696,21 @@ lemma U_672_8 : have hlg : Real.log (116904502074220267 / 160000000000000000 : ℝ) ≤ (-(3138164350541981558903 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (116904502074220267 / 160000000000000000 : ℝ) = - (116904502074220267 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (116904502074220267 / 80000000000000000 : ℚ)) - (U := (3793307452458018441097 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (116904502074220267 / 80000000000000000 : ℝ) ≤ - (3793307452458018441097 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7272008995689799 / 10000000000000000 : ℝ)) (q := - (116904502074220267 / 160000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) - (by norm_num [bρ_8]) (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (116904502074220267 / 160000000000000000 : ℚ)) + (r' := (116904502074220267 / 80000000000000000 : ℚ)) + (U := (-(3138164350541981558903 / 10000000000000000000000 : ℚ))) + (U' := (3793307452458018441097 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (7272008995689799 / 10000000000000000 : ℚ)) + (q := (116904502074220267 / 160000000000000000 : ℚ)) + (U := (-(3138164350541981558903 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_9 : Uω (aρ 9) (bρ 9) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4313,25 +3718,21 @@ lemma U_672_9 : have hlg : Real.log (22191311289371623 / 32000000000000000 : ℝ) ≤ (-(915087684084109970181 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (22191311289371623 / 32000000000000000 : ℝ) = - (22191311289371623 / 16000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (22191311289371623 / 16000000000000000 : ℚ)) - (U := (817780266665890029819 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (22191311289371623 / 16000000000000000 : ℝ) ≤ - (817780266665890029819 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (686948142062953 / 1000000000000000 : ℝ)) (q := - (22191311289371623 / 32000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (22191311289371623 / 32000000000000000 : ℚ)) + (r' := (22191311289371623 / 16000000000000000 : ℚ)) + (U := (-(915087684084109970181 / 2500000000000000000000 : ℚ))) + (U' := (817780266665890029819 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (686948142062953 / 1000000000000000 : ℚ)) + (q := (22191311289371623 / 32000000000000000 : ℚ)) + (U := (-(915087684084109970181 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_10 : Uω (aρ 10) (bρ 10) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4339,26 +3740,21 @@ lemma U_672_10 : have hlg : Real.log (103931262160899803 / 160000000000000000 : ℝ) ≤ (-(2157220375553611875821 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (103931262160899803 / 160000000000000000 : ℝ) = - (103931262160899803 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (103931262160899803 / 80000000000000000 : ℚ)) - (U := (1308515525946388124179 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (103931262160899803 / 80000000000000000 : ℝ) ≤ - (1308515525946388124179 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6379878668379741 / 10000000000000000 : ℝ)) (q := - (103931262160899803 / 160000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (103931262160899803 / 160000000000000000 : ℚ)) + (r' := (103931262160899803 / 80000000000000000 : ℚ)) + (U := (-(2157220375553611875821 / 5000000000000000000000 : ℚ))) + (U' := (1308515525946388124179 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (6379878668379741 / 10000000000000000 : ℚ)) + (q := (103931262160899803 / 160000000000000000 : ℚ)) + (U := (-(2157220375553611875821 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_11 : Uω (aρ 11) (bρ 11) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4366,26 +3762,21 @@ lemma U_672_11 : have hlg : Real.log (95997107451389363 / 160000000000000000 : ℝ) ≤ (-(2554278773373393057629 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (95997107451389363 / 160000000000000000 : ℝ) = - (95997107451389363 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (95997107451389363 / 80000000000000000 : ℚ)) - (U := (911457128126606942371 / 5000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (95997107451389363 / 80000000000000000 : ℝ) ≤ - (911457128126606942371 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (45363952780437 / 78125000000000 : ℝ)) (q := - (95997107451389363 / 160000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (95997107451389363 / 160000000000000000 : ℚ)) + (r' := (95997107451389363 / 80000000000000000 : ℚ)) + (U := (-(2554278773373393057629 / 5000000000000000000000 : ℚ))) + (U' := (911457128126606942371 / 5000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (45363952780437 / 78125000000000 : ℚ)) + (q := (95997107451389363 / 160000000000000000 : ℚ)) + (U := (-(2554278773373393057629 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_12 : Uω (aρ 12) (bρ 12) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4393,26 +3784,21 @@ lemma U_672_12 : have hlg : Real.log (87448156886536459 / 160000000000000000 : ℝ) ≤ (-(188789903102745975883 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (87448156886536459 / 160000000000000000 : ℝ) = - (87448156886536459 / 80000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (87448156886536459 / 80000000000000000 : ℚ)) - (U := (27818590741004024117 / 312500000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (87448156886536459 / 80000000000000000 : ℝ) ≤ - (27818590741004024117 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5161667231974323 / 10000000000000000 : ℝ)) (q := - (87448156886536459 / 160000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (87448156886536459 / 160000000000000000 : ℚ)) + (r' := (87448156886536459 / 80000000000000000 : ℚ)) + (U := (-(188789903102745975883 / 312500000000000000000 : ℚ))) + (U' := (27818590741004024117 / 312500000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (5161667231974323 / 10000000000000000 : ℚ)) + (q := (87448156886536459 / 160000000000000000 : ℚ)) + (U := (-(188789903102745975883 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_13 : Uω (aρ 13) (bρ 13) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4420,26 +3806,21 @@ lemma U_672_13 : have hlg : Real.log (15742925331419543 / 32000000000000000 : ℝ) ≤ (-(1773362058072074792879 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (15742925331419543 / 32000000000000000 : ℝ) = - (15742925331419543 / 8000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15742925331419543 / 8000000000000000 : ℚ)) - (U := (1692373843427925207121 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (15742925331419543 / 8000000000000000 : ℝ) ≤ - (1692373843427925207121 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (111733942372237 / 250000000000000 : ℝ)) (q := - (15742925331419543 / 32000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15742925331419543 / 32000000000000000 : ℚ)) + (r' := (15742925331419543 / 8000000000000000 : ℚ)) + (U := (-(1773362058072074792879 / 2500000000000000000000 : ℚ))) + (U' := (1692373843427925207121 / 2500000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (111733942372237 / 250000000000000 : ℚ)) + (q := (15742925331419543 / 32000000000000000 : ℚ)) + (U := (-(1773362058072074792879 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_14 : Uω (aρ 14) (bρ 14) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4447,26 +3828,21 @@ lemma U_672_14 : have hlg : Real.log (70389993110883323 / 160000000000000000 : ℝ) ≤ (-(8211227049645739158739 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (70389993110883323 / 160000000000000000 : ℝ) = - (70389993110883323 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70389993110883323 / 40000000000000000 : ℚ)) - (U := (5651716556354260841261 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70389993110883323 / 40000000000000000 : ℝ) ≤ - (5651716556354260841261 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3772705786657681 / 10000000000000000 : ℝ)) (q := - (70389993110883323 / 160000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70389993110883323 / 160000000000000000 : ℚ)) + (r' := (70389993110883323 / 40000000000000000 : ℚ)) + (U := (-(8211227049645739158739 / 10000000000000000000000 : ℚ))) + (U' := (5651716556354260841261 / 10000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (3772705786657681 / 10000000000000000 : ℚ)) + (q := (70389993110883323 / 160000000000000000 : ℚ)) + (U := (-(8211227049645739158739 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_15 : Uω (aρ 15) (bρ 15) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4474,26 +3850,21 @@ lemma U_672_15 : have hlg : Real.log (63302844916412531 / 160000000000000000 : ℝ) ≤ (-(1854487086372971585059 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (63302844916412531 / 160000000000000000 : ℝ) = - (63302844916412531 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63302844916412531 / 40000000000000000 : ℚ)) - (U := (918101634827028414941 / 2000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63302844916412531 / 40000000000000000 : ℝ) ≤ - (918101634827028414941 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (393298192470479 / 1250000000000000 : ℝ)) (q := - (63302844916412531 / 160000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63302844916412531 / 160000000000000000 : ℚ)) + (r' := (63302844916412531 / 40000000000000000 : ℚ)) + (U := (-(1854487086372971585059 / 2000000000000000000000 : ℚ))) + (U' := (918101634827028414941 / 2000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (393298192470479 / 1250000000000000 : ℚ)) + (q := (63302844916412531 / 160000000000000000 : ℚ)) + (U := (-(1854487086372971585059 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672_16 : Uω (aρ 16) (bρ 16) (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4501,26 +3872,21 @@ lemma U_672_16 : have hlg : Real.log (58610198971289891 / 160000000000000000 : ℝ) ≤ (-(10042650893961810327003 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (58610198971289891 / 160000000000000000 : ℝ) = - (58610198971289891 / 40000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (58610198971289891 / 40000000000000000 : ℚ)) - (U := (3820292712038189672997 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (58610198971289891 / 40000000000000000 : ℝ) ≤ - (3820292712038189672997 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1356088224066751 / 5000000000000000 : ℝ)) (q := - (58610198971289891 / 160000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (58610198971289891 / 160000000000000000 : ℚ)) + (r' := (58610198971289891 / 40000000000000000 : ℚ)) + (U := (-(10042650893961810327003 / 10000000000000000000000 : ℚ))) + (U' := (3820292712038189672997 / 10000000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (106849838184611 / 128000000000000 : ℚ)) + (s := (1356088224066751 / 5000000000000000 : ℚ)) + (q := (58610198971289891 / 160000000000000000 : ℚ)) + (U := (-(10042650893961810327003 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_672 : Uρ (106849838184611 / 128000000000000 : ℝ) ≤ @@ -4620,25 +3986,21 @@ lemma U_673_1 : have hlg : Real.log (67048368493290031 / 80000000000000000 : ℝ) ≤ (-(441530894174971766827 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (67048368493290031 / 80000000000000000 : ℝ) = - (67048368493290031 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (67048368493290031 / 40000000000000000 : ℚ)) - (U := (1291337056575028233173 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (67048368493290031 / 40000000000000000 : ℝ) ≤ - (1291337056575028233173 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4190513385979457 / 5000000000000000 : ℝ)) (q := - (67048368493290031 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (67048368493290031 / 80000000000000000 : ℚ)) + (r' := (67048368493290031 / 40000000000000000 : ℚ)) + (U := (-(441530894174971766827 / 2500000000000000000000 : ℚ))) + (U' := (1291337056575028233173 / 2500000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (4190513385979457 / 5000000000000000 : ℚ)) + (q := (67048368493290031 / 80000000000000000 : ℚ)) + (U := (-(441530894174971766827 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_2 : Uω (aρ 2) (bρ 2) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4646,25 +4008,21 @@ lemma U_673_2 : have hlg : Real.log (66857355125838379 / 80000000000000000 : ℝ) ≤ (-(358930625195043976947 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (66857355125838379 / 80000000000000000 : ℝ) = - (66857355125838379 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (66857355125838379 / 40000000000000000 : ℚ)) - (U := (1027363735404956023053 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (66857355125838379 / 40000000000000000 : ℝ) ≤ - (1027363735404956023053 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8357042442606001 / 10000000000000000 : ℝ)) (q := - (66857355125838379 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (66857355125838379 / 80000000000000000 : ℚ)) + (r' := (66857355125838379 / 40000000000000000 : ℚ)) + (U := (-(358930625195043976947 / 2000000000000000000000 : ℚ))) + (U' := (1027363735404956023053 / 2000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (8357042442606001 / 10000000000000000 : ℚ)) + (q := (66857355125838379 / 80000000000000000 : ℚ)) + (U := (-(358930625195043976947 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_3 : Uω (aρ 3) (bρ 3) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4672,25 +4030,21 @@ lemma U_673_3 : have hlg : Real.log (66475640576983063 / 80000000000000000 : ℝ) ≤ (-(1851910609720033326851 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (66475640576983063 / 80000000000000000 : ℝ) = - (66475640576983063 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (66475640576983063 / 40000000000000000 : ℚ)) - (U := (5079561193279966673149 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (66475640576983063 / 40000000000000000 : ℝ) ≤ - (5079561193279966673149 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2077252477935543 / 2500000000000000 : ℝ)) (q := - (66475640576983063 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (66475640576983063 / 80000000000000000 : ℚ)) + (r' := (66475640576983063 / 40000000000000000 : ℚ)) + (U := (-(1851910609720033326851 / 10000000000000000000000 : ℚ))) + (U' := (5079561193279966673149 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (2077252477935543 / 2500000000000000 : ℚ)) + (q := (66475640576983063 / 80000000000000000 : ℚ)) + (U := (-(1851910609720033326851 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_4 : Uω (aρ 4) (bρ 4) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4698,25 +4052,21 @@ lemma U_673_4 : have hlg : Real.log (65842622301709847 / 80000000000000000 : ℝ) ≤ (-(973796252202356616109 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (65842622301709847 / 80000000000000000 : ℝ) = - (65842622301709847 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (65842622301709847 / 40000000000000000 : ℚ)) - (U := (2491939649297643383891 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (65842622301709847 / 40000000000000000 : ℝ) ≤ - (2491939649297643383891 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2057262380997217 / 2500000000000000 : ℝ)) (q := - (65842622301709847 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (65842622301709847 / 80000000000000000 : ℚ)) + (r' := (65842622301709847 / 40000000000000000 : ℚ)) + (U := (-(973796252202356616109 / 5000000000000000000000 : ℚ))) + (U' := (2491939649297643383891 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (2057262380997217 / 2500000000000000 : ℚ)) + (q := (65842622301709847 / 80000000000000000 : ℚ)) + (U := (-(973796252202356616109 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_5 : Uω (aρ 5) (bρ 5) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4724,25 +4074,21 @@ lemma U_673_5 : have hlg : Real.log (12976212444371607 / 16000000000000000 : ℝ) ≤ (-(1047354263203227591767 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12976212444371607 / 16000000000000000 : ℝ) = - (12976212444371607 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12976212444371607 / 8000000000000000 : ℚ)) - (U := (2418381638296772408233 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (12976212444371607 / 8000000000000000 : ℝ) ≤ - (2418381638296772408233 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1621369884672183 / 2000000000000000 : ℝ)) (q := - (12976212444371607 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12976212444371607 / 16000000000000000 : ℚ)) + (r' := (12976212444371607 / 8000000000000000 : ℚ)) + (U := (-(1047354263203227591767 / 5000000000000000000000 : ℚ))) + (U' := (2418381638296772408233 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (1621369884672183 / 2000000000000000 : ℚ)) + (q := (12976212444371607 / 16000000000000000 : ℚ)) + (U := (-(1047354263203227591767 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_6 : Uω (aρ 6) (bρ 6) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4750,25 +4096,21 @@ lemma U_673_6 : have hlg : Real.log (63507569140601767 / 80000000000000000 : ℝ) ≤ (-(2308675365543395899577 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (63507569140601767 / 80000000000000000 : ℝ) = - (63507569140601767 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (63507569140601767 / 40000000000000000 : ℚ)) - (U := (4622796437456604100423 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (63507569140601767 / 40000000000000000 : ℝ) ≤ - (4622796437456604100423 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (247834891505839 / 312500000000000 : ℝ)) (q := - (63507569140601767 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (63507569140601767 / 80000000000000000 : ℚ)) + (r' := (63507569140601767 / 40000000000000000 : ℚ)) + (U := (-(2308675365543395899577 / 10000000000000000000000 : ℚ))) + (U' := (4622796437456604100423 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (247834891505839 / 312500000000000 : ℚ)) + (q := (63507569140601767 / 80000000000000000 : ℚ)) + (U := (-(2308675365543395899577 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_7 : Uω (aρ 7) (bρ 7) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4776,25 +4118,21 @@ lemma U_673_7 : have hlg : Real.log (12329097371660311 / 16000000000000000 : ℝ) ≤ (-(2606266133502291094023 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12329097371660311 / 16000000000000000 : ℝ) = - (12329097371660311 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12329097371660311 / 8000000000000000 : ℚ)) - (U := (4325205669497708905977 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (12329097371660311 / 8000000000000000 : ℝ) ≤ - (4325205669497708905977 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1537771467674359 / 2000000000000000 : ℝ)) (q := - (12329097371660311 / 16000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12329097371660311 / 16000000000000000 : ℚ)) + (r' := (12329097371660311 / 8000000000000000 : ℚ)) + (U := (-(2606266133502291094023 / 10000000000000000000000 : ℚ))) + (U' := (4325205669497708905977 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (1537771467674359 / 2000000000000000 : ℚ)) + (q := (12329097371660311 / 16000000000000000 : ℚ)) + (U := (-(2606266133502291094023 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_8 : Uω (aρ 8) (bρ 8) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4802,25 +4140,21 @@ lemma U_673_8 : have hlg : Real.log (59239271892758979 / 80000000000000000 : ℝ) ≤ (-(375552419867593022027 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (59239271892758979 / 80000000000000000 : ℝ) = - (59239271892758979 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59239271892758979 / 40000000000000000 : ℚ)) - (U := (490881555507406977973 / 1250000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59239271892758979 / 40000000000000000 : ℝ) ≤ - (490881555507406977973 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7370845248326151 / 10000000000000000 : ℝ)) (q := - (59239271892758979 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59239271892758979 / 80000000000000000 : ℚ)) + (r' := (59239271892758979 / 40000000000000000 : ℚ)) + (U := (-(375552419867593022027 / 1250000000000000000000 : ℚ))) + (U' := (490881555507406977973 / 1250000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (7370845248326151 / 10000000000000000 : ℚ)) + (q := (59239271892758979 / 80000000000000000 : ℚ)) + (U := (-(375552419867593022027 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_9 : Uω (aρ 9) (bρ 9) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4828,25 +4162,21 @@ lemma U_673_9 : have hlg : Real.log (56268971067573579 / 80000000000000000 : ℝ) ≤ (-(3518833867664006306331 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (56268971067573579 / 80000000000000000 : ℝ) = - (56268971067573579 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (56268971067573579 / 40000000000000000 : ℚ)) - (U := (3412637935335993693669 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (56268971067573579 / 40000000000000000 : ℝ) ≤ - (3412637935335993693669 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6969235670389801 / 10000000000000000 : ℝ)) (q := - (56268971067573579 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (56268971067573579 / 80000000000000000 : ℚ)) + (r' := (56268971067573579 / 40000000000000000 : ℚ)) + (U := (-(3518833867664006306331 / 10000000000000000000000 : ℚ))) + (U' := (3412637935335993693669 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (6969235670389801 / 10000000000000000 : ℚ)) + (q := (56268971067573579 / 80000000000000000 : ℚ)) + (U := (-(3518833867664006306331 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_10 : Uω (aρ 10) (bρ 10) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4854,26 +4184,21 @@ lemma U_673_10 : have hlg : Real.log (2110519423226207 / 3200000000000000 : ℝ) ≤ (-(4162167202080293224863 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2110519423226207 / 3200000000000000 : ℝ) = - (2110519423226207 / 1600000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2110519423226207 / 1600000000000000 : ℚ)) - (U := (2769304600919706775137 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2110519423226207 / 1600000000000000 : ℝ) ≤ - (2769304600919706775137 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4050811457597 / 6250000000000 : ℝ)) (q := - (2110519423226207 / 3200000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2110519423226207 / 3200000000000000 : ℚ)) + (r' := (2110519423226207 / 1600000000000000 : ℚ)) + (U := (-(4162167202080293224863 / 10000000000000000000000 : ℚ))) + (U' := (2769304600919706775137 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (4050811457597 / 6250000000000 : ℚ)) + (q := (2110519423226207 / 3200000000000000 : ℚ)) + (U := (-(4162167202080293224863 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_11 : Uω (aρ 11) (bρ 11) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4881,26 +4206,21 @@ lemma U_673_11 : have hlg : Real.log (48807527807521887 / 80000000000000000 : ℝ) ≤ (-(4941420751005724572059 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (48807527807521887 / 80000000000000000 : ℝ) = - (48807527807521887 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (48807527807521887 / 40000000000000000 : ℚ)) - (U := (1990051051994275427941 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (48807527807521887 / 40000000000000000 : ℝ) ≤ - (1990051051994275427941 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2955455257538439 / 5000000000000000 : ℝ)) (q := - (48807527807521887 / 80000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (48807527807521887 / 80000000000000000 : ℚ)) + (r' := (48807527807521887 / 40000000000000000 : ℚ)) + (U := (-(4941420751005724572059 / 10000000000000000000000 : ℚ))) + (U' := (1990051051994275427941 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (2955455257538439 / 5000000000000000 : ℚ)) + (q := (48807527807521887 / 80000000000000000 : ℚ)) + (U := (-(4941420751005724572059 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_12 : Uω (aρ 12) (bρ 12) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4908,26 +4228,21 @@ lemma U_673_12 : have hlg : Real.log (44552635240304839 / 80000000000000000 : ℝ) ≤ (-(1463388324566729199727 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (44552635240304839 / 80000000000000000 : ℝ) = - (44552635240304839 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (44552635240304839 / 40000000000000000 : ℚ)) - (U := (269479626183270800273 / 2500000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (44552635240304839 / 40000000000000000 : ℝ) ≤ - (269479626183270800273 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (329430466872351 / 625000000000000 : ℝ)) (q := - (44552635240304839 / 80000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (44552635240304839 / 80000000000000000 : ℚ)) + (r' := (44552635240304839 / 40000000000000000 : ℚ)) + (U := (-(1463388324566729199727 / 2500000000000000000000 : ℚ))) + (U' := (269479626183270800273 / 2500000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (329430466872351 / 625000000000000 : ℚ)) + (q := (44552635240304839 / 80000000000000000 : ℚ)) + (U := (-(1463388324566729199727 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_13 : Uω (aρ 13) (bρ 13) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4935,26 +4250,21 @@ lemma U_673_13 : have hlg : Real.log (40217736294292543 / 80000000000000000 : ℝ) ≤ (-(687718534739097609481 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (40217736294292543 / 80000000000000000 : ℝ) = - (40217736294292543 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (40217736294292543 / 40000000000000000 : ℚ)) - (U := (5428645560902390519 / 1000000000000000000000 : ℚ)) - 3 (by decide +kernel)) : - Real.log (40217736294292543 / 40000000000000000 : ℝ) ≤ - (5428645560902390519 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2293272237524771 / 5000000000000000 : ℝ)) (q := - (40217736294292543 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (40217736294292543 / 80000000000000000 : ℚ)) + (r' := (40217736294292543 / 40000000000000000 : ℚ)) + (U := (-(687718534739097609481 / 1000000000000000000000 : ℚ))) + (U' := (5428645560902390519 / 1000000000000000000000 : ℚ)) + 1 3 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (2293272237524771 / 5000000000000000 : ℚ)) + (q := (40217736294292543 / 80000000000000000 : ℚ)) + (U := (-(687718534739097609481 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_14 : Uω (aρ 14) (bρ 14) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4962,25 +4272,21 @@ lemma U_673_14 : have hlg : Real.log (288837284746911 / 640000000000000 : ℝ) ≤ (-(994505843548616338199 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (288837284746911 / 640000000000000 : ℝ) = - (288837284746911 / 160000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (288837284746911 / 160000000000000 : ℚ)) - (U := (738362107201383661801 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (288837284746911 / 160000000000000 : ℝ) ≤ - (738362107201383661801 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (31217622678899 / 80000000000000 : ℝ)) (q := - (288837284746911 / 640000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) (by norm_num [bρ_14]) - (by norm_num) (by norm_num [aρ_14, bρ_14]) (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (288837284746911 / 640000000000000 : ℚ)) + (r' := (288837284746911 / 160000000000000 : ℚ)) + (U := (-(994505843548616338199 / 1250000000000000000000 : ℚ))) + (U' := (738362107201383661801 / 1250000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (31217622678899 / 80000000000000 : ℚ)) + (q := (288837284746911 / 640000000000000 : ℚ)) + (U := (-(994505843548616338199 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_15 : Uω (aρ 15) (bρ 15) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -4988,26 +4294,21 @@ lemma U_673_15 : have hlg : Real.log (32628910325302671 / 80000000000000000 : ℝ) ≤ (-(8968279189791174831113 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (32628910325302671 / 80000000000000000 : ℝ) = - (32628910325302671 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32628910325302671 / 20000000000000000 : ℚ)) - (U := (4894664416208825168887 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32628910325302671 / 20000000000000000 : ℝ) ≤ - (4894664416208825168887 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1646419272631037 / 5000000000000000 : ℝ)) (q := - (32628910325302671 / 80000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32628910325302671 / 80000000000000000 : ℚ)) + (r' := (32628910325302671 / 20000000000000000 : ℚ)) + (U := (-(8968279189791174831113 / 10000000000000000000000 : ℚ))) + (U' := (4894664416208825168887 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (1646419272631037 / 5000000000000000 : ℚ)) + (q := (32628910325302671 / 80000000000000000 : ℚ)) + (U := (-(8968279189791174831113 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673_16 : Uω (aρ 16) (bρ 16) (54051600444471 / 64000000000000 : ℝ) ≤ @@ -5015,26 +4316,21 @@ lemma U_673_16 : have hlg : Real.log (6070097983094999 / 16000000000000000 : ℝ) ≤ (-(387685589835395029451 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (6070097983094999 / 16000000000000000 : ℝ) = - (6070097983094999 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6070097983094999 / 4000000000000000 : ℚ)) - (U := (166832154404604970549 / 400000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (6070097983094999 / 4000000000000000 : ℝ) ≤ - (166832154404604970549 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (575121018863031 / 2000000000000000 : ℝ)) (q := - (6070097983094999 / 16000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6070097983094999 / 16000000000000000 : ℚ)) + (r' := (6070097983094999 / 4000000000000000 : ℚ)) + (U := (-(387685589835395029451 / 400000000000000000000 : ℚ))) + (U' := (166832154404604970549 / 400000000000000000000 : ℚ)) + 2 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (54051600444471 / 64000000000000 : ℚ)) + (s := (575121018863031 / 2000000000000000 : ℚ)) + (q := (6070097983094999 / 16000000000000000 : ℚ)) + (U := (-(387685589835395029451 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_673 : Uρ (54051600444471 / 64000000000000 : ℝ) ≤ @@ -5127,25 +4423,21 @@ lemma U_674_1 : have hlg : Real.log (34307537698640223 / 40000000000000000 : ℝ) ≤ (-(383785914618737645777 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (34307537698640223 / 40000000000000000 : ℝ) = - (34307537698640223 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34307537698640223 / 20000000000000000 : ℚ)) - (U := (1349082036131262354223 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34307537698640223 / 20000000000000000 : ℝ) ≤ - (1349082036131262354223 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8576865575404799 / 10000000000000000 : ℝ)) (q := - (34307537698640223 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34307537698640223 / 40000000000000000 : ℚ)) + (r' := (34307537698640223 / 20000000000000000 : ℚ)) + (U := (-(383785914618737645777 / 2500000000000000000000 : ℚ))) + (U' := (1349082036131262354223 / 2500000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (8576865575404799 / 10000000000000000 : ℚ)) + (q := (34307537698640223 / 40000000000000000 : ℚ)) + (U := (-(383785914618737645777 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_2 : Uω (aρ 2) (bρ 2) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5153,25 +4445,21 @@ lemma U_674_2 : have hlg : Real.log (34212040880202477 / 40000000000000000 : ℝ) ≤ (-(48844312258711844961 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (34212040880202477 / 40000000000000000 : ℝ) = - (34212040880202477 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34212040880202477 / 20000000000000000 : ℚ)) - (U := (167764181585038155039 / 312500000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34212040880202477 / 20000000000000000 : ℝ) ≤ - (167764181585038155039 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4276443089347963 / 5000000000000000 : ℝ)) (q := - (34212040880202477 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34212040880202477 / 40000000000000000 : ℚ)) + (r' := (34212040880202477 / 20000000000000000 : ℚ)) + (U := (-(48844312258711844961 / 312500000000000000000 : ℚ))) + (U' := (167764181585038155039 / 312500000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (4276443089347963 / 5000000000000000 : ℚ)) + (q := (34212040880202477 / 40000000000000000 : ℚ)) + (U := (-(48844312258711844961 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_3 : Uω (aρ 3) (bρ 3) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5179,25 +4467,21 @@ lemma U_674_3 : have hlg : Real.log (34021212980809573 / 40000000000000000 : ℝ) ≤ (-(404738031473057972023 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (34021212980809573 / 40000000000000000 : ℝ) = - (34021212980809573 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34021212980809573 / 20000000000000000 : ℚ)) - (U := (1328129919276942027977 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34021212980809573 / 20000000000000000 : ℝ) ≤ - (1328129919276942027977 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4252434167674737 / 5000000000000000 : ℝ)) (q := - (34021212980809573 / 40000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34021212980809573 / 40000000000000000 : ℚ)) + (r' := (34021212980809573 / 20000000000000000 : ℚ)) + (U := (-(404738031473057972023 / 2500000000000000000000 : ℚ))) + (U' := (1328129919276942027977 / 2500000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (4252434167674737 / 5000000000000000 : ℚ)) + (q := (34021212980809573 / 40000000000000000 : ℚ)) + (U := (-(404738031473057972023 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_4 : Uω (aρ 4) (bρ 4) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5205,25 +4489,21 @@ lemma U_674_4 : have hlg : Real.log (1348191267778473 / 1600000000000000 : ℝ) ≤ (-(342479473035474896289 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1348191267778473 / 1600000000000000 : ℝ) = - (1348191267778473 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1348191267778473 / 800000000000000 : ℚ)) - (U := (1043814887564525103711 / 2000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1348191267778473 / 800000000000000 : ℝ) ≤ - (1043814887564525103711 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (42124734366203 / 50000000000000 : ℝ)) (q := - (1348191267778473 / 1600000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1348191267778473 / 1600000000000000 : ℚ)) + (r' := (1348191267778473 / 800000000000000 : ℚ)) + (U := (-(342479473035474896289 / 2000000000000000000000 : ℚ))) + (U' := (1043814887564525103711 / 2000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (42124734366203 / 50000000000000 : ℚ)) + (q := (1348191267778473 / 1600000000000000 : ℚ)) + (U := (-(342479473035474896289 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_5 : Uω (aρ 5) (bρ 5) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5231,25 +4511,21 @@ lemma U_674_5 : have hlg : Real.log (33224192580018133 / 40000000000000000 : ℝ) ≤ (-(185601151129559812207 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (33224192580018133 / 40000000000000000 : ℝ) = - (33224192580018133 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (33224192580018133 / 20000000000000000 : ℚ)) - (U := (507546029170440187793 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (33224192580018133 / 20000000000000000 : ℝ) ≤ - (507546029170440187793 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4151421117676877 / 5000000000000000 : ℝ)) (q := - (33224192580018133 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (33224192580018133 / 40000000000000000 : ℚ)) + (r' := (33224192580018133 / 20000000000000000 : ℚ)) + (U := (-(185601151129559812207 / 1000000000000000000000 : ℚ))) + (U' := (507546029170440187793 / 1000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (4151421117676877 / 5000000000000000 : ℚ)) + (q := (33224192580018133 / 40000000000000000 : ℚ)) + (U := (-(185601151129559812207 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_6 : Uω (aρ 6) (bρ 6) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5257,25 +4533,21 @@ lemma U_674_6 : have hlg : Real.log (32537881332450541 / 40000000000000000 : ℝ) ≤ (-(1032372319093198975119 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (32537881332450541 / 40000000000000000 : ℝ) = - (32537881332450541 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (32537881332450541 / 20000000000000000 : ℚ)) - (U := (2433363582406801024881 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (32537881332450541 / 20000000000000000 : ℝ) ≤ - (2433363582406801024881 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4063463493354979 / 5000000000000000 : ℝ)) (q := - (32537881332450541 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (32537881332450541 / 40000000000000000 : ℚ)) + (r' := (32537881332450541 / 20000000000000000 : ℚ)) + (U := (-(1032372319093198975119 / 5000000000000000000000 : ℚ))) + (U' := (2433363582406801024881 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (4063463493354979 / 5000000000000000 : ℚ)) + (q := (32537881332450541 / 40000000000000000 : ℚ)) + (U := (-(1032372319093198975119 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_7 : Uω (aρ 7) (bρ 7) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5283,25 +4555,21 @@ lemma U_674_7 : have hlg : Real.log (31607766959490703 / 40000000000000000 : ℝ) ≤ (-(1177382868026010592239 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (31607766959490703 / 40000000000000000 : ℝ) = - (31607766959490703 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (31607766959490703 / 20000000000000000 : ℚ)) - (U := (2288353033473989407761 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (31607766959490703 / 20000000000000000 : ℝ) ≤ - (2288353033473989407761 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7885531180990039 / 10000000000000000 : ℝ)) (q := - (31607766959490703 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (31607766959490703 / 40000000000000000 : ℚ)) + (r' := (31607766959490703 / 20000000000000000 : ℚ)) + (U := (-(1177382868026010592239 / 5000000000000000000000 : ℚ))) + (U' := (2288353033473989407761 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (7885531180990039 / 10000000000000000 : ℚ)) + (q := (31607766959490703 / 40000000000000000 : ℚ)) + (U := (-(1177382868026010592239 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_8 : Uω (aρ 8) (bρ 8) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5309,25 +4577,21 @@ lemma U_674_8 : have hlg : Real.log (30406513722986933 / 40000000000000000 : ℝ) ≤ (-(2742226011902361903109 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (30406513722986933 / 40000000000000000 : ℝ) = - (30406513722986933 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30406513722986933 / 20000000000000000 : ℚ)) - (U := (4189245791097638096891 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30406513722986933 / 20000000000000000 : ℝ) ≤ - (4189245791097638096891 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3784223107039077 / 5000000000000000 : ℝ)) (q := - (30406513722986933 / 40000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30406513722986933 / 40000000000000000 : ℚ)) + (r' := (30406513722986933 / 20000000000000000 : ℚ)) + (U := (-(2742226011902361903109 / 10000000000000000000000 : ℚ))) + (U' := (4189245791097638096891 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (3784223107039077 / 5000000000000000 : ℚ)) + (q := (30406513722986933 / 40000000000000000 : ℚ)) + (U := (-(2742226011902361903109 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_9 : Uω (aρ 9) (bρ 9) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5335,25 +4599,21 @@ lemma U_674_9 : have hlg : Real.log (28924874733777511 / 40000000000000000 : ℝ) ≤ (-(129671004603477111227 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28924874733777511 / 40000000000000000 : ℝ) = - (28924874733777511 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28924874733777511 / 20000000000000000 : ℚ)) - (U := (147587867516522888773 / 400000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28924874733777511 / 20000000000000000 : ℝ) ≤ - (147587867516522888773 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7168592347833443 / 10000000000000000 : ℝ)) (q := - (28924874733777511 / 40000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28924874733777511 / 40000000000000000 : ℚ)) + (r' := (28924874733777511 / 20000000000000000 : ℚ)) + (U := (-(129671004603477111227 / 400000000000000000000 : ℚ))) + (U' := (147587867516522888773 / 400000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (7168592347833443 / 10000000000000000 : ℚ)) + (q := (28924874733777511 / 40000000000000000 : ℚ)) + (U := (-(129671004603477111227 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_10 : Uω (aρ 10) (bρ 10) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5361,26 +4621,21 @@ lemma U_674_10 : have hlg : Real.log (5435644174946641 / 8000000000000000 : ℝ) ≤ (-(483079380526028675361 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5435644174946641 / 8000000000000000 : ℝ) = - (5435644174946641 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5435644174946641 / 4000000000000000 : ℚ)) - (U := (383354594848971324639 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (5435644174946641 / 4000000000000000 : ℝ) ≤ - (383354594848971324639 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (668382445180629 / 1000000000000000 : ℝ)) (q := - (5435644174946641 / 8000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5435644174946641 / 8000000000000000 : ℚ)) + (r' := (5435644174946641 / 4000000000000000 : ℚ)) + (U := (-(483079380526028675361 / 1250000000000000000000 : ℚ))) + (U' := (383354594848971324639 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (668382445180629 / 1000000000000000 : ℚ)) + (q := (5435644174946641 / 8000000000000000 : ℚ)) + (U := (-(483079380526028675361 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_11 : Uω (aρ 11) (bρ 11) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5388,26 +4643,21 @@ lemma U_674_11 : have hlg : Real.log (25211467739382093 / 40000000000000000 : ℝ) ≤ (-(576975617282524960421 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (25211467739382093 / 40000000000000000 : ℝ) = - (25211467739382093 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (25211467739382093 / 20000000000000000 : ℚ)) - (U := (289458358092475039579 / 1250000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (25211467739382093 / 20000000000000000 : ℝ) ≤ - (289458358092475039579 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3059462255167867 / 5000000000000000 : ℝ)) (q := - (25211467739382093 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (25211467739382093 / 40000000000000000 : ℚ)) + (r' := (25211467739382093 / 20000000000000000 : ℚ)) + (U := (-(576975617282524960421 / 1250000000000000000000 : ℚ))) + (U' := (289458358092475039579 / 1250000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (3059462255167867 / 5000000000000000 : ℚ)) + (q := (25211467739382093 / 40000000000000000 : ℚ)) + (U := (-(576975617282524960421 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_12 : Uω (aρ 12) (bρ 12) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5415,26 +4665,21 @@ lemma U_674_12 : have hlg : Real.log (23102315404187439 / 40000000000000000 : ℝ) ≤ (-(2744733037009107092033 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (23102315404187439 / 40000000000000000 : ℝ) = - (23102315404187439 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (23102315404187439 / 20000000000000000 : ℚ)) - (U := (721002864490892907967 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (23102315404187439 / 20000000000000000 : ℝ) ≤ - (721002864490892907967 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5488048439423407 / 10000000000000000 : ℝ)) (q := - (23102315404187439 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (23102315404187439 / 40000000000000000 : ℚ)) + (r' := (23102315404187439 / 20000000000000000 : ℚ)) + (U := (-(2744733037009107092033 / 5000000000000000000000 : ℚ))) + (U' := (721002864490892907967 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (5488048439423407 / 10000000000000000 : ℚ)) + (q := (23102315404187439 / 40000000000000000 : ℚ)) + (U := (-(2744733037009107092033 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_13 : Uω (aρ 13) (bρ 13) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5442,26 +4687,21 @@ lemma U_674_13 : have hlg : Real.log (20964131438699567 / 40000000000000000 : ℝ) ≤ (-(3230332515999585509361 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20964131438699567 / 40000000000000000 : ℝ) = - (20964131438699567 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20964131438699567 / 20000000000000000 : ℚ)) - (U := (235403385500414490639 / 5000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20964131438699567 / 20000000000000000 : ℝ) ≤ - (235403385500414490639 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4818338198274471 / 10000000000000000 : ℝ)) (q := - (20964131438699567 / 40000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20964131438699567 / 40000000000000000 : ℚ)) + (r' := (20964131438699567 / 20000000000000000 : ℚ)) + (U := (-(3230332515999585509361 / 5000000000000000000000 : ℚ))) + (U' := (235403385500414490639 / 5000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (4818338198274471 / 10000000000000000 : ℚ)) + (q := (20964131438699567 / 40000000000000000 : ℚ)) + (U := (-(3230332515999585509361 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_14 : Uω (aρ 14) (bρ 14) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5469,26 +4709,21 @@ lemma U_674_14 : have hlg : Real.log (3790326625954983 / 8000000000000000 : ℝ) ≤ (-(298795737915287152287 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3790326625954983 / 8000000000000000 : ℝ) = - (3790326625954983 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3790326625954983 / 2000000000000000 : ℚ)) - (U := (255722006324712847713 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3790326625954983 / 2000000000000000 : ℝ) ≤ - (255722006324712847713 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (831203265771429 / 2000000000000000 : ℝ)) (q := - (3790326625954983 / 8000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3790326625954983 / 8000000000000000 : ℚ)) + (r' := (3790326625954983 / 2000000000000000 : ℚ)) + (U := (-(298795737915287152287 / 400000000000000000000 : ℚ))) + (U' := (255722006324712847713 / 400000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (831203265771429 / 2000000000000000 : ℚ)) + (q := (3790326625954983 / 8000000000000000 : ℚ)) + (U := (-(298795737915287152287 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_15 : Uω (aρ 15) (bρ 15) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5496,26 +4731,21 @@ lemma U_674_15 : have hlg : Real.log (17272069640599751 / 40000000000000000 : ℝ) ≤ (-(2099471820989259101859 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (17272069640599751 / 40000000000000000 : ℝ) = - (17272069640599751 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17272069640599751 / 10000000000000000 : ℚ)) - (U := (1366264080510740898141 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17272069640599751 / 10000000000000000 : ℝ) ≤ - (1366264080510740898141 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3575807861684563 / 10000000000000000 : ℝ)) (q := - (17272069640599751 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17272069640599751 / 40000000000000000 : ℚ)) + (r' := (17272069640599751 / 10000000000000000 : ℚ)) + (U := (-(2099471820989259101859 / 2500000000000000000000 : ℚ))) + (U' := (1366264080510740898141 / 2500000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (3575807861684563 / 10000000000000000 : ℚ)) + (q := (17272069640599751 / 40000000000000000 : ℚ)) + (U := (-(2099471820989259101859 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674_16 : Uω (aρ 16) (bρ 16) (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5523,26 +4753,21 @@ lemma U_674_16 : have hlg : Real.log (16188477844103073 / 40000000000000000 : ℝ) ≤ (-(9045797086010213353117 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (16188477844103073 / 40000000000000000 : ℝ) = - (16188477844103073 / 10000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16188477844103073 / 10000000000000000 : ℚ)) - (U := (4817146519989786646883 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16188477844103073 / 10000000000000000 : ℝ) ≤ - (4817146519989786646883 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (199148975934139 / 625000000000000 : ℝ)) (q := - (16188477844103073 / 40000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16188477844103073 / 40000000000000000 : ℚ)) + (r' := (16188477844103073 / 10000000000000000 : ℚ)) + (U := (-(9045797086010213353117 / 10000000000000000000000 : ℚ))) + (U' := (4817146519989786646883 / 10000000000000000000000 : ℚ)) + 2 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (27652481574401 / 32000000000000 : ℚ)) + (s := (199148975934139 / 625000000000000 : ℚ)) + (q := (16188477844103073 / 40000000000000000 : ℚ)) + (U := (-(9045797086010213353117 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_674 : Uρ (27652481574401 / 32000000000000 : ℝ) ≤ @@ -5633,25 +4858,21 @@ lemma U_675_1 : have hlg : Real.log (70181782143953017 / 80000000000000000 : ℝ) ≤ (-(1309378706805599354279 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (70181782143953017 / 80000000000000000 : ℝ) = - (70181782143953017 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (70181782143953017 / 40000000000000000 : ℚ)) - (U := (5622093096194400645721 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (70181782143953017 / 40000000000000000 : ℝ) ≤ - (5622093096194400645721 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8772704339521223 / 10000000000000000 : ℝ)) (q := - (70181782143953017 / 80000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (70181782143953017 / 80000000000000000 : ℚ)) + (r' := (70181782143953017 / 40000000000000000 : ℚ)) + (U := (-(1309378706805599354279 / 10000000000000000000000 : ℚ))) + (U' := (5622093096194400645721 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (8772704339521223 / 10000000000000000 : ℚ)) + (q := (70181782143953017 / 80000000000000000 : ℚ)) + (U := (-(1309378706805599354279 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_2 : Uω (aρ 2) (bρ 2) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5659,25 +4880,21 @@ lemma U_675_2 : have hlg : Real.log (69990807353880377 / 80000000000000000 : ℝ) ≤ (-(1336627245042598542631 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (69990807353880377 / 80000000000000000 : ℝ) = - (69990807353880377 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69990807353880377 / 40000000000000000 : ℚ)) - (U := (5594844557957401457369 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69990807353880377 / 40000000000000000 : ℝ) ≤ - (5594844557957401457369 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8748729654513063 / 10000000000000000 : ℝ)) (q := - (69990807353880377 / 80000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69990807353880377 / 80000000000000000 : ℚ)) + (r' := (69990807353880377 / 40000000000000000 : ℚ)) + (U := (-(1336627245042598542631 / 10000000000000000000000 : ℚ))) + (U' := (5594844557957401457369 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (8748729654513063 / 10000000000000000 : ℚ)) + (q := (69990807353880377 / 80000000000000000 : ℚ)) + (U := (-(1336627245042598542631 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_3 : Uω (aρ 3) (bρ 3) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5685,25 +4902,21 @@ lemma U_675_3 : have hlg : Real.log (69609207654522701 / 80000000000000000 : ℝ) ≤ (-(1391297819368064538101 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (69609207654522701 / 80000000000000000 : ℝ) = - (69609207654522701 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (69609207654522701 / 40000000000000000 : ℚ)) - (U := (5540173983631935461899 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (69609207654522701 / 40000000000000000 : ℝ) ≤ - (5540173983631935461899 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2175181459005911 / 2500000000000000 : ℝ)) (q := - (69609207654522701 / 80000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (69609207654522701 / 80000000000000000 : ℚ)) + (r' := (69609207654522701 / 40000000000000000 : ℚ)) + (U := (-(1391297819368064538101 / 10000000000000000000000 : ℚ))) + (U' := (5540173983631935461899 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (2175181459005911 / 2500000000000000 : ℚ)) + (q := (69609207654522701 / 80000000000000000 : ℚ)) + (U := (-(1391297819368064538101 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_4 : Uω (aρ 4) (bρ 4) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5711,25 +4924,21 @@ lemma U_675_4 : have hlg : Real.log (68976493674625433 / 80000000000000000 : ℝ) ≤ (-(741304296202974127503 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (68976493674625433 / 80000000000000000 : ℝ) = - (68976493674625433 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (68976493674625433 / 40000000000000000 : ℚ)) - (U := (2724431605297025872497 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (68976493674625433 / 40000000000000000 : ℝ) ≤ - (2724431605297025872497 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8620841522114327 / 10000000000000000 : ℝ)) (q := - (68976493674625433 / 80000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (68976493674625433 / 80000000000000000 : ℚ)) + (r' := (68976493674625433 / 40000000000000000 : ℚ)) + (U := (-(741304296202974127503 / 5000000000000000000000 : ℚ))) + (U' := (2724431605297025872497 / 5000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (8620841522114327 / 10000000000000000 : ℚ)) + (q := (68976493674625433 / 80000000000000000 : ℚ)) + (U := (-(741304296202974127503 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_5 : Uω (aρ 5) (bρ 5) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5737,25 +4946,21 @@ lemma U_675_5 : have hlg : Real.log (13603135906815797 / 16000000000000000 : ℝ) ≤ (-(1622883744341165361017 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13603135906815797 / 16000000000000000 : ℝ) = - (13603135906815797 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13603135906815797 / 8000000000000000 : ℚ)) - (U := (5308588058658834638983 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (13603135906815797 / 8000000000000000 : ℝ) ≤ - (5308588058658834638983 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1699765581262543 / 2000000000000000 : ℝ)) (q := - (13603135906815797 / 16000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13603135906815797 / 16000000000000000 : ℚ)) + (r' := (13603135906815797 / 8000000000000000 : ℚ)) + (U := (-(1622883744341165361017 / 10000000000000000000000 : ℚ))) + (U' := (5308588058658834638983 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1699765581262543 / 2000000000000000 : ℚ)) + (q := (13603135906815797 / 16000000000000000 : ℚ)) + (U := (-(1622883744341165361017 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_6 : Uω (aρ 6) (bρ 6) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5763,25 +4968,21 @@ lemma U_675_6 : have hlg : Real.log (66643885998227629 / 80000000000000000 : ℝ) ≤ (-(913316624783847168869 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (66643885998227629 / 80000000000000000 : ℝ) = - (66643885998227629 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (66643885998227629 / 40000000000000000 : ℚ)) - (U := (2552419276716152831131 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (66643885998227629 / 40000000000000000 : ℝ) ≤ - (2552419276716152831131 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2080779974372469 / 2500000000000000 : ℝ)) (q := - (66643885998227629 / 80000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (66643885998227629 / 80000000000000000 : ℚ)) + (r' := (66643885998227629 / 40000000000000000 : ℚ)) + (U := (-(913316624783847168869 / 5000000000000000000000 : ℚ))) + (U' := (2552419276716152831131 / 5000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (2080779974372469 / 2500000000000000 : ℚ)) + (q := (66643885998227629 / 80000000000000000 : ℚ)) + (U := (-(913316624783847168869 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_7 : Uω (aρ 7) (bρ 7) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5789,25 +4990,21 @@ lemma U_675_7 : have hlg : Real.log (64785418593637181 / 80000000000000000 : ℝ) ≤ (-(527365195200048172033 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (64785418593637181 / 80000000000000000 : ℝ) = - (64785418593637181 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (64785418593637181 / 40000000000000000 : ℚ)) - (U := (1205502755549951827967 / 2500000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (64785418593637181 / 40000000000000000 : ℝ) ≤ - (1205502755549951827967 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1010270553387783 / 1250000000000000 : ℝ)) (q := - (64785418593637181 / 80000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (64785418593637181 / 80000000000000000 : ℚ)) + (r' := (64785418593637181 / 40000000000000000 : ℚ)) + (U := (-(527365195200048172033 / 2500000000000000000000 : ℚ))) + (U' := (1205502755549951827967 / 2500000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1010270553387783 / 1250000000000000 : ℚ)) + (q := (64785418593637181 / 80000000000000000 : ℚ)) + (U := (-(527365195200048172033 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_8 : Uω (aρ 8) (bρ 8) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5815,25 +5012,21 @@ lemma U_675_8 : have hlg : Real.log (62386425724127397 / 80000000000000000 : ℝ) ≤ (-(1243394595876810300753 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (62386425724127397 / 80000000000000000 : ℝ) = - (62386425724127397 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (62386425724127397 / 40000000000000000 : ℚ)) - (U := (2222341305623189699247 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (62386425724127397 / 40000000000000000 : ℝ) ≤ - (2222341305623189699247 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3882978930532409 / 5000000000000000 : ℝ)) (q := - (62386425724127397 / 80000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (62386425724127397 / 80000000000000000 : ℚ)) + (r' := (62386425724127397 / 40000000000000000 : ℚ)) + (U := (-(1243394595876810300753 / 5000000000000000000000 : ℚ))) + (U' := (2222341305623189699247 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (3882978930532409 / 5000000000000000 : ℚ)) + (q := (62386425724127397 / 80000000000000000 : ℚ)) + (U := (-(1243394595876810300753 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_9 : Uω (aρ 9) (bρ 9) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5841,25 +5034,21 @@ lemma U_675_9 : have hlg : Real.log (59429772916198877 / 80000000000000000 : ℝ) ≤ (-(2972313060724690363641 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (59429772916198877 / 80000000000000000 : ℝ) = - (59429772916198877 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (59429772916198877 / 40000000000000000 : ℚ)) - (U := (3959158742275309636359 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (59429772916198877 / 40000000000000000 : ℝ) ≤ - (3959158742275309636359 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (28780313622823 / 39062500000000 : ℝ)) (q := - (59429772916198877 / 80000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (59429772916198877 / 80000000000000000 : ℚ)) + (r' := (59429772916198877 / 40000000000000000 : ℚ)) + (U := (-(2972313060724690363641 / 10000000000000000000000 : ℚ))) + (U' := (3959158742275309636359 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (28780313622823 / 39062500000000 : ℚ)) + (q := (59429772916198877 / 80000000000000000 : ℚ)) + (U := (-(2972313060724690363641 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_10 : Uω (aρ 10) (bρ 10) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5867,26 +5056,21 @@ lemma U_675_10 : have hlg : Real.log (55948350270039657 / 80000000000000000 : ℝ) ≤ (-(893994214702231111179 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (55948350270039657 / 80000000000000000 : ℝ) = - (55948350270039657 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (55948350270039657 / 40000000000000000 : ℚ)) - (U := (838873736047768888821 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (55948350270039657 / 40000000000000000 : ℝ) ≤ - (838873736047768888821 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6885963659397883 / 10000000000000000 : ℝ)) (q := - (55948350270039657 / 80000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (55948350270039657 / 80000000000000000 : ℚ)) + (r' := (55948350270039657 / 40000000000000000 : ℚ)) + (U := (-(893994214702231111179 / 2500000000000000000000 : ℚ))) + (U' := (838873736047768888821 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (6885963659397883 / 10000000000000000 : ℚ)) + (q := (55948350270039657 / 80000000000000000 : ℚ)) + (U := (-(893994214702231111179 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_11 : Uω (aρ 11) (bρ 11) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5894,26 +5078,21 @@ lemma U_675_11 : have hlg : Real.log (10407046827545529 / 16000000000000000 : ℝ) ≤ (-(215052782857109338981 / 500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (10407046827545529 / 16000000000000000 : ℝ) = - (10407046827545529 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (10407046827545529 / 8000000000000000 : ℚ)) - (U := (131520807292890661019 / 500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (10407046827545529 / 8000000000000000 : ℝ) ≤ - (131520807292890661019 / 500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (79077015656561 / 125000000000000 : ℝ)) (q := - (10407046827545529 / 16000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (10407046827545529 / 16000000000000000 : ℚ)) + (r' := (10407046827545529 / 8000000000000000 : ℚ)) + (U := (-(215052782857109338981 / 500000000000000000000 : ℚ))) + (U' := (131520807292890661019 / 500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (79077015656561 / 125000000000000 : ℚ)) + (q := (10407046827545529 / 16000000000000000 : ℚ)) + (U := (-(215052782857109338981 / 500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_12 : Uω (aρ 12) (bρ 12) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5921,26 +5100,21 @@ lemma U_675_12 : have hlg : Real.log (9570090251541869 / 16000000000000000 : ℝ) ≤ (-(1027892171772619989907 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9570090251541869 / 16000000000000000 : ℝ) = - (9570090251541869 / 8000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9570090251541869 / 8000000000000000 : ℚ)) - (U := (358402188827380010093 / 2000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (9570090251541869 / 8000000000000000 : ℝ) ≤ - (358402188827380010093 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1140733125841061 / 2000000000000000 : ℝ)) (q := - (9570090251541869 / 16000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9570090251541869 / 16000000000000000 : ℚ)) + (r' := (9570090251541869 / 8000000000000000 : ℚ)) + (U := (-(1027892171772619989907 / 2000000000000000000000 : ℚ))) + (U' := (358402188827380010093 / 2000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1140733125841061 / 2000000000000000 : ℚ)) + (q := (9570090251541869 / 16000000000000000 : ℚ)) + (U := (-(1027892171772619989907 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_13 : Uω (aρ 13) (bρ 13) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5948,26 +5122,21 @@ lemma U_675_13 : have hlg : Real.log (43626607223548973 / 80000000000000000 : ℝ) ≤ (-(1212718825538876018277 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (43626607223548973 / 80000000000000000 : ℝ) = - (43626607223548973 / 40000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (43626607223548973 / 40000000000000000 : ℚ)) - (U := (173575535061123981723 / 2000000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (43626607223548973 / 40000000000000000 : ℝ) ≤ - (173575535061123981723 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1261771590565053 / 2500000000000000 : ℝ)) (q := - (43626607223548973 / 80000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (43626607223548973 / 80000000000000000 : ℚ)) + (r' := (43626607223548973 / 40000000000000000 : ℚ)) + (U := (-(1212718825538876018277 / 2000000000000000000000 : ℚ))) + (U' := (173575535061123981723 / 2000000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1261771590565053 / 2500000000000000 : ℚ)) + (q := (43626607223548973 / 80000000000000000 : ℚ)) + (U := (-(1212718825538876018277 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_14 : Uω (aρ 14) (bρ 14) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -5975,26 +5144,21 @@ lemma U_675_14 : have hlg : Real.log (7935641994942533 / 16000000000000000 : ℝ) ≤ (-(280489785711701105503 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (7935641994942533 / 16000000000000000 : ℝ) = - (7935641994942533 / 4000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7935641994942533 / 4000000000000000 : ℚ)) - (U := (274027958528298894497 / 400000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (7935641994942533 / 4000000000000000 : ℝ) ≤ - (274027958528298894497 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (880782867019227 / 2000000000000000 : ℝ)) (q := - (7935641994942533 / 16000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7935641994942533 / 16000000000000000 : ℚ)) + (r' := (7935641994942533 / 4000000000000000 : ℚ)) + (U := (-(280489785711701105503 / 400000000000000000000 : ℚ))) + (U' := (274027958528298894497 / 400000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (880782867019227 / 2000000000000000 : ℚ)) + (q := (7935641994942533 / 16000000000000000 : ℚ)) + (U := (-(280489785711701105503 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_15 : Uω (aρ 15) (bρ 15) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -6002,26 +5166,21 @@ lemma U_675_15 : have hlg : Real.log (36416061511973109 / 80000000000000000 : ℝ) ≤ (-(7870167065046628959241 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (36416061511973109 / 80000000000000000 : ℝ) = - (36416061511973109 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36416061511973109 / 20000000000000000 : ℚ)) - (U := (5992776540953371040759 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36416061511973109 / 20000000000000000 : ℝ) ≤ - (5992776540953371040759 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1923975248413123 / 5000000000000000 : ℝ)) (q := - (36416061511973109 / 80000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36416061511973109 / 80000000000000000 : ℚ)) + (r' := (36416061511973109 / 20000000000000000 : ℚ)) + (U := (-(7870167065046628959241 / 10000000000000000000000 : ℚ))) + (U' := (5992776540953371040759 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1923975248413123 / 5000000000000000 : ℚ)) + (q := (36416061511973109 / 80000000000000000 : ℚ)) + (U := (-(7870167065046628959241 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675_16 : Uω (aρ 16) (bρ 16) (56558325853133 / 64000000000000 : ℝ) ≤ @@ -6029,26 +5188,21 @@ lemma U_675_16 : have hlg : Real.log (34336658657888021 / 80000000000000000 : ℝ) ≤ (-(4229065425846391883387 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (34336658657888021 / 80000000000000000 : ℝ) = - (34336658657888021 / 20000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34336658657888021 / 20000000000000000 : ℚ)) - (U := (2702406377153608116613 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34336658657888021 / 20000000000000000 : ℝ) ≤ - (2702406377153608116613 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1740235717407487 / 5000000000000000 : ℝ)) (q := - (34336658657888021 / 80000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34336658657888021 / 80000000000000000 : ℚ)) + (r' := (34336658657888021 / 20000000000000000 : ℚ)) + (U := (-(4229065425846391883387 / 5000000000000000000000 : ℚ))) + (U' := (2702406377153608116613 / 5000000000000000000000 : ℚ)) + 2 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (56558325853133 / 64000000000000 : ℚ)) + (s := (1740235717407487 / 5000000000000000 : ℚ)) + (q := (34336658657888021 / 80000000000000000 : ℚ)) + (U := (-(4229065425846391883387 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_675 : Uρ (56558325853133 / 64000000000000 : ℝ) ≤ diff --git a/LeanPool/Zeta5Irrational/Table/U56.lean b/LeanPool/Zeta5Irrational/Table/U56.lean index 41e1aa1415..04c44b1dce 100644 --- a/LeanPool/Zeta5Irrational/Table/U56.lean +++ b/LeanPool/Zeta5Irrational/Table/U56.lean @@ -24,25 +24,21 @@ lemma U_676_1 : have hlg : Real.log (358742443718067 / 400000000000000 : ℝ) ≤ (-(108859842802811722997 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (358742443718067 / 400000000000000 : ℝ) = - (358742443718067 / 200000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (358742443718067 / 200000000000000 : ℚ)) - (U := (584287337497188277003 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (358742443718067 / 200000000000000 : ℝ) ≤ - (584287337497188277003 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (44842715334423 / 50000000000000 : ℝ)) (q := - (358742443718067 / 400000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (358742443718067 / 400000000000000 : ℚ)) + (r' := (358742443718067 / 200000000000000 : ℚ)) + (U := (-(108859842802811722997 / 1000000000000000000000 : ℚ))) + (U' := (584287337497188277003 / 1000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (44842715334423 / 50000000000000 : ℚ)) + (q := (358742443718067 / 400000000000000 : ℚ)) + (U := (-(108859842802811722997 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_2 : Uω (aρ 2) (bρ 2) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -50,25 +46,21 @@ lemma U_676_2 : have hlg : Real.log (17889382993662361 / 20000000000000000 : ℝ) ≤ (-(223049730527027750149 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17889382993662361 / 20000000000000000 : ℝ) = - (17889382993662361 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17889382993662361 / 10000000000000000 : ℚ)) - (U := (1163244630072972249851 / 2000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (17889382993662361 / 10000000000000000 : ℝ) ≤ - (1163244630072972249851 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8944572887153611 / 10000000000000000 : ℝ)) (q := - (17889382993662361 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17889382993662361 / 20000000000000000 : ℚ)) + (r' := (17889382993662361 / 10000000000000000 : ℚ)) + (U := (-(223049730527027750149 / 2000000000000000000000 : ℚ))) + (U' := (1163244630072972249851 / 2000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (8944572887153611 / 10000000000000000 : ℚ)) + (q := (17889382993662361 / 20000000000000000 : ℚ)) + (U := (-(223049730527027750149 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_3 : Uω (aρ 3) (bρ 3) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -76,25 +68,21 @@ lemma U_676_3 : have hlg : Real.log (3558799294975663 / 4000000000000000 : ℝ) ≤ (-(1168711495788115444963 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3558799294975663 / 4000000000000000 : ℝ) = - (3558799294975663 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3558799294975663 / 2000000000000000 : ℚ)) - (U := (5762760307211884555037 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3558799294975663 / 2000000000000000 : ℝ) ≤ - (5762760307211884555037 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1779316494943913 / 2000000000000000 : ℝ)) (q := - (3558799294975663 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3558799294975663 / 4000000000000000 : ℚ)) + (r' := (3558799294975663 / 2000000000000000 : ℚ)) + (U := (-(1168711495788115444963 / 10000000000000000000000 : ℚ))) + (U' := (5762760307211884555037 / 10000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (1779316494943913 / 2000000000000000 : ℚ)) + (q := (3558799294975663 / 4000000000000000 : ℚ)) + (U := (-(1168711495788115444963 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_4 : Uω (aρ 4) (bρ 4) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -102,25 +90,21 @@ lemma U_676_4 : have hlg : Real.log (8817926734849447 / 10000000000000000 : ℝ) ≤ (-(628991572116585160863 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8817926734849447 / 10000000000000000 : ℝ) = - (8817926734849447 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8817926734849447 / 5000000000000000 : ℚ)) - (U := (2836744329383414839137 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8817926734849447 / 5000000000000000 : ℝ) ≤ - (2836744329383414839137 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1102091706325643 / 1250000000000000 : ℝ)) (q := - (8817926734849447 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8817926734849447 / 10000000000000000 : ℚ)) + (r' := (8817926734849447 / 5000000000000000 : ℚ)) + (U := (-(628991572116585160863 / 5000000000000000000000 : ℚ))) + (U' := (2836744329383414839137 / 5000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (1102091706325643 / 1250000000000000 : ℚ)) + (q := (8817926734849447 / 10000000000000000 : ℚ)) + (U := (-(628991572116585160863 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_5 : Uω (aρ 5) (bρ 5) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -128,25 +112,21 @@ lemma U_676_5 : have hlg : Real.log (1087233551180307 / 1250000000000000 : ℝ) ≤ (-(55802843000971698371 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1087233551180307 / 1250000000000000 : ℝ) = - (1087233551180307 / 625000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1087233551180307 / 625000000000000 : ℚ)) - (U := (221456029119028301629 / 400000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1087233551180307 / 625000000000000 : ℝ) ≤ - (221456029119028301629 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4347403459563081 / 5000000000000000 : ℝ)) (q := - (1087233551180307 / 1250000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1087233551180307 / 1250000000000000 : ℚ)) + (r' := (1087233551180307 / 625000000000000 : ℚ)) + (U := (-(55802843000971698371 / 400000000000000000000 : ℚ))) + (U' := (221456029119028301629 / 400000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (4347403459563081 / 5000000000000000 : ℚ)) + (q := (1087233551180307 / 1250000000000000 : ℚ)) + (U := (-(55802843000971698371 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_6 : Uω (aρ 6) (bρ 6) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -154,25 +134,21 @@ lemma U_676_6 : have hlg : Real.log (1705298599747893 / 2000000000000000 : ℝ) ≤ (-(398517382703400588829 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1705298599747893 / 2000000000000000 : ℝ) = - (1705298599747893 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1705298599747893 / 1000000000000000 : ℚ)) - (U := (1334350568046599411171 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (1705298599747893 / 1000000000000000 : ℝ) ≤ - (1334350568046599411171 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (425964823643009 / 500000000000000 : ℝ)) (q := - (1705298599747893 / 2000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1705298599747893 / 2000000000000000 : ℚ)) + (r' := (1705298599747893 / 1000000000000000 : ℚ)) + (U := (-(398517382703400588829 / 2500000000000000000000 : ℚ))) + (U' := (1334350568046599411171 / 2500000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (425964823643009 / 500000000000000 : ℚ)) + (q := (1705298599747893 / 2000000000000000 : ℚ)) + (U := (-(398517382703400588829 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_7 : Uω (aρ 7) (bρ 7) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -180,25 +156,21 @@ lemma U_676_7 : have hlg : Real.log (16588788113255563 / 20000000000000000 : ℝ) ≤ (-(1870052209910470026807 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16588788113255563 / 20000000000000000 : ℝ) = - (16588788113255563 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16588788113255563 / 10000000000000000 : ℚ)) - (U := (5061419593089529973193 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16588788113255563 / 10000000000000000 : ℝ) ≤ - (5061419593089529973193 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8278759969396813 / 10000000000000000 : ℝ)) (q := - (16588788113255563 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16588788113255563 / 20000000000000000 : ℚ)) + (r' := (16588788113255563 / 10000000000000000 : ℚ)) + (U := (-(1870052209910470026807 / 10000000000000000000000 : ℚ))) + (U' := (5061419593089529973193 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (8278759969396813 / 10000000000000000 : ℚ)) + (q := (16588788113255563 / 20000000000000000 : ℚ)) + (U := (-(1870052209910470026807 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_8 : Uω (aρ 8) (bρ 8) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -206,25 +178,21 @@ lemma U_676_8 : have hlg : Real.log (3997468331946279 / 5000000000000000 : ℝ) ≤ (-(1118883342221099544697 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3997468331946279 / 5000000000000000 : ℝ) = - (3997468331946279 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3997468331946279 / 2500000000000000 : ℚ)) - (U := (2346852559278900455303 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3997468331946279 / 2500000000000000 : ℝ) ≤ - (2346852559278900455303 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3981693417633183 / 5000000000000000 : ℝ)) (q := - (3997468331946279 / 5000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3997468331946279 / 5000000000000000 : ℚ)) + (r' := (3997468331946279 / 2500000000000000 : ℚ)) + (U := (-(1118883342221099544697 / 5000000000000000000000 : ℚ))) + (U' := (2346852559278900455303 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (3981693417633183 / 5000000000000000 : ℚ)) + (q := (3997468331946279 / 5000000000000000 : ℚ)) + (U := (-(1118883342221099544697 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_9 : Uω (aρ 9) (bρ 9) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -232,25 +200,21 @@ lemma U_676_9 : have hlg : Real.log (1906534407118849 / 2500000000000000 : ℝ) ≤ (-(2710035841923158558309 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1906534407118849 / 2500000000000000 : ℝ) = - (1906534407118849 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1906534407118849 / 1250000000000000 : ℚ)) - (U := (4221435961076841441691 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (1906534407118849 / 1250000000000000 : ℝ) ≤ - (4221435961076841441691 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3783377196396021 / 5000000000000000 : ℝ)) (q := - (1906534407118849 / 2500000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1906534407118849 / 2500000000000000 : ℚ)) + (r' := (1906534407118849 / 1250000000000000 : ℚ)) + (U := (-(2710035841923158558309 / 10000000000000000000000 : ℚ))) + (U' := (4221435961076841441691 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (3783377196396021 / 5000000000000000 : ℚ)) + (q := (1906534407118849 / 2500000000000000 : ℚ)) + (U := (-(2710035841923158558309 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_10 : Uω (aρ 10) (bρ 10) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -258,26 +222,21 @@ lemma U_676_10 : have hlg : Real.log (7192355444655383 / 10000000000000000 : ℝ) ≤ (-(3295663745591862291993 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7192355444655383 / 10000000000000000 : ℝ) = - (7192355444655383 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7192355444655383 / 5000000000000000 : ℚ)) - (U := (3635808057408137708007 / 10000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (7192355444655383 / 5000000000000000 : ℝ) ≤ - (3635808057408137708007 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (885968632330877 / 1250000000000000 : ℝ)) (q := - (7192355444655383 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7192355444655383 / 10000000000000000 : ℚ)) + (r' := (7192355444655383 / 5000000000000000 : ℚ)) + (U := (-(3295663745591862291993 / 10000000000000000000000 : ℚ))) + (U' := (3635808057408137708007 / 10000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (885968632330877 / 1250000000000000 : ℚ)) + (q := (7192355444655383 / 10000000000000000 : ℚ)) + (U := (-(3295663745591862291993 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_11 : Uω (aρ 11) (bρ 11) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -285,26 +244,21 @@ lemma U_676_11 : have hlg : Real.log (6705589958471729 / 10000000000000000 : ℝ) ≤ (-(999108980076215164303 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6705589958471729 / 10000000000000000 : ℝ) = - (6705589958471729 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6705589958471729 / 5000000000000000 : ℚ)) - (U := (733758970673784835697 / 2500000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (6705589958471729 / 5000000000000000 : ℝ) ≤ - (733758970673784835697 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1633173678121177 / 2500000000000000 : ℝ)) (q := - (6705589958471729 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6705589958471729 / 10000000000000000 : ℚ)) + (r' := (6705589958471729 / 5000000000000000 : ℚ)) + (U := (-(999108980076215164303 / 2500000000000000000000 : ℚ))) + (U' := (733758970673784835697 / 2500000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (1633173678121177 / 2500000000000000 : ℚ)) + (q := (6705589958471729 / 10000000000000000 : ℚ)) + (U := (-(999108980076215164303 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_12 : Uω (aρ 12) (bρ 12) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -312,25 +266,21 @@ lemma U_676_12 : have hlg : Real.log (618634644546397 / 1000000000000000 : ℝ) ≤ (-(4802404152764222826933 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (618634644546397 / 1000000000000000 : ℝ) = - (618634644546397 / 500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (618634644546397 / 500000000000000 : ℚ)) - (U := (2129067650235777173067 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (618634644546397 / 500000000000000 : ℝ) ≤ - (2129067650235777173067 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (591790778315419 / 1000000000000000 : ℝ)) (q := - (618634644546397 / 1000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) (by norm_num [bρ_12]) - (by norm_num) (by norm_num [aρ_12, bρ_12]) (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (618634644546397 / 1000000000000000 : ℚ)) + (r' := (618634644546397 / 500000000000000 : ℚ)) + (U := (-(4802404152764222826933 / 10000000000000000000000 : ℚ))) + (U' := (2129067650235777173067 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (591790778315419 / 1000000000000000 : ℚ)) + (q := (618634644546397 / 1000000000000000 : ℚ)) + (U := (-(4802404152764222826933 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_13 : Uω (aρ 13) (bρ 13) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -338,26 +288,21 @@ lemma U_676_13 : have hlg : Real.log (11328588692629349 / 20000000000000000 : ℝ) ≤ (-(2842013848850894396079 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (11328588692629349 / 20000000000000000 : ℝ) = - (11328588692629349 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (11328588692629349 / 10000000000000000 : ℚ)) - (U := (623722052649105603921 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (11328588692629349 / 10000000000000000 : ℝ) ≤ - (623722052649105603921 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5273185326450599 / 10000000000000000 : ℝ)) (q := - (11328588692629349 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (11328588692629349 / 20000000000000000 : ℚ)) + (r' := (11328588692629349 / 10000000000000000 : ℚ)) + (U := (-(2842013848850894396079 / 5000000000000000000000 : ℚ))) + (U' := (623722052649105603921 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (5273185326450599 / 10000000000000000 : ℚ)) + (q := (11328588692629349 / 20000000000000000 : ℚ)) + (U := (-(2842013848850894396079 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_14 : Uω (aρ 14) (bρ 14) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -365,26 +310,21 @@ lemma U_676_14 : have hlg : Real.log (1294789970322837 / 2500000000000000 : ℝ) ≤ (-(6579422346950211503277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1294789970322837 / 2500000000000000 : ℝ) = - (1294789970322837 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1294789970322837 / 1250000000000000 : ℚ)) - (U := (352049456049788496723 / 10000000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (1294789970322837 / 1250000000000000 : ℝ) ≤ - (352049456049788496723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2323421840724473 / 5000000000000000 : ℝ)) (q := - (1294789970322837 / 2500000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1294789970322837 / 2500000000000000 : ℚ)) + (r' := (1294789970322837 / 1250000000000000 : ℚ)) + (U := (-(6579422346950211503277 / 10000000000000000000000 : ℚ))) + (U' := (352049456049788496723 / 10000000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (2323421840724473 / 5000000000000000 : ℚ)) + (q := (1294789970322837 / 2500000000000000 : ℚ)) + (U := (-(6579422346950211503277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_15 : Uω (aρ 15) (bρ 15) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -392,26 +332,21 @@ lemma U_676_15 : have hlg : Real.log (4781659866852911 / 10000000000000000 : ℝ) ≤ (-(7377973537692901902479 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4781659866852911 / 10000000000000000 : ℝ) = - (4781659866852911 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4781659866852911 / 2500000000000000 : ℚ)) - (U := (6484970068307098097521 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4781659866852911 / 2500000000000000 : ℝ) ≤ - (6484970068307098097521 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8030111191381 / 19531250000000 : ℝ)) (q := - (4781659866852911 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4781659866852911 / 10000000000000000 : ℚ)) + (r' := (4781659866852911 / 2500000000000000 : ℚ)) + (U := (-(7377973537692901902479 / 10000000000000000000000 : ℚ))) + (U' := (6484970068307098097521 / 10000000000000000000000 : ℚ)) + 2 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (8030111191381 / 19531250000000 : ℚ)) + (q := (4781659866852911 / 10000000000000000 : ℚ)) + (U := (-(7377973537692901902479 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676_16 : Uω (aρ 16) (bρ 16) (7226461069683 / 8000000000000 : ℝ) ≤ @@ -419,26 +354,21 @@ lemma U_676_16 : have hlg : Real.log (4530658134130151 / 10000000000000000 : ℝ) ≤ (-(7917178800593945107141 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (4530658134130151 / 10000000000000000 : ℝ) = - (4530658134130151 / 2500000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4530658134130151 / 2500000000000000 : ℚ)) - (U := (5945764805406054892859 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (4530658134130151 / 2500000000000000 : ℝ) ≤ - (5945764805406054892859 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (117555784876611 / 312500000000000 : ℝ)) (q := - (4530658134130151 / 10000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4530658134130151 / 10000000000000000 : ℚ)) + (r' := (4530658134130151 / 2500000000000000 : ℚ)) + (U := (-(7917178800593945107141 / 10000000000000000000000 : ℚ))) + (U' := (5945764805406054892859 / 10000000000000000000000 : ℚ)) + 2 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (7226461069683 / 8000000000000 : ℚ)) + (s := (117555784876611 / 312500000000000 : ℚ)) + (q := (4530658134130151 / 10000000000000000 : ℚ)) + (U := (-(7917178800593945107141 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_676 : Uρ (7226461069683 / 8000000000000 : ℝ) ≤ @@ -531,25 +461,21 @@ lemma U_677_1 : have hlg : Real.log (37440950769403939 / 40000000000000000 : ℝ) ≤ (-(82643010106364090371 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (37440950769403939 / 40000000000000000 : ℝ) = - (37440950769403939 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37440950769403939 / 20000000000000000 : ℚ)) - (U := (783790965268635909629 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37440950769403939 / 20000000000000000 : ℝ) ≤ - (783790965268635909629 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4680110210289891 / 5000000000000000 : ℝ)) (q := - (37440950769403939 / 40000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37440950769403939 / 40000000000000000 : ℚ)) + (r' := (37440950769403939 / 20000000000000000 : ℚ)) + (U := (-(82643010106364090371 / 1250000000000000000000 : ℚ))) + (U' := (783790965268635909629 / 1250000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (4680110210289891 / 5000000000000000 : ℚ)) + (q := (37440950769403939 / 40000000000000000 : ℚ)) + (U := (-(82643010106364090371 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_2 : Uω (aρ 2) (bρ 2) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -557,25 +483,21 @@ lemma U_677_2 : have hlg : Real.log (37345489271458807 / 40000000000000000 : ℝ) ≤ (-(85834148424330625231 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (37345489271458807 / 40000000000000000 : ℝ) = - (37345489271458807 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (37345489271458807 / 20000000000000000 : ℚ)) - (U := (780599826950669374769 / 1250000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (37345489271458807 / 20000000000000000 : ℝ) ≤ - (780599826950669374769 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (291758083878663 / 312500000000000 : ℝ)) (q := - (37345489271458807 / 40000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (37345489271458807 / 40000000000000000 : ℚ)) + (r' := (37345489271458807 / 20000000000000000 : ℚ)) + (U := (-(85834148424330625231 / 1250000000000000000000 : ℚ))) + (U' := (780599826950669374769 / 1250000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (291758083878663 / 312500000000000 : ℚ)) + (q := (37345489271458807 / 40000000000000000 : ℚ)) + (U := (-(85834148424330625231 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_3 : Uω (aρ 3) (bρ 3) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -583,25 +505,21 @@ lemma U_677_3 : have hlg : Real.log (7430953291820317 / 8000000000000000 : ℝ) ≤ (-(368936939244914093781 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7430953291820317 / 8000000000000000 : ℝ) = - (7430953291820317 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7430953291820317 / 4000000000000000 : ℚ)) - (U := (3096798962255085906219 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (7430953291820317 / 4000000000000000 : ℝ) ≤ - (3096798962255085906219 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1857658676857721 / 2000000000000000 : ℝ)) (q := - (7430953291820317 / 8000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7430953291820317 / 8000000000000000 : ℚ)) + (r' := (7430953291820317 / 4000000000000000 : ℚ)) + (U := (-(368936939244914093781 / 5000000000000000000000 : ℚ))) + (U' := (3096798962255085906219 / 5000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (1857658676857721 / 2000000000000000 : ℚ)) + (q := (7430953291820317 / 8000000000000000 : ℚ)) + (U := (-(368936939244914093781 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_4 : Uω (aρ 4) (bρ 4) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -609,25 +527,21 @@ lemma U_677_4 : have hlg : Real.log (36838613308049463 / 40000000000000000 : ℝ) ≤ (-(82332884107747569223 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (36838613308049463 / 40000000000000000 : ℝ) = - (36838613308049463 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36838613308049463 / 20000000000000000 : ℚ)) - (U := (610814296192252430777 / 1000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36838613308049463 / 20000000000000000 : ℝ) ≤ - (610814296192252430777 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1151063873728443 / 1250000000000000 : ℝ)) (q := - (36838613308049463 / 40000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36838613308049463 / 40000000000000000 : ℚ)) + (r' := (36838613308049463 / 20000000000000000 : ℚ)) + (U := (-(82332884107747569223 / 1000000000000000000000 : ℚ))) + (U' := (610814296192252430777 / 1000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (1151063873728443 / 1250000000000000 : ℚ)) + (q := (36838613308049463 / 40000000000000000 : ℚ)) + (U := (-(82332884107747569223 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_5 : Uω (aρ 5) (bρ 5) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -635,25 +549,21 @@ lemma U_677_5 : have hlg : Real.log (36358704876728341 / 40000000000000000 : ℝ) ≤ (-(477229023155082316277 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (36358704876728341 / 40000000000000000 : ℝ) = - (36358704876728341 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (36358704876728341 / 20000000000000000 : ℚ)) - (U := (2988506878344917683723 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (36358704876728341 / 20000000000000000 : ℝ) ≤ - (2988506878344917683723 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9086746693501983 / 10000000000000000 : ℝ)) (q := - (36358704876728341 / 40000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (36358704876728341 / 40000000000000000 : ℚ)) + (r' := (36358704876728341 / 20000000000000000 : ℚ)) + (U := (-(477229023155082316277 / 5000000000000000000000 : ℚ))) + (U' := (2988506878344917683723 / 5000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (9086746693501983 / 10000000000000000 : ℚ)) + (q := (36358704876728341 / 40000000000000000 : ℚ)) + (U := (-(477229023155082316277 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_6 : Uω (aρ 6) (bρ 6) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -661,25 +571,21 @@ lemma U_677_6 : have hlg : Real.log (35673940604441891 / 40000000000000000 : ℝ) ≤ (-(1144589866729602112133 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (35673940604441891 / 40000000000000000 : ℝ) = - (35673940604441891 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (35673940604441891 / 20000000000000000 : ℚ)) - (U := (5786881936270397887867 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (35673940604441891 / 20000000000000000 : ℝ) ≤ - (5786881936270397887867 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4455802466249379 / 5000000000000000 : ℝ)) (q := - (35673940604441891 / 40000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (35673940604441891 / 40000000000000000 : ℚ)) + (r' := (35673940604441891 / 20000000000000000 : ℚ)) + (U := (-(1144589866729602112133 / 10000000000000000000000 : ℚ))) + (U' := (5786881936270397887867 / 10000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (4455802466249379 / 5000000000000000 : ℚ)) + (q := (35673940604441891 / 40000000000000000 : ℚ)) + (U := (-(1144589866729602112133 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_7 : Uω (aρ 7) (bρ 7) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -687,25 +593,21 @@ lemma U_677_7 : have hlg : Real.log (34747104376406801 / 40000000000000000 : ℝ) ≤ (-(1407832126127480045027 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (34747104376406801 / 40000000000000000 : ℝ) = - (34747104376406801 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (34747104376406801 / 20000000000000000 : ℚ)) - (U := (5523639676872519954973 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (34747104376406801 / 20000000000000000 : ℝ) ≤ - (5523639676872519954973 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8671848199241213 / 10000000000000000 : ℝ)) (q := - (34747104376406801 / 40000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (34747104376406801 / 40000000000000000 : ℚ)) + (r' := (34747104376406801 / 20000000000000000 : ℚ)) + (U := (-(1407832126127480045027 / 10000000000000000000000 : ℚ))) + (U' := (5523639676872519954973 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (8671848199241213 / 10000000000000000 : ℚ)) + (q := (34747104376406801 / 40000000000000000 : ℚ)) + (U := (-(1407832126127480045027 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_8 : Uω (aρ 8) (bρ 8) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -713,25 +615,21 @@ lemma U_677_8 : have hlg : Real.log (6710473013911293 / 8000000000000000 : ℝ) ≤ (-(1757720990443800197271 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (6710473013911293 / 8000000000000000 : ℝ) = - (6710473013911293 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (6710473013911293 / 4000000000000000 : ℚ)) - (U := (5173750812556199802729 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (6710473013911293 / 4000000000000000 : ℝ) ≤ - (5173750812556199802729 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1671604039431209 / 2000000000000000 : ℝ)) (q := - (6710473013911293 / 8000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (6710473013911293 / 8000000000000000 : ℚ)) + (r' := (6710473013911293 / 4000000000000000 : ℚ)) + (U := (-(1757720990443800197271 / 10000000000000000000000 : ℚ))) + (U' := (5173750812556199802729 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (1671604039431209 / 2000000000000000 : ℚ)) + (q := (6710473013911293 / 8000000000000000 : ℚ)) + (U := (-(1757720990443800197271 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_9 : Uω (aρ 9) (bρ 9) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -739,25 +637,21 @@ lemma U_677_9 : have hlg : Real.log (1283317593561117 / 1600000000000000 : ℝ) ≤ (-(2205550341869910017897 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1283317593561117 / 1600000000000000 : ℝ) = - (1283317593561117 / 800000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1283317593561117 / 800000000000000 : ℚ)) - (U := (4725921461130089982103 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (1283317593561117 / 800000000000000 : ℝ) ≤ - (4725921461130089982103 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (318570928410071 / 400000000000000 : ℝ)) (q := - (1283317593561117 / 1600000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1283317593561117 / 1600000000000000 : ℚ)) + (r' := (1283317593561117 / 800000000000000 : ℚ)) + (U := (-(2205550341869910017897 / 10000000000000000000000 : ℚ))) + (U' := (4725921461130089982103 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (318570928410071 / 400000000000000 : ℚ)) + (q := (1283317593561117 / 1600000000000000 : ℚ)) + (U := (-(2205550341869910017897 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_10 : Uω (aρ 10) (bρ 10) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -765,26 +659,21 @@ lemma U_677_10 : have hlg : Real.log (30358020869620537 / 40000000000000000 : ℝ) ≤ (-(2758186921991172196263 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (30358020869620537 / 40000000000000000 : ℝ) = - (30358020869620537 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (30358020869620537 / 20000000000000000 : ℚ)) - (U := (4173284881008827803737 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (30358020869620537 / 20000000000000000 : ℝ) ≤ - (4173284881008827803737 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7490372759043081 / 10000000000000000 : ℝ)) (q := - (30358020869620537 / 40000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (30358020869620537 / 40000000000000000 : ℚ)) + (r' := (30358020869620537 / 20000000000000000 : ℚ)) + (U := (-(2758186921991172196263 / 10000000000000000000000 : ℚ))) + (U' := (4173284881008827803737 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (7490372759043081 / 10000000000000000 : ℚ)) + (q := (30358020869620537 / 40000000000000000 : ℚ)) + (U := (-(2758186921991172196263 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_11 : Uω (aρ 11) (bρ 11) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -792,26 +681,21 @@ lemma U_677_11 : have hlg : Real.log (28428127279949587 / 40000000000000000 : ℝ) ≤ (-(426875502031516809391 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (28428127279949587 / 40000000000000000 : ℝ) = - (28428127279949587 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (28428127279949587 / 20000000000000000 : ℚ)) - (U := (439558473343483190609 / 1250000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (28428127279949587 / 20000000000000000 : ℝ) ≤ - (439558473343483190609 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3471951295206303 / 5000000000000000 : ℝ)) (q := - (28428127279949587 / 40000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (28428127279949587 / 40000000000000000 : ℚ)) + (r' := (28428127279949587 / 20000000000000000 : ℚ)) + (U := (-(426875502031516809391 / 1250000000000000000000 : ℚ))) + (U' := (439558473343483190609 / 1250000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (3471951295206303 / 5000000000000000 : ℚ)) + (q := (28428127279949587 / 40000000000000000 : ℚ)) + (U := (-(426875502031516809391 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_12 : Uω (aρ 12) (bρ 12) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -819,26 +703,21 @@ lemma U_677_12 : have hlg : Real.log (26378568806350523 / 40000000000000000 : ℝ) ≤ (-(4163275610179741765353 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (26378568806350523 / 40000000000000000 : ℝ) = - (26378568806350523 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (26378568806350523 / 20000000000000000 : ℚ)) - (U := (2768196192820258234647 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (26378568806350523 / 20000000000000000 : ℝ) ≤ - (2768196192820258234647 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3171411725149037 / 5000000000000000 : ℝ)) (q := - (26378568806350523 / 40000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (26378568806350523 / 40000000000000000 : ℚ)) + (r' := (26378568806350523 / 20000000000000000 : ℚ)) + (U := (-(4163275610179741765353 / 10000000000000000000000 : ℚ))) + (U' := (2768196192820258234647 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (3171411725149037 / 5000000000000000 : ℚ)) + (q := (26378568806350523 / 40000000000000000 : ℚ)) + (U := (-(4163275610179741765353 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_13 : Uω (aρ 13) (bρ 13) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -846,26 +725,21 @@ lemma U_677_13 : have hlg : Real.log (4866307285834539 / 8000000000000000 : ℝ) ≤ (-(4971061494768781944211 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4866307285834539 / 8000000000000000 : ℝ) = - (4866307285834539 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4866307285834539 / 4000000000000000 : ℚ)) - (U := (1960410308231218055789 / 10000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (4866307285834539 / 4000000000000000 : ℝ) ≤ - (1960410308231218055789 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (35741806270651 / 62500000000000 : ℝ)) (q := - (4866307285834539 / 8000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4866307285834539 / 8000000000000000 : ℚ)) + (r' := (4866307285834539 / 4000000000000000 : ℚ)) + (U := (-(4971061494768781944211 / 10000000000000000000000 : ℚ))) + (U' := (1960410308231218055789 / 10000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (35741806270651 / 62500000000000 : ℚ)) + (q := (4866307285834539 / 8000000000000000 : ℚ)) + (U := (-(4971061494768781944211 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_14 : Uω (aρ 14) (bρ 14) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -873,26 +747,21 @@ lemma U_677_14 : have hlg : Real.log (4489505310941811 / 8000000000000000 : ℝ) ≤ (-(2888495107361552193757 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4489505310941811 / 8000000000000000 : ℝ) = - (4489505310941811 / 4000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4489505310941811 / 4000000000000000 : ℚ)) - (U := (577240794138447806243 / 5000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (4489505310941811 / 4000000000000000 : ℝ) ≤ - (577240794138447806243 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (256030567555867 / 500000000000000 : ℝ)) (q := - (4489505310941811 / 8000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4489505310941811 / 8000000000000000 : ℚ)) + (r' := (4489505310941811 / 4000000000000000 : ℚ)) + (U := (-(2888495107361552193757 / 5000000000000000000000 : ℚ))) + (U' := (577240794138447806243 / 5000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (256030567555867 / 500000000000000 : ℚ)) + (q := (4489505310941811 / 8000000000000000 : ℚ)) + (U := (-(2888495107361552193757 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_15 : Uω (aρ 15) (bρ 15) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -900,26 +769,21 @@ lemma U_677_15 : have hlg : Real.log (20923588733206163 / 40000000000000000 : ℝ) ≤ (-(810002854756473131841 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (20923588733206163 / 40000000000000000 : ℝ) = - (20923588733206163 / 20000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (20923588733206163 / 20000000000000000 : ℚ)) - (U := (56431120618526868159 / 1250000000000000000000 : ℚ)) - 4 (by decide +kernel)) : - Real.log (20923588733206163 / 20000000000000000 : ℝ) ≤ - (56431120618526868159 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2309107858890447 / 5000000000000000 : ℝ)) (q := - (20923588733206163 / 40000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (20923588733206163 / 40000000000000000 : ℚ)) + (r' := (20923588733206163 / 20000000000000000 : ℚ)) + (U := (-(810002854756473131841 / 1250000000000000000000 : ℚ))) + (U' := (56431120618526868159 / 1250000000000000000000 : ℚ)) + 1 4 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (2309107858890447 / 5000000000000000 : ℚ)) + (q := (20923588733206163 / 40000000000000000 : ℚ)) + (U := (-(810002854756473131841 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677_16 : Uω (aρ 16) (bρ 16) (30159206983063 / 32000000000000 : ℝ) ≤ @@ -927,26 +791,21 @@ lemma U_677_16 : have hlg : Real.log (3994892943791167 / 8000000000000000 : ℝ) ≤ (-(434015474906195459093 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 2 - (show - (3994892943791167 / 8000000000000000 : ℝ) = - (3994892943791167 / 2000000000000000 : ℝ) / 2 ^ 2 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3994892943791167 / 2000000000000000 : ℚ)) - (U := (432418500468804540907 / 625000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (3994892943791167 / 2000000000000000 : ℝ) ≤ - (432418500468804540907 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (429602536216573 / 1000000000000000 : ℝ)) (q := - (3994892943791167 / 8000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3994892943791167 / 8000000000000000 : ℚ)) + (r' := (3994892943791167 / 2000000000000000 : ℚ)) + (U := (-(434015474906195459093 / 625000000000000000000 : ℚ))) + (U' := (432418500468804540907 / 625000000000000000000 : ℚ)) + 2 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (30159206983063 / 32000000000000 : ℚ)) + (s := (429602536216573 / 1000000000000000 : ℚ)) + (q := (3994892943791167 / 8000000000000000 : ℚ)) + (U := (-(434015474906195459093 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_677 : Uρ (30159206983063 / 32000000000000 : ℝ) ≤ @@ -1037,25 +896,21 @@ lemma U_678_1 : have hlg : Real.log (4875957115579501 / 5000000000000000 : ℝ) ≤ (-(31401869492385685679 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (4875957115579501 / 5000000000000000 : ℝ) = - (4875957115579501 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (4875957115579501 / 2500000000000000 : ℚ)) - (U := (835032105882614314321 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (4875957115579501 / 2500000000000000 : ℝ) ≤ - (835032105882614314321 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9751897653092379 / 10000000000000000 : ℝ)) (q := - (4875957115579501 / 5000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (4875957115579501 / 5000000000000000 : ℚ)) + (r' := (4875957115579501 / 2500000000000000 : ℚ)) + (U := (-(31401869492385685679 / 1250000000000000000000 : ℚ))) + (U' := (835032105882614314321 / 1250000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (9751897653092379 / 10000000000000000 : ℚ)) + (q := (4875957115579501 / 5000000000000000 : ℚ)) + (U := (-(31401869492385685679 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_2 : Uω (aρ 2) (bρ 2) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1063,25 +918,21 @@ lemma U_678_2 : have hlg : Real.log (9728052738201763 / 10000000000000000 : ℝ) ≤ (-(275713462460201346549 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9728052738201763 / 10000000000000000 : ℝ) = - (9728052738201763 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9728052738201763 / 5000000000000000 : ℚ)) - (U := (6655758340539798653451 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9728052738201763 / 5000000000000000 : ℝ) ≤ - (6655758340539798653451 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9727943679687901 / 10000000000000000 : ℝ)) (q := - (9728052738201763 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9728052738201763 / 10000000000000000 : ℚ)) + (r' := (9728052738201763 / 5000000000000000 : ℚ)) + (U := (-(275713462460201346549 / 10000000000000000000000 : ℚ))) + (U' := (6655758340539798653451 / 10000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (9727943679687901 / 10000000000000000 : ℚ)) + (q := (9728052738201763 / 10000000000000000 : ℚ)) + (U := (-(275713462460201346549 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_3 : Uω (aρ 3) (bρ 3) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1089,25 +940,21 @@ lemma U_678_3 : have hlg : Real.log (3872153429302717 / 4000000000000000 : ℝ) ≤ (-(20302229308895077003 / 625000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3872153429302717 / 4000000000000000 : ℝ) = - (3872153429302717 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3872153429302717 / 2000000000000000 : ℚ)) - (U := (412914758378604922997 / 625000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (3872153429302717 / 2000000000000000 : ℝ) ≤ - (412914758378604922997 / 625000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (242000036403699 / 250000000000000 : ℝ)) (q := - (3872153429302717 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3872153429302717 / 4000000000000000 : ℚ)) + (r' := (3872153429302717 / 2000000000000000 : ℚ)) + (U := (-(20302229308895077003 / 625000000000000000000 : ℚ))) + (U' := (412914758378604922997 / 625000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (242000036403699 / 250000000000000 : ℚ)) + (q := (3872153429302717 / 4000000000000000 : ℚ)) + (U := (-(20302229308895077003 / 625000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_4 : Uω (aρ 4) (bρ 4) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1115,25 +962,21 @@ lemma U_678_4 : have hlg : Real.log (9601375777845239 / 10000000000000000 : ℝ) ≤ (-(81357388672044063251 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9601375777845239 / 10000000000000000 : ℝ) = - (9601375777845239 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9601375777845239 / 5000000000000000 : ℚ)) - (U := (1304936971927955936749 / 2000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9601375777845239 / 5000000000000000 : ℝ) ≤ - (1304936971927955936749 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9600280046389853 / 10000000000000000 : ℝ)) (q := - (9601375777845239 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9601375777845239 / 10000000000000000 : ℚ)) + (r' := (9601375777845239 / 5000000000000000 : ℚ)) + (U := (-(81357388672044063251 / 2000000000000000000000 : ℚ))) + (U' := (1304936971927955936749 / 2000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (9600280046389853 / 10000000000000000 : ℚ)) + (q := (9601375777845239 / 10000000000000000 : ℚ)) + (U := (-(81357388672044063251 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_5 : Uω (aρ 5) (bρ 5) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1141,25 +984,21 @@ lemma U_678_5 : have hlg : Real.log (592592069951071 / 625000000000000 : ℝ) ≤ (-(532453962168235848837 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (592592069951071 / 625000000000000 : ℝ) = - (592592069951071 / 312500000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (592592069951071 / 312500000000000 : ℚ)) - (U := (6399017840831764151163 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (592592069951071 / 312500000000000 : ℝ) ≤ - (6399017840831764151163 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9478664648468647 / 10000000000000000 : ℝ)) (q := - (592592069951071 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (592592069951071 / 625000000000000 : ℚ)) + (r' := (592592069951071 / 312500000000000 : ℚ)) + (U := (-(532453962168235848837 / 10000000000000000000000 : ℚ))) + (U' := (6399017840831764151163 / 10000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (9478664648468647 / 10000000000000000 : ℚ)) + (q := (592592069951071 / 625000000000000 : ℚ)) + (U := (-(532453962168235848837 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_6 : Uω (aρ 6) (bρ 6) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1167,25 +1006,21 @@ lemma U_678_6 : have hlg : Real.log (3724180260044697 / 4000000000000000 : ℝ) ≤ (-(357237988318402216991 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3724180260044697 / 4000000000000000 : ℝ) = - (3724180260044697 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3724180260044697 / 2000000000000000 : ℚ)) - (U := (3108497913181597783009 / 5000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (3724180260044697 / 2000000000000000 : ℝ) ≤ - (3108497913181597783009 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (465193004269893 / 500000000000000 : ℝ)) (q := - (3724180260044697 / 4000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3724180260044697 / 4000000000000000 : ℚ)) + (r' := (3724180260044697 / 2000000000000000 : ℚ)) + (U := (-(357237988318402216991 / 5000000000000000000000 : ℚ))) + (U' := (3108497913181597783009 / 5000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (465193004269893 / 500000000000000 : ℚ)) + (q := (3724180260044697 / 4000000000000000 : ℚ)) + (U := (-(357237988318402216991 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_7 : Uω (aρ 7) (bρ 7) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1193,25 +1028,21 @@ lemma U_678_7 : have hlg : Real.log (1815819399022757 / 2000000000000000 : ℝ) ≤ (-(966103549437018389189 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1815819399022757 / 2000000000000000 : ℝ) = - (1815819399022757 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1815819399022757 / 1000000000000000 : ℚ)) - (U := (5965368253562981610811 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1815819399022757 / 1000000000000000 : ℝ) ≤ - (5965368253562981610811 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1812962831232389 / 2000000000000000 : ℝ)) (q := - (1815819399022757 / 2000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1815819399022757 / 2000000000000000 : ℚ)) + (r' := (1815819399022757 / 1000000000000000 : ℚ)) + (U := (-(966103549437018389189 / 10000000000000000000000 : ℚ))) + (U' := (5965368253562981610811 / 10000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (1812962831232389 / 2000000000000000 : ℚ)) + (q := (1815819399022757 / 2000000000000000 : ℚ)) + (U := (-(966103549437018389189 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_8 : Uω (aρ 8) (bρ 8) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1219,25 +1050,21 @@ lemma U_678_8 : have hlg : Real.log (17562226044293351 / 20000000000000000 : ℝ) ≤ (-(1299819252231914866819 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17562226044293351 / 20000000000000000 : ℝ) = - (17562226044293351 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17562226044293351 / 10000000000000000 : ℚ)) - (U := (5631652550768085133181 / 10000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17562226044293351 / 10000000000000000 : ℝ) ≤ - (5631652550768085133181 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4376193930783863 / 5000000000000000 : ℝ)) (q := - (17562226044293351 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17562226044293351 / 20000000000000000 : ℚ)) + (r' := (17562226044293351 / 10000000000000000 : ℚ)) + (U := (-(1299819252231914866819 / 10000000000000000000000 : ℚ))) + (U' := (5631652550768085133181 / 10000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (4376193930783863 / 5000000000000000 : ℚ)) + (q := (17562226044293351 / 20000000000000000 : ℚ)) + (U := (-(1299819252231914866819 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_9 : Uω (aρ 9) (bρ 9) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1245,25 +1072,21 @@ lemma U_678_9 : have hlg : Real.log (16830113098059219 / 20000000000000000 : ℝ) ≤ (-(172562545086624586799 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16830113098059219 / 20000000000000000 : ℝ) = - (16830113098059219 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16830113098059219 / 10000000000000000 : ℚ)) - (U := (520584635213375413201 / 1000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (16830113098059219 / 10000000000000000 : ℝ) ≤ - (520584635213375413201 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4180620271846797 / 5000000000000000 : ℝ)) (q := - (16830113098059219 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16830113098059219 / 20000000000000000 : ℚ)) + (r' := (16830113098059219 / 10000000000000000 : ℚ)) + (U := (-(172562545086624586799 / 1000000000000000000000 : ℚ))) + (U' := (520584635213375413201 / 1000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (4180620271846797 / 5000000000000000 : ℚ)) + (q := (16830113098059219 / 20000000000000000 : ℚ)) + (U := (-(172562545086624586799 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_10 : Uω (aρ 10) (bρ 10) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1271,26 +1094,21 @@ lemma U_678_10 : have hlg : Real.log (7986104091424179 / 10000000000000000 : ℝ) ≤ (-(2248820499400769661627 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7986104091424179 / 10000000000000000 : ℝ) = - (7986104091424179 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7986104091424179 / 5000000000000000 : ℚ)) - (U := (4682651303599230338373 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7986104091424179 / 5000000000000000 : ℝ) ≤ - (4682651303599230338373 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7891894661977733 / 10000000000000000 : ℝ)) (q := - (7986104091424179 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7986104091424179 / 10000000000000000 : ℚ)) + (r' := (7986104091424179 / 5000000000000000 : ℚ)) + (U := (-(2248820499400769661627 / 10000000000000000000000 : ℚ))) + (U' := (4682651303599230338373 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (7891894661977733 / 10000000000000000 : ℚ)) + (q := (7986104091424179 / 10000000000000000 : ℚ)) + (U := (-(2248820499400769661627 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_11 : Uω (aρ 11) (bρ 11) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1298,26 +1116,21 @@ lemma U_678_11 : have hlg : Real.log (7507407468771171 / 10000000000000000 : ℝ) ≤ (-(286694897106712835459 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7507407468771171 / 10000000000000000 : ℝ) = - (7507407468771171 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7507407468771171 / 5000000000000000 : ℚ)) - (U := (406452283193287164541 / 1000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (7507407468771171 / 5000000000000000 : ℝ) ≤ - (406452283193287164541 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7352978042876717 / 10000000000000000 : ℝ)) (q := - (7507407468771171 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7507407468771171 / 10000000000000000 : ℚ)) + (r' := (7507407468771171 / 5000000000000000 : ℚ)) + (U := (-(286694897106712835459 / 1000000000000000000000 : ℚ))) + (U' := (406452283193287164541 / 1000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (7352978042876717 / 10000000000000000 : ℚ)) + (q := (7507407468771171 / 10000000000000000 : ℚ)) + (U := (-(286694897106712835459 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_12 : Uω (aρ 12) (bρ 12) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1325,26 +1138,21 @@ lemma U_678_12 : have hlg : Real.log (3500466007121139 / 5000000000000000 : ℝ) ≤ (-(44567725956253433693 / 125000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3500466007121139 / 5000000000000000 : ℝ) = - (3500466007121139 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3500466007121139 / 2500000000000000 : ℚ)) - (U := (42075671581246566307 / 125000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (3500466007121139 / 2500000000000000 : ℝ) ≤ - (42075671581246566307 / 125000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6763727230503931 / 10000000000000000 : ℝ)) (q := - (3500466007121139 / 5000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3500466007121139 / 5000000000000000 : ℚ)) + (r' := (3500466007121139 / 2500000000000000 : ℚ)) + (U := (-(44567725956253433693 / 125000000000000000000 : ℚ))) + (U' := (42075671581246566307 / 125000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (6763727230503931 / 10000000000000000 : ℚ)) + (q := (3500466007121139 / 5000000000000000 : ℚ)) + (U := (-(44567725956253433693 / 125000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_13 : Uω (aρ 13) (bρ 13) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1352,26 +1160,21 @@ lemma U_678_13 : have hlg : Real.log (12995632859396249 / 20000000000000000 : ℝ) ≤ (-(4311189061635353508999 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (12995632859396249 / 20000000000000000 : ℝ) = - (12995632859396249 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (12995632859396249 / 10000000000000000 : ℚ)) - (U := (2620282741364646491001 / 10000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (12995632859396249 / 10000000000000000 : ℝ) ≤ - (2620282741364646491001 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (96201215672041 / 156250000000000 : ℝ)) (q := - (12995632859396249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (12995632859396249 / 20000000000000000 : ℚ)) + (r' := (12995632859396249 / 10000000000000000 : ℚ)) + (U := (-(4311189061635353508999 / 10000000000000000000000 : ℚ))) + (U' := (2620282741364646491001 / 10000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (96201215672041 / 156250000000000 : ℚ)) + (q := (12995632859396249 / 20000000000000000 : ℚ)) + (U := (-(4311189061635353508999 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_14 : Uω (aρ 14) (bρ 14) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1379,26 +1182,21 @@ lemma U_678_14 : have hlg : Real.log (3019123210339151 / 5000000000000000 : ℝ) ≤ (-(504471450642891062021 / 1000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3019123210339151 / 5000000000000000 : ℝ) = - (3019123210339151 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3019123210339151 / 2500000000000000 : ℚ)) - (U := (188675729657108937979 / 1000000000000000000000 : ℚ)) - 7 (by decide +kernel)) : - Real.log (3019123210339151 / 2500000000000000 : ℝ) ≤ - (188675729657108937979 / 1000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5581665070015979 / 10000000000000000 : ℝ)) (q := - (3019123210339151 / 5000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3019123210339151 / 5000000000000000 : ℚ)) + (r' := (3019123210339151 / 2500000000000000 : ℚ)) + (U := (-(504471450642891062021 / 1000000000000000000000 : ℚ))) + (U' := (188675729657108937979 / 1000000000000000000000 : ℚ)) + 1 7 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (5581665070015979 / 10000000000000000 : ℚ)) + (q := (3019123210339151 / 5000000000000000 : ℚ)) + (U := (-(504471450642891062021 / 1000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_15 : Uω (aρ 15) (bρ 15) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1406,26 +1204,21 @@ lemma U_678_15 : have hlg : Real.log (5670023356259313 / 10000000000000000 : ℝ) ≤ (-(1134783711466407468651 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (5670023356259313 / 10000000000000000 : ℝ) = - (5670023356259313 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (5670023356259313 / 5000000000000000 : ℚ)) - (U := (251510649133592531349 / 2000000000000000000000 : ℚ)) - 6 (by decide +kernel)) : - Real.log (5670023356259313 / 5000000000000000 : ℝ) ≤ - (251510649133592531349 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (5104792218593001 / 10000000000000000 : ℝ)) (q := - (5670023356259313 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (5670023356259313 / 10000000000000000 : ℚ)) + (r' := (5670023356259313 / 5000000000000000 : ℚ)) + (U := (-(1134783711466407468651 / 2000000000000000000000 : ℚ))) + (U' := (251510649133592531349 / 2000000000000000000000 : ℚ)) + 1 6 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (5104792218593001 / 10000000000000000 : ℚ)) + (q := (5670023356259313 / 10000000000000000 : ℚ)) + (U := (-(1134783711466407468651 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678_16 : Uω (aρ 16) (bρ 16) (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1433,25 +1226,21 @@ lemma U_678_16 : have hlg : Real.log (435429698376879 / 800000000000000 : ℝ) ≤ (-(1520695928810576621543 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (435429698376879 / 800000000000000 : ℝ) = - (435429698376879 / 400000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (435429698376879 / 400000000000000 : ℚ)) - (U := (212172021939423378457 / 2500000000000000000000 : ℚ)) - 5 (by decide +kernel)) : - Real.log (435429698376879 / 400000000000000 : ℝ) ≤ - (212172021939423378457 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (96057192340127 / 200000000000000 : ℝ)) (q := - (435429698376879 / 800000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) (by norm_num [bρ_16]) - (by norm_num) (by norm_num [aρ_16, bρ_16]) (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (435429698376879 / 800000000000000 : ℚ)) + (r' := (435429698376879 / 400000000000000 : ℚ)) + (U := (-(1520695928810576621543 / 2500000000000000000000 : ℚ))) + (U' := (212172021939423378457 / 2500000000000000000000 : ℚ)) + 1 5 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (15706284843697 / 16000000000000 : ℚ)) + (s := (96057192340127 / 200000000000000 : ℚ)) + (q := (435429698376879 / 800000000000000 : ℚ)) + (U := (-(1520695928810576621543 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_678 : Uρ (15706284843697 / 16000000000000 : ℝ) ≤ @@ -1547,10 +1336,14 @@ lemma U_679_1 : (r := (1316908394254119 / 1250000000000000 : ℚ)) (U := (32589570407983029189 / 625000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (2633812952158351 / 2500000000000000 : ℝ)) (q := - (1316908394254119 / 1250000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (2633812952158351 / 2500000000000000 : ℚ)) + (q := (1316908394254119 / 1250000000000000 : ℚ)) + (U := (32589570407983029189 / 625000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_2 : Uω (aρ 2) (bρ 2) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1563,10 +1356,14 @@ lemma U_679_2 : (r := (164240821186893 / 156250000000000 : ℚ)) (U := (99752968003727494617 / 2000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (2627827906249951 / 2500000000000000 : ℝ)) (q := - (164240821186893 / 156250000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (2627827906249951 / 2500000000000000 : ℚ)) + (q := (164240821186893 / 156250000000000 : ℚ)) + (U := (99752968003727494617 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_3 : Uω (aρ 3) (bρ 3) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1579,10 +1376,14 @@ lemma U_679_3 : (r := (20927527742097363 / 20000000000000000 : ℚ)) (U := (226665678130179312083 / 5000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10463410361524863 / 10000000000000000 : ℝ)) (q := - (20927527742097363 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (10463410361524863 / 10000000000000000 : ℚ)) + (q := (20927527742097363 / 20000000000000000 : ℚ)) + (U := (226665678130179312083 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_4 : Uω (aρ 4) (bρ 4) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1595,10 +1396,14 @@ lemma U_679_4 : (r := (20769620260968647 / 20000000000000000 : ℚ)) (U := (75518162225807609173 / 2000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10383797061461147 / 10000000000000000 : ℝ)) (q := - (20769620260968647 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (10383797061461147 / 10000000000000000 : ℚ)) + (q := (20769620260968647 / 20000000000000000 : ℚ)) + (U := (75518162225807609173 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_5 : Uω (aρ 5) (bρ 5) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1611,10 +1416,14 @@ lemma U_679_5 : (r := (4106015675897693 / 4000000000000000 : ℚ)) (U := (261587752722163667687 / 10000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (2052489019863193 / 2000000000000000 : ℝ)) (q := - (4106015675897693 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (2052489019863193 / 2000000000000000 : ℚ)) + (q := (4106015675897693 / 4000000000000000 : ℚ)) + (U := (261587752722163667687 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_6 : Uω (aρ 6) (bρ 6) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1627,10 +1436,14 @@ lemma U_679_6 : (r := (20188628247545629 / 20000000000000000 : ℚ)) (U := (23468035726243644037 / 2500000000000000000000 : ℚ)) 3 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10088235342513129 / 10000000000000000 : ℝ)) (q := - (20188628247545629 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (10088235342513129 / 10000000000000000 : ℚ)) + (q := (20188628247545629 / 20000000000000000 : ℚ)) + (U := (23468035726243644037 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_7 : Uω (aρ 7) (bρ 7) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1638,25 +1451,21 @@ lemma U_679_7 : have hlg : Real.log (19727169305494247 / 20000000000000000 : ℝ) ≤ (-(17169293930414594967 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19727169305494247 / 20000000000000000 : ℝ) = - (19727169305494247 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19727169305494247 / 10000000000000000 : ℚ)) - (U := (849264681444585405033 / 1250000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19727169305494247 / 10000000000000000 : ℝ) ≤ - (849264681444585405033 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9850437781221747 / 10000000000000000 : ℝ)) (q := - (19727169305494247 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19727169305494247 / 20000000000000000 : ℚ)) + (r' := (19727169305494247 / 10000000000000000 : ℚ)) + (U := (-(17169293930414594967 / 1250000000000000000000 : ℚ))) + (U' := (849264681444585405033 / 1250000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (9850437781221747 / 10000000000000000 : ℚ)) + (q := (19727169305494247 / 20000000000000000 : ℚ)) + (U := (-(17169293930414594967 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_8 : Uω (aρ 8) (bρ 8) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1664,25 +1473,21 @@ lemma U_679_8 : have hlg : Real.log (19133647745154483 / 20000000000000000 : ℝ) ≤ (-(13838695655646965701 / 312500000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19133647745154483 / 20000000000000000 : ℝ) = - (19133647745154483 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19133647745154483 / 10000000000000000 : ℚ)) - (U := (202769798188103034299 / 312500000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19133647745154483 / 10000000000000000 : ℝ) ≤ - (202769798188103034299 / 312500000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9540457872221983 / 10000000000000000 : ℝ)) (q := - (19133647745154483 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19133647745154483 / 20000000000000000 : ℚ)) + (r' := (19133647745154483 / 10000000000000000 : ℚ)) + (U := (-(13838695655646965701 / 312500000000000000000 : ℚ))) + (U' := (202769798188103034299 / 312500000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (9540457872221983 / 10000000000000000 : ℚ)) + (q := (19133647745154483 / 20000000000000000 : ℚ)) + (U := (-(13838695655646965701 / 312500000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_9 : Uω (aρ 9) (bρ 9) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1690,25 +1495,21 @@ lemma U_679_9 : have hlg : Real.log (9203015949090823 / 10000000000000000 : ℝ) ≤ (-(4152692092358634187 / 50000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9203015949090823 / 10000000000000000 : ℝ) = - (9203015949090823 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9203015949090823 / 5000000000000000 : ℚ)) - (U := (30504666922641365813 / 50000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (9203015949090823 / 5000000000000000 : ℝ) ≤ - (30504666922641365813 / 50000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4576903826804573 / 5000000000000000 : ℝ)) (q := - (9203015949090823 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9203015949090823 / 10000000000000000 : ℚ)) + (r' := (9203015949090823 / 5000000000000000 : ℚ)) + (U := (-(4152692092358634187 / 50000000000000000000 : ℚ))) + (U' := (30504666922641365813 / 50000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (4576903826804573 / 5000000000000000 : ℚ)) + (q := (9203015949090823 / 10000000000000000 : ℚ)) + (U := (-(4152692092358634187 / 50000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_10 : Uω (aρ 10) (bρ 10) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1716,26 +1517,21 @@ lemma U_679_10 : have hlg : Real.log (8777954317313903 / 10000000000000000 : ℝ) ≤ (-(325854264266228926319 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8777954317313903 / 10000000000000000 : ℝ) = - (8777954317313903 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8777954317313903 / 5000000000000000 : ℚ)) - (U := (1407013686483771073681 / 2500000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8777954317313903 / 5000000000000000 : ℝ) ≤ - (1407013686483771073681 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4346121711775153 / 5000000000000000 : ℝ)) (q := - (8777954317313903 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8777954317313903 / 10000000000000000 : ℚ)) + (r' := (8777954317313903 / 5000000000000000 : ℚ)) + (U := (-(325854264266228926319 / 2500000000000000000000 : ℚ))) + (U' := (1407013686483771073681 / 2500000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (4346121711775153 / 5000000000000000 : ℚ)) + (q := (8777954317313903 / 10000000000000000 : ℚ)) + (U := (-(325854264266228926319 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_11 : Uω (aρ 11) (bρ 11) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1743,26 +1539,21 @@ lemma U_679_11 : have hlg : Real.log (8305600284736179 / 10000000000000000 : ℝ) ≤ (-(928275361804200092781 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (8305600284736179 / 10000000000000000 : ℝ) = - (8305600284736179 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (8305600284736179 / 5000000000000000 : ℚ)) - (U := (2537460539695799907219 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (8305600284736179 / 5000000000000000 : ℝ) ≤ - (2537460539695799907219 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4083005992299929 / 5000000000000000 : ℝ)) (q := - (8305600284736179 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (8305600284736179 / 10000000000000000 : ℚ)) + (r' := (8305600284736179 / 5000000000000000 : ℚ)) + (U := (-(928275361804200092781 / 5000000000000000000000 : ℚ))) + (U' := (2537460539695799907219 / 5000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (4083005992299929 / 5000000000000000 : ℚ)) + (q := (8305600284736179 / 10000000000000000 : ℚ)) + (U := (-(928275361804200092781 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_12 : Uω (aρ 12) (bρ 12) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1770,26 +1561,21 @@ lemma U_679_12 : have hlg : Real.log (3123529863022419 / 4000000000000000 : ℝ) ≤ (-(98932252879129752837 / 400000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3123529863022419 / 4000000000000000 : ℝ) = - (3123529863022419 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3123529863022419 / 2000000000000000 : ℚ)) - (U := (178326619240870247163 / 400000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (3123529863022419 / 2000000000000000 : ℝ) ≤ - (178326619240870247163 / 400000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1519232165384919 / 2000000000000000 : ℝ)) (q := - (3123529863022419 / 4000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3123529863022419 / 4000000000000000 : ℚ)) + (r' := (3123529863022419 / 2000000000000000 : ℚ)) + (U := (-(98932252879129752837 / 400000000000000000000 : ℚ))) + (U' := (178326619240870247163 / 400000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (1519232165384919 / 2000000000000000 : ℚ)) + (q := (3123529863022419 / 4000000000000000 : ℚ)) + (U := (-(98932252879129752837 / 400000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_13 : Uω (aρ 13) (bρ 13) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1797,26 +1583,21 @@ lemma U_679_13 : have hlg : Real.log (3659719606775781 / 5000000000000000 : ℝ) ≤ (-(1560256889330704127261 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3659719606775781 / 5000000000000000 : ℝ) = - (3659719606775781 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3659719606775781 / 2500000000000000 : ℚ)) - (U := (1905479012169295872739 / 5000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (3659719606775781 / 2500000000000000 : ℝ) ≤ - (1905479012169295872739 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (219274115015957 / 312500000000000 : ℝ)) (q := - (3659719606775781 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3659719606775781 / 5000000000000000 : ℚ)) + (r' := (3659719606775781 / 2500000000000000 : ℚ)) + (U := (-(1560256889330704127261 / 5000000000000000000000 : ℚ))) + (U' := (1905479012169295872739 / 5000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (219274115015957 / 312500000000000 : ℚ)) + (q := (3659719606775781 / 5000000000000000 : ℚ)) + (U := (-(1560256889330704127261 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_14 : Uω (aρ 14) (bρ 14) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1824,26 +1605,21 @@ lemma U_679_14 : have hlg : Real.log (13754605439581289 / 20000000000000000 : ℝ) ≤ (-(748717128402485919173 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (13754605439581289 / 20000000000000000 : ℝ) = - (13754605439581289 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (13754605439581289 / 10000000000000000 : ℚ)) - (U := (637577232197514080827 / 2000000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (13754605439581289 / 10000000000000000 : ℝ) ≤ - (637577232197514080827 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (6476425978033789 / 10000000000000000 : ℝ)) (q := - (13754605439581289 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (13754605439581289 / 20000000000000000 : ℚ)) + (r' := (13754605439581289 / 10000000000000000 : ℚ)) + (U := (-(748717128402485919173 / 2000000000000000000000 : ℚ))) + (U' := (637577232197514080827 / 2000000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (6476425978033789 / 10000000000000000 : ℚ)) + (q := (13754605439581289 / 20000000000000000 : ℚ)) + (U := (-(748717128402485919173 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_15 : Uω (aρ 15) (bρ 15) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1851,26 +1627,21 @@ lemma U_679_15 : have hlg : Real.log (2611054459411399 / 4000000000000000 : ℝ) ≤ (-(2132701068385280181461 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2611054459411399 / 4000000000000000 : ℝ) = - (2611054459411399 / 2000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2611054459411399 / 2000000000000000 : ℚ)) - (U := (1333034833114719818539 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (2611054459411399 / 2000000000000000 : ℝ) ≤ - (1333034833114719818539 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1207333222584899 / 2000000000000000 : ℝ)) (q := - (2611054459411399 / 4000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2611054459411399 / 4000000000000000 : ℚ)) + (r' := (2611054459411399 / 2000000000000000 : ℚ)) + (U := (-(2132701068385280181461 / 5000000000000000000000 : ℚ))) + (U' := (1333034833114719818539 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (1207333222584899 / 2000000000000000 : ℚ)) + (q := (2611054459411399 / 4000000000000000 : ℚ)) + (U := (-(2132701068385280181461 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679_16 : Uω (aρ 16) (bρ 16) (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1878,26 +1649,21 @@ lemma U_679_16 : have hlg : Real.log (3157287040140563 / 5000000000000000 : ℝ) ≤ (-(2298623924628737086939 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (3157287040140563 / 5000000000000000 : ℝ) = - (3157287040140563 / 2500000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (3157287040140563 / 2500000000000000 : ℚ)) - (U := (1167111976871262913061 / 5000000000000000000000 : ℚ)) - 8 (by decide +kernel)) : - Real.log (3157287040140563 / 2500000000000000 : ℝ) ≤ - (1167111976871262913061 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (720364203492469 / 1250000000000000 : ℝ)) (q := - (3157287040140563 / 5000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (3157287040140563 / 5000000000000000 : ℚ)) + (r' := (3157287040140563 / 2500000000000000 : ℚ)) + (U := (-(2298623924628737086939 / 5000000000000000000000 : ℚ))) + (U' := (1167111976871262913061 / 5000000000000000000000 : ℚ)) + 1 8 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (4239911887007 / 4000000000000 : ℚ)) + (s := (720364203492469 / 1250000000000000 : ℚ)) + (q := (3157287040140563 / 5000000000000000 : ℚ)) + (U := (-(2298623924628737086939 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_679 : Uρ (4239911887007 / 4000000000000 : ℝ) ≤ @@ -1989,10 +1755,14 @@ lemma U_680_1 : (r := (22637239812565641 / 20000000000000000 : ℚ)) (U := (1238640559424707941031 / 10000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5659302811463133 / 5000000000000000 : ℝ)) (q := - (22637239812565641 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (5659302811463133 / 5000000000000000 : ℚ)) + (q := (22637239812565641 / 20000000000000000 : ℚ)) + (U := (1238640559424707941031 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_2 : Uω (aρ 2) (bρ 2) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2005,10 +1775,14 @@ lemma U_680_2 : (r := (5647385623161349 / 5000000000000000 : ℚ)) (U := (121754804071227033031 / 1000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (11294677315516021 / 10000000000000000 : ℝ)) (q := - (5647385623161349 / 5000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (11294677315516021 / 10000000000000000 : ℚ)) + (q := (5647385623161349 / 5000000000000000 : ℚ)) + (U := (121754804071227033031 / 1000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_3 : Uω (aρ 3) (bρ 3) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2021,10 +1795,14 @@ lemma U_680_3 : (r := (22494280367204911 / 20000000000000000 : ℚ)) (U := (117528797438582498587 / 1000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (175731426506649 / 156250000000000 : ℝ)) (q := - (22494280367204911 / 20000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (175731426506649 / 156250000000000 : ℚ)) + (q := (22494280367204911 / 20000000000000000 : ℚ)) + (U := (117528797438582498587 / 1000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_4 : Uω (aρ 4) (bρ 4) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2037,10 +1815,14 @@ lemma U_680_4 : (r := (22336465769744637 / 20000000000000000 : ℚ)) (U := (17263797762555920119 / 156250000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5583645440015131 / 5000000000000000 : ℝ)) (q := - (22336465769744637 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (5583645440015131 / 5000000000000000 : ℚ)) + (q := (22336465769744637 / 20000000000000000 : ℚ)) + (U := (17263797762555920119 / 156250000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_5 : Uω (aρ 5) (bρ 5) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2053,10 +1835,14 @@ lemma U_680_5 : (r := (22097149691943109 / 20000000000000000 : ℚ)) (U := (49858176718355945399 / 500000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5523082360781867 / 5000000000000000 : ℝ)) (q := - (22097149691943109 / 20000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (5523082360781867 / 5000000000000000 : ℚ)) + (q := (22097149691943109 / 20000000000000000 : ℚ)) + (U := (49858176718355945399 / 500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_6 : Uω (aρ 6) (bρ 6) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2069,10 +1855,14 @@ lemma U_680_6 : (r := (21756207605261641 / 20000000000000000 : ℚ)) (U := (841668503982988491161 / 10000000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5436231505011133 / 5000000000000000 : ℝ)) (q := - (21756207605261641 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (5436231505011133 / 5000000000000000 : ℚ)) + (q := (21756207605261641 / 20000000000000000 : ℚ)) + (U := (841668503982988491161 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_7 : Uω (aρ 7) (bρ 7) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2085,10 +1875,14 @@ lemma U_680_7 : (r := (10647904735856001 / 10000000000000000 : ℚ)) (U := (125556082777140847159 / 2000000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10635726257232627 / 10000000000000000 : ℝ)) (q := - (10647904735856001 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (10635726257232627 / 10000000000000000 : ℚ)) + (q := (10647904735856001 / 10000000000000000 : ℚ)) + (U := (125556082777140847159 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_8 : Uω (aρ 8) (bρ 8) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2101,10 +1895,14 @@ lemma U_680_8 : (r := (10352175778881961 / 10000000000000000 : ℚ)) (U := (34611624805998184127 / 1000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10327809994624547 / 10000000000000000 : ℝ)) (q := - (10352175778881961 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (10327809994624547 / 10000000000000000 : ℚ)) + (q := (10352175778881961 / 10000000000000000 : ℚ)) + (U := (34611624805998184127 / 1000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_9 : Uω (aρ 9) (bρ 9) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2112,25 +1910,21 @@ lemma U_680_9 : have hlg : Real.log (19980490485952811 / 20000000000000000 : ℝ) ≤ (-(9759515284691867981 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19980490485952811 / 20000000000000000 : ℝ) = - (19980490485952811 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19980490485952811 / 10000000000000000 : ℚ)) - (U := (6921712287715308132019 / 10000000000000000000000 : ℚ)) - 15 (by decide +kernel)) : - Real.log (19980490485952811 / 10000000000000000 : ℝ) ≤ - (6921712287715308132019 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (2486228637793359 / 2500000000000000 : ℝ)) (q := - (19980490485952811 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19980490485952811 / 20000000000000000 : ℚ)) + (r' := (19980490485952811 / 10000000000000000 : ℚ)) + (U := (-(9759515284691867981 / 10000000000000000000000 : ℚ))) + (U' := (6921712287715308132019 / 10000000000000000000000 : ℚ)) + 1 15 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (2486228637793359 / 2500000000000000 : ℚ)) + (q := (19980490485952811 / 20000000000000000 : ℚ)) + (U := (-(9759515284691867981 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_10 : Uω (aρ 10) (bρ 10) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2138,26 +1932,21 @@ lemma U_680_10 : have hlg : Real.log (9568386474729171 / 10000000000000000 : ℝ) ≤ (-(441205039158688405329 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (9568386474729171 / 10000000000000000 : ℝ) = - (9568386474729171 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (9568386474729171 / 5000000000000000 : ℚ)) - (U := (6490266763841311594671 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (9568386474729171 / 5000000000000000 : ℝ) ≤ - (6490266763841311594671 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9489756048173967 / 10000000000000000 : ℝ)) (q := - (9568386474729171 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (9568386474729171 / 10000000000000000 : ℚ)) + (r' := (9568386474729171 / 5000000000000000 : ℚ)) + (U := (-(441205039158688405329 / 10000000000000000000000 : ℚ))) + (U' := (6490266763841311594671 / 10000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (9489756048173967 / 10000000000000000 : ℚ)) + (q := (9568386474729171 / 10000000000000000 : ℚ)) + (U := (-(441205039158688405329 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_11 : Uω (aρ 11) (bρ 11) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2165,26 +1954,21 @@ lemma U_680_11 : have hlg : Real.log (18202307438725301 / 20000000000000000 : ℝ) ≤ (-(235459762249886509823 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (18202307438725301 / 20000000000000000 : ℝ) = - (18202307438725301 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18202307438725301 / 10000000000000000 : ℚ)) - (U := (1497408188500113490177 / 2500000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (18202307438725301 / 10000000000000000 : ℝ) ≤ - (1497408188500113490177 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (4486883581822963 / 5000000000000000 : ℝ)) (q := - (18202307438725301 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18202307438725301 / 20000000000000000 : ℚ)) + (r' := (18202307438725301 / 10000000000000000 : ℚ)) + (U := (-(235459762249886509823 / 2500000000000000000000 : ℚ))) + (U' := (1497408188500113490177 / 2500000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (4486883581822963 / 5000000000000000 : ℚ)) + (q := (18202307438725301 / 20000000000000000 : ℚ)) + (U := (-(235459762249886509823 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_12 : Uω (aρ 12) (bρ 12) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2192,26 +1976,21 @@ lemma U_680_12 : have hlg : Real.log (2153002525543727 / 2500000000000000 : ℝ) ≤ (-(186784175247454332741 / 1250000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (2153002525543727 / 2500000000000000 : ℝ) = - (2153002525543727 / 1250000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (2153002525543727 / 1250000000000000 : ℚ)) - (U := (679649800127545667259 / 1250000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (2153002525543727 / 1250000000000000 : ℝ) ≤ - (679649800127545667259 / 1250000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8419180025955441 / 10000000000000000 : ℝ)) (q := - (2153002525543727 / 2500000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (2153002525543727 / 2500000000000000 : ℚ)) + (r' := (2153002525543727 / 1250000000000000 : ℚ)) + (U := (-(186784175247454332741 / 1250000000000000000000 : ℚ))) + (U' := (679649800127545667259 / 1250000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (8419180025955441 / 10000000000000000 : ℚ)) + (q := (2153002525543727 / 2500000000000000 : ℚ)) + (U := (-(186784175247454332741 / 1250000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_13 : Uω (aρ 13) (bρ 13) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2219,26 +1998,21 @@ lemma U_680_13 : have hlg : Real.log (16266139392844263 / 20000000000000000 : ℝ) ≤ (-(2066466640027391588759 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16266139392844263 / 20000000000000000 : ℝ) = - (16266139392844263 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16266139392844263 / 10000000000000000 : ℚ)) - (U := (4865005162972608411241 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16266139392844263 / 10000000000000000 : ℝ) ≤ - (4865005162972608411241 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (982585119505611 / 1250000000000000 : ℝ)) (q := - (16266139392844263 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16266139392844263 / 20000000000000000 : ℚ)) + (r' := (16266139392844263 / 10000000000000000 : ℚ)) + (U := (-(2066466640027391588759 / 10000000000000000000000 : ℚ))) + (U' := (4865005162972608411241 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (982585119505611 / 1250000000000000 : ℚ)) + (q := (16266139392844263 / 20000000000000000 : ℚ)) + (U := (-(2066466640027391588759 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_14 : Uω (aρ 14) (bρ 14) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2246,26 +2020,21 @@ lemma U_680_14 : have hlg : Real.log (15407311007233661 / 20000000000000000 : ℝ) ≤ (-(521780271597462009859 / 2000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (15407311007233661 / 20000000000000000 : ℝ) = - (15407311007233661 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (15407311007233661 / 10000000000000000 : ℚ)) - (U := (864514089002537990141 / 2000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (15407311007233661 / 10000000000000000 : ℝ) ≤ - (864514089002537990141 / 2000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (3672889927739643 / 5000000000000000 : ℝ)) (q := - (15407311007233661 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (15407311007233661 / 20000000000000000 : ℚ)) + (r' := (15407311007233661 / 10000000000000000 : ℚ)) + (U := (-(521780271597462009859 / 2000000000000000000000 : ℚ))) + (U' := (864514089002537990141 / 2000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (3672889927739643 / 5000000000000000 : ℚ)) + (q := (15407311007233661 / 20000000000000000 : ℚ)) + (U := (-(521780271597462009859 / 2000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_15 : Uω (aρ 15) (bρ 15) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2273,24 +2042,21 @@ lemma U_680_15 : have hlg : Real.log (46043263943697 / 62500000000000 : ℝ) ≤ (-(3055850814904569992253 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (46043263943697 / 62500000000000 : ℝ) = (46043263943697 / 31250000000000 : ℝ) / 2 ^ 1 by - norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (46043263943697 / 31250000000000 : ℚ)) - (U := (3875620988095430007747 / 10000000000000000000000 : ℚ)) - 10 (by decide +kernel)) : - Real.log (46043263943697 / 31250000000000 : ℝ) ≤ - (3875620988095430007747 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1386377317528733 / 2000000000000000 : ℝ)) (q := - (46043263943697 / 62500000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) (by norm_num [bρ_15]) - (by norm_num) (by norm_num [aρ_15, bρ_15]) (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (46043263943697 / 62500000000000 : ℚ)) + (r' := (46043263943697 / 31250000000000 : ℚ)) + (U := (-(3055850814904569992253 / 10000000000000000000000 : ℚ))) + (U' := (3875620988095430007747 / 10000000000000000000000 : ℚ)) + 1 10 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (1386377317528733 / 2000000000000000 : ℚ)) + (q := (46043263943697 / 62500000000000 : ℚ)) + (U := (-(3055850814904569992253 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680_16 : Uω (aρ 16) (bρ 16) (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2298,26 +2064,21 @@ lemma U_680_16 : have hlg : Real.log (14326574032209963 / 20000000000000000 : ℝ) ≤ (-(834040341612878975103 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (14326574032209963 / 20000000000000000 : ℝ) = - (14326574032209963 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (14326574032209963 / 10000000000000000 : ℚ)) - (U := (898827609137121024897 / 2500000000000000000000 : ℚ)) - 9 (by decide +kernel)) : - Real.log (14326574032209963 / 10000000000000000 : ℝ) ≤ - (898827609137121024897 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1669246952345147 / 2500000000000000 : ℝ)) (q := - (14326574032209963 / 20000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (14326574032209963 / 20000000000000000 : ℚ)) + (r' := (14326574032209963 / 10000000000000000 : ℚ)) + (U := (-(834040341612878975103 / 2500000000000000000000 : ℚ))) + (U' := (898827609137121024897 / 2500000000000000000000 : ℚ)) + 1 9 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (18213010252359 / 16000000000000 : ℚ)) + (s := (1669246952345147 / 2500000000000000 : ℚ)) + (q := (14326574032209963 / 20000000000000000 : ℚ)) + (U := (-(834040341612878975103 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_680 : Uρ (18213010252359 / 16000000000000 : ℝ) ≤ @@ -2409,10 +2170,14 @@ lemma U_681_1 : (r := (2420394504208369 / 2000000000000000 : ℚ)) (U := (381566729181073695513 / 2000000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (4727327797749 / 3906250000000 : ℝ)) (q := - (2420394504208369 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (4727327797749 / 3906250000000 : ℚ)) + (q := (2420394504208369 / 2000000000000000 : ℚ)) + (U := (381566729181073695513 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_2 : Uω (aρ 2) (bρ 2) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2425,10 +2190,14 @@ lemma U_681_2 : (r := (603906451432549 / 500000000000000 : ℚ)) (U := (944056028915092092057 / 5000000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (1207804118996571 / 1000000000000000 : ℝ)) (q := - (603906451432549 / 500000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (1207804118996571 / 1000000000000000 : ℚ)) + (q := (603906451432549 / 500000000000000 : ℚ)) + (U := (944056028915092092057 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_3 : Uω (aρ 3) (bρ 3) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2441,10 +2210,14 @@ lemma U_681_3 : (r := (4812205315787301 / 4000000000000000 : ℚ)) (U := (1848611035360319879371 / 10000000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (2406041163590051 / 2000000000000000 : ℝ)) (q := - (4812205315787301 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (2406041163590051 / 2000000000000000 : ℚ)) + (q := (4812205315787301 / 4000000000000000 : ℚ)) + (U := (1848611035360319879371 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_4 : Uω (aρ 4) (bρ 4) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2457,10 +2230,14 @@ lemma U_681_4 : (r := (23903292644316659 / 20000000000000000 : ℚ)) (U := (44570985859756852759 / 250000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (11950766064395409 / 10000000000000000 : ℝ)) (q := - (23903292644316659 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (11950766064395409 / 10000000000000000 : ℚ)) + (q := (23903292644316659 / 20000000000000000 : ℚ)) + (U := (44570985859756852759 / 250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_5 : Uω (aρ 5) (bρ 5) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2473,10 +2250,14 @@ lemma U_681_5 : (r := (739505383293149 / 625000000000000 : ℚ)) (U := (210287390033879084137 / 1250000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5914917802397259 / 5000000000000000 : ℝ)) (q := - (739505383293149 / 625000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (5914917802397259 / 5000000000000000 : ℚ)) + (q := (739505383293149 / 625000000000000 : ℚ)) + (U := (210287390033879084137 / 1250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_6 : Uω (aρ 6) (bρ 6) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2489,10 +2270,14 @@ lemma U_681_6 : (r := (2915458645235873 / 2500000000000000 : ℚ)) (U := (38434103813816542803 / 250000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5828286438220367 / 5000000000000000 : ℝ)) (q := - (2915458645235873 / 2500000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (5828286438220367 / 5000000000000000 : ℚ)) + (q := (2915458645235873 / 2500000000000000 : ℚ)) + (U := (38434103813816542803 / 250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_7 : Uω (aρ 7) (bρ 7) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2505,10 +2290,14 @@ lemma U_681_7 : (r := (22864183623441699 / 20000000000000000 : ℚ)) (U := (1338393787175108167323 / 10000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (11420748718755449 / 10000000000000000 : ℝ)) (q := - (22864183623441699 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (11420748718755449 / 10000000000000000 : ℚ)) + (q := (22864183623441699 / 20000000000000000 : ℚ)) + (U := (1338393787175108167323 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_8 : Uω (aρ 8) (bρ 8) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2521,10 +2310,14 @@ lemma U_681_8 : (r := (22274490047633971 / 20000000000000000 : ℚ)) (U := (538549030281882261609 / 5000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (11114596794287721 / 10000000000000000 : ℝ)) (q := - (22274490047633971 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (11114596794287721 / 10000000000000000 : ℚ)) + (q := (22274490047633971 / 20000000000000000 : ℚ)) + (U := (538549030281882261609 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_9 : Uω (aρ 9) (bρ 9) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2537,10 +2330,14 @@ lemma U_681_9 : (r := (10776905848559021 / 10000000000000000 : ℚ)) (U := (748204042513207311507 / 10000000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (670930254508237 / 625000000000000 : ℝ)) (q := - (10776905848559021 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (670930254508237 / 625000000000000 : ℚ)) + (q := (10776905848559021 / 10000000000000000 : ℚ)) + (U := (748204042513207311507 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_10 : Uω (aρ 10) (bρ 10) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2553,11 +2350,14 @@ lemma U_681_10 : (r := (20715460896111329 / 20000000000000000 : ℚ)) (U := (351480511177384359847 / 10000000000000000000000 : ℚ)) 4 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10285092304620079 / 10000000000000000 : ℝ)) (q := - (20715460896111329 / 20000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (10285092304620079 / 10000000000000000 : ℚ)) + (q := (20715460896111329 / 20000000000000000 : ℚ)) + (U := (351480511177384359847 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_11 : Uω (aρ 11) (bρ 11) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2565,26 +2365,21 @@ lemma U_681_11 : have hlg : Real.log (19789443919795677 / 20000000000000000 : ℝ) ≤ (-(26459032811501839539 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19789443919795677 / 20000000000000000 : ℝ) = - (19789443919795677 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19789443919795677 / 10000000000000000 : ℚ)) - (U := (1706408917938498160461 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19789443919795677 / 10000000000000000 : ℝ) ≤ - (1706408917938498160461 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9777551954509427 / 10000000000000000 : ℝ)) (q := - (19789443919795677 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19789443919795677 / 20000000000000000 : ℚ)) + (r' := (19789443919795677 / 10000000000000000 : ℚ)) + (U := (-(26459032811501839539 / 2500000000000000000000 : ℚ))) + (U' := (1706408917938498160461 / 2500000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (9777551954509427 / 10000000000000000 : ℚ)) + (q := (19789443919795677 / 20000000000000000 : ℚ)) + (U := (-(26459032811501839539 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_12 : Uω (aρ 12) (bρ 12) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2592,26 +2387,21 @@ lemma U_681_12 : have hlg : Real.log (18823493977979713 / 20000000000000000 : ℝ) ≤ (-(151566259945222584619 / 2500000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (18823493977979713 / 20000000000000000 : ℝ) = - (18823493977979713 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (18823493977979713 / 10000000000000000 : ℚ)) - (U := (1581301690804777415381 / 2500000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (18823493977979713 / 10000000000000000 : ℝ) ≤ - (1581301690804777415381 / 2500000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9235302109378463 / 10000000000000000 : ℝ)) (q := - (18823493977979713 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (18823493977979713 / 20000000000000000 : ℚ)) + (r' := (18823493977979713 / 10000000000000000 : ℚ)) + (U := (-(151566259945222584619 / 2500000000000000000000 : ℚ))) + (U' := (1581301690804777415381 / 2500000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (9235302109378463 / 10000000000000000 : ℚ)) + (q := (18823493977979713 / 20000000000000000 : ℚ)) + (U := (-(151566259945222584619 / 2500000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_13 : Uω (aρ 13) (bρ 13) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2619,26 +2409,21 @@ lemma U_681_13 : have hlg : Real.log (1788207217931651 / 2000000000000000 : ℝ) ≤ (-(1119336165660419824783 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1788207217931651 / 2000000000000000 : ℝ) = - (1788207217931651 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1788207217931651 / 1000000000000000 : ℚ)) - (U := (5812135637339580175217 / 10000000000000000000000 : ℚ)) - 13 (by decide +kernel)) : - Real.log (1788207217931651 / 1000000000000000 : ℝ) ≤ - (5812135637339580175217 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (434663102615513 / 500000000000000 : ℝ)) (q := - (1788207217931651 / 2000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1788207217931651 / 2000000000000000 : ℚ)) + (r' := (1788207217931651 / 1000000000000000 : ℚ)) + (U := (-(1119336165660419824783 / 10000000000000000000000 : ℚ))) + (U' := (5812135637339580175217 / 10000000000000000000000 : ℚ)) + 1 13 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (434663102615513 / 500000000000000 : ℚ)) + (q := (1788207217931651 / 2000000000000000 : ℚ)) + (U := (-(1119336165660419824783 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_14 : Uω (aρ 14) (bρ 14) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2646,26 +2431,21 @@ lemma U_681_14 : have hlg : Real.log (17042696554316489 / 20000000000000000 : ℝ) ≤ (-(800052579600481050621 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (17042696554316489 / 20000000000000000 : ℝ) = - (17042696554316489 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (17042696554316489 / 10000000000000000 : ℚ)) - (U := (2665683321899518949379 / 5000000000000000000000 : ℚ)) - 12 (by decide +kernel)) : - Real.log (17042696554316489 / 10000000000000000 : ℝ) ≤ - (2665683321899518949379 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (8197813712355239 / 10000000000000000 : ℝ)) (q := - (17042696554316489 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (17042696554316489 / 20000000000000000 : ℚ)) + (r' := (17042696554316489 / 10000000000000000 : ℚ)) + (U := (-(800052579600481050621 / 5000000000000000000000 : ℚ))) + (U' := (2665683321899518949379 / 5000000000000000000000 : ℚ)) + 1 12 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (8197813712355239 / 10000000000000000 : ℚ)) + (q := (17042696554316489 / 20000000000000000 : ℚ)) + (U := (-(800052579600481050621 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_15 : Uω (aρ 15) (bρ 15) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2673,26 +2453,21 @@ lemma U_681_15 : have hlg : Real.log (16388388784320793 / 20000000000000000 : ℝ) ≤ (-(1991591901709806684277 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (16388388784320793 / 20000000000000000 : ℝ) = - (16388388784320793 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (16388388784320793 / 10000000000000000 : ℚ)) - (U := (4939879901290193315723 / 10000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (16388388784320793 / 10000000000000000 : ℝ) ≤ - (4939879901290193315723 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (7803079219774543 / 10000000000000000 : ℝ)) (q := - (16388388784320793 / 20000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (16388388784320793 / 20000000000000000 : ℚ)) + (r' := (16388388784320793 / 10000000000000000 : ℚ)) + (U := (-(1991591901709806684277 / 10000000000000000000000 : ℚ))) + (U' := (4939879901290193315723 / 10000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (7803079219774543 / 10000000000000000 : ℚ)) + (q := (16388388784320793 / 20000000000000000 : ℚ)) + (U := (-(1991591901709806684277 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681_16 : Uω (aρ 16) (bρ 16) (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2700,26 +2475,21 @@ lemma U_681_16 : have hlg : Real.log (7997356374547131 / 10000000000000000 : ℝ) ≤ (-(1117370294237785446319 / 5000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (7997356374547131 / 10000000000000000 : ℝ) = - (7997356374547131 / 5000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (7997356374547131 / 5000000000000000 : ℚ)) - (U := (2348365607262214553681 / 5000000000000000000000 : ℚ)) - 11 (by decide +kernel)) : - Real.log (7997356374547131 / 5000000000000000 : ℝ) ≤ - (2348365607262214553681 / 5000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (1890443709014503 / 2500000000000000 : ℝ)) (q := - (7997356374547131 / 10000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (7997356374547131 / 10000000000000000 : ℚ)) + (r' := (7997356374547131 / 5000000000000000 : ℚ)) + (U := (-(1117370294237785446319 / 5000000000000000000000 : ℚ))) + (U' := (2348365607262214553681 / 5000000000000000000000 : ℚ)) + 1 11 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (1946637295669 / 1600000000000 : ℚ)) + (s := (1890443709014503 / 2500000000000000 : ℚ)) + (q := (7997356374547131 / 10000000000000000 : ℚ)) + (U := (-(1117370294237785446319 / 5000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_681 : Uρ (1946637295669 / 1600000000000 : ℝ) ≤ @@ -2811,10 +2581,14 @@ lemma U_682_1 : (r := (2733735486528567 / 2000000000000000 : ℚ)) (U := (1562609017187395006033 / 5000000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (1366866560502567 / 1000000000000000 : ℝ)) (q := - (2733735486528567 / 2000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (1366866560502567 / 1000000000000000 : ℚ)) + (q := (2733735486528567 / 2000000000000000 : ℚ)) + (U := (1562609017187395006033 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_2 : Uω (aρ 2) (bρ 2) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2827,10 +2601,14 @@ lemma U_682_2 : (r := (13644842494784013 / 10000000000000000 : ℚ)) (U := (621553036055481657661 / 2000000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (6822382370909013 / 5000000000000000 : ℝ)) (q := - (13644842494784013 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (6822382370909013 / 5000000000000000 : ℚ)) + (q := (13644842494784013 / 10000000000000000 : ℚ)) + (U := (621553036055481657661 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_3 : Uω (aρ 3) (bρ 3) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2843,10 +2621,14 @@ lemma U_682_3 : (r := (5438900839273781 / 4000000000000000 : ℚ)) (U := (768206569321752291863 / 2500000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (2719396010993781 / 2000000000000000 : ℝ)) (q := - (5438900839273781 / 4000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (2719396010993781 / 2000000000000000 : ℚ)) + (q := (5438900839273781 / 4000000000000000 : ℚ)) + (U := (768206569321752291863 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_4 : Uω (aρ 4) (bρ 4) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2859,10 +2641,14 @@ lemma U_682_4 : (r := (1351845172554389 / 1000000000000000 : ℚ)) (U := (3014704537217327050923 / 10000000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (675883674537639 / 500000000000000 : ℝ)) (q := - (1351845172554389 / 1000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (675883674537639 / 500000000000000 : ℚ)) + (q := (1351845172554389 / 1000000000000000 : ℚ)) + (U := (3014704537217327050923 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_5 : Uω (aρ 5) (bρ 5) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2875,10 +2661,14 @@ lemma U_682_5 : (r := (1339905270349957 / 1000000000000000 : ℚ)) (U := (585197835390417916143 / 2000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (669853268299957 / 500000000000000 : ℝ)) (q := - (1339905270349957 / 1000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (669853268299957 / 500000000000000 : ℚ)) + (q := (1339905270349957 / 1000000000000000 : ℚ)) + (U := (585197835390417916143 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_6 : Uω (aρ 6) (bρ 6) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2891,10 +2681,14 @@ lemma U_682_6 : (r := (26458322685085169 / 20000000000000000 : ℚ)) (U := (1399192462686000616281 / 5000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (13224523019225169 / 10000000000000000 : ℝ)) (q := - (26458322685085169 / 20000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (13224523019225169 / 10000000000000000 : ℚ)) + (q := (26458322685085169 / 20000000000000000 : ℚ)) + (U := (1399192462686000616281 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_7 : Uω (aρ 7) (bρ 7) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2907,10 +2701,14 @@ lemma U_682_7 : (r := (13000163388913701 / 10000000000000000 : ℚ)) (U := (40996380119763539301 / 156250000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (6495094246363701 / 5000000000000000 : ℝ)) (q := - (13000163388913701 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (6495094246363701 / 5000000000000000 : ℚ)) + (q := (13000163388913701 / 10000000000000000 : ℚ)) + (U := (40996380119763539301 / 156250000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_8 : Uω (aρ 8) (bρ 8) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2923,10 +2721,14 @@ lemma U_682_8 : (r := (25413491697247327 / 20000000000000000 : ℚ)) (U := (2395479286330499915887 / 10000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (12686895063487327 / 10000000000000000 : ℝ)) (q := - (25413491697247327 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (12686895063487327 / 10000000000000000 : ℚ)) + (q := (25413491697247327 / 20000000000000000 : ℚ)) + (U := (2395479286330499915887 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_9 : Uω (aρ 9) (bρ 9) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2939,10 +2741,14 @@ lemma U_682_9 : (r := (24697917409205917 / 20000000000000000 : ℚ)) (U := (2109866511084314583863 / 10000000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (12312286403805917 / 10000000000000000 : ℝ)) (q := - (24697917409205917 / 20000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (12312286403805917 / 10000000000000000 : ℚ)) + (q := (24697917409205917 / 20000000000000000 : ℚ)) + (U := (2109866511084314583863 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_10 : Uω (aρ 10) (bρ 10) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2955,11 +2761,14 @@ lemma U_682_10 : (r := (11934028186673021 / 10000000000000000 : ℚ)) (U := (1768087379828123108613 / 10000000000000000000000 : ℚ)) 7 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5935492200720521 / 5000000000000000 : ℝ)) (q := - (11934028186673021 / 10000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (5935492200720521 / 5000000000000000 : ℚ)) + (q := (11934028186673021 / 10000000000000000 : ℚ)) + (U := (1768087379828123108613 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_11 : Uω (aρ 11) (bρ 11) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2972,11 +2781,14 @@ lemma U_682_11 : (r := (11477584138870181 / 10000000000000000 : ℚ)) (U := (1378108348866220666213 / 10000000000000000000000 : ℚ)) 6 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (5688286466020181 / 5000000000000000 : ℝ)) (q := - (11477584138870181 / 10000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (5688286466020181 / 5000000000000000 : ℚ)) + (q := (11477584138870181 / 10000000000000000 : ℚ)) + (U := (1378108348866220666213 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_12 : Uω (aρ 12) (bρ 12) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -2989,11 +2801,14 @@ lemma U_682_12 : (r := (22007962546276019 / 20000000000000000 : ℚ)) (U := (956720482436799679737 / 10000000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10853067297261019 / 10000000000000000 : ℝ)) (q := - (22007962546276019 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (10853067297261019 / 10000000000000000 : ℚ)) + (q := (22007962546276019 / 20000000000000000 : ℚ)) + (U := (956720482436799679737 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_13 : Uω (aρ 13) (bρ 13) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -3006,11 +2821,14 @@ lemma U_682_13 : (r := (21090872444982791 / 20000000000000000 : ℚ)) (U := (531080877900712560969 / 10000000000000000000000 : ℚ)) 5 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (10335358937562791 / 10000000000000000 : ℝ)) (q := - (21090872444982791 / 20000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (10335358937562791 / 10000000000000000 : ℚ)) + (q := (21090872444982791 / 20000000000000000 : ℚ)) + (U := (531080877900712560969 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_14 : Uω (aρ 14) (bρ 14) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -3023,11 +2841,14 @@ lemma U_682_14 : (r := (20279378520574633 / 20000000000000000 : ℚ)) (U := (34680649393365873701 / 2500000000000000000000 : ℚ)) 3 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (9867792298199633 / 10000000000000000 : ℝ)) (q := - (20279378520574633 / 20000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (9867792298199633 / 10000000000000000 : ℚ)) + (q := (20279378520574633 / 20000000000000000 : ℚ)) + (U := (34680649393365873701 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_15 : Uω (aρ 15) (bρ 15) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -3035,26 +2856,21 @@ lemma U_682_15 : have hlg : Real.log (1965169040399109 / 2000000000000000 : ℝ) ≤ (-(175689130303678076623 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (1965169040399109 / 2000000000000000 : ℝ) = - (1965169040399109 / 1000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (1965169040399109 / 1000000000000000 : ℚ)) - (U := (6755782672696321923377 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (1965169040399109 / 1000000000000000 : ℝ) ≤ - (6755782672696321923377 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (949967745903109 / 1000000000000000 : ℝ)) (q := - (1965169040399109 / 2000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (1965169040399109 / 2000000000000000 : ℚ)) + (r' := (1965169040399109 / 1000000000000000 : ℚ)) + (U := (-(175689130303678076623 / 10000000000000000000000 : ℚ))) + (U' := (6755782672696321923377 / 10000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (949967745903109 / 1000000000000000 : ℚ)) + (q := (1965169040399109 / 2000000000000000 : ℚ)) + (U := (-(175689130303678076623 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682_16 : Uω (aρ 16) (bρ 16) (2746637295669 / 2000000000000 : ℝ) ≤ @@ -3062,26 +2878,21 @@ lemma U_682_16 : have hlg : Real.log (19276430760921297 / 20000000000000000 : ℝ) ≤ (-(368491277579048029599 / 10000000000000000000000 : ℝ)) := by - have h := - log_le_of_split_neg 1 - (show - (19276430760921297 / 20000000000000000 : ℝ) = - (19276430760921297 / 10000000000000000 : ℝ) / 2 ^ 1 - by norm_num) - (by norm_num) - ((by - simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using log_le_of_ge_one_rat - (r := (19276430760921297 / 10000000000000000 : ℚ)) - (U := (6562980525420951970401 / 10000000000000000000000 : ℚ)) - 14 (by decide +kernel)) : - Real.log (19276430760921297 / 10000000000000000 : ℝ) ≤ - (6562980525420951970401 / 10000000000000000000000 : ℝ)) - linarith only [h, Real.log_two_gt_d9] - exact - Uω_le_right_certificate (s := (9276789467471297 / 10000000000000000 : ℝ)) (q := - (19276430760921297 / 20000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg] using + log_le_of_split_neg_rational + (r := (19276430760921297 / 20000000000000000 : ℚ)) + (r' := (19276430760921297 / 10000000000000000 : ℚ)) + (U := (-(368491277579048029599 / 10000000000000000000000 : ℚ))) + (U' := (6562980525420951970401 / 10000000000000000000000 : ℚ)) + 1 14 (by decide +kernel) (by decide +kernel) + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (2746637295669 / 2000000000000 : ℚ)) + (s := (9276789467471297 / 10000000000000000 : ℚ)) + (q := (19276430760921297 / 20000000000000000 : ℚ)) + (U := (-(368491277579048029599 / 10000000000000000000000 : ℚ))) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_682 : Uρ (2746637295669 / 2000000000000 : ℝ) ≤ @@ -3169,10 +2980,14 @@ lemma U_683_1 : (r := (33604172798388249 / 20000000000000000 : ℚ)) (U := (648647470165495546441 / 1250000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (16802076777300749 / 10000000000000000 : ℝ)) (q := - (33604172798388249 / 20000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (16802076777300749 / 10000000000000000 : ℚ)) + (q := (33604172798388249 / 20000000000000000 : ℚ)) + (U := (648647470165495546441 / 1250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_2 : Uω (aρ 2) (bρ 2) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3185,10 +3000,14 @@ lemma U_683_2 : (r := (16778263776351059 / 10000000000000000 : ℚ)) (U := (646873916084388180027 / 1250000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8389100272062309 / 5000000000000000 : ℝ)) (q := - (16778263776351059 / 10000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (8389100272062309 / 5000000000000000 : ℚ)) + (q := (16778263776351059 / 10000000000000000 : ℚ)) + (U := (646873916084388180027 / 1250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_3 : Uω (aρ 3) (bρ 3) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3201,10 +3020,14 @@ lemma U_683_3 : (r := (16730709809385323 / 10000000000000000 : ℚ)) (U := (5146608484439031249377 / 10000000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8365244358271573 / 5000000000000000 : ℝ)) (q := - (16730709809385323 / 10000000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (8365244358271573 / 5000000000000000 : ℚ)) + (q := (16730709809385323 / 10000000000000000 : ℚ)) + (U := (5146608484439031249377 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_4 : Uω (aρ 4) (bρ 4) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3217,10 +3040,14 @@ lemma U_683_4 : (r := (16652004933609187 / 10000000000000000 : ℚ)) (U := (637431915769893316069 / 1250000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8325686573027937 / 5000000000000000 : ℝ)) (q := - (16652004933609187 / 10000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (8325686573027937 / 5000000000000000 : ℚ)) + (q := (16652004933609187 / 10000000000000000 : ℚ)) + (U := (637431915769893316069 / 1250000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_5 : Uω (aρ 5) (bρ 5) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3233,10 +3060,14 @@ lemma U_683_5 : (r := (16532836162270769 / 10000000000000000 : ℚ)) (U := (15711355649568528379 / 31250000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8265612761357019 / 5000000000000000 : ℝ)) (q := - (16532836162270769 / 10000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (8265612761357019 / 5000000000000000 : ℚ)) + (q := (16532836162270769 / 10000000000000000 : ℚ)) + (U := (15711355649568528379 / 31250000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_6 : Uω (aρ 6) (bρ 6) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3249,10 +3080,14 @@ lemma U_683_6 : (r := (2045432067349599 / 1250000000000000 : ℚ)) (U := (1231163739354149495203 / 2500000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (4089926662726521 / 2500000000000000 : ℝ)) (q := - (2045432067349599 / 1250000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (4089926662726521 / 2500000000000000 : ℚ)) + (q := (2045432067349599 / 1250000000000000 : ℚ)) + (U := (1231163739354149495203 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_7 : Uω (aρ 7) (bρ 7) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3265,10 +3100,14 @@ lemma U_683_7 : (r := (16135508405435549 / 10000000000000000 : ℚ)) (U := (4784372414919632677529 / 10000000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8063735882471799 / 5000000000000000 : ℝ)) (q := - (16135508405435549 / 10000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (8063735882471799 / 5000000000000000 : ℚ)) + (q := (16135508405435549 / 10000000000000000 : ℚ)) + (U := (4784372414919632677529 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_8 : Uω (aρ 8) (bρ 8) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3281,10 +3120,14 @@ lemma U_683_8 : (r := (15844083326734951 / 10000000000000000 : ℚ)) (U := (1150527614874777660297 / 2500000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (7914081629441201 / 5000000000000000 : ℝ)) (q := - (15844083326734951 / 10000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (7914081629441201 / 5000000000000000 : ℚ)) + (q := (15844083326734951 / 10000000000000000 : ℚ)) + (U := (1150527614874777660297 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_9 : Uω (aρ 9) (bρ 9) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3297,10 +3140,14 @@ lemma U_683_9 : (r := (15489801450345909 / 10000000000000000 : ℚ)) (U := (4375967434278497798067 / 10000000000000000000000 : ℚ)) 10 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (7730282567232159 / 5000000000000000 : ℝ)) (q := - (15489801450345909 / 10000000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (7730282567232159 / 5000000000000000 : ℚ)) + (q := (15489801450345909 / 10000000000000000 : ℚ)) + (U := (4375967434278497798067 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_10 : Uω (aρ 10) (bρ 10) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3313,11 +3160,14 @@ lemma U_683_10 : (r := (6032235606512157 / 4000000000000000 : ℚ)) (U := (4108233282580037516371 / 10000000000000000000000 : ℚ)) 10 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (3006139859965657 / 2000000000000000 : ℝ)) (q := - (6032235606512157 / 4000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (3006139859965657 / 2000000000000000 : ℚ)) + (q := (6032235606512157 / 4000000000000000 : ℚ)) + (U := (4108233282580037516371 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_11 : Uω (aρ 11) (bρ 11) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3330,11 +3180,14 @@ lemma U_683_11 : (r := (29265542826264307 / 20000000000000000 : ℚ)) (U := (761357075335845670987 / 2000000000000000000000 : ℚ)) 10 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (14553540719736807 / 10000000000000000 : ℝ)) (q := - (29265542826264307 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (14553540719736807 / 10000000000000000 : ℚ)) + (q := (29265542826264307 / 20000000000000000 : ℚ)) + (U := (761357075335845670987 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_12 : Uω (aρ 12) (bρ 12) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3347,11 +3200,14 @@ lemma U_683_12 : (r := (28342232281010363 / 20000000000000000 : ℚ)) (U := (139448290184602758597 / 400000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (14053930271167863 / 10000000000000000 : ℝ)) (q := - (28342232281010363 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (14053930271167863 / 10000000000000000 : ℚ)) + (q := (28342232281010363 / 20000000000000000 : ℚ)) + (U := (139448290184602758597 / 400000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_13 : Uω (aρ 13) (bρ 13) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3364,11 +3220,14 @@ lemma U_683_13 : (r := (6863769907032257 / 5000000000000000 : ℚ)) (U := (3168189274869361871549 / 10000000000000000000000 : ℚ)) 9 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (1695769919985191 / 1250000000000000 : ℝ)) (q := - (6863769907032257 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (1695769919985191 / 1250000000000000 : ℚ)) + (q := (6863769907032257 / 5000000000000000 : ℚ)) + (U := (3168189274869361871549 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_14 : Uω (aρ 14) (bρ 14) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3381,11 +3240,14 @@ lemma U_683_14 : (r := (13338298652980011 / 10000000000000000 : ℚ)) (U := (288054402101994101473 / 1000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (6565802161378761 / 5000000000000000 : ℝ)) (q := - (13338298652980011 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (6565802161378761 / 5000000000000000 : ℚ)) + (q := (13338298652980011 / 10000000000000000 : ℚ)) + (U := (288054402101994101473 / 1000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_15 : Uω (aρ 15) (bρ 15) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3398,11 +3260,14 @@ lemma U_683_15 : (r := (3259910100253591 / 2500000000000000 : ℚ)) (U := (1327044432574458074269 / 5000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (3198465274060307 / 2500000000000000 : ℝ)) (q := - (3259910100253591 / 2500000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (3198465274060307 / 2500000000000000 : ℚ)) + (q := (3259910100253591 / 2500000000000000 : ℚ)) + (U := (1327044432574458074269 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683_16 : Uω (aρ 16) (bρ 16) (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3415,10 +3280,14 @@ lemma U_683_16 : (r := (803888497956787 / 625000000000000 : ℚ)) (U := (2517089256916817378273 / 10000000000000000000000 : ℚ)) 8 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (3147845970084921 / 2500000000000000 : ℝ)) (q := - (803888497956787 / 625000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) (by norm_num [bρ_16]) - (by norm_num) (by norm_num [aρ_16, bρ_16]) (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (6746637295669 / 4000000000000 : ℚ)) + (s := (3147845970084921 / 2500000000000000 : ℚ)) + (q := (803888497956787 / 625000000000000 : ℚ)) + (U := (2517089256916817378273 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_683 : Uρ (6746637295669 / 4000000000000 : ℝ) ≤ @@ -3503,10 +3372,14 @@ lemma U_684_1 : Uω (aρ 1) (bρ 1) (2 : ℝ) ≤ (431197938622519678389 / 62500 (r := (19935494672365351 / 10000000000000000 : ℚ)) (U := (431197938622519678389 / 625000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (9967743281407851 / 5000000000000000 : ℝ)) (q := - (19935494672365351 / 10000000000000000 : ℝ)) (aρ_lt_bρ 1 (by decide)) (by norm_num [bρ_1]) - (by norm_num) (by norm_num [aρ_1, bρ_1]) (by norm_num [aρ_1, bρ_1]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 1) (t := (2 : ℚ)) + (s := (9967743281407851 / 5000000000000000 : ℚ)) + (q := (19935494672365351 / 10000000000000000 : ℚ)) + (U := (431197938622519678389 / 625000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_2 : Uω (aρ 2) (bρ 2) (2 : ℝ) ≤ (1721803564318625397281 / 2500000000000000000000 : ℝ) := by @@ -3518,10 +3391,14 @@ lemma U_684_2 : (r := (39823360975531723 / 20000000000000000 : ℚ)) (U := (1721803564318625397281 / 2500000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (19911627206126723 / 10000000000000000 : ℝ)) (q := - (39823360975531723 / 20000000000000000 : ℝ)) (aρ_lt_bρ 2 (by decide)) (by norm_num [bρ_2]) - (by norm_num) (by norm_num [aρ_2, bρ_2]) (by norm_num [aρ_2, bρ_2]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 2) (t := (2 : ℚ)) + (s := (19911627206126723 / 10000000000000000 : ℚ)) + (q := (39823360975531723 / 20000000000000000 : ℚ)) + (U := (1721803564318625397281 / 2500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_3 : Uω (aρ 3) (bρ 3) (2 : ℝ) ≤ (3431657896680287743107 / 5000000000000000000000 : ℝ) := by @@ -3533,10 +3410,14 @@ lemma U_684_3 : (r := (993207572309059 / 500000000000000 : ℚ)) (U := (3431657896680287743107 / 5000000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (124149782683171 / 62500000000000 : ℝ)) (q := - (993207572309059 / 500000000000000 : ℝ)) (aρ_lt_bρ 3 (by decide)) (by norm_num [bρ_3]) - (by norm_num) (by norm_num [aρ_3, bρ_3]) (by norm_num [aρ_3, bρ_3]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 3) (t := (2 : ℚ)) + (s := (124149782683171 / 62500000000000 : ℚ)) + (q := (993207572309059 / 500000000000000 : ℚ)) + (U := (3431657896680287743107 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_4 : Uω (aρ 4) (bρ 4) (2 : ℝ) ≤ (6823648472170288821807 / 10000000000000000000000 : ℝ) := by @@ -3548,10 +3429,14 @@ lemma U_684_4 : (r := (39571023506073419 / 20000000000000000 : ℚ)) (U := (6823648472170288821807 / 10000000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (19784980024083419 / 10000000000000000 : ℝ)) (q := - (39571023506073419 / 20000000000000000 : ℝ)) (aρ_lt_bρ 4 (by decide)) (by norm_num [bρ_4]) - (by norm_num) (by norm_num [aρ_4, bρ_4]) (by norm_num [aρ_4, bρ_4]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 4) (t := (2 : ℚ)) + (s := (19784980024083419 / 10000000000000000 : ℚ)) + (q := (39571023506073419 / 20000000000000000 : ℚ)) + (U := (6823648472170288821807 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_5 : Uω (aρ 5) (bρ 5) (2 : ℝ) ≤ (6763315653946060878467 / 10000000000000000000000 : ℝ) := by @@ -3563,10 +3448,14 @@ lemma U_684_5 : (r := (7866599825072169 / 4000000000000000 : ℚ)) (U := (6763315653946060878467 / 10000000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (3933029112541169 / 2000000000000000 : ℝ)) (q := - (7866599825072169 / 4000000000000000 : ℝ)) (aρ_lt_bρ 5 (by decide)) (by norm_num [bρ_5]) - (by norm_num) (by norm_num [aρ_5, bρ_5]) (by norm_num [aρ_5, bρ_5]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 5) (t := (2 : ℚ)) + (s := (3933029112541169 / 2000000000000000 : ℚ)) + (q := (7866599825072169 / 4000000000000000 : ℚ)) + (U := (6763315653946060878467 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_6 : Uω (aρ 6) (bρ 6) (2 : ℝ) ≤ (333849709093393011791 / 500000000000000000000 : ℝ) := by have hlg : @@ -3577,10 +3466,14 @@ lemma U_684_6 : Uω (aρ 6) (bρ 6) (2 : ℝ) ≤ (333849709093393011791 / 50000 (r := (1949746605406931 / 1000000000000000 : ℚ)) (U := (333849709093393011791 / 500000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (974715946031181 / 500000000000000 : ℝ)) (q := - (1949746605406931 / 1000000000000000 : ℝ)) (aρ_lt_bρ 6 (by decide)) (by norm_num [bρ_6]) - (by norm_num) (by norm_num [aρ_6, bρ_6]) (by norm_num [aρ_6, bρ_6]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 6) (t := (2 : ℚ)) + (s := (974715946031181 / 500000000000000 : ℚ)) + (q := (1949746605406931 / 1000000000000000 : ℚ)) + (U := (333849709093393011791 / 500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_7 : Uω (aρ 7) (bρ 7) (2 : ℝ) ≤ (3279879678491493456121 / 5000000000000000000000 : ℝ) := by @@ -3592,10 +3485,14 @@ lemma U_684_7 : (r := (38540444995663327 / 20000000000000000 : ℚ)) (U := (3279879678491493456121 / 5000000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (19263493188908327 / 10000000000000000 : ℝ)) (q := - (38540444995663327 / 20000000000000000 : ℝ)) (aρ_lt_bρ 7 (by decide)) (by norm_num [bρ_7]) - (by norm_num) (by norm_num [aρ_7, bρ_7]) (by norm_num [aρ_7, bρ_7]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 7) (t := (2 : ℚ)) + (s := (19263493188908327 / 10000000000000000 : ℚ)) + (q := (38540444995663327 / 20000000000000000 : ℚ)) + (U := (3279879678491493456121 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_8 : Uω (aρ 8) (bρ 8) (2 : ℝ) ≤ (6408070500101273547501 / 10000000000000000000000 : ℝ) := by @@ -3607,10 +3504,14 @@ lemma U_684_8 : (r := (37960241040023251 / 20000000000000000 : ℚ)) (U := (6408070500101273547501 / 10000000000000000000000 : ℚ)) 14 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (18966830884608251 / 10000000000000000 : ℝ)) (q := - (37960241040023251 / 20000000000000000 : ℝ)) (aρ_lt_bρ 8 (by decide)) (by norm_num [bρ_8]) - (by norm_num) (by norm_num [aρ_8, bρ_8]) (by norm_num [aρ_8, bρ_8]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 8) (t := (2 : ℚ)) + (s := (18966830884608251 / 10000000000000000 : ℚ)) + (q := (37960241040023251 / 20000000000000000 : ℚ)) + (U := (6408070500101273547501 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_9 : Uω (aρ 9) (bρ 9) (2 : ℝ) ≤ (3110439556119279087301 / 5000000000000000000000 : ℝ) := by @@ -3622,10 +3523,14 @@ lemma U_684_9 : (r := (298050139723413 / 160000000000000 : ℚ)) (U := (3110439556119279087301 / 5000000000000000000000 : ℚ)) 13 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (148830583506973 / 80000000000000 : ℝ)) (q := - (298050139723413 / 160000000000000 : ℝ)) (aρ_lt_bρ 9 (by decide)) (by norm_num [bρ_9]) - (by norm_num) (by norm_num [aρ_9, bρ_9]) (by norm_num [aρ_9, bρ_9]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 9) (t := (2 : ℚ)) + (s := (148830583506973 / 80000000000000 : ℚ)) + (q := (298050139723413 / 160000000000000 : ℚ)) + (U := (3110439556119279087301 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_10 : Uω (aρ 10) (bρ 10) (2 : ℝ) ≤ (6000773764786687711391 / 10000000000000000000000 : ℝ) := by @@ -3637,11 +3542,14 @@ lemma U_684_10 : (r := (3644519589963523 / 2000000000000000 : ℚ)) (U := (6000773764786687711391 / 10000000000000000000000 : ℚ)) 13 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (1818131040607523 / 1000000000000000 : ℝ)) (q := - (3644519589963523 / 2000000000000000 : ℝ)) (aρ_lt_bρ 10 (by decide)) - (by norm_num [bρ_10]) (by norm_num) (by norm_num [aρ_10, bρ_10]) - (by norm_num [aρ_10, bρ_10]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 10) (t := (2 : ℚ)) + (s := (1818131040607523 / 1000000000000000 : ℚ)) + (q := (3644519589963523 / 2000000000000000 : ℚ)) + (U := (6000773764786687711391 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_11 : Uω (aρ 11) (bρ 11) (2 : ℝ) ≤ (5755005827102536483859 / 10000000000000000000000 : ℝ) := by @@ -3653,11 +3561,14 @@ lemma U_684_11 : (r := (35560407008524539 / 20000000000000000 : ℚ)) (U := (5755005827102536483859 / 10000000000000000000000 : ℚ)) 13 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (17714998141169539 / 10000000000000000 : ℝ)) (q := - (35560407008524539 / 20000000000000000 : ℝ)) (aρ_lt_bρ 11 (by decide)) - (by norm_num [bρ_11]) (by norm_num) (by norm_num [aρ_11, bρ_11]) - (by norm_num [aρ_11, bρ_11]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 11) (t := (2 : ℚ)) + (s := (17714998141169539 / 10000000000000000 : ℚ)) + (q := (35560407008524539 / 20000000000000000 : ℚ)) + (U := (5755005827102536483859 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_12 : Uω (aρ 12) (bρ 12) (2 : ℝ) ≤ (1099230232572658765387 / 2000000000000000000000 : ℝ) := by @@ -3669,11 +3580,14 @@ lemma U_684_12 : (r := (34651720907416137 / 20000000000000000 : ℚ)) (U := (1099230232572658765387 / 2000000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (17230012136746137 / 10000000000000000 : ℝ)) (q := - (34651720907416137 / 20000000000000000 : ℝ)) (aρ_lt_bρ 12 (by decide)) - (by norm_num [bρ_12]) (by norm_num) (by norm_num [aρ_12, bρ_12]) - (by norm_num [aρ_12, bρ_12]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 12) (t := (2 : ℚ)) + (s := (17230012136746137 / 10000000000000000 : ℚ)) + (q := (34651720907416137 / 20000000000000000 : ℚ)) + (U := (1099230232572658765387 / 2000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_13 : Uω (aρ 13) (bρ 13) (2 : ℝ) ≤ (2621030225880535406049 / 5000000000000000000000 : ℝ) := by @@ -3685,11 +3599,14 @@ lemma U_684_13 : (r := (8445586165416359 / 5000000000000000 : ℚ)) (U := (2621030225880535406049 / 5000000000000000000000 : ℚ)) 12 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (4190004408147609 / 2500000000000000 : ℝ)) (q := - (8445586165416359 / 5000000000000000 : ℝ)) (aρ_lt_bρ 13 (by decide)) - (by norm_num [bρ_13]) (by norm_num) (by norm_num [aρ_13, bρ_13]) - (by norm_num [aρ_13, bρ_13]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 13) (t := (2 : ℚ)) + (s := (4190004408147609 / 2500000000000000 : ℚ)) + (q := (8445586165416359 / 5000000000000000 : ℚ)) + (U := (2621030225880535406049 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_14 : Uω (aρ 14) (bρ 14) (2 : ℝ) ≤ (250733810854960598567 / 500000000000000000000 : ℝ) := by @@ -3701,11 +3618,14 @@ lemma U_684_14 : (r := (16511427463010601 / 10000000000000000 : ℚ)) (U := (250733810854960598567 / 500000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8172227590995601 / 5000000000000000 : ℝ)) (q := - (16511427463010601 / 10000000000000000 : ℝ)) (aρ_lt_bρ 14 (by decide)) - (by norm_num [bρ_14]) (by norm_num) (by norm_num [aρ_14, bρ_14]) - (by norm_num [aρ_14, bρ_14]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 14) (t := (2 : ℚ)) + (s := (8172227590995601 / 5000000000000000 : ℚ)) + (q := (16511427463010601 / 10000000000000000 : ℚ)) + (U := (250733810854960598567 / 500000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_15 : Uω (aρ 15) (bρ 15) (2 : ℝ) ≤ (2418686312017971573191 / 5000000000000000000000 : ℝ) := by @@ -3717,11 +3637,14 @@ lemma U_684_15 : (r := (16221253963311517 / 10000000000000000 : ℚ)) (U := (2418686312017971573191 / 5000000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (8011840730004017 / 5000000000000000 : ℝ)) (q := - (16221253963311517 / 10000000000000000 : ℝ)) (aρ_lt_bρ 15 (by decide)) - (by norm_num [bρ_15]) (by norm_num) (by norm_num [aρ_15, bρ_15]) - (by norm_num [aρ_15, bρ_15]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 15) (t := (2 : ℚ)) + (s := (8011840730004017 / 5000000000000000 : ℚ)) + (q := (16221253963311517 / 10000000000000000 : ℚ)) + (U := (2418686312017971573191 / 5000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684_16 : Uω (aρ 16) (bρ 16) (2 : ℝ) ≤ (4730867613563951102639 / 10000000000000000000000 : ℝ) := by @@ -3733,11 +3656,14 @@ lemma U_684_16 : (r := (1604940623761263 / 1000000000000000 : ℚ)) (U := (4730867613563951102639 / 10000000000000000000000 : ℚ)) 11 (by decide +kernel)) - exact - Uω_le_right_certificate (s := (791617883006013 / 500000000000000 : ℝ)) (q := - (1604940623761263 / 1000000000000000 : ℝ)) (aρ_lt_bρ 16 (by decide)) - (by norm_num [bρ_16]) (by norm_num) (by norm_num [aρ_16, bρ_16]) - (by norm_num [aρ_16, bρ_16]) hlg + simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using + Uω_le_right_certificate_rational + (j := 16) (t := (2 : ℚ)) + (s := (791617883006013 / 500000000000000 : ℚ)) + (q := (1604940623761263 / 1000000000000000 : ℚ)) + (U := (4730867613563951102639 / 10000000000000000000000 : ℚ)) + (by decide +kernel) + (by simpa only [Rat.cast_div, Rat.cast_ofNat, Rat.cast_neg, Rat.cast_zero] using hlg) lemma U_684 : Uρ (2 : ℝ) ≤ (1138744120442109294651 / 2000000000000000000000 : ℝ) := by rw [Uρ_expand, cρ_1, cρ_2, cρ_3, cρ_4, cρ_5, cρ_6, cρ_7, cρ_8, cρ_9, cρ_10, cρ_11, cρ_12, cρ_13, diff --git a/LeanPool/Zeta5Irrational/Table/UpperCertificate.lean b/LeanPool/Zeta5Irrational/Table/UpperCertificate.lean index eeed4a6faf..dd6b11424e 100644 --- a/LeanPool/Zeta5Irrational/Table/UpperCertificate.lean +++ b/LeanPool/Zeta5Irrational/Table/UpperCertificate.lean @@ -10,7 +10,11 @@ public import LeanPool.Zeta5Irrational.Table.Common public import LeanPool.Zeta5Irrational.Certificates public import Mathlib.Analysis.Complex.ExponentialBounds -/-! # Reusable upper certificates for arcsine potentials -/ +/-! # Reusable upper certificates for arcsine potentials + +The rational versions read endpoints from the existing table and transfer their closed +arithmetic certificates to the real analytic lemmas once. +-/ @[expose] public section @@ -36,4 +40,54 @@ lemma Uω_le_right_certificate {a b t s q U : ℝ} (hab : a < b) (ht : b ≤ t) apply (Real.log_le_log (by linarith) ?_).trans hlog linarith +/-- The left endpoint of an arcsine interval, evaluated in the rationals. -/ +def rationalLeftEndpoint (j : ℕ) : ℚ := + ((table1.getD (j - 1) (0, 0, 0)).1 : ℚ) / 10 ^ 12 + +/-- The right endpoint of an arcsine interval, evaluated in the rationals. -/ +def rationalRightEndpoint (j : ℕ) : ℚ := + ((table1.getD (j - 1) (0, 0, 0)).2.1 : ℚ) / 10 ^ 12 + +lemma aρ_eq_rationalLeftEndpoint (j : ℕ) : aρ j = (rationalLeftEndpoint j : ℝ) := by + simp only [aρ, rationalLeftEndpoint, Rat.cast_div, Rat.cast_natCast, + Rat.cast_pow, Rat.cast_ofNat] + +lemma bρ_eq_rationalRightEndpoint (j : ℕ) : bρ j = (rationalRightEndpoint j : ℝ) := by + simp only [bρ, rationalRightEndpoint, Rat.cast_div, Rat.cast_natCast, + Rat.cast_pow, Rat.cast_ofNat] + +/-- A rational certificate to the left of a tabulated arcsine interval. -/ +lemma Uω_le_left_certificate_rational {j : ℕ} {t s q U : ℚ} + (certificate : rationalLeftEndpoint j < rationalRightEndpoint j ∧ + t ≤ rationalLeftEndpoint j ∧ 0 ≤ s ∧ + (t - rationalLeftEndpoint j) * (t - rationalRightEndpoint j) ≤ s ^ 2 ∧ + ((rationalLeftEndpoint j + rationalRightEndpoint j) / 2 - t + s) / 2 ≤ q) + (hlog : Real.log (q : ℝ) ≤ (U : ℝ)) : + Uω (aρ j) (bρ j) (t : ℝ) ≤ (U : ℝ) := by + rw [aρ_eq_rationalLeftEndpoint, bρ_eq_rationalRightEndpoint] + apply Uω_le_left_certificate (s := (s : ℝ)) (q := (q : ℝ)) + · exact_mod_cast certificate.1 + · exact_mod_cast certificate.2.1 + · exact_mod_cast certificate.2.2.1 + · exact_mod_cast certificate.2.2.2.1 + · exact_mod_cast certificate.2.2.2.2 + · exact hlog + +/-- A rational certificate to the right of a tabulated arcsine interval. -/ +lemma Uω_le_right_certificate_rational {j : ℕ} {t s q U : ℚ} + (certificate : rationalLeftEndpoint j < rationalRightEndpoint j ∧ + rationalRightEndpoint j ≤ t ∧ 0 ≤ s ∧ + (t - rationalLeftEndpoint j) * (t - rationalRightEndpoint j) ≤ s ^ 2 ∧ + (t - (rationalLeftEndpoint j + rationalRightEndpoint j) / 2 + s) / 2 ≤ q) + (hlog : Real.log (q : ℝ) ≤ (U : ℝ)) : + Uω (aρ j) (bρ j) (t : ℝ) ≤ (U : ℝ) := by + rw [aρ_eq_rationalLeftEndpoint, bρ_eq_rationalRightEndpoint] + apply Uω_le_right_certificate (s := (s : ℝ)) (q := (q : ℝ)) + · exact_mod_cast certificate.1 + · exact_mod_cast certificate.2.1 + · exact_mod_cast certificate.2.2.1 + · exact_mod_cast certificate.2.2.2.1 + · exact_mod_cast certificate.2.2.2.2 + · exact hlog + end Zeta5Irrational